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JOURNAL OF FINANCIAL ECONOMICS Aims and Scope: The Journal of Financial Economics provides a specialized forum for the publication of research in the area of financial economics and the theory of the firm, placing primary emphasis on the highest quality analytical, empirical, and clinical contributions in the following major areas: capital markets, financial institutions, corporate finance, corporate governance, and the economics of organizations. Managing Editor: G. WILLIAM SCHWERT, William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627 (email: [email protected]) Founding Editor: MICHAEL C. JENSEN, Graduate School of Business Administration, Harvard University, Boston, MA 02163 (email: [email protected]) Advisory Editors: EUGENE F. FAMA, Graduate School of Business, University of Chicago, Chicago, IL 60637; KENNETH R. FRENCH, Tuck School of Business, Dartmouth College, Hanover, NH 03755-1798; WAYNE MIKKELSON, Charles H. Lundquist College of Business, University of Oregon, Eugene, OR 97403; JAY SHANKEN, Goizueta Business School, Emory University, Atlanta, GA 30322; ANDREI SHLEIFER, Department of Economics, Harvard University, Cambridge, MA02138; CLIFFORD W. SMITH, JR., William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627; RENÈ M. STULZ, Ohio State University, Columbus, OH 43210. Editorial Assistant: KATHLEEN MADSEN, William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627. Associate Editors: HENDRIK BESSEMBINDER, University of Utah; JOHN CAMPBELL, Harvard Economics Department; HARRY DeANGELO, University of Southern California; DARRELL DUFFIE, Stanford University, San Francisco, CA; BENJAMIN ESTY, Harvard University; RICHARD GREEN, Carnegie-Mellon; JARRAD V.T. HARFORD, University of Washington; CHRISTOPHER JAMES, University of Florida; SIMON JOHNSON, Massachusetts Institute of Technology; STEVEN KAPLAN, University of Chicago; ANDREW KAROLYI, The Ohio State University; JOSH LERNER, Harvard Business School; TIM LOUGHRAN, University of Notre Dame; MICHELLE LOWRY, Penn State University; KEVIN MURPHY, University of Southern California; MICAH OFFICER, University of Southern California; LUBOS PASTOR, University of Chicago; NEIL PEARSON, University of Illinois; JAY RITTER, University of Florida; RICHARD G. SLOAN, University of Michigan; JEREMY C. STEIN, Harvard Economics Department; JERRY WARNER, University of Rochester; TONI WHITED, University of Wisconsin; KAREN WRUCK, Ohio State University, DAVID YERMACK, New York University. Submission Fee: Unsolicited manuscripts must be accompanied by a submission fee of $500 for authors who are current Journal of Financial Economics subscribers and $550 for non-subscribers. 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Journal of Financial Economics 99 (2011) 1–10

Contents lists available at ScienceDirect

Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec

Simple formulas for standard errors that cluster by both firm and time$ Samuel B. Thompson Arrowstreet Capital L.P., The John Hancock Tower, 200 Clarendon Street 30th Floor, Boston, MA 02116, USA

a r t i c l e in fo

abstract

Article history: Received 13 July 2006 Received in revised form 15 May 2009 Accepted 7 July 2009 Available online 14 October 2010

When estimating finance panel regressions, it is common practice to adjust standard errors for correlation either across firms or across time. These procedures are valid only if the residuals are correlated either across time or across firms, but not across both. This paper shows that it is very easy to calculate standard errors that are robust to simultaneous correlation along two dimensions, such as firms and time. The covariance estimator is equal to the estimator that clusters by firm, plus the estimator that clusters by time, minus the usual heteroskedasticity-robust ordinary least squares (OLS) covariance matrix. Any statistical package with a clustering command can be used to easily calculate these standard errors. & 2010 Elsevier B.V. All rights reserved.

JEL classification: C23 G12 G32 Keywords: Cluster standard errors Panel data Finance panel data

1. Introduction A typical finance panel data set contains observations on multiple firms across multiple time periods. Although OLS standard errors will be consistent as long as the regression residuals are uncorrelated across both firms and months, such uncorrelatedness is unlikely to hold in a finance panel. For example, market-wide shocks will induce correlation between firms at a moment in time, and persistent firm-specific shocks will induce correlation across time. Furthermore, persistent common shocks, like

$ I thank Eugene Fama, Megan MacGarvie, Antti Petajisto, Mitchell Petersen and Christopher Polk for helpful comments. The comments of two anonymous referees led to revisions which significantly improved the paper. I owe special thanks to John Campbell and Tuomo Vuolteenaho. The idea of computing a forward-looking HerfindahlHirschman Index (used in the empirical application) was communicated to me by Tuomo Vuolteenaho. E-mail address: [email protected]

0304-405X/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2010.08.016

business cycles, can induce correlation between different firms in different years. A number of techniques are available for adjusting standard errors for correlation along a single dimension. Fama and MacBeth (1973) propose a sequential timeseries of cross-sections procedure that produces standard errors robust to correlation between firms at a moment in time. Huber (1967) and Rogers (1983) show how to compute ‘‘clustered’’ standard errors which are robust either to correlation across firms at a moment in time or to correlation within a firm across time. None of these techniques correctly adjusts standard errors for simultaneous correlation across both firms and time. If one clusters by firm, observations may be correlated within each firm, but must be independent across firms. If one clusters by time, observations may be correlated within each time period, but correlation across time periods is ruled out. This paper describes a method for computing standard errors that are robust to correlation along two dimensions. To make the discussion concrete, we call one

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S.B. Thompson / Journal of Financial Economics 99 (2011) 1–10

dimension time, and the other firm, but the results trivially generalize to any two-dimensional panel data setting. In addition, these standard errors are easy to compute. In the simplest case, we have firm and time effects, but no persistent common shocks. In this case, the b is variance estimate for an OLS estimator b bÞ ¼ V b firm þ V b time,0 V b white,0 , d b Varð b firm and V b time,0 are the estimated variances that where V b white,0 is the cluster by firm and time, respectively, and V usual heteroskedasticity-robust OLS variance matrix (White, 1980).1 Thus, any statistical package with a clustering command (e.g., STATA) can be used to easily calculate these standard errors. The paper also provides valid standard errors for the more complicated case which allows for persistent common shocks. This paper also discusses the pros and cons of doubleclustered standard errors. I analyze the standard error formulas using the familiar trade-off between bias and variance. The various standard error formulas are estimates of true, unknown standard errors. The more robust formulas have less bias, but more estimation variance. The lower bias improves the performance of test statistics, but the increased variance can lead to size distortions. I use Jensen’s inequality to show that, when sample sizes are small, the more robust standard errors lead us to find statistical significance even when it does not exist. When is the bias reduction likely to be important? I argue that double clustering is likely to be most helpful in data sets with the following characteristics: the regression errors include significant time and firm components, the regressors themselves include significant firm and time components, and the number of firms and time periods is not too different. So, if the regressors vary by time but not by firm, then clustering by time may be good enough, and double clustering may not make a large difference. If there are far more firms than time periods, clustering by time eliminates most of the bias unless within-firm correlations are much larger than within-time period correlations. I also point out special considerations related to persistent common shocks. Correcting for correlations between different firms in different time periods involves estimating autocovariances between residuals. As Hurwicz (1950) and many subsequent authors have shown, autocovariance estimates are biased downward. Thus, standard errors that correct for persistent common shocks will tend to be biased downward. Eliminating the bias requires a large number of time periods. I use a Monte Carlo to evaluate how large sample sizes must be in practice. When I apply pure double clustering, and do not adjust for persistent common shocks, the standard errors are reliable in data sets with at least 25 firms observed over 25 time periods. When I correct for

1 The double-clustering problem was also solved in Cameron, Gelbach, and Miller (2006). I was unaware of their paper while working on these results. Their paper was made available on the Web at roughly the same time as this one.

persistent common shocks, the number of time periods should be greater than 50. This leads to reasonably simple advice for applied researchers. Double clustering is worth doing because it is an easy robustness check, and the standard error estimates are accurate in small samples. However, we should not expect it to make a big difference in all data sets, especially when there are far more firms than time periods. I do not make as strong a case for adjusting for persistent common shocks. The standard error formulas are a bit more complicated, and a larger number of time periods is needed for the estimates to be accurate. 2. Firm effects, time effects, and persistent common shocks Consider the panel regression yit ¼ x0it b þ eit :

ð1Þ

yit is the dependent variable, eit is the error term, xit is the covariate vector, and b is the coefficient vector. We have i= 1,y,N firms observed over t = 1,y,T time periods. More generally, index i could refer to any unit of observation, such as an industry- or country-level observation, and t could refer to any other unit. I write in terms of firms and time periods because it makes the discussion more concrete. The errors may be heteroskedastic, but must have zero conditional mean, so Eðeit jxit Þ ¼ 0. We make the following assumptions about the correlations between errors. Assumption 1. Firm effects: The errors may exhibit firm effects, meaning that errors may have arbitrary correlation across time for a particular firm: Eðeit eik jxit ,xik Þa0 for all tak. Assumption 2. Time effects: The errors may exhibit time effects, meaning that errors may have arbitrary correlation across firms at a moment in time: Eðeit ejt jxit ,xjt Þa0 for iaj. Assumption 3. Persistent common shocks: The errors may exhibit persistent common shocks, meaning that we allow some correlation between different firms in different time periods, but these shocks die out over time, and may be ignored after L periods. So Eðeit ejk jxit ,xjk Þ ¼ 0 if iaj and jtkj4 L. To understand the difference between time effects, firm effects, and persistent common shocks, consider the following data-generating process:

eit ¼ h0i f t þ Zit þ uit , Zit ¼ jZi,t1 þ Bit , Zi0 ¼ 0:

ð2Þ

ft is a vector of random factors common to all firms, and hi is a vector of factor loadings specific to firm i. uit and Bit are random shocks, uncorrelated across both firm and time. The Zit term generates firm effects—shocks specific to firm i. h0i f t generates both time effects and persistent common shocks. When ft is uncorrelated across time, we have time effects but no persistent common shocks—firms are correlated with one another at a moment in time, but


different firms in different time periods are uncorrelated. When ft is persistent, we have both time effects and persistent common shocks. We assume that the autocorrelations for ft disappear after L months.2 2.1. Examples The assumptions cover many interesting corporate finance applications. Consider a capital structure regression as in Petersen (2009), where the dependent variable is the ratio of firm debt to assets. The residual probably includes a firm-specific effect (our Zit term) as well as common persistent business-cycle shocks that affect all firms (our ft term). Later in this paper, I consider profitability regressions as in Fama and French (2000), where the dependent variable is profitability measured as the ratio of firm earnings to book value of equity. The residual probably includes firm-specific components, as well as common components that vary over time. Other examples come from the literature that links a country’s growth rate of output to its financial development. A country’s growth rate is probably influenced by country-specific and business-cycle shocks. Rajan and Zingales (1998) run regressions at the country and industry level, and use country and industry dummies to control for common effects. Papers such as Larrain (2006) and Li, Morck, Yang, and Yeung (2004) estimate countrylevel panel regressions. For an asset-pricing example, consider predictive panel regressions with overlapping returns. The dependent variable yit is a J-period overlapping return, so P yit ¼ Jk ¼ 1 Ri,t þ k , where Ri,t is the return on company i’s stock in month t. The regression errors will likely contain shocks common to many stocks, and the overlapping structure of the dependent variable will induce correlations across different firms in different time periods. Thus, is it likely that we will have time effects and persistent common shocks, but we may be able to rule out firm effects. Predictive regressions with overlapping returns have been well studied in the univariate case. For example, Hansen and Hodrick (1980) show how to calculate correct standard errors when predicting a univariate time-series of exchange rates. The panel regression case is less well understood. Cohen, Polk, and Vuolteenaho (2003) is an example of a paper that handles the problem carefully— the formulas in this paper generalize and simplify their calculations. 2.2. Alternative approaches This paper provides standard error formulas that correctly handle these examples. In order to better

3

understand the usefulness of this result, let us consider other approaches that an applied researcher might take. One approach would be to use the usual standard errors that do not adjust for correlation between observations. Petersen (2009) and many other have shown that can lead to standard errors that are too small. Small standard errors lead to large t-statistics, and the researcher will see statistical significance even when it does not exist. Another approach is to cluster along a single dimension. Similarly, we could use the standard errors of Fama and MacBeth (1973), since they also solve the singleclustering problem [see Petersen (2009) for further explanation]. Again, this can lead to understated standard errors. Consider an application to model firm profitability. We might cluster by time, meaning that we allow firms to be correlated with one another at a moment in time. This will ignore persistent firm-specific effects. The residual may contain unobserved components that cause one company to be persistently more profitable than others. One way to simultaneously handle firm and time effects is to use firm and time dummies. For example, we could cluster the standard errors by time and include firm fixed effects (e.g., we could include firm-specific dummy variables in the regression). This is a sensible procedure that will work well in many cases. However, fixed effects will not handle many relevant forms of correlated errors. In our example data-generating process (Eq. 2), the time effect has the factor structure h0i f t and the firm effect follows the autoregressive process Zit . Time dummies will not correctly model the factor structure if the loadings hi vary across firms, and firm dummies will not correctly model the autoregressive process. Another limitation with firm or time fixed effects is that they limit the kinds of covariates that can be included. If we use time dummies, we cannot include macroeconomic variables in the regression, since they are collinear with the dummies. Similarly, dummies can significantly increase the standard errors when the covariate does not vary much along a dimension. For example, consider a regression where the covariate is the yield on a firm’s long-term debt. If the firms in our sample have similar credit quality, this covariate may vary significantly across time, but may not vary much across firms at a moment in time. While it is possible to include time dummies in this regression, they will be highly correlated with the covariate and therefore, will cause the standard errors to increase. 3. Standard error formulas What is the variance of the OLS estimator? The estimator satisfies " # X b b ¼ H1 b u , it

i,t 2 More generally, shocks to ft could decay slowly but not completely disappear after L periods. For example, ft could follow a first-order autoregressive process. While this would violate the assumption, I assume that after some time the correlation between shocks is small enough that it can be ignored. Autoregressive processes could be handled by allowing the lag length L to grow with the sample size (see, for example, Newey and West, 1987).

P with uit ¼ xit eit and H ¼ i,t xit x0it . In large samples, the estimator variance can be approximated by H 1GH 1, P where G ¼ Var½ i,t uit . The term G may be written as X Eðuit u0jk Þ: G¼ i,j,t,k

4


Under the error assumptions, we can simplify the formula as G ¼ Gfirm þ Gtime,0 Gwhite,0 þ

L X

ðGtime,l þ G0time,l Þ

l¼1

L X

ðGwhite,l þ G0white,l Þ,

l¼1

with Gfirm

X Eðci c0i Þ, i

Gwhite,l

Gtime,l

X Eðst s0t þ l Þ, t

X Eðuit u0i,t þ l Þ: i,t

P

ci ¼ t uit is the sum over all observations for firm i, P and st ¼ i uit is the sum over all observations for time t. The variance can be consistently estimated by bÞ ¼ V d b b firm þ V b time,0 V b white,0 þ PL ðV b time,l þ V b0 Varð l¼1 time,l Þ 0 PL b b l ¼ 1 ðV white,l þ V white,l Þ, where X 0 1 b firm H1 b bi H , cic V b time,l H1 V

i X 0 b stb s t þ l H1 ,

b white,l H1 V

t X X b it u b 0i,t þ l H1 : u t

ð3Þ

i

P P b it , b b it , and b b it ¼ xit b e it , cbi ¼ t u st ¼ iu e it is the residual u 0 b b firm is the usual formula for standard errors yit xit b . V b time,0 is the usual formula for standard clustered by firm, V b white,0 are the usual OLS errors clustered by time, and V b time,l standard errors robust to heteroskedasticity. The V b and V white,l terms for l Z 1 correct for persistent shocks common to many firms. b white,0 to correct for double-counting the We subtract V b firm and V b time,0 sum over the within-firm variance. Both V b 0it . Since that cross product appears in b it u cross product u b white,0 , we eliminate the double-counting by subtraction. V b firm , the variance that clusters by firm, includes Similarly, V b 0i,t þ l within firm i. These b it u all residual cross products u b time,l , so we subtract V b white,l cross products also appear in V to avoid double-counting. b time,l terms are less familiar. V b time,l estimates The V P H1 t Covðst ,st þ l ÞH1 , a weighted autocovariance between time clusters. The autocovariances are induced by b time,l terms the persistent common shocks. Why do the V appear twice? Recall that, when we take the variance of a univariate sum, the result is the sum of variances plus two times the sum of covariances. In the vector case, we have a similar result: ! T T1 X Tt X X X Var st ¼ Varðst Þ þ Covðst ,st þ l Þ t¼1

trivially calculated using a statistical package that has a built-in clustering command.3 Special case (Persistent common shocks, but no doubleclustering): Consider the predictive regression where yit is P an L-period overlapping return, so yit ¼ Lk ¼ 1 Ri,t þ k , where Ri,t is the return on company i’s stock in month t. This regression is typically run under the assumption that there is no persistent firm-specific shock. In this case, bÞ ¼ V d b b time,0 þ PL the variance estimator becomes Varð l¼1 0 b b ðV time,l þ V time,l Þ. Asymptotic consistency: Asymptotic consistency of the standard errors is demonstrated in Appendix A. Consistency requires that both N and T become large. I assume that T ¼ aN, where a is a positive constant, and then take the probabilistic limit as N-1. The relative magnitudes do not matter; for example consistency holds if N is twice as big as T, as long as both approach infinity. However, consistency will not necessarily hold if T goes to infinity while N is fixed, or if N goes to infinity while T is fixed. The intuition for this result is that we need T to become large b time,l to be consistent, and we need N to become large for V b firm to be consistent. When either T or N are small, for V b time,l or there may be too much sampling variability in V b firm . V

t

þ

t ¼1l¼1 T1 X Tt X

Covðst ,st þ l Þu:

t ¼1l¼1

The covariance terms Covðst ,st þ l Þ appear twice, just as they do in the univariate case. Special case (Double-clustering, but no persistent common shocks): If the residuals do not contain persistent common shocks, then L=0 and the variance estimator bÞ ¼ V d b b firm þ V b time,0 V b white,0 . This estimator is becomes Varð

4. When should we use robust standard errors? Is there a downside to double-clustering the standard errors? Should we always adjust standard errors to handle persistent common shocks? In fact, it is not always best to use the ‘‘most robust’’ standard error formula. The various standard error formulas are estimates of true, unknown standard errors. In this section, I point out that the more robust standard error formulas tend to have less bias, but more variance. The lower bias improves the performance of test statistics. But the increased variance often leads us to find statistical significance even when it does not exist (e.g., we erroneously reject a true null hypothesis). 4.1. Bias More robust standard errors have less bias. When is this effect likely to be important? Consider a researcher who uses single-clustered standard errors, and is considering double-clustering and adjusting for persistent common shocks. When will the more robust formulas make a difference? In this section, I argue that the researcher should think about three features of the data set: the distribution of the errors, the distribution of the regressors, and relative number of observations along the two clustering dimensions. To make the discussion more concrete, consider a few scenarios. 3 For example, in STATA we would issue the command ‘‘reg y x, b firm , ‘‘reg y x, cluster(time)’’ to compute cluster(firm)’’ to compute V b time,0 , and ‘‘reg y x, robust’’ to compute V b white,0 . Here, ‘‘y’’ is the V dependent variable, ‘‘x’’ is the single regressor (we could have more than one), ‘‘firm’’ is an index number unique to each firm, and ‘‘time’’ is an index number unique to each time period.


Scenario #1: The researcher should double-cluster, but instead single-clusters by firm. The double-clustered b firm þ V b time,0 V b white,0 , while the single-clusformula is V b firm . Thus, the researcher omits tered formula is V b white,0 . b time,0 V V Scenario #2: The researcher should double-cluster, but instead single-clusters by time. The researcher omits b white,0 . b firm V V Scenario #3: The researcher should adjust for persistent common shocks but fails to do so. The researcher b time,l V b white,l for l Z 1. omits V These scenarios show us that robust standard b firm V b white,0 , errors are most helpful when terms like V b white,0 , and V b time,l V b white,l are large. When are b time,0 V V these terms large? Start with scenario #1. The bias comes from omitting the time clustering. In large samples we can approximate the bias with XX b time,0 EV b white,0 H1 EV Covðxit eit ,xjt ejt ÞH1 : ð4Þ t

iaj

This formula tells us three things: the distribution of the errors matters, the distribution of the regressors matters, and the balance between the number of observations on firms and time periods matters. Let us first consider the distribution of the errors, then come back to the other points. If, conditional on the regressors, errors are not correlated across firms, then there is no bias in scenario #1. To put it in mathematical terms, we know that E½eit ejt jxit ,xjt ¼ 0 implies Covðxit eit ,xjt ejt Þ ¼ 0. We can make similar statements for the other scenarios. If the errors are conditionally uncorrelated across time then there is no bias in scenario #2, and if the errors are not conditionally autocorrelated then there is no bias in scenario #3. Next consider the distribution of the regressors. Suppose that the errors exhibit strong time effects, so Covðeit , ejt Þ 40, but the regressors xit and xjt are independent of each other and of the errors. Then Covðxit eit ,xjt ejt Þ ¼ 0, and we do not need to cluster by time, even though the residuals have strong time effects. The same argument holds for scenario #2. When we fail to b firm V b white,0 . This term cluster by firm, we omit the term V is a sum over Covðxit eit ,xik eik ÞFthe covariance between observations on the same firm in different time periods. If the regressors are not correlated across time, clustering by firm will not affect the standard errors, even if the errors have significant firm components. The same argument can also be applied to scenario #3. We need to adjust for persistent common shocks if the regressors are correlated across time. Otherwise the adjustment is not important. To better understand this point, consider a few examples. Suppose the regressor is the growth rate of gross domestic product. This does not vary at all by firm, but varies across time and is persistent. Omitting the corrections for time effects and persistent common shocks may lead to bias. Thus, the researcher should worry about scenarios #1 and #3, but #2 is less important. Now suppose that the regressor is the return on the aggregate stock market. This does not vary by firm, but is not

5

persistent. So scenario #1 is important, but #2 and #3 may not be a problem. Next consider the dividend yield of a firm. This varies by both firm and time. However, if most of the variation is across firms, and not across time, then omitting the firm clustering will create more bias than omitting the time clustering. Double-clustering is most useful when both scenarios #1 and #2 lead to bias. In this case, clustering in either dimension will not eliminate the bias. This is likely to happen when the regressors exhibit both time and firm effects. For example, a regressor like the dividend yield has both time and firm variation, although most of the variation may be at the firm level. Another important case is a multivariate regression where some regressors vary by time, and some vary by firm. For example, if one regressor is the dividend yield, and another regressor is growth in gross domestic product, then time clustering alone would not get the standard errors right for the dividend yield, and firm clustering alone would not get the standard errors right for the other regressor. The only way to get both standard errors right is to double-cluster. Finally, consider the relative number of firms and time periods in a data set. Suppose that we have 1,000 firms observed over ten years, for 10,000 total observations. The b white,0 relies on the assumption that we have OLS formula V 10,000 uncorrelated observations. Probably we have far fewer. If we cluster by time, we allow arbitrary correlation between observations in the ten time periods, thus, we assume that we have only ten uncorrelated observations. If we cluster by firm, we assume 1,000 uncorrelated observations. Going from 10,000 observations to ten probably has a bigger effect than going from 10,000 to 1,000. In this example, omitting the time clustering is likely to be more important than omitting the firm clustering. The general point is that, all else equal, it is more important to cluster along the dimension with fewer observations. If we have a sample with ten firms and 1,000 time periods, the bigger bias reduction will probably come from clustering by firm. In fact, we can make a stronger statement—if the dimensions are extremely unbalanced, we do not need to double-cluster at all. If we fix the number of observations in one dimension, and let the number of observations in the other become very large, the bias disappears (so long as we single-cluster on the less-numerous dimension). Here is a mathematical statement of this claim when N is fixed and T is very large: b firm þ V b time,0 V b white,0 V ¼ 1: b fixed V firm

lim

T-1,N

This is a counter-intuitive result. To understand it, b becomes more precise as we recall that our estimate b add more independent observations. The estimator variance reflects this and converges to zero in large samples. b time,0 is constructed based on the assumption The term V that observations in different time periods are independent. Thus, it will converge to zero as T becomes large,

6


whether or not the assumption is in fact true.4 Likewise, b white,0 converges to zero as the total number of observaV b firm relies on the tions becomes large. In contrast, V assumption that observations are independent across b firm will not converge to zero. Stated firms. If we fix N, V loosely, as T becomes large, we average away noise due to variation across time, but we do not average away noise due to variation across firms. I should not over-sell this point. To be clear, the effect of clustering is determined by an interaction between the number of observations in each dimension and the magnitude of the correlation between observations. If there is no firm effect, so observations on a given firm are uncorrelated across time periods, then we do not need to cluster by firm, even if there are 1,000 time periods and only ten firms. However, if the data have significant firm and time effects, then it is probably more important to cluster along the dimension with fewer observations. This analysis suggests that double-clustering is most important when the number of firms and time periods are not too different. For example, Fama and French (2000) predict firm-level profitability in a panel with thousands of firms and roughly 35 years of annual accounting data. In this case, clustering by time is probably good enough as the increase in bias from failing to also cluster by firm will likely be small. In the empirical application later in this paper, I run profitability regressions at the industry level. There are far fewer industries than firms, and in that application double-clustering significantly changes the standard errors relative to single-clustering by time. 4.2. Variance In many cases of interest, the more robust standard error estimates have higher variances. In some simple cases we can verify this statement with analytic results. Consider a regression with a single regressor where the errors are independent, so that we do not need to cluster. When N and T are both large, the single-clustered standard error estimate always has a higher variance than the OLS standard errors. In more complicated cases we can carry out simulations. For example, consider a regression model with a single independent and identically distributed (iid) standard normal regressor and iid standard normal errors. Suppose we have ten firms observed over ten time periods, for 100 observations total. This is a model where the OLS standard errors are appropriate, and we do not need to single-cluster, doublecluster, or adjust for persistent common shocks. I generate 10,000 samples from this model and calculate the various standard error estimates. White standard errors (with no 4 To see this mathematically, return to the formula for the estimator in Eq. (3):

b time,0 H1 V

X 0 1 b stb st H :

clustering) had a simulation standard deviation of 1.4%, and single-clustered standard errors had simulation standard deviations of 2.6%, whether clustering was done by firm or time. The double-clustered standard errors that exclude persistent common shocks had a simulation standard deviation of 3.2%, and when allowing for persistent common shocks with L=2 lags, the standard deviation was 3.6%. From this simple experiment we see that more robust standard error estimates tend to have more sampling variability. Increasing the variance of a standard error estimate may lead us to see statistical significance where it does not exist. This result comes from Jensen’s inequality. Suppose we have a single coefficient, and we test the null hypothesis that b ¼ bnull . We reject the null for large b b j=seðb b Þ. If b b and seðb bÞ values of the t-statistic b t ¼ jb null

b Þ increases, are independent, then as the variance of seðb the expected value of the test statistics Eðb tÞ will rise. Larger test statistics mean that we too often reject a true b and seðb b Þ are null hypothesis. In many cases of interest, b independent or are close to independent. For example, in a regression with independent normal errors, the estimate b is asymptotically independent of all the standard error b estimators proposed in this paper. If we repeat the simulation experiment in the previous paragraph, we get approximately zero correlations between the coefficient estimate and all the standard error estimates. For the clustered standard errors, the variance of the standard error estimate becomes large as the number of clusters decreases. Clustered standard errors are estimated by averaging across clusters. Few clusters means a small number of terms in the average, and thus more estimation error. Consider, for example, the standard errors that cluster by time: X 0 1 b time,0 H1 b V stb st H : t 0 s t . As we increase T, This is an average over the products b stb we increase the number of terms in the average, and the variance of the standard error estimate declines. Thus, we b time,l , and we need need large T to shrink the variance of V b firm . If either T or N are large N to shrink the variance of V small, then double-clustered standard errors can do more harm than good. Consider the situation where a researcher sees very different results when going from single- to double-clustered standard errors. The researcher may take this as evidence that it is important to cluster along both dimensions. But if there are too few clusters in either the time or firm dimension, the double-clustered standard error estimate will be noisy. The different results could be spurious and due to noise. Thus, double clustering makes sense only when we have sufficient clusters along both dimensions. How many clusters do we need in practice? In the next section, I investigate this question with a Monte Carlo experiment.

t

P s t is a summation over N H is xit x0it , a summation over NT terms. b P b b0 is a summation over TN2 terms. Therefore, terms, so t st st b time,0 r KðN 1 T 1 ÞðTN 2 ÞðN 1 T 1 Þ ¼ KðT 1 Þ, where K is a finite constant. EV b time,0 is non-negative, this inequality implies that V b time,0 Since V converges to zero as T becomes large. This holds whether or not observations are truly independent across time.

4.3. Added bias when adjusting for persistent common shocks There is a special consideration when adjusting for persistent common shocks. The estimator is biased, and it


is not a simple thing to fix this bias. We handle persistent b time,l and V b white,l . Both of common shocks with the terms V b time,l these terms involve estimates of autocorrelations: V P 0 0 b white,l uses P u b b b b uses , and V . In general, s s u t it t tþl t i,t þ l estimates of non-negative autocorrelations are biased downward. Thus, we have identified two factors that cause these standard errors to falsely reject true null hypotheses—they have larger estimation variances than simpler formulas, and they exhibit downward bias. We can see the bias in a simple example. Suppose we have data fZt gTt ¼ 1 . The first-order autocovariance is CovðZt ,Zt1 Þ ¼ EZt Zt1 ðEZt Þ2 . We estimate this with X 2 d t ,Zt1 Þ ¼ ðT1Þ1 Zt Zt1 Z , CovðZ tZ2

where Z ¼ T 1

P

t Z 1 Zt . The expectation of the estimate is 2

d t ,Zt1 Þ ¼ EZt Zt1 EZ : ECovðZ 2

If EZ ¼ ðEZ Þ2 , then this estimate is unbiased. But 2 Jensen’s inequality tells us that EZ Z ðEZ Þ2 , which shrinks the estimate. The downward bias is present even when the true autocorrelation is zero—in this case the expected value of the estimate is negative. The bias of autocorrelation estimates is an old and unsolved statistical problem that dates at least back to Hurwicz (1950). Nickell (1981) points out some of the problems this effect causes in panel regressions. Stambaugh (1999) shows that it makes conventional inference in predictive time-series regressions unreliable. Petersen (2009) shows that the effect leads to bias in adjusted Fama-MacBeth standard errors. Petersen’s critique applies here as well. Two useful facts about the bias are that it increases with the magnitude of the correlation, and it disappears as the sample becomes large. Therefore, we expect these standard errors to perform well when the correlations are close to zero, and the sample size is large. Of course, if the correlations are low then we can just ignore them and use simpler formulas. The only case where these standard errors are unambiguously preferred is when the correlations are significant and the sample size is large enough to correct the bias. I perform Monte Carlos to see how big the samples need to be. 5. Monte Carlo experiments In this section, I use Monte Carlo simulations to investigate the small-sample performance of the robust standard errors. I simulate 5,000 draws from the panel regression, yit ¼ b0 þ b1 x1,it þ b2 x2,it þ eit , with b0 ¼ 0 and b1 ¼ b2 ¼ 1. The simulation is repeated for various sample sizes and error dependencies. For each sample, I estimate the regression and carry out two-sided t-tests of the nulls that b1 ¼ 1 and b2 ¼ 1. Table 1 reports rejection frequencies for t-tests constructed from many different variance estimators: the usual OLS variance b white,0 , the estimator that clusters by firm, estimator, V b b time,0 , the V firm,0 , the estimator that clusters by time, V estimator that clusters by both firm and time but does not

7

b firm þ V b time,0 V b white,0 , allow persistent common shocks, V and the full variance estimator that clusters by firm and time and allows persistent common shocks (with L= 2). The Monte Carlo also considers fixed-effects regressions—I run the regression with firm fixed effects and cluster the standard errors by time, and run the regression with time fixed effects and cluster the standard errors by firm. Since the null hypothesis is true, we prefer standard errors that deliver rejection frequencies close to 5%. I consider three different data-generating processes. Panel A: The errors and regressors are distributed N(0,1) and independent across both i and t. Panel B: x1 has time effects, x2 has firm effects, and the errors have both. There are no persistent common shocks. x1,it ¼ xt , where xt Nð0,1Þ and independent across t. x2,it ¼ Zit , where Zit ¼ 0:9Zi,t1 þ Bit , with Bit Nð0,1Þ and independent across i and t. eit ¼ x~ t þ Z~ it , where x~ t and Z~ it have the same distributions as xt and Zit . Panel C: x1 has a persistent common shock, x2 has firm effects, and the errors have a persistent common shock but no firm effects. eit ¼ yi ft þ uit , where yi Nð0,0:25Þ and independent across firms, ft ¼ 0:5ft1 þ nt , with nt Nð0,1Þ and independent across time. x1,it ¼ yi f~ t , where f~ t has the same distribution as ft, and yi is the same loading used to generate eit . x2,it ¼ Zi , where Zi Nð0,1Þ and independent across firms. Notice that, in Panels B and C, the regressors exhibit correlations similar to those in the errors. As argued in Section 4.1, double-clustering matters most when both the regressors and the errors exhibit time and firm effects. In Panel A all the variance estimators are valid and should deliver rejection frequencies of 5%. Instead we see that the simpler formulas get the size right, but the more robust formulas over-reject in small samples. For example, in the simulation with T=25 and N=50, the standard errors that are robust to persistent common shocks reject a true null at least 12% of the time. The size distortion diminishes, but does not disappear, when we go to a sample with 100 time periods. This is consistent with the arguments made in Section 4.2: in small samples the more robust formulas have higher estimation noise, and via Jensen’s inequality this causes us to over-reject a true null hypothesis. In Panel B we need to double-cluster. The OLS rejection frequencies are all at least 40%. Single-clustering by firm gets the size right for b2 but not for b1 . Likewise, singleclustering by time gets the size right for b1 but not for b2 . This happens because x1 has only time effects, x2 has only firm effects, and the two regressors are uncorrelated. Thus, even though the errors have both firm and time effects, single-clustering works for either b1 or b2 . In order to get the size right for both regressors, we need to double-cluster. The fixed effects do not help much. The time fixed effects are collinear with x1, so we cannot estimate b1 . The firm fixed effects do not capture the actual firm dynamics, which follow an autoregressive process. In Panel C we need to use standard errors robust to persistent common shocks. However, from our results in Panel A we know that these standard errors have poor small-sample properties. We see a similar effect here—there are size distortions for all sample sizes, and they are smallest in the biggest sample. It is worth

8


Table 1 Monte Carlo comparison of standard error formulas. The table shows results of a Monte Carlo evaluation of various standard error formulas. I simulate 5,000 samples from the regression model yit ¼ b0 þ b1 x1it þ b2 x2it þ eit with b0 ¼ 0 and b1 ¼ b2 ¼ 1. For each sample, I estimate the regression and carry out two-sided t-tests of the nulls that b1 ¼ 1 and b2 ¼ 1. The table reports rejection frequencies from various estimator variance formulas: (1) ‘‘OLS std errors’’ denotes Vwhite, (2) ‘‘cluster by firm’’ denotes Vfirm, (3) ‘‘cluster by time’’ denotes Vtime, (4) ‘‘cluster by firm, time FE’’ denotes time fixed effects with Vfirm, (5) ‘‘cluster by time, firm FE’’ denotes firm fixed effects with Vtime, (6) ‘‘cluster by both firm and time (not robust to persistent common shocks)’’ denotes Vfirm + Vtime Vwhite, and (7) ‘‘cluster by both firm and time (robust to persistent common shocks, L= 2)’’ denotes Vfirm + Vtime Vwhite + {corrections for persistent common shocks with L= 2}. Panel A: Both regressors and eit are iid N(0,1) across both i and t, so OLS error assumptions are satisfied T= 25, N = 50

OLS std errors Cluster by firm Cluster by time Cluster by firm, time FE Cluster by time, firm FE Cluster by both firm and time (not robust to persistent common shocks) Cluster by both firm and time (robust to persistent common shocks, L= 2)

T= 50, N= 50

T =100, N = 100

b1

b2

b1

b2

b1

b2

0.049 0.053 0.058 0.057 0.065

0.048 0.056 0.065 0.056 0.067

0.050 0.056 0.057 0.060 0.060

0.047 0.053 0.056 0.058 0.059

0.049 0.052 0.052 0.051 0.051

0.056 0.055 0.059 0.058 0.062

0.069

0.070

0.062

0.064

0.054

0.059

0.127

0.123

0.100

0.100

0.069

0.078

Panel B: Errors have both time and firm effects, and persistent common shocks. x1it has time fixed effects (and no persistent common shock), and x2it has firm effects that follow an autoregressive process T= 25, N = 50


T= 50, N= 50

T =100, N = 100

b1

b2

b1

b2

b1

b2

0.560 0.695 0.093 – 0.093

0.425 0.058 0.531 0.058 0.369

0.519 0.635 0.074 – 0.074

0.482 0.059 0.533 0.058 0.466

0.640 0.707 0.056 – 0.056

0.478 0.053 0.501 0.054 0.477

0.105

0.066

0.081

0.061

0.060

0.055

0.174

0.103

0.113

0.080

0.076

0.062

Panel C: Errors have both time and firm effects, and persistent common shocks. x1it has time effects with persistent common shocks, and x2it has firm fixed effects T= 25, N = 50


T= 50, N= 50

T =100, N = 100

b1

b2

b1

b2

b1

b2

0.747 0.906 0.169 0.654 0.167

0.563 0.074 0.865 0.074 –

0.765 0.916 0.155 0.672 0.157

0.673 0.074 0.906 0.074 –

0.809 0.931 0.139 0.726 0.140

0.750 0.056 0.924 0.056 –

0.176

0.087

0.162

0.081

0.143

0.058

0.201

0.127

0.145

0.100

0.098

0.067

pointing out that, since x2 has only firm effects, we can get the right test size for b2 by clustering on firm, and we do not need to adjust for persistent common shocks. The Monte Carlos are generally supportive of using robust standard errors. Single-clustered standard errors cannot handle regressions where one regressor has significant time effects and another has significant firm effects. If we are willing to accept false rejections of up to 10% in a test with 5% size, then double-clustering works well so long as we have more than 25 observations on both firms and time periods. Correcting for persistent common shocks requires between 50 and 100 time periods.

6. Application to modeling industry profitability I demonstrate the standard errors with an application to modeling industry profitability. I consider the hypothesis that profits are higher in more concentrated industries, and measure concentration with a forwardlooking variant of the Herfindahl-Hirschman Index (HHI) (Hirschman, 1964). The HHI is a widely used measure of industry concentration. For example, the U.S. Department of Justice uses the index to help determine whether a merger is anticompetitive (see USDOJ and FTC, 1997).


The HHI is usually calculated from historical sales data. I calculate a variant based on market capitalization. We have M industries, indexed by m= 1,y,M. For each industry m, the value of the index is HHIm,t ¼ 1002

X

market cap of firm i in industry m at time t total market cap of all firms in industry m at time t

i2Im

2

,

where Im is the set of all firms i in industry m. While sales data are backward looking, market capitalization is a forward-looking measure of earnings (and payouts). I test the predictive power of our index in a panel data set of US industries. The sample consists of annual Compustat data observed from 1964 to 2007. I predict ROAm,t, a measure of industry profitability given by the ratio of earnings to assets. Industries are based on four-digit Standard Industrial Classification (SIC) codes. The panel is unbalanced—there are 434 SIC categories and 44 years, for a total of 15,066 observations. The regression is ROAm,t ¼ b0 þ b1 lnðHHIm,t1 Þ þ b2 PBm,t1 þ b3 DBm,t1 þ b4 ROA t1 þ em,t : PB and DB are industry-level price-to-book and dividend-tobook ratios, respectively. Fama and French (2000) identify these variables as strongly contemporaneously associated with firm-level profitability. My regression is predictive, but takes their contemporaneous regression model as a starting point. Fama and French (2000) argue that high price-tobook ratios indicate that the market predicts higher future earnings, and that high dividend-to-book ratios indicate that company management anticipates higher earnings. ROA t is the return on assets for the market as a whole in year t. It controls for market-wide trends in profitability. The data and regressors are described in more detail in Appendix B. Notice that this example uses industry-level rather than firm-level data. Even though the text of this paper has mostly referred to the clustering dimensions as firms and time periods, the results trivially generalize to clustering along any two dimensions. I picked this example in part because it is

9

one where double-clustering is likely to make a significant difference. If I used an example with firm-level data, there would be many more firms than time periods. As discussed in Section 4.1, double-clustering is most useful when the number of observations in each dimension is not too far apart. This data set has 434 industries and 43 years, but US firm-level data would have many more than 434 firms. Results appear in Table 2. HHI positively predicts industry profitability, indicating that profits tend to be persistently higher in more concentrated industries. Like Fama and French (2000), I find that PB and DB are significant positive predictors of profitability. ROA is also positive, suggesting that higher-than-usual profits one year predict higher-than-usual profits the next. It is interesting to compare the effects of single- and double-clustering. For the regressor lnðHHIÞ, double-clustered standard errors are similar to standard errors from singleclustering on industry. For ROA, double-clustering gives results similar to single-clustering by year. Industry concentration varies a lot between industries, and does not vary as much over time within an industry. In contrast, ROA varies across time, but does not vary at all across industries. As discussed in Section 4.1, clustering makes a big difference when both the error and the regressor are correlated within the clustering dimension. We need to cluster by industry to get the right standard error for lnðHHIÞ, and we need to cluster by time to get the right standard error for ROA. Double-clustering gets the right standard error for both. Correcting for persistent common shocks generally increases the standard errors. The largest effect is for ROA, and the smallest effect is for lnðHHIÞ. This makes sense, since ROA is positively correlated across time, while lnðHHIÞ has very weak time effects. 7. Conclusion This paper derives easy-to-compute formulas for standard errors that cluster by both firm and time. Both the statistical theory and the Monte Carlo results suggest that

Table 2 Application to modeling industry profitability. The table shows a regression to model industry profitability. The dependent variable is ROAm,t, the ratio of earnings-to-assets in industry m in year t. The regressors are as follows. ln(HHIm,t 1) is the log of the Hefindahl-Hirschman concentration index for the industry, computed from market caps. Price/Book equitym,t 1 is the price-to-book ratio. Dividends/Book equitym,t 1 is the dividends-to-book ratio. Market ROAt 1 is the market-wide (not industry-specific) ratio of earnings-to-assets. ‘‘Estimate’’ denotes ordinary-least-squares estimates. t-Statistics are presented for different standard error formulas: (1) ‘‘White’’ denotes Vwhite, (2) ‘‘single- clustered, time’’ denotes Vtime, (3) ‘‘single-clustered, firm’’ denotes Vfirm, (3) ‘‘double-clustered, L= 0’’ denotes Vtime + Vfirm Vwhite, and (4) ‘‘double-clustered, L =2’’ denotes Vfirm + Vtime Vwhite + {corrections for persistent common shocks} with L= 2. See Appendix B for details about the data. t-Statistics Single-clustered

Double-clustered

Regressor

Estimate

White

Time

Industry

L =0

L= 2

ln(HHIm,t 1) Price/Book equitym,t 1 Dividends/Book equitym,t 1 Market ROAt 1 Intercept

0.0049 0.0072 0.3171 1.0631 0.0521

10.530 17.670 20.700 32.720 14.461

9.988 5.604 9.877 8.667 9.148

4.314 11.062 10.083 19.958 5.847

4.274 5.212 7.505 8.195 5.240

4.610 3.394 5.482 4.924 4.714

R-squared: 19.29%

10


simultaneously clustering by firms and time leads to significantly more accurate inference in finance panels. Monte Carlo experiments suggest that, as long as we do not allow for persistent common shocks, clustering on both firm and time works adequately when we have at least 25 firms and time periods. However, allowing for persistent common shocks requires a larger number of time periods. This paper leaves a number of issues unresolved. The standard errors that correct for persistent common shocks do not behave well in small samples. Further work could be done to improve their small-sample performance. There is also more work to be done with the pure doubleclustering problem, some of which has already been carried out by Cameron, Gelbach, and Miller (2006). They show how to extend two-way clustering to clustering along more dimensions. They also describe how to apply these methods to nonlinear estimators. Appendix A. Demonstration of asymptotic consistency To establish consistency, normalize the estimator as b ¼ N1 d 1=2 T 1 Hb Var½N

X

Wfirm,i þ T 1

þ

ðWtime,0,t Wols,0,t Þ

t

i

" X

X

T 1

X

0 0 ðWtime,l,t Wols,l,t þWtime,l,t Wols,l,t Þ,

I also carried out the empirical analysis adjusting earnings and book value for deferred income taxes and investment tax credits, as in Fama and French (2000). The results did not meaningfully change. Industry-level ratios were calculated by aggregating firm-level ratios. Aggregation is carried out at the fourdigit Standard Industrial Classification (SIC) level. Industry-year pairs that contain only one firm are excluded. The results are not sensitive to inclusion of the single-firm industries. They are also not sensitive to screening out industry-year pairs with five firms. Before calculating industry-level data, I first drop all observations with book values less than $5 million and assets less than $10 million. To calculate industry-level return on assets, I calculate the firm-level earnings-to-assets ratio, then winsorize within each yearly cross-section at the 1% and 99% percentiles. Industry-level ROA is the asset-weighted average of firmlevel ratios. Similarly, market-wide ROA is calculated as the asset-weighted average over the entire market. To calculate industry-level dividends-to-book, I calculate the firm-level dividends-to-book, winsorize at yearly 1% and 99% percentiles, and form the book-weighted average of firm-level ratios. Industry-level market-tobook is calculated in the same way.

t

l

References P

b b where Wfirm,i ¼ T Wtime,l,t ¼ a N t,k xit e it e ik xik , P P 0 b b and Wwhite,l,t ¼ a1 N2 i xit b e it be i,t þ l i,j xit e it e j,t þ l xj,t þ l , 0 xi,t þ l . Tedious manipulations lead to the results that 2

covðWfirm,i ,Wfirm,j Þ ¼ OðT 1 Þ

0

1

2

for iaj,

and covðWtime,l,t ,Wtime,l,k Þ ¼ OðN1 Þ

for jtkj 4 L:

Therefore, we can show by direct calculation that " # X lim Var T 1 Wtime,l,t ¼ 0, T-1

t

P which implies that T 1 t Wtime,l,t converges to its expectation in mean square. A similar argument demonstrates that P P N 1 i Wfirm,i and N1 i Wwhite,l,t converge to their expectations. Consistency of the standard errors follows. Appendix B. Data construction for empirical application The data used for the application to forecasting firm profitability come from Compustat. Data construction details and Compustat codes follow. Firm-level earnings are Compustat item IB, earnings before extraordinary items. Firm-level assets are item AT. Firm-level liabilities are item LT. Book value is calculated as Assets–Liabilities–Preferred Stock. To calculate the value of preferred stock, I use the redemption value of preferred stock (item PSTKRV). If that is not available I use the liquidating value (PSTKL), and if that is not available the carrying value (UPSTK) is used. Market capitalization is common shares outstanding (CSHO) multiplied by the closing price at the end of the fiscal year (PRCC_F). Dividends are item DVC.

Cameron, C., Gelbach, J., Miller, D., 2006. Robust inference with multiway clustering. NBER Technical Working Paper no. 327. Cohen, R., Polk, C., Vuolteenaho, T., 2003. The value spread. Journal of Finance 58, 609–641. Fama, E., MacBeth, J., 1973. Risk, return, and equilibrium. Journal of Political Economy 81, 607–636. Fama, E., French, K., 2000. Forecasting profitability and earnings. Journal of Business 73, 161–175. Hansen, L., Hodrick, R., 1980. Forward exchange rates as optimal predictors of future spot rates: an econometric analysis. Journal of Political Economy 88, 829–853. Hirschman, A., 1964. The paternity of an index. The American Economic Review 54, 761–762. Huber, P., 1967. The behavior of the maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1; 1967, pp. 221–233. Hurwicz, L., 1950. Least-squares bias in time series. In: Koopmans, T. (Ed.), Statistical Inference in Dynamic Economic Models. John Wiley and Sons, New York, pp. 365–383. Larrain, B., 2006. Do banks affect the level and composition of industrial volatility? Journal of Finance 61, 1897–1925 Li, K., Morck, R., Yang, F., Yeung, B., 2004. Firm-specific variation and openness in emerging markets. Review of Economics and Statistics 86, 658–669. Newey, W., West, K., 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Nickell, S., 1981. Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426. Petersen, M., 2009. Estimating standard errors in finance panel data sets: comparing approaches. Review of Financial Studies 22, 435–480. Rajan, R., Zingales, L., 1998. Financial dependence and growth. American Economic Review 88, 559–586. Rogers, W., 1983. Analyzing Complex Survey Data. Rand Corporation Memorandum, Santa Monica, CA. Stambaugh, R., 1999. Predictive regressions. Journal of Financial Economics 54, 375–421. United States Department of Justice and the Federal Trade Commission, 1997. Horizontal Merger Guidelines. Available at: /http://www. usdoj.gov/atr/public/guidelines/hmg.pdfS. White, H., 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–838.




Bank CEO incentives and the credit crisis$ ¨ Rudiger Fahlenbrach a, Rene´ M. Stulz b,c,d,n a

Swiss Finance Institute, Ecole Polytechnique Fe´de´rale de Lausanne, 1015 Lausanne, Switzerland The Ohio State University, Fisher College of Business, 806 Fisher Hall, Columbus, OH 43210, USA c National Bureau of Economic Research (NBER), Cambridge, MA 02138, USA d European Corporate Governance Institute (ECGI), 1180 Brussels, Belgium b

a r t i c l e in fo

abstract

Article history: Received 17 August 2009 Received in revised form 21 December 2009 Accepted 25 January 2010

We investigate whether bank performance during the recent credit crisis is related to chief executive officer (CEO) incentives before the crisis. We find some evidence that banks with CEOs whose incentives were better aligned with the interests of shareholders performed worse and no evidence that they performed better. Banks with higher option compensation and a larger fraction of compensation in cash bonuses for their CEOs did not perform worse during the crisis. Bank CEOs did not reduce their holdings of shares in anticipation of the crisis or during the crisis. Consequently, they suffered extremely large wealth losses in the wake of the crisis. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G01 G21 G32 Keywords: Financial crisis CEO compensation CEO incentives Insider trading

1. Introduction

$

We thank an anonymous referee, Marco Becht, Graef Crystal, Franc-ois Degeorge, Michel Habib, Joseph Grundfest, Michael Jensen, Steve Kaplan, Ira Kay, Thomas Kirchmaier, Andrew Kuritzkes, Fre´de´ric ¨ Lelie vre, Claudio Loderer, Hamid Mehran, Holger Muller, Jean-Charles Rochet, Myron Scholes, Lemma Senbet, and seminar and conference participants at the joint session of the American Economic Association and Association of Financial Economists at the 2010 ASSA meetings, Bank of England, European School of Management and Technology Berlin, University of Lugano, the fourth Swiss Finance Institute annual meeting, the ECGI and CEPR conference on the governance and regulation of financial institutions: lessons from the crisis, the Columbia Business School conference on governance, executive compensation and excessive risk in the financial services industry, and the ninth FDIC-JFSR annual bank research conference for helpful comments and suggestions. Mike Anderson, Robert Prilmeier, Je´rôme Taillard, and Scott Yonker provided excellent research assistance. Fahlenbrach acknowledges financial support from the Dice Center for Research in Financial Economics, the Swiss Finance Institute, and the National Center of Competence in Research ‘‘Financial Valuation and Risk Management’’ (NCCR FINRISK). n Corresponding author. Tel.: +1 614 292 1970; fax: +1 614 292 2359. E-mail address: stulz_1@fisher.osu.edu (R.M. Stulz). 0304-405X/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2010.08.010

In the search of explanations for the dramatic collapse of the stock market capitalization of much of the banking industry in the US during the credit crisis, one prominent argument is that executives at banks had poor incentives. For instance, Alan Blinder argues that these poor incentives are ‘‘one of [the] most fundamental causes’’ of the credit crisis (Wall Street Journal, 2009a). The argument seems to be that executives’ compensation was not properly related to long-term performance, leading the Obama administration to discuss ways to change compensation practices ‘‘to more closely align pay with longterm performance’’ and to give more voice to shareholders through the adoption of ‘‘say on pay’’ for firms that received public funds through the Troubled Asset Relief Program (TARP).1 Eventually, ‘‘say on pay’’ and other

1 See Reuters (2009), Wall Street Journal (2009b), and Washington Post (2009).

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R. Fahlenbrach, R.M. Stulz / Journal of Financial Economics 99 (2011) 11–26

related governance measures became part of the DoddFrank Wall Street Reform and Consumer Protection Act. We investigate in this paper how closely the interests of bank chief executive officers (CEOs) were aligned with those of their shareholders before the start of the crisis, whether the alignment of interests between CEOs and shareholders can explain the banks’ performance in the cross section during the credit crisis, and how CEOs fared during the crisis. Traditionally, corporate governance experts and economists since Adam Smith have considered that management’s interests are better aligned with those of shareholders if managers’ compensation increases when shareholders gain and falls when shareholders lose. As Murphy (1999) puts it in a widely cited review of the academic literature on managerial compensation: ‘‘Stock ownership provides the most direct link between shareholder and CEO wealth.’’ Yet our results show that no evidence exists that banks with a better alignment of the CEO’s interests with those of the shareholders had higher stock returns during the crisis. Some evidence shows that banks led by CEOs whose interests were better aligned with those of their shareholders had worse stock returns and a worse return on equity. Though options have been blamed for leading to excessive risk-taking, there is no evidence in our sample that greater sensitivity of CEO pay to stock volatility led to worse stock returns during the credit crisis. We also do not find evidence that bank returns were lower if CEOs had higher cash bonuses. A plausible explanation for these findings is that CEOs focused on the interests of their shareholders in the buildup to the crisis and took actions that they believed the market would welcome. Ex post, these actions were costly to their banks and to themselves when the results turned out to be poor. These poor results were not expected by the CEOs to the extent that they did not reduce or hedge their holdings of shares in anticipation of poor outcomes. There are many versions of the poor incentives explanation of the crisis. One version is that CEOs had strong incentives to focus on the short run instead of the long run. Another version is that option compensation gave incentives to CEOs to take more risks than would have been optimal for shareholders. A third version is that the high leverage of financial institutions implies that CEOs can increase the value of their shares by increasing the volatility of the assets because the shares are effectively options on the value of the assets. Though the incentives of CEOs can be such that they focus too much on the short run, that they take too much risk, and that they choose excessive leverage, it is by no means obvious that CEO incentives in banks had these implications. In particular, large holdings of equity by CEOs could in fact lead them to focus appropriately on the long run, to avoid some risks that might be profitable for shareholders, and to avoid excessive leverage. To the extent that the market for a bank’s stock is efficient, changes in a bank’s long-term performance are properly reflected in the stock price. Thus, greater sensitivity of a CEO’s wealth to his bank’s stock price makes it advantageous for the CEO to improve his bank’s long-term performance when it makes economic sense to

do so. Focusing on the short run instead of the long run would be costly for CEOs because their stock price would be lower than if they had taken actions to maximize shareholder wealth. This argument is ignored by most critics who have blamed the crisis on compensation structures and who have focused on the ‘‘Wall Street bonus culture.’’ The above conclusion does not hold if the market is not efficient, because in that case the market might put more weight on short-run results and misvaluation could create pressure on management to take actions it would not take in an efficient market.2 In an inefficient market, CEOs might have concluded that they had no choice but to focus on short-run profit maximization because they feared losing their job had they not grown their banks’ business aggressively. For instance, they might have chosen to grow the subprime securitization business because of fears that the market would have reacted poorly to lack of growth even though shareholders would have benefitted in the long run from the absence of such growth. However, even if the market is efficient and in principle CEOs have proper incentives to focus on the long-run consequences of their actions, CEOs might irrationally focus more on cash bonuses than on potential increases in their equity wealth not realizable until much later. Much attention has been paid to the role of options in compensation. However, the incentive effects of options depend on the CEO’s holdings of shares because they would be diluted in the CEO’s portfolio if he had large holdings of shares. Further, when the CEO’s portfolio of options is composed mostly of in-the-money options, the incentive effects of options do not differ much from the incentive effects of common stock holdings. Keeping the CEO’s wealth constant, greater sensitivity of his wealth to increases in the volatility of his firm’s stock return brought about by greater stock option holdings would increase the CEO’s incentives to take risks as long as these options are not too much in the money. But, generally, granting options also affects the CEO’s wealth, which can change his willingness to take risks (see Ross, 2004). Whether greater sensitivity of CEO wealth to volatility makes the CEO’s interests better aligned with the interests of shareholders would seem to depend on many considerations. For example, if the CEO’s holdings of stock make him more conservative, greater sensitivity of his wealth to volatility would help in aligning the CEO’s incentives with those of shareholders. For given asset volatility and expected cash flows from assets, an increase in bank leverage would lead to an increase in the value of equity because equity is an option on the value of the assets for levered firms. However, higher leverage can also have costs. Many lines of business of banks are sensitive to the risk of their senior claims. For instance, derivatives trading businesses generally require a high credit rating for senior claims.

2 See Bolton, Scheinkman, and Xiong (2006) for a model in which optimal compensation puts more weight on short-run results to take advantage of speculative behavior in the stock market and Jensen (2005) for an analysis of the implications of overvalued equity for the incentives of management.


Further, even if an increase in leverage increases stock prices, CEOs with a large equity stake in their firm could choose more conservative leverage to reduce the risk of their wealth. CEOs with greater incentive alignment would therefore be expected to take different risks from those with weaker incentive alignment. To the extent that the bank exposures that performed poorly during the crisis were viewed as risky by CEOs in 2006, we would expect that bank CEOs with greater incentive alignment would have chosen to take fewer such exposures than CEOs with poor incentive alignment. CEOs with low holdings of shares would have had much less to lose in the event of bad outcomes as a result of these exposures. We find that bank CEOs had substantial wealth invested in their banks. For the median CEO, the value of stock and options in his portfolio was more than eight times the value of his total compensation in 2006. Consequently, changes in his bank’s stock price could easily wipe out all of a CEO’s annual compensation. The median CEO owned 0.4% of the outstanding shares of his bank. Taking into account vested, but unexercised options, this fraction increases to 1.0%. The large holdings of vested unexercised options are striking. They are not consistent with the view that somehow the typical CEO knew that there was a substantial risk of a crash in the stock price of his bank. A bank’s stock return performance in 2007–2008 is negatively related to the dollar incentives derived from its CEO’s holdings of shares and options in 2006. This effect is substantial. An increase of one standard deviation in dollar incentives is associated with lower returns of 9.6 percentage points. Similarly, a bank’s return on equity in 2008 is negatively related to its CEO’s dollar incentives in 2006. A one standard deviation increase in dollar incentives is associated with a lower return on equity of 10.5 percentage points. This evidence suggests that CEOs took exposures that they felt were profitable for their shareholders ex ante but that these exposures performed very poorly ex post. The convexity introduced by options does not appear to have had an adverse impact on stock return performance or accounting performance measured by the return on equity (ROE) or by the return on assets (ROA). Much concern has been expressed about the incentives of non-CEO bank executives. For instance, Blinder states that the top executives face incentives such that ‘‘[f]or them, it’s often: Heads, you become richer than Croesus ever imagined; tails, you receive a golden parachute that still leaves you richer than Croesus. So they want to flip those big coins, too’’ (Wall Street Journal, 2009a). Data are available on the compensation of the top four highly paid non-CEO bank executives. We use that data to examine whether the incentives of non-CEO bank executives are related to bank performance during the crisis. We do not find evidence that the incentives of non-CEO executives at the end of 2006 are related to subsequent bank performance during the crisis. However, if we look at the sum of the incentives of the top five executives, we find that our results on CEO incentives are robust to this alternative specification. It could be that the incentive effects of compensation policies were different for the subset of banks that made

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large losses or that were more systemically important. One way to identify such a subset is to examine firms that received funding from TARP. When we look at the subset of the 54 banks that received such funding in our data set we find no statistically significant difference in the relation between dollar equity incentives and returns in the subsamples of TARP and no-TARP recipients. CEOs could have sharply decreased their holdings after 2006 but before the full impact of the crisis, so that they did not have to bear the cost of the exposures they took. In that case, they would have appeared to have incentives aligned with those of the other shareholders in 2006, but they would have traded out of these incentives or would have hedged them. Consequently, their behavior in 2006 might have been based on their knowledge that they would trade out of these incentives before the value of their portfolio fell substantially. For such a strategy to make sense, CEOs would have had to be able to anticipate the crisis. We investigate the insider trading of bank CEOs in 2007–2008. We find no evidence that they traded out of their positions. CEOs therefore had to bear the losses associated with the poor outcomes of the exposures their banks had at the end of 2006. Our evidence on CEO trading of shares in 2007 and 2008 is consistent with the hypothesis that the crisis and its evolution were unexpected for bank top executives. It is inconsistent with the hypothesis that CEOs focused knowingly and suboptimally on the short term. Some might argue that they should have known better, but our evidence also shows that they had stronger incentives than most to understand the risks they were taking and the overall performance of their bank. A long literature on the compensation of bank CEOs helps put our results in perspective. This literature shows not only that CEO compensation depends on stock return and accounting performance (Barro and Barro, 1990) as does the compensation of CEOs generally, but also that the composition of pay differs from CEOs of other industries. In particular, the share of pay in the form of stock and options for bank CEOs is lower than in other industries (e.g., Adams and Mehran, 2003; Houston and James, 1995). More recently, Kaplan and Rauh (2010) estimate and compare adjusted gross incomes for nonfinancial firm executives and financial service sector employees. Their evidence indicates that the financial industry has relatively more highly compensated individuals than the nonfinancial industry. Several papers investigate the impact of deregulation and greater competition on bank CEO compensation. In particular, Hubbard and Palia (1995) and Crawford, Ezzell, and Miles (1995) conclude that deregulation led to greater pay-for-performance sensitivity of CEO pay at banks. Finally, Mehran and Rosenberg (2007) investigate the incentive effects of option grants for bank CEOs. They find that asset volatility is higher for banks that grant more options. But, at the same time, these banks have less leverage, showing that the effects of option grants on bank policies are complex. Cheng, Hong, and Scheinkman (2009) examine size-adjusted annual compensation and show that it is related to bank risk measures. Though much of the recent debate concerns the alignment of incentives between managers and shareholders, the

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existing literature suggests that greater pay-for-performance sensitivity could lead to more systemic risk, indicating that a conflict could arise between shareholder wealth maximization and financial stability. In particular, Crawford, Ezzell, and Miles (1995) find that, following deregulation, pay-forperformance sensitivity of CEO pay increased more at less well capitalized institutions. They interpret this result as evidence of a moral hazard problem induced by the existence of deposit insurance priced in a way that does not reflect the risks taken on by individual banks. More recently, a series of papers has analyzed whether bank CEO compensation is optimally designed to trade off two types of agency problems: the standard managerial agency problem as well as the risk-shifting problem between shareholders and debtholders that could be particularly severe in highly leveraged institutions (e.g., John, Mehran, and Qian, 2008; John and Qian, 2003). These papers argue that leverage should reduce the pay-for-performance sensitivity of bank CEOs compared with other CEOs because of monitoring by debtholders. Accordingly, John and Qian (2003) show that bank CEOs have lower pay-for-performance sensitivity than other CEOs. This literature emphasizes that it could be optimal for shareholders to take more risks because doing so increases the value of the put granted to banks by the Federal Deposit Insurance Corporation (FDIC). John, Saunders, and Senbet (2000) develop a model in which it is optimal for the FDIC to set insurance premiums, taking into account the compensation contract of the bank’s CEO. The paper proceeds as follows. In Section 2, we introduce our sample of banks. In Section 3, we present data on CEO compensation and equity ownership at the end of fiscal year 2006. We then turn to the relation between CEO compensation, equity ownership, and bank performance during the crisis in Section 4. In Section 5, we investigate the relation between the incentives of the top four non-CEO executives and bank performance. Section 6 examines the incentive structure and its relation to performance in banks that received money from the Troubled Asset Relief Program, and Section 7 analyzes the trading of CEOs in shares of their own bank after the end of 2006 and how their equity ownership evolves during the crisis. We conclude in Section 8.

2. The sample of banks Our study requires compensation data, which we obtain from Standard and Poor’s (S&P) Execucomp. We use that database as the starting point for the formation of our sample. We download all firm-year observations for firms with Standard Industry Classification (SIC) codes between 6000 and 6300 in fiscal year 2006. This yields 132 unique firms. We exclude firms with SIC code 6282 (Investment Advice), because these are not in the lending business (e.g., Janus, T Rowe Price). In addition, we manually go through the list of firms with SIC code 6199 (Finance Services) and SIC code 6211 (Security Brokers and Dealers). Such a manual search is necessary because SIC code 6211 includes not only investment banks but also pure brokerage houses such as Charles

Schwab.3 Though our sample has investment banks, we exclude pure brokerage houses. We also report tests that exclude investment banks. Further, SIC code 6199 contains both American Express and Citigroup even though American Express is not a bank in the traditional sense. For increased transparency, we list in the appendix the firms we exclude from our analysis and those we include. Our final raw sample contains 98 firms. Three of those banks do not have complete data on CEO compensation and equity holdings. In addition to compensation data, we obtain accounting data from Compustat, banking data from Compustat Bank, insider trading data from Thomson Financial, and stock return data from the Center for Research in Security Prices (CRSP). Table 1 provides summary statistics for our sample of banks. It shows that we cover very large financial institutions. This is not surprising because ExecuComp is biased toward larger firms. The median asset value is $15.5 billion, and the mean asset value is $129.3 billion. The sum of total assets of sample firms at fiscal year-end 2006 is $12.3 trillion. At the end of 2006, the average (median) market capitalization of sample banks is $18.7 billion ($2.8 billion). The average net income over assets (over equity) is 1.2% (13.5%). We also report two measures of capital strength: the Tier 1 capital ratio and tangible common equity divided by tangible assets. The Tier 1 capital ratio is on average 9.7% and the tangible common equity ratio is 6.7% at fiscal year-end 2006. The average Tier 1 capital ratio makes these banks well capitalized. Even the lowest Tier 1 ratio (5.73%) is substantially above the regulatory minimum of 4%. No bank in our sample has negative net income in 2006. Our study examines the accounting and stock return performance of the sample banks until the end of 2008. Table 2 shows the attrition of sample firms from fiscal year-end 2006 to the end of 2008. Of the 95 banks with complete CEO compensation data in 2006, 77 survived until December 2008. Twelve banks were acquired, and 6 banks were delisted from the exchange due to a violation of listing requirements or bankruptcy.

3. CEO compensation and equity ownership at the end of fiscal year 2006 We now turn to an examination of CEOs’ and other proxy-named executives’ compensation and of their equity and option holdings at the end of 2006. In 2006, the Securities and Exchange Commission (SEC) adopted new disclosure requirements concerning, among other items, executive compensation. The amendments to the compensation disclosure rules were intended to provide investors with a clearer and fuller picture of the compensation of named executive officers. The new rules were designed to improve tabular presentation and to offer material qualitative information regarding the manner and context in which compensation is awarded and earned. Firms had to comply with the new rules if their fiscal year ended on or after 3 Using the finer North American Industry Classification System (NAICS) does not resolve the issues. For example, Goldman Sachs Group is classified as 523110 (Investment Banking & Brokerage), while Bear Stearns is classified as 523120 (Securities Brokerage).


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Table 1 Sample summary statistics for fiscal year 2006. The table shows summary statistics for key variables for a sample of 95 bank holding companies and investment banks for fiscal year 2006. Sample selection criteria are described in Section 2. The list of sample banks is provided in the Appendix. The data are from the Compustat annual and Compustat Bank annual databases. Tier 1 capital ratio is calculated according to the Basel Accord for reporting risk-adjusted capital adequacy and is taken from the Compustat Bank database. The tangible common equity ratio is defined as tangible common equity divided by total assets less intangible assets (including goodwill). Those data are provided by the Compustat annual database. All accounting variables are measured in millions of dollars.

Variable Total assets Total liabilities Market capitalization Net income/total assets Net income/book equity Cash/total assets Dividend per share Book-to-market ratio Tier 1 capital ratio Tangible common equity ratio

Number

Minimum

Lower Quartile

Median

Upper Quartile

Maximum

Mean

Standard deviation

95 95 94 95 95 95 95 94 83 83

2008.5 1788.8 366.5 0.03% 0.33% 0.38% 0.00 0.27 5.73% 1.63%

6717.6 6083.5 1222.5 0.84% 10.42% 1.63% 0.45 0.43 8.43% 5.32%

15,497.2 14,685.0 2788.4 1.16% 13.01% 2.26% 0.88 0.50 9.42% 6.36%

60,712.2 56,768.3 13,273.0 1.45% 16.63% 2.79% 1.30 0.64 11.09% 7.40%

1,459,737.0 1,324,465.0 273,598.1 2.55% 29.18% 6.47% 2.32 0.87 19.04% 22.91%

129,307.2 119,265.6 18,725.5 1.17% 13.46% 2.35% 0.93 0.53 9.70% 6.69%

303,878.5 280,902.5 44,489.8 0.47% 5.67% 1.20% 0.58 0.15 2.00% 2.73%

December 15, 2006. We use the new table on outstanding equity awards at fiscal year-end that provides detailed information on exercise prices and expiration dates for each outstanding option grant to calculate the option’s BlackScholes value as well as its sensitivity to volatility and stock price changes. In addition, we use the narrative on executive compensation to analyze what fraction of the annual accounting bonus was paid in cash and what fraction was paid in equity. The summary tables on executive compensation, which are available through ExecuComp, report equity grants for annual performance in the year the grant was made, and not in the year during which performance was measured.4 Hence, we manually retrieve the information on the decomposition of the annual bonus for operating performance into cash bonus and equity bonus by reading the narrative on executive compensation and by looking at the following year’s proxy statement.5 Five of our sample firms have fiscal years ending before December 15, 2006 (Bear Stearns, Goldman Sachs, Lehman Brothers, Morgan Stanley, and Washington Federal Savings) and do not report executive compensation according to the new disclosure rules. For those firms, only aggregate information on exercisable and unexercisable past option grants is available. We use the methodology of Core and Guay (2002) to calculate the average characteristics of previously granted unexercisable and exercisable options. Core and Guay (2002) treat all previously granted unexercisable and all previously

4 For example, the proxy statement of CitiGroup for fiscal year 2006 (filed in March 2007) accurately describes the problem: ‘‘In accordance with SEC regulations, the stock awards granted in January 2006 in respect of the executive’s performance during 2005 are required to be reported in this proxy statement, which generally describes awards made in respect of performance in 2006. Barring a change in the SEC regulations, the stock awards granted in January 2007 in respect of each executive’s 2006 performance will be reported in the Grants of PlanBased Awards Table in the 2008 proxy statement if the executive is a named executive officer in 2007.’’ 5 We are unable to identify equity grants for 2006 performance for about 20% of the sample because of turnover or because the equity grants are not separated into grants for annual operating performance and other long-term objectives such as retention.

Table 2 Attrition of banks included in sample. The sample includes 95 commercial and investment banks covered by ExecuComp in fiscal year 2006. ‘‘Remaining in sample’’ signifies that the bank is still listed on a major US exchange in December 2008. ‘‘Merged or acquired’’ signifies that the bank left the sample due to an acquisition or merger during the sample period, and ‘‘Delisted by exchange’’ signifies a delisting of the bank due to a violation of listing requirements or bankruptcy. Event

Remaining in sample Merged or acquired Delisted by exchange

Number of observations 77 12 6

Frequency (percent) 81.1 12.6 6.3

granted exercisable options as two single grants. The exercise price of each aggregated grant is then derived from the reported average realizable value of the options. In addition, Core and Guay (2002) assume that unexercisable options have a time-to-maturity that is three years greater than that of the exercisable options. We use the two aggregated grants and their imputed characteristics to approximate the Black-Scholes value and delta and vega of the previously granted options for these five firms. Core and Guay (2002) show the validity and robustness of their approximation. Columns 1 and 2 of Table 3 provide means and medians of CEOs’ compensation, annual bonus for 2006 performance, equity portfolio, equity incentives, and equity risk. Columns 3 and 4 provide statistics for the next four highest paid executives, measured by total pay. We first average compensation variables by firm across the four non-CEO executives and then calculate the crosssectional mean and median. Columns 1 and 2 have 95 observations because three firms do not report CEO equity holdings for 2006 as a result of a change in CEO. The total compensation (including new option and stock grants, but excluding gains from exercising options) of sample CEOs was on average $7.8 million for 2006, and the median compensation was $2.5 million. The next five rows split the total pay into its components. The majority of CEO

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Table 3 Executive compensation and equity ownership at the end of fiscal year 2006. The table shows summary statistics for key compensation variables for a sample of 95 bank holding companies and investment banks for fiscal year 2006. The data are from the Compustat Execucomp database. Values are reported in thousands of dollars. Most of the variables of the table are taken directly from ExecuComp. Columns 1 and 2 show the means and medians for chief executive officers (CEOs) only. Columns 3 and 4 show means and medians for the average values of the next four highest paid proxy-named executives. ‘‘Cash bonus’’ is defined as the sum of bonus and non-equity incentive awards payouts. ‘‘Bonus paid for 2006 performance’’ shows the total bonus if the portion of equity awards explicitly granted in 2007 for 2006 performance is allocated to 2006. ‘‘Percentage ownership’’ uses the detailed information on current and previous option grants to calculate the options’ delta and multiplies the number of options held in each series by its delta when calculating the percentage ownership. ‘‘Dollar gain from +1%’’ is equal to the dollar change in the executive’s stock and option portfolio value for a 1% change in the stock price. ‘‘Percentage equity risk’’ is defined as the percentage change in the equity portfolio value for a 1% increase in stock volatility and is calculated from all option series held by the CEO. ‘‘Dollar equity risk’’ is equal to the dollar change in the executive’s equity portfolio value for a 1% change in stock volatility. CEO

Average of non-CEO executives

Mean Annual compensation Total compensation Salary Cash bonus Dollar value of annual stock grant Dollar value of annual option grant Other compensation Cash bonus/salary Bonus paid for 2006 performance Total bonus Cash bonus Equity bonus Total bonus/salary Cash bonus/total bonus Equity portfolio value Value of total equity portfolio Value of shares Value of exercisable options (Black-Scholes) Value of unexercisable options (Black-Scholes) Value of unvested restricted stock Value of total equity portfolio/total annual compensation Value of shares/salary Equity portfolio incentives Percentage ownership from shares Percentage ownership Dollar gain from + 1% Equity portfolio risk exposure Percentage equity risk Dollar equity risk

compensation stems from performance-based pay, as the average base salary of $760,000 is less than 10% of the average total compensation. John and Qian (2003) use a sample constructed similarly to ours and investigate compensation for 120 commercial banks from 1992 to 2000. In that study, they find that the ratio of average salary to average total direct compensation is higher than what we find (16% versus 10%). However, the distribution of that ratio is skewed. The median base salary of $750,000 is about 30% of the median total compensation. The last row in the first part of the table shows that cash bonuses are large relative to cash salary. The average value of cash bonus (measured as the sum of nonincentive-based pay, bonus, and long-term incentive plan payouts) over cash salary is 2.8, with a median of 0.9. When executives receive high cash bonuses for success but when bonuses cannot go below zero for failure, executives potentially have incentives to take risks that are not in the interests of the shareholders or of the safety and soundness of their institutions because that part of

Median

Mean

Median

7797.7 761.5 2137.7 2652.7 1608.3 637.5 2.8

2453.5 747.8 636.8 295.7 196.0 129.0 0.9

3791.6 392.4 1363.0 1112.5 549.2 370.7 3.2

1104.6 351.4 257.1 97.0 115.7 80.2 0.7

5314.2 2390.1 2924.1 7.1 0.6

1370.0 637.8 409.5 1.8 0.6

3102.8 1517.1 1588.4 7.4 0.6

619.5 262.8 216.3 1.6 0.6

87,466.9 61,189.6 17357.7 3242.6 5677.0 17.3 102.6

35,557.0 22,255.3 5729.1 929.3 0.0 8.1 25.7

20,156.0 11,014.1 4934.6 1586.7 2602.0 7.6 28.5

5993.0 3151.9 1073.9 277.4 8.5 4.2 8.6

1.6 2.4 1119.3

0.4 1.0 467.8

0.2 0.4 278.1

0.1 0.2 83.2

0.4 189.0

0.3 53.1

0.6 60.4

0.5 19.5

their compensation is not affected by the size of the loss that results from their actions. Consequently, we include the ratio of cash bonus to salary in all regressions. Annual bonuses for achievements of accounting based goals are paid both in cash and equity to align incentives of CEOs and shareholders. The next subset of statistics shows the decomposition of the annual bonus for 2006 performance into cash and equity grants. A significant fraction of 40% of the annual bonus for accounting performance is paid in equity. Furthermore, this statistic is somewhat understating the true significance of equity bonuses, because the higher the total bonus for 2006 performance, the higher the fraction that is paid in equity (the correlation between cash bonus divided by total bonus and total bonus is -0.22). This result has important implications for critics’ argument that annual bonuses are distorting incentives. More than 40% of the annual bonus is paid in equity, which does not vest for several years to come. Given the size of the annual bonuses, it is not surprising that the cash flows to executives from cash


bonuses and sales of vested shares were large.6 However, our focus is not on the size of compensation but on the incentive effects of compensation and, more precisely, on the incentives of CEOs immediately before the crisis. As Hall and Liebman (1998) and Core and Guay (1999) point out, most CEO equity incentives stem from the existing portfolio of stock and options, and not from annual grants. A similar result holds for our sample. We define the total dollar value of equity of a CEO at the end of fiscal year 2006 as the sum of unrestricted and restricted shares held multiplied by the end-of-year share price plus the Black-Scholes value of exercisable and unexercisable stock options plus the fair value of unearned equity incentive plans.7 The mean (median) value of the CEO’s equity stake is $87.5 million ($35.6 million). Twenty-one CEOs in our sample have equity stakes valued at more than $100 million. The top five equity positions at the end of fiscal year 2006 are held by James Cayne (Bear Stearns, $1,062 million), Richard Fuld (Lehman Brothers, $911.5 million), Stan O’Neal (Merrill Lynch, $349 million), Angelo Mozilo (Countrywide Financial, $320.9 million), and Robert J. Glickman (Corus Bankshares, $281.1 million). Most of the value of the executives’ equity portfolio stems from shares and vested, exercisable options, which are voluntarily held.8 The value of the equity portfolio is large relative to the total annual compensation. The median ratio of the value of the overall equity portfolio divided by total annual compensation is 8.1 for CEOs. The median CEO ownership percentage from shares in our sample is 0.4. John and Qian (2003) found median CEO equity holdings of 0.25% for their sample of commercial banks. The median percentage ownership from shares and exercisable options, as reported in the bank’s proxy statement, is 1.0%. We use the detailed option plan table (or the Core and Guay (2002) approximation) to calculate the delta and vega of each option grant (current and past grants). To calculate delta and vega, we need the option’s exercise price, expiration date, volatility, the current stock price, the relevant interest rate, and the dividend yield. Option exercise price and expiration date come directly from ExecuComp. We use the fiscal year-end closing price of 2006 as the current stock price, the 3-year lagged

6 Bebchuk, Cohen, and Spamann (2009) provide statistics on the cumulative cash flows to executives at Bear Stearns and Lehman from cash bonuses and share sales. 7 The treatment of restricted shares in the ‘‘ownership by officers and directors’’ table, from which ExecuComp derives the total number of shares held by executives, is not consistent across firms. We manually go through the proxy statements and determine whether unvested restricted shares are counted toward the number of shares held by executives. If not, we add the number of unvested restricted shares to the number reported in the beneficial ownership table to determine the total ownership from shares. For an example, see the proxy statement of Goldman Sachs filed on February 21, 2007. 8 Many companies have established target stock ownership plans for their executives, so that the executive is not free to sell his or her entire stake (see, e.g., Core and Larcker, 2002). These target plans typically require the CEO to hold three to five times his base salary in stock. These values are largely exceeded in our study. For example, Table 3 shows that the median CEO holds shares worth more than 25 times his base salary.

17

volatility at the end of 2006 as an estimate of the volatility, and the annual cash dividend for 2006 divided by the fiscal year-end closing price as an estimate of the dividend yield. The 10-year Treasury rate is used as an estimate of the risk-free interest rate. Table 3 presents two measures of sensitivity of the equity portfolio of the CEO to changes in the bank’s stock price. We show that the average (median) CEO ownership from shares and delta-weighted options (percentage ownership) represents 2.4% (1.0%) of the outstanding shares. In other words, the average (median) CEO’s wealth increases by $24 ($10) for every $1,000 in created shareholder wealth. By way of comparison, Murphy (1999) shows that the median gain for the CEO of a firm in the largest half of the S&P 500 is $4.36 for every $1,000 in created shareholder wealth in 1996, which is much less than the median gain for the bank CEOs in our sample. The second measure is the dollar gain for a 1% increase in shareholder value (dollar gain from + 1%). Table 3 shows that the average (median) dollar gain is $1.1 million ($0.5 million) for a 1% change in firm equity value. We calculate the percentage change in the equity portfolio value of a CEO for a 1% increase in volatility using options only. We call this measure percentage equity risk sensitivity. Although common stock has some exposure to volatility (because it can be considered a call option), Guay (1999) shows that, for the typical firm, the volatility exposure of common stock is negligible. This result might not apply to banks because they are highly levered. Nevertheless, we use the traditional approach to estimate the equity risk sensitivity because its interpretation is well understood. By proceeding this way, we could understate the equity risk sensitivity of CEOs. The median CEO in our sample stands to gain 0.3% of his total portfolio value if the stock price volatility increased by 1%. Alternatively, we can estimate the change in the dollar value of the CEO’s wealth for a 1% increase in stock price volatility. We call this measure the dollar equity risk sensitivity. In our sample, the median dollar equity risk sensitivity is $53,100. A risk-averse CEO would have to trade off the monetary value of an increase in volatility against its impact on the volatility of his wealth. Columns 3 and 4 show the decomposition of total pay for non-CEO executives. While the level of total pay is lower, the decomposition of pay is remarkably similar. In particular, non-CEO executives also receive a significant cash bonus. The ratio of cash bonus over salary is very similar to the ratio for CEOs. Non-CEO executives also hold large equity portfolios, holding on average (median) $20.2 million ($6 million) worth of equity. There are 19 non-CEO executives who hold in excess of $100 million in equity and 12 of these executives work for investment banks. However, options contribute more to the value of the equity portfolio than they do for CEO equity portfolios. For non-CEO executives, the median percentage ownership is 0.2%, and the median dollar gain from + 1% is $83,000. Concerning the equity risk measures, for nonCEO executives, the percentage equity risk sensitivity is slightly larger than for CEOs, because their equity portfolio consists of proportionally more options.

18


It is interesting to compare two ratios between nonCEOs and CEOs. The ratio of cash bonus to salary for nonCEOs is high. This appears to be a distinguishing feature of the financial industry. The average ratio of cash bonus to salary for non-CEO executives for nonfinancial firms in the ExecuComp universe is only 1.1 for fiscal year 2006, compared with 3.2 for sample firms. No statistically significant difference emerges between CEOs and nonCEOs. However, the relative measure of the importance of equity incentives, value of total equity portfolio divided by total annual compensation, is much smaller for nonCEO executives than for CEOs. These results suggest that cash bonuses are more important for non-CEO executives. 4. CEO incentives and bank performance during the crisis In this section, we investigate the relation between CEO incentives as of the end of fiscal year 2006 and bank performance during the crisis. For the purpose of this paper, we consider the returns of banks from July 1, 2007 to December 31, 2008, to correspond to the returns during the crisis period. Admittedly, the crisis did not end in December 2008. Bank stocks lost substantial ground in the first quarter of 2009. However, during the period we consider the banking sector suffered losses not observed since the Great Depression. The subsequent losses were at least partly affected by uncertainty about whether banks would be nationalized. Because it is not clear how the impact on bank stocks of the threat of nationalization would be affected by the incentives of CEOs before the crisis, it could well be that it is better to evaluate returns only until the end of 2008. A long-standing debate exists in the corporate finance literature on how to assess long-run performance (see Fama, 1998; Loughran and Ritter, 2000). One approach is to use buy-and-hold returns. Using buy-and-hold returns is generally a better approach when attempting to explain the cross-sectional variation in performance when performance can be affected by many factors. Another approach is to construct portfolios and evaluate the abnormal performance of these portfolios from the intercept of regressions of the returns of the portfolios on known risk factors. This approach has the advantage of evaluating performance in the context of a portfolio strategy. In this paper, we report buy-and-hold returns.9 We use three measures to describe short-term and equity incentives and two measures to describe the equity risk exposure of bank CEOs. We study the ratio of cash bonus to cash salary to gauge short-term incentives. The equity incentive measures are dollar gain from +1% and percentage ownership. The equity risk exposure is measured by dollar equity risk sensitivity and percentage equity risk sensitivity. 9 However, we have verified that using long-short portfolios sorted on executive ownership and equity risk characteristics yields similar results. The characteristics-adjusted alphas (using the three FamaFrench factors) for portfolios long in high equity ownership (equity risk) and short in low equity ownership (equity risk) are qualitatively similar to the results reported in Table 4, but generally of lower significance.

We investigate the determinants of returns of individual banks using multiple regressions of buy-and-hold returns of banks from July 1, 2007 to December 31, 2008, on various bank characteristics.10 The first five regressions of Table 4 use each one of our incentive and risk exposure measures, respectively. Other determinants of stock performance are the performance of the bank’s stock in 2006, the equity book-to-market ratio, and the log of the bank’s market value. Past returns, the book-to-market ratio, and the log of market value are all variables known to be related to returns. However, here, these variables could affect performance for reasons other than for their role as risk factors that affect expected returns. For instance, it could be that larger banks were able to take more risks. A log transformation is applied to both the percentage ownership and the percentage equity risk sensitivity. This transformation reduces the influence of extreme values of these variables and makes the distribution closer to the normal distribution (e.g., Demsetz and Lehn, 1985; Himmelberg, Hubbard, and Palia, 1999). We winsorize the dollar incentive measures at the 2nd and 98th percentile. Columns 1 through 5 show results from regressions of the buy-and-hold returns on each of the five incentive and risk exposure measures without controls. Regression 1 uses the measure of cash bonus over salary as an indicator of high short-term CEO incentives. The coefficient is negative and statistically significant, suggesting that firms with CEOs who receive more short-term incentives have lower returns. However, this result is not robust to the inclusion of control variables in Columns 6 through 9.11 Column 2 examines the logarithm of dollar gain from + 1%. The coefficient on dollar gain from +1% is significantly negative and remains significant in all specifications. The coefficient on percentage ownership in Regression 3 is negative as well but not significant. We also estimate this regression without the log transformation, in which case the coefficient on percentage ownership is negative and marginally significant. However, the significance is driven by a few large values and disappears when we winsorize percentage ownership at the 5% level. We then turn to equity risk exposure. Regression 4 uses the dollar measure. The coefficient is negative and insignificant. In Regression 5, the coefficient on the percentage measure is positive and significant. In Regressions 6 through 9 respectively, we use cash bonus, dollar and percentage equity incentives, and dollar and percentage risk exposure measures, and we control for other determinants of performance measured as of the end of 2006. In Regression 6, the dollar gain from the + 1% measure has a negative significant coefficient.

10 If banks delist or merge prior to December 2008, we put proceeds in a cash account until December 2008. We have verified that our results are qualitatively and quantitatively similar if proceeds are put in a bank industry index (using the Fama-French 49 bank industry classification) instead. 11 The effect does not disappear because of the inclusion of several incentive and risk exposure measures. The significant coefficient on cash bonus disappears once we control for the market value and the book-tomarket ratio.


19

Table 4 Buy-and-hold returns and chief executive officer (CEO) annual cash bonus, ownership incentives, and equity risk sensitivity. The table shows results from cross-sectional regressions of buy-and-hold returns for banks from July 2007 to December 2008 on CEO cash bonus, equity incentives, equity risk, and firm characteristics measured at the end of fiscal year 2006. ‘‘Cash bonus/salary’’ is the dollar amount of the annual bonus for 2006 performance paid in cash divided by the cash salary. ‘‘Dollar gain from + 1%’’ is the dollar change in the value of the CEO’s equity portfolio for a 1% change in the stock price. ‘‘Ownership (%)’’ is the sum of all shares (restricted and unrestricted) and delta-weighted options (exercisable and unexercisable) held by the CEO divided by the total number of shares outstanding multiplied by 100. ‘‘Equity risk ($)’’ is defined as the dollar change in the equity portfolio value for a 1% increase in stock volatility. ‘‘Equity risk (%)’’ is defined as the percentage change in the equity portfolio value for a 1% increase in stock volatility and is calculated from all option series held by the executive. A log transformation is applied to both the percentage ownership and percentage equity risk measure. The firm characteristics are measured at the end of year 2006. These characteristics include the stock return in 2006, the book-to-market ratio, the natural logarithm of the market capitalization, and the Tier 1 capital ratio. Standard errors are reported in parentheses. Statistical significance at the 1%, 5%, and 10% level is indicated by nnn, nn, and n, respectively. (1) Cash bonus/salary

(2)

(3)

(4)

(5)

0.010nn (0.004) 0.078nnn (0.022)

Dollar gain from + 1% Ownership (%)

(6)

(7)

0.003 (0.005) 0.062n (0.030)

0.003 (0.005)

0.025 (0.027)

Equity risk ($)

0.013 (0.017)

0.025 (0.020) 0.030n (0.018)

Stock return in 2006 Book-to-market Log (market value)

94 0.12

94 0.01

This effect is economically significant. The standard deviation of the logarithm of dollar incentives is 1.54. Consequently, an increase of one standard deviation in dollar gain from + 1% is associated with lower returns of 9.6% (0.062 1.54). Neither the cash bonus nor the equity risk measure shows coefficients that are significantly different from zero. Also, a bank’s return during the crisis is negatively related to the bank’s stock return performance in 2006, although the result is not statistically significant. Beltratti and Stulz (2009) find this result, but with statistical significance, for a sample of international banks. This result suggests that banks that took on more exposures that the market rewarded in 2006 suffered more during the crisis. We find next that banks with a higher book-to-market ratio in 2006 have worse performance during the crisis. A possible explanation for this result is that banks with less franchise value took more risks that worked out poorly during the crisis. Turning to Regression 7, percentage ownership has a negative insignificant coefficient and percentage equity risk sensitivity has a positive insignificant coefficient. The coefficients on the other explanatory variables are similar to those of Regression 6. Regressions 8 and 9 require information on the Tier 1 capital ratio of banks. This requirement removes from the sample all nondepository banks. In particular, all investment banks drop out of the sample. Banks that were better capitalized at the end of 2006 fared better during the crisis. The coefficients on the incentive and risk exposure variables of CEOs are largely the same. It follows, therefore,

90 0.01

90 0.03

(9) 0.015 (0.025)

0.049 (0.032) 0.030 (0.024)

0.148 (0.279) 0.607nnn (0.234) 0.027 (0.032)

0.022 (0.019) 0.147 (0.280) 0.601nnn (0.234) 0.064nn (0.026)

88 0.20

88 0.20

Tier 1 capital ratio 93 0.06

0.014 (0.025) 0.079nn (0.035)

0.036 (0.030)

Equity risk (%)

Number of observations R-squared

(8)

0.295 (0.302) 0.583nn (0.240) 0.014 (0.042) 0.038nn (0.018) 77 0.23

0.023 (0.022) 0.310 (0.304) 0.577nn (0.240) 0.035 (0.036) 0.039nn (0.018) 77 0.23

that our results cannot be explained by the large share ownership of some CEOs of investment banks that performed poorly. The results of Table 4 are robust to changes in the sample period, inclusion of additional control variables, and different treatment of outliers. In regressions not reproduced here, we use tangible common equity to assets as a measure of the capital ratio and obtain similar results. We also find similar results if we use returns from January 1, 2007 to December 31, 2008, or if we use only 2008. The same results hold if we do not winsorize dollar incentives or if we truncate dollar incentives. So far, we have focused on bank performance measured by stock returns. We now turn to the performance of banks using two measures of accounting performance: return on assets and return on equity. In Fig. 1, we show the evolution of quarterly ROA from 2005Q4 to 2008Q3. Not surprisingly, the average ROA plummets in 2008. For our regression analysis, return on assets is defined as the cumulative quarterly net income from 2007Q3 to 2008Q3 divided by total assets at the end of 2007Q2.12 For return on equity, we divide the cumulative quarterly net income by the book value of equity at the end of 2007Q2.

12 Our definition of ROA is common in the literature, but it creates a measure that systematically changes with capital structure. We have verified that our results are not driven by the influence of capital structure and reestimated regressions with operating profits over assets as the left-hand side variable. Our results on CEO equity incentives remain unchanged.

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1.50%

Net income / assets (percent)

1.00%

0.50%

0.00% 2005Q4 2006Q1 2006Q2 2006Q3 2006Q4 2007Q1 2007Q2 2007Q3 2007Q4 2008Q1 2008Q2 2008Q3

-0.50%

ROA (mean)

ROA (median)

-1.00% Quarter Fig. 1. Evolution of the return on assets (ROA), 2005Q4–2008Q3. The figure plots the evolution of average and median return on assets, defined as net income divided by total assets, of a sample of 95 bank holding companies and investment banks for 12 quarters from 2005Q4 to 2008Q3.

Table 5 shows results for ROA; Table 6 shows results for ROE. In the regressions we report in Tables 5 and 6, we use the same control variables as those used in Table 4. The first two regressions use all banks; the last two regressions require availability of the Tier 1 capital ratio and thus exclude investment banks. Table 5 shows that the CEO dollar incentive measure has a significantly negative relation with ROA. A one standard deviation increase in dollar gain from the + 1% measure (1.54) decreases the ROA by 0.77%, which appears economically significant relative to the sample mean ROA of 1.13%. The result is robust to the exclusion of investment banks (Column 3). Regarding the other ownership measures we examine, the percentage ownership measure is statistically significantly negative in the subsample that excludes investment banks. The economic magnitude is smaller than that of dollar gain from the + 1% measure. A one standard deviation increase in percentage ownership is associated with a higher ROA of 0.52%. With the equity risk sensitivity measures, neither the dollar measure nor the percentage measure is significant. Our measure of shortterm incentives, cash bonus divided by salary, is not related to ROA. The only other explanatory variable that is significant in the regressions is the book-to-market ratio. Turning to the four ROE regressions in Table 6, the CEO’s dollar incentive measure always has a negative significant coefficient. The economic magnitude appears large. A one standard deviation increase in dollar gain from the +1% measure decreases ROE by 10.5% (11.2%) in Column 1 (Column 3). These effects are similar in magnitude to the effects reported for the buy-and-hold

return regressions in Table 4. In Regression 4, which uses the sample of depository banks only, the percentage ownership measure also has a negative significant coefficient. Neither the cash bonus nor the risk sensitivity measures are significant. In addition to book-to-market, the lagged ROE is significant in Regressions 1 and 2. We estimate other regressions using ROA and ROE that we do not reproduce in a table. First, we estimate regressions in which the additional explanatory variables besides the CEO incentive and risk exposure measures are the log of the bank’s market value at the end of 2006, the volatility of its stock return in the three previous years, and the Tier 1 capital ratio. We find that the coefficient on dollar gain from the + 1% measure is negative and significant in the ROE regression. The coefficient on volatility is negative and significant. We also estimate these regressions on changes in ROA and changes in ROE. The dollar gain from the + 1% measure has a significant negative coefficient and the dollar equity risk sensitivity measure has a positive significant coefficient.

5. Non-CEO executive incentives, risk exposure, and bank performance during the crisis While a long-standing tradition in executive compensation is to treat the CEO as a sufficient statistic for the rest of the organization (e.g., Jensen and Murphy, 1990; Hall and Liebman, 1998; Core and Guay, 1999), pervasive concerns have arisen that the incentives of non-CEO bank executives led to excessive risk-taking. For instance, the


Table 5 Return on assets (ROA) and CEO annual cash bonus, ownership incentives, and equity risk sensitivity. The table shows results from cross-sectional regressions of the return on assets on CEO cash bonus, ownership incentives, equity risk exposure, and control variables. Return on assets is defined as the cumulative quarterly net income from 2007Q3 to 2008Q3 divided by the total assets at the end of 2007Q2. ‘‘Dollar gain from + 1%’’ is the dollar change in the value of the CEO’s equity portfolio for a 1% change in the stock price. ‘‘Ownership (%)’’ is the sum of all shares (restricted and unrestricted) and delta-weighted options (exercisable and unexercisable) held by the CEO divided by the total number of shares outstanding multiplied by 100. ‘‘Equity risk ($)’’ is defined as the dollar change in the CEO’s equity portfolio value for a 1% increase in stock volatility. ‘‘Equity risk (%)’’ is defined as the percentage change in the equity portfolio value for a 1% increase in stock volatility and is calculated from all option series held by the executive. A log transformation is applied to both the percentage ownership and percentage equity risk measure. The control variables include the natural logarithm of the market capitalization, the Tier 1 capital ratio, and the book-to-market ratio, all measured at the end of fiscal year 2006. Lagged return is the lagged return on assets, measured over the five previous quarters to be consistent. Standard errors are reported in parentheses. Statistical significance at the 1%, 5%, and 10% level is indicated by nnn, nn, and n, respectively.

Cash bonus/salary Dollar gain from + 1% Equity risk ($)

(1)

(2)

(3)

(4)

0.000 (0.000) 0.005n (0.003) 0.002 (0.002)

0.000 (0.000)

0.000 (0.002) 0.007nn (0.003) 0.002 (0.002)

0.000 (0.002)

Ownership (%)

0.126 (0.236) 0.053nn (0.020) 0.000 (0.002)

0.003 (0.002) 0.002 (0.001) 0.131 (0.235) 0.052nn (0.020) 0.003 (0.002)

84

85

Equity risk (%) Lagged ROA Book-to-market Log (market value) Tier 1 capital ratio Number of observations R-squared

0.13

0.13

0.360 (0.513) 0.066nnn (0.022) 0.005 (0.003) 0.002 (0.002) 73 0.22

Table 6 Return on equity (ROE) and CEO annual cash bonus, ownership incentives, and equity risk sensitivity. The table shows results from cross-sectional regressions of the return on equity on CEO cash bonus, ownership incentives, equity risk exposure, and control variables. Return on equity is defined as the cumulative quarterly net income from 2007Q3 to 2008Q3 divided by the book value of common equity at the end of 2007Q2. ‘‘Dollar gain from + 1%’’ is the dollar change in the value of the CEO’s equity portfolio for a 1% change in the stock price. ‘‘Ownership (%)’’ is the sum of all shares (restricted and unrestricted) and delta-weighted options (exercisable and unexercisable) held by the CEO divided by the total number of shares outstanding multiplied by 100. ‘‘Equity risk ($)’’ is defined as the dollar change in the CEO’s equity portfolio value for a 1% increase in stock volatility. ‘‘Equity risk (%)’’ is defined as the percentage change in the equity portfolio value for a 1% increase in stock volatility and is calculated from all option series held by the CEO. A log transformation is applied to both the percentage ownership and percentage equity risk measure. The control variables include the natural logarithm of the market capitalization, the Tier 1 capital ratio, and the book-to-market ratio, all measured at the end of fiscal year 2006. Lagged return is the lagged return on equity, measured over the five previous quarters to be consistent. Standard errors are reported in parentheses. Statistical significance at the 1%, 5%, and 10% level is indicated by nnn, nn, and n, respectively.

Cash bonus/salary Dollar gain from + 1% Equity risk ($)

0.004n (0.002) 0.002 (0.002) 0.386 (0.512) 0.066nnn (0.022) 0.000 (0.003) 0.002 (0.002) 73 0.22

Federal Reserve stated in a press release that ‘‘[f]laws in incentive compensation practices were one of many factors contributing to the financial crisis. Inappropriate bonus or other compensation practices can incent senior executives or lower level employees, such as traders or mortgage officers, to take imprudent risks that significantly and adversely affect the firm.’’13 To examine this issue, we analyze the relation between stock and accounting performance and the average incentives and risk exposure for the next four highest paid non-CEO proxy-named executives (measured by total compensation). In addition, we estimate regressions that use the sum of the incentives and risk exposure of the top five executives, including the CEO, to analyze whether our

13 See press release of October 22, 2009, announcing a ‘‘proposal designed to ensure that incentive compensation policies of banking organizations do not undermine the safety and soundness of their organizations.’’

21

(1)

(2)

(3)

(4)

0.000 (0.004) 0.068nn (0.027) 0.025 (0.016)

0.000 (0.004)

0.009 (0.021) 0.073nn (0.028) 0.022 (0.019)

0.009 (0.020)

Ownership (%)

0.532nn (0.249) 0.754nnn (0.232) 0.016 (0.025)

0.043 (0.026) 0.024 (0.015) 0.533nn (0.248) 0.748nnn (0.231) 0.028 (0.022)

83

83

Equity risk (%) Lagged ROE Book-to-market Log (market value) Tier 1 capital ratio Number of observations R-squared

0.21

0.23

0.406 (0.474) 0.821nnn (0.239) 0.043 (0.033) 0.019 (0.018) 74 0.29

0.051nn (0.024) 0.019 (0.017) 0.426 (0.472) 0.820nnn (0.239) 0.008 (0.029) 0.020 (0.018) 74 0.29

conclusions from Section 4 are robust to this alternative specification. To conserve space, we describe, but do not report, results from these additional tests. When we analyze buy-and-hold returns and non-CEO incentives we find, similar to the results for CEOs, some weak evidence that the ratio of cash bonus to salary is negatively related to buy-and-hold returns. But, again, once we include control variables, this result disappears. In regressions including firm-specific control variables, none of the non-CEO incentive and risk exposure measures has explanatory power for buy-and-hold returns. We also analyze buy-and-hold returns and the sum of the incentives and risk exposure of the top five executives, including the CEO. The results are consistent with our earlier analysis of CEOs only. In particular, the dollar gain from the +1% measure displays an economically strong inverse relation with buy-and-hold returns.

22


We do not find evidence that non-CEO executive equity incentives or risk exposure are associated with ROA or ROE in any of the specifications. We finally examine the relation between ROA and ROE and the sum of the equity incentives and risk exposure of the top five highest paid executives and corroborate our earlier findings for CEOs only. Some weak evidence shows a relation between dollar gain from + 1% of the executive team and return on assets in the specification that excludes investment banks. In addition, a strong link exists between dollar gain from the + 1% measure of the entire executive team and return on equity. For all other incentive and risk exposure measures, we do not find coefficients that are statistically different from zero. Overall, the evidence in this section suggests that the relation between executive equity incentives and performance of sample banks is driven by the equity incentives of the CEO. 6. Executive equity incentives, risk exposure, and bank performance for TARP recipients A possible concern with our analysis is that short-term incentives, equity incentives, and risk exposure might have played a different role in banks that made larger losses or were more systemically important. One approach to identify such banks, albeit ex post and with inherent selection biases, is to use the subset of banks that received funding from the Troubled Asset Relief Program. Because there are obvious concerns with respect to stock returns (the granting of TARP money could have increased returns toward the end of our sample period relative to the returns of other banks), we focus in this section on the accounting returns that are measured at the end of the third quarter of 2008 and thus prior to the distribution of TARP money. We identify sample banks that received TARP funding from a comprehensive list of TARP recipients published by USA Today.14 In our sample of 98 banks, 54 received TARP money. In unreported tests, we compare the CEO incentives and risk measures of TARP firms with those of non-TARP firms at the end of 2006. At the 5% level, we cannot reject the null hypothesis that average and median CEO incentives and risk measures are identical for TARP and non-TARP firms. In Table 7, we reestimate the regressions of Tables 5 and 6, Column 1, but interact the incentive and risk exposure measures with an indicator variable equal to one if a firm received TARP money. To avoid having outliers determine the regression estimates in the subsamples, we truncate ROA and ROE at the 1% level. In all regressions in Table 7, the coefficient on the incentive or risk exposure measure indicates the association between the measure and the return for the group of non-TARP firms. The coefficient on the interaction term of

Table 7 Troubled Asset Relief Program (TARP) recipients, ownership incentives, equity risk sensitivity, and return on assets (ROA) and return on equity (ROE). The table shows results from cross-sectional regressions of the return on assets (column 1) and the return on equity (column 2) on chief executive officer (CEO) cash bonus, ownership incentives, equity risk exposure, and control variables. Return on assets (return on equity) is defined as the cumulative quarterly net income from 2007Q3 to 2008Q3 divided by the book value of assets (common equity) at the end of 2007Q2. ‘‘Dollar gain from +1%’’ is the dollar change in the value of the executive’s equity portfolio for a 1% change in the stock price. ‘‘Equity risk ($)’’ is defined as the dollar change in the executive’s equity portfolio value for a 1% increase in stock volatility. TARP recipient indicator is an indicator variable equal to one if the bank received funding from the Troubled Asset Relief Program and zero otherwise. The control variables include the natural logarithm of the market capitalization and the bookto-market ratio, all measured at the end of fiscal year 2006. Lagged return is the lagged return on assets (equity), measured over the five previous quarters to be consistent. Standard errors are reported in parentheses. Statistical significance at the 1%, 5%, and 10% level is indicated by nnn, nn, and n, respectively. ROA TARP recipient indicator Cash bonus/salary TARP indicator cash bonus/salary Dollar gain from + 1% TARP indicator dollar gain from +1% Equity risk ($) TARP indicator Equity risk ($) Lagged return Log (market value) Book-to-market Number of observations R-squared

0.016 (0.024) 0.000 (0.000) 0.001 (0.002) 0.006n (0.003) 0.005 (0.005) 0.001 (0.002) 0.001 (0.004) 0.176 (0.235) 0.002 (0.003) 0.049nn (0.024) 83 0.19

ROE 0.281 (0.230) 0.006 (0.004) 0.003 (0.016) 0.086nnn (0.032) 0.066 (0.049) 0.020 (0.017) 0.007 (0.036) 0.471nn (0.227) 0.008 (0.027) 0.687nnn (0.217) 82 0.28

TARP and the incentive or risk exposure measure shows how the association between the measure and the return differs between TARP firms and non-TARP firms. Statistical significance on the interaction term hence demonstrates that a statistically different association exists in firms that receive TARP funding and those that do not. The first column in Table 7 shows the results for ROA. There is no evidence that incentives or risk exposure in TARP firms had a different effect on the ROA than incentives or risk exposure in non-TARP firms. Column 2 shows the results for ROE. Again, there is no evidence that incentives or risk exposure had a different impact for TARP firms than other firms. 7. CEO equity losses during the crisis

14

See http://www.usatoday.com/money/economy/tarp-chart.htm. In unreported regressions, we also add firms that would in all likelihood have received TARP funding but did not survive long enough (e.g., Bear Stearns, Lehman Brothers, Countrywide, IndyMac, WashingtonMutual, and Wachovia). Adding these firms does not change our results reported in Table 7.

We have uncovered no evidence supportive of the view that better alignment of incentives between CEOs and shareholders would have led to better bank performance during the crisis or that larger risk exposure through


option compensation is to blame for the poor performance of banks. Our evidence is consistent with the hypothesis that CEOs who took exposures that performed poorly during the crisis did so because they thought that doing so was good for shareholders as well as for themselves. Our evidence provides no support for the hypothesis that option compensation led CEOs to take on more exposures that performed poorly during the crisis. Finally, our evidence is consistent with the hypothesis that CEOs did not expect these exposures to work out poorly. So far we proceeded with our analysis using CEO share and option holdings at the end of 2006. If CEOs saw the crisis coming some time after the end of 2006, they could have sold their holdings—at least as long as they were not concerned about or could avoid insider trading litigation risks—and hence would not have been affected adversely by their decisions. We investigate in this section how share ownership of CEOs evolved during the crisis. For this analysis, we use ExecuComp and the database on insider transactions from Thomson Financial. We aggregate CEO transactions by firm and quarter. We are able to match 88 of the 95 bank CEOs in ExecuComp to the Thomson Financial database. Fig. 2 reports the quarterly mean CEO net share purchases between 2007Q1 and 2008Q4, divided by their ownership from shares at the end of 2006. We do not include ownership through options in the denominator, because most of the options are underwater by the end of 2008. Scaling by ownership from shares at the end of 2006 thus takes better into account the effective sales of the CEOs. Throughout the crisis period, in all but one quarter, CEOs sell around 2% of their holdings per quarter. The exception is the quarter ending in September 2008, when, conditional on trading, CEOs sell almost 10% of their holdings on average. In any given quarter, less than 50% of all CEOs trade at all. Fig. 2 also shows the increase in ownership of CEOs through new grants of stock. They receive grants throughout the period. Overall, taking sales and new grants into account, there is no evidence of large selling efforts by CEOs except for those who traded in the quarter ending in September 2008, a quarter marked by the Lehman bankruptcy. The solid line, capturing total changes in CEO ownership, oscillates around zero throughout the sample period. In Table 8, we attempt to estimate the dollar loss of CEOs in our sample on their stock holdings resulting from the fall in the value of their holdings over the period from the end of fiscal year 2006 through December 31, 2008. Our starting point for each CEO is the shares held at the end of 2006. We use the insider trading data to evaluate the price at which the CEO sold shares, if he sold shares.15 15

We implicitly assume that a CEO first sells the shares he already owned in 2006 and does not sell shares from more recent stock grants. Given the vesting restrictions on new stock grants and our relatively short sample period, we do not believe this is a major cause of concern. We are able to exclude sales of shares linked to option exercises, if the option exercise and subsequent sale are reported concurrently. Shares that are acquired through option exercises and immediately sold receive a special code in the Thomson Financial Database, and we exclude those transactions. However, if the executive exercises the options in 2007, acquires the shares, and then waits a week before selling them, we

23

The CEO’s total dollar loss is then defined as the loss in value of the shares not sold, evaluated using the price of the shares at the end of December 2008 or when the CEO loses his job plus the loss from selling shares, measured as the difference between the value of shares at the end of 2006 and the price of the shares sold. The average value of shares held at the end of 2006 is $61.503 million. On average, a CEO lost $28.771 million on the shares not sold and $2.719 million on the shares sold. More than threequarters of the CEOs did not report any insider sales. On average, a CEO lost $31.490 million. The median loss is sharply less, however, at $5.084 million. It follows from Table 8 that CEOs made large losses on their wealth during the crisis and that most of these losses come from holding on to their shares. Had CEOs seen the crisis coming, they presumably could have avoided most of these losses by selling their shares. They clearly did not do so. We also investigate what happened to the options held by CEOs. Strikingly, only 12% of the options granted before 2007 were out of the money at fiscal year-end 2006. In contrast, approximately 70% of all options granted before 2007 were out of the money at the end of the sample period. Consequently, CEOs suffered large losses on their option portfolios as well.16 A valid concern is whether we overestimate the equity losses of insiders. We could be missing hedging activities by insiders that are carried out through off-market equity transactions such as zero-cost equity collars, exchange funds, equity swaps, or variable prepaid forward contracts. All these transactions have in common that the insider does not sell the shares and thus retains the voting rights of the stock while receiving significant downside protection. It is important to note that the SEC has mandated reporting of such hedging transactions since 1996. Thomson Financial, our data provider for insider transactions, has specific fields that capture trading of prepaid variable forward contracts, exchange funds, and equity swaps. When we search for zero-cost collars, exchange funds, and prepaid variable forward contracts by the CEOs of sample banks, we do not find a single hedging transaction.17 While some debate is ongoing on the issue of whether insiders underreport hedging transactions, it is argued by most legal experts that not reporting hedging transactions is illegal (see Wall Street Journal, 2004). Overall, we have no reason to believe that significant hedging activities

(footnote continued) would erroneously consider this transaction an outright sale of shares owned in 2006. Because many options had strike prices higher than stock prices during the financial crisis, we do not believe this is a major concern. 16 Murphy (2009) provides additional evidence that the intrinsic value of in-the-money executive stock options decreased dramatically during the financial crisis, in particular for TARP firms. 17 The lack of reported hedging activities is not surprising in light of the very small samples of hedging transactions in two comprehensive studies on off-market equity transactions (see Bettis, Bizjak, and Lemmon, 2001; Jagolinzer, Matsunaga, and Yeung, 2007).

24


Fig. 2. Chief executive officer (CEO) insider trading. The figure shows the average total changes in CEO ownership and ownership changes caused by trading and new grants. The sample contains 80 bank CEOs that are covered by both ExecuComp and Thomson Financial’s insider trading database. A CEO who turned over prior to September 2007 is excluded from the sample. For each CEO, all insider transactions unrelated to option exercises reported by Thomson Financial are aggregated by firm and quarter. If a CEO does not trade or does not receive new grants, he is included in the cross-sectional average for a given quarter with a value of zero. The change in ownership is defined as the number of shares traded or granted divided by the total CEO ownership from stocks, excluding options, at the end of fiscal year 2006.

Table 8 Dollar losses of chief executive officers’ (CEOs’) stock portfolios during the credit crisis. The table shows the cumulative trading losses and the losses from shares held from the beginning to the end of the sample period. The sample contains 80 bank CEOs. A CEO who turned over prior to September 2007 is excluded from the sample. Cumulative trading losses are calculated as shares sold multiplied by the difference of the price at the 2006 fiscal year-end and the transaction price. Sales related to concurrent option exercises are excluded in the calculations. ‘‘Loss from not acting’’ is calculated as the shares held at the end of the sample period multiplied by the difference of the 2006 fiscal yearend price and the stock price at the end of the sample period. End of the sample period is defined as either December 2008, the month of the turnover of the CEO, or the month of the corporate event (merger, delisting), whichever comes first. ‘‘Total dollar loss’’ is calculated as the sum of the cumulative trading loss and the loss from not acting. If Thomson Financial does not report a sale of shares unrelated to options, it is assumed that the CEO did not sell any of his shares, and cumulative trading losses are set to zero. All numbers, except for stock prices, are reported in thousands of dollars. Mean Stock price end of fiscal year 2006 Stock price end of sample period Total value of shares held end of fiscal year 2006 Loss from not acting Cumulative trading loss Total dollar loss

40.36 21.91 61,503.82 28,771.49 2719.45 31,490.94

attenuate the finding of large equity losses shown in Table 8.

8. Conclusion Based on our evidence, lack of alignment of bank CEO incentives with shareholder interests cannot be blamed for the credit crisis or for the performance of banks during

Minimum 11.12 0.10 347.48 13,628.19 686.16 13,628.19

Q1

Median

Q3

Maximum

23.95 7.98 7065.16 784.05 0.00 916.83

35.58 14.72 23,628.25 5076.10 0.00 5084.30

48.75 32.38 57,337.03 19,150.44 56.63 20315.48

152.48 89.65 894,128.54 368,429.27 201,538.71 368,429.27

that crisis. Whether we look at depository banks only or at a larger sample that includes investment banks as well, there is no evidence that banks with CEOs whose incentives were less well aligned with the interests of their shareholders performed worse during the crisis. When we attempt to explain the performance of banks in the cross section, we find evidence that banks where CEOs had better incentives in terms of the dollar value of their stake performed significantly worse than banks where


CEOs had poorer incentives. For the whole sample, neither cash bonus nor stock options had an adverse impact on bank performance during the crisis. We also investigate whether CEO and non-CEO incentives in banks that received TARP funds have a different relation to bank performance than that observed in banks that did not receive TARP funds. We find that the relation between bank performance and CEO incentives does not differ between TARP and non-TARP banks. A possible explanation for our results is that CEOs with better incentives to maximize shareholder wealth took risks that other CEOs did not. Ex ante, these risks looked profitable for shareholders. Ex post, these risks had unexpected poor outcomes. These poor outcomes are not evidence of CEOs acting in their own interest at the expense of shareholder wealth. Support for this possible explanation is provided by our examination of the wealth consequences of the crisis for bank CEOs. If CEOs took risks that they knew were not in the interests of their shareholders, we would expect them to have sold shares ahead of the crisis. We find that this did not happen. CEOs, therefore, made large losses on their holdings of shares and on their holdings of options. On average, CEOs in our sample lost at least $30 million and the median CEO loss is more than $5 million. Appendix A We download all firms that are in Standard and Poor’s ExecuComp database in 2006 and have an SIC code between 6000 and 6300. From this list, we exclude some firms because they are mostly concerned with investment advice, pure brokerage business, or wire transfering and do not match well our definition of a lending institution. Appendix A.1 shows the firms we exclude from the final sample, and appendix A.2 shows all sample firms. A.1. Excluded financial firms in SIC codes 6000–6300

A G Edwards Affiliated Managers Group Inc. American Express Americredit Corp. Bankrate Inc. Bisys Group Capital One Financial Charles Schwab CIT Group CME Group Eaton Vance Corporation E-Trade Financial Group Federated Investors Inc. Financial Federal Corporation Finova Group Franklin Resources Inc Intercontinental Exchange Investment Technology Group Janus Capital Group Inc LaBranche & Co Legg Mason Inc Mellon Financial Corp Metavante Technologies Moneygram International Nuveen Investments Price (T Rowe) Group Raymond James Financial

25

SEI Investments Company Southwest Securities Group (SWS Group) State Street Corporation TD Ameritrade Holding Tradestation Group Waddell&Reed

A.2. Sample firms

1.

Anchor Bancorp Inc./WI

2. 3. 4. 5. 6.

Associated Banc-Corp. Astoria Financial Corp. Bank Mutual Corp. Bank of America Corp. Bank of Hawaii Corp.

7.

Bank of New York Mellon Corp. BB&T Corp. Bear Stearns Companies Inc. Boston Private Financial Holdings Brookline Bancorp Inc. Cascade Bancorp Cathay General Bancorp Central Pacific Financial Corp.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.

50. Investors Financial Services Corp. 51. Irwin Financial Corp. 52. Jefferies Group Inc. 53. JPMorgan Chase & Co. 54. Keycorp 55. Lehman Brothers Holdings Inc. 56. M&T Bank Corp.

57. MAF Bancorp Inc. 58. Marshall & Ilsley Corp. 59. Mercantile Bankshares Corp. 60. Merrill Lynch & Co Inc. 61. Morgan Stanley 62. National City Corp 63. New York Community Bancorp Inc. Chittenden Corp. 64. Northern Trust Corp. Citigroup Inc. 65. PNC Financial Services Group Inc. City National Corp. 66. Popular Inc. Colonial Bancgroup 67. Prosperity Bancshares Inc. Comerica Inc. 68. Provident Bankshares Corp. Commerce Bancorp Inc./NJ 69. Regions Financial Corp. Compass Bancshares Inc. 70. SLM Corp. Corus Bankshares Inc. 71. South Financial Group Inc. Countrywide Financial Corp. 72. Sovereign Bancorp Inc. Cullen/Frost Bankers Inc. 73. Sterling Bancorp/NY Dime Community Bancshares 74. Sterling Bancshares/TX Downey Financial Corp. 75. Sterling Financial Corp./ WA East West Bancorp Inc. 76. Suntrust Banks Inc. Fannie Mae 77. Susquehanna Bancshares Inc. Fifth Third Bancorp 78. SVB Financial Group First Bancorp 79. Synovus Financial Corp. First Commonwealth Financial 80. TCF Financial Corp. Corp./PA First Financial Bancorp Inc./OH 81. TD Banknorth Inc. First Horizon National Corp. 82. Trustco Bank Corp/NY First Indiana Corp. 83. US Bancorp First Midwest Bancorp Inc. 84. UCBH Holdings Inc. First Niagara Financial Group 85. Umpqua Holdings Corp. Firstfed Financial Corp./CA 86. Unionbancal Corp. Firstmerit Corp. 87. United Bankshares Inc./ WV Flagstar Bancorp Inc. 88. United Community Banks Inc. Franklin Bank Corp. 89. Wachovia Corp. Fremon General Corp. 90. Washington Fed Inc. Glacier Bancorp Inc. 91. Washington Mutual Inc. Goldman Sachs Group 92. Webster Financial Corp. Greater Bay Bancorp 93. Wells Fargo & Co. Hanmi Financial Corp. 94. Westamerica Bancorporation Hudson City Bancorp Inc. 95. Wilmington Trust Corp. Huntington Bancshares 96. Wilshire Bancorp. Inc. Independent Bank Corp. 97. Wintrust Financial Corp. Indymac Bancorp Inc. 98. Zions Bancorporation

26


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Houston, J., James, C., 1995. CEO compensation and bank risk: is compensation in banking structured to promote risk-taking? Journal of Monetary Economics 36, 405–431. Hubbard, R., Palia, D., 1995. Executive pay and performance: evidence from the US banking industry. Journal of Financial Economics 39, 105–130. Jagolinzer, A., Matsunaga, S., Yeung, E., 2007. An analysis of insiders’ use of prepaid variable forward transactions. Journal of Accounting Research 45, 1055–1079. Jensen, M., 2005. Agency costs of overvalued equity. Financial Management 34, 5–19. Jensen, M., Murphy, K., 1990. Performance pay and top-management incentives. Journal of Political Economy 98, 225–264. John, K., Mehran, H., Qian, Y., 2008. Outside monitoring and CEO compensation in the banking industry. Unpublished working paper. New York University, New York. John, K., Qian, Y., 2003. Incentive features in CEO compensation in the banking industry. Federal Reserve Bank of New York Economic Policy Review 9, 109–121. John, K., Saunders, A., Senbet, L., 2000. A theory of bank regulation and management compensation. Review of Financial Studies 13, 95–112. Kaplan, S., Rauh, J., 2010. Wall Street and Main Street: what contributes to the rise in the highest incomes? Review of Financial Studies 23, 1004–1050. Loughran, T., Ritter, J., 2000. Uniformly least powerful tests of market efficiency. Journal of Financial Economics 55, 361–389. Mehran, H., Rosenberg, J., 2007. The effect of employee stock options on bank investment choice, borrowing, and capital. Staff report 305. Federal Reserve Bank of New York, New York. Murphy, K., 1999. Executive compensation. In: Ashenfelter, O., Card, D. (Eds.), Handbook of Labor Economics, vol. 3b. North-Holland, Amsterdam, pp. 2485–2563. Murphy, K., 2009. Compensation structure and systemic risk. Unpublished working paper. University of Southern California, Los Angeles, CA. Reuters, 2009. US SEC proposes say on pay for TARP companies. J. Pehtokoukis, July 1. Ross, S., 2004. Compensation, incentives, and the duality of risk aversion and riskiness. Journal of Finance 59, 207–225. Wall Street Journal, 2004. The insiders’ magic way to sell: SEC investigates securities firms that used derivatives contracts to help executives trade quietly. R. Smith, J. Eisinger, March 19. Wall Street Journal, 2009a. Crazy compensation and the crisis. A. Blinder, May 28. Wall Street Journal, 2009b. US eyes bank pay overhaul: administration in early talks on ways to curb compensation across finance. D. Solomon, D. Paletta, May 13. Washington Post, 2009. US targets excessive pay for top executives. D. Cho, Z. Goldfarb and T. Murakami Tse, June 11.




Institutional cross-holdings and their effect on acquisition decisions$ Jarrad Harford a,n, Dirk Jenter b,1, Kai Li c,2 a b c

Foster School of Business, University of Washington, Seattle, WA 98195-3200, USA Stanford University and NBER, Graduate School of Business, 518 Memorial Way, Stanford, CA 94305-5015, USA Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC V6T 1Z2, USA

a r t i c l e in fo

abstract

Article history: Received 4 March 2008 Received in revised form 22 December 2009 Accepted 31 December 2009 Available online 10 August 2010

Cross-holdings are created when a shareholder of one firm holds shares in other firms as well, and cross-holdings alter shareholder preferences over corporate decisions that affect those other firms. Prior evidence suggests that such cross-holdings explain the puzzle of why shareholders allow acquisitions that reduce the value of the bidder. Conducting a shareholder-level analysis of cross-holdings, we instead find that crossholdings are too small to matter in most acquisitions and that bidders do not bid more aggressively even in the few cases in which cross-holdings are large. We conclude that cross-holdings do not explain value-reducing acquisitions. Beyond acquisitions, we find that institutional cross-holdings between large firms have, in fact, increased rapidly over the last 20 years, but mostly due to indexing and quasi-indexing. As in acquisitions, cross-holdings by active investors are typically too small to matter. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G30 G34 Keywords: Cross-holdings Institutional investors Mergers and acquisitions Shareholder preferences Value-reducing acquisitions

$ We thank an anonymous referee, Nittai Bergman, Murray Carlson, Alex Edmans, Adlai Fisher, Ron Giammarino, John Graham, Jon Karpoff, Alan Kraus, Kalina Manova, Gregor Matvos, Wayne Mikkelson, Pablo Moran, Hernan Ortiz-Molina, Michael Ostrovsky, Jon Reuter, Frederik Schlingemann, Jeremy Stein, Hongping Tan, Ralph Walkling, and seminar and conference participants at the Bank of Canada, Bentley College, Boston College, Chinese University of Hong Kong, the City University of Hong Kong, Concordia, the Federal Reserve Board of Governors, Hong Kong University of Science and Technology, the MIT Finance Lunch, Rotterdam, Rutgers, the Stanford Corporate Governance Lunch, Simon Fraser, Tilburg, Toronto, Tsinghua, University of British Columbia, UCLA, University of Northern BC, University of Texas at Austin, Vanderbilt, Warwick, York, the Pacific Northwest Finance Conference (Seattle), the 13th Mitsui Life Symposium on Value Creation at the University of Michigan (Ann Arbor), and the 2007 Western Finance Association Meetings (Big Sky) for useful comments and discussions. We acknowledge the financial support from the Social Sciences and Humanities Research Council of Canada. All remaining errors are our own. n Corresponding author. Tel.: + 1 206 543 4796. E-mail addresses: [email protected] (J. Harford), [email protected] (D. Jenter), [email protected] (K. Li). 1 Tel.: + 1 650 498 4411. 2 Tel.: + 1 604 822 8353.


1. Introduction Institutional ownership of equity has risen to the point where two firms frequently have several institutional investors in common. Matvos and Ostrovsky (2008) hypothesize that such cross-holdings can explain the vexing puzzle of why bidder shareholders regularly allow value-destroying acquisitions. Specifically, they argue that gains on target shares held by the bidder’s institutional investors more than offset their losses on bidder shares in such transactions. This conclusion, while appealing, is rejected when we examine cross-holdings at the shareholder level. The observed effects of cross-holdings are much too small to explain the persistence of bidder valuereducing mergers. Matvos and Ostrovsky treat all cross-held shares in the target as a consolidated block, implicitly assuming that all bidder shareholders with cross-holdings agree on the relative importance of bidder and target value.

28

J. Harford et al. / Journal of Financial Economics 99 (2011) 27–39

Our shareholder-by-shareholder analysis shows that this assumption is incorrect. Empirically, influential investors with large bidder stakes tend to have only small stakes in the target and, thus, care little about target value. Investors with large target stakes, meanwhile, tend to have only small stakes in the bidder and are unlikely to affect bidder behavior. Simply adding up bidder shareholders’ stakes in the target creates a spurious link between the large target stakes of some shareholders and the large bidder stakes of others, leading to incorrect conclusions about shareholders’ objectives. Examining a comprehensive sample of acquisitions of public targets by public bidders from 1984 to 2006, we find that investors with substantial cross-holdings are not influential enough to impact the characteristics of most bids. In the vast majority of the deals, most institutional shareholders of the bidder have no investment in the target, and bidder shareholders wishing to put large weight on target value tend to control only a small fraction of the bidder’s equity. As a result, cross-holdings do little to improve bidder shareholders’ returns. In the average acquisition with a negative bidder announcement return, only 4% of the bidder’s shares are held by institutions with large enough gains in the target to compensate for their losses in the bidder. Thus, crossholdings are not an empirically important reason why institutional investors fail to oppose acquisitions that reduce bidder value. Nonetheless, there is a small subset of acquisitions in which institutional shareholders with large cross-holdings control enough of the bidder’s equity to be potentially influential. We carefully examine whether bidder managements react by pursuing targets more aggressively. We find no evidence that large cross-holdings are associated with more negative bidder announcement returns, a lower bidder share of synergies, or other changes in bid characteristics. There is some indication of an effect of cross-holdings on target selection, but it is likely attributable to unobserved common factors determining both suitable merger partners and the types of firms each institutional shareholder chooses to invest in. Thus, in the few acquisitions in which cross-holdings appear large enough to matter, the evidence indicates that bidder management ignores them. This is consistent with the observation that managers are given few incentives to take between-firm externalities into account and with the observation that many cross-holdings are held by passive investors. Because targets are typically small and as such attract less institutional investment, we explore the possibility that cross-holdings, while small in the merger and acquisition setting, could have risen to potentially influential levels between larger firms. Among Standard & Poor’s (S&P) 500 firms, we do find that institutional cross-holdings have increased rapidly over the last 20 years, mostly due to indexing and quasi-indexing. However, even among these firms, we conclude that cross-holdings by active investors, while of growing importance, are typically not large enough to influence corporate policy. The next section motivates our approach to measuring cross-holdings. Section 3 describes the data. Section 4

analyzes the importance and effects of cross-holdings in acquisitions. Section 5 presents evidence on the size and the evolution of cross-holdings among S&P 500 firms. The last section summarizes and concludes. 2. The role of shareholder cross-holdings This section examines how cross-holdings affect shareholder preferences over corporate decisions and explains how we measure cross-holdings. We frame the discussion in terms of a corporate acquisition, but the results apply to any corporate action that imposes an externality on other firms in shareholders’ portfolios.3 2.1. The preferences of shareholders with cross-holdings Consider a shareholder who owns aB percent of the equity of a bidder and aT percent of the equity of its acquisition target. The shareholder’s wealth gain (or loss) from the acquisition depends on her stakes in the two firms and on the distribution of takeover gains. Specifically, the shareholder receives aB percent of any change in bidder value and aT percent of any change in target value:

DWpre-to-post-deal ¼ aB ðD bidder valueÞ þ aT ðtakeover premiumÞ ð1Þ Empirically, the gains to bidders are often negative, while takeover premiums are usually positive and large. Because our bidder shareholder also owns a stake in the target, she shares some of the gains accruing to target shareholders. Thus, as long as her gains in the target exceed her losses in the bidder, she supports a ‘‘bad’’ acquisition that lowers the value of the bidder. In the extreme, if the shareholder owns a larger percentage stake of the target than of the bidder (aT 4 aB ), then the effect of a higher takeover premium on her wealth becomes positive, and she wants the bidder to overpay. 2.2. Measuring cross-holdings We use two complementary approaches to capture the cross-holdings of bidder shareholders. The first approach focuses on the ten largest institutional shareholders of each bidder. To capture the strength of their incentives to lobby management, we examine, shareholder by shareholder, the magnitudes of their aB stake in the bidder and aT stake in the target. There are two reasons why large shareholders deserve most of our attention. First, large shareholders are more likely to have the ability to influence bidder management. Second, as Eq. (1) makes clear, a shareholder’s loss from overpayment increases in her percentage stake in the bidder. As a result, the largest shareholders have the strongest incentives to resist overpayment in acquisitions, and cross-holdings are more 3 The general result that diversified shareholders prefer corporate policies that maximize portfolio values to policies that narrowly maximize the values of individual firms has been developed in Easterbrook and Fischel (1982), Hansen and Lott (1996), and Rubin (2006). Fama (1978) first highlighted this application of the Coase Theorem in the context of equity and bondholders of the same firm.


likely to weaken shareholder resistance if held by large shareholders. The second approach extends the analysis to all institutional shareholders of the bidder. To aggregate preferences across shareholders, we re-scale each shareholder’s bidder and target stakes and turn them into weights:

29

about target value. Shareholders with large target stakes, however, tend to have only small stakes in the bidder and are thus unlikely to have much influence on bidder management. Simply adding up bidder shareholders’ stakes masks this heterogeneity and leads to incorrect conclusions about bidder shareholders’ objectives.

DWpre-to-post-deal ¼ aB ðD bidder valueÞ þ aT ðtakeover premiumÞ ¼ ðaB þ aT Þ þ

aT aB þ aT

3. Sample formation

aB

ðD bidder valueÞ aB þ aT ðtakeover premiumÞ

ð2Þ

Thus, a shareholder with both bidder and target stakes wants to maximize a weighted average of both firms’ values, with weight aB =ðaB þ aT Þ on bidder value and weight aT =ðaB þ aT Þ on target value.4 For the empirical analysis, we order each bidder’s institutional shareholders by the weights they assign to target value and then report the fraction of bidder shares held by institutions that put more than 0% weight, more than 10% weight, and so on to finally more than 50% weight on target value. In addition to the cross-holdings themselves, we report the extent to which cross-holdings improve the wealth effects of takeovers on institutional shareholders. Bidder shareholders’ incentives to resist overpayment are stronger the more those shareholders lose on their bidder stakes, but are weaker the more they gain on their target stakes (if any). To capture whether shareholder resistance is significantly weakened by cross-holdings, we compare the changes in the values of bidder and target stakes around takeover bids for the largest and for all institutional shareholders of each bidder. 2.3. The Matvos and Ostrovsky approach to measuring cross-holdings Matvos and Ostrovsky (2008) do not analyze crossholdings and wealth effects shareholder by shareholder. Instead, they aggregate the holdings of all bidder institutions in the bidder and the target into a representative investor: ! N X aggregate DWpre-to-post-deal ¼ aB,i ðD bidder valueÞ þ

i¼1 N X

!

aT,i ðtakeover premiumÞ

ð3Þ

i¼1

where N is the number of institutional shareholders in the bidder. This approach implicitly assumes that all bidder institutions agree with one another on the relative importance of bidder and target value and act in concert. Our analysis shows that this assumption is incorrect. In the data, shareholders with large bidder stakes tend to have only small stakes in the target and, thus, care little 4

What the weights fail to capture is the magnitude of each shareholder’s wealth change. A larger shareholder [i.e., a shareholder with a larger (aB + aT)] loses or gains more in dollar value from a given deal than a smaller shareholder with the same bidder and target weights.

We employ two different samples in our empirical analysis. The first sample consists of mergers and acquisitions between public firms from 1984 to 2006. Acquisitions create between-firm externalities that are large and easily observable, making acquisitions the most promising setting to find an effect of cross-holdings on corporate behavior. The second sample contains all firms in the S&P 500 index in each of 1985, 1995, and 2005. We analyze S&P 500 firms because of their collective economic importance. Matching with institutional ownership data as well as Center for Research in Security Prices (CRSP) and Compustat leaves fewer than five hundred firms in each year: 447, 446, and 459 firms in 1985, 1995, and 2005, respectively.5 The acquisition sample starts with all announced (both completed and canceled) US mergers with announcement dates between January 1, 1984 and December 31, 2006 from Thomson Financial’s Securities Data Company (SDC) database. We use all deals in which both the bidder and the target are public firms and the form of deal is coded as a merger, an acquisition of majority interest, or an acquisition of assets (9,260 deals). Next, we match with Compustat and CRSP data and only retain an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% after the bid. For completed deals, we require that the bidder owns more than 90% of the target after the deal completes. These filters yield 3,639 deals. Merging with the CDA/Spectrum 13F data on institutional shareholdings leaves 3,540 merger attempts in which both the bidder and target have data on institutional holdings in the quarter-end prior to the bid announcement. Ideally, we would also like to measure cross-holdings at the individual investor level. Using data on institutional investors adds a layer of intermediation and masks the extent to which the ultimate owners of the stocks are diversified across firms. However, given the greater size of their stakes, the cross-holdings of institutional investors are more likely to affect company policies than the crossholdings of individuals. Another complication is that an institutional portfolio reported to the Securities and Exchange Commission (SEC) could be an aggregate of several distinct portfolios run by different asset managers. This would make it less likely that any of the individual 5 Institutional ownership data are available because a 1978 amendment to the Securities and Exchange Act of 1934 requires all institutional investors with greater than $100 million of equity securities under discretionary management to report every quarter all common stock positions greater than 10,000 shares or $200,000 using the Securities and Exchange Commission form 13F.

30


Table 1 Summary statistics on merger bids. The sample consists of 3,540 acquisition attempts announced during the period January 1, 1984 to December 31, 2006. The bidders and targets are listed in the Securities Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. All dollar amounts are in 2006 millions of dollars, and all percentages are in real numbers. In Panel A, Complete, All Cash, All Stock, Competing, and Diversifying are dummy variables that take the value of one for completed acquisitions, if only cash is used to pay for the acquisition, if only equity is used, if there are multiple bids for the same target within one year, and if the bidder and target are from two different industries, respectively, and zero otherwise. Relative Size is the transaction value divided by the market value of bidder assets at the end of the fiscal year prior to the bid announcement. Toehold measures the percentage of the target’s shares directly held by the bidder prior to the bid announcement. Premium is the ratio of the final offer price to the target stock price four weeks prior to the original announcement date minus one. In Panel B, the abnormal announcement period returns (CAR3) are over days ( 1, + 1), where day 0 is the date of the initial bid announcement by the acquiring firm. Daily abnormal stock returns are computed using the market model and the value-weighted CRSP index. The estimation window is days ( 200, 60) prior to the acquisition announcement date. Following Bradley, Desai, and Kim (1988), Synergies (percent) is the percentage synergy gain is defined as the cumulative abnormal return over the ( 1, + 1) event window for a value-weighted portfolio of the bidder and the target. The weights for the bidder and the target are based on the market value of equity two days prior to the bid announcement. The target weight adjusts for the percentage of target shares held by the bidder prior to the bid announcement, with the adjustment set to zero for missing toehold values. Synergies (dollar) is the dollar value synergy gain is defined as the percentage synergy gain times the sum of the market values of equity for the bidder and target in million dollars, again adjusted for target shares held by the bidder prior to the bid announcement. The bidder share of synergies is the abnormal increase in the bidder’s market value of equity over days ( 1, + 1) divided by the dollar value synergy gain. The bidder share of synergies is calculated for bids with positive synergies only and is winsorized at the 1% level. Variable

Number of observations

Panel A: Deal characteristics Complete All cash All stock Competing Diversifying Relative size Toehold Premium

3,540 3,540 3,540 3,540 3,540 3,285 3,540 3,177

Panel B: Abnormal announcement period returns and synergies Bidder CAR3 3,540 Target CAR3 3,540 Synergies (percent) 3,540 Synergies (dollars) 3,540 Bidder share of synergies (percent) 2,129

Mean

Median

Standard deviation

5th percentile

95th percentile

0.758 0.237 0.387 0.123 0.465 0.301 0.007 0.428

1.000 0.000 0.000 0.000 0.000 0.104 0.000 0.346

0.428 0.425 0.487 0.328 0.499 0.667 0.043 0.563

0.000 0.000 0.000 0.000 0.000 0.004 0.000 0.054

1.000 1.000 1.000 1.000 1.000 1.090 0.000 1.137

0.013 0.194 0.019 47.077 0.294

0.009 0.147 0.011 9.443 0.266

0.084 0.242 0.082 1683.547 2.644

0.128 0.067 0.081 756.149 4.483

0.091 0.609 0.144 1028.233 1.027

managers would lobby firms to take the institution’s overall cross-holdings into account. 4. Cross-holdings in acquisitions This section describes institutional shareholders’ stakes in bidders and targets and examines whether crossholdings significantly affect bidder shareholders’ returns. We specifically assess whether cross-holdings can explain why bidder institutions allow deals that reduce bidder value. 4.1. Sample overview Table 1 presents descriptive statistics on the announced merger deals in our sample. Panel A establishes that our acquisition sample is similar to those used in other studies of mergers between public firms. In Panel B, we show that the average three-day abnormal announcement period return (CAR3) for the bidder is 1.3%, and the average CAR3 for the target is 19%. This uneven distribution of takeover gains is typical and the reason for the potential importance of bidder shareholders’ crossholdings in targets. Based on the abnormal announcement returns, the average percentage synergy gain is 1.9%,

corresponding to an average dollar value synergy gain of $47 million.6 This implies that, once we account for the large positive announcement return to the target, mergers in our sample are on average welfare-improving. For mergers with positive synergies, the median bidder share of the synergies is 27%, which means that 73% accrue to target shareholders. Table 2 summarizes the institutional shareholdings in bidders and targets. On average, institutional investors own 48% of the equity of bidders and 35% of the equity of targets. However, in about one-seventh of the sample bids, institutional investors own less than 20% of the bidder’s equity, calling into question their potential to influence bidder management. Focusing on cross-holding institutional shareholders, we find that bidder institutions that also own shares in the target control 16% of all bidder shares, or 33% of the bidder shares owned by institutions. Target institutions that also own shares in the bidder hold 20% of the target’s equity, or more than half of the generally smaller institutional holdings in the target.

6 Following Bradley, Desai, and Kim (1988), we compute the dollar value of the synergistic gains as bidder CAR3 bidder market capitalization+ target CAR3 (1–toehold) target market capitalization and the percentage synergy gains as synergy in dollars/(bidder market capitalization + (1–toehold) target market capitalization).


31

Table 2 Institutional ownership in bidders and targets. The sample consists of 3,540 acquisition attempts announced during the period January 1, 1984 to December 31, 2006. The bidders and targets are listed in the Securities Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. All dollar amounts are in 2006 millions of dollars, and all percentages are in real numbers. In Panel A, Total Institutional Ownership is the fraction of a bidder’s stock that is owned by institutional investors. Ownership by Bidder Institutions That Also Own Shares in Target is the fraction of a bidder’s stock that is owned by institutions that also have a stake in the target. Fraction of Bidder Institutional Ownership Owned by Institutions with Shares in Target gives the percentage of the bidder’s institutional ownership that is held by institutions that also own shares in the target. In Panel B, Total Institutional Ownership is the fraction of a target’s stock that is owned by institutional investors. Ownership by Target Institutions That Also Own Shares in Bidder is the fraction of a target’s stock that is owned by institutions that also have a stake in the bidder. Fraction of Target Institutional Ownership Owned by Institutions with Shares in Bidder gives the percentage of the target’s institutional ownership that is held by institutions that also own shares in the bidder. Number of observations

Mean Median

Standard Deviation

5th percentile

95th percentile

Panel A: Institutional ownership in bidders Total Institutional Ownership Ownership by Bidder Institutions That Also Own Shares in Target Fraction of Bidder Institutional Ownership Owned by Institutions with Shares in Target

3,540 3,540 3,540

0.484 0.162 0.330

0.501 0.109 0.275

0.240 0.156 0.247

0.069 0.003 0.016

0.869 0.480 0.808

Panel B: Institutional ownership in targets Total Institutional Ownership Ownership by Target Institutions That Also Own Shares in Bidder Fraction of Target Institutional Ownership Owned by Institutions with Shares in Bidder

3,540 3,540 3,540

0.353 0.198 0.538

0.310 0.138 0.553

0.251 0.187 0.276

0.020 0.003 0.058

0.812 0.583 0.970

Again, these descriptive statistics suggest that our sample is similar to the one used by Matvos and Ostrovsky (2008) and many others.

4.2. The effect of cross-holdings on the institutions with the largest bidder stakes Table 3 reports the ownership stakes and crossholdings of the ten largest institutional shareholders of each bidder. The results are unequivocal: In most acquisitions, the largest institutional investors in the bidder do not have significant cross-holdings in the target. On average, the bidder’s largest institutional shareholder owns 7% of the bidder, owns 1% of the target, and puts less than 10% weight on target value (and thus more than 90% weight on bidder value). The weights assigned to target value increase slightly when looking at the second to tenth largest investors, but they never exceed 15%. The median weights on target value are uniformly zero for each of the ten largest institutional investors, which means that most large bidder institutions have no stakes in the target at all. Extending the analysis to the 50 largest bidder institutions yields similar results (untabulated). This evidence is hard to reconcile with the idea that cross-holdings explain the lack of shareholder resistance against bad acquisitions. Because large shareholders lose the most when a bidder overpays for an acquisition, cross-holdings cannot meaningfully reduce shareholder opposition to overpayment unless held by large investors. At the bottom of Table 3, we follow Matvos and Ostrovsky (2008) and aggregate bidder shareholders by separately adding up their bidder and their target stakes.

This approach implicitly assumes that bidder institutions negotiate side payments with one another and align their preferences. The table reports results for different coalitions of investors, with the bottom row showing a coalition of all bidder institutions, which is the aggregate analyzed by Matvos and Ostrovsky. This aggregate of all institutional shareholders puts an average (median) weight of 26% (25%) on target value. The fact that all institutions combined put substantial weight on the target, while most large bidder institutions put no weight on it, suggests that the group’s cross-holdings are predominantly from small bidder shareholders with very large target stakes. The aggregation creates a spurious link between the large target stakes of these shareholders and the large bidder stakes of others. In reality, only a small percentage of bidder shares is controlled by investors with large cross-holdings, and in light of the legal difficulties associated with side-payments between shareholders, their influence is likely to be limited. Next, we examine whether cross-holdings help improve the returns from acquisitions for the bidders’ largest institutional shareholders. The abnormal announcement returns in Table 1 suggest that most takeover gains accrue to target shareholders, with the return to bidder shareholders close to zero or even slightly negative. Hence, a large stake in the target could significantly improve the wealth effect experienced by a bidder shareholder from an acquisition, altering the shareholder’s stance toward the deal. To specifically assess whether cross-holdings can reverse the negative wealth effect of bad acquisitions, we restrict the sample to the 2,096 bids with negative abnormal bidder announcement returns. Table 4 reports the dollar losses on bidder stakes and dollar gains on cross-holdings for the ten largest bidder

32


Table 3 Cross-holdings of targets by the largest bidder institutional shareholders. The base sample consists of 3,540 acquisition attempts announced during the period January 1, 1984 to December 31, 2006. The bidders and targets are listed in the Securities Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. For each of the ten largest institutional shareholders of the bidder, we calculate the weight she puts on the takeover target in her objective function as the ratio of her percentage ownership in the target divided by the sum of her percentage ownerships in the bidder and the target. We report the ten largest bidder institutional shareholders’ mean and median ownership stakes, cross-holdings, and weights assigned to target value. We also report the percentage of acquisitions in which one of the ten largest bidder institutions owns a higher percentage stake in the target than in the bidder. Finally, we report the same set of statistics for various coalitions of bidder institutions. Number of Mean stake Mean stake Mean weight Median stake Median stake Median weight Percent with larger stake observations in the bidder in the target on target value in the bidder in the target on target value in target than in bidder Shareholder rank in the bidder: 1 3,540 2 3,528 3 3,512 4 3,488 5 3,466 6 3,445 7 3,425 8 3,398 9 3,380 10 3,354 Coalition of investors 1–10 Coalition of investors 11–20 Coalition of investors 21–30 Coalition of investors 31–40 Coalition of investors 41–50 Coalition of all institutional investor

3,540

7.28% 4.40% 3.28% 2.63% 2.21% 1.92% 1.70% 1.51% 1.37% 1.24% 27.1%

1.00% 0.86% 0.72% 0.71% 0.61% 0.58% 0.55% 0.51% 0.46% 0.42%

9.6% 11.5% 12.3% 13.6% 14.1% 14.2% 14.6% 14.0% 14.1% 14.3%

6.28%

18.1%

6.23% 3.96% 2.99% 2.45% 2.10% 1.84% 1.64% 1.50% 1.36% 1.24% 25.8%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

6% 9% 9% 10% 11% 12% 12% 11% 12% 12%

3.90%

14.4%

4%

3,327

8.23%

3.22%

24.7%

8.31%

1.84%

21.5%

13%

3,102

4.68%

2.16%

25.3%

4.68%

0.99%

20.6%

16%

2,908

3.06%

1.62%

26.4%

3.14%

0.69%

21.9%

19%

2,756

2.15%

1.38%

28.0%

2.16%

0.52%

23.3%

22%

25.4%

8%

3,540

48.4%

19.8%

26.2%

institutional shareholders. The results are again clear. In the vast majority of bad deals, the most influential bidder shareholders do not benefit. On average, the largest (tenth largest) bidder institution loses $27 million ($6 million) on the bidder side but gains only $6 million ($2 million) on the target side. In about two-thirds of the deals, each of the ten largest bidder institutions gains nothing at all from cross-holdings. Similar results obtain when we extend the analysis to the 50 largest bidder institutions and to various investor coalitions, including a coalition of all bidder institutions. Hence, at least for the bidders’ largest institutional investors, the notion that bidder shareholders do not lose from bidder-value reducing acquisitions because of their cross-holdings is clearly rejected by the data.7

7 Matvos and Ostrovsky reach the opposite conclusion by adding up all target shares owned by bidder institutions and treating these crossheld shares as owned by a single investor. We follow their approach at the bottom of Table 4 and find that bidder institutions’ combined gains on target shares ($95 million) on average offset more than a third of their combined losses on bidder shares ( $268 million). Even with this approach, though, the median offset is small ($3 million target gain versus $27 million bidder loss), and in only 18% of the bids do bidder

50.1%

13.8%

4.3. The overall effect of cross-holdings on bidder institutions Next, we extend the analysis beyond large institutions to all institutional shareholders of the bidder. Panel A of Table 5 describes the distribution of bidder institutions’ cross-holdings in targets. On average, only 16% of the bidder’s shares are held by institutional investors with any cross-holdings in the target, with a median of 11%. Continuing down the mean column, only 9% of the bidder’s shares belong to institutions that put more than 30% weight on target value, and only 4% to institutions that favor a wealth transfer to the target (put more than 50% weight on target value). Thus, confirming the results from Table 3, the vast majority of investors in a typical bidder want management to maximize own-firm value, with little regard for the value of the target. Notably, the table reveals that there are some deals in which a substantial fraction of bidder shareholders puts

(footnote continued) institutions as a group recover all their losses on bidder shares through gains on target shares.


33

Table 4 Wealth improvements from cross-holdings for the largest bidder institutional shareholders in bad deals. The sample consists of 2,096 acquisition attempts with negative abnormal bidder announcement returns during the period January 1, 1984 to December 31, 2006. The bidders and targets are listed in the Securities Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. The abnormal announcement period returns are over days ( 1, +1), where day 0 is the date of the initial bid announcement by the acquiring firm. Daily abnormal stock returns are computed using the market model and the value-weighted CRSP index. The estimation window is days ( 200, 60) prior to the acquisition announcement date. We report dollar gains and losses from bid announcements for the ten largest bidder institutional shareholders. We also report the percentage of deals in which one of the ten largest bidder institutions makes up none, more than 50%, or more than 100% of her loss in the bidder through gains in the target. Finally, we report the same set of statistics for various coalitions of bidder institutions. Deals in which gain on cross-holding compensates for given percentage of loss on bidder stake Number of observations

Shareholder rank in the bidder 1 2,096 2 2,091 3 2,080 4 2,071 5 2,055 6 2,045 7 2,038 8 2,023 9 2,015 10 2,002 Coalition of investors 1–10 Coalition of investors 11–20 Coalition of investors 21–30 Coalition of investors 31–40 Coalition of investors 41–50

2,096

Coalition of all institutional investors

2,096

Mean loss on bidder stake (millions)

$27.34 $18.33 $14.61 $11.73 $10.05 $9.03 $8.14 $7.32 $6.77 $6.21 $117.8

Mean gain on target stake (millions)

Median loss on bidder stake (millions)

Median gain on target stake (millions)

None

Greater than 50%

Greater than 100%

$5.62 $4.35 $5.48 $2.82 $2.97 $2.09 $2.16 $1.96 $2.26 $2.13

$3.62 $2.26 $1.75 $1.43 $1.26 $1.10 $1.02 $0.93 $0.85 $0.80

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

68% 69% 68% 67% 66% 68% 67% 67% 69% 67%

9% 12% 12% 14% 14% 14% 16% 16% 14% 16%

7% 8% 8% 10% 10% 10% 12% 11% 10% 11%

$31.32

$15.07

$0.74

23%

20%

13%

1,991

$43.46

$13.94

$5.32

$0.33

25%

27%

17%

1,870

$26.63

$8.54

$3.34

$0.24

29%

27%

19%

1,762

$19.04

$6.93

$2.38

$0.16

31%

28%

19%

1,678

$14.51

$5.76

$1.73

$0.11

34%

30%

20%

$2.54

17%

29%

18%

$268

$95

large weight on target value, even though these deals represent the exception, not the rule. The 95th percentile column shows that, in 5% of all deals, one-third of the bidder’s shares is held by institutional investors that put at least 20% weight on target value, and one-quarter by institutions that put more than 40% weight on the target. It is worth noting that, even in the extreme, it is rare to see bidder shareholders preferring a wealth-transfer to the target. The 95th percentile of the ‘‘Greater than 50%’’ row shows that, in the most extreme 5% of all deals, still only 15% of the bidder’s ownership put more weight on target than bidder value. Panel B of Table 5 extends the analysis of investors’ returns to all bidder institutions. Focusing again on the 2,096 bids with negative bidder announcement returns, we find that the wealth effects remain negative for the vast majority of the bidders’ ownership even after crossholdings are taken into account. On average, only 14% of the bidder’s shares belong to institutional investors with any gains from cross-holdings, consistent with the Table 4

$26.6

results for the largest institutional shareholders. Only 6% of the bidder’s equity is held by institutions that see more than half of their losses on bidder shares offset by target gains. Overall, the results here and in subsection 4.2 unequivocally show that cross-holdings cannot explain why bidder institutions allow acquisitions with negative bidder returns. Even accounting for cross-holdings, we find that the vast majority of the bidders’ institutional shares are held by investors that continue to lose money from bids that lower bidder value.

4.4. The effect of unusually large cross-holdings on bidder behavior While the observed cross-holdings are clearly too small to have any effect in most acquisitions, Table 5 shows a subset of deals in which shareholders with large cross-holdings control enough of the bidder’s equity to be

34


Table 5 Cross-holdings of targets by bidder institutional shareholders. The base sample consists of 3,540 acquisition attempts announced during the period January 1, 1984 to December 31, 2006. The bidders and targets are listed in the Securities Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. For each institutional shareholder of the bidder, we calculate the weight she puts on the takeover target in her objective function as the ratio of her percentage ownership in the target divided by the sum of her percentage ownerships in the bidder and the target. We report the fraction of the bidder’s shares that is held by institutional investors who want to put greater than 0%, 10%, 20%, 30%, 40%, and 50% weight on target value. The sample is further limited to the 2,096 bids with negative abnormal bidder announcement returns. The abnormal announcement period returns are over days ( 1, + 1), where day 0 is the date of the initial bid announcement by the acquiring firm. Daily abnormal stock returns are computed using the market model and the value-weighted CRSP index. The estimation window is days ( 200, 60) prior to the acquisition announcement. A bidder shareholders’ relative return improvement is defined as the abnormal dollar gain on her target stake divided by the absolute value of the abnormal dollar loss on her bidder stake. The relative return improvement thus measures the percentage of the dollar loss on the bidder stake that is compensated for by the shareholder’s gain on her target stake. Panel A: Cross-holdings in targets by bidder institutional shareholders Weight on target value

None Greater Greater Greater Greater Greater Greater

than than than than than than

0% 10% 20% 30% 40% 50%


3,540 3,540 3,540 3,540 3,540 3,540 3,540

Percent of bidder shares held by institutions that put the given weight on the value of the target Mean

Median

75th percentile

90th percentile

95th percentile

32% 16% 13% 11% 9% 7% 4%

31% 11% 8% 7% 6% 4% 3%

46% 24% 19% 16% 13% 10% 6%

59% 40% 31% 27% 23% 18% 11%

67% 48% 39% 34% 29% 24% 15%

Panel B: Return improvements from cross-holdings for bidder institutional shareholders in bad deals Percentage of loss on bidder stake compensated by gain on cross-holding


Percent of bidder shares held by institutions that receive the given relative return improvement Mean Median

None Greater Greater Greater Greater Greater Greater


0% 10% 20% 50% 75% 100%

influential. In this subsection, we search for evidence that bidder management changes its behavior in such cases. If managers believe that cross-holdings weaken shareholder resistance to aggressive bids, then acquisitions with high cross-holdings should on average be worse deals for bidder shareholders (disregarding any gains on crossholdings). To test this hypothesis, Table 6 examines whether unusually large cross-holdings are associated with lower bidder announcement returns or a smaller share of the synergies going to the bidder. We use dummy variables to identify the small subset of deals in which a large percentage of bidder shares is held by institutions with significant cross-holdings. We do this by ranking the deals by the fraction of the bidder’s shares held by institutions that put more than 10%, 30%, or 50% weight on target value and identifying, for each weight, the most extreme decile of deals. The dependent variable is the bidder announcement return in the first three columns and the bidder share of synergies in the last three.

2,096 2,096 2,096 2,096 2,096 2,096 2,096

34% 14% 10% 8% 6% 5% 4%

33% 9% 5% 4% 2% 1% 1%

75th percentile

90th percentile

95th percentile

48% 22% 15% 12% 8% 6% 5%

63% 39% 28% 25% 18% 16% 13%

72% 47% 38% 34% 26% 23% 20%

Table 6 shows that the estimated coefficients on the high cross-holdings dummies are all insignificant. A wide variety of alternative specifications and robustness checks yield similar results (untabulated). We conclude that cross-holdings have no observable effect on either bidder returns or the bidder share of synergies. There is thus no evidence that acquisitions with high cross-holdings are worse deals for bidder shareholders, which suggests that bidder management does not change its bidding strategy when its shareholders’ cross-holdings are large.8 Next, we examine whether bidder managers consider their shareholders’ cross-holdings when selecting acquisition targets. We pair each bidder with both its actual target and a control target, chosen by matching on total institutional ownership from similarly sized firms in the

8 In untabulated tests, we also find that cross-holdings have no effect on target announcement returns or on the likelihood of deal completion.


35

Table 6 The effect of cross-holdings on abnormal bidder announcement returns and bidder shares of synergies. The sample consists of 3,540 acquisition attempts announced during the period January 1, 1984 to December 31, 2006. The bidders and targets are listed in the Security Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. Because of missing control variables, only 3,271 bids are used in the regressions. For each institutional shareholder of the bidder, we calculate the weight she puts on the takeover target in her objective function as the ratio of her percentage ownership in the target divided by the sum of her percentage ownerships in the bidder and the target. Columns 1 to 3 regress abnormal bidder announcement returns on dummy variables identifying the 10% of deals with the highest fraction of the bidder’s shares held by institutional investors putting more than 10%, 30%, or 50% weight on target value, respectively. The bidder announcement return (Bidder CAR3) is over days ( 1, 1), where day 0 is the date of the initial bid announcement. Daily abnormal stock returns are computed using the market model and the value-weighted CRSP index. The estimation window is days ( 200, 60) prior to the announcement date. Columns 4 to 6 regress the bidder share of synergies on dummy variables identifying the 10% of deals with the highest fraction of the bidder’s shares held by institutional investors putting more than 10%, 30%, or 50% weight on target value, respectively. For bids with positive synergies, the Bidder Share of Synergies is the abnormal increase in bidder value over days ( 1, +1) divided by the dollar value synergy gain. For bids with negative synergies, the Bidder Share of Synergies is one minus the abnormal increase in bidder value over days ( 1, +1) divided by the dollar value synergy gain. Synergy (dollars) is the sum of the abnormal increases in bidder and target value over the same window, adjusted for any target shares held by the bidder before the bid announcement. All Cash, All Stock, Competing, and Diversifying are dummy variables that take the value of one for completed acquisitions, if only cash is used to pay for the acquisition, if only equity is used, if there are multiple bids for the same target within one year, and if the bidder and target are from two different industries, respectively, and zero otherwise. Relative Size is the transaction value divided by the market value of bidder assets at the end of the fiscal year prior to the bid announcement. Bidder (Target) Total Institutional Ownership is the fraction of the bidder’s (target’s) shares held by institutional investors. All accounting values are obtained at the fiscal year-end prior to the announcement of the bid. All regressions include year and industry fixed effects. nnn, nn, and n correspond to statistical significance at the 1%, 5%, and 10% level respectively. Robust p-values are reported in brackets. Bidder CAR3 Bidder CAR3 (1) (2)

Dummy: fraction of bidder shares held by institutions that put at least 10% weight on target value is in the highest decile across deals Dummy: fraction of bidder shares held by institutions that put at least 30% weight on target value is in the highest decile across deals Dummy: fraction of bidder shares held by institutions that put at least 50% weight on target value is in the highest decile across deals

Bidder CAR3 (3)

0.007 [0.261]

All Stock Competing Diversifying Bidder Total Institutional Ownership Target Total Institutional Ownership Bidder Market Capitalization Target Market Capitalization Bidder Market Leverage Target Market Leverage Bidder Market-to-Book Ratio Target Market-to-Book Ratio Bidder Return on Assets Target Return on Assets Bidder Prior Year Stock Return Target Prior Year Stock Return Intercept Relative Size Decile Dummies

Bidder share of synergies (5)

0.002 [0.739]

0.214 [0.445] 0.004 [0.475]

0.012 [0.001]nn 0.009 [0.028]n 0.001 [0.887] 0.002 [0.715] 0.017 [0.040]n 0.002 [0.823] 0.001 [0.721] 0.005 [0.074] 0.003 [0.837] 0.001 [0.937] 0.002 [0.121] 0.001 [0.525] 0.001 [0.939] 0.003 [0.818] 0.004 [0.175] 0.001 [0.495] 0.04 [0.026]n Yes


0.119 [0.664]

Synergy (dollars) All Cash


0.012 [0.001]nn 0.009 [0.028]n 0.001 [0.899] 0.001 [0.733] 0.016 [0.054] 0.003 [0.732] 0.001 [0.730] 0.005 [0.087] 0.003 [0.828] 0.001 [0.927] 0.002 [0.124] 0.001 [0.514] 0.001 [0.944] 0.003 [0.814] 0.004 [0.178] 0.001 [0.493] 0.038 [0.034]n Yes

0.012 [0.001]nn 0.009 [0.027]n 0.001 [0.905] 0.001 [0.748] 0.016 [0.054] 0.002 [0.804] 0.001 [0.733] 0.005 [0.083] 0.003 [0.822] 0.001 [0.923] 0.002 [0.123] 0.001 [0.507] 0.001 [0.940] 0.003 [0.808] 0.004 [0.179] 0.001 [0.495] 0.039 [0.030]n Yes

0.017 [0.953] 6.229 [0.000]nn 0.448 [0.006]nn 0.032 [0.860] 0.026 [0.894] 0.036 [0.800] 0.27 [0.515] 0.356 [0.357] 0.113 [0.141] 0.078 [0.323] 0.520 [0.356] 0.723 [0.085] 0.041 [0.113] 0.055 [0.097] 0.373 [0.146] 0.335 [0.229] 0.114 [0.111] 0.108 [0.116] 0.557 [0.416] Yes

6.236 [0.000]nn 0.448 [0.006]nn 0.032 [0.859] 0.026 [0.895] 0.035 [0.803] 0.274 [0.503] 0.382 [0.317] 0.114 [0.137] 0.075 [0.342] 0.514 [0.361] 0.719 [0.087] 0.041 [0.115] 0.054 [0.102] 0.373 [0.146] 0.332 [0.232] 0.114 [0.112] 0.109 [0.112] 0.597 [0.388] Yes

6.235 [0.000]nn 0.444 [0.007]nn 0.031 [0.865] 0.027 [0.889] 0.034 [0.812] 0.295 [0.467] 0.323 [0.401] 0.113 [0.140] 0.084 [0.281] 0.524 [0.351] 0.721 [0.086] 0.042 [0.109] 0.055 [0.099] 0.370 [0.150] 0.336 [0.226] 0.113 [0.114] 0.108 [0.117] 0.507 [0.454] Yes

36


same industry.9 We then estimate a conditional logit model predicting which of the two potential targets will be chosen by the bidder. The explanatory variables include a large set of target characteristics that have been shown to predict target selection in the prior literature.10 To test whether cross-holdings influence target selection, we include cross-holdings by bidder institutions in the actual target and in the control target as explanatory variables. The results in Table 7 show that higher crossholdings do, in fact, predict which of the two firms is chosen as the target. This result has two interpretations. First, it could be that, on the margin, bidder managers do consider their shareholders’ cross-holdings when selecting merger targets. Second, it could be that some unmodeled firm characteristics make the bidder and the target suitable merger partners and simultaneously lead institutional investors to hold both firms. Given the weight of the rest of the evidence, particularly the evidence that crossholdings appear to have no effect on bid characteristics or reception, the latter interpretation is more likely the correct one. 5. Institutional cross-holdings between S&P 500 firms An important reason for the scarcity of significant institutional cross-holdings in acquisitions is the small size of most targets. Small firms attract less institutional ownership, making it less likely that the same institution will hold a stake in both a bidder and its target. However, it is still possible that significant shareholder crossholdings exist between large firms and that these crossholdings have important effects on investor and manager incentives.11 To test this possibility, we examine institutional cross-holdings between S&P 500 firms. Because of high institutional ownership and especially the presence of index funds, S&P 500 firms are likely to have the highest institutional cross-holdings of any large group of U.S. firms and can, therefore, serve as a useful upper bound on the importance of cross-holdings. Tables 8 and 9 present the magnitude and the evolution of institutional cross-holdings between S&P 500 firms from 1985 to 2005. Using the index in 1985, 1995, and 2005, we form all possible pairs of firms that are in the S&P 500 in the same year. For each firm, we then calculate its institutional shareholders’ cross-holdings in every other index firm. For clarity, we call the firm from whose perspective cross-holdings are computed the base firm, and the firm in which the cross-ownership stakes are held the cross-held firm. Thus, when describing 9 We require the control firm’s institutional ownership and market capitalization to be within 25% of the sample firm’s and exclude control firms involved in mergers in the same quarter, producing 2,815 matches. 10 See, for example, Palepu (1986). We also control for total institutional ownership and for differences in target and bidder characteristics that could affect both cross-holdings and merger likelihood. 11 Matvos and Ostrovsky (2008) emphasize that cross-holdings are higher in acquisitions with large targets. We find the same pattern using our approach to measure cross-holdings. Almost all the acquisitions with large cross-holdings presented in Table 5 involve large targets.

the cross-holdings of firm A’s institutional shareholders in firm B, we label A the base firm and B the cross-held firm. Because B’s cross-holdings in A will not mirror A’s crossholdings in B, each pair of firms appears twice. Table 8 shows that the holdings and cross-holdings of the five largest institutional shareholders of S&P 500 firms have increased rapidly and have reached remarkably high levels. In 1985, the five largest shareholders of an S&P 500 firm together hold, on average, 17% of that firm and have combined cross-holdings of only 2% in a randomly selected second index firm. By 2005, the five largest shareholders of an S&P 500 firm own, on average, 26% of that firm and 10% of a randomly selected second index firm. So, both institutional holdings and cross-holdings have increased, with the proportional rise in crossholdings outpacing the increase in holdings and ownership concentration. By 2005, it is also common for some of the largest shareholders in the base firm to assign more than 50% weight to the cross-held firm. In 8% (28%) of the firm pairs, the base firm’s largest (fifth largest) institutional shareholder owns an even larger stake in the crossheld firm. For the same firm pairs, Table 9 presents summary statistics for the cross-holdings of all institutional investors as well as for the number of institutional investors per firm. The message is the same as in Table 8: Institutional cross-holdings have become large. In 1985, 25% of the shares in an average S&P 500 firm are held by institutions that put positive weight on externalities imposed on a randomly selected second index firm. By 2005, that fraction has increased to 54%. Looking further at 2005, almost one-quarter of the shares belongs to institutions that put more than 40% weight on the other firm’s value and fully 15% belong to institutions that put more than 50% weight on the other firm. Investors with a higher percentage stake in the cross-held than in the base firm benefit when value is transferred from the base to the cross-held firm. Thus, in a hypothetical conflict between two S&P 500 firms in 2005, 15% of the equity in either firm would on average be held by institutional investors that prefer the other side to win. While surprising in its magnitude, the rise in crossholdings is consistent with the increasing role of institutional investors in stock markets shown by Gompers and Metrick (2001) and with the rise of index and quasi-index investing as an investment style (see, for example, Cremers and Petajisto (2009). To assess the importance of indexing in creating cross-holdings, we use the Cremers and Petajisto Active Share measure to identify index funds. Briefly, the Active Share measures the proportion of an institution’s portfolio that deviates from its benchmark index [see p. 3335 of Cremers and Petajisto (2009) for the details]. We define an ‘‘indexer’’ as an institution with an Active Share of less than 30%. In untabulated results, we find that excluding indexers from the analysis results in much smaller cross-holdings between S&P 500 firms. For example, in an average S&P 500 firm in 2005, only 28% of the shares are held by nonindexing institutional shareholders that have any cross-holdings in a randomly selected second index firm (compared with 54% when all institutional investors are


37

Table 7 The effect of cross-holdings on target selection. The sample consists of 2,815 acquisition attempts announced during the period January 1, 1984 to December 31, 2006 and 2,815 actual bidder–control target pairs. The bidders and targets are listed in the Securities Data Company’s Mergers and Acquisitions database and have institutional holding data in the CDA/Spectrum database. We keep an acquisition if the bidder owns less than 50% of the target prior to the bid and is seeking to own greater than 50% of the target. For completed deals, we require that the bidder owns greater than 90% of the target after the deal completion. Because of missing control variables, only 2,768 bids are used in the regressions. For each institutional shareholder of the bidder, we calculate the weight she puts on the (actual or control) takeover target in her objective function as the ratio of her percentage ownership in the target divided by the sum of her percentage ownerships in the bidder and the target. We then determine the fraction of the bidder’s shares that is held by institutional investors who want to put at least 10%, 20%, 30%, 40%, or 50% weight on target value. Columns 1–5 present results from conditional logit regression using these fractions as the key explanatory variable. The dependent variable takes the value of one for an actual target and zero for a control target. All absolute differences in firm characteristics are between the actual bidder and the actual or control target. nnn, nn, and n correspond to statistical significance at the 1%, 5%, and 10% level respectively. Robust p-values are reported in brackets. (1) Fraction of bidder shares held by institutions that put at least 10% weight on target value Fraction of bidder shares held by institutions that put at least 20% weight on target value Fraction of bidder shares held by institutions that put at least 30% weight on target value Fraction of bidder shares held by institutions that put at least 40% weight on target value Fraction of bidder shares held by institutions that put at least 50% weight on target value Target Total Institutional Ownership Target Market Capitalization Target Market Leverage Target Market-to-Book Ratio Target Earnings-to-Price Ratio Target Asset Liquidity Target Return on Assets Target Prior Year Stock Return Absolute Difference in Total Institutional Ownership Absolute Difference in Market Capitalization Absolute Difference in Market-to-Book Ratio Absolute Difference in Return on Assets Absolute Difference in Prior Stock Return Bidder Fixed Effects Number of observations Pseudo R2

(2)

(3)

(4)

(5)

8.380nnn [0.000] 8.190nnn [0.000] 8.230nnn [0.000] 7.654nnn [0.000]

4.340nnn [0.000] 2.148nnn [0.000] 0.191 [0.399] 0.023 [0.618] 0.163n [0.066] 0.367n [0.057] 0.894nnn [0.001] 0.312nnn [0.000] 1.528 [0.235] 1.529nnn [0.003] 0.357nnn [0.000] 1.417nnn [0.000] 0.200nn [0.013] Yes 5,536 0.137

included). Only 5% of the shares are held by nonindexers that put more than 50% weight on such externalities, again much less than the 15% when all institutions are included (see Table 9). We conclude that, by 2005, most institutional investors in S&P 500 firms do not want corporate managers to narrowly maximize the value of their own firm. Instead, investors would see their portfolio values maximized if managers internalized a large percentage of any externalities imposed on other index firms. However, this change in investor objectives is to a substantial extent driven by the rise of index investors. Because index and quasi-index funds tend to be passive, this lessens the

4.298nnn [0.000] 2.121nnn [0.000] 0.236 [0.296] 0.019 [0.676] 0.172n [0.061] 0.431nn [0.025] 0.894nnn [0.001] 0.323nnn [0.000] 1.729 [0.176] 1.620nnn [0.002] 0.355nnn [0.000] 1.415nnn [0.000] 0.213nnn [0.007] Yes 5,536 0.132

3.934nnn [0.001] 2.118nnn [0.000] 0.215 [0.344] 0.019 [0.677] 0.176n [0.057] 0.412nn [0.032] 0.923nnn [0.001] 0.321nnn [0.000] 1.497 [0.242] 1.623nnn [0.002] 0.363nnn [0.000] 1.438nnn [0.000] 0.208nnn [0.009] Yes 5,536 0.129

3.942nnn [0.001] 2.272nnn [0.000] 0.185 [0.415] 0.017 [0.706] 0.196nn [0.032] 0.406nn [0.034] 0.925nnn [0.001] 0.319nnn [0.000] 1.482 [0.240] 1.510nnn [0.004] 0.367nnn [0.000] 1.457nnn [0.000] 0.223nnn [0.004] Yes 5,536 0.121

7.018nnn [0.000] 3.858nnn [0.001] 2.278nnn [0.000] 0.15 [0.507] 0.019 [0.688] 0.191nn [0.033] 0.382nn [0.044] 1.008nnn [0.000] 0.315nnn [0.000] 1.347 [0.281] 1.577nnn [0.002] 0.373nnn [0.000] 1.513nnn [0.000] 0.230nnn [0.003] Yes 5,536 0.113

chance that the increase in cross-holdings will change firm behavior. Further, the fact that the rise in cross-holdings is largely due to indexing suggests that cross-holdings will be smaller in firm pairs outside the most popular indexes, a fact confirmed in the acquisition sample. 6. Summary and conclusion Diversified shareholders prefer corporate policies that maximize their portfolio values to policies that narrowly maximize the values of individual firms. This observation, along with the rising holdings of institutional investors, creates the possibility that influential shareholders with

38


Table 8 Cross-holdings between S&P 500 firms by the largest institutional shareholders. This table reports the ownership stakes and cross-holdings of the five largest institutional investors in S&P 500 firms in 1985, 1995, and 2005. We use all constituent firms of the index with available data from CRSP/Compustat and institutional holding data from the CDA/Spectrum database. The final sample consists of 447, 446, and 459 firms in 1985, 1995, and 2005, respectively. We next form all possible pairs of firms that are in the index in the same year. Specifically, if there are n firms with available data in the S&P 500 in one of the three sample years, then we form nn(n 1) unique pairs for that year. We denote one firm out of each pair the base firm and the other firm the cross-held firm. For each of the five largest institutional shareholders of the base firm, we calculate the weight she puts on the cross-held firm in her objective function as the ratio of her percentage ownership in the cross-held firm divided by the sum of her percentage ownerships in the base firm and the cross-held firm. We report these five largest shareholders’ mean and median ownership stakes, cross-holdings, and the weights assigned to the value of the cross-held firm. We also report the percentage of firm pairs in which one of the five largest base-firm institutions owns a higher percentage stake in the cross-held than in the base firm. Shareholder rank in the base firm 1985 1 2 3 4 5 Coalition of investors 1–5 1995 1 2 3 4 5 Coalition of investors 1–5 2005 1 2 3 4 5 Coalition of investors 1–5

Mean stake Mean stake in in the base the crossfirm held firm

Mean weight on cross-held firm value

Median stake in the base firm

Median stake in the crossheld firm

Median weight on cross-held firm value

Larger stake in Number cross-held than in of firms base firm

Number of firm pairs

6.47% 3.48% 2.68% 2.20% 1.88% 16.71%

0.45% 0.50% 0.48% 0.49% 0.53% 2.44%

7.3% 10.9% 12.7% 15.4% 17.8%

4.92% 3.17% 2.43% 2.01% 1.74% 15.05%

0.00% 0.02% 0.01% 0.03% 0.08% 1.79%

0.0% 0.5% 0.3% 1.4% 3.9%

3% 6% 8% 10% 12%

447 447 447 447 447

199,362 199,362 199,362 199,362 199,362

7.36% 4.49% 3.38% 2.75% 2.37% 20.34%

1.44% 1.14% 1.05% 1.07% 0.99% 5.70%

13.8% 16.6% 18.5% 22.7% 22.6%

6.58% 3.98% 3.01% 2.50% 2.28% 19.48%

0.25% 0.16% 0.17% 0.44% 0.32% 4.64%

3.4% 3.4% 4.5% 13.8% 12.1%

8% 12% 15% 18% 19%

446 446 446 446 446

198,470 198,470 198,470 198,470 198,470

8.98% 5.86% 4.53% 3.71% 3.19% 26.27%

2.16% 1.98% 1.97% 2.19% 2.07% 10.38%

17.3% 21.1% 24.8% 30.6% 31.9%

8.30% 5.38% 4.06% 3.45% 3.08% 25.27%

0.81% 0.76% 1.03% 2.23% 2.16% 9.60%

9.0% 12.0% 18.4% 38.5% 40.5%

8% 13% 19% 27% 28%

459 459 459 459 459

210,222 210,222 210,222 210,222 210,222

cross-holdings will support policies that lower firm value, if these policies create positive externalities on other firms. Matvos and Ostrovsky (2008) propose this idea as an explanation for why large shareholders do not oppose bidder-value destroying mergers. We show how to correctly measure shareholder preferences when shareholders hold shares in other firms as well, and we show the prevalence and size of institutional cross-holdings in samples of mergers and acquisitions and of S&P 500 firms. In acquisitions, we find that most institutional shareholders of the bidder have no investment in the target and that bidder shareholders with large cross-holdings tend to control only a small fraction of the bidder’s equity. Consequently, cross-holdings cannot explain why bidder shareholders allow deals that reduce the value of the bidder. There is also no evidence that acquirers bid more aggressively in the small subset of deals in which bidder shareholders put large weight on target value. We conclude that shareholder cross-holdings have little effect on firm behavior in acquisitions. This makes it unlikely that cross-holdings affect other corporate decisions in which externalities are generally smaller and harder to assess.

Because cross-holdings are naturally smaller when at least one of the two firms is small, as is typical in an acquisition, we also assess their potential for influence in a sample of large firms—the S&P 500. We find that crossholdings between index firms have increased rapidly over time. By 2005, more than half the shares in an average S&P 500 firm are held by institutions that put some weight on externalities imposed on a randomly selected second index firm, almost a third of the shares belong to institutions that put more than 30% weight on the other firm’s value, and fully 15% of the shares belong to institutions that put more than 50% weight on the other firm. These are large deviations from the standard objective of firm value maximization. However, we also find that most of the increase in cross-holdings is due to the rise of index and quasi-index funds. As a result, the cross-holdings of active investors still appear to be too small to influence corporate policy in most index firms. Although our evidence indicates that institutional cross-holdings are a nonissue in the preponderance of corporate mergers, our findings also suggest that they could occasionally become an issue in mergers of prominent firms (e.g., those in the S&P 500), which


39

Table 9 Institutional cross-holdings between S&P 500 firms. In Panel A, we report summary statistics for each year for the number of institutional investors per S&P 500 firm. In Panel B, we summarize institutional shareholder cross-holdings between pairs of S&P 500 firms in 1985, 1995, and 2005. We use all constituent firms of the index with available data from CRSP/Compustat and institutional holding data from the CDA/Spectrum database. The final sample consists of 447, 446, and 459 firms in 1985, 1995, and 2005, respectively. We next form all possible pairs of firms that are in the index in the same year. Specifically, if there are n firms with available data in the S&P 500 in one of the three sample years, then we form nn(n 1) unique pairs for that year. We denote one firm out of each pair the base firm and the other firm the cross-held firm. For each institutional shareholder of the base firm, we calculate the weight she puts on the cross-held firm in her objective function as the ratio of her percentage ownership in the cross-held firm divided by the sum of her percentage ownerships in the base firm and the crossheld firm. We report the fraction of the base firm’s shares that is owned by institutional investors who want to put greater than 0%, 10%, 20%, 30%, 40%, and 50% weight on the value of the corresponding cross-held firm. The final sample consists of 199,362, 198,470, and 210,222 firm pairs in 1985, 1995, and 2005, respectively Panel A

Number of institutions per firm

1985 1995 2005

Mean

Median

Min

Max

173.1 284.3 454.4

148 244.5 373

14 47 155

634 881 1409

Panel B Fraction of the base firm’s shares held by institutions that put the given weight on the value of the cross-held firm weight on cross-held firm value Mean Median 75th percentile 90th percentile 95th percentile 1985 None Greater Greater Greater Greater Greater Greater


0% 10% 20% 30% 40% 50%

23% 25% 17% 14% 12% 9% 6%

22% 23% 16% 13% 11% 9% 5%

32% 32% 21% 17% 14% 12% 7%

41% 41% 27% 22% 18% 15% 10%

46% 46% 31% 26% 21% 17% 11%

1995 None Greater Greater Greater Greater Greater Greater


0% 10% 20% 30% 40% 50%

20% 39% 27% 22% 19% 16% 9%

19% 38% 26% 21% 18% 15% 9%

26% 47% 32% 26% 22% 18% 12%

34% 55% 38% 31% 26% 22% 15%

38% 60% 41% 35% 29% 24% 16%

2005 None Greater Greater Greater Greater Greater Greater


0% 10% 20% 30% 40% 50%

20% 54% 42% 36% 31% 25% 15%

19% 53% 41% 35% 30% 24% 15%

27% 62% 48% 41% 35% 28% 18%

35% 70% 55% 47% 40% 33% 22%

40% 75% 59% 51% 43% 36% 24%

typically have large amounts of institutional ownership and substantial cross-holdings by index funds. Index funds are generally passive investors, but one can envision scenarios in which public pressure from RiskMetrics, the Corporate Library, and other corporate governance specialists motivate fund managers to exert their influence when there is significant doubt that a given merger proposal truly maximizes the joint value of the bidder and target firms. References Bradley, M., Desai, A., Kim, E.H., 1988. Synergistic gains from corporate acquisitions and their division between the stockholders of target and acquiring firms. Journal of Financial Economics 21, 3–40.

Cremers, K.J.M., Petajisto, A., 2009. How active is your mutual fund manager? A new measure that predicts performance. Review of Financial Studies 22, 3329–3365. Easterbrook, F.H., Fischel, D.R., 1982. Corporate control transactions. Yale Law Journal 91, 698–737. Fama, E.F., 1978. The effects of a firm’s investment and financing decisions on the welfare of its security holders. American Economic Review 68, 272–284. Gompers, P.A., Metrick, A., 2001. Institutional investors and equity prices. Quarterly Journal of Economics 116, 229–259. Hansen, R.G., Lott Jr., J.R., 1996. Externalities and corporate objectives in a world with diversified shareholder/consumers. Journal of Financial and Quantitative Analysis 31, 43–68. Matvos, G., Ostrovsky, M., 2008. Cross-ownership, returns, and voting in mergers. Journal of Financial Economics 89, 391–403. Palepu, K., 1986. Predicting takeover targets: a methodological and empirical analysis. Journal of Accounting and Economics 8, 3–35. Rubin, A., 2006. Diversification and corporate decisions. Corporate Ownership and Control 3, 209–212.




Competition among mutual funds$ Sunil Wahal a,n, Albert (Yan) Wang b,1 a b

WP Carey School of Business, Arizona State University, USA Department of Finance, Faculty of Business Administration, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

a r t i c l e i n f o

abstract

Article history: Received 7 November 2008 Received in revised form 26 January 2010 Accepted 22 February 2010 Available online 27 August 2010

We examine the impact of the entry of new mutual funds on incumbents using the overlap in their portfolio holdings as a measure of competitive intensity. This simple metric delivers powerful economic results. Incumbents that have a high overlap with entrants subsequently engage in price competition by reducing management fees. Distribution fees, however, rise so that investors do not benefit as much from price competition. Funds with high overlap also experience quantity competition through lower investor flows, have lower alphas, and higher attrition rates. These effects only appear after the late 1990s, at which point there appears to be an endogenous structural shift in the competitive environment. We conclude that the mutual fund market has evolved into one that displays the hallmark features of a competitive market. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G11 G23 L11 Keywords: Mutual Funds Competitive market Incumbents

1. Introduction The assets of active, domestic equity mutual funds grew at a compounded annual growth rate of 16% per year between 1980 and 2008 (Investment Company Fact Book, 2009).2 Despite this tremendous growth, with the exceptions noted below, there is precious little direct evidence on the competitive forces at work in this industry. The $ Some work on this paper was done while Wahal was at Dimensional Fund Advisors LP, an investment adviser registered with the Securities and Exchange Commission. This paper contains the opinions of the authors but not necessarily Dimensional or its affiliates. We thank Peter Tufano (the referee), Jeff Busse, Amit Goyal, John Griffin, Vik Nanda, Ashley Wang and seminar participants at Arizona State University, Cass Business School, Chinese University of Hong Kong, the CRSP Forum, and the 2009 Western Finance Association meetings for helpful comments and suggestions. Atif Ikram and Marko Svetina provided valuable research assistance. n Corresponding author. Tel.: + 480 965 8755. E-mail addresses: [email protected] (S. Wahal), [email protected] (A. Wang). 1 Tel.: +852 2696 1914. 2 2009 Investment Company Fact Book is available at the following URL: http://www.icifactbook.org/pdf/2009_factbook.pdf.


first exception is Khorana and Servaes (2004), who find that price competition is important but with a caveat: families that charge lower fees gain market share but only if these fees were initially above average. The second exception is a tour de force of the industrial organization of this area by Coates and Hubbard (2007). Coates and Hubbard (2007) make the observation that the number of class action lawsuits against mutual funds has increased dramatically since 2003, and that several prominent industry and regulatory participants assert that mutual fund advisory fees do not reflect the workings of a competitive marketplace.3 They go on to argue that much of the anti-competitive criticism is ill-founded and easily 3 Coates and Hubbard (2007) cite public pronouncements of John Bogle, founder of The Vanguard Group, David Swensen, Chief Investment Officer of Yale University, and former New York Governor Eliot Spitzer as arguing that fees charged by mutual funds do not reflect a competitive environment. They also cite two academics (Freeman and Brown, 2001;Trzcinka, 1998), and the Chief Economist of the Securities and Exchange Commission (Spatt, 2006) as drawing similar conclusions. Wallison and Litan (2007) also argue that competition among mutual funds is inadequate. A rebuttal of Coates and Hubbard’s criticism of Freeman and Brown (2001) can be found in Freeman (2008).

S. Wahal, A.(Yan) Wang / Journal of Financial Economics 99 (2011) 40–59

refuted using simple economic logic.4 Lastly, Gil-Bazo and Ruiz-Verdu (2009) find that between 1961 and 2003, funds with worse before-fee performance charge higher fees, concluding that competition ‘‘has not been able to prevent funds that cater to performance-insensitive investors from setting high fees nor to quickly drive them out of the market.’’ Two key elements of a competitive marketplace are that, (a) new entry take place, and (b) that entry affect the economic circumstances and behavior of incumbents. Evidence on the magnitude and determinants of entry is provided by Khorana and Servaes (1999). Trade journals also report large increases in the number of funds over time, implying widespread entry. Surprisingly, there is no empirical evidence on the second element of competition: the consequences of entry for prices, revenues, costs, performance, and survival. We perform precisely such an analysis, which can be viewed as a litmus test for a competitive marketplace. Establishing a connection between entrants and incumbents requires us to measure the degree to which an entrant competes with incumbents. This is a notoriously difficult problem in industrial organization and falls under the rubric of product heterogeneity and differentiation (see Berry and Reiss, 2007, for a review). There are two aspects to this problem. The first difficulty is in identification of the cohort group with which an entrant competes. Consider, for example, the entry of a second baseball team in a city. Does this entrant compete with the incumbent baseball team, or all the other professional sports teams in the city? Or, should one also consider non-professional teams as incumbents. Perhaps one might consider all other leisure activities as potentially affected by the entrant. Mutual funds are not immune from this identification problem. Suppose, for example, that a new small cap growth fund enters the marketplace. This entrant could compete with other small cap growth funds, other small cap funds, other growth funds, or even all mutual funds. The second aspect of this problem is that even if homogeneous groups can somehow be identified, product differentiation mechanisms can generate heterogeneity, allowing firms to compete on different dimensions and charge different prices. Even in an extremely homogeneous group of Standard & Poor’s 500 index funds, Elton, Gruber, and Busse (2004) show large variation in fees and performance, and attribute it, at least in part, to investor irrationality. For the same group, Hortac- su and

4 Their opinion was influential in a court ruling issued by Judge Frank Easterbrook that rejected claims by a plaintiff that mutual fund advisory fees are excessive. The case was brought against Harris Associates, manager of the Oakmark Funds, alleging that Oakmark charges higher fees to retail mutual fund investors than institutional investors (plan sponsors). The Easterbrook opinion, as it has become known, relied heavily on Coates and Hubbard (2007). A dissent written by Judge Richard Posner argues that the Easterbrook opinion (a) implicitly rejects the Gartenberg precedent in which a fee is deemed excessive if it bears no resemblance to the services rendered and could not have been the product of an arms-length transaction, and (b) ignores evidence such as Kuhnen (2007) which shows that connections between fund directors and managers can hurt investors. The case has now proceeded to the US Supreme Court for deliberations.

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Syverson (2004) show that extra-portfolio product differentiation can account for variation in fees. Li (2005) develops and tests a structural model in which fund managers increase fees by differentiating products over different states of nature. He suggests, rather startlingly, that funds can increase their profits by almost 30% through differentiation. If we regard the mutual fund portfolio as the ‘‘product,’’ then it is appropriate to think of fund fees as ‘‘prices’’ charged for that product and stock holdings as key ‘‘inputs.’’ Therein lies the advantage to working with mutual funds—the unique nature of mutual fund disclosures allows us to bypass the problems described above, at least to some degree. Knowledge of quarterly stock holdings allows us to create parsimonious metrics with which to measure the overlap between each incumbent and entrant pair. Even though we cannot measure the degree to which a marginal investor considers a portfolio delivered by an entrant fund to be substitutable with a portfolio provided by an incumbent, we can measure one way in which the investor could think about substitutability—the degree to which incumbent and entrant holdings overlap. To the extent that we cannot measure other product differentiation mechanisms (e.g., the bundling of cash management services), such a measure is imperfect, but at least unbiased. To implement this idea, we calculate the ratio of the market value of an overlapping security’s holdings in the entrant’s portfolio to the market value of the same security in the incumbent’s portfolio. We then multiply this ratio by the weight of that security in the incumbent’s portfolio to reflect its importance to the incumbent, and use this product to compute two measures of incumbentlevel overlap: MVOi,t (market value of overlap) and TruncMVOi,t (truncated market value of overlap). Intuitively, both measures capture the degree to which entrants and incumbents compete in their inputs (stock holdings) and therefore, the degree to which their products (portfolios) are substitutable. The null hypotheses in a competitive market are almost elemental: entry should cause incumbents that have higher overlap with entrants to reduce prices, experience reduced quantities’ sold, higher costs, and performance declines. In the extreme case, entry may cause or accelerate exit for incumbents with higher overlap. But before proceeding to tests of these hypotheses, we take stock of the nature of entry between 1980 and 2005. We do so because we expect entry to be endogenous to expected profitability. The number of entrants rises over the early part of the sample period and peaks in the late 1990s. By the end of 2005, entry of active mutual funds declines substantially. A formal Chow Test indicates a structural break in the time-series of entry in 1998. Therefore, data permitting, we perform our tests for the entire sample, as well as pre- and post-1998 subperiods. Our first set of tests focus on Bertrand competition and consist of regressions of post-entry changes in expense ratios, and its components, management fees, nonmanagement fees, and distribution costs, on lagged

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measures of the overlap between incumbents and entrants. We find that after 1998, changes in management fees are negatively related to prior measures of overlap. In addition, incumbents with higher overlap are more likely to employ (ostensibly) temporary fee waivers, and those that do, use larger waivers. Waivers are frequently continued in the years following introduction, thereby becoming de facto permanent changes in prices. And, when waivers are discontinued, roughly half the time the discontinuation is because there is a permanent reduction in management fees. This suggests that, at least on the basis of prices over which fund managers have direct control (management fees), price competition is strong. Interestingly, non-management fees are unrelated to overlap measures; summing up management fees and non-management fees, we find no relation between changes in expense ratios and overlap.5 Thus, while price competition appears to be working, we are less sanguine on the issue of whether all the benefits of competition directly accrue to consumers. It is interesting to ask why that might be the case. The largest observable component of non-management fees is distribution cost, comprising loads and 12b-1 fees. We find that changes in loads are negatively related to overlap measures. However, since the advent of 12b-1 legislation, there has been a movement away from the use of loads to the use of 12b-1 fees in defraying fund distribution costs. Our regressions show that changes in 12b-1 fees are positively correlated with overlap. This could be because, as funds lose market share (due to competition), they attempt to attract new investors by increasing distribution activities. Since there are a limited number of distribution channels, the consequence is that 12b-1 fees rise. This is consistent with Walsh (2004) who finds that funds with 12b-1 plans grow faster but do not have lower expense ratios, and with Casavecchia and Scotti (2009) who report intriguing evidence that changes in distribution fees are negatively related to changes in management fees. Ultimately, the benefits of competition to consumers are tempered by such compensating differentials. To investigate the role of supply-side quantity-based competition, we regress flows on lagged measures of the overlap. Incumbents with higher measures of overlap have lower future flows. This negative correlation is especially strong for poorly performing incumbents. For a fund in the bottom quintile of past one-year performance, an one-standard-deviation increase in MVOi,t decreases the subsequent year’s fund flows by 6.1%. These effects are only present after 1998; in the early part of our sample period, there is no discernible correlation between measures of incumbent-entrant overlap and future asset flows. Although one can imagine a channel by which entry could increase incumbent operating costs (such as raising fund manager wages, auditing fees, custodial charges, 5 Nonetheless, the negative relation between before-expense alpha and expense ratios shown by Gil-Bazo and Ruiz-Verdu (2009) does not exist in the post-1998 sample period, suggesting that price competition is far from dead.

etc.), the data simply do not exist to measure such effects cleanly. The effects of entry on trading costs, however, are measurable, at least to a degree. To the extent that entrants and incumbents compete for the same set of securities, entry should raise incumbent trading costs. We use a measure of net total costs proposed by Kacperczyk, Sialm, and Zheng (2008), the difference between a fund’s reported return and the return on a portfolio that invests in disclosed holdings, to investigate this. This return gap represents the benefits of trading, net of costs. We find that the size of the return gap in years one and two after entry is weakly negatively correlated with our overlap measures. But again, these effects only occur after 1998. Ceteris paribus, if trading costs are higher, then the net portfolio returns delivered by incumbent funds should be lower. We regress individual fund alphas estimated over the 36 months after entry on lagged measures of incumbententrant overlap and control variables. After 1998, post-entry alphas of incumbents with large overlap are lower; a onestandard-deviation increase in MVOi,t decreases subsequent alphas by five basis points per month. We also estimate post-entry incumbent excess returns using the characteristics-based approach of Daniel, Grinblatt, Titman, and Wermers (1997). This serves as a robustness check and permits us to measure excess returns in closer proximity to entry. In addition, it allows us to decompose the holdingbased return into three components: characteristic selectivity, characteristic timing, and average style effects. If lower alphas are due to competition for the underlying securities, then our overlap measures should be negatively correlated with the characteristic selectivity component of returns. That is precisely what we find. Finally, incumbents with high overlap have significantly higher attrition rates than those with low overlap. In the five-year period following entry, the attrition rate of incumbents in the highest decile of (MVOi,t) overlap is 22.1%, compared to only 7.1% for those in the lowest decile. In multivariate settings, in the post-1998 period, a-onestandard deviation increase in MVOi,t increases the implied probability of exit from a baseline level of 10% to 12.1%. Two particular aspects of our results deserve further discussion. First, the effects of competition described above are ameliorated (but not eliminated) for incumbents that are larger and that belong to larger families. This is not surprising—size brings with it scale economies and the ability to defend one’s turf. Second, for the dependent variables that we consider (fees and waivers, flows, costs, alphas, and attrition rates), entry only influences incumbents after 1998. There is nothing magical about 1998 per se; if we use 1997 or 1999 as breakpoints, we obtain largely similar results. But, one might ask why we do not observe these effects in the early part of the sample period. The answer, we believe, lies in the fact that entry is endogenous. Summarizing a voluminous literature, Geroski (1995, p. 425) concludes that entry comes in waves which often ‘‘peak early in the life of many markets’’, and which in a traditional industrial organization framework, drive profitability and price to their longrun competitive levels. In mutual funds, entry increased until the late 1990s, probably because it was attractive. As the industry became saturated, the profitability of


entry also declined, and entrants began to compete more aggressively with incumbents for revenues (flows times fees), and inputs (driving up costs). This ‘‘threshold entry’’ effect is shown in other places by Bresnahan and Reiss (1991), who use it as an alternative to directly measuring price-cost margins. We too cannot directly measure pricecost margins but can confirm endogenous entry with a simple calculation: the correlation between industry revenue in year t 1 (measured as the aggregate dollar value of net flows in year t 1 times the expense ratio) and the total number of entrants in year t, is 0.96 in the pre-1998 period and 0.55 in the post-1998 period. This large decline is consistent with the saturation and threshold argument. Endogenous entry is also consistent with Kosowski, Timmermann, Wermers, and White (2006) and Fama and French (2010). The former conclude that outperforming managers became scarce after 1990, and speculate that ‘‘either markets have become more efficient, or competition among the large number of new funds has reduced the gains from trading’’ (p. 2575). The latter note a marked decline in the persistence of alphas after 1992, and speculate that this is caused either by diseconomies of scale, or that ‘‘perhaps the entry of hordes of mediocre funds posturing as informed managers makes it impossible to uncover the tracks of truly informed managers.’’ Overall, our results point to a competitive market for mutual funds after 1998—one characterized by free entry that influences incumbent prices, revenues, costs, alphas, and ultimately, survival. To some this may be an obvious conclusion, especially based on the casual observation that there are almost 4,000 domestic equity funds competing for investors’ capital. But it is clearly not obvious to others. More importantly, regardless of one’s a priori beliefs, it is important to bring evidence to bear on the competitiveness of a market that managed $2.8 trillion in domestic equity in 2008 (Investment Company Fact Book, 2009). The remainder of the paper is organized as follows. Section 2 describes the data, our sample, and the metrics we use to measure incumbent-entrant overlap. Section 3 contains our results. Section 4 discusses robustness issues and Section 5 concludes.

2. Sample and methods 2.1. Sample construction We start with all active (non-index) equity mutual funds in the Center for Research in Security Prices (CRSP) mutual fund database in the following investment styles: aggressive growth, growth and small growth, income, growth and income, special sector, and others.6 This eliminates balanced, bond, money market, and international equity funds. Since we require portfolio holdings to

6 In Section 3.3.7 of the paper, we provide a brief analysis of the impact of entry on pure index funds and closet indexers.

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construct our measures of incumbent-entrant overlap, we merge this initial sample with holdings information in the Thomson Financial CDA/Spectrum holdings database. This holdings database is, in turn, linked with the CRSP mutual fund files using the MFLINKS file provided by Wharton Research Data Services. We start our sample in 1981 because the holdings database starts in 1980 and we need one prior year’s worth of data to calculate incumbententrant overlap. We end our sample in 2005 because several of our dependent variables require two or three years of post-entry data. To create a sample of entrants and incumbents, we first identify entrants based on their appearance in the CRSP Mutual Fund database. We then impose a sequence of filters. First, we disregard incumbent-entrant pairs in which both the incumbent and entrant belong to the same fund family. Intra-family competition is likely to be endogenously small because of cannibalization concerns. Moreover, intra-family entry is endogenous, causing inference problems for our tests. In contrast, entry of funds from rival families is an exogenous shock to incumbents. Second, we require that an entrant exist for at least one year before it can be regarded as an incumbent. This allows for sufficient time for the competitive process to take effect on incumbent activities and behavior. Third, we require that holdings information be available in reasonable proximity to the birth date of the fund so that we can accurately calculate overlap measures. It is sometimes the case that the first reported quarter of a mutual fund on the CRSP database is not the same as that reported by CDA/Spectrum.7 If the difference between the inception dates in the two databases is larger than two quarters, we exclude that entry observation. For example, if the CRSP database shows the first return of a fund in January 1993 but the first holdings observation is in December 1993, we do not record this fund as an entrant on either date. We do, however, regard this fund as an incumbent, starting January 1994. The consequence of this filter is that the number of entrants in our sample is smaller than one would obtain by a simple tabulation of birth dates from the CRSP database. This filter ensures accurate measurement of the overlap in event time but our conclusions are not sensitive to it. Most of the data (returns, expenses, assets, loads, turnover, etc.) required for our analysis are provided by the CRSP Mutual Fund database and are available for the entire time-series. However, CRSP only provides information about management fees starting in 1998; these fees are reported net of waivers.8 Since waivers are of interest in their own right, we purchase from Lipper Analytical Services a database that contains the name of each fund that waived fees, as well as the magnitude of the fee waiver. These data start from 1998 and are first matched to our sample using CUSIP numbers and then handmatched by fund name.

7 Consistent with this, Wermers (2000) finds that CDA’s reporting of holdings sometimes lags return information in other data sources. 8 See CRSP Survivorship-Bias Free U.S. Mutual Fund Guide, p.8, which can be found at the following URL (http://www.crsp.com/ documentation/pdfs/MFDB_Guide.pdf).

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These sample selection criteria result in a final sample of 4,116 unique funds between 1981 and 2005. Our analysis is conducted at the fund-level because holdings are for each fund, not share classes. Since several of our dependent variables are different for each share class, we use Total-Net-Assets (TNA)-weighted averages of these variables at the fund-level in our analyses.

2.2. Measuring the effects of entry on incumbents To study the effects of entry on incumbents, it is necessary to identify the ‘‘market’’ in which entrant and incumbents compete. One obvious approach would be to use style information. One might suppose that an entrant in a small cap value style, for example, would compete with incumbents in the same style. But this approach faces two difficulties. First, at a conceptual level, style (or, equivalently, ‘‘market’’) identification is ad hoc. That is, it is not obvious why an entrant fund identified with a small cap value strategy would not compete with incumbents in, say, small cap growth.9 Second, at a more practical level, style identification is idiosyncratic. For instance, the CRSP Mutual Fund and the Thomson Financial CDA/Spectrum databases use different style definitions and it is not clear which one is more appropriate. We construct measures of competition between incumbents and entrants that are agnostic to style classifications by using security holdings. Effectively, we are inferring something about competition in the product market (the mutual funds’ portfolios) from overlap in the inputs of the production process (the securities comprising the portfolios). Given the commodity nature of the inputs, we expect the correlation between the two to be high. Philosophically, we rely on the Friedman (1953) argument that from the outcomes, we can presume that investors behave ‘‘as if’’ they observe and understand substitutability between funds. In other words, in this positivist stance, it does not matter if investors observe the complete set of mutual fund holdings, but only that they behave ‘‘as if’’ they do. For readers uncomfortable with this reliance and concerned that holdings are not observable to the marginal investor, we offer other sources of comfort. First, funds regularly report their top holdings in prospectuses and annual reports. Thus, even if all holdings are not observable, most of the important ones are. Second, a cottage industry of firms (such as Morningstar and Lipper) regularly evaluates this information and provides distilled versions to investors. The results in Wermers, Yao, and Zhao (2007) suggest that holdings contain information of some value, suggesting that our overlap measures are not just noise. Third, if our overlap measures are in fact pure noise, as would be the case under the alternative hypothesis, then we should not find any connection between them and our dependent variables. 9 In addition, Sensoy (2009) reports that one-third of actively managed US mutual funds specify a size and value/growth benchmark index in the fund’s prospectus that does not match the fund’s style.

2.2.1. Overlap measures Assume there are i incumbent funds at the beginning of quarter t, i =1, y, M, and j new funds enter during the quarter where j = 1, y, N. Let t represent an overlapping security that appears in both the incumbent and entrant’s portfolio, where t = 1, y, yi,j,t. Also, g represents all (overlapping and non-overlapping) securities in an incumbent’s portfolio, where g =1, y, NSi,t . By definition, t r g and yi,j,t rNSi,t. For each overlapping security within an incumbent-entrant pair, we define a pseudo portfolio weight as 1 !0 P SI Pt,t SEt,t @P t,t1 t,t1 A, ð1Þ wt,t ¼ NSi,t I Pt,t1 SIt,t1 g ¼ 1 Pg,t1 Sg,t1 where Pt,t 1(Pt,t) is the price of overlapping security t at the beginning (end) of quarter t, SEt,t (SIt,t1 ) is the number of shares of that security in the entrant (incumbent’s) portfolio, Pg,t 1 is the price of security g in the incumbent’s portfolio, and SIg,t1 is the number of shares of security g in the incumbent’s portfolio. We use a different time convention (‘‘t’’ for entrants and ‘‘t 1’’ for incumbents) because in the absence of detailed timing information about entry, we assume it takes place at the end of the quarter.10 Intuitively, the first term in Eq. (1) is the ratio of the dollar value of the overlap between entrant and incumbent holdings in each overlapping security. For example, if an entrant (incumbent) has a $2 million ($10 million) position in a security XYZ, the ratio is 0.2. The second term represents the importance (weight) of this security in the incumbent’s portfolio. In the above example, if the incumbent’s total portfolio value is $200 million, the $10 million position in XYZ has a weight of 0.05, implying that wt,t = 0.01. The above pseudo portfolio weight, wt,t, is defined for each overlapping security in an entrant-incumbent pair. To create an incumbent-level measure of overlap (MVOi,t), we sum these weights across all overlapping securities and then average across entrant-incumbent pairs. MVOi,t ¼

yi,j,t N X 1X wt,t : Nj¼1t¼1

ð2Þ

This relatively simple measure aggregates the effect of all entrants on each incumbent. However, it has one potential drawback, best illustrated by way of example. Consider, a situation in which the overlap in holdings between incumbent i and entrant j =1 is 100%, but that the overlap between the same incumbent and entrants j =2 and 3 is zero. By averaging across all incumbent-entrant pairs, MVOi,t takes on a value of 0.33, even though the effect of the entry of j= 1 could be significant in economic terms by reducing incumbent revenues and increasing costs. This averaging could obfuscate the effects that we are interested in. Therefore, we also compute a truncated version of this overlap measure (TruncMVOi,t) in which we 10 Since the numerator and denominator of the first term in Eq. (1) are based on different prices, one might be concerned that the weight is influenced by momentum trading in the same sense as Grinblatt, Titman, and Wermers (1995). We also calculate weights using the average of beginning and end-of-quarter prices and find similar results.


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Table 1 Time-series of entry of new mutual funds. The table shows the number of incumbent mutual funds at the end of each calendar year and the number of new mutual funds created (entrants) during the year. The sample is constructed from the intersection of the CDA/Spectrum mutual fund holdings database with the CRSP Mutual Fund database. It includes all active (non-index) equity mutual funds with returns data and in the following CDA/Spectrum categories: aggressive growth, growth, growth & income, metals, and unclassified. The number of entrants in each style (except ‘‘others’’ and ‘‘special sector’’) is also shown. The style categories correspond to the CRSP style codes. RVW is the compounded value-weighted market return from January 1, 1981. The ratio of the number of entrants to incumbents is reported in percent. The last column shows p-values from a Chow F-test for structural breaks based on the number of entrants. Year

# Incumb.

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

# Entrants

354 351 376 403 423 488 556 612 681 724 879 969 1,285 1,556 1,774 2,004 2,249 2,487 2,577 2,526 2,610 2,582 2,482 2,386 2,201

1 1 18 8 7 23 30 17 16 19 35 62 157 197 145 170 201 278 140 198 117 54 38 19 19

# Entrants in CRSP fund styles Agg. growth

Growth & sml gr.

Income

Growth & inc.

0 1 11 1 3 4 6 4 1 4 5 9 30 28 20 40 45 50 34 47 27 15 3 0 1

1 0 4 4 2 13 11 3 5 7 12 21 45 55 49 69 61 111 58 80 56 26 25 7 10

0 0 1 1 2 3 6 3 2 2 2 3 5 9 5 10 8 3 2 1 1 0 1 0 0

0 0 1 2 0 3 6 7 1 2 8 8 23 15 14 18 21 37 22 20 8 6 5 2 7

only sum across incumbent-entrant pairs with non-zero overlap in holdings. TruncMVOi,t ¼

yi,j,t K X 1X wt,t : K j¼1t¼1

ð3Þ

By definition, TruncMVOi,t is larger in magnitude than MVOi,t but has the same basic properties. All our subsequent tests are conducted with both measures of overlap. 3. Results 3.1. Patterns of entry Table 1 shows the time-series pattern in entry of new mutual funds and of incumbents over the sample period. The number of incumbents at the end of each calendar year (shown in column 2) increases from 354 in 1981 to more than 2000 by the late 1990s, after which it stabilizes somewhat. The number of entrants grows from one to 278 by the end of 1998. After 1998, there is a precipitous decline in the number of entrants, to the extent that there are only 19 entrants in our sample in 2005.11 We also 11 As discussed in Section 2.1, the number of entrants in Table 1 is smaller than what would be obtained by simply calculating entrants from the CRSP Mutual Fund database because of the holdings filter that we impose. However, the time-series pattern of entry is almost identical

RVW

Entrants/Incumb.

Chow p-val

0.96 1.16 1.42 1.46 1.92 2.22 2.26 2.66 3.42 3.21 4.29 4.68 5.22 5.18 7.02 8.51 11.09 13.56 16.99 15.11 13.41 10.62 14.13 15.97 17.14

0.28 0.28 4.79 1.99 1.65 4.71 5.40 2.78 2.35 2.62 3.98 6.40 12.22 12.66 8.17 8.48 8.94 11.18 5.43 7.84 4.48 2.09 1.53 0.80 0.86

– – – – – – – – – 0.60 0.41 0.29 0.17 0.10 0.06 0.04 0.02 0.01 0.04 0.09 0.17 0.26 – – –

report the compounded value-weighted return starting from January 1, 1981 in the last column of the table. The correlation between the number of entrants per year and the aggregate market return is 0.56. What appears to be a permanent decline in entry starting in the late 1990s is suggestive of an industry reaching capacity. That is, the first part of the sample period appears to be one in which funds find it profitable to enter. By the late 1990s, however, the decline in entry suggests that entry is no longer as profitable. This is perhaps best seen in the ratio of the number of entrants to incumbents, shown in the second-to-last column of the table. This ratio peaks in the early 1990s, after which it starts to decline. These changes in entry patterns are important because they suggest that entry’s effect on incumbents’ is likely to be larger in the latter part of the sample. To determine the appropriate place to split our sample, we calculate Chow F-statistics for each year after

(footnote continued) to that reported in Table 1. In both cases, the peak occurs in 1998. The correlation between the number of entrants in our sample and one without the holdings filter is 0.88. We verify that this filter does not create some sort of selection bias by checking the distribution of key variables (returns, management fees, loads, turnover, etc.) between the filtered and unconstrained samples. The differences in means and medians of these variables between the two samples are not statistically significant.

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Table 2 Distribution and characteristics of incumbent-entrant overlap. The sample includes 4116 unique funds between 1981 and 2005. In Panel A, median s is the time-series median of the cross-sectional standard deviation of MVOi,t and TruncMVOi,t. Panel B shows time-series means of MVOi,t or TruncMVOi,t when incumbents are within the same Morningstar style and when they are across different styles. In Panels C and D, incumbents are sorted into deciles based on breakpoints for MVOi,t or TruncMVOi,t in each quarter. Fund characteristics are then averaged across funds in each portfolio. TNA is $ millions. Return is the quarterly net return. Flow is the net percentage quarterly flow, truncated at the top 1% level. Exp is the expense ratio (in percent) of incumbents during the year of entry. Turnover is the minimum of aggregate purchases or sales, divided by TNA during the year of entry. Load is the sum of front-end load and redemption charges (in percent). Age is in years. Panel A: Distribution of overlap measures 10th Percentile 0.0003 0.0011

MVOi,t TruncMVOi,t

Mean 0.0537 0.2204

Median 0.0053 0.0179

Median s 0.1771 0.6295

90th Percentile 0.0869 0.2820

Panel B: Average overlaps within and across Morningstar style boxes TruncMVOi,t

MVOi,t Across Growth Core Value Within Growth Core Value

Large 0.059 0.010 0.031

Mid 0.009 0.011 0.027

Small 0.004 0.006 0.003

Large 0.720 0.086 0.391

Mid 0.087 0.072 0.323

Small 0.027 0.037 0.030

0.092 0.048 0.047

0.003 0.005 0.013

0.001 0.004 0.001

1.153 0.166 0.864

0.146 0.144 0.522

0.058 0.106 0.055

TNA

Return

Flow

Exp

Turnover

Load

Age

3,131 1,507 853 513 347 221 147 92 56 30

1.90 2.61 2.97 2.68 2.83 2.97 2.78 2.72 2.68 2.69

3.92 6.91 7.16 2.71 3.86 4.07 11.62 8.34 48.78 38.69

1.22 1.14 1.16 1.19 1.20 1.24 1.26 1.31 1.39 1.58

0.67 0.79 0.87 0.94 0.91 0.95 0.96 0.98 0.99 1.13

2.32 2.59 2.50 2.48 2.42 2.32 2.29 2.11 2.00 1.69

14.93 15.19 14.41 13.54 12.73 11.80 10.95 10.00 9.17 7.94

Return 2.00 2.66 2.91 2.70 2.91 2.84 2.81 2.67 2.67 2.66

Flow 3.33 11.32 2.11 2.94 3.70 4.39 11.29 44.90 15.55 35.78

Exp 1.16 1.10 1.14 1.20 1.21 1.24 1.26 1.32 1.41 1.65

Turnover 0.69 0.80 0.87 0.91 0.92 0.93 0.96 0.99 0.99 1.14

Load 2.40 2.65 2.46 2.46 2.38 2.35 2.22 2.10 2.05 1.67

Age 16.11 15.58 14.32 13.23 12.29 11.59 10.68 9.77 9.10 8.05

Panel C: MVOi,t deciles

1 (Low) 2 3 4 5 6 7 8 9 10 (High)

Panel D: TruncMVOi,t deciles

1 (Low) 2 3 4 5 6 7 8 9 10 (High)

TNA 3,522 1,389 742 450 307 195 134 85 51 28

1990 and report p-values from this statistic in the last column of Table 1. This test indicates a structural break in the time-series in 1998 and as a result, we conduct our tests on the pre- and post-1998 subperiods, as well as the entire sample.

3.2. Overlap statistics Before we proceed to our tests of competition, we provide some basic descriptive statistics on the overlap measures. Panel A of Table 2 shows the distribution of MVOi,t and TruncMVOi,t over the entire sample period. The median MVOi,t and TruncMVOi,t are 0.0053 and 0.0179, respectively,

and in both cases, the means are much larger (0.0537 and 0.2204, respectively). In the last column we report the (time-series) median of the cross-sectional standard deviation of each variable in the quarter. In both cases, the median standard deviation is over three times the mean. This variation is important since it implies that for some incumbents, the overlap is very large; it is those incumbents for whom we expect the effects of competition to be important. Accordingly, in our main tests to follow, we use the median standard deviation of MVOi,t and TruncMVOi,t to gauge the economic significance of regression coefficients. As described earlier, our overlap measures are indifferent to mutual fund investment style classifications. Nonetheless, to the extent that styles are (coarse)


descriptors of expected competition between incumbents and entrants, one would expect our measures of overlap to be larger (smaller) for incumbents and entrants in the same (different) style. To check if this is the case, we calculate average values of MVOi,t and TruncMVOi,t within and across Morningstar styles. Panel B shows that in most cases, the average overlaps are indeed larger within, rather than across, styles. The results are stronger for TruncMVOi,t because zero-overlap holdings are excluded from the calculation. In Panels C and D of Table 2, we sort incumbents into deciles based on the distribution of MVOi,t and TruncMVOi,t, respectively, in each quarter. For each decile, we show the distribution of variables that we expect to be correlated with the overlap measures. For instance, we expect a mechanical correlation between both overlap measures and TNA; ceteris paribus, smaller incumbents are likely to have larger overlaps with entrants because they hold fewer securities. This is indeed the case as TNA decreases monotonically across deciles. Other variables are naturally correlated with fund size and therefore are correlated with MVOi,t and TruncMVOi,t. Large funds are also typically older, have lower expense ratios because of economies of scale, and generally have lower turnover. As a result, funds with high measures of overlap display the exact opposite patterns—they are generally younger with higher expense ratios and turnover. Since many of these variables are jointly determined, it is important to know these systematic correlations and control for them in multivariate settings. 3.3. The effects of competition Standard economic theory suggests that competitive entry should influence incumbent prices, revenues, costs, profitability, and potentially even survival. In this section, we explore each of these possible outcomes. 3.3.1. Price competition: changes in incumbent fees The revenue stream of a fund consists of assets under management multiplied by fees, analogous to quantity sold multiplied by price in industrial firms. It is wellknown that competitive outcomes can be realized by Bertrand (price) or Cournot (quantity) mechanisms. The existing evidence of price competition between mutual funds generally examines average or aggregate expense ratios, and is mixed at best. For example, Sirri and Tufano (1998) report a decrease in the expense ratio (plus amortized loads) from 1.66% in 1971 to 1.37% in 1990. Similarly, Khorana and Servaes (2004) report a decrease in their sample from 1.4% in 1979 to 1.19% in 1998. But Barber, Odean, and Zheng (2005) report that assetweighted average expense ratios increase from 0.54% in 1962 to 0.90% in 1999. Such diverse results could be because of sampling and methodological variations across these papers. But these are also general statements about the average or aggregate level of fees in the industry, rather than fees charged by individual funds. In contrast, our empirical approach to determining whether fee changes are related to competition directly goes after

47

the intensity of competition (as measured by overlap). We regress post-entry changes in various measures of fees on lagged measures of overlap and control variables. As control variables, we include the size of the fund, the size of the family, fund age, turnover, and the standard deviation of the prior 12 month returns. Fund and family size are included to account for scale effects, and age picks up the effects of experience (Khorana, Servaes, and Tufano, 2005). We estimate these regressions using a Fama-MacBeth approach each quarter and present the time-series averages of the coefficients. t-Statistics are adjusted for serial correlation.12 We use the change in the management fee from quarter t+1 to quarter t+8 (i.e., the two-year change in the fee measured in basis points after entry takes place in quarter t) as the dependent variable. We use two-year changes because entry is determined relatively imprecisely, because we do not have strong priors on how quickly incumbents should respond, and because fee reductions require board approval and are therefore typically annual. The management fee is paid to the fund’s advisor who has the latitude to increase or decrease the fee—thus, it represents a clean measure of the price of the services provided by the advisor.13 These regressions are estimated for the post-1998 sample period because CRSP only reports management fees after 1998. Focusing on our variables of interest (MVOi,t and TruncMVOi,t), the regressions in Panel A of Table 3 show a significant negative relation between our measures of overlap and future changes in fees. The regression estimates suggest that an one-standard-deviation change in the MVOi,t (TruncMVOi,t) is related to a 3.2 (3.6) basis-point reduction in the management fee. The average management fee in our sample is 48 basis points so, in our view, this represents a meaningful change in fees. For the post-1998 period, we can also calculate non-management fees by subtracting management fees from the expense ratio. Non-management fees include advertising costs, auditing and accounting costs, 12b-1 fees, custodial expenses, legal expenses, transfer agent expenses, and other administrative expenses. Ex ante, the effects of competition on the components of nonmanagement fees are hard to sign. If entry increases demand for these ancillary services, one could imagine this causing an increase in non-management fees. On the other hand, if there is a commensurate increase in the supply of such ancillary services, non-management fees may remain the same (or perhaps drop). At an aggregate level, the data show neither: the regressions show no relation between changes in non-management fees and our measures of overlap.

12 The alternative is to estimate regressions using panel data and control for fund-specific fixed effects. But our interest is in crosssectional variation across funds due to overlap in inputs, rather than within-fund variation over time. 13 Nominal fee increases require board and shareholder vote. Of course, a fund can effectively raise fees by not lowering them in response to competition, not having Asset Under Management (AUM) breakpoints, or in the case of multi-manager funds, receiving Securities Exchange Commission (SEC) exemptions.

48


Table 3 The effect of entry on changes in incumbent mutual fund fees. In Panel A, D Mgmt fee, D Non-mgmt fee, D 12b-1 fees, D Load, and D Expense ratio (in basis points) are calculated from quarter t+ 1 to quarter t +8 after entry takes place in quarter t. Non-mgmt fee is calculated by subtracting management fees from the expense ratio. Loads are defined as the sum of maximum front- and back-end sales charges. Panel B shows logistic regressions predicting the probability that a fund uses a fee waiver, and Ordinary Least Square (OLS) regressions of the magnitude of fee waivers (in percent and winsorized at the 99th percentile). Log(family)t is the size of the family to which the fund belongs. Standard deviation of returns is based on the monthly returns during the prior year of entry. Pre-waiver expenset is the expense ratio in the year prior to the waiver. The Waiver dummyt is a dummy variable equal to one if the fund used a waiver in the prior year. With the exception of the logistic regressions (which use year dummies), all specifications are estimated using Fama-MacBeth procedures. t-Statistics, corrected for serial correlation in time-series estimates (up to four lags), are reported in parentheses below the estimates. Panel A: Changes in various fee measures

D Mgmt fee

Intercept MVOi,t TruncMVOi,t Log (TNA)t Log (family)t Log (age)t Turnovert Std. dev. of returnst

19.126 ( 2.78) 17.921 ( 2.21) 0.037 (0.05) 0.929 ( 1.89) 7.662 (2.16) 2.787 (3.48) 8.051 (0.35)

17.562 ( 2.57) 6.026 ( 1.95) 0.226 ( 0.28) 0.911 ( 1.86) 7.721 (2.18) 2.785 (3.48) 8.291 (0.37)

D Non-mgmt fee

54.168 ( 3.98) 8.925 ( 0.89) 6.009 (4.76) 1.411 ( 3.27) 14.078 (3.62) 0.712 (0.36) 43.834 ( 1.82)

53.635 ( 3.91)

D 12b-1 fee

1.145 (3.06) 4.546 (3.23)

2.346 ( 5.02)

4.303 2.129 ( 1.03) (2.64) 5.927 0.032 0.059 (4.59) (0.41) ( 1.08) 1.442 0.154 0.077 ( 3.41) ( 3.37) ( 2.91) 14.129 0.272 0.399 (3.63) (4.67) (6.31) 0.679 0.122 0.204 (0.34) (1.92) (2.69) 43.664 4.784 4.852 ( 1.79) ( 3.05) ( 4.04)

D Load

7.771 (3.51) 13.343 ( 1.96) 1.467 ( 5.82) 0.501 ( 1.99) 2.087 ( 9.52) 0.858 (3.12) 50.304 (4.61)

7.208 (3.31) 4.805 ( 1.84) 1.403 ( 5.81) 0.508 ( 2.01) 2.066 ( 9.42) 0.835 (3.09) 52.584 (4.77)

D Expense ratio Pre-1998

Post-1998

9.174 9.206 ( 2.98) ( 2.99) 13.282 ( 0.65) 8.243 ( 0.91) 0.540 0.551 (1.54) (1.56) 0.262 0.260 ( 1.33) ( 1.32) 2.164 2.118 ( 3.97) ( 4.03) 0.123 0.128 (0.27) (0.28) 50.815 48.876 (2.45) (2.42)

7.008 ( 3.84) 13.280 ( 1.17) 1.269 (4.74) 0.917 ( 6.56) 0.160 ( 0.22) 0.986 ( 1.31) 110.43 ( 3.45)

7.035 ( 3.83) 6.024 ( 0.97) 1.255 (4.72) 0.917 ( 6.58) 0.132 ( 0.18) 0.992 ( 1.32) 110.90 ( 3.46)

Panel B: Fee waivers Prob (waiver) Intercept MVOi,t TruncMVOi,t Pre-waiver expenset Waiver Dummyt Returnt Log (TNA)t Log (age)t Log(family)t Front-end loadt

20.229 (0.21) 0.568 (2.89) – 0.062 (2.58) 0.436 (5.91) 0.198 ( 2.63) 0.089 ( 6.51) 2.231 ( 8.24) 0.598 ( 10.92) 0.595 ( 3.16)

Ideally, one would like separate data on each of the components of non-management fees. While such data are not available, we can examine distribution costs, arguably the largest component of non-management fees. Distribution costs show up in loads or 12b-1 fees. The former are not included in non-management fees (and hence, the expense ratio) but the latter are. To investigate whether competition has affected distribution costs, we report similar regressions for changes in 12b-1 fees and changes in loads. These regressions show that changes in

Magnitude of fee waiver 20.249 (0.23) – 0.232 (2.46) 0.062 (2.59) 0.443 (5.93) 0.194 ( 2.58) 0.092 ( 6.91) 2.233 ( 8.30) 0.584 ( 10.02) 0.615 ( 3.20)

0.266 (10.64) 1.221 (3.03) – 0.061 (6.07) 0.054 (5.49) 0.087 ( 5.31) 0.028 ( 5.05) 0.002 ( 0.72) 0.008 ( 4.07) 0.035 ( 3.54)

0.263 (10.74) – 0.357 (5.83) 0.059 (6.08) 0.054 (5.51) 0.086 ( 5.29) 0.028 ( 5.29) 0.002 ( 0.65) 0.007 ( 3.76) 0.035 ( 4.55)

loads are negatively related to overlap while 12b-1 fees are positively related.14 In unreported regressions, total distribution costs (12b-1 fees plus loads) are positively related to our overlap measures, indicating that the effect

14 As in Sirri and Tufano (1998), we use the sum of front- and backend loads, amortized over a seven-year holding period. We also estimate (but do not report), Tobit regressions. Results are similar to those reported.


of competition between funds is an increase in distribution costs, which appear to be passed on to the consumer. The last four columns in Panel A of Table 3 show regressions of changes in expense ratios on our measures of overlap. Since these data are available for the full-time series, we show regressions for the pre- and post-1998 sample period. The regressions show no relation between changes in expense ratios and MVOi,t or TruncMVOi,t in either subperiod. This is not surprising for at least two reasons. First, the expense ratio is the sum of management and non-management fees, and the latter adds noise to the measurement of the dependent variable as a measure of prices. Second, as an empirical matter, the unconditional correlation between two-year changes in the management fee and non-management fees is 0.84 for the entire panel, and the average fund-by-fund correlation across all funds is 0.30. This implies that in the regressions, increases in non-management fees (mostly distribution costs) offset decreases in management fees, so that expense-ratio regressions show no statistical relation with overlaps. The management fees and expense ratios reported by CRSP are reported net of fee waivers and reimbursements. But waivers are interesting in and of themselves. Consider, for example, a fund that has a gross management fee of 100 basis points in quarters t and t +4, and waivers of 20 basis points in both years. The change in the net management fee reported by CRSP between these two years is zero, implying no change in prices. But the fact that the fund employed a waiver in both years can be viewed as a reduction in price and may reflect the effects of competition. To get at these issues, we also examine waivers separately.15 In Panel B of Table 3, we estimate logistic regressions that predict whether a fund employs a fee waiver. The dependent variable is equal to one if a fund claims a fee waiver in that year, and zero otherwise. For control variables, we follow Christoffersen (2001) and include fund size, age, prior year return, family fund size, and a dummy variable equal to one if a fund has a frontend load. We also include year dummies but do not report them. The coefficient on MVOi,t is 0.568 with a Z-statistic of 2.89. The coefficient on TruncMVOi,t is smaller (0.232) and has a z-statistic of 2.46. Converting the coefficient on MVOi,t to an implied probability with all variables set equal to their means, an one-standard-deviation increase in MVOi,t (TruncMVOi,t) increases the implied probability of using a fee waiver from the baseline level of 20% to 24% (26%). In the last two columns of the panel, we estimate Fama-MacBeth cross-sectional regressions of the

15 As a preliminary exercise, we first sort incumbents into deciles based on either MVOi,t or TruncMVOi,t and then calculate the percentage of funds in each decile that waive some portion of their fees, as well as the median fee waiver. When deciles are formed based on MVOi,t, the percentage of funds using fee waivers increases from 12.22% in decile 1 to 24.54% in decile 10. The increase is monotonic across all deciles but the vast majority of the increase occurs between deciles 1 and 2. This is because decile 1 contains large funds, and fund size is negatively correlated with the propensity to waive fees. The median fee waiver also increases across deciles, from a low of 5.6 basis points in decile 1 to a high of 50.3 basis points in decile 10. We do not report the above decilebased results in a table but they are available upon request.

49

magnitude of the fee waiver on the same set of variables. For these regressions, only funds with positive waivers are included since we wish to capture the cross-sectional variation in the magnitude of fee waivers. Once again, MVOi,t and TruncMVOi,t are positively related to the magnitude of the fee waiver; the coefficients are large and highly statistically significant. An one-standarddeviation increase in MVOi,t (TruncMVOi,t) leads to a 21 (22) basis-point increase in the fee waiver.16 Waivers, like coupons or rebates used in consumer and durable goods industries, could be temporary reductions in price (ubiquitous examples include coupons for cereals and rebates for automobiles). To determine if this is the case, we examine the dynamics of fee changes. Fig. 1 separates the expense ratio into management and non-management fees and tabulates the percentage of funds in which fees increase, decrease, or stay the same relative to the prior year. Since the separation requires data on management fees, the figure is only generated from data after 1998. The data show that there is an increase (decrease) in the management fee in 45% (38%) of the cases (it is unchanged in the remaining 17%). Of the cases in which management fees decline relative to the prior year, 80% of those declines are due to permanent (contractual) changes to the management fee. The remainders (20%) are affected via a fee waiver.17 Of these, the vast majority, 85% and 78%, respectively, are continued in the next one or two years. Our sample shrinks as we move forward in time, but if we look four years after the introduction of the waiver, 50% are continued. Thus, to the extent that the waiver is reapplied year-after-year, it represents a de facto permanent change in fees, albeit one with some flexibility. Even in cases where the waiver is reversed in the following year, in 44% of those cases, the management fee is permanently reduced. In other words, when the waiver is reversed, it is frequently because the management fee has been permanently (contractually) reduced. Our last set of tests of price competition consists of regressions of before-expense performance on expense ratios. Gil-Bazo and Ruiz-Verdu (2009) argue that in equilibrium, after-fee performance should be equalized across funds so that a regression of before-fee performance on fees should have a slope of one. They find a negative relation for funds between 1961 and 2003, and argue that this is because a fraction of investors do not respond to differences in after-fee performance, and because funds take advantage of this sluggishness by charging higher fees. The conclusion that they draw from these results is that mutual fund markets are less than competitive. We replicate their regressions and find that

16 Another alternative is to include all funds in the regression and use a Tobit model to account for censoring. Although we do not report the full set of results, such regressions also have positive coefficients on MVOi,t and TruncMVOi,t. The coefficient on the former (latter) is 1.3 (0.4) with a t-statistic of 2.7 (2.3). 17 This is lower than the rates reported by Christoffersen (2001) and Coates and Hubbard (2007). There are two reasons for the differences. First, the samples across all three studies are quite different. Second, since our analysis is at the fund-level, we combine funds with different share classes (which means that if all three classes waiver fees, we only count that as one waiver).

50


Increase (45%)

Non-management fees

No change (4%)

Decrease (51%)

Expense ratio

Increase (45%)

Non-management fees

No change (17%)

Management fee returns to original t = 1,56% t = 2,55%

Permanent decrease (80%) Waiver reversed t = 1,15% t = 2,22%

Decrease (38%) Waiver (20%)

Waiver continued t = 1,85% t = 2,78%

Management fee permanently reduced t = 1,44% t = 2,45%

Fig. 1. Evolution of changes in fees for mutual funds in the post-1998 period. Non-management fees are calculated by subtracting management fees from the expense ratio. Each cell shows the percentage of incumbent funds for which fees are increased, decreased, or stayed the same after the entry. In the case of management fees decreases, we separate funds into whether the fees are reduced permanently or the fees are reduced through waivers. If the waiver is used, we look ahead to examine whether the waiver is reversed or continued one and two years after the entry. If the waiver is reversed, we examine whether the management fees after the reversion are permanently reduced or return to the same level before the entry. Fund-level fees are calculated as the average of share-class level fees. t presents the number of years after the entry.

the coefficients on expense ratios are indeed negative in the pre-1998 period. Using the four-factor model, the regression coefficient on fees is 0.750 with a p-value of 0.08. However, in the post-1998 period, the coefficients are small (and positive) with large standard errors; using the four-factor model, the coefficient on the expense ratio is 0.079 with a p-value of 0.89. What does one conclude from all these tests? On the prices over which managers have direct control (management fees and waivers), the effects of competition appear to be strong. Non-management fees, on the other hand, are not as responsive, mostly because distribution costs (bundled in 12b-1 fees) are positively correlated with overlap. Thus, while there is evidence of competition at work, it is less clear that the benefits have been passed on to consumers. 3.3.2. Quantity competition: flows We measure net flows using the Sirri and Tufano (1998) approach, except that we cumulate four quarterly flows in the year after entry to obtain annual flows. As before, we estimate regressions of net flows on our measures of overlap and control variables each quarter,

and report the time-series average of the coefficients. Because of the correlations shown in Table 2, we include prior-year measures of size (TNA), age, expenses, turnover, front-end loads, and the standard deviation of the prior 12 monthly returns as control variables. Table 4 presents the results of these regressions for the full sample, as well as for the pre- and post-1998 subperiods. Under supply-side competition, we expect incumbent funds with high measures of overlap to have lower future flows. But this relation is likely to be influenced by the well-known asymmetry between flows and past returns. For incumbents with high prior-period returns and high overlap with entrants, it is entirely possible that higher flows due to improved performance offset lower flows due to increased competition. Because of this asymmetry, we include an interaction term between our overlap measures and the return quintile ranking of the fund. Following Sirri and Tufano (1998), the return rank variable is defined as zero for funds in the bottom quintile of performance (over the prior 12 months), one for funds in the middle 60%, and two for funds in the top 20%. In the pre-1998 period, our measures of overlap are unrelated to


51

Table 4 The effect of entry on incumbent mutual fund flows. This table presents regressions of incumbent mutual fund flows in the year after entry on measures of overlap between incumbents and entrants, as well as control variables. Regressions are estimated quarterly and the table presents the time-series averages of the coefficients. Return_rank is equal to zero for funds in the bottom 20% of performance (over the prior 12 months), one for funds in the middle 60%, and two for funds in the top 20%. The definitions of control variables are the same as in earlier tables. Fama-MacBeth t-statistics, corrected for serial correlation in time-series estimates (up to four lags), are reported in parentheses below the estimates. Full sample Intercept MVOi,t TruncMVOi,t Return_rankt MVOi,tnReturn_rankt TruncMVOi,tnreturn_rankt Log (TNA)t Log (age)t Expense ratiot Turnovert Front-end loadt Std. deviation of returnst Adjusted R2

0.145 (5.17) 1.255 (0.97) – 0.148 (12.06) 6.031 ( 0.94) –

Pre-1998 0.165 (5.23) – 0.852 (0.99) 0.154 (12.64) –

0.025 ( 13.65) 0.065 ( 14.51) 0.284 ( 0.48) 0.015 (3.75) 0.192 (2.18) 0.373 (0.96)

4.273 ( 0.99) 0.025 ( 13.58) 0.065 ( 14.55) 0.401 ( 0.68) 0.015 (3.84) 0.194 (2.20) 0.354 (0.92)

0.09

0.09

post-entry incumbent flows. In the post-1998 subperiod, however, there is a negative relation between flows and overlap. The coefficient on MVOi,t (TruncMVOi,t) is 0.345 ( 0.153) with a t-statistic of 2.29 ( 2.04). For a fund in the bottom quintile of performance, a-one-standard deviation increase in MVOi,t is associated with flows that are lower by 6.1%. Our results thus far show some evidence of price competition as well as some evidence of quantity competition. But quantity-based equilibration could occur with a lag because investors face transaction costs in moving capital from one fund to another. For instance, loads create switching costs for investors. Without instantaneous equilibration, the interaction between price and quantity could be important such that the effects of competition reveal themselves in changes in incumbents’ sensitivity of flows to fees. In other words, in providing capital, investors may be more sensitive to price (fees) if they can find close substitutes (funds with high overlap). To test this hypothesis, we estimate regressions analogous to those in Table 4 but include an interaction term between MVOi,t and TruncMVOi,t and the expense ratio. We expect that funds with high overlap and high fees should have lower flows (i.e., a negative coefficient on the interaction). We do not display the results in a separate table to conserve space, but consistent with our expectation, the coefficient on the interaction term between MVOi,t (TruncMVOi,t) and the expense ratio is 20.05 ( 2.83) with a t-statistic of 3.15 ( 2.48).

0.136 (3.69) 1.945 (0.98) – 0.147 (9.21) 9.423 ( 0.95)

Post-1998 0.133 (3.65) – 1.311 (0.99) 0.153 (9.84) –

0.163 (3.83) 0.345 ( 2.29) – 0.155 (7.83) 0.201 (2.14) –

0.168 (4.02) – 0.153 ( 2.04) 0.157 (7.87) –

0.027 ( 10.58) 0.057 ( 9.92) 0.023 ( 0.03) 0.015 (2.68) 0.067 (0.56) 0.365 (0.69)

6.552 ( 0.98) 0.028 ( 10.33) 0.057 ( 9.97) 0.154 ( 0.18) 0.015 (2.74) 0.065 (0.57) 0.345 (0.65)

0.021 ( 11.27) 0.079 ( 12.62) 0.771 ( 1.65) 0.015 (3.15) 0.424 (3.89) 0.387 (0.76)

0.058 (2.16) 0.021 ( 12.14) 0.080 ( 12.62) 0.861 ( 1.83) 0.014 (3.25) 0.431 (3.93) 0.372 (0.73)

0.09

0.09

0.08

0.08

3.3.3. Incumbent costs Earlier tables show that incumbent non-management expenses are not influenced by entry. However, trading costs could be influenced by competition as entrants vie for the same set of securities as incumbents. Without proprietary data, we have no direct way of measuring post-entry incumbent trading costs. But, we can obtain an estimate of net total costs via an approach proposed by Kacperczyk, Sialm, and Zheng (2008). They calculate a return gap as the difference between the return delivered by the mutual fund and the return of a buy-and-hold portfolio that invests in the same securities as the fund. Naturally, this return gap includes both benefits and costs. As examples of benefits, Kacperczyk, Sialm, and Zheng (2008) cite positive returns from intra-quarter trading, securities lending, and preferential allocations of underpriced Initial Public Offerings (IPOs). Costs consist largely of trade execution (price impact) costs, commissions, as well as (potentially) agency costs. It is impossible to disentangle each of these costs and benefits but the only component of the return gap that is likely to change because of entry is trading costs.18 Assuming that the return gap is an unbiased albeit noisy proxy for trading costs, if trading costs of incumbents’ rise after entry, our overlap measures may be negatively correlated with future return gaps.

18 Consistent with this, Kacperczyk, Sialm, and Zheng (2008) report that the return gap is persistent for up to five years.

52


Table 5 The effect of entry on incumbent return gaps. The return gap is the difference between the reported return and the return on a portfolio that invests in disclosed holdings Kacperczyk, Sialm, and Zheng (2008). RGt + 4 is measured from quarter t+ 1 to quarter t +4 after entry takes place in quarter t. RGt + 8 is measured from quarter t+ 5 to quarter t+ 8. Regressions are estimated quarterly and the table presents the time-series averages of the coefficients. The definitions of control variables are the same as in earlier tables. Fama-MacBeth t-statistics, corrected for serial correlation in time-series estimates (up to four lags), are reported in parentheses below the estimates. Full sample RGt + 4 Panel A: Overlap measured using MVOi,t Intercept 0.029 ( 5.35) MVOi,t 0.049 ( 2.20) Flowst 0.002 ( 1.73) Log (TNA)t 0.002 ( 5.54) Log (age)t 0.000 (0.20) Expensest 0.103 ( 0.72) Turnovert 0.001 ( 1.99) Log(family)t 0.002 (5.92) Std. deviation of returnst 0.483 (6.20) Adjusted R2

0.071

Panel B: Overlap measured using TruncMVOi,t Intercept 0.028 ( 5.24) TruncMVOi,t 0.037 ( 2.09) Flowst 0.001 ( 1.69) Log(size)t 0.002 ( 5.94) Log(age)t 0.000 (0.16) Expensest 0.092 ( 0.66) Turnovert 0.001 ( 2.05) Log(family)t 0.002 (5.86) Std. deviation of returnst 0.490 (6.22) Adjusted R2

0.072

Pre-1998

Post-1998

RGt + 8

RGt + 4

RGt + 8

RGt + 4

RGt + 8

0.025 ( 5.29) 0.045 ( 1.88) 0.002 ( 1.16) 0.002 ( 4.87) 0.001 ( 1.29) 0.098 (0.61) 0.002 ( 3.27) 0.002 (6.24) 0.416 (6.47)

0.036 ( 4.83) 0.044 ( 1.60) 0.002 ( 1.46) 0.002 ( 3.48) 0.001 (0.97) 0.012 (0.06) 0.001 ( 1.54) 0.002 (3.46) 0.538 (5.22)

0.033 ( 5.74) 0.040 ( 1.18) 0.005 ( 2.02) 0.002 ( 4.63) 0.000 (0.19) 0.001 ( 0.01) 0.003 ( 3.66) 0.002 (4.77) 0.592 (7.56)

0.015 ( 2.55) 0.058 ( 1.52) 0.001 ( 2.02) 0.003 ( 5.21) 0.002 ( 2.45) 0.331 ( 1.46) 0.001 ( 1.28) 0.002 (8.07) 0.378 (3.37)

0.008 ( 1.15) 0.053 ( 2.12) 0.003 (1.47) 0.002 ( 2.00) 0.002 ( 3.11) 0.292 (1.02) 0.001 ( 0.83) 0.002 (4.25) 0.070 (0.86)

0.070

0.082

0.081

0.049

0.046

0.025 ( 5.22) 0.015 ( 1.09) 0.002 ( 1.17) 0.002 ( 4.88) 0.001 ( 1.15) 0.108 (0.68) 0.002 ( 3.29) 0.002 (6.22) 0.416 (6.40)

0.128 ( 4.77) 0.04 ( 1.72) 0.002 ( 1.41) 0.002 ( 3.85) 0.001 (0.92) 0.026 (0.14) 0.001 ( 1.60) 0.002 (3.41) 0.548 (5.26)

0.033 ( 5.62) 0.012 ( 0.56) 0.005 ( 2.02) 0.002 ( 4.55) 0.000 (0.30) 0.014 (0.07) 0.003 ( 3.68) 0.002 (4.71) 0.591 (7.43)

0.014 ( 2.41) 0.027 ( 1.32) 0.001 ( 2.05) 0.003 ( 5.13) 0.002 ( 2.48) 0.325 ( 1.45) 0.001 ( 1.28) 0.002 (8.00) 0.378 (3.34)

0.008 ( 1.14) 0.022 ( 2.40) 0.003 (1.48) 0.002 ( 2.09) 0.002 ( 3.07) 0.292 (1.03) 0.001 ( 0.84) 0.002 (4.31) 0.071 (0.87)

0.070

0.084

0.082

0.049

0.046

We calculate the return gap for each incumbent in the first and second year following entry, by compounding the quarterly return gap (from quarter t+1 to t+4, and from quarter t+5 to t+8, respectively). We use this two-year period because we do not have any a priori belief about how quickly competition for securities will be realized in incumbent-level costs. Our empirical modus operandi is as before: we estimate regressions of the return gap on each of our overlap measures every quarter and adjust t-statistics for serial correlation. Following Kacperczyk, Sialm, and Zheng (2008), we include fund flows, size, age, expenses, turnover ratio, affiliated family size, and the standard deviation of fund returns as control variables. The results of these regressions are reported in Table 5. Panel A (B) shows regressions in which the overlap

measure is MVOi,t (TruncMVOi,t). In Panel A, the return gap is negatively correlated with MVOi,t over the entire sample period, at least in year one following entry (and in a more marginal sense in year two as well).19 But again, these effects are pronounced in the post-1998 subperiod. Here, both coefficients on MVOi,t are negative, but only statistically significant in the second year after entry. The same is true for TruncMVOi,t. Thus, there is some weak evidence that incumbent-entrant overlap is negatively related to future return gaps.

19 The return gap is stated as a net benefit, rather than a cost. So a negative coefficient on MVOi,t implies that more competition is correlated with lower net benefits (or larger costs).


53

Table 6 Regression of post entry incumbent alpha. We estimate the alpha of each incumbent in the 36-month period after entry quarter using the four-factor Carhart (1997) approach. Estimated alphas (in percent) are then regressed on measures of overlap between incumbents and entrants, as well as control variables. The definitions of control variables are the same as in earlier tables. Regressions are estimated quarterly and the table presents the time-series averages of the coefficients. Fama-MacBeth tstatistics, corrected for serial correlation in time-series estimates (up to four lags), are reported in parentheses below the estimates. Full sample Intercept MVOi,t TruncMVOi,t Flowst Log(size)t Log(age)t Expensest Turnovert

Adjusted R2

0.244 (12.48) 0.047 ( 0.41) –

Pre-1998 0.242 (12.54) –

0.027 ( 2.32) 0.016 ( 5.96) 0.021 ( 4.89) 13.339 ( 14.66) 0.003 (0.60)

0.031 ( 0.33) 0.027 ( 2.32) 0.016 ( 5.77) 0.022 ( 4.89) 13.294 ( 14.58) 0.004 (0.61)

0.055

0.057

3.3.4. Incumbent performance If entry affects incumbent costs, then the post-entry performance of incumbent funds should be lower for those with larger overlap. To determine if that is the case, we first estimate the alpha of each incumbent in the 36-month period after entry using the Carhart (1997) four- factor model. Estimated alphas are then regressed on our measures of overlap, along with control variables. Table 6 shows the timeseries averages of coefficients from these regressions estimated each quarter.20 In the full sample period, neither measure of overlap appears to be related to future fund performance. But as with our earlier results, in the post-1998 subperiod, there is a significant negative association between the overlap measures and fund alphas. The coefficient on MVOi,t (TruncMVOi,t) is 0.276 (0.055) with a t-statistic of 3.85 ( 2.48). In terms of economic magnitude, a-onestandard deviation increase in MVOi,t decreases subsequent four-factor alphas by 0.05% per month. Although four-factor alphas are a widely accepted metric used to measure mutual fund performance, we also employ a measure of excess returns based on holdings. Following Daniel, Grinblatt, Titman, and Wermers (DGTW, 1997), we calculate the ‘‘excess’’ return of a fund as the difference between a fund’s hypothetical return based on its holdings and the returns of a benchmark portfolio in which each security is matched with a passive portfolio based on size, book-to-market ratio, and momentum.21

20 If higher overlap also causes future attrition (which we show in the next section), then alphas cannot be estimated for the worst performing funds that die since returns are unavailable for the entire 36month period. This renders our results conservative since it biases us against finding any connection between post-entry alphas and measures of overlap. 21 The DGTW benchmarks are available via http://www.smith.umd. edu/faculty/rwermers/ftpsite/Dgtw/coverpage.htm.

0.249 (10.96) 0.051 (0.32) –

Post-1998 0.250 (11.07) –

0.232 (6.01) 0.276 ( 3.85) –

0.224 (5.97) –

0.038 ( 2.31) 0.013 ( 4.85) 0.025 ( 5.37) 15.420 ( 14.04) 0.003 (0.37)

0.021 ( 0.15) 0.037 ( 2.31) 0.013 ( 4.64) 0.026 ( 5.39) 15.392 ( 13.99) 0.003 (0.38)

0.002 ( 0.61) 0.025 ( 3.76) 0.013 ( 1.35) 8.484 ( 7.50) 0.006 (0.55)

0.055 ( 2.48) 0.002 ( 0.62) 0.024 ( 3.62) 0.013 ( 1.32) 8.399 ( 7.43) 0.005 (0.54)

0.059

0.062

0.046

0.045

This helps us assess the robustness of the results in Table 7 and also allows us to measure excess returns over a shorter horizon. In addition, the holding return can be decomposed into its constituent components. HRt ¼ CSt þCTt þ ASt ,

ð4Þ

where CSt is a characteristic selectivity measure, CTt is a characteristic timing measure, and ASt is an average style measure. If the decline in performance is driven by competition for the underlying securities, then we expect our overlap measures to be negatively correlated with the selectivity component (CSt). Table 7 presents regressions of the excess holding return (HRt) and its constituent components on our overlap measures and control variables. Panel A presents results using MVOi,t and Panel B contains results for TruncMVOi,t. Consistent with the four-factor model results in Table 6, post-entry excess returns are negatively related to both overlap measures. And, as before, the effects are only statistically significant in the post-1998 subperiod. The results of regressions of the three return components show that the negative relation between the excess holding return and the overlap measures appears to be driven entirely by the selectivity component of returns. In fact, when CTt + 1 and ASt + 1 are used as dependent variables, neither overlap measure is statistically significant in any subperiod. In contrast, the relation between CSt + 1 and MVOi,t (or TruncMVOi,t) is quite robust and economically large. For instance, a-one-standard deviation increase in MVOi,t decreases the subsequent HRt + 1 (CSt + 1) return by 0.92% (0.28%) per year. 3.3.5. Survival We start our examination of exit by first sorting all incumbents into deciles based on MVOi,t and TruncMVOi,t in each quarter. We then calculate attrition rates for each decile,

54


Table 7 Regressions of post-entry incumbent characteristics-based returns. We estimate the characteristic-based return of each incumbent in the quarter after entry following Daniel, Grinblatt, Titman, and Wermers (1997). This holding based return (HR) is decomposed into three components: CS (reflecting stock selectivity), CT (reflecting timing), and AS (reflecting style). These four are then regressed on measures of overlap between incumbents and entrants, as well as control variables. Regressions are estimated quarterly and the table presents the time-series averages of the coefficients. Fama-MacBeth t-statistics, corrected for serial correlation in time-series estimates (up to four lags), are reported in parentheses below the estimates. Full sample HRt + 1

CSt + 1

CTt + 1

Panel A: Overlap measured using MVOi,t Intercept 0.010 0.046 0.009 ( 0.29) ( 0.94) (0.47) MVOi,t 0.048 0.069 0.002 ( 0.81) ( 1.91) ( 0.06) Flowst 0.004 0.009 0.005 (0.71) (1.22) ( 1.82) Log(size)t 0.003 0.004 0.000 ( 1.29) ( 1.14) (0.24) Log(age)t 0.014 0.016 0.003 (1.11) (0.96) ( 0.55) Expensest 2.004 3.112 0.564 (1.01) (1.16) ( 0.65) Turnovert 0.009 0.005 0.001 ( 1.50) ( 0.70) (0.53) Adj. R2

0.068

0.041

0.112

Panel B: Overlap measured using TruncMVOi,t Intercept 0.012 0.047 0.008 ( 0.34) ( 0.97) (0.48) TruncMVOi,t 0.020 0.032 0.001 ( 1.54) ( 1.66) (0.04) Flowst 0.004 0.010 0.005 (0.71) (1.19) ( 1.81) Log(size)t 0.003 0.003 0.000 ( 1.20) ( 1.06) (0.22) Log(age)t 0.014 0.016 0.003 (1.12) (0.96) ( 0.56) Expensest 1.949 3.054 0.555 (1.01) (1.16) ( 0.65) Turnovert 0.009 0.005 0.001 ( 1.48) ( 0.70) (0.56) Adj. R2

0.069

0.042

0.112

Pre-1998 ASt + 1

HRt + 1

CSt + 1

CTt + 1

ASt + 1

HRt + 1

CSt + 1

CTt + 1

ASt + 1

0.027 (3.47) 0.025 (1.33) 0.001 ( 0.76) 0.001 (1.09) 0.000 ( 0.29) 0.622 ( 2.07) 0.005 ( 3.12)

0.021 ( 0.40) 0.067 ( 0.74) 0.006 (0.72) 0.005 ( 1.27) 0.021 (1.12) 3.025 (1.00) 0.014 ( 1.54)

0.068 ( 0.92) 0.104 ( 0.89) 0.014 (1.22) 0.005 ( 1.08) 0.025 (0.96) 4.693 (1.14) 0.009 ( 0.82)

0.014 (0.51) 0.002 ( 0.05) 0.007 ( 1.65) 0.001 (0.29) 0.005 ( 0.58) 0.886 ( 0.66) 0.002 (0.45)

0.034 (3.13) 0.049 (2.13) 0.001 ( 1.38) 0.001 (0.72) 0.000 ( 0.25) 0.904 ( 1.99) 0.006 ( 2.62)

0.010 (0.53) 0.013 ( 3.58) 0.000 ( 0.00) 0.000 ( 0.35) 0.000 (0.02) 0.097 (0.57) 0.000 (0.20)

0.005 ( 0.18) 0.004 ( 3.33) 0.000 (0.09) 0.001 ( 1.01) 0.000 ( 0.40) 0.161 (1.14) 0.002 (1.61)

0.002 ( 0.10) 0.001 ( 0.05) 0.001 ( 2.45) 0.000 ( 0.37) 0.000 (0.54) 0.037 (0.34) 0.001 (0.42)

0.016 (1.52) 0.021 ( 0.68) 0.001 (3.22) 0.001 (1.71) 0.000 ( 0.29) 0.096 ( 1.22) 0.003 ( 2.17)

0.125

0.079

0.045

0.132

0.147

0.049

0.033

0.076

0.082

0.027 (3.49) 0.013 (2.16) 0.001 ( 0.73) 0.000 (1.12) 0.000 ( 0.28) 0.619 ( 2.10) 0.005 ( 3.17)

0.024 ( 0.45) 0.027 ( 0.47) 0.006 (0.71) 0.005 ( 1.17) 0.021 (1.12) 2.936 (0.99) 0.014 ( 1.52)

0.071 ( 0.95) 0.049 ( 0.65) 0.015 (1.19) 0.005 ( 1.00) 0.025 (0.96) 4.598 (1.14) 0.009 ( 0.81)

0.015 (0.53) 0.003 (0.10) 0.007 ( 1.64) 0.001 (0.27) 0.005 ( 0.58) 0.871 ( 0.67) 0.002 (0.48)

0.034 (3.15) 0.023 (2.82) 0.001 ( 1.33) 0.001 (0.76) 0.000 ( 0.23) 0.899 ( 2.01) 0.006 ( 2.67)

0.010 (0.55) 0.008 ( 2.98) 0.000 ( 0.01) 0.000 ( 0.43) 0.000 (0.01) 0.108 (0.63) 0.000 (0.19)

0.005 ( 0.19) 0.002 ( 2.56) 0.000 (0.09) 0.001 ( 1.08) 0.000 ( 0.39) 0.171 (1.20) 0.002 (1.59)

0.001 ( 0.09) 0.003 ( 2.48) 0.001 ( 2.44) 0.000 ( 0.44) 0.000 (0.53) 0.035 (0.31) 0.001 (0.42)

0.016 (1.53) 0.006 ( 0.90) 0.001 (3.24) 0.001 (1.73) 0.000 ( 0.33) 0.094 ( 1.17) 0.003 ( 2.17)

0.124

0.080

0.047

0.132

0.147

0.049

0.033

0.075

0.081

one, three, and five years after decile formation. Panel A of Table 8 shows the results of this exercise. Between 1981 and 2005, the attrition rates in the MVOi,t—based decile 10 at three (five) years after entry is 16.3% (22.1%), compared with 5.0% (7.1%) see words below for decile 1. These differences are statistically significant. One way to assess their economic significance is to compare them to average (unconditional) attrition rates. Carhart (1997) reports annual attrition rates of 3.5% per year. Clearly, the annual attrition rates in decile 10 are significantly higher than those. These attrition rates suggest that incumbent fund exit is correlated with the degree of post-entry incumbententrant overlap, but as is obvious from the earlier analysis, differences in attrition rates could be because of variation in size, turnover, and other such confounding attributes. Therefore, we also examine the relation between overlap measures and exit using a Cox proportional hazard model. This allows us to explicitly control for other covariates that may influence exit. The specific model that we estimate is Hi ðtÞ ¼ H0i ðtÞexpðb1 MVOit þ b2 LogðsizeÞit þ b3 LogðageÞit þ b4 Expensesit þ b5 Turnoverit Þ,

Post-1998

ð5Þ

Hi ðtÞ denotes the hazard, or the likelihood of exit, for incumbent i at time t. As unobserved fund characteristics can also influence the survival rate of incumbents, we assume the baseline hazard function H0i ðtÞ is fund-specific. This is equivalent to fitting separate Cox proportional hazard models under the constraint that the bi coefficients are equal across incumbents but not the baseline hazard functions. Panel B of Table 8 shows hazard ratios along with Z-scores in parentheses. Consistent with the univariate attrition results, hazard rates are correlated with our measures of overlap. Although the coefficients on MVOi,t and TruncMVOi,t are statistically significant in the entire sample period, it appears that the results are largely generated by the post-1998 sample period. In this latter subperiod, setting all variables to their mean, the baseline probability of exit is 10%. An onestandard-deviation increase in MVOi,t (TruncMVOi,t) increases the implied probability of exit to 12% (14%). 3.3.6. Interaction effects Entry does not take place in a vacuum—incumbents can take strategic and other actions to protect themselves


55

Table 8 The effect of entry on incumbent mutual fund survival. Panel A in this table presents attrition rates (in percent) of incumbent mutual funds in one-, three-, and five-years after entry on measures of overlap between incumbents and entrants. Panel B provides a Cox-model based survival analysis in the entire period, pre 1998 period and post-1998 period. Control variables for the Cox-model include fund size, age, expenses, and turnover. The incumbents that exist till the end of the sample period are marked as censored observations. The hazard ratio is reported with Z-score listed below. Full sample Decile

Panel A: Attrition rates 1(bottom) 2 3 4 5 6 7 8 9 10(top)

MVOi,t

TruncMVOi,t

One year

Three year

Five year

One year

Three year

Five year

2.3 1.6 2.2 2.7 3.4 3.7 4.4 5.3 6.0 8.9

5.0 3.4 4.5 5.5 7.1 7.5 8.8 10.3 11.6 16.3

7.1 5.0 6.8 8.1 10.6 10.9 12.5 15.0 16.5 22.1

1.9 1.3 1.9 2.7 3.2 4.0 4.8 5.0 6.3 9.4

4.3 2.8 4.2 5.5 6.8 8.3 9.4 9.9 12.0 17.0

5.9 4.1 6.4 8.5 9.7 11.9 13.4 14.5 17.1 23.0

Panel B: Cox proportional hazard models Full sample MVOi,t TruncMVOi,t Log(size)t Log(age)t Expensest Turnovert

1.035 (2.06) – 0.806 ( 42.82) 0.796 ( 13.20) 5.339 (14.44) 1.030 (3.23)

Pre-1998 – 1.013 (4.14) 0.791 ( 60.20) 0.800 ( 23.69) 2.235 (9.73) 1.027 (6.93)

from entrants, and entrants too can endogenously and strategically choose which markets to enter. A large literature in industrial organization points to spending on advertising, investment in research, capacity expansion to achieve lower unit costs, and other such mechanisms as ways in which incumbents deter entry (see, for example, Dixit, 1980; Schmalensee, 1982, 1983). Unfortunately, our data are inadequate for precisely testing for such barriers to entry. For example, investment in capacity (via, e.g., employment of human capital), and research are unobservable in our data. Even the simplest entry deterrent, advertising, is unavailable; Gallaher, Kaniel, and Starks (2008) show that advertising is related to flows but use proprietary data to do so. While we do not have context-rich data to address such interesting questions directly, incumbent defensive activities may be correlated with size (see, for example, Roberts and Supina, 2000; Joaquin and Khanna, 2001). In other words, the effects of competition may be ameliorated for larger incumbent funds, or those that belong to larger families; for instance, Gallaher, Kaniel, and Starks (2008) report that advertising expenditures are positively related to family size. To the extent that size serves as a proxy for more fundamental entry-deterrent characteristics, we estimate the regressions described earlier with interaction effects between

0.983 ( 0.71) – 0.828 ( 31.33) 0.775 ( 19.69) 3.470 (20.26) 0.951 ( 4.22)

Post-1998 – 1.007 (0.90) 0.830 ( 31.46) 0.775 ( 19.73) 3.530 (20.26) 0.951 ( 4.22)

1.077 (4.15) – 0.742 ( 57.38) 0.945 ( 4.02) 1.025 (4.30) 1.022 (5.47)

– 1.011 (2.65) 0.741 ( 57.69) 0.946 ( 3.98) 1.023 (4.36) 1.023 (5.50)

our measures of overlap and fund/family size. We estimate full regression specifications of the sort described in earlier tables but report only the coefficients on the overlaps and their interaction effects in Panel A of Table 9. The interaction effects are significant for changes in management fees, waivers, flows, and survival probabilities. For these dependent variables, as a general rule, the interaction effect has the opposite sign as the overlap variable. This implies that the effects of competition for funds belonging to larger families are smaller. Fund size has similar effects, albeit slightly weaker in statistical significance.22 It is also potentially interesting to examine whether the impact of entry could be related to the characteristics of entrants. For example, entry by certain entrants might have a larger impact on incumbents than others. Unfortunately, here too, we face difficult data problems. Characteristics of entrants can only be measured after entry, creating

22 In unreported results, we also explore two other interactions. Fund age generates results that are largely similar to those for size. This is not surprising since the two are correlated. In addition, for the fee waiver regressions, we also interact the overlap variables with a dummy equal to one (zero) if the management fee is above (below) the median. The results suggest that the effects of overlap are larger for high-fee funds.

56


Table 9 Interaction effects. The table shows coefficients on MVOi,t and TruncMVOi,t from regressions in which MVOi,t and TruncMVOi,t are interacted with incumbent-level characteristics (Panel A) or entrant-family characteristics (Panel B). The dependent variables in each of the regressions are identical to those shown in earlier tables: D Mgmt fee from quarter t +1 to t + 8, the fee waiver and flows in the year after entry, return gap in year two after entry, the four-factor alpha in 36 months post-entry, and Cox-model survival analysis. With the exception of survival analysis, the regressions are estimated with a full set of independent variables (not shown) as in prior tables for the post-1998 sample period. Fama-MacBeth t-statistics, corrected for serial correlation in timeseries estimates (up to four lags), are reported in parentheses below the estimates. For survival analysis, the hazard ratio is reported with Z-score listed below. Waiver

Flows

RGt + 8

Alpha

Survival

4.466 (2.01) 0.919 ( 1.84)

0.326 ( 1.88) 0.012 (0.29)

0.001 ( 0.06) 0.019 ( 1.41)

0.267 ( 0.67) 0.061 ( 1.24)

1.127 (6.78) 0.907 ( 3.32)

12.957 ( 2.81) 5.841 (2.66)

1.491 (1.85) 0.119 ( 2.19)

0.053 ( 2.36) 0.006 (0.52)

0.006 (0.71) 0.013 ( 0.89)

0.048 ( 1.81) 0.008 (0.78)

1.017 (6.66) 0.991 ( 2.09)

29.783 ( 33.01) 9.462 (2.27)

2.584 (3.31) 0.166 ( 2.21)

0.609 ( 2.22) 0.159 (1.96)

0.023 ( 0.27) 0.006 (2.03)

1.714 ( 2.61) 0.201 (2.07)

1.126 (4.16) 0.927 ( 2.35)

11.485 ( 2.64) 2.174 (2.17)

0.937 (3.47) 0.269 ( 2.65)

0.132 ( 2.23) 0.049 (2.01)

0.015 ( 0.46) 0.003 (1.89)

1.16 ( 1.79) 0.162 (1.84)

1.019 (4.03) 0.946 ( 3.37)

7.419 (1.01) 0.319 ( 1.76)

1.288 (0.37) 0.300 ( 1.84)

14.625 (1.24) 1.209 ( 1.22)

1.126 (2.46) 0.996 ( 0.82)

3.737 (2.10) 0.203 ( 1.74)

2.054 (1.03) 0.273 ( 2.21)

3.680 (1.59) 0.227 ( 1.27)

1.046 (2.01) 0.999 ( 0.82)

D Mgmt fee Panel A: Interaction effects with incumbent characteristics 33.413 MVOi,t ( 2.63) MVOi,tnlog(TNA) 11.387 (2.42) TruncMVOi,t TruncMVOi,tnlog(TNA) MVOi,t MVOi,tnlog(Family TNA) TruncMVOi,t TruncMVOi,tnlog(Family TNA)

Panel B: Interaction effects with entrant-family characteristics MVOi,t 18.299 3.495 ( 2.01) (2.11) MVOi,tnlog (Family TNA) 3.253 0.301 ( 0.26) (1.23) TruncMVOi,t TruncMVOi,tnlog(Family TNA)

2.484 ( 2.48) 9.552 ( 0.36)

1.034 (1.52) 0.939 (1.38)

3.3.7. Indexers and closet indexers We have thus far deliberately excluded index funds from our analysis because the right tail of the distribution of overlap would be comprised largely of index funds (entrant and incumbent index funds that track the same index should, by definition, have extremely high overlap and would therefore dominate the overall distribution). However, one should expect to see competitive effects in index funds as well. To investigate this, we separate out index funds and ‘‘closet indexers.’’23 We consider three types of incumbent-entrant pairs: (a) where both entrant and incumbent are pure indexers, (b) where the entrant is a pure indexer and the incumbent is

a closet indexer, and (c) where the entrant is a closet indexer and the incumbent is a pure index fund. We do not consider the last combination, where the entrant and incumbent are both closet indexers since they are included in our analysis of active funds.24 For each of these incumbent-entrant pairs, we estimate management-fee-change and flow regressions similar to those presented in earlier tables. Because sample sizes are much smaller, we cannot estimate Fama-MacBeth regressions, so instead we estimate panel regressions with dummies for each calendar year. Panel A (B) of Table 10 shows the results from the management-fee-change (flow) regressions. When the entrant is a closet indexer and the incumbent is a pure index fund, there is no discernible effect of our measures of overlap on incumbent fees. This is probably not surprising since it is unlikely that investors can readily and immediately identify closet indexers from their purported and stated goal as an active fund. When both incumbent and entrant are pure index funds, the effects of competition force should be readily observable because such funds are

23 To identify closet indexers, we use the active share measure of Cremers and Petajisto (2009). Active share is the extent to which an active fund’s portfolio differs from a benchmark index; funds with low active shares are regarded as closet indexers. We gratefully acknowledge the data on closed indexers provided by Antti Petajisto on his Web site.

24 Separately, we ensure that the results we report in earlier tables are not unduly influenced by closet indexers. To do this, we eliminate closet indexers from the data and re-estimate all regressions. The results are largely unchanged from those reported in the paper.

look-ahead (and possibly selection) problems with such an analysis. However, we can measure interactions with entrant family size since that is (exogenously) known at the time of entry. The results of those interactions are presented in Panel B. Here, for the most part, the interaction effects are statistically insignificant.


57

Table 10 Competitive effects for pure and closet indexers. Pure index funds are identified by the CRSP Mutual Fund database. Closet indexers are identified by Cremers and Petajisto (2009). Regressions are estimated separately for entrant-incumbent pairs. The first entry in the column heading shows the incumbent, the second shows the entrant. For example, in the ‘‘closet, pure’’ regressions, the incumbent is a closet indexer and the entrant is a pure index fund. Panel regressions are estimated with year dummies. Robust t-statistics appear in parentheses. (Incumbent, Entrant) pair (Pure, Pure) Panel A: D Mgmt fee regressions Intercept MVOi,t TruncMVOi,t Log (TNA)t Log (family)t Log (age)t Turnovert Std. deviation of returnst Panel B: Flow regressions Intercept MVOi,t

6.468 (2.49) 10.545 ( 2.05) – 0.489 (1.51) 0.356 ( 1.43) 1.823 ( 2.60) 3.142 ( 3.39) 12.825 ( 0.49) 0.298 (4.33) 0.353 ( 2.82)

TruncMVOi,t Return_rankt MVOi,tnReturn_rankt

0.071 (3.06) 0.257 (0.90)

TruncMVOi,tnReturn_rankt Log (TNA)t Log (age)t Expense ratiot Turnovert Front-end loadt Std. deviation of returnst

0.006 ( 0.71) 0.067 ( 3.25) 3.483 ( 1.21) 0.038 (3.31) 2.018 (2.09) 0.224 ( 0.39)

(Closet, Pure)

6.275 (2.43) – 3.026 ( 1.87) 0.519 (1.62) 0.362 ( 1.45) 1.815 ( 2.59) 3.153 ( 3.40) 12.692 ( 0.49) 0.279 (4.12)

0.189 ( 2.09) 0.070 (3.04) – 0.326 (1.27) 0.004 ( 0.48) 0.066 ( 3.40) 3.404 ( 1.18) 0.038 (3.15) 2.015 (2.08) 0.195 ( 0.34)

transparent. Consistent with this, fees and flows for this subgroup of incumbent-entrants are negatively associated with overlaps—what should be a competitive commodity market appears to behave as one. When the entrant is a pure index fund and the incumbent is a closet indexer, the effects are modestly negative but statistically very weak. Overall, it appears that when investors can clearly identify the substitutability of passive funds, we observe competitive effects in both flows and fees.

4. Robustness and empirical issues Three aspects of these results deserve special attention. First, the dependent variables in each of our tests are

2.651 (1.08) 18.745 ( 1.85) – 0.488 (1.46) 0.029 (0.13) 1.495 ( 2.46) 0.181 (0.25) 49.148 ( 1.84) 0.153 (3.75) 1.395 ( 3.27)

0.080 (6.72) 0.637 (2.21)

0.007 ( 2.09) 0.074 ( 3.97) 0.632 (0.41) 0.016 (2.29) 0.042 (0.14) 0.984 (2.74)

(Pure, Closet )

2.479 (1.01) – 0.912 ( 1.73) 0.516 (1.55) 0.026 (0.12) 1.498 ( 2.47) 0.187 (0.26) 49.378 ( 1.85) 0.165 (4.07)

0.267 ( 1.80) 0.084 (7.11) – 0.051 (1.50) 0.007 ( 1.91) 0.074 ( 3.99) 0.595 (0.39) 0.016 (2.34) 0.053 (0.18) 0.907 (2.52)

1.403 (0.39) 7.886 ( 0.68) – 0.323 (0.69) 0.169 ( 0.47) 0.975 ( 1.03) 4.667 ( 3.84) 19.198 (0.46) 0.321 (3.18) 0.563 ( 1.01)

0.099 (2.82) 0.475 (0.75)

0.008 ( 0.71) 0.069 ( 2.71) 5.317 (1.38) 0.005 (1.14) 1.636 (1.17) 0.449 (0.45)

1.253 (0.35) – 0.536 ( 0.44) 0.348 (0.48) 0.170 ( 0.47) 0.997 ( 1.05) 4.658 ( 3.83) 19.473 (0.47) 0.323 (3.13)

0.609 ( 0.93) 0.098 (2.80) – 0.375 (0.73) 0.008 ( 0.71) 0.069 ( 2.69) 5.341 (3.85) 0.004 (1.11) 1.582 (1.13) 0.431 (0.43)

measured after entry. But theory provides no guidance regarding the horizon over which to measure each variable. For instance, in the case of changes in fees, it is not obvious whether we should compute changes one quarter, one year, two years, or five years after entry. In most cases, our choices are guided by data constraints and estimation concerns. For example, we need at least 36 months of monthly returns to estimate alphas, but can estimate characteristic-based returns over shorter horizons (and do so). In other cases, we make choices such that a sufficient amount of time elapses to reflect changes in the data (e.g., we measure return gaps one and two years after entry). Our basic results are unchanged by small-horizon changes to the tests. Second, many of our regressions are estimated on a quarter-by-quarter basis using a Fama-MacBeth approach.

58


This is because we measure overlap every quarter. However, some of our dependent variables are measured annually. To ensure that these timing differences do not influence our results, we re-estimate the regressions annually after summing overlap measures within a year. Obviously, this reduces the number of time-series observations and in some cases, increases standard errors. But our general inferences remain the same. Third, the relations between overlap measures and flows, costs, performance, and survival are only prevalent in the post-1998 period. This begs the obvious question: Is there anything special about 1998? The answer is no. We chose 1998 as a breakpoint in our subperiod analysis because of the Chow Test results in Table 1. But, we re-estimate all our regressions using 1997 and 1999 as breakpoints and present the results in an online appendix. Our results are robust to whether we use 1997 or 1999 to bifurcate our sample. This is not surprising. From 1981 to the early 1990s, the number of entrants and incumbents appears to be continually increasing (along with total assets under management), suggesting an expansion of the industry. A likely source of this expansion is the increased use of mutual funds by retail investors (as opposed to directly investing in stocks), but this is impossible to verify without direct flow-of-funds data. The late 1990s, however, are characterized by a decline in the number of entrants and in the entrant-to-incumbent ratio. This suggests a slowing down in the industry’s expansion. While we cannot estimate price-cost margin models of endogenous entry, the time-series of entry is consistent with it being endogenous. If it is true that the profitability of entry declined in the late 1990s, then entrants must necessarily eke out an existence by competing with incumbents—that is the essence of our results.

5. Conclusions A critical mechanism of competitive markets is that entrants compete for revenues and resources with incumbents. In this paper, we study the effects of the entry of new mutual funds on the prices, revenues, costs, performance, and survival of incumbent funds. A particular advantage of looking at incumbents is that they are unaffected by endogenous entry. Post-entry prices charged by entrants are endogenously related to the decision to enter, but this endogeneity does not influence incumbent behavior—instead, entry is simply a shock to which incumbents react. We find that measures of overlap in holdings between entrants and incumbents are related to both price and quantity competition: incumbents that face stiff competition reduce management fees and experience lower flows. However, distribution costs rise so that benefits to consumers are not as large. We also find that our measures of overlap are marginally related to incumbent trading costs and to future performance. Finally, entrantincumbent overlap is related to the future survival rates, confirming Darwinian notions embedded in the idea of competitive markets. On the whole, the picture that emerges is one of a competitive market.

References Barber, B., Odean, T., Zheng, L., 2005. Out of sight, out of mind: the effects of expenses on mutual fund flows. Journal of Business 78, 2095–2119. Berry, S., Reiss, P., 2007. Empirical models of entry and market structure. In: Armstrong, M., Porter, R. (Eds.), The Handbook of Industrial Organization, vol. 3. Elsevier Science, North Holland, pp. 1845–1886 (Chapter 29). Bresnahan, T., Reiss, P., 1991. Entry and competition in concentrated markets. Journal of Political Economy 99, 977–1009. Carhart, M., 1997. On persistence in mutual fund performance. Journal of Finance 52, 57–82. Casavecchia, L., Scotti, M., 2009. Dynamic setting of mutual fund fees in the US mutual fund industry. Unpublished working paper. University of Technology Sydney. Christoffersen, S., 2001. Why do money fund managers voluntarily waive their fees? Journal of Finance 56, 1117–1140. Coates, J., Hubbard G., 2007. Competition in the mutual fund industry: evidence and implications for policy. Unpublished working paper, Harvard Law School. Cremers, M., Petajisto, A., 2009. How active is your fund manager? A new measure that predicts performance. The Review of Financial Studies 22, 3329–3365. Daniel, K., Grinblatt, M., Titman, S., Wermers, R., 1997. Measuring mutual fund performance with characteristic-based benchmarks. Journal of Finance 52, 1035–1058. Dixit, A., 1980. The role of investment in entry-deterrence. The Economic Journal 90, 95–106. Elton, E., Gruber, M., Busse, J., 2004. Are investors rational? Choices among index funds. Journal of Finance 59, 261–288. Fama, E., French, K., 2010. Luck versus skill in the cross-section of mutual fund returns. Journal of Finance 65. Freeman, J., Brown, S., 2001. Mutual fund advisory fees: the cost of conflicts of interest. Journal of Corporation Law 26, 609–673. Freeman, J., 2008. Responding to the advisory fee analysis in AEI working paper #127, ‘‘Competition and Shareholder Fees in the Mutual Fund Industry: evidence and Implications for Policy’’ by John Coates and R. Glenn Hubbard. Unpublished working paper, University of South Carolina. Friedman, M., 1953. In: The Methodology of Positive Economics, in Essays in Positive Economics. University of Chicago Press, Chicago, II, pp. 2–43. Gallaher, S., Kaniel, R., Starks, L., 2008. Advertising and mutual funds: from families to individual funds. Unpublished working paper, University of Texas at Austin. Geroski, P.A., 1995. What do we know about entry? International Journal of Industrial Organization 13, 421–440. Gil-Bazo, J., Ruiz-Verdu, P., 2009. Yet another puzzle? The relation between price and performance in the mutual fund industry. Journal of Finance 64, 2153–2183. Grinblatt, M., Titman, S., Wermers, R., 1995. Momentum investment strategies, portfolio performance, and herding: a study of mutual fund behavior. American Economic Review 85, 1088–1105. Hortac-su, A., Syverson, C., 2004. Product differentiation, search costs, and competition in the mutual fund industry: a case study of S&P 500 index funds. Quarterly Journal of Economics 119, 403–456. Joaquin, D., Khanna, N., 2001. Investment timing decisions under threat of potential competition: why firm size matters. The Quarterly Review of Economics and Finance 41, 1–17. Kacperczyk, M., Sialm, C., Zheng, L., 2008. Unobserved actions of mutual funds. Review of Financial Studies 21, 2379–2416. Khorana, A., Servaes, H., 1999. The determinants of mutual fund starts. Review of Financial Studies 58, 2033–2058. Khorana, A., Servaes, H., 2004. Conflicts of interest and competition in the mutual fund industry. Unpublished working paper, Georgia Institute of Technology. Khorana, A., Servaes, H., Tufano, P., 2005. Explaning the size of the mutual fund industry around the world. Journal of Financial Economics 78, 145–185. Kosowski, R., Timmermann, A., Wermers, R., White, H., 2006. Can mutual fund ‘‘stars’’ really pick stocks? New evidence from a bootstrap analysis. Journal of Finance 61, 2551–2595. Kuhnen, C., 2007. Social networks, corporate governance, and contracting in the mutual fund industry. Unpublished working paper, Northwestern University. Li, S.J., 2005. Financial product differentiation and fee competition in the mutual fund industry, working paper, AXA Rosenberg Group.


Roberts, M., Supina, D., 2000. Output price and markup dispersion in micro data: the roles of producer heterogeneity and noise. In: Baye, M. (Ed.), Industrial Organization, Advances in Applied Microeconomics, vol. 9. JAI Press, Stamford, CT, pp. 1–36. Schmalensee, R., 1982. Product differentiation advantages of pioneering brands. American Economic Review 72, 349–365. Schmalensee, R., 1983. Advertising and entry deterrence: an exploratory model. Journal of Political Economy 91, 636–653. Sensoy, B., 2009. Performance evaluation and self-designated benchmark indexes in the mutual fund industry. Journal of Financial Economics 92, 25–39. Sirri, E., Tufano, P., 1998. Costly search and mutual fund flows. Journal of Finance 53, 1589–1622. Spatt, C., 2006. Office of Economic Analysis Memorandum (to Investment Company File S7-03-04).

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Trzcinka, C., 1998. Statement, hearing before the subcommittee on finance and hazardous materials of the committee on commerce, house of representatives, 105 Congress, 2nd Session. Wallison, P., Litan, R., 2007. In: Competitive Equity: A Better Way to Organize Mutual Funds. AEI Press, Washington, DC. Walsh, L., 2004. The costs and benefits to fund shareholders of 12b-1 Plans: an examination of fund flows, expenses and returns. Unpublished working paper, Securities and Exchange Commission. Wermers, R., 2000. Mutual fund performance: an empirical decomposition into stock-picking talent, style, transactions costs, and expenses. Journal of Finance 55, 1655–1695. Wermers, R., Tong, Yao, Jane, Zhao, 2007. The investment value of mutual fund portfolio disclosure. Unpublished working paper, University of Maryland.




Speculative capital and currency carry trades$ ¨ Matti Suominen n Petri Jylha, Aalto University, PL 1210, Helsinki 00101, Finland


abstract

Article history: Received 19 November 2008 Received in revised form 9 December 2009 Accepted 5 January 2010 Available online 1 August 2010

In this paper, we study a two-country general equilibrium model with partially segmented financial markets, where hedge funds emerge endogenously. Empirically, we show that the hedge fund investment strategy predicted by our model, which we call the ‘‘risk-adjusted carry trade’’ strategy, explains more than 16% of the overall hedge fund index returns and more than 33% of the fixed income arbitrage sub-index returns. The flow of new money to hedge funds affects market interest rates, exchange rates, and both the hedge funds’ contemporaneous and expected future returns as predicted by the model. & 2010 Elsevier B.V. All rights reserved.

JEL classifications: G15 F31 E43 Keywords: Hedge funds Currency speculation Carry trades

1. Introduction In this paper, we study currency speculation by hedge funds. In the theoretical part of the paper, we study a twocountry general equilibrium model with partially segmented financial markets, where hedge funds emerge endogenously. As in Fama and Farber (1979), the interest rates and the foreign exchange rate are determined by the two countries’ inflation risks and money supplies. In our model,

$ We are grateful to Jussi-Pekka Lyytinen for initiating our interest in currency carry trade research. This paper was previously circulated under the title ‘‘Arbitrage Capital and Currency Carry Trade Returns.’’ We thank Richard Levich (the referee), Rui Albuquerque, Peter Christoffersen, Robin Greenwood, Denis Gromb, Harald Hau, Markku Lanne, Massimo Massa, Stefan Nagel, Vasant Naik, Robert Kosowski, Dimitri Vayanos, Adrien Verdelhan and the seminar participants at INSEAD, Helsinki School of Economics, Bank of Finland, 2009 AFA Meetings in San Francisco, Spring 2008 Adam Smith Asset Pricing Conference at LSE, 2009 SED meetings in Istanbul, and INFINITI 2009 for comments. Jylha¨ thanks the Finnish Foundation for Advancement of Securities Markets and both authors thank the Okobank Group Research Foundation for financial support. n Corresponding author. Tel.: +358 50 5245678; fax: + 358 9 43138678. E-mail address: matti.suominen@hse.fi (M. Suominen).


some of the agents are restricted, and can invest only in domestic fixed income securities, while others, speculators, can borrow and invest freely in all available fixed income securities. When the number of speculators is small, and the two countries’ inflation shocks are highly correlated, all speculators invest in a hedge fund that borrows from the country with the lower Sharpe ratio for fixed income securities and invests in the country with the higher Sharpe ratio. We refer to this strategy as the ‘‘risk-adjusted carry trade’’ investment strategy. When the barriers to international investments are reduced, more investors invest in the hedge fund. The flow of new money to the hedge fund affects market interest rates, the exchange rate, the hedge fund’s leverage, and both its contemporaneous and expected future returns.1 Empirically, we test the predictions of the model using a sample of 11 currencies and 30 years of data. First, our

1 The foreign exchange market has historically been partly segmented due to various barriers in foreign exchange transactions. Also, behavioral barriers, for instance due to lack of knowledge or overestimation of risks, may be important.

P. Jylh¨ a, M. Suominen / Journal of Financial Economics 99 (2011) 60–75

results show that hedge funds do, in fact, engage in the type of currency speculation that our model predicts. The returns from a simple investment strategy, where long and short currency portfolios are formed on the basis of the rankings of the currencies by their expected Sharpe ratios, explains more than 16% of the overall hedge fund index returns and more than 33% of the fixed income arbitrage sub-index returns. The explanatory power of our strategy’s returns is significant even when controlling for the seven Fung and Hsieh (2004) factors that are commonly used to explain hedge fund returns. Under certain assumptions, the investment strategy predicted by our model is identical to the simple carry trade investment strategy, where the long and short portfolios are formed on the basis of interest rate and not Sharpe ratio rankings. Empirically, the returns and portfolio compositions of these two strategies are highly correlated and the returns from the simple carry trade strategy explain equally well the returns of various hedge fund indexes. Second, we show that the increased hedge fund assets under management (AUM) and positive inflows of funds to hedge funds decrease the expected returns from the two carry trade strategies, and decrease interest rates in high Sharpe ratio (high interest rate) countries while increasing the interest rates in low Sharpe ratio (low interest rate) countries. In addition, the flow of funds to hedge funds affects exchange rates, appreciating (depreciating) the exchange rate of the high (low) Sharpe ratio, or high (low) interest rate, currencies. In the fall of 2008, there was a large outflow of funds from the hedge fund industry. In accordance with our theoretical predictions and empirical results, the effect was opposite to hedge fund inflows and as a result of the large outflows from the funds, the low Sharpe ratio (low interest rate) currencies appreciated significantly relative to the high Sharpe ratio (high interest rate) currencies.2 Our paper is connected to an emerging stream of literature on partial market segmentation and limited speculative capital. Gromb and Vayanos (2002) study a segmented market model, similar to ours, where some investors are only allowed to invest in one of the two risky assets, whereas others are allowed to invest in both. In Vayanos and Vila (2009), fixed income markets are endogenously segmented by investors’ differing preferences for different maturities (preferred habitat), while a limited number of arbitrageurs act as a market integrating force. Their model is tested empirically in Greenwood and Vayanos (2008). In these papers, the capital engaged in speculation is limited by either speculators’ financing constraints or their risk aversion. Other papers that study models with limited speculative capital include DeLong, Shleifer, Summers, and Waldmann (1990), Shleifer and Vishny (1997), Kyle and Xiong (2001), and Brunnermeier and Pedersen (2009). One recent paper in this strand of literature—which is very close in spirit to ours and deals with currency speculation—is Brunnermeier, Nagel, and Pedersen (2009). Empirically, they show that carry trades 2 The currency movements in the fall of 2008 were extreme: for instance, the currency with the lowest interest rate, the Japanese yen, appreciated relative to the currency with the highest interest rate, the British pound, by 40% in just a few months.

61

are subject to currency crash risk, i.e., the exchange rate movements of carry trade portfolios are negatively skewed. They argue that the skewness in foreign exchange rates follows from temporary changes in the availability of funding liquidity to speculators. A temporary reduction in funding liquidity results in a rapid unwinding of traders’ positions and thus leads to abrupt changes in exchange rates, which go against the carry traders. This risk, the authors argue, is a major factor affecting traders’ willingness to enter into these ‘‘risk arbitrage’’ positions and arbitrage away the positive returns to carry trades. Their risk-based explanation of carry trade returns complements ours and our finding that hedge fund flows affect both contemporaneous and expected carry trade returns.3, 4 Second, our paper is related to the literature on carry trade profitability, such as Burnside, Eichenbaum, Kleshchelski, and Rebelo (2006) and Lustig, Roussanov, and Verdelhan (2008). We argue, and provide evidence, that one driver of the profitability of the simple carry trade strategy is the number of funds engaging in carry trades. Third, our results are related to the literature on the forward premium puzzle, that is, the observed failure of the uncovered interest rate parity (see, e.g., Bilson, 1981; Fama, 1984; Froot and Thaler, 1990; Bekaert, 1996; Engel, 1996; or Bansal and Dahlquist, 2000).5 In line with Fama and Farber (1979) and Grossman (1995), our results suggest that the failure of the uncovered interest rate parity is due to compensation for risks. In addition, however, our evidence suggests that the historically observed large returns to strategies exploiting the forward premium puzzle, such as carry trades, were due to segmented markets and the gradual integration of fixed income securities markets during the past few decades.6 The rest of the paper is organized as follows: In Section 2, we present the model and in Section 3 the theoretical results. Sections 4–8 contain the empirical part of the paper. We present the data in Section 4. In Section 5,

3 One additional related paper is Gârleanu, Pedersen, and Poteshman (2009), which examines the pricing of different option contracts when market makers’ ability to engage in arbitrage is limited. 4 Also related is the earlier literature on segmented markets and covered interest rate parity. See, for instance, Keynes (1923), Einzig (1961), and Grubel (1965). See also Prachowny (1970), who studies deviations from covered interest rate parity in a model with less than infinitely elastic supply and demand of forward currency. 5 Other relevant papers on this topic include Cumby (1988), Backus, Gregory, and Telmer (1993), Bekaert, Hodrick, and Marshall (1997), Hollifield and Uppal (1997), Mark and Wu (1998), Roll and Yan (2000), Backus, Foresi, and Telmer (2001), Lyons (2001), Gourinchas and Tornell (2004), Lustig and Verdelhan (2007), Albuquerque (2008), Farhi and Gabaix (2008), Wagner (2008), Alvarez, Atkenson, and Kehoe (2009), Bansal and Shaliastovich (2009), Burnside, Eichenbaum, and Rebelo (2009), Burnside, Han, Hirshleifer, and Wang (2010), Plantin and Shin (2010), and Verdelhan (2010). 6 Finally, our paper is also related to the hedge fund literature. Baquero and Verbeek (2009) and Wang and Zheng (2008) show a positive contemporaneous relation between hedge fund flows and returns and Wang and Zheng (2008) and Avramov, Barras, and Kosowski (2009) find evidence of a negative relation between flows and future returns. Our study offers one channel through which flows have a positive return effect on the existing positions but decrease the future expected returns. Our results also complement those of Fung and Hsieh (2000) and Ding, Getmansky, Liang, and Wermers (2007) who study the impact of hedge funds on the financial markets as a whole.

62


we study whether hedge funds are involved in currency speculation. In Section 6, we study how hedge fund flows affect the returns from currency speculation. In Section 7, we look at the effect of hedge fund flows on interest rates, while in Section 8 we examine their effect on exchange rates. Section 9 concludes the paper. 2. The model Our model combines elements from Fama and Farber (1979) and Bacchetta and van Wincoop (2006). Our main point of departure from the former is to assume partially segmented financial markets. Consider a model with two countries, referred to as countries i and j (with no particular order). In both countries, there are N citizens, where N is normalized to one. The citizens produce and consume a single commodity and, as in Bacchetta and van Wincoop (2006), use money in the production of this commodity. Money used in production in period t is recovered at its full nominal value at the beginning of the next period t + 1. In particular, we assume that country i’s citizens’ production function generates f(mi,t) goods in period t + 1, where mi,t denotes agents’ real money holdings of country i’s currency in period t. We assume that f(mi,t) is increasing and concave in mi,t. The purchasing power of country i’s money in period t is denoted by pi,t, so that M units of country i’s currency have a real purchasing power of mi,t =Mpi,t. The future purchasing power of money is random at time t, so that given information available at time t, "

#

"

p~ i,t þ 1 Et p~ i,t þ 1 p~ j,t þ 1 Nðm; RÞ where m ¼ Et p~ j,t þ 1 2

#

max uðc~ t þ 1 Þ ¼ Et eac~ t þ 1

mi,t ,bi,t ,bj,t

3

s2i rsi sj 5: and R ¼ 4 rsi sj s2j

agents, who live for two periods, invest when they are young and consume when they are old.8 Before dying, they sell their money holdings to the next generation. To obtain closed form expressions for asset prices, we assume that period t investors value their random period t +1 consumption using a constant absolute risk aversion (CARA) utility function, maximizing their expected utility, uðc~ t þ 1 Þ ¼ Et eac~ t þ 1 , where a denotes the parameter of risk aversion and c~ t þ 1 their random consumption in period t+ 1. Furthermore, let us denote by bi,t the quantity of country i’s nominal zero-coupon bonds, with a face value of one, that an agent purchases (or sells) in period t in addition to his short position in country i’s bonds, that comes from hedging his currency holdings.9 Similarly, let bj,t refer to purchases of country j’s bonds. We assume that the financial markets are segmented in the following way: a fraction (1 ki)4 0 of country i’s investors have prohibitively high transaction costs of investing abroad, i.e., to hold money or interest-bearing securities in a foreign currency. Fraction ki of country i’s investors, on the other hand, are unrestricted. We call the restricted investors ‘‘domestic investors’’ and the unrestricted ones ‘‘speculators.’’ In both countries, there is a onetime cost f of becoming a speculator and the number of speculators is determined endogenously.10 In contrast to the financial markets, there are no barriers, such as tariffs or transportation costs, in the product market.11 Therefore, assuming period t investors are endowed with a real wealth wt, after choosing whether to become a speculator, country i’s investors at time t maximize:

st:

ð1Þ

Here, Et refers to the expectation operator conditioned on time t information set and a tilde on top of a variable is used to denote a random variable.7 Besides money, there are two other storage technologies in each country: first, a risk-free asset that pays a periodic constant real return rf, and second, a one-period default free zero-coupon bond, sold at a real market price pi,t, that pays one unit of country i’s nominal currency at time t + 1. The risk in this asset comes from the uncertain purchasing power of money in period t + 1. Both risky assets are in zero net supply. Like Fama and Farber (1979), we assume that all consumers first hedge their money holdings in the bond market, and only then look at their investments into bonds. In this case, the effective supply of zero-coupon bonds in the market, denoted in country i’s currency, is country i’s money supply, M i . Our consumers are myopic. Like Bacchetta and van Wincoop (2006), we assume overlapping generations of 7 We take the expected future purchasing power of money Et p~ i,t þ 1 as exogenous to the model, as it is driven, for example, by future money supply.

8 c~ ¼ ðwt mi,t þ pi,t mi,t =pi,t Is fÞð1 þ rf Þ þ f ðmt Þ > < tþ1 þ bi,t ðp~ i,t þ 1 pi,t ð1 þrf ÞÞþ bj,t ðp~ j,t þ 1 pj,t ð1 þ rf ÞÞ > : 9b 9 r x: j,t

ð2Þ

8 Other papers that assume myopic agents in dynamic asset pricing models include Campbell, Grossman, and Wang (1993) and Vives (1995). 9 If an agent’s real money holdings are mi,t, we assume he sells short Mi,t = mi,t/pi,t zero-coupon bonds to hedge his money holdings before considering any other investments into bonds. 10 In our model, f proxies for several different types of real and informational barriers to becoming a currency trader. Examples of these are all regulatory barriers, the direct costs from setting up a currency account, with a facility for foreign currency borrowing, and the costs from acquiring information on the expected returns and risks related to currency trading. In the theoretical part below, we study what happens when f decreases. This is motivated by the observation that the barriers to currency trading most likely decreased during our sample period, i.e., during the last three decades. This, we argue, occurred due to (1) loosening of foreign exchange controls and the associated financial market integration, (2) the emergence of currency hedge funds that are marketed to an ever-increasing fraction of the population, (3) the globalization of media that has increased awareness of currency trading opportunities, and (4) academic research that has pointed out the failure of the uncovered interest rate parity and provided investors with estimates of the historical returns to currency carry trades. 11 This assumption is made for simplicity and because of the focus of the paper. Including some barriers in the product market, such as tariffs and transportation costs, and studying the product market flows, and deviations from purchasing power parity (PPP), might bring some additional economic insights but would result in a more complicated model.


63

3. Equilibrium and model predictions

higher in the country with the higher per capita inflation risk, M i si .12 Let us denote by H the country with the higher per capita inflation risk and by L the country with the lower per capita inflation risk. In the case of autarkies, the higher Sharpe ratio in country H, as compared to country L, is necessary to attract sufficient investment into the risky bonds of country H, in order to clear the market, despite the higher amount of risk being sold. Let us now look at the speculators’ problem. The first order condition of (2) with respect to the speculators’ investment into country i’s bonds, bsi,t, implies

3.1. Equilibrium

bsi,t ¼

There are no restrictions in the product market. Therefore, for all currency transactions, purchasing power parity (PPP) implies that the period t exchange rate, at which country j’s currency can be exchanged to country i’s currency, is

Again, the i and j sub-indexes refer to the currency in which the investment is made. Using (4) and (5) in (8), we can now solve for the equilibrium bond holdings. Solving the set of equations, we obtain that, in equilibrium, all speculators hold

Here, Is is an indicator function that takes the value of one if and only if the investor is a speculator. The second constraint in the agents’ maximization problem is related to financial market segmentation as follows: for domestic investors, x= 0, while for speculators, x= N. Equilibrium prevails when each agent’s action maximizes his expected utility. Finally, note that country i’s citizens do not benefit from country j’s currency in their production activities.

pj,t : pi,t

i=j

St ¼

ð3Þ

Define Mdi,t as the per capita supply of country i’s zerocoupon bonds that must, in equilibrium, be purchased by the domestic investors of country i at time t. Here, as well as below, we use a superscript d to denote a domestic investor and a superscript s to denote a speculator. In other words, if the speculators buy (ki + kj)bsi,t units of country i’s bonds, we define Mdi,t as d Mi,t

M i ðki þ kj Þbsi,t

¼

1ki

:

ð4Þ

Here, we have assumed, as we show later to be the case, that speculators from both countries hold identical bond portfolios. The sub-index i in bsi,t refers to the country in whose currency the investment is made. Now, setting x =0 in (2), taking expectations and the first-order condition of (2) with respect to domestic investors’ bond holdings, bdi,t, d and using the market clearing condition, bdi,t ¼ Mi,t , we obtain that the price of the zero-coupon bond, pi,t, in country i at time t is pi,t ¼

d Et p~ i,t þ 1 as2i Mi,t

1 þ rf

:

ð5Þ

The expected real return from investing in the nominal bonds, i.e., the equilibrium real interest rate, ri,t, is ri,t ¼

d 2 rf þ aMi,t si =Et p~ i,t þ 1 Et p~ i,t þ 1 pi,t ¼ : d s2 =E p pi,t 1aMi,t t ~ i,t þ 1 i

ð6Þ

The standard deviation of the real return from investing in nominal bonds of country i is si/pi,t. Therefore, the Sharpe ratio for the real returns from bond investments is SRi,t ¼

ri,t rf

si =pi,t

d ¼ aMi,t si :

bsi ¼

as2i

:

ð8Þ

M i si ð1 þ ki ÞM j sj rð1ki Þ si ðð1r2 Þð1 þ kj ki Þ þ ð1 þ r2 Þðkj þ ki ÞÞ

ð9Þ

of country i’s bonds, while the domestic investors hold

bdi ¼ Mid ¼ ¼

Mi ðki þkj Þbsi 1ki

M i si ð1þ ki r2 þ r2 kj Þ þ Mj sj rðki þkj Þ si ðð1r2 Þð1 þ kj ki Þ þ ð1 þ r2 Þðkj þ ki ÞÞ

ð10Þ

of such bonds. The asterisk is used to denote an equilibrium value. Using (10) in Eqs. (5)–(7) gives us an easy characterization of the equilibrium interest rates, bond prices, and the Sharpe ratios of bonds in our economy. Given (3), the exchange rate is determined by the purchasing power of the two currencies as follows: Taking the first-order condition of (2) with respect to mi,t, we obtain that for both the speculators and the domestic investors: ð@f ðmi,t Þ=@mi,t Þ pi,t ¼ 1 pi,t ð1 þrf Þ " # ð@f ðM i pi,t Þ=@pi,t Þ ¼ 1 pi,t gðMi , pi,t Þ: ð11Þ M i ð1 þrf Þ Recall that f ðmi,t Þ ¼ f ðM i pi,t Þ is an increasing and concave function of mi,t. This implies that it is also an increasing and concave function of pi,t. Assuming that inflation risk is small enough so that country i’s bond price (5) is positive, this implies that gðMi , pi,t Þ is a strictly increasing function of pi,t, so that for every M i , it has an inverse function g 1 ðM i ,pi,t Þ ¼ pi,t , that is strictly increasing in pi,t. The exchange rate can now be stated as a function of the two countries zero-coupon bond prices as follows:

ð7Þ

These results show that the bond price (interest rate) is decreasing (increasing) in the parameter of risk aversion, a, inflation risk, si, and the per capita supply of bonds in the domestic market, Mdi,t. In the case of an autarky, where ki d and kj are zero, Mi,t ¼ M i , the local money supply. In such perfectly segmented markets, the Sharpe ratio for bonds is

Et p~ i,t þ 1 pi,t ð1 þ rf Þbsj,t arsi sj

i=j

St ¼

pj,t g 1 ðMj ,pj,t Þ ¼ : pi,t g 1 ðMi ,pi,t Þ

ð12Þ

12 Here, per capita inflation risk simply refers to the total amount of inflation risk in the money supply of a given currency divided by the number of investors in that country. This is the amount of inflation risk that each investor must carry in equilibrium in an autarky.

64


segmentation exceeds the minimal degree of segmentation needed to induce speculation (i.e., when kL ok L ). In more integrated markets, where kL 4k L , the speculators’ investments are ‘‘long only.’’ It is intuitive that there are no

Let us now look at the determination of the number of speculators. As ki o1 by assumption, it must be that the benefit of becoming a speculator is less than or equal to the cost of becoming one. In other words,

ui ðc~ dtþ 1 Þ ebi ½Et pi,t þ 1 pi,t ð1 þ rf Þ þ ða=2Þbi si ¼ bs ðE p p ð1 þ r ÞÞbs ðE p p ð1 þ r ÞÞ þ ða=2Þðbs2 s2 þ bs2 s2 þ 2bs bs rs s Þ þ fð1 þ r Þ r 1: t j,t þ 1 t i,t þ 1 j,t i,t i j f f f ui ðc~ st þ 1 Þ j i i i j j i j e d

d2

Using (5) and (10), we can rewrite (13) as a bd2 s2 þ absj bdj s2j þ absi bdi s2i 2 i i a 2 s s ðbs2 s2 þ bs2 ð14Þ j sj þ 2bj bi rsi sj Þ r fð1þ rf Þ: 2 i i Furthermore, Eqs. (13) and (14) must hold as strict equalities when ki 4 0. From (14), it is easy to see that, as the condition is symmetric apart from the first term, the first speculators come from country L, as for an arbitrary small number of speculators bdi M i and M H sH 4 M L sL . Speculators from country H enter only after MLd sL ¼ MHd sH , or alternatively, given (7), when the Sharpe ratios of the bonds in the two countries are equal. We have now completed the characterization of the equilibrium. 3.2. Hedge funds, hedge fund flows, interest rates, and exchange rates As we demonstrate below, in segmented markets, the speculators invest in a hedge fund. Let us start by defining the following two critical parameters:

r

M L sL , M H sH

ð15Þ

MH sH rM L sL : M H sH r þ M L sL

ð16Þ

and kL

For reasons provided in Proposition 1, we call r the minimal level of inflation risk correlation to induce speculation and kL the minimal degree of segmentation needed to induce speculation. We now move on to our propositions, which are proved in Appendix A. Proposition 1. When correlation between inflation shocks is high enough, r 4 r, and the markets are sufficiently segmented, kL o kL , the speculators’ portfolio is a ‘‘currency hedge fund’’ with a short position in currency L and a long position in currency H. The expected returns to the speculators’ hedge fund are positive. The leverage in the speculators’ hedge fund, as defined by bsL , approaches infinity when r-1 and max{kL,kH}-0. The leverage decreases as the number of speculators increases. Here, as well as below, we refer to the speculators’ collective portfolio as a hedge fund when it contains both short and long positions in currencies. As all speculators hold identical portfolios, it is as if they all invested their wealth in the same fund. It is interesting to note that in our model the speculators’ fund is a hedge fund only in sufficiently segmented markets, i.e., when market

2

ð13Þ

hedge funds in highly integrated markets. In perfectly integrated markets, both high and low inflation risk currencies are part of the global market portfolio that all agents hold in some positive quantities in equilibrium, as in Fama and Farber (1979). Proposition 2. Assume r 4 r and kL o kL . A reduction in f, the cost of becoming a speculator, leads to an increase in the number of speculators (which is equivalent to the flow of assets to the hedge fund), the convergence of the Sharpe ratios of the two countries’ domestic bonds, and a decrease in the expected future returns to the speculators’ hedge fund. A decrease in f, through an increase in the number of speculators, leads to a rise in rL and a decrease in rH, a rise in bond price pH, and a decrease in bond price pL, and an increase in the exchange rate SL=H ¼ pH =pL . An increase in the number of speculators in period t affects positively the contemporaneous returns to the period t-1 speculators’ hedge fund. As Proposition 2 shows, an increase in the number of speculators affects interest rates and brings the two countries’ real interest rates and zero-coupon bond prices closer to each other. As bond prices drive the real purchasing power of the currencies, the exchange rate (12) is also affected. The interest rates and the exchange rate move toward values that they would have in an integrated economy with better risk sharing. Hedge funds have commonly been associated with simple currency carry trades (see, e.g., Galati, Heath, and McGuire, 2007), where the investors borrow in the low interest rate currency and invest in the high interest rate currency. When argmaxðMid si ,Mjd sj Þ ¼ argmaxðMid s2i =Et pi,t þ 1 ,Mjd s2j =Et pj,t þ 1 Þ,

ð17Þ the speculators’ hedge fund in our model engages in simple currency carry trades. In other words, in this case, currency L is also the currency with the lower interest rate. Note that the fact that the two strategies are not equal implies that sometimes the speculators’ optimal strategy is to borrow in the high interest rate (but low Sharpe ratio) currency and invest in the low interest rate (but high Sharpe ratio) currency. In this case the speculators invest in the high Sharpe ratio currency, borrowing at the real risk-free rate, and use the short position in the low Sharpe ratio currency to hedge their investment. The possible difference in the real interest rates that may occur in equilibrium due to variations in inflation risks and partial market integration leads to the failure of the uncovered interest rate parity. Denoting by Ri,t the period t nominal interest rate in country i, noting that the rate of inflation in country i equals pi,t =Et pi,t þ 1 1, the uncovered


interest rate parity is violated in equilibrium whenever i=j

ð1þ Ri,t Það1þ Rj,t Þ

Et ðSt þ 1 Þ i=j St

3 ð1 þ ri,t Þ

pi,t Et pi,t þ 1

að1 þrj,t Þ

pj,t Et pj,t þ 1

3 ri,t arj,t :

Et pj,t þ 1 =Et pi,t þ 1 pj,t =pi,t ð18Þ

In our model, this occurs whenever investors are riskaverse and Mid s2i =Et pi,t þ 1 aMjd s2j =Et pj,t þ 1 . The failure of the uncovered interest rate parity (UIP), when it occurs, is an equilibrium phenomenon. Under the assumption that Eq. (17) holds, the failure of UIP is larger, i.e., the ratio of the right- and left-hand sides of (18) is further away from one when financial markets are segmented than when they are integrated.13 4. The data We use a panel data set with data related to 11 main currencies spanning the time period from January 1979 to December 2008.14 The data are on a monthly frequency and contain 3120 currency-month observations. The selection of sample currencies and time period is driven by the availability of reliable data. Although ours is not a complete sample, we cannot think of any favorable systematic bias arising from the fact that not all possible currencies at all times have been included in our data set.15 Testing the predictions of the model requires data on interest rates, exchange rates, inflation risks, per capita money supplies, and hedge fund flows, which we use as a proxy for the change in the number of speculators. First, we obtain end-of-month interbank spot and one-month forward exchange rates as well as one-month interbank interest rates from Datastream. To find a proxy for the time-varying inflation risk, ht, denoting by et the period t inflation shock, we estimate the following AR(1)GARCH(1,1) model for the rate of inflation, dt: dt ¼ b0 þ b1 dt1 þet ,

et Nð0,h2t Þ,

h2t ¼ g0 þ g1 h2t1 þ g2 e2t1 :

ð19Þ

The model is estimated individually for each country using Organisation for Economic Co-operation and Devel13 Note that as investors become less risk averse, so that a-0, the interest rates in both countries approach the risk-free rate, given (6), and hence, the UIP will hold in the limit. 14 The sample currencies are the main currencies of the Euro area (Belgium, France, Germany, Italy, and the Netherlands), Canada, Japan, Switzerland, the United Kingdom, and the United States. Data for the Euro legacy currencies end in December 1998 and data for the Euro area begin in January 1999. Our sample currencies are the same as those used by Burnside, Eichenbaum, Kleshchelski, and Rebelo (2006). 15 On the contrary, we believe that these countries provide for conservative tests of our hypotheses. Our sample consists of major industrial countries with developed financial markets and broadly comparable monetary policy. We believe that finding evidence of capital restrictions and their effect on financial markets in this set of countries is more revealing than in a broader set of countries including those with less-developed financial markets.

65

opment (OECD) data on the monthly rate of year-over-year inflation. We use the mean equation for dt as inflation forecasts and the time-varying variance term, h2t as our proxy for the inflation risk. This approach is similar to those used by Grier and Perry (1998) and Hwang (2001), among others. Our proxy for per capita money supply is M2 divided by the respective country’s stock market capitalization. As the stock market capitalization reflects the size of the financial markets, we believe this ratio captures well a given country’s citizens’ ability to bear the inflation risk related to its monetary assets, thus capturing the intuition of the model.16 The data on M2 are from International Monetary Fund (IMF), National Bank of Belgium, Bank of England, and Mitchell (1992). These data are on a monthly frequency. In the few cases where monthly observations were not available, we calculated monthly estimates assuming that the growth of M2 between annual observations was constant. Stock market capitalizations are from Datastream and World Federation of Exchanges.17 Our proxy for the proportion of speculators is the hedge fund industry’s total assets under management (AUM) divided by the total M2 money supply of the sample countries. The procedure for estimating the hedge fund industry’s AUM is described in Appendix B. Fig. 1 shows the historical development of the hedge fund AUM divided by the total M2 money supply. The total hedge fund AUM grew from just over 0.2% of the total M2 in 1976 to over 6% in 2007. The development of the AUM occurs in cycles, where periods of rapid growth are followed by sharp falls. The last two sharp falls in the AUM were triggered by the Long-Term Capital Management (LTCM) hedge fund crisis in 1998 and the 2008 global financial crisis. We use the net flow of the new assets to hedge funds as our proxy for the change in the number of speculators. Flow is calculated as the difference between the change in the funds’ AUM and the funds’ monthly dollar returns. As before, we normalize the figures by dividing them by M2.18 We use the flow, rather than change in AUM, because of endogeneity problems related to the latter. We believe that using the asset flows is free of endogeneity problems as hedge funds typically require a notification period of up to several months prior to subscriptions and redemptions. The procedure for estimating flows is described in Appendix B. Panel A of Table 1 provides the basic summary statistics of the key variables and rates of changes of the variables.

16 Second, in a more general model, such as Fama and Farber (1979), the market portfolios include the equity markets. In such a model, the relative sizes of the money supply and the equity market affect the covariance of inflation risk with the market portfolio, which in turn affects the equilibrium risk premium in nominal fixed income assets and the equilibrium interest rate in any given country. 17 We use M2 instead of M3, for example, as this is available for all countries during our sample period. 18 The normalization is done either using the aggregate M2 of our sample currencies or, in the case of panel regressions, using individual countries’ M2. The latter approach can be justified by noting that hedge fund flows are likely to have an amplified effect on interest rates and exchange rates of small currencies.

66


6%

Hedge fund AUM per M2

5%

4%

3%

2%

1%

0% 1979

1984

1989

1994 Year

1999

2004

2009

Fig. 1. Historical development of hedge fund assets under management. This figure shows the monthly development of the hedge fund industry’s total assets under management (AUM) divided by the total M2 money supply of the sample countries (Belgium, Canada, Euro area, France, Germany, Italy, Japan, the Netherlands, Switzerland, the United Kingdom, and the United States) from 1979/1 to 2008/12. Sources: Hennessee, HFR, Lipper TASS, authors’ estimates (see Appendix B for details).

5. Do hedge funds engage in currency speculation? Our model predicts that in sufficiently non-integrated markets, speculators set up a hedge fund that borrows in currencies with low Sharpe ratios and invests in currencies with high Sharpe ratios. We refer to this strategy as the ‘‘risk-adjusted carry trade’’ strategy. When (17) holds, this strategy corresponds to the simple currency carry trade strategy, where investors borrow in low interest rate currencies and invest in high interest rate currencies. In this paper, we report the results based on both strategies. We do so because the results related to simple carry trade investments are of interest on their own, as this particular investment strategy is popular and has been widely discussed in the literature. The results are quantitatively and qualitatively similar for the two investment strategies, as the returns and portfolio compositions of the two strategies are highly correlated. We consider the following investment strategies. At the end of each month, we rank the currencies according to their interest rates or estimated Sharpe ratios, which is defined as the nominal interest rate minus the expected inflation divided by the standard deviation of unexpected inflation. We borrow funds in the currencies that rank in the bottom third and invest in the top-third currencies. At the end of the next month, a new ranking is composed and new positions are entered into, accordingly. The borrowing and investing in currencies is executed through short and long positions in one-month currency forwards against the British pound.19 When analyzing the effects of currency

19 The choice of numeraire is inconsequential as the resulting short and long positions in the numeraire currency cancel out.

speculation in the subsequent sections of this paper, we assume that all traders follow these particular strategies.20 Our first prediction is that the expected returns to this type of currency speculation are positive. Panel A of Table 1 presents the descriptive statistics for the monthly gross returns from our two investment strategies, and Fig. 2 shows the cumulative return, in British pounds, to a constant GBP 100-size investment in the two long-short portfolios. The mean monthly return from the simple carry trade strategy is 0.47%, which corresponds to a 5.63% annual return. The standard deviation of the monthly returns is 2.06%, resulting in a monthly Sharpe ratio of 0.228 (0.789 annualized). The results for the risk-adjusted carry trade strategy are similar, with somewhat lower mean and higher standard deviation. The monthly Sharpe ratio of this strategy is 0.159.21, 22 Panel B of Table 1 presents the means of the key variables and their changes when a currency belongs to the lowest-third (‘‘short’’) or the highest-third (‘‘long’’) based

20 Our simple carry trade strategy differs somewhat from that used by Burnside, Eichenbaum, Kleshchelski, and Rebelo (2006) and Burnside, Eichenbaum, and Rebelo (2007) who take a long position in all the currencies that have a higher interest rate than the British pound and take a short position in all the currencies that have a lower interest rate than the British pound. Our approach of leaving out middle-ranking currencies matches that commonly used in the asset pricing literature and is similar to that used for currencies by Lustig and Verdelhan (2007) and Lustig, Roussanov, and Verdelhan (2008). 21 Since these are zero-investment strategies, Sharpe ratio is simply the average of returns divided by the standard deviation of returns. 22 To allow for some comparison, over the same time period, the US stock market had an average monthly return of 0.96%, monthly standard deviation of 4.51%, and monthly Sharpe ratio of 0.109 (0.376 annualized). Our results, related to simple carry trades, are in line with those by Burnside, Eichenbaum, Kleshchelski, and Rebelo (2006), allowing for the fact that their method of constructing portfolios slightly differs from ours.


67

Table 1 Descriptive statistics. Panel A gives the means, standard deviations, medians, and the 25th and the 75th percentiles of the variables used in this study. Panel B presents the means for those currency-month observations that belong to the carry trade short or long portfolios, respectively. Interest rate is the one-month interbank interest rate, inflation forecast is based on Eq. (19), inflation risk is the annualized standard deviation of the error term of the inflation Eq. (19), money supply is M2 scaled by stock market capitalization, exchange rate and forward premium are expressed per an equal-weighted basket of the other sample currencies, country specific hedge fund flow is the net flow of new assets to hedge funds, in dollars, scaled by the M2 money supply of the country, noncountry specific hedge fund flow is the net flow of new assets to hedge funds, in dollars, scaled by the total M2 money supply of all the sample countries, risk-adjusted carry trade is the monthly return to Sharpe ratio ranking-based investment strategy, carry trade is the monthly return to our carry trade strategy, and hedge fund AUM is the assets under management of the hedge fund industry scaled by the total M2 money supply of the sample countries. D denotes monthly change in the variable. The sample period is from 1979/1 to 2008/12 and the sample countries are Belgium, Canada, Euro area, France, Germany, Italy, Japan, the Netherlands, Switzerland, the United Kingdom, and the United States. All data are on a monthly frequency. The number of observations for country specific variables is 3120 and for non-country specific variables, the number of observations is 360. Mean Panel A: Descriptive statistic Country specific Interest rate D Interest rate Inflation forecast D Inflation forecast Inflation riska D Inflation riskb Money supply D Money supply D Exchange rate Forward premium D Forward premium Hedge fund flowc Non-country specific Risk-adjusted carry trade Carry trade Hedge fund AUM Hedge fund flow ( 100)c

Std.

25%

75%

0.0691 0.0002 0.0366 0.0001 0.0135 0.0002 2.0477 0.0042 0.0000 0.0000 0.0000 0.0035

0.0465 0.0128 0.0329 0.0037 0.0141 0.1600 3.6562 0.0570 0.0209 0.0029 0.0011 0.0142

0.0363 0.0024 0.0170 0.0020 0.0097 0.0754 0.7599 0.0367 0.0112 0.0018 0.0002 0.0003

0.0597 0.0000 0.0276 0.0000 0.0116 0.0387 1.2670 0.0064 0.0002 0.0001 0.0000 0.0009

0.0938 0.0014 0.0456 0.0018 0.0143 0.0180 1.8429 0.0253 0.0110 0.0016 0.0002 0.0040

0.0034 0.0047 0.0192 0.0158

0.0215 0.0206 0.0181 0.0448

0.0049 0.0050 0.0036 0.0015

0.0048 0.0067 0.0125 0.0066

0.0147 0.0172 0.0325 0.0321

Risk-adjusted carry trade

Panel B: means Interest rate D Interest rate Inflation forecast D Inflation forecast Inflation riska D Inflation riskb Money supply D Money supply D Exchange rate Forward premium D Forward premium Hedge fund flowc

Median

Carry trade

Short

Long

Short

Long

0.0486 0.0012 0.0339 0.0000 0.0153 0.0035 1.9647 0.0046 0.0009 0.0018 0.0001 0.0035

0.0877 0.0013 0.0395 0.0003 0.0111 0.0097 2.1837 0.0034 0.0010 0.0019 0.0001 0.0033

0.0387 0.0002 0.0204 0.0001 0.0131 0.0012 1.4849 0.0023 0.0000 0.0029 0.0000 0.0040

0.0982 0.0007 0.0533 0.0002 0.0141 0.0032 3.2781 0.0032 0.0002 0.0030 0.0001 0.0027

a

The level of inflation risk is expressed as the annualized standard deviation of the error term of the inflation Eq. (19). Changes in inflation risk and money supply are expressed as changes in the logarithmic value as they enter the regressions in this form. The country specific hedge fund flow uses the country’s M2 as the scaling variable, whereas the non-country specific flow uses the total M2 of all the sample countries. b c

on our rankings of the sample currencies. Note that the real interest rates (nominal interest rate minus expected inflation) are higher for the long than the short currencies. Note also that the long currencies have higher per capita money supply when compared to the short currencies. This corresponds to our intuition that speculators should borrow from capital rich countries, such as Switzerland, Germany, or Japan, where M2 per stock market capitalization (or M2 per investor) is small, and invest the proceeds in less wealthy economies. Our second prediction is that hedge funds should invest in these types of currency carry trading strategies. Table 2

presents the correlation between returns from our two currency trading strategies and select Credit Suisse/ Tremont Hedge Fund indexes. The returns from our strategies are highly correlated with the returns from various hedge fund indexes, indicating that hedge funds do, indeed, apply similar strategies to those that we have identified. Both of our strategies’ returns are highly correlated with the overall hedge fund index returns as well as with the returns to fixed income arbitrage, global macro, and multi-strategy sub-indexes. Incredibly, the risk-adjusted carry trade strategy explains 16% of the overall hedge fund

68


200 Risk-adjusted carry trade Trend, risk-adjusted carry trade Carry trade Trend, carry trade

British pounds

150

100

50

0 1979

1984

1989

1994

1999

2004

2009

Year Fig. 2. Cumulative performance of carry trade strategies. This figure shows the cumulative return, in British pounds, to a constant GBP 100-size investment in carry trade strategies from 1979/1 to 2008/12. The solid lines present the cumulative carry trade returns and the dotted lines present second-order polynomial trends fitted to the cumulative return data.

Table 2 Correlations with hedge fund returns. This table presents the correlations between currency carry trade returns and various hedge fund indexes. Results in column 1 are based on the risk-adjusted carry trade strategy, and results in column 2 are based on returns to the simple carry trade strategy. Monthly return data for the hedge fund indexes are from Credit Suisse/Tremont and span the period from 1994/1 to 2008/12 (180 observations), except for multi-strategy for which data begin in 1994/4 (177 observations). t-values are reported in parentheses for the test that the correlation is equal to zero.

All hedge funds Fixed income arbitrage Global macro Multi-strategy

(1)

(2)

0.4029 (5.87) 0.5779 (9.45) 0.3608 (5.16) 0.3550 (5.02)

0.3246 (4.58) 0.4106 (6.01) 0.2873 (4.00) 0.2495 (3.41)

(2004) by adding the returns to our trading strategies as the eighth factor.24 The results of regressing the returns of the broad hedge fund index as well as global macro, fixed income arbitrage, and multi-strategy indexes on the seven and eight factors are reported in Table 3. All four hedge fund indexes presented have a statistically significant exposure to the currency carry trade factors, even in the presence of the other seven factors. The currency carry trade factors appear to be especially important for the global macro funds. The inclusion of the simple carry trade factor increases the model’s power to explain variation in global macro funds’ returns, measured by R2, from 19% to 28%. These findings suggest that hedge funds in general, and global macro and fixed income arbitrage funds in particular, engage in currency speculation using carry trades.

6. Hedge fund flows and returns to carry trades index returns and 33% of the fixed income arbitrage subindex returns.23 To test if the returns to our currency trading strategies are significant in the presence of other risk factors, we regress the hedge fund index returns on a number of previously used risk factors as well as the returns from our two carry trade strategies. More precisely, we extend the seven hedge fund risk-factor model of Fung and Hsieh

23 Some additional evidence related to hedge funds’ exposure to individual currency carry trade pairs is presented in McGuire and Upper (2007). Our results related to simple carry trades are similar to those in Lyytinen (2007), who shows a positive correlation between currency carry trade and hedge fund returns, and Pojarliev and Levich (2008, 2010) who show that currency hedge fund returns are highly correlated with an index of carry trade returns.

Proposition 2 predicts that as barriers to international currency investments become smaller, new investors invest into hedge funds that engage in currency speculation. As the number of hedge fund investors increases, as the funds’ investments affect market prices, the expected returns from the currency speculation strategies applied by hedge funds decrease. The fitted polynomial trends to 24 The seven factors used by Fung and Hsieh (2004) are three trendfollowing factors (for bonds, currencies, and commodities; Fung and Hsieh, 2001), an equity market factor (Standard & Poor’s 500), a size spread factor (Russell 2000 minus Standard & Poor’s 500), a bond market factor (monthly change in the ten-year treasury constant maturity yield), and a credit spread factor (monthly change in the Moody’s Baa yield minus ten-year treasury constant maturity yield). Data for the trendfollowing factors are available on David Hsieh’s Web site: http://faculty. fuqua.duke.edu/ dah7/DataLibrary/TF-FAC.xls.


69

Table 3 Carry trade factor in hedge fund index returns. This table presents the results of regressing returns of four hedge fund indexes on the seven risk factors introduced by Fung and Hsieh (2001) and currency carry trade returns. Results in columns 2, 5, 8 and 11 are based on returns to risk-adjusted carry trade strategy, and results in columns 3, 6, 9, and 12 are based on simple carry trade returns. Monthly return data for the hedge fund indexes are from Credit Suisse/Tremont and span the period from 1994/1 to 2008/12 (180 observations), except for multi-strategy for which data begin in 1994/4 (177 observations). Data for the Fung and Hsieh factors are available at http://faculty.fuqua.duke.edu/ dah7/HFRFData.htm. Autocorrelation- and heteroskedasticity-consistent t-values (Newey and West, 1987) are reported in parentheses. All hedge funds (1)

Global macro (2)

(3)

Fixed income arbitrage

(4)

(5)

(6)

(7)

(8)

0.0055 0.0044 0.0042 0.0091 0.0075 0.0071 0.0040 (4.56) (3.83) (3.66) (4.75) (3.73) (3.45) (3.48) Bond trend 0.0294 0.0270 0.0263 0.0295 0.0260 0.0246 0.0158 ( 2.60) ( 2.50) ( 2.33) ( 1.88) ( 1.70) ( 1.50) ( 2.17) Currency trend 0.0099 0.0171 0.0181 0.0152 0.0257 0.0280 0.0095 (1.34) (2.27) (2.51) (1.06) (1.85) (2.10) ( 1.56) Commodity trend 0.0182 0.0188 0.0206 0.0191 0.0200 0.0229 0.0085 (1.63) (1.93) (2.12) (0.98) (1.14) (1.27) (1.20) Equity market 0.2568 0.2714 0.2666 0.1414 0.1630 0.1567 0.0047 (5.48) (6.66) (6.91) (1.70) (2.17) (2.19) ( 0.13) Size spread 0.1643 0.1507 0.1598 0.0471 0.0271 0.0400 0.0052 (2.89) (2.72) (3.07) (0.70) (0.43) (0.67) ( 0.30) Bond market 0.0191 0.0118 0.0197 0.0378 0.0269 0.0386 0.0207 ( 3.20) ( 1.84) ( 3.75) ( 4.77) ( 3.50) ( 5.13) ( 4.15) Credit spread 0.0261 0.0085 0.0172 0.0380 0.0120 0.0240 0.0651 ( 2.84) ( 0.80) ( 2.28) ( 2.48) ( 0.70) ( 1.93) ( 5.38) Currency speculation 0.2992 0.3054 0.4417 0.4786 (3.63) (3.58) (2.93) (2.83) R2 0.468 0.535 0.532 0.187 0.271 0.276 0.502 Monthly observations 180 180 180 180 180 180 180

0.0031 (2.82) 0.0139 ( 1.93) 0.0040 ( 0.80) 0.0090 (1.58) 0.0067 (0.21) 0.0158 ( 0.94) 0.0149 ( 3.04) 0.0513 ( 6.00) 0.2346 (4.65) 0.574 180

Constant

Risk-adjusted carry trade 0.8% Mean (left scale) Sharpe (right scale)

(11)

(12)

0.4

0.37 Mean (left scale) Sharpe (right scale)

0.6%

0.3

0.2 0.28%

0.4%

0.2

0.38% 0.15

Sharpe ratio

0.4%

Mean return

0.27 Sharpe ratio

Mean return

(10)

0.0033 0.0062 0.0058 0.0059 (2.77) (5.04) (4.71) (4.67) 0.0141 0.0067 0.0052 0.0054 ( 1.99) ( 0.64) ( 0.49) ( 0.51) 0.0052 0.0071 0.0100 0.0093 ( 1.02) (1.12) (1.72) (1.69) 0.0098 0.0034 0.0037 0.0040 (1.54) (0.48) (0.57) (0.59) 0.0005 0.0398 0.0450 0.0419 (0.02) (1.27) (1.42) (1.38) 0.0077 0.0226 0.0167 0.0212 ( 0.44) (0.83) (0.64) (0.78) 0.0210 0.0086 0.0054 0.0086 ( 4.48) ( 1.73) ( 1.10) ( 1.80) 0.0603 0.0421 0.0350 0.0397 ( 5.21) ( 4.75) ( 4.38) ( 4.49) 0.1640 0.1227 0.0840 (2.75) (2.20) (1.14) 0.534 0.298 0.322 0.309 180 177 177 177

0.69% 0.3

0.51%

(9)

Carry trade 0.8%

0.4

0.6%

Multi-strategy

0.12 0.17% 0.09

0.2%

0.1

0

0% 500bn (2001-2008)

Hedge fund AUM, USD

0.17% 0.09

0.2%

0%

0.1

0 500bn (2001-2008)

Hedge fund AUM, USD

Fig. 3. Carry trade performance and hedge fund assets under management. This figure shows the monthly mean returns (black bar, left scale) and Sharpe ratios (grey bar, right scale) of the two carry trade strategies when the total hedge fund assets under management has been below USD 100 billion (1979– 1992), between USD 100 billion and USD 500 billion (1993–2000), and above USD 500 billion (2001–2008).

the cumulative returns from the two carry trade strategies, shown in Fig. 2, suggest that the returns from our strategies have indeed been decreasing over time, as the volume of assets under management in hedge funds has grown. To show this change in the profitability in another way, we divide our sample period into three sub periods based on the total hedge fund assets under management

and present the returns and the Sharpe ratios for the two strategies in each of the time periods in Fig. 3. During the first period, when hedge fund AUM is below USD 100 billion, the average monthly return to simple carry trade is 0.69% (0.51% for the risk-adjusted carry trade) whereas it is only 0.17% (0.17%) during the last period when hedge fund AUM is over USD 500 billion.

70


Table 4 Returns to carry trades and hedge fund flows. This table gives the results of regressing monthly returns to currency carry trades on proxies of the number of speculators and changes therein. Results in columns 1 and 2 are based on returns to a risk-adjusted carry trade strategy, and results in columns 3 and 4 are based on returns to a simple carry trade strategy. The proxy for the number of speculators is the total hedge fund assets under management (AUM) scaled by the total M2 money supply of the sample countries. The proxy for changes in the number of speculators is the net flow of new funds to hedge funds, scaled by the total M2 money supply of the sample countries. Mkt-R, HML, and SMB are the three Fama and French (1993) risk factors. The sample period is from 1979/1 to 2008/12. Autocorrelation- and heteroskedasticityconsistent t-values (Newey and West, 1987) are reported in parentheses. Dependent: carry trade return Constant Hedge fund flow Hedge fund AUM (t 1) Mkt-Rf SMB HML R2 Monthly observations

(1)

(2)

(3)

(4)

0.0053 0.0045 0.0073 0.0067 (3.29) (2.73) (4.75) (4.38) 10.1932 8.9559 8.9945 8.1611 (1.69) (1.70) (3.75) (3.47) 0.1832 0.1609 0.2133 0.1967 ( 1.90) ( 1.85) ( 3.57) ( 3.35) 0.0640 0.0486 (1.64) (1.88) 0.0045 0.0188 ( 0.10) (0.48) 0.0714 0.0380 (1.59) (0.93) 0.053 0.068 0.056 0.065 360 360 360 360

Table 5 Changes in interest rates, inflation risk, money supply and hedge fund flows. This table gives the results of regressing monthly changes in interest rates on lagged changes in interest rate, changes in forecasted inflation, logarithm of inflation risk (fitted value from a GARCH(1,1) model on monthly inflation), logarithm of money supply (M2 divided by stock market capitalization), and hedge fund flow (scaled by M2 money supply). Hedge fund flow is interacted with the position variable (equal to one if the country is in the long portfolio during the month, negative one if the country is in the short portfolio during the month, and zero otherwise) to allow for opposite effects for high and low Sharpe ratio (or interest rate) countries. The position variable in column 1 is based on Sharpe ratio ranking, and in column 2 on interest rate ranking. The sample period is from 1979/1 to 2008/12 and the sample countries are Belgium, Canada, Euro area, France, Germany, Italy, Japan, the Netherlands, Switzerland, the United Kingdom, and the United States. Country and month fixed effects are included in the estimation. Autocorrelationand heteroskedasticity-consistent t-values (Arellano, 1987) are reported in parentheses. Dependent: D interest rate

D Interest rate (t 1) D Inflation forecast D Log(inflation risk) D Log(money supply) Position Hedge fund flow Position Hedge fund flow

Further, the monthly Sharpe ratio of the simple (risk-adjusted) carry trade strategy decreases from 0.37 (0.27) in the first period to only 0.09 (0.09) in the last period. To study further the relation between the number of speculators and the currency carry trade returns, we regress the returns from the two trading strategies on the previous month’s hedge fund AUM and the current month’s hedge fund flow and report the results in Table 4. The hedge fund AUM has a negative and statistically significant effect on the returns to the simple carry trade strategy, whereas the current month’s hedge fund flow has a significant positive effect. These results, consistent with Proposition 2, hold for both raw returns (column 3) and Fama and French (1993) three-factor risk-adjusted returns (column 4). The results also exhibit economic significance. For instance, according to our estimates for the last 5 years of the sample period (2004–2008), a one-standard deviation increase in hedge fund flows results in a 0.8% increase in the simple carry trade returns, which corresponds to about 40% of this strategy’s returns’ standard deviation during the same period. The results related to the riskadjusted carry trades are of the predicted direction, but their statistical significance is weak.

7. Hedge fund flows and interest rates Proposition 2 predicts that an increase in the number of speculators will decrease (increase) the interest rate in the high (low) per capita inflation risk countries. To test this

R2 Monthly observations

(1)

(2)

0.3197 ( 9.30) 0.0997 (2.24) 0.0014 (2.15) 0.0153 (2.19) 0.0366 ( 3.78) 0.0024 (3.79) 0.0218 ( 1.87) 0.288 3120

0.3133 ( 9.34) 0.0741 (1.68) 0.0007 (1.32) 0.0161 (2.31) 0.0292 ( 2.76) 0.0019 (4.14) 0.0192 ( 1.75) 0.278 3120

prediction, we regress the changes in the interest rates on hedge fund flows and changes in other determinants of interest rates in our model, namely forecasted inflation, inflation risk, and M2 per stock market capitalization. The inflation forecasts are calculated as one-step-ahead forecasts from the inflation model presented in Eq. (19). Since the changes in interest rates exhibit strong negative autocorrelation, we also include the lagged interest rate change as an explanatory variable. As we expect the hedge fund flows (corresponding to changes in the number of speculators) to have opposite effects on interest rates in high and low Sharpe ratio countries, or, assuming (17) holds, on high and low interest rates, we include an indicator variable in the regression to indicate whether the country belongs to a currency speculators’ short or long portfolio and interact this indicator variable with the hedge fund flows. The indicator variable, Position, equals minus one for countries that belong to the lowest one-third in the Sharpe ratio, or interest rate, ranking, plus one for countries that belong to the highest one-third, and zero for the rest. Results of regressing the changes in interest rates on changes in inflation forecast, inflation risk, money supplies, and the Position times the hedge fund flows are presented in Table 5. The Position variable is based on the Sharpe ratio rankings in column 1 and on the interest rate rankings in column 2.


71

Carry trade

Risk-adjusted carry trade 8

8

Long Short

Long Short 6 Sharpe ratio

Sharpe ratio

6

4

4

2

2

0

0

1984

1989

1994

1999

2004

2009

Year

1984

1989

1994

1999

2004

2009

Year

Fig. 4. Sharpe ratios of fixed income investments. This figure shows the development of the average Sharpe ratios of the 1-month fixed income securities in long and short countries of the two carry trade strategies. The Sharpe ratio is defined as the nominal return on the fixed income asset minus expected inflation divided by the standard deviation of unexpected inflation. To smooth out random noise, the graphs depict 5-year moving averages of the Sharpe ratios. The sample period is from 1984/1 to 2008/12.

Changes in interest rates are positively and statistically significantly related to changes in both inflation risk and money supply, providing empirical support for the baseline model. The finding that inflation risk is a significant determinant of interest rates is in line with studies such as Shen (1998) and Buraschi and Jiltsov (2005) that show positive and significant inflation risk premiums in nominal interest rates. The hedge fund flows have a significant effect on interest rates in the direction predicted by the theoretical model: positive flow decreases (increases) the interest rates in high (low) Sharpe ratio, or interest rate, countries. Over the last five years of the sample period (2004–2008), the time-series standard deviation of hedge fund flows per M2 was about 2%. Hence, a one-standard deviation increase in hedge fund flows would result, on average, in a 0.07% decrease (increase) in interest rates in the high (low) Sharpe ratio currencies. Such a change corresponds to about 29% of the standard deviation of interest rate changes over the same period, which is economically significant.25 Proposition 2 further predicts that the Sharpe ratios of the fixed income assets in high- and low-interest rate countries should converge over time as the number of speculators increases. Such convergence is evident in Fig. 4, which shows the average Sharpe ratios for the long and short currencies in the two strategies.26

25 Similarly, a one-standard deviation increase in hedge fund flows would result, on average, in a 0.06% decrease (increase) in interest rates in the high (low) interest rate currencies which corresponds to 23% of the standard deviation of interest rate changes. 26 In addition, it seems that the Sharpe ratios for fixed income investments in general have fallen over time, possibly reflecting better risk sharing in integrated markets.

8. Hedge fund flows and exchange rates A final prediction of the model is that hedge fund flows (corresponding to changes in the number of speculators) affect exchange rates. The prediction is that inflows (outflows) to hedge funds will lead to an appreciation (depreciation) of high (low) Sharpe ratio or, assuming (17) holds, high (low) interest rate currencies. We examine this effect by regressing the changes in spot exchange rates on hedge fund flows, and forward premium, and present the results in Table 6. As we expect the hedge fund flows to have opposite effects on high and low Sharpe ratio (or interest rate) currencies, we interact the hedge fund flows with the Position variables described in Section 7. The Position variable is based on the Sharpe ratio rankings in column 1 and on the interest rate rankings in column 2. The spot exchange rate change is calculated for each currency against a basket containing all the other currencies in the sample. In this way, we mitigate problems arising from using a single currency as a numeraire. The effect of hedge fund flows on spot exchange rates is significantly positive. During months of positive flows, high Sharpe ratio (or high interest rate) currencies appreciate and low Sharpe ratio (or low interest rate) currencies depreciate. Based on estimates from the last 5 years of the sample period (2004–2008), a one-standard deviation increase in hedge fund flows would, on average, result in a 0.09% appreciation (depreciation) in the exchange rate of the high (low) Sharpe ratio currencies. Such a change corresponds to about 4% of the standard deviation of exchange rate changes over the same period, which is economically significant.27

27 Similarly, a one-standard deviation increase in flows would, on average, result in a 0.19% appreciation (depreciation) in the exchange rate

72


Table 6 Changes in exchange rates and number of speculators. This table gives the results of regressing monthly changes in spot exchange rates on the level of forward premium, the change in forward premium, and hedge fund flow (scaled by M2 money supply). Hedge fund flow is interacted with the position variable (equal to one if the country is in the carry trade long portfolio during the month, minus one if the country is in the carry trade short portfolio during the month, and zero otherwise) to allow for opposite effects for high and low Sharpe ratio (or interest rate) currencies. The position variable in column 1 is based on Sharpe ratio ranking, and in column 2 on interest rate ranking. The spot exchange rate change is calculated for each currency as a change in the value of the currency against a basket containing all the other currencies in the sample. Hence, a positive (negative) change indicates appreciation (depreciation) of the currency. The sample period is from 1979/1 to 2008/ 12 and the sample countries are Belgium, Canada, Euro area, France, Germany, Italy, Japan, the Netherlands, Switzerland, the United Kingdom, and the United States. Country fixed effects are included in the estimation. Autocorrelation- and heteroskedasticity-consistent t-values (Arellano, 1987) are reported in parentheses. Dependent: D exchange rate Forward premium (t 1)

D Forward premium Position hedge fund flow Position Hedge fund flow R2 Monthly observations

(1)

(2)

0.6226 (1.70) 1.2247 (2.27) 0.0466 (2.71) 0.0017 (3.19) 0.0177 (0.64) 0.015 3120

0.4620 (1.34) 1.1491 (2.01) 0.0941 (2.21) 0.0023 (2.07) 0.0439 (1.41) 0.016 3120

The results above are in line with those of Evans and Lyons (2002) who find, using daily data, that deal flow explains a large part of variation in exchange rates. The difference is that we are able to trace the origin of some of the deal flow to hedge funds engaged in currency speculation. A similar prediction to ours—that carry trades affect exchange rates—is present in Plantin and Shin (2010) and Brunnermeier, Nagel and Pedersen (2009). During the latter half of 2008, hedge funds experienced a dramatic outflow of capital, with the total industry AUM falling from almost USD 2 trillion by the end of June to USD 1.4 trillion by the end of the year. During this time period, the hedge fund redemptions totaled 17.5% of AUM which corresponds to 4.3 times the standard deviation of the semi-annual flows. At the same time, consistent with Proposition 2, high Sharpe ratio (high interest rate) currencies depreciated significantly while low Sharpe ratio (low interest rate) currencies appreciated. On average, the carry trade short currencies based on the Sharpe ratio (interest rate) rankings appreciated by 6.2% (15.4%) while the carry trade long currencies depreciated by 10.9 (11%) relative to baskets of all other currencies. The magnitude of these currency changes is, on average, 2.2 (3.6) times the standard deviation of the semi-annual exchange rate changes. Based on the estimates in Table 6, hedge fund

(footnote continued) of the high (low) interest rate currencies, which corresponds to about 8% of the standard deviation of exchange rate changes.

flows can account for 26% (22%) of the average appreciation of the low Sharpe ratio (interest rate) currencies and 7% (11%) of the average depreciation of high Sharpe ratio (interest rate) currencies during this time period. According to our estimates, therefore, in the fall of 2008, the carry trade long currencies depreciated by roughly 2.3–4.6% against the carry trade short currencies due to hedge fund flows, providing additional evidence of the economic significance of the effect of hedge fund flows on exchange rates.28 9. Conclusion In this paper, we study a two-country general equilibrium model with partially segmented markets for nominal fixed income securities. In sufficiently segmented markets, when inflation shocks are highly correlated, all unrestricted investors invest in a leveraged hedge fund that borrows from the country with the lower Sharpe ratio for fixed income securities while investing in the country with the higher Sharpe ratio. Under certain assumptions, this strategy coincides with the simple carry trade strategy, where investment decisions are based on interest rate as opposed to Sharpe ratio rankings. In our model, hedge funds play a positive economic role, transferring money from a country with little domestic inflation risk to a country with higher inflation risk, leading to better international risk sharing and an increase in the utilities of all agents. When the costs for making international financial transactions decrease, more investors invest in the hedge fund, whose investments affect market interest rates, the exchange rate, and both the hedge fund’s contemporaneous and expected future returns. Empirically, we show that a long-short investment strategy that is based on the rankings of currencies by their estimated Sharpe ratios (or interest rates) can explain a large fraction of various hedge fund index returns, implying that hedge funds do engage in this type of currency speculation. Our evidence suggests that the hedge fund industry is also large enough, so that the hedge funds’ investments have affected market prices in the fixed income and currency markets. Our estimate of the total hedge fund industry’s assets under management was, in recent years, close to 6% of the M2 money supply of our sample currencies, which include the currencies of the 28 There are at least two reasons, however, why the extreme exchange rate changes in the fall of 2008 may be even to a greater extent due to the unwinding of the hedge funds’ carry trade positions. First, one should recognize that the large hedge fund outflows in the fall of 2008 occurred at the time of a global credit crisis. Given this, the hedge funds have most likely unwound their positions in 2008 not only due to the outflow of money from the funds, but also in an effort to decrease in their leverage ratios, as during this time period the availability of funding credit became very tight. This is, in fact, what Brunnermeier, Nagel, and Pedersen (2009) argue is the case. Second, as predicted by Brunnermeier and Pedersen (2009), it is likely that during the credit crises the liquidity in all markets, including the currency market, was exceptionally low. This implies that at that time the unwinding of the hedge funds’ carry trade positions probably had a much greater effect on exchange rates, as compared to normal times, as in the fall of 2008 also all the other market participants, who normally provide liquidity to the market, were highly constrained.


largest industrialized countries in the world. When assessing the magnitude of this amount, recognizing that hedge funds pursue many different strategies in addition to those that we have identified, one must also recognize that the hedge fund investments are typically highly leveraged, amplifying the amount of money that may have been invested in such trades.29 Given the huge volume of leveraged assets under management, it is hardly surprising that the flow of hedge fund assets under management has had a statistically significant price effect in the fixed income and currency markets. Our results also shed some light on the forward premium puzzle, which has attracted much attention in academia. In our model, the uncovered interest rate parity does not typically hold in equilibrium, as real interest rates differ across countries due to variations in inflation risks and money supplies. Furthermore, under certain assumptions which, according to our estimates are typically satisfied, the failure of the uncovered interest rate parity is larger in segmented financial markets as opposed to an integrated financial market. Under the same assumptions, the process of market integration leads to additional hedge fund investments into high real interest rate currencies, which in turn leads to the appreciation of those currencies, and to short selling and the subsequent depreciation of the low interest rate currencies. Consequently, according to our results, it is likely that the market integration during the past few decades has biased upwards the empirical estimates of the failure of the uncovered interest rate parity. Appendix A. Proofs

decrease as ki increases. Differentiating (21) with respect to bdL and bdH , and using (10) to sign the derivatives, gives

bdH sH bdL sL r @V S 4 0, ¼ 2asH d 1r2 @bH

The claim that the hedge fund’s expected returns are positive follows from the fact that zero positions are also feasible. The proof of all other claims follows directly from Eq. (9) and the first partial derivative of (9) with respect to ki and kj, and are omitted. & Proof of Proposition 2 First, using (5), (8) and (10) we obtain

bdi ðbdj sj r=si Þ 1r2

:

ð20Þ

Here, we have made use of the result, implied by (5) and (10), that Et p~ i,t þ 1 pi,t ð1 þ rf Þ ¼ abdi s2i , in equilibrium. Now, using (20), let us first show that the speculators’ fund’s equilibrium profits,

V s ¼ bsL ðEt p~ L,t þ 1 pL,t ð1 þrf ÞÞ þbsH ðEt p~ H,t þ 1 pH,t ð1 þ rf ÞÞ ¼ bsL bdL a 2L þ bsH bdH a 2H d 2 2 d 2 b a L þ bH a 2H 2bdH bdL a H ¼ L 2 1

s s

ð23Þ

when kL okL . This provides the result as ð@bdL =@ki Þ 4 0 and ð@bdH =@ki Þ o0, where iA{L, H}, given (10), for the range of parameters considered. These last two partial derivatives also prove our claim that the Sharpe ratios converge, as the number of speculators increases, as given (7) and (23), we have

SRL ¼ abdL sL oabdH sH r o abdH sH ¼ SRH :

ð24Þ

This result also implies, given (13), that all the speculators, when kL okL , come from country L. We now prove that a decrease in f leads to an increase in the number of speculators. In equilibrium, the utilities of the two types of investors must be equal. Following a decrease in f, other things equal, the speculators’ utility is higher than that for the domestic investors, prompting more domestic investors to turn into speculators. As we show below, an increase in the number of speculators increases domestic investors’ utility relative to the utility of the speculators. Entry of speculators continues until the utilities are again equal. Using (5) and (10), the ratio of the expected utilities, uðc~ t þ 1 Þ ¼ Et eac~ t þ 1 , where c~ t þ 1 is defined by (2), of the domestic investors and speculators from country L can be written as d2

uL ðc~ dtþ 1 Þ eaðEt c~ L,t þ 1 ða=2ÞbL sL Þ ¼ s s 2 2 s 2 2 s s uL ðc~ st þ 1 Þ eaðEt c~ L,t þ 1 ða=2ÞbL sL ða=2ÞbH sH abL bH rsL sH Þ

Proof of Proposition 1

ð22Þ

bdL sL bdH sH r @V S o0, ¼ 2asL d 1r2 @bL

d

bsi ¼

73

s sL r

r

d 2 2 s d 2 s d 2 s2 2 s2 2 s s ¼ eaðða=2ÞbL sL Þ þ aðabL bL sL þ abH bH sH ða=2ÞbL sL ða=2ÞbH sH abL bH rsL sH fð1 þ rf ÞÞ ,

ð25Þ where we have made use of the fact that the first-order condition of (2) with respect to mi,t implies that the domestic investors and speculators select equal money holdings in equilibrium. As f decreases, (25) increases. When kL o kL , (10) implies that the first term in the exponential of (25), in equilibrium, ðða2 =2ÞðbLd 2 s2L ÞÞ, is decreasing in the number of speculators. We now want to show that the second term in the exponential is also decreasing in the number of speculators. Differentiating this term with respect to bdH and d bL gives @a absL bdL s2L þ absH bdH s2H 2a bsL 2 s2L 2a bsH 2 s2H absL bsH rsL sH fð1 þ rf Þ @bdH

s

s

,

2

ð21Þ

29 In the past, leverage ratios of up to 12:1 have been estimated for some types of hedge funds (see McGuire, Remolona, and Tsatsaronis, 2005).

s s @V s 2 s 2 @bL 2 s 2 @bH a bL sL a bH sH d d d @bH @bH @bH s @b @bs a2 bsH rsL sH dL a2 bsL rsL sH dH @bH @bH

¼a

¼ a2 sH

2bdH sH 2bdL sL r a2 bsH s2H 1r2

74


4 a2 sH ¼ a2 sH

! 2bdH sH 2bdL sL rbdH sH þbdL sL r 1r2 ! bdH sH bdL sL r 40 1r2

ð26Þ

by (22). Similarly by (23), @a absL bdL s2L þ absH bdH s2H 2a bsL 2 s2L 2a bsH 2 s2H absL bsH rsL sH fð1 þ rf Þ @bdL

¼ a 2 sL

Our estimate of the hedge fund industry’s asset flow is based on all funds in the Lipper TASS database and our AUM estimates. We calculate an estimate of percentage asset flow to each fund for each month, when reported asset and return figures are available, take an asset-weighted average of these percentage flows, and multiply this by our estimate of the total hedge fund industry AUM to obtain an estimate of the flow in dollar terms.

2bdL sL 2bdH sH r a2 bsL s2L 1r2

2bdL sL 2bdH sH rbdL sL þ bdH sH r o a sL 1r2 ! bd sL bdH sH r o 0: ¼ a2 sL L 2 1r

References

!

2

ð27Þ

This proves the result as ð@bdL =@kL Þ 4 0 and ð@bdH =@kL Þ o 0 given (10), for the range of parameters considered. The remaining results regarding the interest rates, bond prices, and the contemporaneous profits to the hedge fund follow from (5), (6), and the derivative of (10) with respect to ki and kj. &

Appendix B. Estimation procedures It is quite difficult to obtain reliable monthly estimates for the hedge fund industry’s AUM dating back in time. First, Hedge Fund Research, Inc. (HFR) provides annual estimates of the hedge fund industry’s total AUM from 1990 onwards. Second, we find some evidence on the size of the markets for the earlier period from Hennessee Group LLC, but it is only for years 1974 and 1987. In addition, we use the Lipper TASS database, which provides monthly observations on individual funds dating back to 1977, and covers a large (currently 80%) but varying proportion of the total hedge fund industry. To form a monthly series of the hedge fund AUM, we start with the annual estimates of the total hedge fund AUM by HFR and the two earlier estimates by Hennessee. Next, we calculate asset-weighted averages of returns and new asset flows to all the funds included in the Lipper TASS database for each month. As the year-to-year asset growth of the Lipper TASS funds does not match the growth in the hedge fund industry indicated by the estimates provided by HFR and Hennessee, due to the changing coverage in Lipper TASS, we make the assumption that each year the difference between the two growth figures accumulates steadily over the year. Hence, our estimated hedge fund AUM growth is the asset-weighted average growth in the AUM of the hedge funds reporting to the Lipper TASS database plus onetwelfth of the difference in the current year’s asset growth estimates obtained from HFR or Hennessee and the Lipper TASS database. In this way, we get a monthly estimate of the hedge fund AUM whose end-of-year figure matches the estimates of HFR and Hennessee and whose monthly growth pattern resembles as closely as possible that of the population of funds reporting to the Lipper TASS database.30 30 Some discussion on the difficulties of finding good proxies to measure carry trade activity can be found in Galati, Heath, and McGuire (2007).

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The impact of governance reform on performance and transparency$ Richard Price a,1, Francisco J. Romań b,2, Brian Rountree a,n a b

Jones Graduate School of Management, Rice University, 6100 Main Street, Houston, TX 77005, USA Rawls College of Business, Texas Tech University, College of Business Administration, MS2101, Lubbock, TX 79409, USA


abstract

Article history: Received 18 June 2008 Received in revised form 22 January 2009 Accepted 2 March 2009 Available online 6 August 2010

This study examines the influence of Mexico’s efforts to improve corporate governance on firm performance and transparency. We utilize compliance data from the Code of ‘Best’ Corporate Practices, disclosed annually by public firms in Mexico, as a measure of corporate governance strength. We document a significant increase in compliance over 2000–2004 indicating Mexican companies view non-compliance as costly. However, we find no association between the governance index and firm performance, nor is there a relation with transparency. Instead, we find firms with greater compliance resort to the more costly mechanism of making dividend payments (higher propensity to pay and greater yield) to reduce agency conflicts. We conclude these associations are the direct result of the institutional features of the Mexican business environment, which is characterized by concentrated ownership of insiders, interlocked boards of directors, a lack of insider trading enforcement, and generally poor protection of minority investors. Our results show that monitoring mechanisms alone are not enough to fundamentally change economic behavior. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G34 G38 L51 Keywords: Corporate governance Performance Transparency Dividend policy Earnings management

1. Introduction

$ We would like to thank an anonymous referee, Steve Buchheitt, Daniel Cohen, Gustavo Grullon, Alfonso Flores-Lagunes, Leslie Eldenburg, Karen Nelson, Lynn Rees, Mark Trombley, James Weston, and Steve Zeff, workshop participants at the European Accounting Association Annual Meeting, University of California at Davis, Rice University, and Texas Tech University for helpful comments. We are also grateful to several people at the Mexican Stock Exchange, Mexico’s Banking and Securities Exchange Commission, and Rodriguez and Aguirre Consulting Services for their help including Jonathan Davis (President of the National Banking and Securities Exchange Commission), Rafael Colado, Moises Curiel (Baker-Mackenzie), Angelica Gonzalez-Saravia Cos, Angelica Ortiz, Juan Manuel Sanchez Rosales, Jairo Toledo, and Gustavo Venegas. n Corresponding author. Tel.: + 1 713 348 5328. E-mail addresses: [email protected] (R. Price), [email protected] (F.J. Romań), [email protected] (B. Rountree). 1 Tel.: +713 348 6303. 2 Tel.: +806 742 3188.


Corporate governance systems are designed to ensure that investors receive a fair return on their investment (Shleifer and Vishny, 1997). Using cross-country analysis, the governance literature has demonstrated that stronger governance systems lead to more efficient allocations of capital resources. This, in turn, spurs economic growth and increases the likelihood of investors receiving a return (see, for example, La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny, 1997, 1999, 2000). It is unclear how an economy with generally weak governance can bring about change to improve the investment climate and stimulate economic development. To investigate this, we examine the efficacy of mandated changes in corporate governance in Mexico, which is an emerging market economy with a lack of minority investor protection that is dominated by concentrated ownership.

R. Price et al. / Journal of Financial Economics 99 (2011) 76–96

Mexico offers a rich environment for investigating the influence of improved governance-related disclosures on the behavior and perception of public firms. Governance improvements in a developing economy such as Mexico’s can potentially have meaningful and measurable effects in the market. In Mexico, the efficacy of governance is particularly salient for minority investors in contrast to the marginal influence of governance in the US given the strength of the US legal environment and product markets (Shleifer and Vishny, 1997). If a Mexican firm can commit to better governance, it is more likely to invest properly and provide more transparent financial reports, resulting in a higher probability of providing a fair return to investors. In this study, we address whether this commitment is deemed to be credible by examining if greater compliance leads to improved performance and transparency.3 Mexican firms are required to report each year their compliance with the Code of ‘Best’ Corporate Practices (hereafter, the Code). The purpose of the Code is to strengthen corporate governance systems of publicly listed corporations with the intention of increasing corporate transparency and raising investor confidence in Mexico. Compliance with the Code has increased significantly over the sample period. In 2000, only 28% of sample firms complied with three-quarters or more of the criteria versus 79% in 2004. This increase stands in direct contrast to studies using US data, in which governance is stable over extended periods of time, making it difficult to draw inferences (Gompers, Ishii, and Metrick, 2003; Core, Guay, and Rusticus, 2006). Further, the dramatic increase in compliance indicates that Mexican companies believe there are benefits of compliance or costs of noncompliance. The results indicate that compliance is not associated with various measures of firm performance, earnings management, or the return-earnings relation. The lack of significance is likely due to the business environment in Mexico. Over 90% of sample firms exhibit concentrated ownership, and many have significant levels of interlocking boards that satisfy the independence criteria in the Code but create concerns about the true independence and the monitoring performed by these boards. We perform an extensive set of robustness checks to confirm our main analyses. First, we examine whether firms with large changes in compliance have improved performance or transparency, but we find no evidence of this. Second, we examine a number of subdivisions of the Code including board and audit committee characteristics. With the exception of audit committee compliance, all inferences remain unchanged. Greater audit committee compliance does result in statistically better operating performance in terms of return on assets and market returns, along with slightly greater transparency.

3 Because of concentrated ownership, the takeover market is virtually nonexistent in Mexico. Similarly, bankruptcies, shareholder lawsuits, mergers and acquisitions, chief executive officer turnover, public offerings and share repurchases are all limited in nature. As a result, we focus on performance, financial reporting, and dividend payments as outcome metrics that are directly related to governance.

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However, the economic significance of these effects is small. The statistically significant results for audit committee compliance does alleviate concerns about the statistical power of the tests because we are able to detect a statistically significant, but economically small effect related to Code compliance in Mexico. Overall, the robustness tests reveal that the results are stable across a variety of different methodologies and that we have sufficient statistical power in our tests. Although the relation between compliance with the Code and measures of performance and transparency is minimal, we show that firms with greater compliance have a higher propensity to pay dividends and provide marginally greater dividend yields relative to lower compliance firms that also pay dividends. These results illustrate that Mexican firms that want to commit to better governance must resort to the costly mechanism of paying dividends to reduce agency concerns as opposed to being more transparent via performance and financial reporting. Consistent with La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny (2000), Rajan and Zingales (2003), and Locke, Qin, and Brause (2007), our results suggest that, without significant changes in the legal environment along with the enforcement of necessary regulations to accommodate the concentrated ownership structure, mandated improvements in governance-related disclosures in developing economies such as Mexico are not likely to result in substantial changes in performance or financial reporting. The objective of the Code is to allow market participants to determine which companies have good governance (Lo´pez-de-Silanes, 2002), which, in turn, will create market pressures for other companies to follow. We contribute to the growing literature investigating the effects of corporate governance on firm performance and transparency. Our paper is the first to show that this form of market monitoring is not enough to create fundamental economic improvements for countries such as Mexico that are dominated by insider ownership and weak investor protection. The results have implications for a broad spectrum of global economies. Antoine Van Agtmael, the former deputy director of the International Finance Corporation, estimates that approximately 18%–19% of the world’s market capitalization is located in emerging markets as of 2006. Investors in these countries are often posed with similar problems faced by minority investors in Mexico, namely, wealth transfers to majority owners without legal remedy. A recent article in the Wall Street Journal (2005a) indicates the agency conflicts present in many emerging markets can be reduced via stronger corporate governance. Another article in the Wall Street Journal (2006) suggests reforms in Mexico have been successful in this regard. Our results illustrate this is not the case and suggest that alternative mechanisms have to be developed before substantial improvements are seen in Mexico. This conclusion is consistent with a recent story in the Wall Street Journal (2008), which contrasts the relative rise of the Brazilian stock market to the stagnation and even decline of the Mexican market. The number of publicly listed companies on the Mexican stock exchange

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has been falling for a number of years, with a 15% drop during our sample period. This decline could be attributable to the lack of minority investor protection. Bergman and Nicolaievsky (2007) finds that in weak investor protection environments, private equity accompanied by significant protections provided beyond the law results in an efficient form of capital. Although Brazil represents a similar legal environment to Mexico, Brazil’s experience with the increased governance requirements for listing on the Novo Mercado provide a potential avenue to alter corporate behavior without fundamentally changing the legal environment. The fact that two code law countries have experienced very different success rates in creating well-functioning equity markets is consistent with the theory in Rajan and Zingales (2003) that code law countries suffer more from swings in the political economy, thereby allowing for greater variation in the development of markets (see also Musacchio, 2008a). 2. Corporate governance in Mexico The Mexican business environment has undergone significant changes over the past 20 years. The 1980s and early 1990s were dominated by government control of business, as well as significant protection from foreign competition. Failing businesses were routinely bailed out by the government, with business success often pinned on the political astuteness of its directors rather than the ability to run an efficient enterprise (Austin, 1990). Not surprisingly, corporate governance was not a major concern of business owners or the government. With the privatization of businesses in the 1990s and increased foreign investment, corporate governance has become an issue of great importance to both Mexican businesses and the government. Mexico’s governance

reform initiated with the issuance of a voluntary Code of ‘Best’ Corporate Practices in September 1999 and was followed by the enactment of two legal acts in 2001 and 2003. For a chronology of governance reforms in Mexico, refer to Fig. 1. The reforms aim to strengthen the corporate governance of publicly listed corporations with the intention of increasing corporate transparency and raising investor confidence in Mexican firms. The National Banking and Securities Exchange Commission (CNBV), which issued the Code, described the objectives of the Code as follows. The recommendations of the Code are aimed to define principles which contribute to improve board of directors’ oversight and to reveal more transparent information to shareholders. More specifically, these recommendations seek: (i) to reveal detailed information with regards to the structure of management, the board, and its functions; (ii) to establish mechanisms that ensure that financial information is transparent; (iii) the existence of processes that promote the effective participation and communication of the board of directors; and (iv) the existence of processes that promote adequate disclosures to shareholders. (Report of the Committee of ‘Best’ Corporate Practices, 1999, p. 2). The original Code recommends that firms adopt 55 internal governance mechanisms considered fundamental to promote good governance. Some key provisions in the Code relate to the structure of the board of directors, such as limiting the size to between five and 20 directors, having at least 20% independent (outside) directors with no close ties to management or controlling shareholders, and creating separate board committees to oversee auditing, finance, and executive compensation. Other

Sample period

September 1999 Mexico adopts the Code of ‘Best’ Corporate Governance Practices for publicly traded firms. The code consists of 55 internal governance provisions aimed at improving board oversight and financial reporting. Adherence to this code is voluntary. However, firms are required to report their level of compliance with each provision in the Code.

June 2000 Firms listed on the Mexican stock exchange begin reporting to market regulators and investors the extent of compliance with each provision in the Code via a standard questionnaire filed annually with the Mexican Banking and Securities Exchange mission and the Mexican stock exchange.

June 2001 The Securities Market Law of 2001 requires that firms comply with important provisions in the code: At least 25% of board members must be independent; Board size is limited to between five and 15 directors; Audit committees are required and need to be presided over by an independent director (Article 12, paragraph 10, Securities Market Law, 2001).

March 2003

2005

The Securities Market Law of 2003 officially recognizes the governance Code as part of Mexico’s securities law, making compliance filing mandatory. The law also provides stricter guidelines for the dissemination of financial information to investors.

Fig. 1. Timeline: relevant events, guidelines, and rules related to Mexico’s governance reform. (The timeline is not to scale. It was constructed using the following sources: Codigo de Mejores Practicas Corporativas (1999), Diario Oficial de la Federacion (2001), and Diario Oficial de la Federacion (2003).)


provisions call for improvements in internal controls systems as well as mechanisms to make financial reporting more transparent (e.g., the timely disclosure of all relevant events).4 Adoption of the Code is voluntary, however since its inception, all publicly listed firms are required to report to market regulators and investors their compliance with each governance provision. This is done via a standard questionnaire that is filed annually with the CNBV and is included in annual reports. Besides the enactment of the Code, two recent legal mandates are important aspects of Mexico’s corporate governance reform. The Securities Market Laws of 2001 and 2003 made mandatory several of the Code’s recommendations and raised the standards for several of the Code’s provisions. Among the chief mandates are that firms’ boards have at least 25% independent directors, limit their size to 20 directors, and have audit committees that are presided over by independent directors.5 Although some of the provisions in the Code are now mandatory, there appears to be little oversight by regulators. Company reports are generally not questioned. The implicit assumption by regulators and lawmakers is that companies report truthfully. Lo´pez-de-Silanes (2002, p. 20) notes that ‘‘this code is a substantial step forward in the creation of a culture of investor protection, as it allows investors: (1) to distinguish firms that do have effective corporate governance mechanisms in place; and (2) to reward firms that offer better protection with higher valuation multiples or lower costs of capital.’’ The governance reforms have been implemented to draw greater attention from the foreign investment community. If these reforms are effective, the Mexican economy could grow more quickly. Although these governance reforms are viewed favorably, several accounts in the business press express skepticism concerning whether these efforts are enough for any real improvements.6 Most of the criticism is based on the highly concentrated ownership of public corporations in Mexico among firms’ founding families, or closeknit groups of families (La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny, 1999). According to Lo´pez-de-Silanes (2002), Mexico has the third largest concentration of family ownership in the world at 63%. For decades, Mexico’s boards have been closely held and controlled by founding families. Also, La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny (1999, p. 501) estimate that 95% of

4 The code also aims to improve the rights of shareholders with several provisions intended to facilitate the gathering of relevant information that is subject to shareholders’ voting approval. For instance, it recommends firms disclose to shareholders, within at least 15 days prior to the annual shareholders’ meeting, a report with detailed explanations of all matters subject to shareholder approval. 5 Although the criteria are lax relative to US standards (e.g., 25% independent directors), the ownership environment is substantially different from the US environment calling for different standards in some instances. Further, the fact that a number of firms do not comply with the criteria is a strong signal of weak governance. 6 See, for example, Wall Street Journal (2001) and New York Times (2005).

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family-controlled firms in Mexico have a family member involved in management. Babatz (1998) further notes that it is common for Mexican firms to offer distinct classes of shares with limited voting or nonvoting rights, increasing the agency problem stemming from the separation of ownership and control. He concludes that, unlike the more established capital markets in the US, Canada, and the UK, dual-class shares in Mexico are issued to allow the controlling family to maintain control at lower ownership concentrations. Nonvoting shares in Mexico are allowed to be 25% of the ownership of the firm, thereby reducing the effective control percentage from 50% in the case of a single class to 37.5%. Babatz (1998) estimates that Telefonos de Mexico, one of the largest companies in Mexico, was controlled by only 10.2% of the equity and further illustrates that in excess of 90% of nonfinancial firms in Mexico have concentrated ownership. Our estimates indicate this is still true today with over 90% of the firms in our sample having concentrated ownership in excess of 48% of the voting equity. However, transparency has been greatly improved since Babatz (1998) via the required disclosures in the Code along with the improvements to minority investor protection enacted into law by the Securities Market Laws of 2001 and 2003. For instance, minority investors with 10% of the total shares, which can be voting or nonvoting, now have the right to name a board member, call for a shareholder meeting, and delay the voting on issues for three days. However, to our knowledge, this right has never been exercised. In addition, all investors now have the right to vote by mail. Given that voting is one of the strongest shareholder rights (Shliefer and Vishny, 1997), these improvements could have a substantial effect on the Mexican business and reporting environment. Nevertheless, Mexico has one of the weakest legal systems for the protection of investor rights (La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny, 1997). Siegel (2005) shows that firms cross-listed in the United States from Mexico often escape enforcement of insider trading laws by the Securities and Exchange Commission and minority shareholders. He concludes that cross-listing is not an effective substitution for strong home-country legal systems and enforcement. Siegel (2005) also demonstrates that cross-listed firms that did not expropriate shareholder wealth during the 1994 Mexican financial crisis were more likely to be able to raise additional capital after the crisis, suggesting that firms can bond themselves through their reputations as in Diamond (1991). In contrast, the Code is meant to provide market participants with a mechanism to monitor corporate governance as opposed to a separate reputational commitment by companies. Furthermore, as of the end of our sample period, the commitment of the Mexican judicial system to minority shareholder protection is still untested, creating significant questions about the perceived improvements in minority shareholder protection by stock market participants. The improvements suggest that Mexico is moving in the right direction in terms of providing disclosures about the governance of companies. However, given the


concentrated ownership structure and lack of a demonstrated commitment to minority investor protection via enforcement of insider trading laws, it is unclear whether these mandated disclosures and legal changes have improved the performance and transparency of Mexican companies.

3. Hypothesis development

1.00 0.90 0.80 0.70 Compliance

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0.60 0.50 0.40 0.30

Prior to developing our hypotheses, we examine how compliance with the Code has varied over time. In Fig. 2 we plot the percentage of firms complying with greater than 50, 65%, 75%, and 85% of the Code’s criteria each year. The figure shows that Mexican companies have dramatically increased their compliance over time with 44% complying with 85% or more of the Code in 2004 versus only 12% in 2000.7 This increase stands in direct contrast to studies using US data in which governance is typically stable over extended periods of time (Gomper, Ishii, and Metrick, 2003). The increase in compliance is consistent with the hypothesis of Bushman, Piotroski, and Smith (2004) that the demand for financial and governance transparency by outside investors increases with the protection of their rights. The authors also note the propensity of policy makers to mandate and enforce transparent corporate reporting is expected to be higher with better protection of investors. Mexico has illustrated a clear dedication to the improvement of governance transparency by requiring reporting of compliance with the Code, along with improving the rights of minority shareholders in the Securities Market Laws of 2001 and 2003. The improvements over time in compliance with the Code also indicate that Mexican companies believe there are benefits of compliance (or costs of noncompliance). The improvements in compliance are gradual over the sample period, and there are still a number of criteria unsatisfied, indicating compliance with the Code is not without cost, otherwise we would expect all firms to adopt all aspects of the Code. Further, significant crosssectional variation in compliance exists, which provides the opportunity to investigate whether compliance with the Code is associated with better performance and transparency. The changes in Mexico provide a powerful setting to investigate how governance is related to performance and transparency. However, the continued lack of minority investor protection and the high level of insider ownership create a significant tension in our paper, making it an empirical question whether compliance with the Code improves performance or financial reporting in Mexico. Shleifer and Vishny (1997) note governance systems are designed to ensure that investors receive a return on their investment. La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny (2000) build off of this theory by illustrating 7 This finding is not attributable to increased compliance with the parts of the Code that became mandatory as part of the Securities Market Laws of 2001 and 2003. The vast majority of companies already complied with the aspects that were made mandatory.

> 85% > 75% > 65% > 50%

0.20 0.10 0.00 2000

2001

2002 Year

2003

2004

Fig. 2. Compliance with the Code of ‘Best Corporate Practices 2000 2004. This figure presents for each year in the sample period (2000–2004) the percentage of companies whose compliance with the Code is greater than or equal to the percentages indicated in the legend. For instance, in 2000 (2004) 12% (44%) of firms complied with 85% or more of the Code’s criteria.

that countries with better corporate governance have more efficient allocation of capital resources and hence improved performance, which then increases the likelihood of investors receiving a return in those countries. Numerous other studies have found that specific aspects of governance such as board independence result in better firm performance (see, for example, Brickley, Coles, and Terry, 1994; Byrd and Hickman, 1992; Klein, 1998). In general, governance helps to ensure that manager and shareholder incentives are more directly aligned. Assuming that greater compliance with the Code indicates better governance, we expect firms with higher compliance to have better performance. Hypothesis 1. Greater compliance with the Code leads to better performance. Better stock market performance does not necessarily indicate better operational performance. For instance, Westphal and Zajac (1998) show significant positive excess returns for companies announcing the adoption of long-term incentive plans that were reported to align managerial incentives with shareholder interests. However, no difference exists between the reaction for firms that announced and adopted versus those that announced but never adopted, indicating the market valued the symbolic nature of the plan as opposed to the actual implementation. The same could be true for Mexican companies, which is why we examine operational improvements in addition to stock market returns by examining return on assets and sales growth. Our second hypothesis builds on research investigating the relation between governance and earnings transparency. Leuz, Nanda, and Wysocki (2003) hypothesize that earnings management conceals information from investors to protect private control benefits. Consistent with this, the authors find that companies operating in countries with weaker investor protection exhibit more


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instances of earnings management. The purpose of the Securities Market Laws of 2001 and 2003 is to increase minority investor protection, which, if effective, should reduce earnings management leading to Hypothesis 2.

reforms are effective, then we expect the relation between returns and earnings to improve with governance.

Hypothesis 2. Greater compliance with the Code leads to less earnings management.

Similar to the performance-based tests using stock market returns, it is important to note that if an association exists between transparency and compliance, it will be difficult to disentangle whether this represents true economic differences or simply symbolic associations (as in Westphal and Zajac, 1998) because the market does not necessarily have a means for determining true compliance from the reported figures. Instead, investors could view higher compliance firms as better and therefore place more weight on their reported numbers, creating a greater association between returns and earnings. We rely on the combination of the results related to the three hypotheses to disentangle economic versus symbolic interpretations of any findings. Relatedly, the governance improvements alone might not be strong enough to lead to actual improved financial reporting. La Porta, Lo´pez-de-Silanes, Shleifer, and Vishny (1999) conclude that radical changes in the legal environment could be necessary to reduce the agency conflict between majority and minority shareholders. Although Mexico has shown improvement in this regard, the enforcement of minority investor rights is still in question. For instance, Bhattacharya and Daouk (2002) show that although insider trading laws have existed in Mexico since 1975, they had never been enforced through March 1999. In fact, the first attempt to enforce insider trading laws did not occur until 2005 (New York Times, 2005) and even then was spurred by US efforts without any firm commitment from Mexican authorities. The evidence in the literature suggests that investor protection is a key factor in the development of capital markets (Beck, Demirguc-Kunt, and Levine, 1999; La Porta, Lo´pez-deSilanes, Shleifer, and Vishny, 2000; Doidge, Karolyi, and Stulz, 2004; Doidge, Karolyi, and Stulz, 2007).9 Given the uncertainty surrounding the effects of the changes in Mexico on investor protection, it is an empirical question whether the governance requirements and changes in the legal environment have led to improved performance and transparency in Mexico. Furthermore, compliance with the Code might not indicate true adherence to the underlying principles and therefore there could be no true relation between

Transparency of financial reports is a fundamental component of the development of markets. For instance, Simon (1989) provides evidence that implementation of the US 1933 securities acts helped improve the information available to investors, which, in turn, led to more efficient allocations of capital. Musacchio (2008a) illustrates that a key component of the development of Brazilian markets in the early 1900s was the mandate that companies produce a set of reasonably transparent financial statements that would assist minority investors in evaluating the performance of the corporation. Consistent with the evidence and theory developed in Rajan and Zingales (2003), the findings in Musacchio (2008a) indicate that financial markets can be developed independent of a country’s legal origin. Nevertheless, a commitment from the government to protect the rights of investors, while not a sufficient condition, seems to be necessary to develop active financial markets.8 Finally, following Alford, Jones, Leftwich, and Zmijewski (1993), we examine the association between returns and earnings to assess the usefulness or transparency of earnings over time. Alford, Jones, Leftwich, and Zmijewski (1993) note that differences in accounting standards, disclosure practices, and corporate governance can lead to significant differences in the usefulness of earnings for capital market participants. In our setting, transparency related to corporate governance practices has been mandated by the Code, which has subsequently resulted in increased compliance. We expect firms with higher compliance to provide more transparent earnings, which are more useful to the capital markets. In a more recent paper, Ball, Kothari, and Robin (2000) illustrate that the relation between returns and earnings is systematically related to legal origin, in which common law countries tend to have stronger relations because of the demand for information by outside investors versus code law countries, which are typically dominated by concentrated ownership resulting in less demand for information by outsiders. Mexico is a code law country with concentrated ownership that has mandated improvements in transparency aimed at increasing the amount of public information. The intention of the Code is to increase the willingness of foreign investors to extend capital to Mexican companies by increasing transparency and providing investors with confidence that they will receive a return on their investments. If the 8 For instance, Musacchio (2008b) notes that the legal environment more stringently regulated the issuance of shares in Brazil along with providing criminal penalties for falsification of information and violation of corporate bylaws in addition to the increased disclosure requirements in late 1800s. However, he concludes most of the contractual enforcement was left to the corporate bylaws as opposed to the legal system.

Hypothesis 3. Greater compliance with the Code leads to a stronger relation between returns and earnings.

9 This is separate from the literature on the influence of legal origin on the development of financial markets. For instance, a series of papers illustrate time variation throughout history in the development of financial markets across common and code law countries where at times code law countries have exhibited more active financial markets (see, for example, Rajan and Zingales, 2003; Tilly, 1992; Musacchio, 2008b). Many of these papers contend that the political economy drives much of the differences and that the state of the political economy can vary more over time in code law countries because of the concentration of power. This means during times the ruling power favors development, investors are likely to be protected by the views or legal recourses designed by the current regime even in code law settings. Our argument is that, in the case of Mexico, the current political economy has not illustrated a clear commitment to investor protection.

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compliance and performance or transparency. In an effort to determine the verifiability of the reported compliance figures, we select a subsample of ten companies representing large, medium, and small firms in differing industries, and we attempt to verify their compliance reports for fiscal year 2004. Of the 55 items in the Code, we could verify only 26 with publicly available information. This review took several weeks to perform, indicating that, even for items that are verifiable, many items are difficult to find in publicly available documents of the corporations. Our review reveals that firms reported accurately 94% of the time (we identified 16 instances, or 6% of the items verified in which we found the company’s reported compliance did not agree with other publicly available information). Given the extreme level of difficulty of verification, compliance could be viewed skeptically by the market forcing firms to adopt alternative mechanisms to communicate their quality. Consequently, we also examine the relation between compliance and dividend payments in Section 6.

4. Sample selection and research design Our sample consists of all nonfinancial firms listed on the Mexican stock exchange with stock returns, financial statement data, and governance data over the sample period of 2000 to 2004. Governance data are collected from each company’s Code of ‘Best’ Corporate Practices questionnaire filed with Mexico’s regulators each year. Following prior research (Gompers, Ishii, and Metrick, 2003), we construct a governance score based on the level of compliance with the recommended provisions in the Code and use this score as a proxy for the strength of governance. A translated version of the questionnaire is included in the Appendix. All financial statement and return data are from Economatica, which is a data provider dedicated to the collection and dissemination of information related to Latin American companies. Governance scores are matched to Economatica by hand. The data are examined for consistency across firms and time, as well as for outlying observations prior to conducting any tests.10 Mexico is one of the top 20 countries in the world in terms of gross domestic product according to the 2007 CIA World Factbook and had 151 publicly traded firms on the Mexican stock exchange as of November 2005. Our final sample of 107 firms (see Table 1, Panel A) represents 82% of all nonfinancial firms currently traded on the Mexican stock exchange. Table 1, Panel B provides information on the industry composition of the sample. The greatest concentration of firms is in the food and beverage industry (17 firms) and the trade industry (23 firms), with the remaining firms being spread across 17 other industry classifications. For each individual analysis we use all available observations, which means the sample size varies across analyses. Conclusions are unaltered if we utilize a constant sample for all tests (see Section 7).

Table 1 Sample construction. Panel A: sample selection

Total number of active and delisted firms trading on the Mexican stock exchange with price and financial data in Economatica database Less: banks, financial institutions, and delisted firms Less: firms with incomplete data on price or financial statement variables Total number of firms Total number of firm-year observations 2000 2004

Industry

Number of firms 166

16 43 107 518

Number of firms

Panel B: Distribution of sample firms across industries Agriculture Basic manufacturing and metal fabrication Cement and glass Chemical Construction Electric Food and beverage Hospitality and entertainment Industrial machinery Media Mining Other Publishing Pulp and paper Telecommunications Textile Trade Transportation services Vehicle parts

4 8 8 5 7 1 17 3 2 4 2 3 1 3 7 5 23 3 1

Total

107

4.1. Hypothesis 1: performance Similar to Gompers, Ishii, and Metrick (2003), we examine the relation between governance and firm performance. The measures of firm performance we use are return on assets (ROA) defined as net income before extraordinary items plus interest expense divided by beginning total assets, raw market returns, and one-year sales growth. To test Hypothesis 1, we examine average performance across governance compliance levels, as well as regressing the performance measures on the compliance index and controls identified in the literature. We also measure changes in the compliance index between the first and last year in the sample and investigate its relation with changes in Tobin’s q over the same interval, after controlling for a variety of factors found to be related to Tobin’s q in the prior literature. These tests assess whether the market values compliance with the Code or whether higher compliance is associated with better governance in a meaningful way.

4.2. Hypothesis 2: earnings management 10

All variables are winsorized at the upper and lower 2.5% levels to reduce the influence of outliers. Inferences are unaltered if we use 1%, 5%, and 10% levels or if we do not winsorize.

To assess whether earnings management behavior is related to the improvements in corporate governance, we


utilize the four measures in Leuz, Nanda, and Wysocki (2003)11: 1. Ratio of quarterly earnings volatility (se) to cash flow volatility (sc). 2. Correlation between changes in accruals (DACC) and changes in cash flows (DCFO). 3. Absolute value of accruals scaled by the absolute value of cash flows (ACC_CFO). 4. The propensity of small positive earnings to small negative earnings (SmProfit/Loss) where small profits are defined as earnings divided by total assets that fall in the range [0.00, 0.01] and small losses as [ 0.01, 0.00). The ratio of se to sc captures smoothing behavior with lower values providing evidence consistent with earnings management. Greater variation in cash flows and smaller corresponding variation in earnings suggest that firms are utilizing accruals to smooth earnings relative to cash flows. Similarly, the more negative the correlation between DACC and DCFO, the greater the earnings smoothing because negative (positive) changes in cash flows are counteracted by positive (negative) changes in accruals (Leuz, Nanda, and Wysocki, 2003). The ratio of the absolute value of accruals to cash flows (ACC_CFO) indicates the aggressiveness of companies’ accrual estimates. A large ratio indicates that companies use more accruals, which are more difficult to verify than cash flows. The final measure, SmProfit/Loss, is based on work by Degeorge, Patel, and Zeckhauser (1999) and Burgstahler and Dichev (1997), who find certain benchmarks (i.e., small profits, small positive earnings changes, analysts’ expectations) have a disproportionate number of observations just above the benchmark relative to just below, suggesting managers use discretion to manipulate earnings to meet the benchmark. Our earnings management tests focus on simple tests of differences across two time periods, 2000–2001 and 2003–2004. Fig. 2 shows a significant improvement in compliance between these periods. If the improved compliance has led to improved financial reporting, we expect lower levels of earnings smoothing in the later period, as well as less earnings management. 4.3. Hypothesis 3: returns-earnings relation We examine the stock market transparency of earnings in regression of returns on earnings and earnings changes (Alford, Jones, Leftwich, and Zmijewski, 1993). In Hypothesis 3, we predict that if compliance truly signals better governance, then the relation between annual returns and earnings-related information should be stronger. We estimate the following regression. Rt ¼ g1 þ g2 HIGOVt þ g3 NIt þ g4 NIt HIGOVt þ g5 DNIt 11 Leuz, Nanda, and Wysocki (2003) combine these measures on a country by country basis to form a measure of earnings management at the country level. Our country-specific design prevents the creation of a similar metric.

þ g6 DNIt HIGOVt þ

ln Rt HIGOVt NIt

DNIt

83

X

gk CONTROLS þ e

ð1Þ

natural logarithm; =ln(1 +stock market return for firm i on the Mexican Bolsa stock exchange for year t); =1 if compliance with Code in year t is above the median, 0 otherwise; =ln(1 +net income before extraordinary items divided by beginning market value of equity); =ln(1 +change in net income before extraordinary items between years t 1 and t divided by beginning market value of equity);

Controls MVEt 1 =ln(market value of equity as of the end of year t 1); BMEt 1 =ln(1 +book value of equity divided by market value of equity as of the end of year t 1). We predict a positive and significant coefficient on the interaction of NIt (DNIt) and the indicator variable HIGOVt, suggesting a stronger relation between annual returns and earnings (earnings changes) when compliance is greater.

5. Results 5.1. Hypothesis 1: performance and compliance Table 2 presents descriptive statistics concerning firms’ financial condition and governance scores separately across the HIGOV designation. Overall, both groups of sample firms have a positive return on assets (ROA) of 0.03 as well as statistically equal cash flows from operations scaled by assets (CFO). Sample firms in both panels are relatively small with less than $21 million in assets. Higher compliance firms have more debt in their capital structures with a mean ratio of Debt-to-Assets of 0.521 versus 0.483 for low-compliance firms, which is statistically but not economically significant. Tobin’s q is similar across the governance designation and is line with estimates for US firms (Allayannis and Weston, 2001). Finally, the annual market-adjusted return does not show significant differences in means or medians. Overall, the univariate results from Table 2 suggest that not much difference exists between highcompliance and low-compliance firms when it comes to performance. In an effort to determine whether the improvements in compliance shown in Fig. 2 are indicative of performance differences across compliance levels, we relax the constraints embedded in the univariate analysis in Table 2 by regressing each performance metric on the contemporaneous compliance score (G-index) and the control variables utilized in Gompers, Ishii, and Metrick (2003): the natural logarithm of the market value of equity, MVE; the ratio of the book value of equity to the market value of

84


Table 2 High versus low compliance descriptive statistics. This table presents descriptive statistics for sample firms. Compliance represents the summation of the number of items from the annual report on the Code for ‘Best’ Corporate Practices that are designated as complying with the Code. Firms with compliance scores above the median level in a given year are designated as high compliance, otherwise firms are characterized as low compliance. G-index is the number of items within the Code complied with as of the end of the fiscal year. ROA is net income before extraordinary items plus interest expense divided by beginning total assets. Cash Flow (CFO) equals annual cash flow from operations scaled by beginning of the fiscal year total assets. Total Assets equals total assets at the end of the fiscal year recorded in millions of dollars. Debt-to-assets equals short term plus long term debt all divided by ending total assets. Tobin’s q is book value of equity divided by market value of equity as of the end of the fiscal year. Market-adjusted returns equals the 12-month buy-and-hold firm-specific return less the 12-month buy-and-hold return on the index of securities traded on the Mexican Bolsa stock exchange. Variable

Mean

Panel A: High-compliance firms G-index ROA Cash flow (CFO) Total assets (millions) Debt-to-assets Tobin’s q Market-adjusted returns

46.410 0.032 0.077 20.442 0.521 1.012 0.009

Panel B: Low-compliance firms G-index ROA Cash flow (CFO) Total assets (millions) Debt-to-assets Tobin’s q Market-adjusted returns

35.793 0.034 0.066 17.811 0.483 0.973 0.012

Standard deviation

equity, BME; and year fixed effects. For all regression analyses we take the natural logarithm of the independent and dependent variables, so the resulting slope coefficients are elasticities. This mitigates the influence of outliers and makes the coefficients easier to interpret. Inferences are unchanged without this monotonic transformation. Table 3, Panel A presents the results of the regressions and illustrates that, for all performance metrics, the coefficient on the compliance index is not significantly different from zero. The results in Table 3 do not vary based on the inclusion or exclusion of firm fixed effects, indicating even for firms with significant variation in the Code over time that there is still no relation with performance. Core, Guay, and Rusticus (2006) indicate that the ideal causal test involves using changes in the performance metric regressed on changes in the governance metric. The results remain unchanged if we include annual changes in the compliance index, along with using changes in ROA as a performance measure, leading us to conclude that the changes in compliance with Code have not led to substantial changes in firm performance.12 Following Allayannis and Weston (2001), we regress long run changes (fiscal year 2004 relative to 2000) in the natural logarithm of Tobin’s q on changes in ROA, total assets (SIZE), Sales Growth, Debt-to-Assets, and G-index. This test examines whether there are any long-run valuation implications of adopting more provisions of the Code over time. The results are presented in Table 3, Panel B and once again illustrate no association between compliance and value. Overall, it appears that compliance

12

Sales Growtht and Rt are already change measures.

Q1

Median

Q3

4.351 0.073 0.078 34.918 0.171 1.259 0.517

44.000 0.002 0.032 2.370 0.372 0.334 0.353

47.000 0.036 0.067 8.618 0.551 0.562 0.069

50.000 0.084 0.123 21.658 0.645 1.098 0.253

6.732 0.072 0.089 38.576 0.172 1.221 0.485

31.000 0.001 0.014 0.991 0.360 0.355 0.299

37.000 0.037 0.067 4.124 0.490 0.640 0.104

41.000 0.084 0.118 17.429 0.602 1.051 0.198

with the Code has done little to improve firm operating performance, and it has not altered the market’s assessment of performance. These results are consistent with Locke, Qin, and Brause (2007), who find that the monitoring of working conditions of Nike suppliers in a number of different countries, while diligent and costly, do not lead to systematic improvements in working conditions for employees of Nike suppliers. Instead, most of the variation in working conditions relate to country-level regulation and enforcement as opposed to the act of monitoring. Mexico’s Code during the sample period relies on marketlevel monitoring to bring about economic change, which unfortunately has not led to detectable improvements. The evidence in Locke, Qin, and Brause (2007) indicates that increased monitoring by regulators (CNBV) coupled with costly penalties for noncompliance could be necessary before improvements from better corporate governance are detectable in Mexico and other emerging markets. 5.2. Hypothesis 2: earnings management and compliance The preceding tests fail to reveal significant improvements in performance even though compliance with the governance characteristics in the Code has increased over time. However, this does not preclude an improvement in transparency because market participants now have a mechanism to distinguish whether firms have strong corporate governance as measured by their level of compliance with the Code (Lo´pez-de-Silanes, 2002). The lack of association between performance and compliance could be related to the limited level of industry competition among public firms in Mexico, thereby limiting the ability of


85

Table 3 Performance and compliance. This table presents the relation between firm performance (as measured by return on assets, sales growth, and stock market returns) and value (as measured by Tobin’s q) with governance, as measured by compliance with the Code of ‘Best’ Corporate Practices. The regressions in the upper half of Panel A include unreported fixed year effects, the regressions in the lower half of Panel A include both unreported fixed year and firm effects, and all p-values are calculated using Newey-West standard errors. G-indext equals ln(number of items within the Code complied with in year t) where ln represents the natural logarithm. ROAt equals ln(1+ net income before extraordinary items plus interest expense divided by beginning total assets). Sales Growtht equals ln(1+ annual change in sales between year t 1 and t divided by year t 1 sales). Rt equals ln(1+ stock market return for firm i on the Mexican Bolsa stock exchange for year t). MVEt 1 equals ln(market value of equity as of the end of year t 1). BVEt 1 equals ln(1+book value of equity divided by market value of equity as of the end of year t 1). SIZE equals ln(total assets). Debt-to-assets equals short term plus long term debt all divided by ending total assets. Tobin’s q is book value of equity divided by market value of equity as of the end of the fiscal year. D represents the change in the associated variable between 2004 and 2000. Panel A: Level of compliance Dependent variable Sales Growtht

ROAt

Rt

Variable

Coefficient estimate

p-value


p-value


p-value

G-indext MVEt 1 BMEt 1

0.03 0.01 0.03

0.12 0.00 0.00

0.09 0.01 0.07

0.17 0.07 0.04

0.11 0.03 0.08

0.22 0.03 0.17

Adj. R2

0.24

With firm fixed effects G-indext MVEt 1 BMEt 1 Adj. R2

0.01 0.00 0.01

0.17 0.41 0.31 0.20

0.27

0.26 0.00 0.05

0.79

0.11 0.90 0.27

0.17 0.09 0.16

0.35

0.28 0.10 0.16

0.32

Panel B: Changes in compliance and Tobin’s q

DTobin’s q Variable


p-value

0.05 0.48 0.01 0.16 1.17

0.24 0.41 0.93 0.08 0.00

DG-index DROA DSIZE DSales Growth DDebt-to-Assets Adj. R2

the tests to detect performance differences. The earnings management tests do not suffer from these concerns. Table 4, Panel A presents mean tests of differences of the earnings smoothing measures. We calculate the ratio of earnings volatility to cash flow volatility utilizing at least six quarterly observations. Further, we utilize two separate periods to compare this ratio across the HIGOV designation to ensure the robustness of our results. We expect better-governed firms to have higher ratios, indicating that they manage earnings less. However, the results are not consistent with this prediction in the first period (2000–2002) with both groups of firms exhibiting similar ratios and the second period (2003–2004) showing higher ratios for low-compliance firms.13 Similarly, the correlation between changes in accruals (DACC) and cash flows (DCFO) indicates that highcompliance firms exhibit slightly more smoothing behavior, but the test of differences indicates that this

13 The test of differences in the last column is only suggestive for these comparisons because we are unaware of a statistical test of differences for ratios of variances.

0.29

difference is not significant. Overall, the income smoothing results indicate little difference across the groups, suggesting greater compliance with the Code is not related with this form of earnings management. The ratio of the absolute value of accruals to the absolute value of cash flows (ACC_CFO) is significantly different in the early part of the sample period, indicating that companies with low compliance have more accruals, which could be indicative of greater earnings management. If we use signed total accruals in the numerator, the results become insignificant, indicating low-compliance companies are more likely to have both large positive and negative accruals. Given that it is difficult to argue that large negative accruals are evidence of earnings management in an environment such as Mexico, we do not view this result as providing strong evidence in either direction. The ratios are insignificantly different in the later period, once again indicating that governance as measured by compliance has little impact on transparency. We also report mean tests of differences of the proportion of small profit firms to small loss firms (SmProfit/Loss) in Panel A of Table 4. Following Leuz, Nanda, and Wysocki (2003), we classify firms as small

86


Table 4 Transparency and compliance. This table presents earnings management characteristics (Panel A) and pooled time-series cross-sectional regressions of raw returns (Rt) on earnings and changes in earnings (Panel B). The regressions are estimated on a pooled basis, but for ease of interpretation total coefficients are presented with tests of differences across the HIGOV (1 if compliance with the Code of ‘Best’ Corporate Practices in year t is above the median, 0 otherwise) designation. The regressions include unreported year fixed effects and p-values are calculated using Newey-West standard errors. NI to CFO volatility equals the ratio of the standard deviation of quarterly net income before extraordinary items divided by the standard deviation of quarterly cash flows from operations. A minimum of six observations is required to calculate the firm-specific standard deviations. Corr ACC CFO equals the cross-sectional correlation between annual accruals and cash flows from operations, both scaled by beginning total assets. Accruals are calculated as net income before extraordinary items less cash flows from operations. ACC_CFO equals the absolute value of total accruals divided by the absolute value of cash flows from operations. Small Profit/Loss equals the relative percentage of firms with return on assets of greater than zero and less than or equal to 0.01 versus firms with return on assets less than zero and greater than or equal to 0.01. Rt equals ln(1+ stock market return for firm i on the Mexican Bolsa stock exchange for year t) where ln represents the natural logarithm. NIt equals ln(1+ net income before extraordinary items divided by beginning market value of equity). DNIt equals ln(1+ change in net income before extraordinary items between years t 1 and t divided by beginning market value of equity). MVEt 1 equals ln(market value of equity as of the end of year t 1). BVEt 1 equals ln(1 +book value of equity divided by market value of equity as of the end of year t 1). SIZE equals ln(total assets). Panel A: Earnings Management Compliance Variable NI to CFO volatility NI to CFO volatility Corr ACC CFO ACC_CFO ACC_CFO Small Profit/Loss

Test of differences

Period

High

Low

p-value

2000 2002 2003 2004 2000 2004 2000 2002 2003 2004 2000 2004

0.53 0.62 0.43 0.51 0.62 1.12

0.50 0.99 0.38 0.68 0.57 1.12

0.67 0.24 0.48 0.03 0.97 0.89

Panel B: Returns Earnings Relation HIGOV= 0

HIGOV= 1

Difference

Variable


p-value


p-value

p-value

Intercept NIt DNIt

0.057 0.655 0.619

0.86 0.00 0.03

0.019 0.259 0.136

0.95 0.10 0.58

0.32 0.12 0.20

0.016 0.006

0.07 0.91

CONTROLS MVEt 1 BMEt 1 Adj. R2 Number of observations

0.34 204

229

profit if their return on assets is less than or equal to 0.01, but greater than zero. Conversely, we categorize small loss firms as those firms with return on assets less than zero, but greater than or equal to 0.01. The results indicate both groups have more small profit firms than loss firms, but the proportions are not significantly different. Overall, the earnings management tests indicate no significant relation between compliance with the Code and earnings management attributes. Nevertheless, Mexican regulators are spending considerable time and resources attempting to improve the investing climate. However, as Lo´pez-de-Silanes (2002) notes, the Code could provide the market with a previously undisclosed mechanism for judging the quality of governance in Mexico. Thus it could be that the market rewards companies with better governance by placing greater reliance on their financial reports.

cients on the earnings-related variables to be higher, indicating greater association with contemporaneous returns. Instead, the coefficients do not exhibit any statistical differences across the HIGOV designation, and in fact, generally indicate a lower association between returns and earnings for high-compliance firms. Our results are not consistent with the conjecture in Lo´pez de-Silanes (2002) that compliance with the Code provides the market with a mechanism for judging the governance quality of Mexican companies. Instead, it appears that compliance has no association with performance or transparency. The concentrated ownership environment and weak legal system combine to limit the impact of the Code on capital markets in Mexico. In this setting, market monitoring alone is not enough to create fundamental economic changes.

5.3. Hypothesis 3: returns-earnings relation

6. Governance and dividends

Table 4, Panel B shows the results of the regression of returns on earnings and earnings changes. If compliance is consistent with better governance, we expect the coeffi-

Because the purpose of corporate governance is to ensure that investors receive a fair return on their investment, we also investigate the relation between


compliance and dividends. Given the lack of an association between governance and corporate transparency, it could be that institutional features of the Mexican investment climate force firms to resort to more costly measures to reduce agency costs. We expect bettergoverned firms to be more likely to pay dividends and at higher rates, given the extreme agency conflict between the dominant family owners and minority outside investors. In less concentrated ownership environments, this prediction is unclear. Bushman, Piotroski, and Smith (2004) note that costly governance mechanisms could be adopted to make up for the lack of transparency. In Mexico, the concentrated ownership and lack of investor protection have hindered the ability of firms to clearly delineate transparency, which suggests that more costly measures such as dividend payouts could have to be used to reduce agency concerns. Firms that are committed to better governance are more likely to pay out dividends as opposed to creating wealth transfers from minority shareholders to insider majority shareholders. We use a propensity to pay dividends model similar to Fama and French (2001) to investigate the relation between compliance with the Code and dividends. The dependent variable is equal to one if a dividend is paid in the current fiscal year and zero otherwise. Using logistic regression, we regress the dividend indicator on the market value of equity (MVEt 1), the book-to-market ratio (BMEt 1), return on assets (ROAt), sales growth (Sales Growtht), and the compliance index (G-indext). The results are presented in Table 5. Consistent with the findings in Fama and French (2001), the results reveal the propensity to pay dividends is positively related to our proxy for firm size (MVEt 1) and performance (ROAt) and, at the same time, is negatively related to growth opportunities (i.e., positively related to BMEt 1) and realized growth (Sales Growtht). The coefficient estimates are generally of the same magnitude as those in Fama and French (2001), while

87

the proportion of companies paying dividends in Mexico over the sample period is roughly twice that of US companies as shown in the last year of the sample period in Fama and French (2001). The coefficient estimate of the compliance index indicates that greater compliance is associated with a higher probability of dividend payment. This result is both statistically and economically significant with a 1% change in G-indext, resulting in a 1% change in the odds a company will pay a dividend. We interpret this as evidence that the compliance index is consistent with better governance, because holding all else constant, companies with greater compliance are more likely to provide a return to their shareholders. The results are consistent with companies adopting more costly methods to reduce agency costs as a result of the concentrated ownership and weak legal protection present in Mexico. Table 5 also presents results for a Tobit regression of the dividend yield (dividends per share divided by earnings per share) on the same variables used in the propensity to pay model. The coefficient estimates represent a combined measure of the probability of paying a dividend along with an estimate of the change in dividend yield as a result of a one unit change in the independent variable for those firms paying dividends. We adopt the method of McDonald and Moffitt (1980) to decompose the coefficient estimate into its two components and report the marginal effect of changes in the independent variables on the dividend yield. The results are consistent with the findings of the propensity to pay model, indicating that large, profitable firms are more likely to pay dividends, as well as paying more relative to smaller, less profitable firms that also pay dividends. Similarly, growing firms are less likely to pay and tend to pay less when they do pay dividends. The G-indext coefficient indicates companies with greater compliance are more likely to pay dividends and provide larger dividend yields relative to companies with lower compliance. The marginal effect is somewhat limited, indicating a 1% change

Table 5 Dividends and compliance. This table presents tests of the relation between compliance with the Code of ‘Best’ Corporate Practices and dividend payments. We estimate a logistic (tobit) regression of the propensity to pay dividends (dividend yields) on compliance and control variables. The regressions include unreported fixed year effects. All p-values are based on two-tailed tests. DIVIDEND is the dependent variable in the Propensity to pay regression, which is equal to one if the firm paid a dividend during the year, and zero otherwise. DIVYIELD is the dependent variable in the Dividend yield regression, which is equal to ln(1+ the ratio of dividends per share divided by net income per share) where ln represents the natural logarithm. Results for this regression are restricted to firms with positive net income. ). MVEt 1 equals ln(market value of equity as of the end of year t 1). BEt 1 equals ln(1+ book value of equity divided by market value of equity as of the end of year t 1). ROAt equals ln(1+ net income before extraordinary items plus interest expense divided by beginning total assets). Sales Growtht equals ln(1 +annual change in sales between year t 1 and t divided by year t 1 sales). G-indext equals ln(number of items within the Code complied with in year t). Propensity to pay Variable MVEt 1 BMEt 1 ROAt Sales Growtht G-indext

Dividend yield


p-value


p-value

Marginal effect

0.594 0.564 10.130 0.550 1.450

0.00 0.00 0.00 0.49 0.02

0.009 0.020 0.298 0.041 0.041

0.00 0.00 0.00 0.02 0.01

0.004 0.007 0.114 0.016 0.016

Pseudo R2

0.22

Proportion paying dividends

0.41

88


in G-indext results in a 0.02% change in the dividend yield. To put this in perspective, a movement from one standard deviation below the mean to one standard deviation above the mean of G-indext would result in a 1% increase in dividend yield, which is economically significant but requires a large increase in compliance. Overall, the dividend results provide further evidence that the potential for improved transparency is limited in Mexico as a result of the investing climate. Although companies have made efforts to become more transparent and adopt better governance mechanisms, this has not translated into changes in performance or financial reporting characteristics. In the end, better-governed companies are still forced to rely on costly signals such as dividend payments to reduce agency costs, as opposed to reaping the benefits of improved transparency. We believe this is not likely to change without significant changes to investor protection that account for the concentrated ownership environment. 7. Robustness This section explores the robustness of our results to a number of different regression specifications, estimation methodologies, as well as investigating in greater detail particular aspects of the governance structures of sample firms.

Table 6 Board composition and interlocking. This table presents descriptive statistics for boards of directors of Mexican firms over the pooled 2000–2004 sample period (in this case, pooled means selecting unique firm/director/classification combinations ignoring year, which collapses the data set significantly and makes the descriptive statistics simpler). Panel A presents statistics on the number of directors and the number of independent and affiliated directorships. Panel B shows the number of firms, individual directors, and unique (pooled) board seats that are affected by the different types of interlocking. Independent interlocking occurs when directors serving on the same boards are classified as independent on both boards. Potentially conflicting interlocking occurs when two directors are both affiliated on at least one board. Conflicting interlocking occurs when one director is independent on the first board, and affiliated on the second, while the other director is affiliated on the first board and independent on the second. Panel A: Board composition Number of firms Average board size Number of unique directors Number of unique pooled board seat years (4,474 total board years) Independent board seats Affiliated board seats

107 11 1,159 1,498 606 892

Number of seats Managers related to controlling family Non-managers related to controlling family Unrelated managers Independent board members

126 297 168 591

Panel B: Board interlocking Firms Directors Unique seats

7.1. Interlocking boards of directors Thus far, the results illustrate that simply providing a mechanism for market participants to monitor firms’ corporate governance compliance is not enough to create substantial changes in performance or transparency. One potential factor creating tension in this environment is the lack of true board independence. Although most of the companies satisfy the Code’s 25% independence criteria, the true nature of the independent board members is still uncertain. For instance, the controlling family could simply appoint friends or individuals they know will adhere to the family’s interest, thereby circumventing the intention of the Code without technically violating it. In an effort to better understand the nature of these relations, we conduct an extensive hand-collection effort to identify and classify all board members for the firms in our sample. For each director, we investigate any potential relations, with the controlling family (i.e., marriage, extended familial relations such as cousins, nieces, nephews, etc.) along with examining any publicly available information about the same individuals provided by other listed companies. Using these data, we investigate board independence and interlocking relations and designate each director as independent or affiliated. Results are presented in Table 6. Table 6, Panel A presents descriptive statistics on board composition. A total of 4,474 observations were collected over the 2000–2004 time period. There are 1,159 unique directors serving in these directorships. For the descriptive statistics, we pool across years, which means that we select unique combinations of firm, director, and classification (independent or affiliated), ignoring year. This

Entire sample Number of instances of interlocking Independent interlocking Potentially conflicting interlocking Conflicting interlocking

107 53 32 46 6

1,159 105 70 83 7

1,498 425 200 211 14

results in 1,498 unique pooled board seats. Of these, 606 seats are held by individuals classified as independent, and 892 seats are held by individuals classified as affiliated. Also in Table 6, Panel A is information on the relation between the individual board member and the controlling family of the firm. In an effort to verify the accuracy of the reported classifications, we review each family association based on reported familial relations as well as capturing relations evident from reading other annual reports. We find that 126 board seats are held by managers who are related to a controlling family and that 297 seats are held by non-managers who are related to a controlling family. Further, 168 seats are held by managers who have no relation to the controlling family. Finally, we were able to verify the independence of 591 board members.14 These descriptive statistics show the high number of affiliated board seats that are held (892 of 1,498), which does not violate the Code’s 25% independence criteria but, nevertheless, shows over half of the

14 The total number of board members does not agree with the 1,498 reported in the upper half of Table 6, Panel A because we were unable to find enough detailed information to classify some of the relations.


seats are held by managers or by the controlling family members, indicating that insiders have effective control of the boards. Table 6, Panel B presents descriptive statistics on the interlocking of boards in Mexico. We consider three types of interlocking. The first is independent interlocking in which two independent directors sit concurrently on at least two of the same boards and are designated as independent for both. These relations provide less of a concern about independence problems, unless the same set of independent board members sits on a high percentage of boards. The next classification is potentially conflicting interlocking, which occurs when two individuals are affiliated on at least one board and serve together on another. The third is conflicting interlocking, which occurs when one director is independent on the first board and affiliated on the second, while the other director is affiliated on the first board and independent on the second. Of the 107 sample firms (1,159 directors and 1,498 unique seats), 32 firms have at least one instance of independent interlocking (representing 70 different directors and two hundred unique seats), 46 firms have at least one instance of potentially conflicting interlocking (representing 83 different directors and 211 unique seats), and six firms have conflicting interlocking (representing seven directors and 14 unique seats). Thus, approximately half the firms in our sample exhibit some form of interlocking, as well as potentially conflicting board interlocking. The small number of companies and limited number of board members indicate that true independence is likely compromised in Mexico, which confirms our earlier findings that compliance with the Code is not necessarily consistent with better governance.

7.2. Audit committee results Thus far we have treated each element in the Code equally in the design of our empirical tests. In an effort to determine whether individual elements of the Code are related to improvements in performance or financial reporting, we estimate a factor analysis using all 55 responses from the Code as variables to identify related elements with significant variation. We focus on the first factor, which explains approximately 20% of the variation in Code compliance. The next largest factor explains less than 5% of the variation. The largest factor loadings are on questions 35, 36, and 41 (correlations all 40.70), which are all audit committee-related. The next largest loadings are on questions 44–47 (correlations all 0.65), which are finance committee-related. A review of the underlying responses to questions 44–47 reveals they all have correlations with each other in excess of 0.93, indicating they constitute a single variable, whereas the audit committee variables provide much more variation with correlations spanning the range 0.40–0.74.15 The factor 15

In untabulated analyses, we do not find an association between responses to questions 44–47 and firm performance and transparency.

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analysis is helpful in identifying audit committees as a significant source of variation in the Code. Audit committee characteristics have received a significant amount of attention in the accounting literature. Pincus, Rusbarksy, and Wong (1989) note that audit committees serve to improve the quality of information flow in high agency cost situations; this accurately characterizes the situation in Mexico for minority shareholders. More recently, audit committee independence, meeting frequency, and financial expertise have been linked to improved financial reporting (Carcello and Neal, 2000; Klein, 2002a), reduced cost of debt financing (Anderson, Mansi, and Reeb, 2004), and positive market reactions to the announcement of financial expertise (Defond, Hann, and Hu, 2005). The evidence overall is consistent with audit committees playing a major role in the financial reporting transparency and performance of firms. Given the importance of audit committees shown in the prior literature along with our finding that audit committee compliance is a primary source of variation in overall Code compliance, we construct an audit committee variable that sums all the components of the Code that involve only audit committee-related issues (questions 14, 35, 36, 37, 39, and 41).16 These questions cover the existence, independence, and operation of the audit committee. In Table 7, Panel A, we present changes in compliance with these six audit committee-related guidelines over time. The first column has the number of items complied with, and within each row we report the percentage of firms in a given year that comply with that particular number of items. For instance, only 13% of firms complied with all six audit committee characteristics in 2000 compared with 69% that were fully compliant in 2004. The results illustrate companies have generally been increasing their compliance with audit committee characteristics over time similar to the findings for overall governance compliance. Klein (2002b) hypothesizes and finds that the demand for an independent audit committee is a function of board characteristics (i.e., percentage of outside directors), financial reporting transparency (presence of losses, growth opportunities, etc.), and monitoring substitutes (large outside blockholders). We further examine whether the audit committee compliance is associated with other aspects of the governance structure. In Panel B of Table 7, we regress the audit committee compliance on ownership concentration (Own Concentration), an indicator of whether the chief executive officer is a member of the controlling family (CEO Family), the percentage of outside directors on the board (%Outside Board), whether the company is cross-listed in the US (Crosslist), the percentage of the board that is interlocked (%Interlock), and firm size (Total Assets) as a control variable. These data,

16 Inferences are unchanged if we utilize only those questions identified as significant sources of variation in the factor analysis (questions 35, 36, and 41).

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Table 7 Audit committee compliance. Panel A presents the frequency percentage of firms in each year that complied with the specific number of audit committee characteristics from the Code of ‘Best’ Corporate Practices using questions 14, 35, 36, 37, 39, and 41 as audit committee-related. The difference 2000 2004 represents the 2004 frequency percentage for a given level of compliance less the corresponding frequency percentage in 2000. For instance, in 2000 only 13% of the sample complied with all audit committee criteria compared with 69% in 2004. Panel B regresses audit committee compliance on governance structure variables. The regression includes unreported fixed year effects and p-values are calculated using Newey-West standard errors. All p-values are based on two-tailed tests. Auditt is the dependent variable in Panel B and is equal to ln(1+ number of audit committee characteristics complied with in year t), where ln represents the natural logarithm. Own Concentrationt equals ln(1 +insider ownership percentage in year t). %Outsiderst equals ln(1+ percentage of outside directors on board in year t). CEO Familyt equals one if the chief executive officer (CEO) in year t is a member of the controlling family, and zero otherwise. %Interlockt equals ln(1+ number of directors on board with interlocking relations with other members of board in year t). Crosslistt equals one if the company is cross-listed in the US in year t, and zero otherwise. Total Assetst equals ln(total assets in year t). Panel A: Audit committee compliance by year Difference Audit committee compliance

2000

2001

2002

2003

2004

2000 2004

p-value

0 1 2 3 4 5 6

0.05 0.31 0.07 0.06 0.17 0.21 0.13

0.03 0.14 0.08 0.07 0.11 0.18 0.39

0.02 0.06 0.01 0.06 0.06 0.20 0.59

0.01 0.06 0.02 0.06 0.04 0.15 0.67

0.00 0.03 0.02 0.03 0.07 0.16 0.69

0.05 0.28 0.06 0.02 0.10 0.05 0.56

0.02 0.00 0.05 0.30 0.02 0.38 0.00

Panel B: Audit committee compliance and governance structure Variable Intercept Own Concentration %Outsiders CEO Family %Interlock Crosslist Total Assets Adj. R2 Number of observations

excluding firm size, were hand-collected from companyspecific documents. The results in Table 7, Panel B illustrate that audit committee compliance is negatively related to ownership concentration (coefficient estimate 0.313, p-value 0.05), suggesting that higher ownership concentration is related to lower compliance with audit committee guidelines. Audit committee compliance is positively related to the percentage of outside directors on the board (coefficient estimate 0.372, p-value 0.04), which indicates that firms with greater outside monitoring adopt more of the audit committee provisions. Compliance is negatively associated with the percentage of directors holding interlocking positions (coefficient 0.224, p-value 0.05), suggesting that interlocked directors might compromise the independence of the board and reduce the board’s commitment to monitoring. Finally, the larger the company, the greater the compliance (coefficient 0.056, p-value o0.01). This differs from the findings in Klein (2002b) and likely represents the level of sophistication of Mexican companies when it comes to internal control issues. Audit committee compliance is not significantly related to the presence of a family member as the chief executive officer or cross-listing. Overall, the relations illustrate that audit committee compliance is related to aspects of the governance structure in meaningful and intuitive ways. Given the importance of the audit


p-value

0.615 0.313 0.372 0.005 0.224 0.048 0.056

0.05 0.05 0.04 0.92 0.05 0.35 0.00

0.25 443

committee in ensuring the quality of the reported financial information, we examine whether audit committee compliance is related to firm performance and financial reporting. In Table 8, Panel A, we examine the relation between the measures of firm performance used in Table 3 (ROAt, Sales Growtht, Rt) and audit committee compliance, captured by the variable Auditt. We regress each respective performance measure on Auditt, size (MVEt 1), and the book-to-market ratio (BMEt 1). The results illustrate that Auditt is positively related to all three performance measures and is significantly related to return on assets (ROAt) (coefficient estimate 0.017, p-value 0.04) and stock market returns (Rt) (coefficient estimate 0.087, p-value 0.10). This indicates that companies with stronger audit committee characteristics generally exhibit greater accounting and stock market performance. Because the performance measures and Auditt are logged variables, the resulting coefficients are elasticities, which facilitates the interpretation of the economic magnitude of the results. The coefficient estimates indicate that a 1% change in Auditt results in a 0.02% and 0.09% change in ROAt and Rt, respectively. To put this in perspective, a change from the upper quartile to the lower quartile of Auditt results in a 0.57% change in ROAt, indicating a relatively large change in audit committee


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Table 8 Audit committee compliance, performance and transparency. This table presents the relation between firm performance or transparency and compliance with audit committee characteristics from the Code of ‘Best’ Corporate Practices. The regressions include unreported fixed year effects and p-values are calculated using Newey-West standard errors. All p-values are based on two-tailed tests. Auditt equals ln(1+ number of audit committee characteristics complied with in year t),where ln represents the natural logarithm. ROAt equals ln(1+ net income before extraordinary items plus interest expense divided by beginning total assets). Sales Growtht equals ln(1+ annual change in sales between year t 1 and t divided by year t 1 sales). Rt equals ln(1+ stock market return for firm i on the Mexican Bolsa stock exchange for year t). MVEt 1 equals ln(market value of equity as of the end of year t 1). BVEt 1 equals ln(1+book value of equity divided by market value of equity as of the end of year t 1). AUDITIND equals one if the company is fully compliant with the audit committee characteristics in a given year, and zero otherwise. NI to CFO volatility equals the ratio of the standard deviation of quarterly net income before extraordinary items divided by the standard deviation of quarterly cash flows from operations. A minimum of six observations is required to calculate the firm specific standard deviations. Corr ACC CFO equals the cross-sectional correlation between annual accruals and cash flows from operations, both scaled by beginning total assets. Accruals are calculated as net income before extraordinary items less cash flows from operations. Panel A: Performance Dependent variable ROAt

Sales Growtht

Rt

Variable


p-value


p-value


p-value

AUDITt MVEt 1 BMEt 1

0.017 0.009 0.033

0.04 0.00 0.00

0.031 0.013 0.066

0.18 0.02 0.01

0.087 0.026 0.074

0.10 0.03 0.22

Adj. R2

0.24

0.16

0.27

Panel B: Earnings smoothing AUDITIND Variable NI to CFO volatility NI to CFO volatility Corr ACC CFO

Test of differences

Period

0

1

p-value

2000 2002 2003 2004 2000 2004

0.514 0.600 0.450

0.517 0.570 0.333

0.97 0.76 0.06

compliance has only a limited influence on performance. Overall, the findings indicate that greater compliance with audit committee characteristics generally leads the company in the right direction, but the effect on firm performance is limited. An important implication of these findings is that the power of our tests is strong enough to detect significant differences related to a variable that has limited economic importance in our setting. A potential concern with our previous tests is that the failure to find a significant relation between aggregate Code compliance and performance or financial reporting could be because of the lack of statistical power. These new findings bolster our conclusions that the institutional features of the Mexican ownership and legal environment hinder improvements in performance. We now turn to the financial reporting characteristics in which audit committee characteristics should have even more power because the primary objective of the audit committee is to ensure that the external audit has been completed in a satisfactory manner thereby directly influencing the financial reporting environment. Table 8, Panel B presents earnings smoothing tests. Consistent with Klein (2002a) and Carcello and Neal (2000), we expect firms with stronger audit committee characteristics to engage in less earnings management. We divide the sample into those firms that satisfy all of the audit committee characteristics suggested by the Code (AUDITIND= 1) and those with less than all six (AUDITIND= 0), which represents 49% and 51% of the sample, respectively.

The results indicate no statistical differences between the samples for the ratio of earnings volatility to cash flow volatility. However, companies with greater compliance with the audit committee characteristics exhibit significantly less negative correlations between cash flows and accruals (p-value=0.06), indicating they are less likely to be smoothing earnings via accruals.17 Overall, we find that compliance with audit committee guidelines within the Code is associated with greater independence of the board of directors and lower ownership concentration. This, in turn, appears to marginally benefit firms in terms of performance and, to a lesser extent, financial reporting. Although the findings concerning the determinants of compliance are consistent with US findings related to audit committees, which indicate audit committees play an important monitoring role, the influence of the committees in Mexico is much smaller. We attribute these differences to the variation in the institutional features of each country, which are most notably different in terms of ownership concentration and minority investor protection. 7.3. Code items with large changes in compliance Some items are clearly more important than others in the operation of the firm. For instance, the Code asks if a board member is incapable of fulfilling the specified 17 We also examine the relation with earnings response coefficients but find no statistical differences across the AUDITIND variable.

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duties whether a replacement for the board member is known. This seems relatively unimportant compared with the independence of the board, the internal control procedures, and audit committee-related requirements. Thus far our procedures have been objectively determined using either the entire Code or statistical measures such as factor analysis to classify companies. As a further check, we investigate more subjective measures of governance. We identify 19 items in the Code that experienced in excess of 20% increases in compliance during the sample period (i.e., 2000 compliance was 40%, 2004 compliance was 60%). We group these items into two categories: audit related (questions 14, 31, 32, 33, 35, 36, 39, 38, and 41) and communications-related (questions 3, 4, 7, 8, 12, 13, 17, 51, 53, and 54). Not surprisingly, the first set of questions closely overlaps the audit committee-related analysis performed above. Variation related to the questions not included above (questions 31, 32, and 33) does not provide any incremental explanatory power in explaining variation in performance or transparency relative to the findings in Table 8. Within the communications-related questions, we focus on questions that have a higher probability of creating significant differences in corporations. Consequently, we eliminate the questions concerning how a replacement board member is determined (questions 3 and 4), although their inclusion does not alter any inferences. Using the sum of the compliance for the remaining questions each year, the results indicate there is still no relation to stock returns (coefficient estimate 0.001, p-value 0.88), return on assets (coefficient estimate 0.003, p-value 0.52), or sales growth (coefficient estimate 0.002, p-value 0.93). Furthermore, there is no association with smoothing characteristics and no difference in the relation between returns and earnings or changes in earnings. We also estimate the regressions for each Code item separately without any change in inferences.

7.4. Code items with low compliance As a further test, we also identify those items in the Code that have relatively low compliance at the end of the sample period (items with less than 65% compliance) to see if compliance with these items helps explain variation in performance and transparency. The items identified relate to compensation practices of the firm (questions 28 and 29), independence of committees (question 13), identification of personal use of firm assets (question 23), and communications about board meeting items (questions 52 and 53). Given the relatively low compliance of these items, perhaps companies find it costly to adhere to the principles underlying these aspects of the Code providing a mechanism by which market participants can separate firms. We perform a number of tests with these compliance criteria including using the sum of all the questions, each item considered separately, and eliminating items that satisfy our large change criteria above (question 53). In the end, all performance and transparency tests again fail to reveal significant differences, indicating that the Code has generally not improved the performance and transparency of Mexican firms.

7.5. Additional robustness tests In addition to the tests performed above, we conduct a series of additional robustness tests.

1. Controlling for cross-listing status of companies. 2. Including firm fixed effects in all pooled time-series cross-sectional regressions. 3. Utilizing alternative governance divisions including the continuous version of the compliance score, as well as terciles, quartiles, and quintiles of the compliance index as opposed to the HIGOV median designation. For these latter specifications, we code the extreme rankings as high and low governance and test for differences between the two as well as from the remaining middle group. 4. Limiting the sample to firm-year observations with trading volume above the median level in a given fiscal year. 5. Limiting each analysis to only those observations that have the requisite data for all analyses performed in every table. 6. Using market prices instead of returns, and net income scaled by total assets rather than changes in earnings in the market-related tests. 7. Using the level of debt financing as an alternative measure of agency costs. 8. Not using log transformations of variables where applicable. 9. Including all observations identified as outliers in the regression analyses. 10. Allowing the variables to vary based on insider ownership percentages of varying levels (i.e., controlling or not, continuous, quintiles, quartiles, and terciles). 11. Allowing the coefficients to vary based on the degree of board interlocking relations, as well as the type (i.e., independent–independent, insider–independent). 12. Controlling for leverage (debt to assets), sales growth, size (total assets, market value of equity, book value of equity), analyst coverage, and age in all analyses. 13. Investigating the market response to the issuance of the Code and the Securities Market Laws of 2001 and 2003. We find no discernable reaction to these events on average, and the cross-sectional variation in the response to these events is not related to the eventual compliance. We also investigate the market response to the initial and subsequent compliance disclosures but find no correlation. 14. Using lagged realizations of the compliance index instead of contemporaneous measures. This reduces the sample size but allows for the possibility that the changes in governance could take time to result in changes to performance and transparency. 8. Comparison of Mexico and Brazil Simply enacting the Code and requiring compliance reporting clearly has not been enough to promote improvements in Mexico’s financial markets. Even with significant investments of time and money to issue the


Code and subsequent legal reforms, no sizable economic benefits accrued from the regulations. This is similar to the findings in Locke, Qin, and Brause (2007), that monitoring alone is not enough to fundamentally alter behavior. The concentration of ownership of Mexican firms and the general lack of competition in product and service markets stemming from the relatively recent move to privatization in the late 1980s and early 1990s are significant obstacles in creating fundamental changes in the marketplace. Rajan and Zingales (2003) and Musacchio (2008a) note that the political economy has much to do with financial market developments in addition to legal origin. In Mexico’s case, insiders have vested interests in the status quo and have significant political power because of the amount of wealth they control. This is the situation described in Rajan and Zingales (2003), where legal origin is important given that code law countries are more easily controlled by powerful interests because of the concentration of power. Changing this system is difficult because companies tend to develop path dependencies in terms of their capital structures (Bebchuk and Roe, 1999). However, recent developments in Brazil’s special listing exchange, the Novo Mercado, which requires higher levels of commitment to corporate governance along with offering minority investor protection, has produced an exchange in which entrepreneurs can raise capital and increase the level of competition in the markets. Further, the exchange is characterized by disperse ownership, creating a potential transition of ownership in an economy that has been dominated by family control (Gorga, 2008). The Brazilian experience differs markedly from Mexico’s attempt to improve governance via the Code. The Brazilian stock exchange, Bovespa, developed the Novo Mercado and spent considerable time and money explaining the benefits of the new listing requirements to foreign institutional investors, underwriters, and entrepreneurs. It also altered the investment restrictions placed on Brazilian pension funds allowing funds to make higher levels of investments if the company is listed on the Novo Mercado (Gorga, 2008). Mexico still places restrictions on the investment of its pension funds.18 More important, the Bovespa supported the economic development of the Novo Mercado by putting in place advantages for companies listed on the special exchange. Brazil’s commitment to improved corporate governance was bolstered by the rule of one-share one-vote and the prohibition of preferred or super-voting shares. Essentially, Brazil is attempting to alter the competitive landscape for capital by encouraging firms through real economic benefits to adopt better systems of corporate governance. The legal regime in Brazil is similar to Mexico in that its commitment to investor protection is not clear.

18 Mexico restricts pension funds from investing in any equity securities listed on the Mexican Bolsa and all international exchanges. Pension fund investments have several other stringent restrictions including at least 51% of the funds’ assets must be invested in inflationprotected securities and at least 65% in securities with a maturity date shorter than 183 days. Furthermore, only 35% of fund assets can be invested in corporate bonds.

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However, the Bovespa is attempting to set up a special arbitration panel to expedite grievances, but as of 2009 it is still not implemented and thus represents a significant hurdle that needs to be cleared. However, as Coffee (2000) and Franks, Mayer, and Rossi (2009) note, market forces generally create demands for legal changes to help protect the benefits created. As such, Brazil could have found a mechanism to bring about fundamental changes in the financial markets, which could lead to future legal changes to help protect the efficacy of the new financial system. Brazil has a history of market developments in its past (Musacchio, 2008b), whereas Mexico has consistently lacked active financial markets throughout its recent past. The transition to an open market system is not an easy process, but our results illustrate that more is required than higher levels of monitoring. Fundamental changes to the competitive landscape and the availability of capital, along with mechanisms to reduce agency concerns, need to be implemented before major changes in performance and corporate transparency can occur in Mexico. Whether this is accomplished through legal reform, the introduction of new exchange listing requirements, the relaxation of investing restrictions, or a combination of all three is an open question.

9. Conclusion We examine the relation between compliance with Mexico’s Code of ‘Best’ Corporate Practices and performance and financial reporting transparency to assess the effectiveness of the reform. The Code was developed to provide information to market participants regarding the governance strength of firms trading on the Mexican stock exchange. Our results indicate that compliance with the Code has increased dramatically over time. However, compliance is generally not associated with improved performance or financial reporting transparency, suggesting that monitoring alone is not enough to bring about fundamental changes in Mexico. We do find that greater compliance with the Code is related to increased dividend payments, consistent with better-governed companies being forced to adopt costly measures to reduce agency costs as opposed to obtaining benefits via financial reporting transparency. We attribute these findings to the predominance of concentrated family ownership in Mexico along with the lack of investor protection. Our results have a number of policy implications and indicate that efforts in Mexico need to be supplemented with alternative mechanisms for improvements in financial reporting transparency to occur. Further, it is not clear whether the agency conflict between insiders and minority outside shareholders can be overcome without significant changes in the ownership structure of Mexican firms, as well as the legal environment. Mexico lacks a demonstrated commitment to protecting minority shareholders. Up until 2005 it did not have a single enforcement of the insider trading laws. In 2005, Ricardo Salinas Pliego and one of his companies, TV

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Azteca, were charged with insider trading by the US Securities and Exchange Commission (Wall Street Journal, 2005b). As of 2009, the allegations had yet to be enforced in an official US court. Further, Mexican regulatory authorities have not joined the US in its prosecution, indicating considerable uncertainty still exists concerning the commitment to investor protection. In 2000, Salinas Pliego set the example for other firms to follow after the enactment of the governance Code. He surpassed the Code’s recommendations by appointing an 11 member board for TV Azteca, including five independent board members, among several other initiatives. As a result, his company was chosen by Institutional Shareholders Services to receive an Award for Excellence in Corporate Governance in 2000. Compliance with the Code in this instance clearly did not result in good governance. In 2005, Mexico adopted similar provisions to those included in the US Sarbanes- Oxley Act, hoping that these changes would lead to improvements in the capital markets. However, unless regulators begin rigorously enforcing these laws, our results suggest that further mandates will be of little help and, even then, it is not clear that the laws will necessarily induce the desired economic effects given the different ownership structures in the two countries. Our results have implications for a number of emerging market economies attempting to attract foreign investment. Many of these countries are instituting governance reforms like Mexico’s. These reforms are perhaps steps in the right direction, but market monitoring alone is not likely enough to bring about substantial reform. Further, as noted by Allen, Qian, and Qian (2005), we need a better understanding of the interactions of law, institutions, finance, and growth prior to making broad prescriptions on how individual countries should implement regulations to bring about change. Appendix Per the Code of ‘Best’ Corporate Practices recommendations, negative responses to questions two and ten are labeled compliant, whereas affirmative responses are deemed compliant for the remaining questions. Mexico’s Code of Corporate Governance Practices questionnaire: 1. Does the firm’s board of directors have a minimum of five and a maximum of 15 board members? 2. Is the board solely composed of board members who own stock in the firm? 3. In the event that a ‘‘backup’’ board member is needed to replace a primary one, is it known in advance which of the primary members the ‘‘backup’’ board member will replace? 4. In the event that a primary board member needs to be replaced, does this member recommend to the board who should replace him/her from the secondary group of board members in advance? 5. Does the number of independent directors and directors controlling a majority stake in the firm constitute at least 40 percent of the total board seats?

6. Does the number of independent board members represent at least 20% of the total board seats? 7. Does the annual report identify which board members are independent and which ones hold ownership in the firm? 8. Does the annual report provide information about the category of each board member who owns stock in the firm? 9. Does the annual report provide information about the responsibilities and duties of each board member? 10. Does the entire board of directors carry out the functions of compensation, auditing, and finance? 11. In the event that the firm maintains separate committees for compensation, auditing, and finance, are the committees composed solely of board members holding ownership in the firm (i.e., insiders, independent but have ownership, etc.)? 12. If the firm has any of the committees mentioned above, do these committees have a minimum of three and a maximum of seven board members? 13. Are the compensation, auditing, and finance committees composed of at least one independent board member? 14. Is the audit committee chaired by an independent board member? 15. Does the board meet at least four times a year? 16. Is at least one of the meetings dedicated to discuss the firm’s middle and long-term strategy? 17. With approval of at least 25% of the board, can the committee have an extraordinary session? 18. Do the board members have access to all relevant information prior to each board meeting at least five days in advance? 19. Are there appropriate mechanisms that permit board members to examine relevant issues for the firm prior to the board meeting without having access to information five days in advance? 20. Are newly elected members provided with inductive training about all matters related to the company? 21. Do board members communicate either to the chairman of the board or the acting secretary about any potential conflict of interest in which a member of the board must abstain from voting? 22. Do board members make use of company assets and resources for the whole purpose of conducting business related to the duties of the board? 23. Does the firm have a clear set of rules that indicate when and how board members can use the firm’s assets for personal use? 24. Do board members attend at least 70% of the board meetings as required by the committee? 25. Do board members maintain absolute confidentiality about all relevant matters discussed in the board meetings? 26. Do the acting (full) board members inform the potential substitutes about relevant matters discussed in the board meetings? 27. Is full support provided to the board by the firm and its management through qualified opinions, recommendations, and guidance about the performance of the firm so board members can make informed decisions?


28. Does the compensation committee make sure that the hiring practices as well as the compensation of management are in line according to the guidelines and procedures approved by the board of directors? 29. Is it publicly revealed the structure and guidelines that were taken to determine the compensation package of key top management positions? 30. Do the audit fees paid to the auditing firm in charge of auditing the firm’s financial statements represent 20% or less of the total amount of auditing revenue of the auditing firm? 31. Is the auditor issuing the opinion rotated at least every six years? 32. Is the person who signs the letter of opinion from the auditor different than the person who acts as commissary? 33. Does the annual report provide detailed information about the qualifications of the person acting as the firm’s commissary? 34. Does the firm have a department in charge of performing internal audits? 35. Does the audit committee submit to the board for approval all policies related to its accounting practices (i.e., recommendations for a change in accounting method)? 36. Does the audit committee make sure that the preparation of monthly and quarterly financial statements follows the same principles, criteria, and accounting practices as the ones prepared at year’s end (annual reports)? 37. Does the firm have in place a system of internal control? 38. Are general guidelines and procedures of internal control submitted to the board for approval? 39. Does the audit committee evaluate on a regular basis all related guidelines to internal control and provide its opinion? 40. Does the external auditor also examine the firm’s internal control mechanisms and provide an opinion and a qualified report? 41. Does the audit committee ensure that the existing internal control mechanisms adequately address all the applicable mandated legal dispositions and report regularly to the board? 42. Is a review performed at least once a year to ensure that the firm complies with all applicable legal dispositions? 43. Is the board informed on a regular basis about relevant legal matters? 44. Does the finance committee examine the financial position, providing an evaluation about main investments as well as major financial transactions of the firm? 45. Does the finance committee examine on a regular basis the financial position of the firm, assessing its current performance relative to the strategic plan? 46. Does the finance committee support the board by ensuring that all investment and credit decisions are well aligned with the strategic vision of the firm? 47. Does the finance committee support the board by examining the firm’s financial projections, ensuring these are aligned with the strategic plan of the firm?

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48. During the annual meeting held with investors, did the firm require separate approval for all issues (as opposed to combining issues into one vote)? 49. During the annual meeting, did the firm present related matters for separate votes? 50. Is all relevant information that will be discussed during the annual meeting available to shareholders at least 15 days in advance? 51. Are shareholders provided with detailed information about all matters subject to vote during the shareholders’ meeting? 52. Does the information package provided to the shareholders contain detailed information about the structure of the board, including the professional background of each acting board member or candidate to the board? 53. Does the board of directors communicate to shareholders in writing all the relevant aspects of each committee, including the composition of each committee (i.e., names)? 54. Is each independent committee report available to shareholders? 55. Has the firm established policies and mechanisms to maintain lines of communication with investors and potential investors, informing publicly about all relevant matters related to the firm?

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Leuz, C., Nanda, D.J., Wysocki, P., 2003. Earnings management and investor protection: an international comparison. Journal of Financial Economics 69, 505–528. Locke, R.M., Qin, F., Brause, A., 2007. Does monitoring improve labor standards? Lessons from Nike. Industrial Labor Relations Review 61, 3–31. Lo´pez-de-Silanes, F., 2002. NAFTA and Mexico’s reforms on investor protection. Unpublished working paper, Yale University, New Haven, CT. McDonald, J.F., Moffitt, R.A., 1980. The uses of Tobit analysis. Review of Economics and Statistics 62, 318–321. Musacchio, A., 2008a. Can code law countries get good institutions? Lessons from the history of creditor rights and bond markets in Brazil. Journal of Economic History 68, 80–108. Musacchio, A., 2008b. Laws vs. contracts: legal origins, shareholder protections, and ownership concentration in Brazil 1890 1950. Business History Review 82, 445–473. New York Times, 2005. Charges raise questions about Mexico’s adherence to securities laws. E. Malkin. January 27, p. C8. Pincus, K., Rusbarsky, M., Wong, J., 1989. Voluntary formation of corporate audit committees among NASDAQ firms. Journal of Accounting and Public Policy 8, 239–265. Rajan, R.G., Zingales, L., 2003. The great reversals: the politics of financial development in the 20th century. Journal of Financial Economics 69, 5–50. Shleifer, A., Vishny, R.W., 1997. A survey of corporate governance. Journal of Finance 52, 737–783. Siegel, J., 2005. Can foreign firms bond themselves effectively by renting US securities laws? Journal of Financial Economics 75, 319–359 Simon, C.J., 1989. The effect of the 1933 Securities Act on investor information and the performance of new issues. American Economic Review 79, 295–318. Tilly, R., 1992. An overview of the role of large German banks up to 1914. In: Casis, Y. (Ed.), Finance and Financiers in European History. Cambridge University Press, Cambridge, UK, pp. 1880–1960. Wall Street Journal, 2001. Mexico bids for new investors with financial sector overhaul, June 1. Wall Street Journal, 2005a. Corporate governance (a special report): the global agenda: wherever investors go, demands for better governance follow. M. Jacoby. October 17, p. R7. Wall Street Journal, 2005b. Mexico’s TV Azteca is hit with SEC fraud suit. January 5. Wall Street Journal, 2006. Doing business in Latin America. M. A. O’Grady. September 15, p. A13. Wall Street Journal, 2008. International finance: Mexican market has tried but still lags. A. Harrup. September 12, p. C2. Westphal, J.D., Zajac, E.J., 1998. The symbolic management of stockholders: corporate governance reforms and shareholder reactions. Administrative Science Quarterly 43, 127–153.




Horizontal acquisitions and buying power: A product market analysis$ Sugato Bhattacharyya a,1, Amrita Nain b,n a b

Ross School of Business, University of Michigan, 701 Tappan Street, Ann Arbor, MI 48109, USA Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montreal, QC, Canada H3A 1G5

a r t i c l e in fo

abstract

Article history: Received 21 January 2009 Received in revised form 9 December 2009 Accepted 5 January 2010 Available online 7 August 2010

Horizontal mergers exert price pressure on dependent suppliers and adversely affect their performance. Consistent with the theory of countervailing power, concentrated suppliers and those with greater barriers to entry experience larger price declines after consolidation downstream. Time-series results suggest that consolidation in dependent supplier industries follows mergers in main customer industries, indicating that consolidation activity travels up the supply chain. The findings are broadly consistent with pervasive beliefs in the business community about the buying power effects of horizontal mergers. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G34 D42 D43 Keywords: Takeovers Mergers Buying power

‘‘ y apparel-company executives say they are bracing for store closures, cutbacks and thinner profit margins. The potential fallout reflects the huge negotiating power that a combined Federated-May would wield and the diminishing clout of suppliers. y it could also

accelerate consolidation among apparel suppliers, as they strive to get bigger to better face off against their giant customers.’’ — Wall Street Journal article2

1. Introduction $

The authors thank Kenneth Ahern, Amy Dittmar, E. Han Kim, Francine Lafontaine, Vikram Nanda, Linda Tesar, Bilal Zia, participants at the 2006 Conference on Empirical Research in Corporate Finance at the University of Oregon, 2007 Western Finance Association meetings, the Finance Brownbag series at the University of Michigan, the McGill Finance Seminar series and the Saw Centre Finance Seminar at the National University of Singapore. The second author thanks Institut de finance mathe´matique de Montreál for generous research funding. Comments from the referee, Husayn Shahrur, have helped to improve the paper greatly. n Corresponding author. Tel.: + 1 514 398 8440. E-mail addresses: [email protected] (S. Bhattacharyya), [email protected] (A. Nain). 1 Tel.: + 1 734 763 9777 0304-405X/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2010.08.007

There is a long-standing debate in the economics and finance literatures on the motives for horizontal mergers. While managers of firms undertaking horizontal mergers usually cite expected improvements in productive efficiencies, i.e., synergies, as the key rationale behind such moves, antitrust authorities frequently express concern that horizontal mergers may increase market power vis-a 2 ‘‘Combined Federated-May could stress apparel makers,’’ The Wall Street Journal, March 1, 2005.

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S. Bhattacharyya, A. Nain / Journal of Financial Economics 99 (2011) 97–115

vis customers and suppliers of the merging firms’ industry. The latter view is also often supported in discussions in the business press pertaining to specific deals, as evidenced by the quote above. Academic research has extensively examined the effect of horizontal acquisitions on market power vis-a -vis customers and arrived at conflicting conclusions.3 There is, however, a major selection bias inherent in studies that look for signs of selling power created by horizontal mergers. The bias arises due to the fact that horizontal mergers expected to increase selling power and result in higher prices for customers will be anticipated to be blocked by antitrust authorities. Thus, mergers which clearly enhance selling power may never be observed when one looks for evidence in product or stock markets. The same logic, however, does not hold so far as the impact on suppliers is concerned. Horizontal mergers that increase buying power may contribute to lower costs of production downstream. Moreover, enhanced buying power downstream may counteract established selling power upstream and force suppliers to charge competitive prices. In fact, antitrust authorities may very well look upon such mergers favorably. Consequently, we examine the possible creation of buying power through horizontal acquisitions by studying their impact on suppliers. An auxiliary motivation for looking at the effect of horizontal mergers on supplier industries is that the industrial organization literature already shows the importance of being a large buyer: buyer size and buyer industry concentration have long been known to be correlated with lower seller profits.4 Yet, the upstream effects of a major corporate event – industry consolidation through mergers – that can create large buyers and increase buyer industry concentration remain largely unexamined.5 Thus, the objective of this paper is to ask one overarching question: do horizontal mergers create buying power? We answer this question by first examining the effect of horizontal mergers on profits and product prices in the supplier industry. We use a relatively large, cross-industry sample to examine whether horizontal mergers bring about a decline in the profits of supplier industries and whether such a decline can be attributed to a decline in prices at which supplier industries sell. Using mergers and acquisitions (M&A) data from 1984 to 2003, we construct a sample of industries that experienced a significant jump in horizontal merger activity in a specific quarter. Having identified these downstream merger events, we ask whether supplier industries more dependent on the

3 Focusing primarily on announcement returns, Eckbo (1983), Stillman (1983), Eckbo (1985), Eckbo and Wier (1985), Fee and Thomas (2004), and Shahrur (2005) conclude that horizontal mergers do not create selling power vis-a -vis customers. Looking at product prices directly, Barton and Sherman (1984), Borenstein (1990), Kim and Singal (1993), Singal (1996), Akhavein, Berger, and Humphrey (1997), and Prager and Hannan (1998) conclude that horizontal mergers create selling power. 4 See, for example, Lustgarten (1975), Clevenger and Campbell (1977), McGuckin and Chen (1976), and Schumacher (1991). 5 Exceptions are Fee and Thomas (2004) and Shahrur (2005). Both these studies find some preliminary evidence that downstream mergers adversely affect suppliers in concentrated industries.

downstream merging industry experience greater adverse changes in profits and output prices after the event. We find that supplier industries selling a larger fraction of their output to the downstream consolidating industry have lower cash-flow margins following downstream consolidation. The abnormal cash-flow margin of dependent supplier industries after downstream consolidation is, on average, 3% lower than that of non-dependent supplier industries. Thus, we confirm Fee and Thomas’s (2004) finding that some supplier industries suffer declines in operating profits after a horizontal merger downstream. However, we recognize that a decline in supplier profit margins may also result from changes unrelated to the creation of market power downstream. To attribute deterioration in profit margins upstream to an increase in buying power downstream, we need to also show a decline in upstream selling prices. As a result, we use the Producer Price Index (PPI) as a measure of selling prices to examine changes in selling prices in dependent supplier industries. Controlling for changes in input prices and demand shocks faced by the supplier industry, we first establish that prior to downstream consolidation, changes in the PPI of dependent and non-dependent supplier industries over a three-year period are statistically indistinguishable. In contrast, dependent supplier industries exhibit significantly larger declines in PPI in the three years following downstream consolidation. The differential impact is of the order of 0.1% per month, translating to a difference of up to 3.6% over the three years following downstream consolidation. Our results are robust to alternative regression methods. A difference-in-differences test in the pooled data lends further confirmation of dependent suppliers performing significantly worse than non-dependent suppliers, but only in the postmerger period. To show that such declines are not due to secular time trends independent of downstream consolidation, we create random ‘event dates’ and use them as break points to further examine the evolution of supplier selling prices. We find that there is no difference in the selling prices of dependent suppliers before and after such random event dates. Based on this battery of tests, we conclude that the decline in supplier selling prices may, indeed, be attributed to consolidation downstream. While a decline in supplier prices after downstream consolidation is consistent with the creation of buying power, it may also be consistent with merger-induced improvements in efficiency. For example, if downstream consolidation created production efficiencies resulting in a decline in the demand for inputs, this could also lead to lower supplier selling prices. The existence of such a straightforward alternative explanation, therefore, requires us to design additional tests to attribute the decline in selling prices upstream to enhanced buying power downstream. To this end, we draw on Galbraith’s (1952) theory of countervailing acquisitions where he argues that economic power is held in check by the countervailing power of those who are subject to it. Thus, if sellers earn noncompetitive rents due to small numbers (oligopoly),


practical barriers to entry, or explicit collusion, buyers have an incentive to develop the power with which they can defend themselves.6 In Snyder (1996, 1998), mergers between buyers can intensify competition among colluding sellers leading to lower prices. If suppliers held prices above competitive levels prior to downstream consolidation – either unilaterally or through collusion – countervailing theory implies that increased purchasing power created by downstream consolidation would force them to start competing more aggressively on price. Thus, the selling prices of previously non-competitive suppliers would be more adversely affected by downstream consolidation. We test this implication of the countervailing power hypothesis by regressing the change in supplier industry prices after downstream consolidation on empirical proxies of the level of price competition in an industry. We find that supplier industries with a higher Herfindahl index or a higher four-firm concentration ratio prior to consolidation downstream experience larger price declines post-consolidation. A similar result obtains when we use capital intensity and capital expenditures to proxy for higher barriers to entry upstream. Using proxies for changes in supplier industry concentration prior to downstream consolidation, we find that the post-consolidation decline in supplier selling prices is higher when there is a prior increase in the four-firm concentration upstream. Similarly, suppliers experiencing increased horizontal merger activity prior to downstream consolidation suffer larger price declines post-consolidation. These results are all consistent with the creation of buyer power through downstream consolidation to countervail upstream market power. Our results give rise to several questions about the possible time-series pattern of horizontal merger activity across industries sharing product market relationships. Is downstream consolidation activity exogenous or is it triggered by prior consolidation in supplier industries? Do supplier industries respond to a loss in pricing power by subsequently undertaking horizontal acquisitions of their own? These intriguing questions have not been explored in prior M&A research. Consequently, we make an exploratory attempt to answer these questions using the data on horizontal mergers within industries in the 1984–2003 period. We find that suppliers’ horizontal merger activity in a given year is positively related to consolidation activity in main customer industries over the prior four years. This finding is consistent with the Becker and Thomas (2009) result that changes in customer industry concentration are positively related to subsequent changes in dependent supplier industry concentration, and is in line with the finding in Ahern and Harford (2009) that merger waves propagate along connected industries.7 Although it is hard to definitively establish causality, our result suggests that consolidation by suppliers arises as a reaction to downstream consolidation, consistent with the pattern exposited by our opening quote from the Wall Street Journal. In contrast, we find no statistically significant relationship

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between consolidation activity in customer industries and past merger activity in their main supplier industries. Our results confirm the Fee and Thomas (2004) finding that supplier operating performance deteriorates after downstream consolidation, but we are also able to attribute such deterioration to adverse price changes. The results are also consistent with Shahrur’s (2005) finding that more concentrated suppliers have poorer announcement returns when a downstream merger occurs. Combined, these prior results already point to the possibility of downstream mergers creating buying power. Our paper, in contrast, provides direct evidence that supplier selling prices themselves decline after downstream consolidation. We are also able to attribute this decline to a shift in market power in favor of the downstream merging industry. Our paper is also the first to show that supplier industries subsequently undertake horizontal acquisitions of their own and suggests that such consolidating acquisitions can propagate across industries sharing product market relationships. Finally, in addition to contributing to our understanding of the market power effects of horizontal acquisitions, this paper adds to existing evidence that merger activity is determined by industry-level factors (see Mitchell and Mulherin, 1996; Andrade, Mitchell, and Stafford, 2001). The paper is organized as follows: Section 2 briefly discusses related research. Section 3 motivates the empirical tests. Section 4 contains methodology, data sources, and results. Section 5 addresses issues of robustness. Section 6 concludes. 2. Existing literature Two approaches have been employed in the empirical literature to examine whether horizontal mergers create market power. The indirect approach, commonly found in the finance literature, examines the stock price reactions of merging firms, their rivals, suppliers, and corporate customers to M&A announcements. In this event-study based approach, efficient stock prices are assumed to correctly reflect the anticipated effects of horizontal mergers on factor and output prices. For example, if horizontal mergers enhance market power, rival firms should also be affected. Therefore, Eckbo (1983) and Stillman (1983) examine the announcement returns of rivals to merger announcements and to antitrust challenges to such mergers. However, they do not find any evidence consistent with the creation of market power through horizontal acquisitions. Likewise, Eckbo (1985) and Eckbo and Wier (1985) conclude that horizontal mergers are motivated for efficiency reasons and not for enhanced market power. Fee and Thomas (2004) and Shahrur (2005) examine the stock price reactions of rival firms, customers, and suppliers and also conclude that horizontal mergers are motivated primarily by improvements in production efficiencies. They find no evidence of enhanced selling power.8 However, although this is not

6

See Chapter 9 of Galbraith (1952). Ahern and Harford (2009) use techniques from the socialnetworking literature and determine inter-industry connections based on the strength of supplier and customer relations. 7

8 Although our paper focuses on studying the effect of horizontal mergers on buying power, our sample is consistent with these studies.

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their primary focus, both Fee and Thomas (2004) and Shahrur (2005) find some preliminary evidence that horizontal mergers increase buying power. The direct approach, most commonly found in the industrial organization literature, focuses directly on the effect horizontal mergers have on product prices. Borenstein (1990) and Kim and Singal (1993) find increases in airfares on routes served by merging firms relative to a control group of routes unaffected by mergers. Singal (1996) also examines airfares and concludes that airline mergers result in both increased market power and more efficient operations. Prager and Hannan (1998) examine the effect of bank mergers on deposit rates and attribute declines in such rates to increased concentration brought about by the mergers. Akhavein, Berger, and Humphrey (1997) and Barton and Sherman (1984) also find evidence that horizontal mergers increase market power. These product market studies tend to focus on specific industries like banking and airlines and confine their attention to price levels in the consolidating industries themselves. As a result, it is not clear to what extent the results are specific to the characteristics of the particular industries analyzed. 3. Hypothesis development Merged firms can exercise buying power in different ways. They can, for example, pool purchases to obtain quantity discounts from suppliers, or increase profit margins by squeezing suppliers. Insofar as these actions promote greater efficiency on the part of suppliers, Fee and Thomas (2004) label these as evidence of efficiencyincreasing buying power. A merged firm may also exercise buying power by restricting purchases to monopsony levels causing input prices to fall below marginal cost (see Robinson, 1933). In the presence of sunk costs, such price decreases may be sustained in the short-run but will come at a cost to efficiency. In this paper, we are agnostic about the welfare consequences resulting from the use of market power and focus entirely on the possible exercise of market power alone.9 If horizontal mergers do, indeed, create buying power, we expect this effect to show up in the operating performance of supplier industries. Since merging firms will be able to exercise buying power more effectively when their supplier industries are more dependent, we hypothesize that dependent supplier industries will suffer a greater decline in performance after downstream consolidation than those less dependent on the downstream industry. Since such effects may take some time to (footnote continued) An analysis of selling prices after horizontal mergers provides no evidence of enhanced selling power. 9 Firms are known to publicly justify mergers with the cost savings that would arise due to increased buying power. A proposed merger between Staples and Office Depot in 1997 was blocked by antitrust authorities on the grounds that it would lead to higher prices for consumers. Staples countered with the argument that the merger would allow it to lower selling prices because of the greater purchasing power the transaction would bring. See ‘‘Office Depot Staples deal is blocked,’’ The Wall Street Journal, July 1, 1997.

show up in the data, we hypothesize that such performance effects will be evident over a three-year horizon. We choose this horizon because acquisitions of significant size often take six months to a year to be consummated. Thus, our first hypothesis is: Hypothesis 1. More dependent suppliers experience greater adverse changes in cash flow margins in the three years subsequent to an announcement of downstream consolidation. Declines in operating performance, while consistent with buying power enhancement, are not definitive evidence of the exercise of buying power. Other unrelated factors like increases in production costs or wages may also account for a drop in profitability of supplier industries. If, however, the decline in performance is related to enhanced buying power, we should expect this to also show up in the form of diminished selling prices in the supplier industry. Therefore, our second hypothesis is: Hypothesis 2. More dependent supplier industries experience larger declines in selling prices subsequent to downstream consolidation. When consolidation downstream is mainly predicated on taking advantage of cost-savings, price declines in supplier industries are suggestive of the creation of buying power. However, there are several other channels through which horizontal mergers can affect supplier prices. For example, efficiency-improving horizontal mergers can have either a positive or a negative impact on supplier prices. An increase in productive efficiency downstream can result in lower marginal costs of production, lower selling prices, and higher output levels. Higher output levels can drive up demand for inputs and, therefore, the prices charged by suppliers. On the other hand, if consolidation enables the merging firms to produce the same output with a lower use of inputs, the demand for inputs, and therefore their prices, will fall. Thus, efficiency improvements alone can also result in observed declines in supplier selling prices. Such declines in supplier selling prices may also be explained by an increase in the selling power of the consolidating industry. Diminished competition resulting from consolidation may result in higher selling prices and lower output levels. These lower output levels would translate into lower demand for inputs and, thus, lower input prices, even in the absence of enhanced buying power.10 An observed decline in supplier selling prices could, then, be explained without relying on the enhancement of downstream buying power. Since production efficiencies, monopolistic collusion, and enhanced buying power can coexist when horizontal acquisitions occur, distinguishing clearly between these possible causes for price declines in supplier industries is challenging. We use the hypothesis 10 Jensen (1993) presents another ‘efficiency’ explanation for horizontal mergers where some consolidations are driven by excess capacity. If the need to reduce excess capacity leads to consolidations in both customer and supplier industries, then a decline in supplier prices could be attributed to excess capacity rather than the creation of buying power.


of countervailing acquisitions to see if such price declines can be attributed, at least in part, to enhanced buying power. Galbraith (1952) contends that in the typical modern market of a few sellers, the active restraint to hold prices close to marginal cost is provided not by competitors but by strong buyers. One implication of this theory is that downstream consolidation acts as a check on noncompetitive pricing upstream. More recent models for countervailing power allow for multiple sellers whose ability to collude depends on the characteristics of the buyer. For example, Snyder (1996) presents a dynamic theory of countervailing power in which large buyers are shown to obtain lower prices from colluding sellers. In Snyder (1996, 1998), mergers between buyers intensify competition among colluding sellers. Snyder (1996) shows that mergers in the buyer industry increase profits of all buyers, not just those of the merging firms, at the expense of the seller. Ellison and Snyder (2001), Stole and Zwiebel (1996), and Chipty and Snyder (1999) examine buyer bargaining power relative to a single seller. Their models present reasonable conditions under which large buyers are charged lower prices. Moreover, the notion that large buyers have an advantage in obtaining price concessions from sellers has been verified by a number of empirical studies.11 If downstream consolidation creates countervailing power as these theories suggest, then suppliers who enjoyed some form of non-competitive pricing prior to such consolidation should experience larger price declines ex post. Using industry concentration as a measure of competitive pricing, we formulate our third hypothesis as: Hypothesis 3. If downstream consolidation generates buying power, supplier industries with higher concentration prior to downstream consolidation will experience larger declines in selling prices subsequent to downstream consolidation. In the industrial organization literature, potential entry is viewed as one of the driving forces of competition. In traditional models, an oligopoly can sustain a collusive equilibrium with the credible threat of reversion to lower profits of a non-collusive equilibrium. However, entry threats can break any given degree of collusion provided that entry barriers are low enough.12 Thus, barriers to entry are a structural source of pricing power that can allow firms to collude and hold prices above marginal cost. Not surprisingly, Galbraith (1952) also recognizes barriers to entry as an anti-competitive element that can be offset by the exercise of countervailing power. Insofar as entry barriers confer the ability to price above marginal costs, we can formulate the following complementary hypothesis: Hypothesis 4. If downstream consolidation generates buying power, supplier industries with greater barriers to entry prior to downstream consolidation will experience larger 11 See, for example, Lustgarten (1975), Clevenger and Campbell (1977), McGuckin and Chen (1976), and Schumacher (1991). 12 For formal proofs, see Harrington (1989).

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declines in selling prices subsequent to downstream consolidation. Hypothesis 4 helps to further distinguish efficiency from the creation of buying power. Downstream mergers that generate demand effects upstream only due to enhanced efficiencies should have no effects on prices of supplier industries with low barriers to entry—competitive entry and exit alone will keep prices close to marginal cost. However, the prices charged by suppliers with high barriers to entry will be affected. Efficiency enhancements that increase input demand could increase prices charged by suppliers with market power and increase their profits. In contrast, efficiency enhancements that decrease input demand will have ambiguous effects on the profits of and prices charged by suppliers with market power. While a decreased demand for inputs may result in lower quantity supplied, suppliers with market power will tend to counteract by increasing prices. As a result, there is no strong reason to suspect that, in the absence of newly created buying power downstream, prices facing a supplier with market power will decline. Thus, evidence consistent with Hypothesis 4 would be supportive of the hypothesis that horizontal mergers do create buying power. Galbraith (1952) contends that countervailing power can act as a restraint on both buying power and selling power. Implicit in the theory of countervailing power is the idea that consolidation in an industry can be a reaction to consolidation upstream or downstream. The possibility that mergers in one industry trigger countervailing mergers in related industries is an intriguing avenue of research that has remained largely unexplored. The hypotheses delineated above lead to a number of follow-on questions. Are downstream mergers exogenous events or are they themselves triggered by consolidation upstream? Do adversely affected supplier industries subsequently undertake mergers to offset the loss of market power engendered by downstream consolidation? Theory provides no guidance as to who merges first and the consequent sequence of countervailing consolidations. Therefore, for most of our analysis, we remain agnostic about who actually merges first and focus primarily on the effect of downstream mergers on upstream profits and selling prices. However, in Section 4.5, we attempt to shed some light on the possible sequencing of consolidation activity across industries sharing product market ties. 4. Data sources, methodology, and results 4.1. Data construction We begin by constructing a sample of industries that experienced an identifiable increase in consolidation activity in order to obtain distinct pre- and post-merger periods. We obtain from Securities Data Company (SDC) Platinum all acquisitions announced between 1984 and 2003 that meet the following criteria: (i) the target and acquirer both were U.S.-based, (ii) the target and acquirer shared the same primary four-digit Standard Industrial Classification (SIC) code, (iii) the announced acquisition

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was eventually completed, and (iv) the acquirer bought more than 50% of the target’s stock. From SDC Platinum we also obtain the transaction value associated with each merger, that is, the total value of consideration paid by the acquirer, excluding fees and expenses. For each four-digit SIC code in the merger sample, we measure quarterly acquisition activity as the total transaction value of all horizontal acquisitions announced in a quarter as a proportion of industry total assets. We classify an industry as having experienced a merger event in a given quarter when the following conditions hold: (i) quarterly acquisition activity in the current quarter is greater than 10% and (ii) quarterly acquisition activity in any of the previous 12 quarters did not exceed 2.5%. The first condition ensures that the selected industries experienced significant consolidation in a particular quarter, while the second condition ensures that we have a clean pre-event period during which there was little horizontal merger activity. This definition enables us to identify 259 four-digit SIC codes that experienced at least one merger event between 1984 and 2003.13 Next, we use the make and use tables from the 1992 and 1997 Benchmark I–O accounts of the Bureau of Economic Analysis (BEA). The make table is a matrix showing the industry production of each commodity in the economy at producer prices. The use table is a matrix showing the commodities consumed, or used, by each industry and final consumers at producer prices. We follow the methodology detailed in the Appendix of Allayannis and Ihrig (2001) to create an input–output matrix from the make and use tables.14 We use the 1992 input–output matrix to match suppliers to industries consolidating in or before 1994 and the 1997 input– output matrix to match suppliers to industries consolidating in 1995 or after. We are able to find suppliers for 141 merging industries.15 Table 1, Panel A lists these merging industries along with the number of mergers that

13 Existing research provides no specific guidance on whether merger activity should be measured by quarter or by year. In some industries, spurts in merger activity may last longer than in others. Therefore, we also calculate an annual measure of industry merger activity with the same cutoff percentages. We find that using an annual measure results in a slightly smaller merger-event sample that has an 85% overlap with the sample identified using the quarterly measure. The results of the paper remain unchanged if we use the sample based on the annual measure of merger activity. 14 The make and use tables are based on IO codes. The BEA provides a mapping from IO codes to SIC codes for the 1992 tables and from IO codes to North American Industrial Classification System (NAICS) codes for the 1997 tables. For 1992, we focus only on industries that have unique IO-SIC codes matching and, for 1997, only those with unique IONAICS matching. To convert the NAICS match to SIC codes, we use correspondence tables provided by the U.S. Census Bureau. We restrict our sample to cases where NAICS data are fully derivable from SIC data: an SIC code is matched to a NAICS code when 100% of its sales/receipts are included within the corresponding NAICS code. Note that this allows for matching multiple SIC codes to the same NAICS code. Finally, we match all census data to M&A data using SIC codes provided by SDC Platinum. 15 Some of the merging industries experience more than one horizontal merger event and, therefore, appear more than once in the sample of 141 industries. Moreover, industries in our merger-event sample can share customer-supplier relationships. We discuss the robustness of our results to these issues in Section 5.

contribute to each merger event and the ratio of the merger transaction value to industry total assets. In Section 5 of the paper, we discuss robustness of our results to alternative sample selection methods. Using the input–output matrix, we also calculate the fraction, fmj, of supplier industry j’s output sold to the consolidating industry m. Higher values of fmj indicate that the supplier industry j is more dependent on the consolidating industry. For each consolidating industry, we identify up to ten supplier industries with the highest values of fmj. With 141 consolidating industries, we can, at most, get 1,410 consolidating industry–supplier industry pairs. We are able to obtain data on fmj for 1,155 consolidating industry–supplier industry pairs. By choosing to work with as many as ten suppliers per consolidating industry, we include industries selling a very small fraction of their output to the merging industry and are, therefore, unlikely to be affected significantly by downstream merger activity. This allows our cross-sectional tests to have greater power in detecting any relation between supplier dependence and profit or price changes experienced by the supplier industry. We define dependent suppliers as those with values of fmj in the top quintile of the distribution. Remaining suppliers are classified as non-dependent.16 Table 1, Panel B provides the distribution of fmj for dependent and nondependent suppliers. Dependent suppliers provide, on average, 15.7% of their output to the consolidating industry, while non-dependent suppliers provide 1.7%. 4.2. Supplier industry operating performance Pursuant to our first hypothesis, we examine the impact of downstream consolidation on supplier industry operating performance. We measure the operating performance of an industry by the cash flow-to-sales ratio of the median firm in the industry. As in Fee and Thomas (2004), the cash flow-to-sales ratio of a firm is the ratio of operating income (Compustat item 13) to sales (Compustat item 12). We then define an industry’s abnormal operating performance as the deviation of its operating performance from that of the median industry in the economy. We first regress abnormal operating performance prior to downstream consolidation on supplier dependence. Separately, we also regress abnormal operating performance after downstream consolidation on supplier dependence. Supplier dependence is captured by a dummy variable, D, that equals one for dependent suppliers and is zero otherwise. Control variables are derived from previous research on the determinants of industry profitability.17 Profit margins are likely to be higher in less 16 Our findings are robust to changes in the fmj cutoff used to classify suppliers as being dependent. For example, our results continue to hold if we define dependent suppliers as those in the top quartile of fmj. Moreover, instead of defining a binary variable to capture supplier dependence, we have also used the continuous variable fmj as a measure of supplier dependence (unreported). Our results continue to hold, albeit with smaller statistical significance. 17 See, for example, Schumacher (1991).


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Table 1 Description of industries that experienced a horizontal merger event. Panel A lists the SIC code of 141 industries that experience a horizontal merger event between 1984 and 2003, the size of the merger event, and the number of deals contributing to the merger event. A horizontal merger is defined as a merger between two firms within the same primary four-digit SIC code. An industry is classified as having experienced a merger event in a given quarter if the total transaction value (TV) of all horizontal acquisitions announced in that quarter exceeds 10% percent of industry total assets (TA). TV is the total value of consideration paid by the acquirer excluding fees and expenses (in millions). TA is the book value of total assets (in millions) Panel B provides the distribution of fmj, the percentage of supplier industry j’s output sold to the merging industry m for a sample of 1,155 merger industry–supplier industry pairs. Higher values of fmj indicate that the supplier industry j is more dependent on the consolidating industry for buying its output. Dependent suppliers are defined as those with fmj in the top quintile. Remaining suppliers are classified as non-dependent suppliers. Panel A: SIC code of merging industries, merger year, and size of merger event SIC

Year

Quarter

TV/TA

No. of deals

SIC

Year

Quarter

TV/TA

No. of deals

2047 3944 4953 2035 7331 8743 2086 2721 3429 2434 2599 3635 3549 3084 3823 3691 1479 2992 4131 2822 7331 2611 3911 2099 2064 2062 3851 2241 3537 3353 3524 3556 3612 3823 7323 7215 8733 2448 2514 3641 4724 4222 3631 2037 3826 6361 2062 2091 2251 3634 2992 2273 3534 2833 3357 3452 3691 7322 2252

1984 1984 1984 1984 1984 1984 1984 1985 1985 1985 1985 1985 1986 1986 1986 1987 1987 1987 1987 1987 1988 1988 1988 1988 1988 1988 1988 1989 1989 1989 1989 1989 1989 1990 1990 1996 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1998 1998 1998 1998 1998 1998 1998 1998 1998 1999 1999

2 2 2 2 3 3 4 1 2 3 4 4 1 3 4 1 1 2 2 3 1 2 3 3 3 3 4 1 2 3 3 3 4 2 2 4 1 1 1 1 2 2 3 3 3 3 3 4 1 1 1 3 3 4 4 4 4 2 2

0.114 0.116 0.160 0.492 0.163 0.172 0.159 0.192 0.131 0.750 0.246 0.465 1.462 0.252 0.166 0.127 0.904 0.100 0.156 0.144 0.102 0.146 0.125 0.145 0.281 0.318 0.404 0.206 0.218 0.127 0.136 1.651 0.204 0.104 0.437 0.266 0.464 0.582 1.681 41.906 0.106 0.351 0.101 0.109 0.123 0.138 0.680 0.135 0.123 0.261 0.361 0.194 1.277 0.164 0.328 0.439 0.529 0.153 0.206

1 1 1 1 1 1 2 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 2 1 1 1 1 2 1 1 1 2 4 4 2 6 1

7261 1446 7371 2656 4222 7322 2842 3482 3533 8072 3463 2393 3944 3592 2299 2041 3851 2063 2064 2677 2297 3792 3931 7374 2676 2813 3556 2092 3431 7521 2499 2652 3433 3944 7221 2893 3812 3441 4922 7841 8712 7311 3911 2671 2911 3995 7382 3825 3821 3949 3571 3444 7323 3999 6282 2452 3491 7322 8711

1991 1991 1992 1992 1992 1992 1992 1993 1993 1993 1993 1993 1993 1993 1994 1994 1994 1994 1994 1994 1995 1995 1995 1995 1995 1995 1995 1996 1996 1996 1996 1996 1996 1996 1996 2000 2000 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 2002 2002 2002 2002 2002 2002 2002 2002

2 2 1 1 3 3 4 2 3 3 3 3 3 4 1 3 3 3 3 4 1 2 2 2 3 4 4 1 1 1 2 2 3 4 4 4 4 1 1 1 1 1 2 2 2 2 2 3 3 3 3 1 1 2 2 2 2 3 3

0.109 0.266 0.207 0.261 0.105 0.181 0.339 0.220 0.139 0.173 0.298 0.323 0.336 2.242 0.182 0.150 0.168 0.277 0.280 0.225 0.240 0.123 0.220 0.296 0.766 0.153 1.739 0.143 0.179 0.189 0.477 0.815 0.245 0.146 0.252 0.104 0.147 0.144 0.149 0.349 0.373 1.223 0.134 0.178 0.201 0.323 0.333 0.102 0.102 0.138 2.699 0.451 6.354 0.343 1.204 1.932 2.737 0.136 1.417

2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 2 2 2 1 1 1 1 2 1 2 2 4 1 1 1 1

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Table 1 (continued ) Panel A: SIC code of merging industries, merger year, and size of merger event SIC

Year

Quarter

7374 1999 2 2035 1999 2 7291 1999 3 3663 1999 3 3334 1999 3 1446 1999 4 3315 1999 4 2834 1999 4 3669 1999 4 3594 2000 1 3851 2000 2 3931 2000 3 Panel B: Fraction of supplier output sold to fmj Dependent suppliers Non-dependent suppliers All

TV/TA

No. of deals

0.325 0.543 0.147 0.204 0.265 0.106 0.109 0.422 0.869 0.158 0.119 0.114 merging industry

7 1 1 4 1 1 1 7 2 1 1 1

SIC

Year

Quarter

TV/TA

No. of deals

2844 2999 3826 3714 3651 3562 3443 3842 3577 8111 3823

2002 2002 2002 2002 2002 2002 2003 2003 2003 2003 2003

3 3 4 4 4 4 1 1 3 3 4

1.976 243.384 0.130 0.174 2.411 3.696 0.107 0.178 0.205 28.791 1.268

1 1 2 2 1 1 1 1 3 3 2

N

Min (%)

Max (%)

Mean

Median (%)

231 924 1,155

5.48 0.04 0.04

93.27 5.42 93.27

15.70 1.68 4.48

9.66 1.35 1.76

competitive industries, in industries with greater barriers to entry, and in industries with greater product differentiation. We use the Herfindahl index, calculated as the sum of squared market shares of the firms in an industry, as a measure of competition within an industry. Since a high capital requirement is likely to function as a barrier to entry, we use capital intensity and capital expenditures as control variables when estimating industry profitability. For each four-digit SIC, we calculate Capital intensity as industry total assets (Compustat item 6) divided by industry total sales (Compustat item 12). Capital expenditures are calculated as an industry’s total capital expenditure (Compustat item 128) divided by industry total assets. While Capital intensity provides a scaled measure of the total capital stock in an industry at a point in time, Capital expenditures provide a scaled measure of the annual capital investment required in an industry. Finally, we use Advertising intensity to proxy for product differentiation, where this is calculated as industry total advertising expense (Compustat item 45) divided by industry total sales. Table 2 presents estimates using ordinary least squares, with robust standard errors clustered at the two-digit SIC level.18 In the first column of Table 2, the dependent variable is the three-year average of supplier industry abnormal operating performance preceding the downstream merger. The coefficient on the dependence dummy is statistically insignificant. This indicates that, controlling for general factors affecting industry profit margins, the profitability of dependent suppliers is statistically indistinguishable from that of non-dependent suppliers prior 18 The 318 observations used in the analysis of supplier industry profit margins comprise 98 unique industries at the four-digit SIC level. The sample is small because Compustat SIC codes are often aggregated at the two- or three- digit SIC level and, therefore, we are unable to obtain profit margin data for a number of four-digit SIC codes.

to the downstream merger event. The dependent variable in the second column is supplier industry abnormal operating performance averaged over the three years following the downstream merger event. The coefficient on the dependence dummy is now negative and significant at the 95% confidence level. The magnitude of the coefficient indicates that the abnormal cash-flow margin of dependent supplier industries is 3% lower than that of non-dependent supplier industries. We note that cashflow margins are higher in industries with greater barriers to entry and in industries with greater product differentiation.

4.3. Supplier industry selling prices The results in the previous subsection, while establishing deterioration in the performance of dependent suppliers after downstream consolidation, say nothing about why the deterioration occurs. Deterioration in operating margins can occur due to a rise in costs or a fall in selling prices. If consolidation downstream creates buying power, we should observe a decline in supplier selling prices. Therefore, we now test whether selling prices of dependent suppliers decline more after downstream consolidation. An auxiliary advantage of examining selling prices is that supplier cash-flow margins are available only for a subset of four-digit supplier SIC codes (see footnote 17). Since product price data compiled by the Bureau of Labor Statistics (henceforth BLS) are available for a larger sample of supplier industries, we can both enlarge our sample of supplier industries and answer the question of buying power creation more directly. Prior product market studies have examined the effects of horizontal mergers on the selling prices of the consolidating industry itself using a control-group


Table 2 Supplier operating performance. This table presents a multivariate analysis of abnormal cash flow margins (ACFM) of supplier industries. We identify the 10 most dependent suppliers of each of the 141 industries that experienced a merger event between 1984 and 2003. ACFM of an industry is defined as that industry’s median cash flow-to-sales ratio minus the cash flow-tosales ratio of the median industry in the economy. The cash flow-to-sales ratio of a firm is the ratio of operating income (Compustat item 13) to sales (Compustat item 12). In column 1, the dependent variable is the average ACFM in supplier industries over the three years preceding the downstream merger event. In column 2, the dependent variable is the average ACFM in supplier industries over the three years following downstream consolidation. The dependence dummy equals one if the supplier industry belongs to the top quintile of fmj, the fraction of industry j’s output sold to the downstream merging industry, and zero otherwise. Herfindahl index is the sum of the squared sales market shares of firms in the supplier industry. Capital intensity is industry total assets (Compustat item 6) divided by industry sales (Compustat item 12). Capital expenditure is the supplier industry’s total capital expenditure (Compustat item 128) divided by the industry’s total assets. Advertising expense is the supplier industry’s total advertising expense (Compustat item 45) divided by the industry’s total sales. t-Statistics based on robust standard errors clustered at the two-digit SIC level are in parentheses. Bold font indicates significance at least at the 10% level. The superscripts a, b, and c indicate significance at the 1%, 5%, and 10% levels, respectively.

Dependence dummy Herfindahl index Capital intensity Capital expenditure Advertising expense R-squared F-statistic Observations

1 Dependent variable ACFM before downstream consolidation

2 Dependent variable ACFM after downstream consolidation

0.022 (1.49) 0.017 (0.90) 0.060 (6.75)a 0.535 (1.87)c 0.111 (0.43)

0.030 (2.07)b 0.038 (1.10) 0.057 (6.14)a 0.812 (2.02)c 0.455 (1.90)c

0.27 15.33a 318

0.31 8.40a 317

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For each supplier of a consolidating industry, we obtain the Producer Price Index (PPI) from the BLS.19 The PPI series allows us to measure the change over time in the selling prices received by domestic producers of goods and services. We adjust the PPI series for inflation using the Gross Domestic Product (GDP) price deflator, and call it the Real Producer Price Index (RPPI). Table 3 presents summary statistics of supplier industry RPPI. The table shows the average value of RPPI for suppliers as a whole over the three years before the downstream merger, the average value three years after the downstream merger, as well as the difference between the two values. The difference is negative and significant at the 99% confidence level, suggesting that supplier industries, on average, experience a decline in selling prices after downstream consolidation. Next, we split the sample into two groups: dependent suppliers and non-dependent suppliers. Table 3 shows that dependent suppliers had significantly lower prices than the non-dependent suppliers, both before and after the downstream consolidation. Although both groups experience a decline in prices after the downstream merger, the difference-in-differences test in the last row shows that the fall in prices is significantly larger for dependent suppliers. These univariate results support the hypothesis that downstream consolidation has greater adverse effects on dependent suppliers. However, the finding that dependent suppliers have lower prices than non-dependent suppliers both before and after the downstream merger event requires that we account for the possibility that more dependent suppliers are fundamentally different from less dependent ones in terms of average price levels over time. Moreover, since univariate tests show that both groups of suppliers experience significant price drops after the downstream merger, we need to control for the possibility that, due to exogenous factors, price levels after downstream consolidation are lower for all industries. Our multivariate analysis begins with the following regression model estimated using pooled OLS with Newey-West standard errors.

Drppijt ¼ a0 þ a1 Dj þ a2 Drppi_inp1jt þ a3 Drppi_inp2jt approach. These studies compare changes in prices charged by the merging firms to those charged by a control group of firms in the same industry. The control group is assumed to be similarly impacted by other factors that affect price changes in an industry like demand conditions, changes in input prices, and the like. For example, Kim and Singal (1993) compare airfare changes on routes affected by airline mergers with airfare changes on unaffected routes. For our study, a controlgroup approach would require us to identify, for each supplier industry, another industry experiencing identical changes in demand conditions and factor prices but that is not itself affected by downstream consolidation, and is not an upstream or downstream industry to the supplier industry. This is, clearly, a tall order. As a result, we abandon this approach and, instead, explicitly account for changes in input prices and demand shocks that a supplier industry may face.

þ a4 Dwagejt þ a5 Dtpt þ ejt

ð1Þ

where rppi is the natural logarithm of the RPPI of supplier industry j. The dummy variable, D, identifies dependent 19 The Producer Price Index series reflect price movements for the net output of goods-producing sectors of the U.S. economy. To the extent possible, prices used in constructing the indexes are the actual revenue or net transaction prices producers receive for sales of their outputs. Scientific (probability) sampling techniques are used to select reporting establishments, products, and transactions for all types and volumes of output. The PPI measures changes in prices received by domestic producers; imported products are not priced in the survey. In concept, the PPI is calculated using the modified Laspeyres formula: P It ¼ QQaa PPt0 100, where It is the price index in the current period; P0 is the price of a commodity in the comparison period; Pt is the current price of the commodity; and Qa represents the quantity shipped during the weight-base period. More details can be found in Chapter 14, Producer Prices, BLS Handbook of Methods http://www.bls.gov/opub/ hom/pdf/homch14.pdf.

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Table 3 Supplier selling prices: univariate analysis. This table compares prices in supplier industries during the three years before and three years following consolidation in a downstream industry. We identify the 10 most dependent suppliers of each of the 141 industries that experienced a merger event between 1984 and 2003. Producer Price Index (PPI) data for supplier industries are obtained from the Bureau of Labor Statistics (BLS). The PPI for each supplier is deflated using the GDP price deflator to obtain the Real PPI (RPPI). The table includes all merger industry–supplier industry pairs for which RPPI data are available. Dependent suppliers are supplier industries with the top 1/5th of values for fmj, the fraction of industry j’s output sold to the downstream merging industry. Non-dependent suppliers include all remaining supplier industries. U.S. Census Bureau’s 1992 and 1997 benchmark input–output tables are used to calculate supplier dependence. t-Statistics are provided in parentheses. Bold font indicates significance at least at the 10% level. The superscripts a, b, and c indicate significance at the 1%, 5%, and 10% levels, respectively. 1 Before downstream merger

2 After downstream merger

N

RPPI

N

RPPI

N

DRPPI

All supplier industries

895

1.416

929

1.391

889

Dependent suppliers

174

1.371

184

1.326

173

Non-dependent suppliers

721

1.427

745

1.407

716

0.025 (5.63)a 0.044 (5.28)a 0.019 (4.13)a 0.024 (2.22)b

Difference

0.056 (2.29)b

suppliers. The control variables rppi_inp1ij and rppi_inp2ij represent the RPPI of supplier industry j’s two primary inputs, again in logs, which we identify using benchmark I–O tables.20 To this end, we first calculate the weights, wji, that represent the fraction of supplier industry j’s input provided by industry i. We take the two industries, i, with the highest values of wji as the main contributors to input prices for the supplier industry j. Price data for these inputs are obtained from the BLS. The control variable wage is the log of average hourly earnings of production workers compiled by the BLS. Hourly earnings are available only for production workers in the mining and manufacturing industries and are often provided only at the three-digit SIC level. When wage data are available only at the three-digit level, we apply them to all four-digit industries within the three-digit SIC. The industrial production index, tp, obtained from the Federal Reserve Board, measures log of the real output of the manufacturing, mining, and electric and gas utilities industries and is used to control for the demand conditions in the economy. The regression includes a time trend, industry dummies at the two-digit SIC level, and year dummies. We first estimate Eq. (1) for all supplier industries over the 36 months preceding downstream consolidation and then separately over the 36 months following downstream consolidation, ignoring the merger-event quarter. Results from these two regressions are in columns 1 and 2 of Table 4. Column 1 shows that the coefficient on the dependence dummy, D, is statistically insignificant in the period prior to the downstream merger event. Thus, once

20 It is important that the input prices used as control variables in this regression are unaffected by events occurring in the merging industry. To reduce the possibility of endogenous input prices, we ensure that the industries that provide the main inputs of the supplier industry have no product market relation with the downstream merging industry.

3 Change

0.080 (3.06)a

factor prices and demand conditions are controlled for, price changes in dependent supplier industries prior to downstream consolidation are not significantly different from those in other supplier industries. However, in the post-merger sample presented in column 2, the dependence dummy is significantly negative at the 99% confidence level. Therefore, after the downstream consolidation, dependent suppliers do experience adverse price changes relative to non-dependent suppliers. The magnitude of the regression coefficient in column 2 suggests that the decline in prices for dependent supplier industries is greater by about 0.1% per month relative to non-dependent supplier industries. While the analysis indicates diminished price performance post-downstream consolidation, it does not prove conclusively that the coefficient on the dependence dummy is different between the two periods. To do that, we estimate the following regression using the full 72month panel:

Drppijt ¼ a0 þ a1 Dj þ a2 PMjt þ a3 Dj PMjt þ a4 Drppi_inp1jt þ a5 Drppi_inp2jt þ a6 Dwagejt þ a7 Dtpt þ ejt :

ð2Þ

The dummy variable, D, again captures supplier dependence and the coefficient a1 captures differentials in average price levels of dependent suppliers over time. For any supplier industry–merger industry pair, the postconsolidation dummy variable, PM, equals one after the downstream merger event and zero before. Its coefficient, a2, captures the change in average price levels after consolidation for all suppliers. It also controls for exogenous shocks that might affect prices in supplier industries as well as trigger mergers in the downstream industry. The coefficient of primary interest is, however, a3: if dependent suppliers suffer larger declines in selling prices due to downstream consolidation, the coefficient on the interaction of D and PM should be negative. All other variables are as described earlier for Eq. (1).


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Table 4 Supplier selling prices: multivariate analysis. This table presents a multivariate analysis of selling prices in the supplier industry during the six years surrounding downstream consolidation. We identify the 10 most dependent suppliers of each of the 141 industries that experienced a merger event between 1984 and 2003. For each supplier of a consolidating industry, we obtain the Producer Price Index (PPI) from the Bureau of Labor Statistics (BLS) starting from three years before the downstream merger event to three years after the downstream merger event. The PPI series are adjusted for inflation using the GDP price deflator to obtain RPPI. Columns 1–3 contain estimates of panel regressions. In column 1 (column 2) the data are restricted to the 36 months preceding (following) the downstream merger event. Column 3 contains estimates of the full panel of the 72-month period. The dependent variable in columns 1–3 is the monthly RPPI in log-differences. The dummy variable, D, identifies suppliers who are highly dependent on the downstream consolidating industry: D equals one if the fraction of supplier output, fmj, sold to the downstream industry lies in the top quintile, and zero otherwise. For a given supplier, the Post-merger dummy (PM) equals one in the months following the downstream event, and zero for the months preceding. The control variables rppi_inp1 and rppi_inp2 represent the real PPI of the supplier industry’s two primary inputs, again in log-differences. The variable wage represents log-differences of average hourly earnings of production workers compiled by the BLS. tp, obtained from the Federal Reserve Board, measures log-differences of the real output of the manufacturing, mining, and electric and gas utilities industries. The panel regression includes a time trend, industry dummies at the two-digit SIC level, and year dummies. t-Statistics are based on Newey-West standard errors. Column 4 presents estimates of a cross-sectional regression in which the dependent variable is a supplier industry’s average log RPPI over the three years after the downstream merger minus the average log RPPI over the three years prior to the downstream merger. For control variables, we calculate the change in average input prices, wages, and total production in the same manner. The explanatory variable of interest is the dependence dummy D. Column 5 presents a similar cross-sectional regression but with randomly generated event quarters between 1984 and 2003. Changes in control variables are similarly calculated around the random-event quarter. In columns 4 and 5, t-Statistics (in parentheses) are based on robust standard errors clustered at the two-digit SIC level. In all regressions, bold font indicates significance at least at the 10% level. The superscripts a, b, and c indicate significance at the 1%, 5%, and 10% levels, respectively.

Dependent variable: change in supplier RPPI Dependence dummy (D) 1

Input price 1 (rppi_inp ) Input price 2 (rppi_inp2) Wages (wage) Total production (tp)

1 Panel: before downstream merger

2 Panel: after downstream merger

3 Full panel (difference-indifferences)

4 Crosssectional

5 Cross-sectional: Random

0.0003 ( 1.58) 0.245 (10.97)a 0.152 (10.98)a 0.0240 (3.13)a 0.007 (0.42)

0.001 ( 2.69)a 0.165 (12.63)a 0.150 (11.23)a 0.00492 (0.53) 0.0496 (2.39)b

0.0002 ( 1.08) 0.209 (15.08)a 0.153 (15.70)a 0.0151 (2.54)b 0.0266 (2.04)b 0.00 (0.52) 0.001 ( 1.99)b

0.0134 ( 2.44)b 0.391 (4.13)a 0.108 (2.21)a 0.356 (2.04)b 0.130 (2.10)b

0.00 (0.03) 0.451 (6.21)a 0.072 (2.08)b 0.085 (0.51) 0.127 (2.57)a

0.20 16,325

0.12 13,494

0.16 29,819

0.32 586

0.35 418

Post-merger dummy (PM) D PM R-squared Observations

Column 3 of Table 4 presents the estimation results for Eq. (2). The coefficient on the interaction of the dependence dummy and the post-merger dummy, a3, is negative and significant at the 95% confidence level indicating that dependent suppliers experience larger price declines post-downstream consolidation compared to non-dependent suppliers. Since level effects are controlled for, the interaction term isolates the differential impact of downstream consolidation on upstream prices for dependent suppliers. The coefficients on the postmerger dummy and the dependence dummy are both statistically indistinguishable from zero indicating an absence of evidence in favor of the hypotheses that (i) prices for all suppliers are lower post-downstream consolidation and (ii) dependent suppliers always face lower prices. As expected, the results on input prices, wages, and total production confirm that higher input prices do pass through to output prices and that demand shocks also impact output prices. To demonstrate that the differential impact of downstream consolidation on prices faced by dependent suppliers is not sensitive to the regression methodology used, we also employ an alternative to the difference-in-differences

method described above. We run the following crosssectional regression using OLS with robust standard errors clustered at the two-digit SIC level:

D lnRPPIj ¼ a0 þ a1 Dj þ a2 D ln RPPI_INPj1 þ a3 D ln RPPI_INPj2 þ a4 D ln WAGEj þ a5 D ln TP þ ej :

ð3Þ

where D ln RPPIj is the supplier j’s average log RPPI over the three years after the downstream merger minus the average log RPPI over the three years prior to the downstream merger. As control variables, we use the changes in average input prices, wages, and total production. Again the explanatory variable of interest is the dependence dummy D. Results are presented in column 4 of Table 4. As expected, the coefficient on the dummy variable D is negative and statistically significant: dependent suppliers experience larger declines in prices in the wake of downstream consolidation. A remaining concern is that prices faced by dependent suppliers may trend downwards with time even in the absence of downstream consolidation. To address this concern, we conduct an experiment where, for each

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supplier in our sample, we generate a random ‘eventquarter’ between 1984 and 2003 drawn from a uniform distribution. Then we repeat a cross-sectional regression similar to that in Eq. (3) with one key difference—we use the randomly generated date as the break point. That is, the change in supplier prices is calculated as the average price three years after the randomly selected quarter minus the average price three years before. Changes in control variables are calculated in a similar manner. If prices in dependent supplier industries were to naturally trend downwards, the dependence dummy would be significantly negative in this randomized sample as well. Column 5 of Table 4 shows that this coefficient is no longer statistically significant. This finding reinforces the significance of the downstream merger event as the structural break in prices faced by dependent suppliers. 4.4. Disentangling efficiency and buyer power hypotheses While the tests in Section 4.3 clearly establish a decline in the prices of dependent supplier industries after downstream consolidation, attributing such a decline to increased buyer power is not straightforward. As discussed earlier, an increase in selling power downstream, perhaps due to greater collusion or concentration, could also result in lower demand for inputs and, consequently, lower input prices. In unreported tests, we find no evidence of higher selling prices in the downstream industry after consolidation activity. Therefore, enhanced selling power does not appear to be the cause of the decline in supplier prices. However, consolidation-induced productive efficiencies could also result in similarly reduced demand for inputs and consequent price declines. To disentangle the buying power effects of downstream consolidation from efficiency-generated effects, we take recourse to the theory of countervailing power. Countervailing power theory suggests that suppliers with prior pricing power would be the natural targets of buying power generated by consolidation downstream. Efficiency-increasing consolidation, in contrast, does not clearly predict a differential impact among suppliers, as discussed in Section 3. To test Hypothesis 3, we use two different proxies for pricing power of supplier industries: the Census Bureau’s estimates21 of the four-firm concentration ratio (sup_con) and the Herfindahl index (sup_herf) obtained from the 1982, 1987, and 1992 census conducted at the four-digit SIC level.22 For downstream consolidation that occurred between 1993 and 1997 21 Ali, Klasa, and Yeung (2008) show that industry concentration measures calculated with Compustat data, which cover only public firms, are poor proxies for actual industry concentration. These measures have correlations of only 13% with the corresponding U.S. Census measures that are based on all public and private firms in an industry. Their results indicate that product market research using Compustatbased industry concentration measures may lead to incorrect conclusions. 22 From 1997 onwards, U.S. Census Bureau data are provided on the NAICS basis instead of SIC. Since there is not necessarily an one-to-one correspondence between NAICS and SIC, we avoid creating more noise in the concentration measures and do not attempt to match subsequent NAICS-based industry concentration data to our SIC-based sample.

(inclusive), we use the 1992 census to obtain sup_con and sup_herf. For consolidation that occurred between 1988 and 1992 (inclusive), we use the 1987 census and for consolidation activity between 1983 and 1987 (inclusive), we use the 1982 census. Thus, for a subsample, we are able to obtain reliable measures of supplier industry concentration prior to downstream consolidation. We reestimate Eq. (3) above with sup_con and sup_herf as the explanatory variables in place of the dependence dummy, D. The results presented in columns 1 and 2 of Table 5 show that suppliers with higher values of sup_con and sup_herf experienced larger price declines after downstream consolidation. That is, suppliers that were more concentrated prior to downstream consolidation experienced greater price declines, indicating support for the buying power hypothesis. These results are further reinforced when we abandon reliance on summary measures of concentration and focus directly on the structural attributes of market power. Since barriers to entry are a structural source of pricing power, Hypothesis 4 states that suppliers with high entry barriers should experience larger price declines after downstream consolidation. Consistent with this, we saw in Table 2 that supplier industries with higher capital intensity and higher capital expenditures, both of which are common proxies for barriers to entry, on average have higher abnormal profits. Moreover, advertising expenses, a proxy for barriers to entry as well as product differentiation, is positively related to profits in one of the two regressions presented in Table 2. Therefore, we test Hypothesis 4 using capital intensity, capital expenditures, and advertising expenses as proxies for barriers to entry. We calculate supplier capital intensity (sup_ks), supplier capital expenditure (sup_capex), and supplier advertising expenses (sup_advert) for the year prior to downstream consolidation using Compustat data as already described in Section 4.2. Although these variables are available on an annual basis, they suffer from two disadvantages. First, matching price data with Compustat data results in smaller sample size. Second, the three Compustat variables are measured for public firms only. Nonetheless, we run regression Eq. (3) again with sup_ks, sup_capex, or sup_advert as the primary explanatory variable. Results are provided in columns 3–5 of Table 5. We see that capital expenditures and capital intensity both have negative and statistically significant coefficients. Overall, Table 5 shows that four out of our five proxies for non-competitive pricing in supplier industries are associated with larger supplier price declines after downstream consolidation. In the final test of this section, we use two measures of the change in concentration of the supplier industry prior to downstream consolidation. Since horizontal mergers reduce the number of firms operating in an industry and increase concentration, we use a measure of horizontal merger activity in the supplier industry as a proxy for possible changes in concentration. The variable sup_horiz is calculated for each supplier industry as the number of horizontal acquisitions announced in the three years preceding downstream consolidation divided by the average number of firms in that industry during the same


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Table 5 Changes in supplier selling prices and supplier pricing power prior to consolidation downstream. This table examines the relation between the change in supplier selling prices post-downstream consolidation and various measures of prior supplier pricing power. We identify the 10 most dependent suppliers of each of the 141 industries that experienced a merger event between 1984 and 2003. For each supplier to a consolidating industry, we obtain the Producer Price Index (PPI) from the Bureau of Labor Statistics (BLS) starting from three years before the downstream merger event to three years after the downstream merger event. The PPI series are adjusted for inflation using the GDP price deflator to obtain RPPI. All six columns present estimates of cross-sectional regression in which the dependent variable is a supplier industry’s average log RPPI over the three years’ post-downstream consolidation minus the average log RPPI over the three years prior. The change in average input prices (rppi_inp1 and rppi_inp2), wages (wage), and total production (tp) are calculated in the same manner. sup_con is the four-firm concentration ratio of the supplier industry prior to the downstream merger and sup_herf its Herfindahl index. Both sup_con and sup_herf are obtained from the Census Bureau. The following variables are obtained from Compustat as of the year prior to downstream consolidation: sup_ks is supplier industry total assets divided by supplier industry total sales, sup_capex is equal to supplier industry capital expenditures divided by supplier industry assets, sup_advert is supplier advertising expenses divided by supplier industry total sales. t-Statistics (in parentheses) are based on robust standard errors clustered at the two-digit SIC level. In all regressions, bold font indicates significance at least at the 10% level. The superscripts a, b, and c indicate significance at the 1%, 5%, and 10% levels, respectively. 1 4-Firm concentration ratio (sup_con)

2

3

4

0.079 (3.85)a

Herfindahl index (sup_herf)

0.002 (2.29)b

Capital intensity (sup_ks)

0.041 (1.91)c

Capital expenditures (sup_capex)

0.567 (2.21)b

Advertising expenses (sup_advert) 1

Change in input price 1 (rppi_inp ) Change in input price 2 (rppi_inp2) Change in wages (wage) Change in total production (tp) Observations R-squared

5

0.332 (3.14)a 0.198 (2.88)b 0.021 (0.18) 0.095 (1.42)

0.332 (3.03)a 0.192 (2.63)b 0.004 (0.04) 0.074 (1.09)

0.283 (3.27)a 0.051 (1.16) 0.314 (3.09)b 0.021 (0.35)

0.484 (3.18)a 0.111 (1.53) 0.809 (3.07)a 0.186 (2.02)c

0.127 (0.48) 0.505 (3.35)a 0.109 (1.51) 0.863 (3.27)a 0.145 (1.66)

314 0.36

314 0.33

180 0.35

192 0.47

192 0.45

period. We also calculate the change in supplier industry concentration (Dsup_con) more directly using the fourfirm concentration ratio.23 Although this direct measure of supplier industry concentration is available for only a small subsample, it serves as a useful robustness test of the countervailing power hypothesis. We regress the change in supplier industry price after downstream consolidation on sup_horiz and Dsup_con. The results are presented in Table 6. We see that suppliers experiencing greater horizontal merger activity prior to downstream consolidation experienced greater declines in price after downstream consolidation. Likewise, supplier industries that experienced an increase in the four-firm concentration ratio prior to downstream consolidation suffer more adverse price changes after. For comparison purposes, we also regress the change in supplier industry price after downstream consolidation on measures of non-horizontal

23 Since Census data are not annual, it is not possible to get accurate measures of changes in supplier industry concentration during the few years preceding a downstream merger. Nonetheless, we conduct an approximate test with a subsample. If a downstream merger is announced between 1986 and 1989 (inclusive), we calculate the change in supplier industry concentration as the 1987 census measure minus the 1982 Census measure. If a downstream merger is announced between 1991 and 1994 (inclusive), we calculate the change in supplier industry concentration as the 1992 Census measure minus the 1987 census measure.

merger activity (sup_nonhoriz) and unrelated merger activity (sup_unrelated) in the supplier industry prior to downstream consolidation.24 Table 6 shows that these other measures of merger activity in the supplier industry prior to downstream consolidation bear no significant relation with subsequent declines in selling prices.25 The relation between supplier horizontal acquisitions and subsequent price changes could be explained away with the argument that perhaps periods of high horizontal merger activity in an industry usually precede price declines in the industry, perhaps due to increase in efficiencies being passed on through lower prices and that such a decline in prices would have happened regardless of a downstream merger. To address this concern, we conduct an experiment similar in spirit to the random-event exercise in Table 4. We begin with a 24 Non-horizontal acquisitions are defined as deals where an acquirer in the supplier industry buys a target firm that does not share the same four-digit SIC code. However, the acquirer and target could share the same primary three-digit, two-digit, or one-digit SIC code. Unrelated acquisitions are defined as deals where an acquirer in the supplier industry buys a target firm that does not even share the same one-digit SIC code. 25 We note that it is not an error or a coincidence that the number of observations in columns 1, 3, and 4 of Table 6 is the same: In these three regressions, we use the same set of supplier industries. However, the dependent variables capture different types of merger activity in the supplier industries.

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Table 6 Relating the change in supplier selling prices to prior supplier merger activity and change in supplier concentration. This table examines the relation between the change in supplier selling price after downstream consolidation and (i) merger activity in a supplier industry prior to downstream consolidation and (ii) change in supplier industry concentration prior to downstream consolidation. We identify the 10 most dependent suppliers of each of the 141 industries that experienced a merger event between 1984 and 2003. For each supplier of a consolidating industry, we obtain the Producer Price Index (PPI) from the Bureau of Labor Statistics (BLS) starting from three years before the downstream merger event to three years after. We adjust the PPI series for inflation using the GDP price deflator and use the deflated series as the dependent variable (called RPPI). Columns 1–4 present estimates of cross-sectional regressions where the dependent variable is a supplier industry’s average log RPPI over the three years after downstream consolidation minus the average log RPPI over the three years prior. The sample includes all supplier industry–merger industry pairs for which supplier RPPI data are available. Supplier horizontal mergers (sup_horiz) are defined as the number of horizontal mergers announced in supplier industries during the three years preceding downstream consolidation divided by the number of firms in the industry. A horizontal merger is defined as a merger where both the acquirer and target operate in the same primary four-digit SIC code. Dsup_con is the change in the four-firm concentration ratio of the supplier industry prior to downstream consolidation. The variables sup_nonhoriz and sup_unrelated also capture merger activity in supplier industries during the three years preceding downstream consolidation. sup_nonhoriz is calculated as the number of deals announced in which the acquirer in the supplier industry buys a target firm that does not share the same four-digit SIC code divided by the number of firms in the supplier industry. The variable unrelated mergers is calculated as the number of announced deals in which an acquirer in the supplier industry buys a firm that does not share even the same one-digit SIC code divided by the number of firms in the supplier industry. For control variables, we calculate the change in input prices, wages, and total production as the three-year average after downstream consolidation minus the three-year average prior to it. Column 5 presents a similar crosssectional regression for all unique four-digit SIC industries for which RPPI data are available. In column 5, randomly generated quarters between 1984 and 2003 serve as the event dates. Changes in prices are calculated as the average price three years after the randomly selected quarter minus the average price three years prior. Changes in control variables are similarly calculated around the random-event quarter. t-Statistics (in parentheses) are based on robust standard errors clustered at the two-digit SIC level. In all regressions, bold font indicates significance at least at the 10% level. The superscripts a, b, and c indicate significance at the 1%, 5%, and 10% levels, respectively. Dependent variable: change in supplier RPPI

Horizontal mergers (sup_horiz)

1

2

3

0.435 (2.07)b

Change in four-firm concentration ratio (Dsup_con)

0.001 (2.21)b 0.192 (0.66)

Unrelated mergers (sup_unrelated) 1

Change in input price 1 (rppi_inp ) Change in input price 2 (rppi_inp2)

Change in total production (tp) Observations R-squared

5 Random-event sample 0.590 (0.93)

Non-horizontal mergers (sup_nonhoriz)

Change in wages (wage)

4

0.407 (4.46)a 0.092 (1.65) 0.379 (1.97)c 0.144 (2.71)a 674 0.36

sample of all four-digit SIC industries for which producer price data are available. For each industry, we create a random-event quarter between 1984 and 2003. We then calculate D ln RPPIj as industry j’s average log RPPI over the three years after the random-event quarter minus the average log RPPI over the three years prior to the randomevent quarter. Changes in input prices, wages, and total industrial production are calculated in the same way as earlier. For each industry, we calculate the number of horizontal acquisitions announced in the three years preceding the random-event quarter divided by the total number of firms in the industry. We then estimate Eq. (3) for this random-event sample. Results are presented in Column 5 of Table 6. We see that the coefficient on prior horizontal merger activity is insignificant: industries engaging in higher horizontal merger activity prior to the random-event quarter did not experience larger price declines after the random-event quarter. Thus, we do not find evidence that any given period of high horizontal merger activity is followed by price declines in that industry.

0.317 (3.12) 0.303 (2.21) 0.019 (0.14) 0.158 (1.06) 107 0.43

0.399 (4.66)a 0.092 (1.61) 0.387 (2.09)b 0.150 (2.74)a 674 0.35

0.326 (0.54) 0.396 (4.87)a 0.095 (1.72) 0.392 (2.20)b 0.152 (2.83)a 674 0.35

0.307 (2.54)b 0.075 (1.98)c 0.306 (1.21) 0.182 (1.98)c 180 0.19

4.5. Merger activity patterns in customer and supplier industries The previous section provides robust evidence that dependent suppliers and those with some degree of market power are adversely affected by downstream consolidation. These results establish that horizontal mergers create buying power. However, our finding that supplier industries engaging in prior horizontal merger activity of their own experience larger price declines introduces the intriguing possibility that downstream mergers are themselves countervailing responses to upstream consolidation. The logic of the countervailing power hypothesis would, however, argue that buying power created by such downstream consolidation would, in turn, create incentives for further consolidation upstream. A time-series pattern of sequential merger activity amongst connected industries could then offer some insights about the propagation patterns of merger waves across industries. In addition, the existence of any such patterns of propagation would go toward


distinguishing our story from the alternate hypothesis that exogenous changes trigger contemporaneous consolidation all along the supply chain. In this section, therefore, we examine whether there exist any sequential patterns in consolidation activity across supplier-customer industry pairs. To investigate such patterns, we need a sufficiently long time-series of horizontal merger activity for all industries. Therefore, we work with the full sample of horizontal acquisitions initially identified from SDC and described in Section 4.1. Using the full set of four-digit SIC codes in the 1992 benchmark I–O tables, we create two separate samples. In the first sample, for each four-digit industry, i, we identify ten customer industries that buy the largest fraction fij of industry i’s output: the larger the value of fij, the more dependent is that supplier industry i on customer industry j. We call this the supplier-main customer sample. Since some values of fij are quite small, we are able to exploit the variation in fij to our advantage. For each supplier industry and customer industry, we also create an annual panel data of horizontal merger activity over the 1984–2003 period, defined as the number of horizontal mergers announced as a proportion of the number of firms in the industry. In an analogous fashion, we also create a customermain supplier sample. In this, we match each four-digit industry, i, to ten supplier industries from which industry i buys the largest fraction, wji of its inputs: the larger the value of wji, the more dependent is the customer industry i on purchasing inputs from supplier industry j. As before, we create an annual panel data of supplier and customer industry horizontal mergers from 1984–2003. To examine whether dependent suppliers consolidate in response to prior consolidation in customer industries, we use the supplier-main customer sample to run panel regressions in which horizontal merger activity (MA) at time t in the supplier industry i is regressed on various measures of past horizontal merger activity in customer industries. The general set-up of the panel regression is: MAit ¼ a0 þ a1 Past_CMAit þ a2 Di þ a3 Past_CMAit Di þ a4 Curr_CMAit þ a5 MAit1 þ a6 Energyi þ a7 RnDit þ a8 Shocki þ a9 MktPEt þ eit : ð4Þ The variable Past_CMA captures prior horizontal merger activity in customer industries. In the primary regressions, we use three different measures of Past_CMA: (i) horizontal merger activity in customer industries in year t 1, or (ii) cumulative horizontal merger activity in customer industries in years t 1 and t 2, or (iii) cumulative horizontal merger activity in customer industries in years t 1, t 2, and t 3. As before, we capture supplier dependence with the dummy variable D, which is equal to one when the value of fij is in the top quintile and zero otherwise. The coefficient of primary interest, a3, measures the impact of the interaction of Past_CMA and D. A positive a3 supports the hypothesis that consolidation in dependent supplier industries is a response to consolidation in their main customer industries. To account for common shocks that may affect both customers and suppliers concurrently, we control for contemporaneous merger activity in the customer industry (Curr_CMA).

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Since mergers may occur in waves that persist for more than a year, we control for lagged values of merger activity in supplier industry i itself (MAit 1). We also include variables identified by Mitchell and Mulherin’s (1996) study of the inter-industry patterns in the rate of takeovers and restructurings. These include supplier industry sales shocks, employment shocks, energy dependence, and research and development (R&D) expenditures.26 Energy dependence, Energy, is calculated as the fraction of the supplier industry’s input that is obtained from SIC codes 12, 13, and 29 using the 1992 benchmark input–output tables. R&D over sales ratio, RnD, is calculated for each supplier industry as of the prior fiscal year. As in Mitchell and Mulherin (1996), the sales shock variable is the absolute value of abnormal industry sales growth. Abnormal industry sales growth for the supplier industry in year t is calculated as the industry’s sales growth during the five preceding years minus the average sales growth of all industries over the same time period. Similarly, the employment shock variable is the absolute value of abnormal employment growth. Abnormal employment growth in the supplier industry in year t is calculated as employment growth during the five preceding years minus the average employment growth of all industries over the same period. These industry shock variables are calculated with employment data and valueof-sales data obtained from the National Bureau of Economic Research (NBER) and the U.S. Census Bureau. We find that the sales shock and employment shock variables are highly positively correlated. Therefore, we use factor analysis to extract the principal factor and use this factor, labeled Shock, as the economic shock variable. Finally, since merger waves are highly correlated with stock market valuations, we include the price-to-earnings ratio of the market (MktPE) as a control variable.27 In Panel A of Table 7, we present estimates of Eq. (4) using the three different measures of Past_CMA. In column 1, Past_CMA is horizontal merger activity in the customer industry in year t 1. In column 2, Past_CMA is horizontal merger activity in the customer industry in years t 1 and t 2. In column 3, Past_CMA is horizontal merger activity in the customer industry in years t 1, t 2, and t 3. We see that the coefficient on the interaction of Past_CMA and the dummy variable D is positive and statistically significant in all three regressions. Thus, horizontal merger activity in supplier industries is significantly higher when their main customers (i.e. customers on which they are dependent) engaged in consolidation activity in the previous three years. We also note that the contemporaneous relation between customer and

26 Deregulation is also considered an important determinant of merger activity (see, for example, Mitchell and Mulherin, 1996; and Andrade, Mitchell, and Stafford, 2001). Andrade, Mitchell, and Stafford (2001) classify the following industries as having experienced deregulation during the sample period we cover: broadcasting (1996), banks and thrifts (1994), utilities (1992), and telecommunications (1996). Since our sample is restricted to mining and manufacturing sectors, none of these industries is present in our sample. 27 We use the price-to-earnings ratio of the Standard and Poor’s (S&P) 500 index as calculated by Robert Shiller and provided on his Web site http://www.econ.yale.edu/ shiller/data.htm.

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Table 7 Merger patterns: merger activity in supplier industries and their main customer industries. This table presents the time-series relation between horizontal merger activity in supplier industries and their top customers. For each of 324 four-digit SIC codes, we use the BEA input–output tables to identify ten customer industries that purchase the largest fraction of the supplier industry’s output. A panel data of annual horizontal merger activity from 1984 to 2003 is constructed for each supplier industry and its ten customer industries. Horizontal merger activity in an industry is defined as the number of acquisitions announced in that industry in year t where both acquirer and target operate in the same fourdigit SIC code divided by the number of firms operating in that industry in year t. The dependent variable is merger activity in a supplier industry in year t. The dummy variable, D, captures dependence of the supplier industry on the customer industry: D equals one if the fraction of supplier output, fmj, sold to customer industry lies in the top quintile, and zero otherwise. In Panel A, the explanatory variable Past_CMA represents three different measures of merger activity in the customer industry. In column 1, Past_CMA equals customer merger activity in year t 1. In column 2, Past_CMA equals customer merger activity in years t 1 and t 2. In column 3, Past_CMA equals customer merger activity in years t 1, t 2 and t 3. In each column, the key variable of interest is the interaction of Past_CMA and D. Control variables are as follows: R&D expense in year t 1; energy dependence as of 1992 benchmark I O tables; economic shock is the principal factor of the sales growth and employment growth over the years t 5 to t 1; Market PE ratio is the price-earnings ratio in year t. In Panel B, we provide only the coefficient on the interaction term CMA D (along with the t-statistic) for six separate panel regressions. Column 1 of Panel B presents the same regression as in Column 1 of Panel A. In columns 2–6 of Panel B, the Past_CMA variable captures customer merger activity in the year (t–k) where k ranges from 2–6. t-Statistics based on robust standard errors clustered at the two-digit SIC level are in parentheses. Bold font indicates significance at least at the 10% level. The superscripts a, b, c and indicate significance at the 1%, 5%, and 10% levels, respectively. Panel A Past_CMA =Customer merger activity in

Past_CMA Dependence dummy (D) Past_CMA D Customer mergers (t) Supplier mergers (t 1) Research and development expense Energy dependence Economic shock Market price-earnings Observations R-squared Panel B

Year (t 1)

Years (t 1) and (t 2)

Years (t 1), (t 2), and (t 3)

0.008 (0.79) 0.000 (0.93) 0.061 (4.02)a 0.015 (1.77)c 0.249 (5.78)a 0.023 (2.30)b 0.008 (1.08) 0.000 (0.09) 0.003 (2.32)b 18,090 0.10

0.016 (2.38)b 0.000 (0.93) 0.037 (2.53)b 0.004 (0.34) 0.251 (5.03)a 0.023 (2.14)b 0.009 (1.07) 0.000 (0.04) 0.003 (1.85)b 16,925 0.10

0.011 (2.21)b 0.000 (0.71) 0.023 (2.33)b 0.007 (0.56) 0.262 (5.09)a 0.024 (2.11)c 0.007 (1.03) 0.000 (0.34) 0.003 (1.73) 15,756 0.11

Past_CMA= Customer merger activity in

Coefficient on Past_CMA D t-Stat

Year (t 1)

Year (t 2)

Year (t 3)

Year (t 4)

Year (t 5)

Year (t 6)

0.061 (4.02)a

0.029 (1.69)c

0.065 (2.04)c

0.063 (2.60)b

0.019 (0.30)

0.004 (0.08)

supplier industry mergers is weak. Moreover, supplier merger activity in year t is significantly positively correlated with supplier merger activity in year t 1, and supplier merger activity is positively correlated with the market price-to-earnings ratio and research and development expenses. To get an estimate of the length of the effect of customer merger activity on subsequent supplier merger activity, we run the same regression several times without cumulating customer merger activity in recent years. That is, we define Past_CMA as customer merger activity in a given year t-k, where k ranges from 2 to 6. Panel B of Table 7 presents a3 and its t-statistics for all of these regressions in columns 2–6. For comparison, column 1 of Panel B presents again the coefficient from the first regression shown in Table 7 Panel A (where k=1). We see that horizontal merger activity in dependent suppliers is

positively correlated with horizontal merger activity in top customers for up to four years in the past. We then turn to examining the impact of supplier industry consolidation on customer industries. For this analysis, we use the customer-main supplier sample to run the following panel regression: MAit ¼ a0 þ a1 Past_SMAit þ a2 Di þ a3 Past_SMAit Di þ a4 Curr_SMAit þ a5 MAit1 þ a6 Energyi þ a7 RnDit þ a8 Shocki þ a9 MktPEt þ eit : ð5Þ In this sample, the dependent variable MA now denotes horizontal merger activity in the customer industry. The variable Past_SMA is used to capture past horizontal merger activity in supplier industries. We control for contemporaneous mergers in the supplier industry, Curr_SMA, as well as for lagged mergers in the customer industry itself (MAi,t 1). The dummy variable, D,


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Table 8 Merger patterns: merger activity in customer industries and their main supplier industries. This table presents the time-series relation between horizontal merger activity in customer industries and their top suppliers. For each of 324 four-digit SIC codes, we use the BEA input–output tables to identify ten supplier industries that provide the largest fraction of the customer industry’s input. A panel data of annual merger activity from 1984 to 2003 is constructed for each customer industry and its ten supplier industries. Horizontal merger activity in an industry is defined as the number of acquisitions announced in that industry in year t where both acquirer and target operate in the same four-digit SIC code divided by the number of firms operating in that industry in year t. The dependent variable is merger activity in a customer industry in year t. The dummy variable, D, captures dependence of the customer industry on the supplier industry: D equals one if the fraction of customer industry input provided by the supplier industry lies in the top quintile, and zero otherwise. In Panel A, the explanatory variable Past_SMA represents three different measures of merger activity in the supplier industry. In column 1, Past_SMA equals supplier merger activity in year t 1. In column 2, Past_SMA equals supplier merger activity in years t 1 and t 2. In column 3, Past_SMA equals supplier merger activity in years t 1, t 2, and t 3. In each column, the key variable of interest is the interaction of Past_SMA times D. Control variables are as follows—R&D expense in year t 1; energy dependence as of 1992 benchmark I–O tables; economic shock is the principal factor of the sales growth and employment growth over the years t 5 to t 1; market PE ratio is the price-earnings ratio in year t. In Panel B, we provide only the coefficient on the interaction term Past_SMA D (along with the t-statistic) for six separate panel regressions. Column 1 of Panel B presents the same regression as in column 1 of Panel A. In columns 2–6 of Panel B, the Past_SMA variable captures supplier merger activity in the year (t–k) where k ranges from 2 to 6. t-Statistics based on robust standard errors clustered at the two-digit SIC level are in parentheses. Bold font indicates significance at least at the 10% level. The superscripts a, b, c and indicate significance at the 1%, 5%, and 10% levels, respectively. Panel A Past_SMA = Supplier merger activity in

Past_SMA Dependence dummy (D) Past_SMA D Supplier mergers (t) Customer mergers (t 1) Research and development expense Energy dependence Economic shock Market price-earnings Observations R-squared

Year (t 1)

Years (t 1) and (t 2)

Years (t 1), (t 2), and (t 3)

0.002 (0.15) 0.000 (0.95) 0.009 (0.68) 0.003 (0.30) 0.225 (7.97)a 0.031 (3.84)a 0.013 (1.43) 0.000 (0.69) 0.003 (2.30)b 15,445 0.098

0.002 (0.20) 0.000 (0.71) 0.001 (0.12) 0.004 (0.30) 0.230 (6.80)a 0.032 (3.44)a 0.013 (1.39) 0.000 (0.59) 0.003 (1.68) 14,439 0.102

0.002 (0.35) 0.000 (0.74) 0.000 (0.01) 0.004 (0.26) 0.238 (7.62)a 0.034 (3.61)a 0.011 (1.40) 0.000 (0.81) 0.003 (1.82)c 13,431 0.104

Panel B Past_SMA= Supplier merger activity in

Coefficient on Past_SMA D t-Stat

Year (t 1)

Year (t 2)

Year (t 3)

Year (t 4)

Year (t 5)

Year (t 6)

0.000 (0.01)

0.009 (0.69)

0.014 (0.93)

0.011 (0.63)

0.001 (0.07)

0.003 (0.22)

captures the dependence of the customer industry on the supplier industry: it equals one for the top quintile of values of the fraction wji. Control variables are analogous to the ones employed in the last set of regressions. The first three columns of Table 8, Panel A present estimates of this equation using measures of Past_SMA for years t 1, t 1 and t 2 cumulated, and t 1 through t 3 cumulated, respectively. The coefficient a3 is not statistically significant in any of the three regressions. In Panel B of Table 8, we repeat the same panel regression several times without cumulating past supplier merger activity. Here, Past_SMA is supplier merger activity in a given year t k, with k ranging from 2 to 6. For comparison purposes, column 1 of Panel B also presents the coefficient from the first regression shown in Table 8 Panel A (where k= 1). We see that the coefficient a3 is never significant, indicating

the absence of a relationship between consolidation activity in customer industries and past consolidation in their top supplier industries. In summary, the results of this section support the hypothesis that supplier industries undertake consolidation activity in response to consolidation in their main customer industries. We do not find corresponding evidence that customer industry consolidation follows supplier industry consolidation.28 Thus, our results

28 Our inability to find any significant impact on the merger decisions of customer industries subsequent to upstream consolidation is consistent with our (unreported) finding that downstream prices do not exhibit increases after consolidation activity. Although studies such as Kim and Singal (1993) have shown changes in output prices after consolidation in particular industries, other cross-industry studies have

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indicate strong support for the notion that consolidation activity tends to travel up the supply chain in line with the Becker and Thomas (2009) finding that changes in the concentration of main customer industries are followed by similar changes in concentration of supplier industries but not vice-versa.

5. Robustness issues Our results are robust with respect to alternate methods of sample construction. Our measure of a merger event in the main analysis uses the ratio of merger transaction value to industry total assets to identify significant consolidation activity. Since the transaction value data use market values obtained from SDC, they should ideally be scaled by the market value of industry assets. Unfortunately, such scaling produces significant data loss as the Compustat main files often provide data aggregated to the three-digit SIC level. As a result, we have had to scale by the book value of industry assets available from the Compustat business segment files at the four-digit SIC level. An unfortunate side effect is that we have 20 industries where the market value of the targets purchased exceeds the book value of industry total assets. Indeed, for three industries, the ratio exceeds 20. An alternative standardization can be obtained by utilizing industry total sales (also available from Compustat’s business segment files). As a robustness check, we classified an industry as having experienced a merger event in a given quarter if the following conditions hold: (i) the total transaction value of deals announced is greater than 10% of industry total sales and (ii) the total transaction value of deals announced in any of the previous 12 quarters did not exceed 2.5% of industry total sales. This method gives us 130 ‘merging’ industries with identifiable suppliers. Although this alternative sample of merger events is slightly smaller, 105 of the 130 merger events (80%) are identical to our main sample. Our main results continue to hold in this alternative sample. Some industries in our initial sample of consolidating industries also experienced multiple merger events between 1984 and 2003: 14 industries experienced two, and four industries experienced three merger events during this period. By design, any two merger events within the same industry are more than three years apart, thus enabling us to study the price impacts of these distinct merger events separately. However, for robustness, we have also dropped all industries that experienced more than one horizontal merger event from our initial sample and found that our results continue to hold in this setting. Finally, it is possible that some suppliers classified as less dependent on one downstream merging industry are (footnote continued) also failed to detect higher output prices subsequent to horizontal mergers. This lack of impact on prices could be due to the sample selection bias we refer to in the introduction: anti-competitive mergers likely to affect selling prices are anticipated to get blocked by antitrust authorities and are never embarked upon. Given such a bias, and given that horizontal mergers may also be driven by efficiency and strategic concerns, it could be that cross-industry studies inherently have weak power in the detection of selling power.

classified as dependent on another downstream industry that happened to experience a merger event around the same time. If this were a common occurrence, the power of our tests would be low. In the initial sample of supplier industry-merging industry pairs, there are 63 cases (out of 1,155) where suppliers classified as ‘not dependent’ on one downstream merging industry are classified as dependent suppliers for other downstream industries that underwent significant consolidation within a threeyear period. Excluding these observations makes no qualitative difference to our results.

6. Conclusion This paper conducts the first comprehensive, crossindustry tests of the product market impact of horizontal acquisitions on supplier industries through their effects on profits and prices. We find strong evidence that horizontal mergers do, in fact, create buying power and impact the performance of dependent suppliers. Dependent suppliers suffer significant declines in both their profits and their selling prices in the three years following major downstream consolidation activity, consistent with the creation of buying power through consolidation downstream. To ensure that our results are not a mere artifact of merger-induced improvements in production efficiency, we explore the implications of the exercise of market power upstream via the channels hypothesized in the theory of countervailing power. This leads to the prediction of differential impact of such newly created buying power on supplier industries with different degrees of market power of their own. We show that supplier industries with higher Herfindahl index values and with higher four-firm concentration ratios prior to downstream consolidation experience larger price declines after downstream consolidation. We also show that supplier industries enjoying higher barriers to entry prior to downstream consolidation experience larger price declines after. This evidence suggests that downstream consolidations create countervailing buying power that is exercised in their wake. To our knowledge, we are the first to establish that dependent supplier industries experience adverse selling price changes consequent to downstream consolidation. We are also the first to provide direct evidence that horizontal mergers countervail upstream market power. Our results point to one possible transmission mechanism for merger waves: consolidation in one industry triggering countervailing consolidations in industries that share product market relationships. We provide suggestive evidence of horizontal mergers in supplier industries following horizontal mergers in their main customer industries. References Ahern, K., Harford, J., 2009. The importance of industry links in merger waves. Unpublished Working Paper, University of Michigan, Ann Arbor. Akhavein, J., Berger, A., Humphrey, D., 1997. The effects of megamergers on efficiency and prices: evidence from a bank profit function. Review of Industrial Organization 12, 95–139.


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Harrington, J., 1989. Collusion and predation under (almost) free entry. International Journal of Industrial Organization 7, 381–401. Jensen, M., 1993. The modern industrial revolution, exit, and the failure of internal control systems. Journal of Finance 48, 831–880. Kim, E., Singal, V., 1993. Mergers and market power: evidence from the airline industry. American Economic Review 83, 549–569. Lustgarten, S., 1975. The impact of buyer concentration in manufacturing industries. Review of Economics and Statistics 57, 125–132. McGuckin, R., Chen, H., 1976. Interactions between buyer and seller concentration and industry price-cost margins. Industrial Organization Review 4, 123–132. Mitchell, M., Mulherin, J., 1996. The impact of industry shocks on takeover and restructuring activity. Journal of Financial Economics 41, 193–229. Prager, R., Hannan, T., 1998. Do substantial horizontal mergers generate significant price effects? Evidence from the banking industry. Journal of Industrial Economics 46, 433–452. Robinson, J., 1933. In: The Economics of Imperfect Competition. Macmillan and Co., London. Schumacher, U., 1991. Buyer structure and seller performance in U.S. manufacturing industries. Review of Economics and Statistics 73, 277–284. Shahrur, H., 2005. Industry structure and horizontal takeovers: analysis of wealth effects of rivals, suppliers, and corporate customers. Journal of Financial Economics 76, 61–98. Singal, V., 1996. Airline mergers and competition: an integration of stock and product price effects. Journal of Business 69, 233–268. Snyder, C., 1996. A dynamic theory of countervailing power. Rand Journal of Economics 27, 747–769. Snyder, C., 1998. Why do large buyers pay lower prices? Intense supplier competition. Economic Letters 58, 205–209. Stillman, R., 1983. Examining anti-trust policy towards horizontal mergers. Journal of Financial Economics 11, 224–240. Stole, L., Zwiebel, J., 1996. Organizational design and technology choice under intrafirm bargaining. American Economic Review 86, 195–222.




The effect of banking crisis on bank-dependent borrowers$ Sudheer Chava a, Amiyatosh Purnanandam b, a b

College of Management, Georgia Institute of Technology, Atlanta, GA 30308, USA Ross School of Business, University of Michigan, Ann Arbor, MI 48109, USA


abstract

Article history: Received 5 January 2009 Received in revised form 17 August 2009 Accepted 24 September 2009 Available online 7 August 2010

We provide causal evidence that adverse capital shocks to banks affect their borrowers’ performance negatively. We use an exogenous shock to the U.S. banking system during the Russian crisis of Fall 1998 to separate the effect of borrowers’ demand of credit from the supply of credit by the banks. Firms that primarily relied on banks for capital suffered larger valuation losses during this period and subsequently experienced a higher decline in their capital expenditure and profitability as compared to firms that had access to the public-debt market. Consistent with an adverse shock to the supply of credit, crisisaffected banks decreased the quantity of their lending and increased loan interest rates in the post-crisis period significantly more than the unaffected banks. Our results suggest that the global integration of the financial sector can contribute to the propagation of financial shocks from one economy to another through the banking channel. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G21 G32 D82 Keywords: Banking crisis Russian default Bank loans Credit crunch

1. Introduction $ We are grateful to an anonymous referee, Viral Acharya, Adam Ashcraft, Kerry Back, Sreedhar Bharath, Ran Duchin, Tom George, Todd Gormley, John Graham, Charles Hadlock, Andrew Hertzberg, Shane Johnson, Steve Kaplan, Anil Kashyap, Han Kim, Dmitry Livdan, Paolo Pasquariello, Uday Rajan, Michael Roberts, Anthony Saunders, Philip Strahan, Amir Sufi, Bhaskaran Swaminathan, Sheridan Titman, Haluk Unal, Toni Whited, Andrew Winton, Luigi Zingales, and seminar participants at Arizona State University, Michigan State University, Rice University, Texas A&M University, University of Illinois at UrbanaChampaign, University of Maryland, University of Miami, University of Minnesota, University of Texas at Austin, University of Washington, St. Louis, European Finance Association’s 2006 meetings in Zurich, FDIC, FDIC-CFR Conference, 42nd Bank Structure Conference at Federal Reserve Bank of Chicago, Federal Reserve Bank of New York, Financial Intermediation Research Society’s meetings in Shanghai, Systemic Risk Conference at Federal Reserve Bank of Atlanta, and Western Finance Association’s 2006 meetings in Keystone for helpful comments. Financial support from FDIC’s Center for Financial Research is gratefully acknowledged. Chava gratefully acknowledges financial support from Mays Research Fellowship and Gina and William H. Flores Fellowship. Corresponding author. Tel.: + 1 734 764 6886; fax: + 1 734 936 0279. E-mail addresses: [email protected] (S. Chava), [email protected] (A. Purnanandam).


The current subprime mortgage crisis and the associated losses to the U.S. banking system reemphasize the need to understand the impact of shocks to providers of capital on their borrowers. If a firm can easily access external capital markets or switch from one source of private capital to another, then its performance should be insensitive to the shocks experienced by its capital providers. Adverse selection and moral hazard frictions, however, can limit even a profitable and growing firm’s ability to raise external capital or to substitute between private sources of capital (Holmstrom and Tirole, 1997).1 With such frictions in the economy, shocks that affect banks’ ability to supply capital might result in suboptimal investment and working-capital management decisions for 1 See Diamond (1984), Ramakrishnan and Thakor (1984), Leland and Pyle (1977), Boyd and Prescott (1986), Rajan (1992), Bernanke and Blinder (1988); and a large literature surveyed in Gorton and Winton (2003), and James and Smith (2000).

S. Chava, A. Purnanandam / Journal of Financial Economics 99 (2011) 116–135

firms that extensively depend on them. Therefore, a firm’s performance should be sensitive to unanticipated shocks experienced by the suppliers of its capital over and above the firm-specific demand-side characteristics such as profitability and growth opportunities.2 Establishing this link between a borrower’s performance and its bank’s health has important implications for corporate finance and monetary policies, and in this paper we attempt to provide evidence in support of this link using shocks to the U.S. banking system during the Russian crisis as a natural experiment [see Kho, Lee, and Stulz, 2000 for further discussions about the crisis]. Empirical studies that attempt to establish this relationship face a fundamental identification challenge of separating the effect of firm-specific demand-side shocks (such as profitability and growth opportunity) from the supplyside shock. If deterioration in a bank’s health is itself caused by its borrowers’ poor performance, then researchers face an uphill task in establishing the causation in the other direction (Fama, 1980; King and Plosser, 1984).3 In addition, if common economic shocks affect the performance of both the banking sector and the real economy, then the task of separating the effect of firm-specific factors from bank-specific shocks becomes more difficult. We use shocks to the U.S. banking system during the Russian crisis of Fall 1998 to isolate the effect of supplyside frictions on firm performance. The crisis started with an announcement of the Russian government’s intention to default on their sovereign debt obligations on August 17, 1998 (Kho, Lee, and Stulz, 2000). Subsequently, related events such as the announcement of the suspension of ruble trading on August 28, 1998, and massive flight of capital from Brazil on September 3, 1998 resulted in a severe financial crisis in the United States during midAugust and early September of 1998. Many U.S. banks had substantial exposure to these two countries, exposing them to significant losses and liquidity constraints during this short period.4 This resulted in a significant loss of

2 It is important to note that the information and/or agency friction should affect both banks and borrowers to produce this outcome. If these frictions only affect firms, then banks can raise enough money from the external market to fund their borrower’s positive NPV project. However, due to frictions faced at the level of banks (Stein, 1998), a deterioration in bank-health can affect the supply of bank loans through at least three related channels: (i) there can be a direct reduction in loanable internal funds available with them; (ii) poor bank health may limit their ability to raise external capital; and (iii) due to their lower risk-appetite (e.g., due to capital adequacy constraints), banks may be inclined to change their asset mix in favor of safer securities rather than risky commercial and industrial (C&I) loans. 3 For example, prior to the failure of Continental Illinois Bank, some of its key borrowers such as International Harvesters and Nucorp Energy had experienced financial distress. Dahiya, Saunders, and Srinivasan (2003) show that there is a significant negative wealth effect for the shareholders of the lead bank when borrowers of the bank experience distress. Their evidence is consistent with the notion that borrowers’ health causes deterioration in the bank’s health. 4 Gatev, Strahan, and Schuermann (2004) show that bank stocks performed very poorly during this period, losing over 10% of market capitalization in such a short window. Accounting-based measures also indicate that the banking sector’s financial health was under tremendous pressure in late August and early September resulting in a credit crunch for the bank-dependent borrowers [see FDIC’s quarterly report for 1998Q3 and 1998Q4].

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equity capital for several U.S. banks, which in turn adversely affected their ability to make loans. Since the decisions of the Russian government to default on their debt obligations and to suspend the currency convertibility were exogenous to the U.S. economy, we argue that this shock resulted in an exogenous inward shift in the supply of bank loans. This, in turn, allows us to trace a causal link from bank health to borrowers’ performance. First, we exploit the variation generated by this shock across firms that have access to the public-debt market and firms that do not have such access and, therefore, depend solely on their banks for debt. In particular, we make use of the fact that during our crisis period (i.e., from August 14, 1998 to September 3, 1998), the public-debt market was functioning at reasonably normal levels, whereas banks were severely affected by the events in Russia and Brazil.5 Thus, by comparing the stock market performance of bank-dependent and rated firms, we hope to isolate the effect of supply shock on firm value. We find that bank-dependent firms experienced significantly larger valuation loss as compared to their rated counterparts during the crisis period. Other results show that bank-dependent firms cut their capital expenditure significantly more than the rated firms in the quarters immediately following the crisis as compared to the earlier quarters. In addition, their operating profits dropped considerably more in the post-crisis quarters as compared to the corresponding decline for the rated firms. We also investigate the effect of injection of liquidity into the banking sector by the Federal Reserve Bank in the immediate aftermath of the crisis and find that bank-dependent firms recovered a part of their initial valuation loss after these policy interventions. In our tests we control for several proxies of firm risk, growth opportunities, and other firm characteristics that might influence the stock’s return during the crisis period. To further rule out the possibility that our results are driven by large observable differences in the characteristics of rated and bank-dependent firms, we conduct a matched sample analysis. We carefully match rated and bank-dependent firms along the dimensions of firm size, default risk, stock market liquidity, and growth opportunities. We find that bank-dependent firms lose significantly higher equity value than their rated counterparts during the crisis period even on this subsample. We conduct several tests within the set of bankdependent firms to further understand the role of supplyside friction on their performance. In these tests we exploit the heterogeneity in their main bank’s exposure to the Russian crisis. We first construct a matched sample of bank-dependent firms and their banks using multiple data sources. Using banks’ quarterly call report data and their annual statements, we measure the nature and extent of

5 During our crisis period (i.e., from August 14, 1998 to September 3, 1998), public-debt markets seemed to be functioning at relatively normal levels as is evident by the modest levels of paper-bill spread – a broadly used measure of the overall liquidity situation in the economy (see Fig. 1). It was only later in October 1998 that liquidity dried up from the public-debt market as well (see Gatev, Strahan, and Schuermann, 2004; Gatev and Strahan, 2006).

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Fig. 1. Paper-bill spread during 1997–1998. This figure plots the spread between commercial paper and treasury bill rates from September 1997 to November 1998.

exposure of these banks to the crisis. We find considerable heterogeneity in the bank’s exposure to the crisis, ranging from very high exposure for banks like Citicorp, Bank of America, and Chase Manhattan to little to negligible exposure for banks such as Banc One Corporation, and Wells Fargo. We compare the stock market performance of the borrowers of the affected banks with those of the unaffected banks and find that the affected banks’ borrowers experienced significantly higher valuation loss as compared to the unaffected banks’ borrowers. This result is especially powerful since it is free from any selection-bias concerns that might influence comparison of rated and unrated firms. This result provides more direct evidence on the international propagation of shocks in the real sectors through linkages in the banking sector. Our next test is also performed within the sample of bank-dependent firms, where we exploit the variation in their ability to obtain funds in a time of credit crunch. When information asymmetry between the lenders and the borrowers leads to credit rationing, borrowers with higher collateral can obtain funds more easily [e.g., see Bester’s, 1985 extension of Stiglitz and Weiss, 1981]. Collateral also can serve as a mitigating device for moral hazard problems (Tirole, 2006). Motivated by these theoretical models, we use a firm’s unpledged collateral, i.e., collateral available for future borrowing, as a measure of its ability to negate the adverse consequences of the credit crunch. We find significant evidence that bankdependent firms with higher unpledged assets perform better. Our final test directly investigates the lending behavior of banks around the crisis period. We structure our empirical tests in the framework of an equilibrium model of demand and supply of bank credit. With a downward sloping demand curve and an upward sloping supply curve for bank credit, an adverse shock to the bank’s capital should result in an inward shift in the supply curve. The supply shock-induced credit crunch, therefore, should result in a decrease in the equilibrium quantity of

credit and increase in its price. We find that, as compared to the pre-crisis period, in the post-crisis period, the crisis-affected banks decreased their lending volume and increased loan spreads as compared to the unaffected banks. This evidence is consistent with an inward shift in the loan-supply curve for the bank-dependent borrowers after the Russian crisis. Our study is related to various strands of literature in banking, corporate finance, and monetary policy. It is closely related to a large literature that studies the effect of bank-borrower relationship and the effect of the bank’s health on borrower performance (see important contributions from Slovin, Sushka, and Polonchek, 1993; Kang and Stulz, 2000; Ongena, Smith, and Michalsen, 2003; Khawaja and Mian, 2008; Paravisini, 2008 ). Our paper is also related to Peek and Rosengren (2000), Ashcraft (2005), and Garmaise and Moskowitz (2006), who study the real effects of deterioration in bank health or credit market competition. The key contribution of our paper is to exploit a shock that originated in a different geographical region and use it to isolate the supply-side effect. In the process, we are able to trace the valuation implications of bank-dependence at the time of crisis. Equally important, our paper provides evidence that as financial markets become integrated, shocks can propagate from one economy to the other through linkages in the banking sector. This has important implications for the monetary policy interventions in light of the increasing integration of the global financial markets. At a broader level, we contribute to the empirical literature on the special role of banks in mitigating value relevant frictions in the economy (see James, 1987; Puri, 1996; Houston and James, 1996; Hadlock and James, 2002; Dahiya, Puri, and Saunders, 2003; and a large literature surveyed in Gorton and Winton, 2003). Our study is also related to the monetary economics literature on the role of credit channel in the transmission of monetary policy shocks to the real economy (Bernanke, 1983; Bernanke and Blinder, 1992; Kashyap, Stein, and


Wilcox, 1993; Gertler and Gilchrist, 1994; Kashyap and Stein, 2000). Finally, we contribute to the broader debate on the role of debt market in easing access to funds as well as the effect of financial constraints on corporate financial policies (Fazzari, Hubbard and Petersen, 1988; Whited, 1992; Kaplan and Zingales, 1997; Sufi, 2009; Lemmon and Roberts, forthcoming). Our results also have implications for the effect of the current subprime mortgage crisis on the real sector. Within the U.S., bank-dependent borrowers of banks that have been more adversely affected by the subprime mortgage crisis are predicted to be more severely affected by the crisis. In addition, countries with tighter linkages of their banking system with the U.S. banking system are predicted to be affected more severely by the crisis. These topics have been left for future research. The rest of the paper is organized as follows. In Section 2, we describe the banking crisis of Fall 1998 and our identification strategy in more detail. Section 3 describes the data. Section 4 presents the empirical results and Section 5 concludes the paper.

2. Russian crisis and identification strategy In the Fall of 1998, several important events took place in the international financial markets. On August 17, 1998, the Russian currency was devalued and the government announced its intention to default on sovereign debt obligations. On August 28, ruble convertibility was suspended. In related events, on September 3, 1998, there was a significant outflow of capital from Brazil. LTCM’s losses became public news on September 2, 1998. All these events caused significant losses to the U.S. banks during late August and early September of 1998 as evidenced by a sharp decline in banks’ stock prices over this period. There were many reasons for banks’ losses including (a) direct exposure to the Russian government bonds, (b) exposure to the Russian private borrowers, (b) losses in the derivatives market, (c) losses on brokerage credit to LTCM, and (e) increased counter-party risks in the U.S. banking system. Gatev, Strahan, and Schuermann (2004) show that an equally weighted bank price index fell by about 11% during this two-week period. They also show a dramatic increase in the stock return volatility, a measure of banks’ overall risk, over this time period. Fissel, Goldberg, and Hanweck (2006) find that default spreads on bank subordinated debt increased significantly during this period. Accounting-based measures of bank performance confirm the deterioration in bank health obtained from the forward-looking market-based measures. FDIC’s quarterly report for 1998Q3 shows that during the crisis quarter, banks made remarkably higher charge-offs and incurred significant losses on account of their overseas operations. Banks lost a significant amount of their capital in this period (Gorton and Winton, 2003). Such a large loss in their capitalization along with a dramatic increase in their risks directly compromised the banks’ ability to supply funds to their borrowers. The possibility of a credit crunch

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induced by this adverse shock to the bank capital forms the basis of our analysis in this paper. To directly analyze the effect of this crisis on the supply of bank loans, we obtain data on loan issuance from the Loan Pricing Corporation’s Dealscan database.6 We collect all loans on a monthly basis from this database and classify firms as bank-dependent or not based on their access to the public-debt market. We focus on the six-month period before (i.e., from February 1998 to July 1998) and after (i.e., from August 1998 to January 1999) the crisis for our analysis.7 Next, we compute the periodby-period growth in supply of loans by simply estimating the growth in number and amount of loans for a given period as compared to the previous six-month period. As shown in Fig. 2, there is a remarkable drop (21–28%) in both the number and amount of loans issued after the crisis as compared to the pre-crisis period. The decline in the issuance of new loans is more pronounced in the subsample of bank-dependent firms. When we analyze the commercial paper (CP) rate (see Fig. 1), a proxy for liquidity shock for the overall economy, we do not find any abnormal patterns during the event window, i.e., in the event window of August 14, 1998 to September 4, 1998. Unreported analyses also show that the yields on corporate debt and outstanding volume of Commercial Papers for non-financial firms in this period remained broadly in line with the earlier periods. Thus, this period presents a unique setting where banks suffered huge losses, but the liquidity in the public-debt market remained at the normal levels. We exploit this feature of the economy to investigate the effect of bank health on their borrowers’ performance. 2.1. Identification strategy Our interest is in estimating the effect of adverse shocks to the capital of the suppliers of credit on their borrowers’ performance. To motivate our empirical design, we consider a model of the following general form: Yit ¼ a þ bf ðdemandshockÞit þ ggðsupplyshockÞit þ eit : Yit is a measure of firm i’s performance such as its value at time t. f(demandshock) denotes firm-specific factors such as shocks to its profitability and growth rates that are likely to have an influence on Yit. g(supplyshock) measures shocks experienced by the supplier of the firm’s capital and our goal is to estimate g, the coefficient on this variable. The main difficulty in this estimation exercise lies in clearly isolating the effect of a supply shock from correlated demand shocks. Poor economic conditions often lead to an overall decline in the banking sector’s financial health as well as a deterioration in the corporate sector’s investment opportunity set at the same time. Additionally, the estimate 6 It is worth noting that unlike the call-report data that provides quarterly information on loans disbursed to the borrowers that may be related to prior commitments, the Dealscan database allows us to capture the incremental decisions of bank managers by focusing on sanctions of new loans around this period. 7 Results are similar for other reasonable windows, such as three months or nine months, around the crisis period.

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20.00%

10.00%

Growth rate

0.00%

-10.00%

-20.00%

-30.00% Six Months Before Crisis Six Months After Crisis -40.00% # of loans to all borrowers

Amount of loans to all borrowers

# of loans to bank- Amount of loans to dependent borrowers bank-dependent borrowers

Fig. 2. Growth in bank loans. This figure plots the growth rates in number and amount of loans around the Russian crisis period. We obtain data from the Dealscan database for all loans made during six months before the crisis (i.e., from February 1998 to July 1998) and six months after the crisis (i.e., during August 1998 to January 1999). We plot the growth in number and amount of loans during these two periods as compared to previous six months. Thus, pre-crisis numbers are compared with loan data from August 1997 to January 1998 and the post-crisis numbers are compared with the pre-crisis numbers. We provide the growth rates for all firms as well as the subset of bank-dependent firms, i.e., firms without access to the public-debt market.

can be biased due to the reverse causality since poor performance of the corporate sector can in itself cause a deterioration in the performance of the banking sector. Our identification strategy is aimed at exploiting an exogenous perturbation of the supply-shock function for U.S. banks during the Russian crisis. Since the crisis was reasonably exogenous to the U.S. borrowers’ demand shocks, it perturbed the supply of credit disproportionately more for the bank-dependent firms as compared to their rated counterparts. This exogenous shock to the supply-side function allows us to estimate the causal effect of banks’ ability to supply funds on their borrowers’ performance. In the base case, we estimate the following cross-sectional regression model to estimate the effect of this shock on firm value: ri ¼ b0 þ b1 bankdepi þ

kX ¼K

fk Xi þ ei ,

k¼1

where ri is the market model adjusted stock return of firm i during the crisis period.8 We first compare bank-dependent firms with their rated counterparts to exploit the disproportionate effect of this crisis on the 8 We use the standard event-study methodology to compute the market model adjusted return (Kothari and Warner, 2007). For every sample firm, first we estimate the market-model beta using 250 trading days, ending 50 trading days prior to the crisis period. Based on these beta estimates, we compute the market-model adjusted returns for the event window for all firms.

banking sector as compared to the public-debt market. Second, within the set of bank-dependent firms, we compare the performance of firms that rely heavily on banks affected by the Russian crisis with firms that do not. The second test allows us to exploit the variation generated by the intensity of shocks experienced by different banks during the Russian crisis. Xki is a set of control variables discussed below.

2.2. Alternative hypotheses We are mainly concerned with four alternative channels that might differentially affect the value of rated and bank-dependent firms at the time of crisis. They are: (i) firm size, (ii) default risk, (iii) growth opportunities, and (iv) stock market liquidity. There are several reasons to expect a relation between firm size and stock returns during the crisis period. As compared to large firms, small firms are more likely to have higher operating risks. They are also more likely to face asymmetric information problems and they are less likely to have access to alternative sources of funds. All these factors can have an impact on the firm’s valuation during the crisis period, which is independent of the bank channel that we are primarily interested in. Since bank-dependent firms are much smaller than the rated firms, we need to separate the effect of firm size from the access-to-capital effect that we intend to capture.


The second alternative channel is the firm’s defaultrisk. Firms with high risk of default are likely to be more sensitive to economic downturns than their low defaultrisk counterparts. The increased possibility of bankruptcy as well as the higher incidence of indirect bankruptcy costs can result in larger downward revision in the valuation of high default-risk stocks. In addition, high default-risk stocks may suffer large valuation loss due to the increased risk-aversion during the crisis period. Investors may shift their capital from riskier to safer assets purely out of increased risk-aversion concerns during a period of crisis. This flight-to-quality consideration has been one of the most widely discussed implications of the Russian crisis in the popular press. We want to separate the effect of flight-to-quality due to poor credit quality of firms from the poor access to capital. We follow recent models developed in the credit risk literature to obtain meaningful proxies of default risk. There are two popular models of credit risk used in the literature. One is based on a reduced-form statistical approach, popularly known as the hazard-rate model; whereas the other is based on a structural modeling of a firm’s equity as a call option on the firm value. The hazard-rate model (see Shumway, 2001; Chava and Jarrow, 2004) uses a maximum-likelihood approach to estimate a firm’s default likelihood conditional on a set of observable characteristics. These papers show that a firm’s size, past stock return, stock return volatility, and leverage are the most important determinants of its default risk. The structural approach solves for the distance-to-default and effectively measures how many standard deviations away a firm’s value is from the default threshold. We compute the distance-to-default measure based on Merton-model and use it as a proxy for default risk (see Bharath and Shumway, 2008; Chava and Purnanandam, 2010). In addition, motivated by the hazard model literature, we also use firm size, past stock return, leverage, and return volatility as controls for default risk. The distance-to-default estimate is obviously correlated with these covariates, but it might contain additional information since it is a non-linear combination of these variables.9 The third alternative channel is the firm’s growth opportunity set. Growth opportunities affect the demand of capital and firms’ subsequent investments and cash flows. If firms with different growth opportunities respond differently to the crisis and if there are significant differences in the bank-dependent and rated firm’s growth rates, then we need to account for this channel. We use market-to-book ratio and industry fixed effects as proxies for growth opportunities. Finally, we control for the firm’s liquidity in the stock market. The stock market liquidity, i.e., the ease with which a firm’s stock can be bought and sold in the market, can have an impact on a firm’s stock return during the crisis period. A large quantity of stock sold during the crisis period can result in a relatively larger price drop for

9 Our results are robust to using either the distance-to-default measure or the set of other covariates alone.

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illiquid stocks as compared to their liquid counterparts. If bank-dependent firms have higher price impact of trades than their rated counterparts, then some of the drop in their stock value can be explained by this trading channel rather than the lack of access to capital. For example, if there is a higher likelihood of adverse selection in trades of bank-dependent firms, then they might have higher price impact of trade (Kyle, 1985). We measure stock market liquidity by the proportional bid–ask spread computed using daily stock price data over the past three months.

3. Data, sample construction and descriptive statistics We obtain accounting and return data from Compustat (active and research) and CRSP tapes, respectively. We start with all firms in the intersection of these two databases having information on stock returns for the crisis period and sales and total assets for the prior fiscal year. We remove financial firms (SIC codes between 6000 and 6999) and utilities (SIC codes between 4910 and 4940). To remove the effect of bid–ask bounce from our analysis, we also exclude firms with less than a $1 stock price as of the end of the prior fiscal year. To prevent outliers from affecting our results, we winsorize data at 1% and 99% in all our analyses. We remove firms with exposure to the crisis-affected regions. We do so to prevent any demand-side considerations from affecting our results. From the Compustat Geographical Segments file, we obtain data on all geographic segments of the firms for the prior fiscal year. If a firm reports operations in Russia or Brazil, we remove it from our sample. Instead of reporting country-level segments, many firms club their operations in various countries into a bigger geographical area such as Europe or South America. To make sure that our results are not driven by demand-side considerations, we adopt a conservative screening criteria and remove all firms that report any business activity in Russia, Brazil, Europe, Eurasia, Eastern Europe, or South America. In line with the earlier papers such as Kashyap, Lamont, and Stein (1994), we use the absence of publicdebt rating as the proxy for bank-dependence. We drop junk-rated firms from the sample since we are interested in comparing bank-dependent firms with firms that have better access to capital in the public-debt market. In a time of crisis of this magnitude, investment-grade rated firms are likely to have better access to alternative sources of capital in both the public-debt market and the commercial-paper market. Not surprisingly, none of the junk-rated firms have access to the commercial-paper market as compared to approximately 50% for the investment-grade rated firms that do. As we explain later, eventually we compare the bank-dependent firms with rated firms with similar default risk, which minimizes any concern about our results being driven by differences in credit risk of these two groups of firms. A firm without debt will always be classified as a bankdependent firm in this classification scheme, since such firms do not have public-debt ratings. These firms may be

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either completely rationed by the debt market due to informational frictions (Stiglitz and Weiss, 1981) or they may have chosen not to rely on debt financing even though they could have accessed the public-debt market. Thus, for these firms it is not clear if the lack of a publicdebt rating can be taken as a meaningful proxy for bank dependence. To avoid any potential misclassification errors, we remove from our sample firms with zero debt in the prior fiscal year. This leaves us with a sample of 2,665 bank-dependent and 304 rated firms for our base case analysis. All accounting and market variables used in the study are obtained as of May 1998. The accounting data is lagged so that the information is available to the market during the event period. Table 1 provides descriptive statistics for the sample. The average rated firm has annual sales of $2.8 billion, which is more than six times larger than the average bank-dependent firm. There are other remarkable differences across the two groups, Table 1 Descriptive statistics. This table reports summary statistics of key variables used in the analysis based on the entire sample of non-financial firms in the intersection of CRSP-Compustat databases with non-missing observations on the required data, having non-zero leverage and with no direct business exposure to the crisis affected regions. All firm-level information is lagged by at least six months and is extracted as of May-1998. Presence or absence of long-term credit rating is taken as a proxy for bank-dependence. The summary statistics for the rated and bankdependent firms are given in Panels A and B respectively. sales is the sales of the firm measured in millions of U.S. dollars. lever is the ratio of total debt (sum of long-term debt and short-term debt) to the total assets of the firm. mtb is the ratio of the market value of assets to total assets, where the numerator is defined as the sum of market equity, total debt, and preferred stock liquidation value less deferred taxes and investment tax credits. defg is the percentile ranking of the firm based on its expected default frequency. sigmaequity is the equity volatility of the firm measured over the past one year. pastret is the past one year stock return of the firm. ebitda/sales is the ratio of EBITDA to the sales of the firm. bidask is the average bid–ask spread of the firm over the past three months using daily stock data. CAR is the firm’s market-model adjusted stock return from 14-August-1998 to 4-September-1998. Mean

25th pctl

Median

75th pctl

2839.98 0.29 2.01 0.32 0.34 0.13 0.20 1.54 2.74

716.90 0.19 1.29 0.15 0.28 0.02 0.11 0.85 8.22

1243.49 0.29 1.66 0.28 0.32 0.16 0.17 1.10 2.02

3147.11 0.37 2.30 0.47 0.36 0.31 0.26 1.77 3.81

3782.97 0.15 1.15 0.22 0.10 0.31 0.14 1.30 10.41

391.04 0.34 2.48 0.75 0.78 0.34 0.16 4.42 0.09

1017.75 0.20 1.51 0.29 0.32 0.53 2.24 3.40 16.25

Panel B: Bank-dependent firms (N = 2665) sales lever mtb defg sigmaequity pastret ebitda/sales bidask CAR (%)

430.83 0.23 2.16 0.49 0.63 0.02 0.34 3.56 10.31

27.24 0.06 1.22 0.25 0.40 0.27 0.02 1.39 19.84

101.38 0.19 1.65 0.50 0.56 0.05 0.09 2.47 9.23

4. Results We first provide regression results based on the entire sample of rated and bank-dependent firms, followed by a matched sample analysis. In later sections, we exploit the variation within the subsample of bank-dependent firms. 4.1. Full sample analysis

Std. dev.

Panel A: Rated firms (N =304) sales lever mtb defg sigmaequity pastret ebitda/sales bidask CAR (%)

notably in terms of their default risk, equity return volatility, leverage, profitability, and bid–ask spread. The average bank-dependent firm is significantly riskier than the rated firm based on the default risk measure. Bankdependent firms also have higher effective bid–ask spreads than the rated firms. Overall, we find that there are considerable differences in the size, default risk, and stock market liquidity of rated and bank-dependent firms. Since these characteristics by themselves can explain the return differential between the two groups, we need to properly account for them in our analysis. One approach is to use a linear regression model that controls for these effects. The advantage of this approach is that we can make use of the entire sample and our inference will not suffer from the external validity considerations. However, given the large differences, especially in the firm size in the two groups, a matched sample approach is also appealing. In such an approach, we have the advantage of finding rated and bankdependent firms in the common-support zone, i,e., in a range of broadly comparable size, default risk, and liquidity position. In Fig. 3, we plot the distribution of firm size for the rated and unrated firms. As shown in Table 1, the rated firms’ size distribution is shifted considerably to the right of the bank-dependent firms. However, the upper tail of the bank-dependent firms’ distribution has reasonable overlap with the lower tail of the rated firms. In our matching technique, we effectively exploit the variation across rated and bank-dependent firms in the overlap zone.

Table 1 presents the distribution of returns across rated and bank-dependent firms during the crisis period. In the 16-day crisis period that started one trading day before the Russian debt default and ended one trading day after the onset of the Brazilian crisis, the median (mean) bank-dependent firm earned 9.23% ( 10.31%) marketmodel adjusted return as compared to 2.02% ( 2.74%) for the rated firms. The differences in both the mean and median returns are statistically significant at the 1% level. In Table 2, we provide the regression result for the base model. All models include industry fixed effects based on Fama-French industry classification. Model 1 shows that bank-dependent firms earned 3.61% lower return than firms with access to the public-debt market after controlling for firm size, leverage, and market-to-book ratio. It also shows that larger firms and firms with lower leverage earned better returns. We include several additional variables in Model 2 motivated by alternative hypotheses discussed earlier. In order to avoid a skewness


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Fig. 3. Distribution of key characteristics: before and after matching. The plots give the kernel density functions of the key characteristics of the firms before and after matching. More details on the matching are provided in Section 4.2.1 of the paper. Distribution for the entire sample (before matching) is presented in the first column and distribution for the matched sample is presented in the second column. The first row plots log(Sales) and the second row plots distance-to-default constructed as in Bharath and Shumway (2008).

problem with distance-to-default measure of risk, we first rank all firms into percentiles based on their default likelihood. We use the percentile ranking as the covariate in the regression model. We include the average bid-ask spread, calculated over the past three months, to account for the liquidity differences. In addition, motivated by the hazard rate estimates of default-likelihood, we include the prior year’s stock return, return volatility, and firms’ profitability as measured by its EBIDTA-to-sales ratio in the model. The estimate on bankdep drops marginally to 3.10% in this specification, which remains significant at the 1% statistical level. Other estimates show that stocks with high default risk, high equity return volatility, and high past returns experienced a larger value drop during this period. In this regression, we find a positive coefficient on the bid-ask spread, indicating that illiquid stocks performed better. We investigate this further and find that the relationship between spread and returns is negative at the univariate level. This relationship reverses in the multivariate regression after we control for the firm size. One potential explanation of this finding is that large institutional investors are more likely to sell their holdings of liquid stocks during the period of crisis to generate immediate cash flows. This, in turn, causes greater decline in the equity prices of liquid stocks during periods of crisis (Pasquariello, 2007).

In Model 3, we include the interaction of market-tobook ratio with the bank-dependent indicator variable. We do so to investigate the effect of supply shock across firms with varying intensity of growth opportunities. We conjecture that the valuation effect is likely to be higher for those bank-dependent firms that are likely to forego positive NPV projects due to the lack of funds. These are more likely to be growth firms. The results from Model 3 confirm this intuition. Within the set of bank-dependent firms, firms with high market-to-book (mtb) ratio earn considerably lower returns. In this specification, the coefficient on market-to-book ratio becomes positive and significant. Together, these results indicate that the growth firms with access to the public-debt market performed well during the crisis period. In contrast, bank-dependent growth firms lost considerable market value. In unreported tests, we also include the interaction of bankdep with other explanatory variables of the model. We find that the negative coefficient on the interaction of bankdep and mtb remains robust to the inclusion of these other interaction terms in the model. 4.1.1. Returns during a random period Our estimation exercise is based on one shock experienced during Fall 1998. To benchmark our results against any random period, we undertake a bootstrapping

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Table 2 Impact of Russian crisis on bank-dependent borrowers: full sample. Panel A of this table presents regression results relating the firm’s stock return around the Russian crisis to its characteristics. The dependent variable is the market model adjusted stock return from 14-August-1998 to 4-September-1998. Variable definitions appear in Appendix A. The empirical distribution of the coefficient on bankdep using the same regression as in Panel A, but based on a bootstrapping exercise of 100 random samples is presented in Panel B. The panel also presents empirical distribution based on samples drawn exclusively from periods of large negative market movements. Industry fixed effects using Fama-French 48 industry codes are included in all regressions. Robust t-statistics are reported in brackets. Adjusted R2 and the number of observations are reported in the last two rows. This estimation is based on the entire sample of non-financial firms in the intersection of CRSP-Compustat databases with non-missing observations on the required data, having non-zero leverage and with no direct business exposure to the crisis-affected regions. Panel A: Regression results from the crisis period Model 1

bankdep log(sales) mtb lever defg bidask pastret sigmaequity ebitda/sales bankdep mtb R2 N Fixed effects

Model 2

Model 3

Estimate

t-val

Estimate

t-val

Estimate

0.0361 0.0164 0.0012 0.0495

( 3.79) (8.12) (0.47) ( 2.88)

0.0310 0.0166 0.0022 0.0247 0.0488 0.0053 0.0625 0.0453 0.0004

( 3.17) (6.58) (0.84) ( 1.00) ( 2.00) (4.37) ( 6.99) ( 2.27) ( 0.19)

0.0021 0.0160 0.0154 0.0238 0.0490 0.0051 0.0630 0.0464 0.0005 0.0142

0.082 2,969 FF Industry


t-val ( 0.15) (6.33) (3.50) ( 0.97) ( 2.01) (4.25) ( 7.05) ( 2.33) ( 0.24) ( 2.94)


Panel B: Regression results from bootstrapped sample Variable Random-period Down-market

Mean

p1

p5

p25

p50

p75

p90

p99

0.0021 0.0044

0.0252 0.0187

0.0178 0.0133

0.0069 0.0101

0.0017 0.0039

0.0030 0.0017

0.0084 0.0050

0.0219 0.0096

exercise. Our goal is to re-estimate the regression model of Table 2 for several randomly generated samples of 16 contiguous days of stock returns in exactly the same manner as we do for the crisis period. This allows us to compare the crisis-period return with an empirically generated distribution of returns from the random periods. This approach is analogous to a portfolio-based approach of stock returns where we consider bankdependent firms as a portfolio of stocks with some unique characteristics and compare this portfolio’s return during the Russian crisis with its return during other normal periods. This test also allows us to compute the statistical significance of our results after accounting for any non-normality in the data. Finally, it allows us to comment on the economic magnitude of our results as compared to a random period. We perform the bootstrapping exercise for 100 randomly generated 16-day period returns drawn between January 1985 and December 1998. For every random period, we obtain the accounting variables from the Compustat tapes for the prior fiscal years. We then estimate the Model 1 of Table 2 and collect the coefficient estimate on the bankdep variable. The empirical distribution of these estimates is provided in Panel B of Table 2. In the median period, the estimate on the bank-dependent indicator variable is an insignificant 0.17% as compared to our crisis period estimate of 3.61%. There is a slight

negative skewness in the empirical distribution; other than that, the distribution is fairly evenly distributed on both sides of the mean. Our crisis-period estimate of 3.61% falls below the first percentile estimate of 2.52%. These estimates provide confidence in the economic and statistical significance of our results. We extend this exercise by generating a bootstrapped sample solely from the periods of low market returns. This exercise allows us to rule out the possibility that bankdependent firms always perform worse than their rated counterparts during periods with large negative market returns. We find 21 non-overlapping periods with lower than 5% market returns in 16 contiguous trading days during 1985–1997. We repeat the regression estimation for these samples and present the distribution of estimated coefficients on the bankdep variable in Panel B of Table 2.10 The results show that the abnormally low return of bank-dependent firms during the Fall of 1998 is not an artifact of low returns of these firms during any market downturn. In fact, the estimated coefficient of 3.61% for our estimation period is lower than the coefficient that we find for each of the 21 periods 10 Since there are only 21 coefficients for this exercise, the percentile values are coarser. For example, the value corresponding to the bottom one percentile equals the minimum value of estimated coefficients across all periods.


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and provide the results in Models 1 and 2 of Panel A, Table 3. We find that younger firms have significantly lower returns than older firms during this period, consistent with our main argument that firms that are more likely to face frictions in raising external capital at the time of crisis experience more negative returns. Our second measure is not a direct measure of financial constraint per se, but a measure of the firm’s dependence on external financing based on Rajan and Zingales (1998). We hypothesize that firms that rely more on external capital are more likely to suffer from unanticipated shocks to the banking sector. For every firm, we compute a measure of external financing dependence by computing the difference between total investments (Compustat data item 311) and cash flow from operations (item 308) scaled by cash flow from operations. To minimize the outlier problems, we construct this measure at the industry level based on four-digit SIC codes. We compute the median ratio for every industry in a year and then take the median across all years from 1987 to 1997 as the measure of external

considered in the bootstrapped exercise. Overall, these results establish that bank-dependent firms were more adversely affected than their rated counterparts during the Russian crisis of 1998. 4.1.2. Other measures of financial constraints It is an extremely challenging task to find a good proxy of financial constraint. Since the Russian crisis had a disproportionately larger impact on the banking sector, we focus on lack of access to the public-debt market as the key proxy for financial constraint in this paper. We consider two alternative measures in the robustness exercise. We first consider a firm’s age as an alternative measure of financial constraint since older firms are likely to have better credit history allowing them to overcome informational frictions in raising external capital. They also have a longer history of access to the public equity markets, which can further alleviate financial constraints (see Holod and Peek, 2006). We compute a firm’s age based on the date of its listing on a public stock exchange. We regress crisis-period equity returns on this measure

Table 3 Other measures of financial constraints and firm performance. Panel A of this table presents regression results relating the firm’s stock return around the Russian crisis to two alternative measures of financial constraints. The dependent variable is the market model adjusted stock return from 14-August-1998 to 4-September-1998. listage measures the firm’s age since its listing on a stock exchange. exdep measures the extent of dependence on external financing and is computed at the industry level. Variable definitions appear in Appendix A. Robust t-statistics are reported in brackets. Adjusted R2 and the number of observations are reported in the last two rows. In Models 3 and 4, all standard errors are clustered at the FF-industry level. Panel B presents the firm fixed effect regression results for the effect of crisis on firm’s investment and profitability. The dependent variables are: quarterly investments scaled by lagged assets in Model 1, and quarterly operating income to total asset ratio in Model 2. after is an indicator variable that takes a value of zero for quarters before 1998Q3, and one otherwise. Robust standard errors are presented in the brackets. These estimations are based on the entire sample of non-financial firms in the intersection of CRSPCompustat databases with non-missing observations on the required data, having non-zero leverage and with no direct business exposure to the crisis affected regions. Panel A: Other measures of financial constraints Model 1

listage exdep logsales mtb lever defg bidask pastret sigmaequity ebitda/sales R2 N Fixed effects

Model 2

Model 3

Estimate

t-val

Estimate

t-val

0.0006

(2.73)

0.0005

(2.12)

0.0176 0.0020 0.0477

(9.98) (0.85) ( 2.77)

0.0177 0.0030 0.0254 0.0441 0.0048 0.0627 0.0462 0.0007 0.120 2,904 FF Industry

(7.77) (1.14) ( 1.03) ( 1.79) (3.91) ( 6.99) ( 2.28) ( 0.35)


Model 4

Estimate

t-val

Estimate

t-val

0.0268 0.0164 0.0035 0.0566

( 2.37) (11.40) (1.71) ( 2.68)

0.0292 0.0155 0.0040 0.0239 0.0571 0.0048 0.0674 0.0476 0.0007 0.096 2,904 None

( 2.64) (4.64) (1.91) ( 0.91) ( 2.54) (4.66) ( 7.18) ( 2.69) ( 0.23)

0.049 2,917 None

Panel B: Other measures of firm performance Model 1:Capex

after bankdep after R2 N Fixed effects

Model 2:Profitability

Estimate

t-val

Estimate

0.0011 0.0026 0.527 32,748 Firm

( 2.80) ( 5.56)

0.0012 0.0056 0.619 33,516 Firm

47

t-val ( 1.87) ( 6.33)

126


dependence. We re-estimate the regression model using this exdep measure as a proxy for the likely adverse effect of the Russian crisis. Since the key explanatory variable is industry specific, we do not include industry fixed effects in these models. All standard errors, however, are clustered at the industry level. Results are provided in Models 3 and 4 of Panel A, Table 3. We find that firms that are more dependent on external financing have significantly higher valuation losses. A useful extension of our analysis will be to compare the effect of this crisis on firms with and without access to the public equity market. Since our exercise only includes publicly traded firms, we are unable to conduct this analysis in the paper. Some recent papers have made considerable progress on this dimension by analyzing the effect of liquidity shocks on publicly traded versus private banks (Holod and Peek, 2006; Ashcraft and Bleakley, 2006). Our proxy based on a firm’s age since its listing is in the spirit of these papers. 4.1.3. Effect on investments and profitability We focus on stock returns during the crisis period as the key outcome variable since it allows us to sharply detect the unanticipated effect of the crisis on firm value. The market-based analysis is also relatively immune to the effect of subsequent policy interventions by the Fed in response to the crisis itself. As a complement to the stock return-based analysis, we study the effect of the crisis on the firm’s real outcomes as well. We do so by estimating the following firm fixed effect regression model: Yiq ¼ ai þ b bankdepi þ g afterq þ y bankdepi after q þ eiq : Yiq measures real outcome such as investments and profitability of firm i in quarter q; ai denotes firm fixed effects; bankdepi is an indicator variable for bankdependence; afterq equals zero for quarters before 1998Q3, and one otherwise. Since bankdep is a timeinvariant variable for a firm in our sample, it is subsumed by the firm fixed effect in the regression model. We identify the effect of the crisis on firms’ real outcome by the coefficient on the interaction term. It measures the changes in real outcome for bank-dependent firms around the crisis quarters as compared to changes experienced by their rated counterparts over the same time period. We estimate this model using data from six quarters before the crisis and six quarters after it, i.e., from 1997Q1 to 1999Q4.11 We consider two measures of performance: (i) capital expenditure scaled by lagged asset (quarterly investments calculated from Compustat data item 90 scaled by lagged value of item 44), and (ii) operating income to total asset ratio (item 8 scaled by lagged value of item 44). Results are provided in Panel B of Table 3. In Model 1 we find that bank-dependent firms cut their investments significantly after the crisis as compared to their rated counterparts. The coefficient on the interaction of bankdep and after is about 22% of the median level of quarterly investments by 11

Results are robust to alternative windows around the crisis period.

the sample firms. Therefore, the decrease in investments by bank-dependent firms is strong in economic terms as well. In Model 2, we show that bank-dependent firms experienced significant decline in their operating profits. The estimated decrease in profitability is about 67% of the sample median. These results show the detrimental effect of the crisis on bank-dependent firms’ real outcomes, consistent with the negative equity returns experienced by these firms during the crisis period. 4.1.4. Liquidity injection by the Fed Subsequent to the Russian crisis and the collapse of LTCM, the Federal Reserve Bank held two important meetings in Fall 1998. In these meetings several measures were undertaken by the Fed to provide liquidity support to the banking sector. The same theoretical argument that predicts a negative effect of poor bank-health on bank-dependent borrowers also implies that these firms should perform better when the banking system receives unexpected positive shocks from the policy makers. On September 29, 1998, the Federal Reserve Bank cut the Fed Funds rate by 25 basis points. This action was somewhat expected by the market. Subsequently on October 15, in a largely unanticipated move the Fed Funds rate was decreased by 25 basis points. The discount lending rate was also cut by the same magnitude in the October meeting. Since the Fed rarely altered the discount lending rate during that period, we expect to find a larger effect of the October 15 FOMC actions as compared to the September 29 meeting. We regress the market-model adjusted return around a two-day window surrounding these meetings on the bank-dependence dummy and other control variables. Results are provided in Table 4. We find that bank-dependent firms earned 0.65–0.97% higher returns than firms with access to the public-debt market around the September meeting (Models 1 and 2), which is significant in one of the two specifications. Around the October meeting, bank-dependent firms earned about 1.10% higher returns, which is economically large and statistically significant for both specifications (Models 3 and 4). These findings lend further support to our argument, in a reverse direction, that the market value of bank-dependent firms significantly depends on the financial health of the banking sector and its ability to supply loans to borrowers. 4.2. Matched sample analysis Given the disparity in some observable characteristics of rated and bank-dependent firms, we now conduct a matched sample analysis. We find pairs of bank-dependent and rated firms that are identical along every meaningful dimension except for the access to the public-debt market. The dimensions along which we match are motivated by competing hypotheses outlined earlier. 4.2.1. Propensity score matching We use a propensity score method for the matching exercise (Rosenbaum and Rubin, 1983). In the first step, a


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Table 4 Liquidity injection by the Federal Reserve Bank. This table presents regression results relating the firms’ stock return around the periods of liquidity injection by the Federal Reserve Bank to bank dependence. The dependent variable is the market-model adjusted stock return around the Federal Funds rate change announcements on September 29, 1998 (Models 1 and 2), and October 15, 1998 (Models 3 and 4). The event window is (0, + 1) days, where day zero corresponds to the rate announcement date. Variable definitions appear in Appendix A. Industry fixed effects using Fama-French 48 industry codes are included in all regressions. Robust t-statistics are reported in brackets. Adjusted R2 and the number of observations are reported in the last two rows. This estimation is based on the entire sample of non-financial firms in the intersection of CRSP-Compustat databases with non-missing observations on the required data, having non-zero leverage and with no direct business exposure to the crisis affected regions. Model 1:Sep 29, 1998 Estimate bankdep logsales mtb lever defg bidask pastret sigmaequity ebitda/sales R2 N

0.0097 0.0009 0.0003 0.0114

0.015 2,878

t-val (2.19) (1.00) ( 0.30) ( 1.41)

Model 2:Sep 29, 1998 Estimate

Model 3:Oct 15, 1998

t-val

0.0065 0.0010 0.0000 0.0133 0.0048 0.0003 0.0007 0.0167 0.0011 0.019 2,865

probit model is estimated with the presence of public-debt rating as the binary dependent variable. We model this choice as a function of the firm’s size, market-to-book ratio, leverage, past stock return, stock market liquidity, profitability, and default risk. In addition, we add Fama-French industry dummies to control for industry-specific factors. Model 1 (pre-match) of Table 5 presents the estimation results. The propensity of obtaining a credit rating is positively correlated with firm size, leverage, and profitability; and negatively correlated with equity return volatility and past stock returns. We obtain a pseudoR-square of 70%, which indicates a reasonable fit of the model.12 After estimating the probit model, we obtain the probability of getting rated (i.e., the propensity score) for every firm in the sample. In the final step, for every bankdependent firm we find a rated firm with the closest propensity score. We ensure that the rated firm’s propensity score is within 72.5% of the bank-dependent firm’s score.13 This technique uses the nearest neighborhood caliper matching approach of Cochran and Rubin (1973). We face a trade-off in terms of finding a unique rated firm as a match for every bank-dependent firm and the sample size. This, in turn, presents a trade-off between bias and efficiency in our analysis. To maximize the number of firms in our sample, we allow a rated firm to serve as a match for up to three bank-dependent firms.14 In a setting like ours, where we have many more subjects in the treatment group as compared to the control group, it is advisable to have one control firm serve as a match

12 It is worth noting that this estimation exercise is not intended for making any causal inferences about a firm’s choice of obtaining a credit rating. Our limited goal is to project relevant firm characteristics on the bank-dependence choice and use the resulting likelihood score as the matching dimension. 13 Our results are robust to changing this band to 7 5% or other comparable range. 14 Our results are robust with two or four repetitions.

Estimate

(1.44) ( 0.87) (0.03) ( 1.15) (0.44) (0.61) ( 0.18) ( 1.91) (1.10)

0.0100 0.0036 0.0011 0.0042

Model 4:Oct 15, 1998

t-val

Estimate

(1.90) (3.32) ( 0.81) (0.42)

0.022 2,854

t-val

0.0110 0.0021 0.0022 0.0164 0.0127 0.0013 0.0093 0.0017 0.0004 0.026 2,841

(2.03) (1.54) ( 1.46) (1.16) ( 0.88) ( 2.03) ( 1.90) ( 0.16) ( 0.40)

Table 5 Matching estimation results. The following table presents the results of a probit regression with access to the public-debt market as the dependent variable. In Pre-match model, the entire sample of firms in the intersection of CRSP-Compustat databases with non-missing observations on the required data, having non-zero leverage and with no direct business exposure to the crisisaffected regions is used and in Post-match model, only those bankdependent firms that can be matched to the rated firms based on the propensity score from the Pre-Match model are used. Robust t-statistics are reported in brackets. Pseudo-R2 and the number of observations are reported in the last two rows. Pre-match

log(sales) mtb lever sigmaequity ebitda/sales bidask pastret defg R2 N Fixed effects

Estimate 1.0363 0.0058 0.9326 2.5941 4.3155 0.0657 0.4812 0.9152 0.701 2942 FF Industry

t-val (13.00) (0.08) (2.34) ( 3.86) (5.37) ( 0.59) ( 2.55) ( 1.07)

Post-match Estimate 0.0770 0.0421 0.1635 0.7068 0.9066 0.1127 0.1866 0.5628

t-val ( 0.97) ( 0.63) (0.42) ( 1.08) (1.39) ( 0.84) ( 0.84) (0.66)

0.045 470 FF Industry

for multiple treatment firms (see Dahejia and Wahba, 2002; Smith and Todd, 2005). The matching exercise yields a sample of 235 bankdependent firms that could get matched with a rated firm, resulting in a sample size of 470 firms. Since one rated firm can serve as a match for multiple bank-dependent firms, we ensure that all standard errors are clustered at the firm level in analysis involving the matched sample. Before computing the difference-in-difference estimate on the matched sample, we analyze the efficacy of our matching technique. We estimate the probit model of obtaining a rating on the matched sample and present the results in Model 2 (post-match) of Table 5. None of the

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insignificant difference of 10 basis points between these two groups in the average random period. The empirical distribution reveals that there is only a 1% chance of getting a return difference of 4.09% or lower for the bank-dependent firms as compared to their matched rated counterparts. The crisis period return difference of 3.94% is very close to this number. Similar to the full sample study, we also generate random samples from the periods of very low market returns only. Based on the empirically generated distribution from these periods, we find that the crisis period return difference falls between the first and the fifth percentiles of the distribution (see Panel B of Table 6).

variables is significant in this estimation, indicating that after the match firms are equally balanced between rated and bank-dependent groups along these dimensions. The model’s R-squared, not surprisingly, drops to 4.5% on the matched sample. In Fig. 3, we plot the distribution of two key characteristics of the firms before and after the matching exercise. As explained earlier, there is a large difference in the distribution of firm size before the matching. After the matching, however, the distributions of rated and unrated firms are almost identical. A quick glance at the figure reveals that the post-matched sample consists of reasonably large firms in both groups. The second plot is for the firm’s default risk as measured by its distance-to-default. The bank-dependent firms have higher default risk as compared to the rated firms before the match. After the match, the distribution is almost identical. In a nutshell, the matched sample is equally balanced on the observable dimensions that might influence stock returns during this period.

4.2.3. Other matching criteria As a robustness check, we adopt a dimension-bydimension matching approach as opposed to the propensity score-based method. For every bank-dependent firm, we find all rated firms in the same industry within 725% of the bank-dependent firm’s size. From all rated firms in this band, we pick the closest firm in terms of distance-todefault. As before, we allow a rated firm to serve as a match for up to three bank-dependent firms. The advantage of this approach is that it ensures as precise a match as possible on the dimension of firm size. Results are provided in Model 4 of Panel A of Table 6. Bank-dependent firms significantly underperformed their rated counterparts by 3.61% during the crisis period on this subsample.

4.2.2. Results The matched sample results are provided in Table 6. The bank-dependent firms earned an average return of 6.61% as compared to 2.67% for the rated firms during the crisis period. The difference of 3.94% is significant at the 1% level. We find similar patterns for the median as well as the entire distribution of returns (unreported). We also conduct a bootstrapping test similar to the test on the entire sample. For each bootstrapping period, we create a matched sample of bank-dependent and rated firms using the propensity score matching in exactly the same manner as in our main exercise. Then, we compare the returns of the two groups and report their empirical distribution in Panel B of Table 6. There is a positive but

4.3. Evidence from variations within bank-dependent borrowers We now exploit the variation across bank-dependent firms’ ability to raise external capital. This test allows us to meaningfully relate the frictions in raising external capital

Table 6 Evidence from matched sample. This estimation is based on the matched samples of rated and bank-dependent firms where matching has been done either based on the propensity score method or on the basis of firm size. Column 1 of Panel A provides the mean abnormal returns of bank-dependent and rated firms during August 14, 1998 to September 4, 1998, i.e., during the crisis-period. In the second and third columns, the returns are measured over several random samples of 16 contiguous days during January 1985 to December 1998. We report average returns across all random periods in these columns. In the second column, Down market, we draw random samples from periods of low market returns. In the third column, Random Period, random samples are drawn without conditioning on market return. In these three models, the construction of treatment (treat = 1 for bank-dependent firms) and control (treat = 0 for rated firms) groups is based on the propensity score matching method. The fourth column labeled Size Match provides the crisis-period return for bankdependent and rated firms for a matched sample based on firm size within the same industry. For all four models, the mean return for the treatment and control groups and the difference between the returns of these two groups are presented in the first three rows. The fourth row contains the t-statistic for the difference in the mean returns for the treatment and control groups. In Panel B, we provide the empirical distribution of CAR for the treatment and control group from the bootstrapping exercises. Panel A: CAR for treatment and control groups

CARtreat = 0 CARtreat = 1 CARtreat = 1 CARtreat = 0 t-stat for DCAR N

Crisis-period

Down-market

Random period

Size match

0.0267 0.0661 0.0394 2.52 470

0.0214 0.0217 0.0003 0.36 –

0.0016 0.0005 0.0010 0.58 –

0.0481 0.0842 0.0361 2.18 253

Panel B: CAR for treatment and control groups from bootstrapped samples Variable Random-period Down-market

Mean

p1

p5

p25

p50

p75

p90

p99

0.0010 0.0003

0.0409 0.0488

0.0280 0.0152

0.0078 0.0133

0.0005 0.0060

0.0083 0.0023

0.0283 0.0454

0.0469 0.0520


to firm value. In addition, since we draw inferences based on the bank-dependent subsample only, this analysis does not suffer from any biases created by observable or unobservable differences across rated and unrated firms. We investigate if other sources of funds or financial flexibility mitigate the negative effect of bank dependence during the time of crisis. A bank-dependent firm can weaken its dependence on banks by maintaining higher financial flexibility through free borrowing capacity. We proxy a firm’s free borrowing capacity by the extent of unpledged tangible assets available at the time of the crisis. In a lending market with adverse selection problems, collateral can serve as a mechanism to alleviate the lemons problem (see Bester, 1985; Besanko and Thakor, 1987). We hypothesize that a bank-dependent firm with a higher fraction of unpledged assets should suffer less. These firms should be able to raise funds relatively easily by offering their collateral at the time of crisis. Dealscan database allows us to investigate this hypothesis since it provides information on whether a bank loan is secured or not. By definition, bank-dependent borrowers have only borrowed from banks. Therefore, by observing their past borrowing in this data set, we are able to construct a reasonable estimate of the total secured loans.15 We obtain all bank loans outstanding at the time of the crisis and gather information on whether they are secured or not. Our sample size decreases to 630 bank-dependent firms for this analysis due to three main reasons: (a) since Dealscan database only provides the names of the borrowers, we need to hand-match this data set with the Compustat-CRSP data set using firm names, leading to a loss of many observations, (b) many loan facilities do not have information on whether the loan is secured or not, and (c) we consider only those firms that have bank loans outstanding as of August 1998. Given these data limitations, we need to interpret the results of this section with some caution. These results are based on a sample of bank-dependent firms that are relatively larger and have lower default risk than the average bank-dependent firm in our entire sample. In addition, the collateral availability and firm leverage are likely to be determined endogenously. Due to these selection issues, the coefficients on other explanatory variables in this model are not directly comparable to other models of the paper. We create three proxies of available collateral: (a) the fraction of past loans that are unsecured, (b) one minus the ratio of dollar amount of secured loans to total dollar amount of loans, and (c) one minus the ratio of dollar amount of secured loans to the firm’s total tangible assets (Compustat item number 8). Regression results are provided in Table 7. We find that bank-dependent firms with higher free collateral perform significantly better, suggesting that higher financial flexibility weakens the

15 This assumes that firms have negligible secured borrowing from non-banking private institutions. For firms that borrow from these sources and provide their assets as collateral, our proxy will be noisy.

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effect of bank-dependence on firm valuation during the time of crisis. 4.4. Evidence from variations across the banks We now investigate whether borrowers of banks that are severely affected by the Russian crisis perform worse than borrowers of unaffected banks. This allows us to directly comment on the effect of banks’ losses in the international market on their domestic borrowers’ performance. We estimate the following model on the subsample of bank-dependent firms16: ri ¼ b0 þ b1 affbanki þ

kX ¼K

fk Xi þ ei ,

k¼1

where affbanki measures the exposure of firm i’s bank to the Russian crisis. This measure is independent of the bank’s activities in the U.S. domestic market and, therefore, exogenous to the demand-side considerations. To estimate this model, we first need to classify banks into affected and unaffected categories based on their exposure to the Russian crisis. We use quarterly call reports filed by every FDIC-insured commercial bank to get this information. We augment this data source with information contained in the footnotes to the banks’ annual statements. The latter data are provided by Kho, Lee, and Stulz (2000), who read the financial statements of 78 large banks covered in Datastream data set. 4.4.1. Identification of the bank’s exposure We first gather information on the identity of the firm’s main banks from the Dealscan data set and then obtain data on the extent of their exposure to the Russian crisis using the call reports and annual statements. From Dealscan we collect all loans made to the borrowing firms that are outstanding at the time of the crisis. We restrict our attention to loans made by 78 large banks covered in the Datastream data set. The choice of these banks is driven by the study of Kho, Lee, and Stulz (2000), which is one of the sources of information about the banks’ exposure to the crisis. Since we need to manually match the identity of banks in the Dealscan data set with the identity of banks in the call report data set, it becomes easier from the data-collection viewpoint to focus on this sample.17 This list contains all the large U.S. banks and for all practical purposes imposes no restriction on our sample. If a firm has multiple banking relationships, we keep the bank with the maximum loan amount as the firm’s main bank.18 16 We also estimate a specification where we use the rated firms in the sample as well. We estimate the model with bankdep, affbank, and their interaction term as the key right-hand side variables. All our results are robust. We focus on this model since it alleviates omitted-variable and selection-bias concerns. 17 We hand-match the identity of banks from the Dealscan database with the call report database. We ensure that we obtain proper matches for banks that have merged since then, i.e., we ensure that we match borrowers with their banks as of August 1998. 18 We have experimented with other definitions such as the average exposure of all banks of the borrower. Our results are similar.

130


Table 7 Impact of collateral availability. This table analyzes the impact of financial flexibility (as measured by collateral availability) on the stock market reaction during the Russian crisis. Firms’ market-model adjusted stock return from 14-August-1998 to 4-September-1998 is the dependent variable. loansec is (1-number of firm’s loans that are secured divided by total number of firms’ outstanding loans in the dealscan database). amtsec is (1-the amount of firm’s loans that are secured divided by total amount of firms’ outstanding loans). sectan is (1-the amount of firm’s loans that are secured divided by the firms’ tangible assets (as proxied by the net plant, property and equipment)). Robust t-statistics are reported in brackets. Adjusted R2 and the number of observations are reported in the last two rows. The sample is restricted to bank-dependent firms with coverage on Dealscan database and with non-missing observations on security of their loans. Model 1

loansec amtsec sectan log(sales) mtb lever defg bidask pastret sigmaequity ebitda/sales R2 N Fixed effects

Model 2

Estimate

t-val

0.0306

(2.00)

0.0079 0.0092 0.0432 0.0115 0.0029 0.0511 0.0597 0.0337

(1.24) (1.24) ( 0.85) (0.22) (1.21) ( 2.62) ( 1.26) (1.05)


We collect information on banks’ financial condition as of the third quarter of 1998 from call reports. Though banks do not report the extent of their business activity on a country-by-country basis in this data set, they do report losses suffered in foreign markets as a whole. We construct the first measure of exposure based on quarterly charge-offs during 1998Q3 on loans and leases made to foreign borrowers including foreign individuals, corporations, banks, and governments. This measure does not directly capture the losses on foreign debt and equity securities, which motivates the use of our second proxy. We consider investments in foreign securities, both debt and equity, held as of 1998Q1 as the second proxy of a bank’s exposure to the crisis. We lag the security holding data by two quarters to ensure that the measurement of the explanatory variable is not contaminated by the crisis event itself. These two measures have their own advantages and shortcomings. While the foreign securities-based measure captures the extent of exposure across both debt and equity securities, it does not measure the quality of these investments. On the other hand, the charge-off-based measure is closer in spirit to the adverse capital shocks faced by the banks, but it misses the extent of losses on foreign securities. We find that both measures classify banks into affected and unaffected groups in roughly the same manner. The rank correlation between the two measures is about 70%; therefore, it is not surprising that our results remain similar based on either of the two proxies. In our empirical tests we divide both these measures by the lagged asset value of the bank to construct a scaled measure of exposure. We complement this data by classifying banks into affected and unaffected groups based on Kho, Lee, and Stulz (2000). If a bank is classified as having exposure to

Model 3

Estimate

t-val

0.0333

(2.22)

0.0077 0.0091 0.0429 0.0121 0.0029 0.0510 0.0588 0.0327

(1.21) (1.23) ( 0.84) (0.23) (1.22) ( 2.62) ( 1.24) (1.02)


Estimate

t-val

0.0026 0.0086 0.0087 0.0311 0.0008 0.0026 0.0530 0.0612 0.0332

(2.27) (1.39) (1.17) ( 0.60) ( 0.02) (1.10) ( 2.74) ( 1.30) (1.04)


the Russian or LTCM crises in their study, we classify that bank as an affected bank. We set the indicator variable affbanki to one for affected banks, and zero otherwise. This measure has a high correlation (over 80%) with the measures based on the call report data. In Fig. 4 we plot the quarterly trend in the U.S. banks’ losses on account of their foreign operations. We present two plots: one based on the quarterly charge-off data that we use for our subsequent analysis and the other based on the extent of non-performing foreign loans. Non-performing foreign loans are constructed by dividing the foreign loans and leases that are past due for over 90 days by the total assets. A clear pattern emerges from these plots. Banks experienced significant increase in losses due to their international operations around 1998Q3. The quarterly charge-off ratio in 1998Q3 is significantly higher than the preceding quarters. We find that the charge-offs increased by about 200% in this quarter as compared to the average charge-offs over the preceding four quarters. The pattern in non-performing assets is equally clear. Since we are considering 90-day overdue loans for the definition of non-performing assets (NPAs), this ratio shows a remarkable jump in 1998Q4. The foreign non-performing asset ratio in 1998Q4 is about 80% higher than the average value of this ratio measured over the preceding five quarters. Though our subsequent tests are based on cross-sectional variation in losses across banks, the time-series pattern in losses revealed by these figures provides confidence in our identification strategy.19

19 Since we focus on exploiting cross-sectional variations in banks’ exposure to the crisis, we do not closely investigate the lead-lag relationship between charge-offs and NPAs in this paper.


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Fig. 4. Trend in banks’ NPA and charge-offs. The plots give the quarterly trend in U.S. banks’ non-performing assets (assets past due 90 days) and chargeoffs on their foreign loan portfolios around the Russian crisis. Quarter zero corresponds to 1998Q3. We plot the ratio of non-performing assets to banks’ total assets in percentage terms in the first figure. The second figure plots the ratio of quarterly charge-offs to lagged value of banks’ total assets in percentage terms.

There are about 400 bank-dependent firms for which we could obtain the identity of their main banks and the banks’ exposure to the crisis. Citicorp, Bank of America, Bankers Trust Corporation, Chase Manhattan Corporation, and Bank Boston Corporation rank among the top exposure banks. We find a large concentration of charge-offs within these banks. Some of the banks that had little to no exposure to the crisis include Keycorp, US Bancorp, Banc One Corporation, Wells Fargo, and National City Bank.

4.4.2. Regression results Regression results are provided in Panel A of Table 8. All standard errors are clustered at the bank level. In our first test, we use charge-offs during 1998Q3 (scaled by lagged assets) as the measure of the bank’s exposure to the crisis. We find a significant negative coefficient on charge-offs, indicating that borrowers of the crisisaffected banks lost significantly higher value than their counterparts that borrowed from unaffected banks. Based on the estimated coefficient, we find that a one-standarddeviation increase in the bank’s charge-offs resulted in a decrease of about 1.4% in market returns of their borrowers. In Model 2, we use the cumulative chargeoffs during 1998Q3 and 1998Q4 as the measure of banks’ exposure and find similar results. Model 3 uses the foreign securities-based measure and confirms the findings. Finally, in Model 4 we use an indicator variable based on Kho, Lee, and Stulz (2000) as the proxy for exposure to the crisis.20 We find that the crisis-affected banks’ borrowers earned 3.54% lower returns than the unaffected banks’ borrowers after controlling for the effect of firm size, default risk, and growth opportunities. It is hard to argue that the borrowers of the affected banks are systematically different from the unaffected banks on unobservable dimensions in such a manner that they earn lower returns during the crisis period due to those unobservable differences. These results suggest that 20 We do so to ensure that we do not miss any bank that reports its exposure in the annual statements, but had little exposure as of the datareporting date.

firms face value-relevant frictions in raising external capital. Further, the evidence also supports the view that the global integration of financial markets can cause shocks to propagate from one economy to another through the banking channel. To ensure that our results are not driven by large outliers, we perform additional statistical tests. We use DFITS (see Welsch and Kuh, 1977) statistics to identify the influential observations (see Ashcraft, 2006). We first fit an OLS model using all available data points and then classify an observation as an outlier pffiffi if the DFITS statistic exceeds the threshold of 2 ðk=nÞ, where k is the number of independent variables including the intercept and n denotes the sample size. We re-estimate all four models after excluding the outliers and present the results in Panel B of Table 8. We find that all results remain robust to the outlier correction. In other words, our estimation results are not driven by a few influential observations, instead they represent a general tendency in the data that borrowers of crisis-affected banks lost higher market value than their counterparts that banked with unaffected financial institutions. 4.4.3. Evidence from shift in loan supply curve In our final test, we directly investigate the lending behavior of banks around the crisis period. A shock to the supply of credit should lead to an inward shift in the supply curve, and the resulting credit crunch should result in a decrease in the equilibrium quantity of credit and an increase in its price. It is an extremely challenging task to empirically test these implications of credit crunch because we are unable to observe the entire demand and supply curve. The issue is further complicated due to the possibility of credit rationing (Stiglitz and Weiss, 1981) as well as the possibility of changes in the composition of borrowers before and after the crisis. With these limitations in mind, we proceed with a difference-in-difference approach. We compare the changes in the quantity and the price of bank credit around the Russian crisis for crisisaffected banks as compared to the unaffected banks. The double-difference technique allows us to remove the effect of any time trend in bank credit.

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Table 8 Evidence from matched sample of banks and borrowers. This table provides regression results from a matched sample of banks and borrowers. The sample is restricted to banks and borrowers that we are able to match across CRSP, Compustat, call report data, and Dealscan. The dependent variable is the market-model adjusted stock return from 14-August-1998 to 4-September-1998. chargeoff measures the quarterly charge-off scaled by lagged asset value of the firm’s main bank during 1998Q3. chargeoff2q is charge-off scaled by lagged assets computed over 1998Q3 and 1998Q4. foreignsec measures investments in foreign securities by the firm’s main bank scaled by total assets. This variable is constructed as of 1998Q1. KLS is a dummy that takes the value of one for the banks that are classified as exposed to Russia by Kho, Lee, and Stulz (2000), and zero otherwise. Other variable definitions are given in Appendix A. All models include industry fixed effects using Fama-French industry classifications. Robust t-statistics adjusted for clustering at the bank level are reported in brackets. Adjusted R2 and the number of observations are reported in the last two rows. In Panel B, we restrict the sample to firms that are not classified as outliers based on the influence statistics computed using DFITS (see Welsch and Kuh, 1977). Panel A: Entire sample Model 1

log(sales) mtb lever charegoff charegoff2q foreignsec KLS R2 N

Model 2

Model 3

Model 4

Estimate

t-val

Estimate

t-val

Estimate

t-val

Estimate

t-val

0.0315 0.0041 0.0591 0.8934

(6.03) (0.59) ( 0.94) ( 3.10)

0.0334 0.0032 0.0539

(6.00) (0.46) ( 0.82)

0.0306 0.0033 0.0398

(6.60) (0.46) ( 0.61)

0.0308 0.0068 0.0495

(5.97) (0.92) ( 0.72)

0.6984

( 3.01) 1.1101

( 2.15) 0.0354 0.201 402

( 1.95)

0.206 406

0.213 391

0.211 406

Panel B: Outlier corrected sample Model 1

log(sales) mtb lever chargeoff chargeoff2q foreignsec KLS R2 N

Model 2

Model 3

Model 4

Estimate

t-val

Estimate

t-val

Estimate

t-val

Estimate

t-val

0.0208 0.0030 0.1105 0.7456

(5.71) (0.47) ( 2.19) ( 3.39)

0.0241 0.0063 0.0923

(6.21) (0.93) ( 1.43)

0.0224 0.0059 0.0756

(6.37) (0.88) ( 1.20)

0.0205 0.0089 0.0925

(5.88) (1.47) ( 1.71)

0.6198

( 2.99) 1.0866

( 2.89) 0.0260 0.199 375

( 1.94)

0.189 377

0.212 365

To estimate this effect, we first obtain all bank loans from the Dealscan database in a two-year period surrounding the Russian crisis. We conduct the analysis both at loan level and at the bank level. In general, we estimate the following model with the loan-level data: Yit ¼ ai þ b postcrisisit þ g affectedi þ y postcrisisit affectedi þ k macrovar it þ eit : Yit is either the loan spread, our proxy for the price of bank credit, or the loan amount given by bank i at time t. postcrisisit equals one for observations after August 1998, and zero otherwise. affectedi is a dummy variable that equals one for loans from banks affected by the crisis, and zero otherwise. We use a composite measure of a bank’s exposure to the crisis using information in both call reports and the Kho, Lee, and Stulz (2000) study. We classify a bank as affected by the crisis if it is classified as crisis-affected by KLS or if it falls in the top 10% of quarterly charge-off distribution.21 We are interested in estimating y that measures the change in loan spread 21 All banks that fall in the top 10% are also classified as crisisaffected by the KLS measure. Thus, the second measure becomes a redundant conditioning variable for this part of the analysis.

0.208 378

or loan amount for crisis-affected banks as compared to the unaffected ones. To account for any observable or unobservable bank-specific time-invariant factors, we estimate this model with bank fixed effects. Thus, affectedi gets subsumed by the fixed effects in the model. We include two macroeconomic variables, credit-spread and term-spread, as additional control variables. Results are provided in Table 9. In Model 1, we estimate the loan spread model. We obtain a positive and significant coefficient on the postcrisis affected interaction term. After the Russian crisis, crisis-affected banks increased their loan spread by almost 24%. Model 2 shows that the amount of loans from the crisis-affected banks also decreased disproportionately more than the unaffected banks. Since Model 2 is estimated at the loan-level data, it does not directly estimate the overall decline in bank lending by the affected banks. To do so, we aggregate the loan-level data at the bank level per week. We then estimate the same model with total lending at the bank-week level as the dependent variable. In this estimation, presented in Model 3, the coefficient on the interaction term directly measures the decline in weekly lending volume of the crisis-affected banks as compared to unaffected ones. We find that the total


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Table 9 Impact of Russian crisis on lending by affected banks. In this table we analyze the impact of the Russian crisis on the lending by affected banks. The sample is restricted to banks and borrowers that we are able to match across CRSP, Compustat, call report data, and Dealscan. A bank is classified as affected if it is classified as exposed to the crisis by Kho, Lee, and Stulz (2000). post is a dummy variable that takes the value of one if the loan is originated after August 1, 1998, zero otherwise. In Model 1, the dependent variable is the natural log of all-in-drawn loan spread measured as the spread over LIBOR as of the loan origination date. In Model 2, the dependent variable is the natural log of the loan amount measured in millions of US dollars. Model 1 and Model 2 are estimated at loan level, with each observation representing a loan given by the bank. The sample is restricted to loans given by the banks within two years before and after the Russian crisis (August 1998). In Model 3, the dependent variable is the log of loan amount, aggregated at the bank level for each week of the sample period. All three models include bank fixed effects. Robust t-statistics are reported in brackets. Adjusted R2 and the number of observations are reported in the last two rows. log(Loan spread)

log(Loan amount)

log(Bank lending)

Estimate

t-val

Estimate

t-val

Estimate

t-val

post affected postcrisis termspread creditspread

0.2424 0.0093 0.0633 0.7041

(4.13) (0.17) ( 0.94) (4.46)

0.2488 0.1041 0.1854 0.0964

( 2.80) (1.15) (1.79) (0.37)

0.3336 0.1361 0.4490 0.6798

( 2.26) (0.99) (2.82) (1.64)

R2 N Fixed effects

0.173 3,887 Bank

lending volume declined significantly for the crisisaffected banks. Overall, these results point toward an inward shift in the supply of bank credit for the crisis-affected banks. Taken together with the earlier results, we show that the Russian crisis of 1998 resulted in a credit crunch for bankdependent borrowers, especially those that relied on banks affected by the crisis. This, in turn, was reflected in a disproportionately larger valuation loss for bankdependent firms, especially for those that were dependent on the crisis-affected banks.

5. Discussion and conclusion The Russian crisis of Fall 1998 resulted in a significant loss of equity capital for the U.S. banks. The crisis originated with the Russian government’s decision to default on their obligations, and therefore, the crisis was triggered by an event that was reasonably exogenous to the investment opportunity set of the U.S. domestic firms. This natural experiment allows us to investigate the effect of adverse shocks to banks’ equity capital on their borrowers’ performance in a setting that is not contaminated by the borrowers’ demand-side considerations. Our results strongly support the hypothesis that bank-dependent firms face adverse valuation consequences when the banking sector’s financial health deteriorates. Bank-dependent firms lost disproportionately higher market value and suffered larger declines in capital investments and profitability following the crisis as compared to firms with access to the public-debt market. Among bank-dependent firms, the drop in valuation was higher for firms with lower financial flexibility and those that relied on banks with larger exposure to the crisis. Consistent with an inward shift in the loan supply curve, the crisis-affected banks decreased the quantity of loans and increased their price in the postcrisis period. Overall, we provide causal evidence that firms face value-relevant frictions in raising external capital.

0.101 3,887 Bank

0.184 1,585 Bank

Our results have important implications for literature in banking, corporate finance, and macroeconomics. We highlight the role of banks in providing capital and the role of the corporate bond market in the economy. In the past, then Fed chairman Alan Greenspan has noted the importance of corporate bond markets during the time of banking crises in emerging markets. As quoted from The Economist (November 17, 2005) y: :Financial crises have a cruel way of revealing what an economy lacks. When many emerging markets suffered a sudden outflow of capital in the late 1990s, one painful lesson was that their financial systems had relied too heavily on bank lending and paid too little attention to developing other forms of finance. The lack of a spare tyre, said Alan Greenspan, chairman of America’s Federal Reserve, in 1999, is of no concern if you do not get a flat. East Asia had no spare tyres. If a functioning capital market had existed, remarked Mr. Greenspan, the East Asian crisis might have been less severe. Developing deep and liquid corporatebond markets, in particular, could make emerging economies less vulnerabley: : Our results support this spare tyre view by demonstrating that corporate bond markets can have a positive impact even in developed economies such as the U.S. At a broader level, our results provide evidence in support of the presence of supply-side frictions in raising external financing, an assumption frequently made in various theoretical models of corporate finance and macroeconomics. Finally, our results suggest that the global integration of the financial sector can contribute to the propagation of shocks from one economy to another through the banking channel. These findings have implications for the ongoing subprime mortgage crisis as well as future policy designs by monetary and banking authorities.

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Appendix A. Variable definitions bankdep is a proxy for bank dependence of the firm. It is a dummy variable that takes the value of one for firms with a S&P long-term credit rating, and zero for firms without the credit rating. log(sales) is the natural logarithm of sales of the firm measured in millions of U.S. dollars. lever measures leverage and is the ratio of total debt from the balance sheet to total assets. market-to-book(mtb) is the ratio of the market value of assets to total assets, where the numerator is defined as the sum of market equity, total debt, and preferred stock liquidation value less deferred taxes and investment tax credits. exdep is computed as the difference between total investments (Compustat item 311) and cash flow from operations (item 308) scaled by cash flow from operations. We compute this variable at the industry level by taking the median number for each four-digit SIC industry code on a yearly basis. def g is a measure of the default risk of the firm. It is the percentile ranking of the firm’s default risk based on its distance to default (constructed as in Bharath and Shumway, 2008). We first compute the distance-to-default as logðE þ F=FÞ þ ðrit1 s2V =2ÞT pffiffiffi , sV T where E is the market value of equity, F is the face value of debt, sV is the asset volatility, rit 1 is the firm’s stock return over the previous year, and T is the time horizon that is set to one year. We convert it to expected default frequency to obtain the firm’s default risk. sigmaequity is the equity volatility of the firm over the past one year. pastret is the past one-year stock return. ebitda/sales is the ratio of EBITDA to the sales of the firm. bidask is a proxy for the stock market liquidity of the firm and computed as the mean of the proportional bid–ask spread over the past three months of daily stock data. termspread is the difference in the yields on a 10-year treasury bond and a one-year treasury bond taken from the Fed’s H.15 release. creditspread is the spread in the yields between a BAA-rated bond and a AAA-rated bond taken from the Fed’s H.15 release.

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The world price of liquidity risk Kuan-Hui Lee n,1 Korea University Business School, 518 LG-Posco, Anam-Dong, Seongbuk-Gu, Seoul 136-701, South Korea


abstract

Article history: Received 14 November 2006 Received in revised form 24 December 2009 Accepted 18 January 2010 Available online 7 August 2010

This paper empirically tests the liquidity-adjusted capital asset pricing model of Acharya and Pedersen (2005) on a global level. Consistent with the model, I find evidence that liquidity risks are priced independently of market risk in international financial markets. That is, a security’s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity, as well as the covariance of its own liquidity with local and global market returns. I also show that the US market is an important driving force of global liquidity risk. Furthermore, I find that the pricing of liquidity risk varies across countries according to geographic, economic, and political environments. The findings show that the systematic dimension of liquidity provides implications for international portfolio diversification. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G12 G15 F36 Keywords: Asset pricing International finance Liquidity Liquidity risk Liquidity-adjusted capital asset pricing model Commonality in liquidity Market integration Market segmentation Mildly segmented market Zero return Emerging market Developed market

1. Introduction Liquidity has been shown to affect the cross-sectional differences of asset returns in the US market through two different channels, that is, as either a characteristic

n

(Amihud and Mendelson, 1986; Brennan and Subrahmanyam, 1996; Amihud, 2002) or a risk factor (Pa´stor and Stambaugh, 2003; Acharya and Pedersen, 2005; Liu, 2006; Sadka, 2006; Watanabe and Watanabe, 2008). Encompassing multiple channels through which liquidity affects

Tel.: + 82 2 3290 2836; fax: +82 2 3290 5346. E-mail address: [email protected] 1 This paper is based on Chapter 2 of my dissertation at the Fisher College of Business at Ohio State University and is revised mostly while I was at Rutgers Business School. I am deeply indebted to my dissertation committee, Kewei Hou, G. Andrew Karolyi (chair), Rene´ M. Stulz, and Ingrid M. Werner. I thank Carole Gresse, Bing Han, Jean Helwege, Michael Imerman, Dong-Wook Lee, Sergei Sarkissian, and Alvaro Taboada for helpful comments. I also thank seminar participants at Drexel University, Financial Management Association Annual Meeting of 2007, Korea Advanced Institute of Science and Technology, Korea Development Institute School of Public Policy and Management, Korea University, Nanyang Business School, Ohio State University, Queen’s University, Rutgers University, Seoul National University, Singapore Management University, Sungkyunkwan (SKK) Graduate School of Business, Southern Methodist University, Texas A&M University, University of Arizona, and Wayne State University. I thank the Whitcomb Center for Research in Financial Services of Rutgers Business School for partial financial support. All errors are my own. 0304-405X/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2010.08.003

K.-H. Lee / Journal of Financial Economics 99 (2011) 136–161

asset prices, Acharya and Pedersen (2005) propose the liquidity-adjusted capital asset pricing model (LCAPM), which incorporates three different types of liquidity risk that are independent of traditional market risk: the covariance of liquidity with market liquidity (commonality in liquidity), the covariance of liquidity with market return, and the covariance of return with market liquidity. In their paper, Acharya and Pedersen (2005) also show empirical evidence supporting the LCAPM in the US market. However, to date, the potential importance of liquidity has not been explored as extensively in international financial markets as it has in the US market. In the study of world market liquidity, earlier research has primarily focused on liquidity level (Rouwenhorst, 1999; Brockman and Chung, 2003; Chiyachantana, Jain, Jiang, and Wood, 2004; Lesmond, 2005; Eleswarapu and Venkataraman, 2006), while researchers have recently paid more attention to the systematic aspects of liquidity (Liang and Wei, 2006; Bekaert, Harvey, and Lundblad, 2007; Brockman, Chung, and Pe´rignon, 2009; Karolyi, Lee, and van Dijk, 2009). Brockman, Chung, and Pe´rignon (2009) and Karolyi, Lee, and van Dijk (2009) investigate the commonality in liquidity in global financial markets. Liang and Wei (2006) examine the pricing of liquidity risk that arises from the sensitivity of stock returns to market-wide liquidity in 23 developed-market countries. However, the pricing of multiple liquidity risks in a unified framework such as the LCAPM has not been fully investigated for international financial markets. Recently, Bekaert, Harvey, and Lundblad (2007) investigate various forms of liquidity risk, but at the level of country portfolios, not individual stocks. Moreover, they restrict the sample to 19 emergingmarket countries, leaving the importance of liquidity in asset pricing in developed markets for future research. I contribute to the literature by empirically investigating an equilibrium asset pricing relation with liquidity both as a characteristic and as a risk factor in international financial markets by using 30 thousand stocks from 50 countries from January 1988 to December 2007. To my knowledge, this is the first paper that assesses multiple forms of liquidity risk as well as market risk, as specified in the LCAPM, in global financial markets. I evaluate the unconditional version of the LCAPM on a global level under different assumptions on the degree of world financial market integration. I specifically investigate the following research questions in this paper. First, I examine whether supporting evidence of the LCAPM in the US is also prevalent in global financial markets. In particular, I investigate whether liquidity risks are priced independently of market risk and examine which type of liquidity risk is most significant in pricing. I employ a crosssectional regression framework and factor model regressions to investigate this issue. Second, I examine whether the US market plays an important role in the pricing of global liquidity risk. To achieve this goal, I compare the pricing of liquidity risk with respect to US factors with the pricing of liquidity risk with respect to global aggregates that are independent of both local and US factors. Third, I investigate the differences in the relative importance of local and global liquidity risk in asset pricing and further

137

examine the sources of such differences according to geographic, economic, and political environments across countries. An extension to global markets of the investigation of the pricing of liquidity risks is important for at least the following three reasons. First, the importance of liquidity could be more pronounced in markets other than the US, where liquidity is allegedly high. Hence, extending the study of liquidity to world markets could provide a good opportunity to evaluate the role of liquidity as an additional source of systematic risk. Second, liquidity could be a global phenomenon as can be seen from episodes such as the Asian financial crisis, the meltdown of Long-Term Capital Management, and the ongoing subprime mortgage crisis. As shown by these incidents, liquidity-related events are not restricted to either developed-market or emerging-market countries, but they are pervasive worldwide, making it necessary to investigate both developed and emerging markets together when studying liquidity in global markets. Third, the geographic, economic, and political environment could affect the importance of liquidity risk differently across countries. Extending the scope to global markets provides a unique opportunity to investigate such crosscountry or cross-regional variations in the pricing of liquidity risk. I find that market liquidity is persistent in most of the sample countries, consistent with US results in the literature (Pa´stor and Stambaugh, 2003; Acharya and Pedersen, 2005; Korajczyk and Sadka, 2008). In addition to this confirmatory evidence, I find some new and interesting results. First, consistent with the LCAPM, I find supporting evidence that liquidity risks are priced factors, independent of market risk, in international financial markets. Specifically, cross-sectional regressions show that, after controlling for market risk, liquidity level, size, and book-to-market, a security’s required rate of return depends on the following two covariances: the covariance of its own liquidity with the liquidity aggregated at the local market, and the covariance of its own liquidity with local and global market returns. Factor model regressions show that trading based on local liquidity risk produces 7.6% annual excess returns (trading alpha) in the overall world market and 13.6% in emerging markets. The corresponding figure is 1.8% in the overall world market when trading is based on global liquidity risk. Second, I provide evidence that the global liquidity risk arising from the covariance of individual stock liquidity with US market return is priced. This highlights the key role of the US in global financial markets, contrasting sharply with the finding that the global liquidity risk formed by excluding the US is not priced or is priced with the wrong sign. Third, the pattern of the pricing of liquidity risk varies across geographic, political, and economic environments. On the one hand, global liquidity risk is shown to be more important than local liquidity risk in countries that are more open, that is, in developed countries as well as in countries with high transparency, low political risk, and large cross-border portfolio holdings. On the other hand, in countries with the contrary properties, i.e., where global investors are

138


rare, I find that local liquidity risk is more important than global liquidity risk. The findings of this paper have important implications for international investment and portfolio diversification. In the traditional capital asset pricing model, any systematic fluctuation of asset prices is captured solely by market risk. Therefore, the covariance of stock returns with (global) market returns is the key to the success of (international) portfolio diversification. However, the findings in this paper show that the commonality in liquidity and the covariance of liquidity with market returns are channels, independent of market risk, through which liquidity systematically affects asset prices. Hence, the findings provide an additional layer to consider when investors seek to diversify away risks in global financial markets. In this regard, theoretical models of the liquidity constraints of financial intermediaries shed some light on the importance of the findings in this paper in that they share the common feature of the increasing importance of liquidity as arbitrageurs are forced to liquidate their positions in the face of large market declines (Kyle and Xiong, 2001; Morris and Shin, 2004; Brunnermeier and Pedersen, 2009). This implies that liquidity risk is a relevant factor in asset pricing because arbitrageurs could demand compensation for bearing liquidity risk. The importance of liquidity risk is cited not only in the academic literature but also in the financial press: ‘‘Whenever the market turns against you, you take the biggest losses in illiquid securities,’’ says Richard Bookstaber, former head of risk management at Salomon Bros. ‘‘Because there are so few buyers, you’re forced to sell at a discount that is both huge and highly unpredictable’’ (p. 49, Fortune, November 26, 2007). The significant pricing of global liquidity risk in developed counties and in countries with low information asymmetry, low political risk, and large cross-border holdings implies the importance of global investors and the relatively high degree of financial market integration in such countries. Supporting this view, Chan, Covrig, and Ng (2005) show that countries with these properties attract more global investors. The finding reveals that stocks whose liquidity improves in market downturns are valued by global investors because liquidity is an important concern, especially when investors rebalance their portfolios globally in the face of down markets. One challenge in a study of liquidity at the global level is finding a suitable proxy for liquidity. In international financial markets, intra-day data are seldom available and trading volume data, upon which other popular proxies such as that of Amihud (2002) and turnovers are based, are also rare with the quality not being guaranteed. In addition, these data do not cover a sufficiently long period for many countries. Hence, it might be most appropriate to use a liquidity proxy that is based solely on returns. I employ the zero-return proportion measure, suggested by Lesmond, Ogden, and Trzcinka (1999), which is the ratio of the number of zero-return days to the total number of trading days in a given month. The economic intuition behind this measure is that informed traders will not trade on a given

day, thus leading to a zero-return day, when the trading cost is high enough to offset the gains from informed trading. The zero-return proportion measure has been widely employed in the literature. It is used to evaluate the impact of trading costs in a momentum strategy (Lesmond, Schill, and Zhou, 2004), to examine the relation between market liquidity and political risks in emerging markets (Lesmond, 2005), and to investigate the implications of liquidity for asset pricing in emerging markets (Bekaert, Harvey, and Lundblad, 2007). The validity of this measure has been established both in the US market (Lesmond, Ogden, and Trzcinka, 1999; Goyenko, Holden, and Trzcinka, 2009) and in world financial markets (Lesmond, 2005; Bekaert, Harvey, and Lundblad, 2007). The rest of the paper is organized as follows. In the next section, I briefly introduce the LCAPM of Acharya and Pedersen (2005). Section 3 describes the data and the sample construction procedure. Section 4 explains the methodology. Empirical evidence on the pricing of local and global liquidity risk as well as robustness tests are presented in Section 5. Section 6 demonstrates how the pricing of liquidity risk varies across countries with different geographic, economic, and political environments. Section 7 presents empirical results based on factor model regressions. I conclude in Section 8. 2. The liquidity-adjusted capital asset pricing model The liquidity-adjusted capital asset pricing model of Acharya and Pedersen (2005) is derived in a framework similar to the traditional CAPM in that risk-averse investors maximize their expected utility under a given wealth constraint in an overlapping-generation economy. However, in the LCAPM, the trading cost-free stock price, Pi,t , is replaced with the price that is adjusted by the stochastic trading cost, Pi,t Ci,t , where Ci,t is the trading cost as an absolute amount. As a result, the LCAPM shown in Eq. (1) has three covariance terms that are related to stochastic trading costs in addition to the traditional market risk component Et ðRi,t þ 1 Ci,t þ 1 Þ ¼ Rf þ lt

D Covt ðRi,t þ 1 Ci,t þ 1 ,RD t þ 1 Ct þ 1 Þ : D D Vart ðRt þ 1 Ct þ 1 Þ

ð1Þ Ri,t is the gross return of stock i, Rf ,t is the gross riskfree rate, lt is the risk premium, and Ci,t is the trading cost per price (Ci,t Ci,t =Pi,t1 ), all at time t. The subscript t for expectation, covariance, and variance denotes that these operators are conditional on the information set available up to time t. The superscript D denotes that the variable is defined in terms of the local market portfolio (D stands for the domestic market). It is clear that without the trading cost terms CD and Ci, the LCAPM in Eq. (1) is equivalent to the traditional CAPM. By assuming constant conditional variances or a constant premium, the unconditional version of the model is derived as D 1,D

EðRi,t Rf ,t Þ ¼ EðCi,t Þ þ l bi

D 2,D

D 3,D

D 4,D

þ l bi l bi l bi ,

ð2Þ


where

b1,D i

CovðRi,t ,RD t Þ , D VarðRD C t t Þ

b2,D i

CovðCi,t ,CtD Þ , D VarðRD t Ct Þ

b3,D i

CovðRi,t ,CtD Þ , D VarðRD t Ct Þ

b4,D i

CovðCi,t ,RD t Þ : D VarðRD t Ct Þ

ð3Þ D

D

The risk premium is defined as l Eðlt Þ ¼ D EðRD t Ct Rf ,t Þ. In addition, following Acharya and Pedersen (2005), I define the liquidity net beta as a linear combination of the three liquidity betas, excluding the market beta: 2,D 3,D 4,D b5,D bi bi bi : i

ð4Þ

The liquidity net beta helps to distinguish the pricing effect of liquidity risks from that of market risk. Each beta in Eq. (3) has an economic interpretation. b1,D is similar to the market beta of CAPM except for i the additional term that is related to the trading cost in 2,D the denominator. bi is a liquidity risk that arises from the comovement of individual stock liquidity with market liquidity (Chordia, Roll, and Subrahmanyam, 2000; Hasbrouck and Seppi, 2001; Huberman and Halka, 2001; Coughenour and Saad, 2004; Kamara, Lou, and Sadka, 2,D 2008; Karolyi, Lee, and van Dijk, 2009).2 bi is positively related to the expected returns in the LCAPM, implying that stocks whose liquidity negatively comoves with market liquidity are traded at a premium because such stocks are easier to sell when the market is highly illiquid. An unexpected decrease in market liquidity causes a potential wealth reduction for investors who need to immediately liquidate stocks that are highly sensitive to market liquidity. This is because the liquidation of such stocks would be costlier under low market liquidity 3,D (Pa´stor and Stambaugh, 2003; Sadka, 2006). bi captures this liquidity risk and is negatively related to the expected returns in the LCAPM because investors are willing to accept low returns on stocks for which the expected return is high when the market is illiquid. The fourth beta, b4,D i , is negatively related to expected returns because stocks that become more liquid in a down market are preferred by investors and, thus, are traded at a premium. I investigate the LCAPM under three different assumptions on the degree of world financial market integration. If world financial markets are fully segmented, the local market version of the LCAPM in Eqs. (2) and (3) should be able to explain the cross-sectional differences of expected returns. However, in fully integrated world financial markets, countries are irrelevant and, hence, individual stocks should comove with global factors instead of with local factors. Thus, the superscripts D of Eqs. (2) and (3) are replaced with W (for world) to signify that each beta is computed with respect to global factors instead of local factors under fully integrated financial markets. It could be reasonable to assume that the degree of integration of world financial markets lies somewhere between full segmentation and perfect integration (Errunza and Losq, 1985; Bekaert and Harvey, 1995). 2

2 Throughout this paper, bi is sometimes referred to as a commonality beta or commonality risk.

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When local and global liquidity risks are jointly tested under this assumption of mildly segmented world financial markets, the relative importance of local and global risks is affected by the degree of integration. To obtain an econometric model, I decompose the global factors into local factors and nonlocal global components: D WD RW , t ¼ oRt þð1oÞRt

CtW ¼ oCtD þð1oÞCtWD :

ð5Þ

The weight o is the ratio of the market values of local and world markets. RWD and CtWD denote nonlocal t global market returns and illiquidity, respectively, and are obtained by orthogonalizing the global factors to the local factors of a given country of interest (Jorion and Schwartz, 1986). By inserting Eq. (5) into the global version of Eqs. (2) and (3), I obtain the LCAPM under the assumption of mildly segmented global financial markets: D

1,D

EðRi,t Rf ,t Þ ¼ EðCi,t Þ þ l ðbi WD

þl

2,D

þ bi

3,D

bi

4,D

bi

Þ

1,WD 2,WD 3,WD 4,WD ðbi þ bi bi bi Þ:

ð6Þ

The covariance terms with the superscript D (WD) in the numerator of the betas are defined with respect to local (nonlocal global) factors, and the weight o is forced to be D

WD

in the included in the estimated premiums of l and l empirical tests. All of the betas in Eq. (6) have a common denominator of a variance that is related to global market returns and illiquidity, viz., Var Rt W Ct W .3 The liquidity net beta is defined in a manner similar to Eq. (4). In empirical tests of the LCAPM, I posit the null hypotheses of zero intercept and zero premiums for illiquidity, market risk, and liquidity risks. The alternative hypotheses are nonzero intercepts and nonzero premiums for market risk and liquidity risks. Because the frequency of data matters in testing EðCi,t Þ, the null hypothesis of a zero premium for illiquidity is tested against a positive premium for the illiquidity term.4 3. Data Daily returns are calculated using a daily total return index, which is adjusted for stock splits and dividend payments, from Datastream for all available stocks from 50 countries for the period of January 1988 to December 2007. According to the International Financial Corporation (IFC) of the World Bank Group, there are 22 developedmarket countries (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Singapore, Spain, Sweden, Switzerland, the UK, and the US) and 28 emerging-market countries (Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Greece, Hungary, India, Indonesia, Israel, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Poland, Portugal, 3 In empirical tests in this paper, I use global factors only for the period that overlaps with local factors. For example, if the data in a given country start from 1993 (e.g., Luxembourg), the variance of global factors in the denominator of the betas is calculated over the period commencing from 1993. 4 I thank the referee for pointing this out.

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Russia, South Africa, South Korea, Sri Lanka, Taiwan, Thailand, Turkey, and Venezuela) in the sample. The initial sample covers more than 58,300 stocks from around the world. To build a reliable sample, I use the following screening procedure. For a stock to be included in the sample, it should have market capitalization data (in US dollars) at the end of each year. I select only stocks from major exchanges, which are defined as those in which the majority of stocks for a given country are traded. Most countries in the sample have a single major exchange except for China (Shenzen and Shanghai stock exchanges), Germany (Frankfurt stock exchange and Xetra), Japan (Osaka and Tokyo stock exchanges), and the US (Amex, NYSE, and Nasdaq). In addition, I use only common stocks by excluding stocks with special features.5 Hence, Depository Receipts (DRs), Real Estate Investment Trusts (REITs), and preferred stocks are excluded.6 To avoid survivorship bias, I retain all data for dead stocks in the sample. In empirical tests in this paper, I use the zero-return proportion proposed by Lesmond, Ogden, and Trzcinka (1999) as a measure of illiquidity. Thus, it is important to exclude nontrading days from the sample because Datastream fills a nontrading day with the return index of the prior trading day, a process that inflates zero-return proportions. Similar to Lesmond (2005), I drop any day from the sample as a nontrading day if more than 90% of stocks in a given exchange have zero returns on that day.7 Ince and Porter (2006) emphasize the need for caution in handling data from Datastream. Similar to their

5 Because Datastream/Worldscope do not provide any code for discerning noncommon shares from common shares, the exclusion of stocks with special features is performed manually by examining the names of the securities. Examples of such name filters are as follows. I extracted stocks with names including ‘‘REIT,’’ ‘‘REAL EST,’’ ‘‘GDR,’’ ‘‘PF,’’ ‘‘PREF,’’ or ‘‘PRF’’ because these terms could represent real estate investment trusts, global depository receipts, or preferred stocks. By examining the names of these extracted stocks more carefully, I dropped stocks for which these terms represent such special features. In Belgium, AFV and VVPR shares are dropped because they have preferential dividend or tax incentives. In Canada, income trusts are excluded by removing stocks with names including ‘‘INC.FD.’’ In Mexico, shares of the types ACP and BCP are removed because they have the special feature of being convertible into series A and B shares, respectively, after one year. In France, shares of the types ADP and CIP are dropped because they carry no voting rights but carry preferential dividend rights. In Germany, type-GSH shares are excluded because they offer fixed dividends and carry no voting rights. In Italy, RSP shares are dropped due to their nonvoting provisions. For US stocks, I deleted American depository receipts (ADRs) by examining the names of stocks. I also used the Committee on Uniform Security Identification Procedures (CUSIP) for US stocks to exclude noncommon shares because the seventh and eighth digits of the CUSIP are 1 and 0, respectively, for common shares. 6 Worldscope usually tracks one share for each firm and it is mostly the PN share in Brazil. Though PN shares are preferred stocks, they are not excluded because they account for the majority of stocks in Brazil. 7 Lesmond (2005) uses a similar criterion but with a cutoff of 100% instead of 90%. I use a 90% cutoff for the following reason. If only one stock, for example, has a nonzero return on an actual nontrading day, then that actual nontrading day is not captured by this 100% rule. In this case, because all other stocks have zero returns on that day, the zeroreturn proportion for the corresponding month is inflated. I indeed find days in the sample when only a handful of stocks have nonzero returns while all others have zero returns.

suggestion of screening, I set the daily return to be missing if any daily return above 100% (inclusive) is reversed the following day. Specifically, the daily returns for both days t and t 1 are set to missing if Ri,t Ri,t1 1 r0:5, where Ri,t is the gross return for day t, and at least one of the two returns is 200% or greater. Daily returns that are calculated from a very small total return index could exaggerate the proportion of zeroreturn days because the return index is reported to the nearest tenth. Thus, the daily return is set to missing if either the total return index for the previous day or that of the current day is less than 0.01. Similar to Chordia, Roll, and Subrahmanyam (2000), Amihud (2002), and Pa´stor and Stambaugh (2003), I require sample stocks to have prices within a specific range. If the price at the end of the previous year is in the extreme 2.5% (inclusive) at the top or bottom of the cross section for each country, the corresponding stock is dropped from the sample for that year. The monthly sample is constructed based on the daily file obtained through the procedure described above. The proxy for illiquidity, the zero-return proportion, is calculated as the ratio of the number of zero-return days to the number of non-missing trading days in a given month. To improve the precision of the illiquidity measure, I drop a stock-month observation from the sample if the total number of non-missing return days within a given month is less than ten or the zero-return proportion in that month is more than 80%, similar to Amihud (2002), Pa´stor and Stambaugh (2003), and Lesmond (2005).8 The month-end total return index together with the month-end exchange rate is used to calculate the monthly US dollar-return. I obtain foreign exchange rate data from WM/Reuters through Datastream. By choosing US dollar-denominated returns, the returns across countries are comparable and the effect of different inflation rates across countries is reflected through purchasing power parity (Harvey, 1991, 1995; Rouwenhorst, 1999). However, as a robustness check, I also report empirical results that are based on local currency in Section 5.5. I use the 30-day US Treasury bill as a risk-free asset. The Treasury bill rates from Ibbotson Associates are obtained through K. French’s data library.9 As with the screening of daily returns, any monthly returns (either in US dollars or in local currency) calculated from the total return index of less than 0.01, as well as those that exceed 300% and are reversed within a month, are set to missing. To handle splits, mergers, and potential data errors, monthly returns of the extreme 0.1% (inclusive) at the top or bottom of the cross section of each country are set

8 By applying both these rules, 11.63% of stock-month observations are deleted from the sample (452,094 stock-months out of total 3,885,814 stock-month observations). To check whether these criteria are crucial to the results in this paper, I perform the empirical tests using a sample that is constructed without applying these screening rules. I find that the results are very similar. The results are available upon request. 9 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/da ta_library.html. I thank K. French for making the data publicly available.


to missing for that month (Amihud, 2002; Hou, Karolyi, and Kho, 2006). After implementation of all these screens, a stock should have at least 12 months of data for the period 1988–2007 to be included in the sample. The number of stocks in the sample and the descriptive statistics of returns and zero-return proportions are reported in Table 1. The total number of stocks in the sample is 30,069 and varies across countries and years. The country with the largest number of stocks in the sample is the US (5,754 stocks), and Venezuela, the country with the smallest coverage, has only 21 stocks. There are more than 9,000 stocks for all but one year in the 1990s and more than 18,000 stocks for all sample years in the 2000s. The year with the largest number of stocks in the sample is 2006 (20,958 stocks). The starting year of sample coverage also varies across countries. Hungary, which has the shortest sample period, has data beginning with 2000, while the starting year is 1988 for most countries in developed markets. The last four columns of Table 1 show averages of the cross-sectional averages of monthly returns and zeroreturn proportions as well as cross-sectional averages of the standard deviations of the same variables. The figures are all expressed as percentages and are computed on the basis of local currency returns. Zero-return days are frequent in emerging markets and in developed markets. To check whether stocks are less liquid in countries with low gross domestic product (GDP) per capita, I collect data on GDP (in US dollars) and the total population, both as of 2003, from the World Development Indicator. Consistent with my conjecture, the correlation between the average zero-return proportions and GDP per capita is negative, viz., 0.07. Average zero-return proportions and the ranks of countries by average zero-return proportions are similar to those in Lesmond (2005) and Bekaert, Harvey, and Lundblad (2007) for emerging markets in spite of differences in sample periods and data frequencies. For example, Table 1 shows that Malaysia, Philippines, Poland, Taiwan, and Venezuela have average zero-return proportions of 23.9%, 42.4%, 18.7%, 10.3%, and 31.0%, respectively. In Lesmond (2005), the corresponding figures are 25.1%, 44.1%, 19.4%, 11.6%, and 30.0% for these countries. The (rank) correlation between the zero-return proportions in Table 1 and those in Lesmond is 0.85 (0.82). For emerging market countries, average zero-return proportions are consistent with Bekaert, Harvey, and Lundblad (2007), who show that India, Korea, and Taiwan are the most liquid markets, while Chile, Colombia, and Indonesia are the least liquid. The average zero-return proportions are 16.9%, 11.7%, and 10.3%, respectively, for India, Korea, and Taiwan and 31.6%, 38.1%, and 39.6%, respectively, for Chile, Colombia, and Indonesia. The correlation between the zero-return proportions in Table 1 and those in Bekaert, Harvey, and Lundblad (2007) for countries that are included in both studies is 0.74, and the rank correlation is 0.69. It is striking that the average zero-return proportion for the UK is 37.8%, which is larger than that of most other countries in the sample. In unreported analyses, I investigate the UK data further and find that this high average zero-return proportion is widespread among UK stocks and does not stem from outliers. I form

141

size-quintile portfolios for UK stocks and find that the zero-return proportions are high in all size-groups except for the largest-stock portfolio. In light of concern that potential problems in the UK data might have on inferences, I perform the cross-sectional regressions without the UK stocks. I find that the main results of the paper remain unaffected. Turning to returns, the averages and standard deviations are generally greater in emerging-market countries than in developed-market countries. The average of the returns shown in the table is 2.53% for emerging markets and 1.19% for developed markets. The correlation between the average (standard deviation) and GDP per capita is 0.41 ( 0.30). The standard deviations of returns exceed 15% for ten emerging-market countries, whereas only four developed-market countries exhibit such large standard deviations. The average of the standard deviations in emerging markets is 14.14%, and it is 11.91% for developed markets (not reported). 4. Methodology In this section, I describe methodology. Specifically, I present evidence of persistence of market illiquidity and show how I construct innovations in illiquidity in Section 4.1. In Section 4.2, I demonstrate the details on the crosssectional regression tests. 4.1. Innovations of illiquidity I form local (world) market return and illiquidity by calculating equally weighted averages of individual stocks’ returns and zero-return proportions in a given country (across countries). Consistent with US results (Pa´stor and Stambaugh, 2003; Acharya and Pedersen, 2005; Sadka, 2006; and Korajczyk and Sadka, 2008), market illiquidity is highly persistent in most sample countries. Specifically, first-order serial correlations of local market illiquidity range from 0.48 (Luxembourg) to 0.99 (US), with 45 sample countries showing serial correlations of greater than 0.60. The countries aside from the US with the highest first-order serial correlations are Canada (0.97), India (0.96), Japan (0.93), Greece (0.92), Sweden (0.92), Switzerland (0.91), Israel (0.91), and South Africa (0.91). On the contrary, Thailand (0.48), Philippines (0.51), Hungary (0.52), and Sri Lanka (0.53) have relatively low first-order serial correlations. The serial correlation of world market illiquidity is 0.97. Given the persistence of market illiquidity, I obtain the innovations through AR(1) filtering of the first-differences of illiquidity, as shown in Eq. (7). This method of constructing innovations of illiquidity is also adopted by Liu (2006) and is similar in spirit to Pa´stor and Stambaugh (2003) and Acharya and Pedersen (2005) S S DCi,t ¼ ri DCi,t1 þ uSi,t ,

ð7Þ

where D is a first-difference operator and the superscript S denotes whether the market illiquidity, Ci, is the local aggregate (S= D) or the global aggregate (S= W; the subscript for country i vanishes in this case). I compute

Number of stocks in the sample

Country

N

Emerging markets Argentina 74 Brazil 257 Chile 166 China 1,245 Colombia 30 Czech Repulic 77 Egypt 45 Greece 359 Hungary 40 India 937 Indonesia 243 Israel 119 Malaysia 722 Mexico 142 Morocco 23 Pakistan 112 Peru 50 Philippines 190 Poland 224 Portugal 106

146 29 63 392 38 4 102 159 102 32 113 997

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

Return

ZR

Return

ZR

249 309 322 353 33 37 46 50 67 69 69 68 511 540 603 638 105 120 117 132 21 31 32 36 139 319 370 379 293 308 319 334 225 236 248 296 38 41 37 40 123 128 138 141 1,501 1,724 1,831 1,889

420 61 68 680 141 39 391 315 346 40 143 1,949 15 139 61 73 149 107 139 147 388 2,039

465 65 69 771 160 43 405 339 401 42 145 1,997 16 140 75 83 166 112 151 147 419 2,293

535 71 72 812 154 62 439 330 428 43 144 2,075 15 148 76 91 186 117 172 139 409 2,477

565 74 77 836 155 69 474 361 455 42 157 2,172 17 151 76 106 201 117 180 146 472 2,647

790 76 84 891 176 85 534 416 490 46 174 2,225 17 159 88 123 211 123 192 166 491 2,857

813 78 99 956 159 93 604 457 525 47 188 2,262 16 170 91 141 227 137 245 172 500 2,914

857 73 106 983 167 104 672 583 548 48 202 2,303 15 173 91 147 234 128 262 185 463 2,842

946 76 124 1,016 169 118 715 855 590 52 218 2,318 15 181 94 131 253 135 284 198 1,385 3,518

1,033 74 122 999 151 125 773 1,143 631 53 250 2,400 16 169 99 126 289 133 301 201 1,492 3,529

1,033 72 120 1,023 126 124 760 1,172 677 50 254 2,407 16 157 105 126 293 132 300 206 1,467 3,509

1,058 61 112 1,040 145 124 710 1,144 743 46 238 2,429 16 143 101 125 313 124 297 196 1,446 3,459

1,131 66 116 1,028 147 116 692 1,175 761 45 234 2,462 14 141 101 132 338 118 288 197 1,450 3,365

1,242 63 111 1,039 143 118 677 1,214 779 43 231 2,525 13 134 99 138 378 119 282 190 1,498 3,391

1,343 69 114 1,047 147 117 682 1,293 818 41 235 2,561 13 127 98 145 401 116 279 193 1,518 3,354

1,276 66 107 953 142 116 637 1,239 840 39 228 2,496 13 119 90 141 395 111 271 188 1,401 3,096

1.39 1.07 1.09 1.55 1.33 1.19 1.23 0.62 1.89 1.37 0.84 0.45 1.36 1.18 1.09 1.51 1.31 1.10 1.22 0.96 1.03 1.45

27.19 24.72 26.38 25.23 34.66 26.71 19.98 21.82 28.53 12.45 11.21 18.62 27.37 19.89 36.66 28.62 28.16 16.89 25.44 29.22 37.76 16.40

16.80 8.53 8.06 16.58 9.01 10.76 13.03 15.15 21.30 10.03 9.93 11.89 6.32 10.08 9.35 12.17 13.88 9.49 14.12 8.70 13.40 13.54

14.63 15.06 13.33 13.91 16.87 15.05 13.03 14.25 16.91 10.59 9.09 12.77 12.32 12.96 14.12 14.62 15.23 13.05 14.01 14.92 15.34 10.13

22

49 4 113 119 19 27

46 65 119 202 17 42

54 75 119 221 15 71

53 87 108 582 16 71 24 198

46 114 107 678 17 58 26 220

652 56 63 501 83 19 65 14 150 64 82

678 112 85 505 86 20 70 12 156 103 76

48 167 102 766 13 44 32 252 34 680 108 87 512 83 20 77 12 146 118 65

37 152 96 894 14 36 33 290 32 717 68 85 521 77 21 77 10 122 128 57

50 142 88 960 18 9 35 295 32 741 78 90 532 77 21 80 12 117 147 55

57 159 88 1,024 18 9 36 295 31 747 87 92 551 77 21 90 14 106 150 50

57 153 94 1,073 21 10 37 286 30 775 107 92 586 85 19 88 13 117 152 51

54 160 96 1,157 21 11 38 267 28 789 110 93 601 81 21 91 16 132 170 50

54 170 93 1,144 20 7 39 256 27 804 101 95 610 87 21 93 15 138 188 50

56 181 88 1,102 18 6 38 249 25 790 116 92 569 81 20 92 13 147 182 45

7.67 5.17 2.32 2.61 2.49 0.90 1.43 2.15 1.04 3.38 2.12 1.85 1.58 2.38 1.58 2.25 2.28 1.72 2.97 0.73

24.08 28.97 31.59 4.96 38.08 24.71 9.86 17.26 20.86 16.94 39.55 19.10 23.89 15.58 36.78 23.48 18.64 42.40 18.74 28.36

16.73 15.42 11.02 14.12 10.78 13.03 11.48 16.82 9.28 19.30 14.81 10.97 14.94 11.39 6.84 14.28 13.47 20.28 14.81 9.29

15.69 15.16 16.10 8.43 18.29 19.52 10.56 12.54 12.90 14.37 16.25 10.81 15.33 14.16 15.59 16.04 14.09 17.58 12.77 16.07

120 124 130 131 133 16 43 41 44 48 51 56 58 59 58 106 109 114 125 135 52 58 94 101 104 45 75 92 98 106 113 123 131 133 132 394 419 432 389 387 1,609 1,658 1,664 1,708 1,856 9

46

19 196

7

Standard deviation (percentage)

20 205 16

9 72

10 4 90

12 9 96 8

51

77

89

105

113

155

174

58 90 119 395 17 73 23 191

22 217 20

374 80 16 250 25

411 85 17 278 38

442 99 31 317 52 52 20 60 6 63

500 99 57 345 70 4 57 27 81 9 64

571 117 58 377 73 8 58 38 113 18 66

636 159 59 414 74 10 62 42 135 27 71

645 170 62 466 88 15 57 42 156 38 75

7

31

45

6 7 47

43

52

58

60

100 27 18


Developed markets Australia 1,856 Austria 121 Belgium 164 Canada 1,690 Denmark 250 Finland 161 France 1,084 Germany 1,597 Hong Kong 1,006 Ireland 71 Italy 344 Japan 3,106 Luxembourg 24 Netherlands 229 New Zealand 161 Norway 278 Singapore 504 Spain 188 Sweden 473 Switzerland 299 UK 2,417 US 5,754

1988

Average (percentage)

142

Table 1 The number of stocks and the summary statistics of returns and zero-return proportions by country and year. The table shows the number of stocks in the sample by country and year, the averages of the cross-sectional averages of monthly returns and zero-return proportions (ZR) and the cross-sectional averages of the standard deviation of returns and zero-return proportions (all in percentage) that are based on local currency. N denotes the total number of stocks across all sample periods in a given country.

30,069 5,410 6,991 7,992 9,078 9,695 10,583 11,710 12,699 13,752 15,171 15,801 16,427 18,829 19,646 19,757 19,870 20,078 20,573 20,958 20,057 Total

Russia South Africa South Korea Sri Lanka Taiwan Thailand Turkey Venezuela

76 616 822 34 748 568 246 21

61 325 9 26 84

60 402 10 46 115 42

64 486 12 139 147 52

184 514 13 156 178 77 7

166 531 15 179 226 93 7

189 535 18 208 260 105 4

230 545 22 231 296 118 7

227 574 25 259 330 136 10

18 339 600 23 289 351 151 13

25 388 651 25 351 354 169 14

35 396 645 26 389 330 188 10

25 425 637 26 444 313 193 9

31 392 622 27 505 294 190 11

37 343 594 27 558 286 212 13

51 293 583 28 583 293 210 8

49 260 576 28 636 331 207 11

58 252 554 30 658 342 207 14

64 247 569 32 653 374 210 11

63 257 585 33 653 422 208 14

57 241 576 33 640 416 204 16

4.75 1.97 1.69 1.86 1.22 1.73 6.26 2.78

20.22 35.64 11.65 38.58 10.32 26.72 18.95 31.01

15.66 16.13 17.52 11.44 14.12 16.55 21.32 14.22

16.34 16.32 9.59 17.40 8.91 14.62 11.09 17.05


143

the innovations of illiquidity for individual stocks in a similar way. For 47 sample countries, the first-differences of local market illiquidity have serial correlation that is significant at the 1% level. The serial correlation is significant at the 5% level for two other countries, leaving China as the only country in the sample that has insignificant correlation. The average t-statistic of the estimates of ri in Eq. (7) across countries is 5.33. However, no countries have serial correlation that is significant at the 1% level for the residuals from AR(1) D fitting, uD i,t . This validates the use of ui,t as the innovation in aggregate local market illiquidity. In the case of world market illiquidity, the first-differences have the coefficient r of 0.31 in Eq. (7) with a t-value of 5.10. However, the residuals from the AR(1) regressions, which are used as innovations in world market illiquidity, are again not significantly serially correlated.

4.2. Estimation of betas I employ individual stocks as test assets because an analysis at the level of individual stocks provides the following benefits.10 First, the use of individual stocks as test assets helps to avoid potentially spurious results that could arise when characteristic-based portfolios are used as test assets (Brennan, Chordia, and Subrahmanyam, 1998; Berk, 2000). Second, potential loss of information contained in each stock can be minimized by performing empirical tests at the level of individual stock. Third, a stock-level analysis could increase the power of the test by providing ample observations for empirical tests. It is also suitable for controlling for individual stock characteristics, such as market capitalization and book-tomarket ratio. On the cost side, the loadings estimated at the level of individual stock generally have a higher level of noise than those estimated at the portfolio level. Therefore, considering these benefits and costs, I estimate market risk and liquidity risks at the portfolio level and subsequently assign these estimated loadings to individual stocks to perform cross-sectional regressions at the individual stock level. This methodology is similar to that of Fama and French (1992). However, while Fama and French form portfolios on the basis of size and pre-ranking beta, I form portfolios on the basis of one-dimensional sorting determined solely on pre-ranking beta. This one-dimensional sorting could help to exclude potential bias that could arise from the use of characteristic-based sorting. The formation of portfolios based on pre-ranking beta has been widely used in the literature on empirical asset pricing, because the estimation of post-ranking beta for portfolios sorted on pre-ranking beta provide a wide dispersion of estimates across portfolios, while minimizing loss of information that might be caused by portfolio formation (Fama and MacBeth, 1973). A detailed description of the crosssectional regression procedure follows. 10 In Section 5.5, however, I also show empirical results when portfolios on size, book-to-market, and illiquidity are used as test assets.

144


For each stock i, I estimate beta k (k=1,y,4) of year t (pre-ranking beta) by Eq. (3) using the monthly returns and innovations of illiquidity over the years t 5 to t 1 with respect to local or global factors. The innovations in market illiquidity are obtained over the same 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. The window rolls forward at annual intervals. To have pre-ranking beta k of year t, stocks should have at least 36 monthly returns and innovations in illiquidity within the given 5-year window. Then, at the beginning of year t, stocks are sorted into ten equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Because sufficient numbers of stocks are needed to form 10 portfolios for each country, 12 countries for which the total number of stocks shown in Table 1 is less than one hundred are dropped.11 Subsequently, I estimate beta k of portfolio p (post-ranking beta) for all ten portfolios (p = 1,y,10) by Eq. (3) over the sample period and assign it to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure for all k, I compute the liquidity net beta by Eq. (4). Finally, I perform crosssectional regressions for each month using individual stock returns and post-ranking betas. I then report the averages of the estimated premiums. The sample period is relatively short. In addition, unlike the case of the US, the quality of data from countries other than the US is not guaranteed (Ince and Porter, 2006; Bekaert, Harvey, and Lundblad, 2007). Given these potential problems, I perform the cross-sectional regressions over economic or geographic regions instead of over each country, restricting the coefficients to be equal across stocks in a given region. I run each regression with country dummy variables to provide an interpretation of the coefficient estimates in terms of within-country effects and to control for unknown country-specific effects (McLean, Pontiff, and Watanabe, 2009). Table 2 shows averages across countries of postranking betas for each of the portfolios based on preranking betas. The four columns on the left under the label ‘‘Local’’ are for betas with respect to local factors, and the rest of the columns are for betas with respect to global factors. The market beta and the commonality beta 3,S 4,S are positive, while b and b are negative regardless of whether they are estimated with respect to local (S= D) or global factors (S = W). As intended, the betas are sufficiently dispersed and monotonic across the portfolios sorted on the pre-ranking betas. For example, the local commonality beta increases from 0.063 for the lowest commonality beta portfolio to 0.144 for the highest commonality beta portfolio in the overall sample (Panel A). Likewise, b3,Dand b4,D grow monotonically from 0.055 and 0.113 to 0.035 and 0.058, respectively. This monotonic relation is observed not only in the overall 38 countries (Panel A), but also in 11 These are Argentina, Colombia, Czech Republic, Egypt, Hungary, Ireland, Luxembourg, Morocco, Peru, Russia, Sri Lanka, and Venezuela. However, the returns and illiquidity of stocks from these countries do contribute to form global market returns and illiquidity.

the developed- and emerging-market categories (Panels B and C). Monotonic patterns are generally seen for the global betas as well. The local risks b1,D, b3,D, and b4,D are generally larger in absolute value in emerging markets than in developed markets, implying that stocks in emerging market countries generally have high liquidity risk originated in domestic markets. On the contrary, the local commonality beta has larger absolute values in developed markets than in emerging markets. Furthermore, local commonality risk is generally larger than global commonality risk in all pre-ranking beta portfolios. This is consistent with Brockman, Chung, and Pe´rignon (2009), who show that roughly two-thirds of variation in commonality stems from local, not global, commonality. Overall, it seems that my goal of estimating postranking betas that are sufficiently dispersed and monotonic across pre-ranking beta portfolios is fairly achieved.

5. Asset pricing of liquidity risk: cross-sectional regressions I present the results of the cross-sectional regressions in this section. The pricing of local liquidity risk and global liquidity risk is presented in Section 5.1 and 5.2, respectively. In Section 5.3, I investigate the importance of US market in the pricing of global liquidity risk. I show the relative importance of local and global liquidity risk in asset pricing in Section 5.4. Robustness tests are presented in Section 5.5.

5.1. Empirical results for local liquidity risks This subsection reports empirical results of the test of the LCAPM under the assumption that world financial markets are fully segmented. Table 3 shows time series averages of the estimated risk premiums in crosssectional regressions over all countries, developed markets, and emerging markets in Panels A, B, and C, respectively. US results are also reported in a separate panel. I use the lagged month’s zero-return proportion, ZR, as a proxy for the expected illiquidity at time t, E(Ci,t). In each panel, I first show the results of the specification, where the liquidity net beta is included together with the market beta in a single regression equation. This specification could efficiently show whether liquidity risks are priced factors that are independent of market risk, as modeled in the LCAPM. Subsequently in each panel, I report the result for one liquidity beta at a time, in addition to the level of illiquidity and the market beta. In this way, I avoid a multi-collinearity problem that could arise from including all betas in a single regression equation (Acharya and Pedersen, 2005). To control for size and book-to-market, which potentially could be related to the pricing of liquidity and liquidity risks (Amihud, 2002; Pa´stor and Stambaugh, 2003; Acharya and Pedersen, 2005), I include in the regressions the log of the market capitalization and the log of the book-tomarket ratio of each stock at the end of the previous year.


145

Table 2 Average post-ranking betas. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to either market returns or the innovations in market illiquidity. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which the stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into 10 equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The table shows the averages of these post-ranking betas for each portfolio across the countries in a given region specified in each panel. Local Portfolio

Global

Beta 1

Beta 2

Beta 3

Beta 4

Beta 1

Beta 2

Beta 3

Beta 4

Panel A: All countries 1 (Small) 0.460 2 0.529 3 0.573 4 0.607 5 0.643 6 0.670 7 0.726 8 0.765 9 0.800 10 (Large) 0.892

0.063 0.062 0.071 0.087 0.097 0.104 0.114 0.121 0.127 0.144

0.055 0.050 0.045 0.043 0.048 0.036 0.038 0.039 0.036 0.035

0.113 0.086 0.071 0.061 0.046 0.042 0.036 0.028 0.036 0.058

0.692 0.744 0.784 0.848 0.861 0.911 0.923 1.004 1.044 1.166

0.049 0.038 0.039 0.039 0.037 0.043 0.043 0.051 0.048 0.063

0.021 0.017 0.015 0.010 0.012 0.007 0.007 0.005 0.010 0.014

0.154 0.083 0.082 0.055 0.057 0.050 0.050 0.065 0.062 0.071

Panel B: Developed markets 1 (Small) 0.391 2 0.439 3 0.496 4 0.550 5 0.581 6 0.622 7 0.682 8 0.738 9 0.788 10 (Large) 0.903

0.072 0.072 0.074 0.100 0.107 0.126 0.137 0.144 0.150 0.176

0.049 0.045 0.039 0.037 0.041 0.030 0.030 0.031 0.036 0.033

0.110 0.073 0.059 0.052 0.044 0.032 0.032 0.020 0.039 0.062

0.524 0.567 0.623 0.681 0.721 0.755 0.792 0.876 0.957 1.068

0.053 0.038 0.038 0.039 0.038 0.051 0.045 0.061 0.053 0.070

0.022 0.017 0.017 0.011 0.016 0.009 0.006 0.004 0.008 0.015

0.157 0.089 0.061 0.057 0.031 0.042 0.028 0.050 0.039 0.054

Panel C: Emerging markets 1 (Small) 0.538 2 0.629 3 0.658 4 0.670 5 0.712 6 0.724 7 0.774 8 0.796 9 0.813 10 (Large) 0.879

0.053 0.052 0.067 0.073 0.086 0.080 0.088 0.095 0.101 0.109

0.062 0.056 0.051 0.048 0.056 0.043 0.047 0.048 0.037 0.039

0.116 0.100 0.083 0.070 0.047 0.052 0.041 0.036 0.033 0.054

0.878 0.940 0.964 1.034 1.016 1.084 1.070 1.147 1.142 1.275

0.044 0.037 0.040 0.040 0.036 0.035 0.040 0.040 0.043 0.057

0.019 0.017 0.013 0.009 0.008 0.004 0.008 0.006 0.013 0.014

0.150 0.077 0.106 0.054 0.085 0.060 0.075 0.082 0.088 0.090

Table 3 shows that the liquidity net beta is significantly priced in both the US and emerging markets, but not in the developed and overall world markets. In the overall world market (Panel A), the premium on the liquidity net beta is positive (0.007), but it is not statistically significant. However, without size and bookto-market controls, the liquidity net beta is priced with a premium of 0.009 and a t-value of 1.83 (unreported). In emerging markets (Panel C), the liquidity net beta is significantly priced at the 1% level, with a premium of 0.027 and a t-value of 3.80. The significant pricing of the liquidity net beta in the US (Panel D) is consistent with Acharya and Pedersen (2005). It can be seen by observing each liquidity risk 4,D separately, that b , which arises from the covariance of individual stock liquidity with market return, is priced even after controlling for size and book-to-market. The estimated coefficient is 0.010 and the t-value is 1.70

(Panel A). Consistent with the US evidence of Acharya and 4,D Pedersen (2005), who find that b is most significant among the three liquidity betas that are specified in the 4,D LCAPM, b is significantly priced in the US with a coefficient of 0.052 and a t-value of 2.52. In emerging markets, the same liquidity risk has a coefficient of 0.034 and is highly significant at the 1% level (t-value of 3.69). The local commonality beta is priced in emerging markets at the 1% level of significance (the premium is 0.048 with a t-value of 2.91). However, the commonality beta is not priced in any other panel. In an unreported specification, I find that the commonality beta is priced at the 10% significance level for the US (a premium of 0.092 with a t-value of 1.75) when the size and book-to-market are not controlled for. 3,D Liquidity risk b , which is derived from the sensitivity of the return to market-wide illiquidity, is never priced in

146


Table 3 Cross-sectional regressions of local liquidity risk. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to either local market returns or the innovations in local market illiquidity. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into 10 equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is computed by Eq. (4). Cross-sectional regressions with country dummies are performed for each month over all the sample countries (Panel A), developed countries (Panel B), emerging markets (Panel C), and the US (Panel D). The table shows the averages of the estimated coefficients together with the tvalues in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 106. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and ***denote significance at the 10%, 5%, and 1% level, respectively. Intercept

ZR

Beta 1

Panel A: All countries 0.0082 0.0022 1.27 0.93 0.0083 0.0020 1.29 0.83 0.0087 0.0016 1.36 0.68 0.0085 0.0020 1.32 0.84

0.0036 0.84 0.0037 0.86 0.0038 0.89 0.0037 0.86

Panel B: Developed markets 0.0000 0.0079** 2.40 0.01 0.0076** 0.0000 2.20 0.01 0.0068* 0.0002 1.73 0.07 0.0081** 0.0000 2.49 0.01

0.0037 0.86 0.0037 0.86 0.0038 0.90 0.0037 0.86

Panel C: Emerging markets 0.0103 0.0120 1.18 3.44 0.0091 0.0119 1.04 3.28 0.0108 0.0095 1.29 2.91 0.0102 0.0111 1.17 3.35

0.0008 0.10 0.0017 0.22 0.0031 0.39 0.0027 0.33

Panel D: US 0.0084*** 2.63 0.0077** 2.08 0.0087*** 2.75 0.0094*** 3.00

0.0054 1.16 0.0054 1.18 0.0053 1.16 0.0054 1.17

0.0003 0.06 0.0005 0.10 0.0003 0.06 0.0001 0.02

Beta 2

Beta 3

Beta 4

Beta 5

0.0417 0.66 0.0393 0.61 0.0376 0.58 0.0403 0.63

0.0050*** 8.88 0.0050*** 8.89 0.0050*** 8.91 0.0050*** 8.88

0.0022 0.46

0.0392 0.64 0.0372 0.60 0.0382 0.61 0.0387 0.62

0.0044*** 6.70 0.0045*** 6.71 0.0044*** 6.72 0.0044*** 6.70

0.0272*** 3.80

0.4982 0.95 0.5727 1.09 0.5367 1.02 0.4825 0.93

0.0062*** 8.48 0.0062*** 8.48 0.0062*** 8.60 0.0062*** 8.52

0.0458** 2.23

0.0690 0.83 0.0747 0.89 0.0767 0.92 0.0739 0.88

0.0038*** 4.01 0.0038*** 4.01 0.0038*** 4.05 0.0038*** 4.02

0.0039 0.18 0.0096* 1.70

0.0021 0.33 0.0111 0.50 0.0037 0.61

0.0481*** 2.91 0.0016 0.05 0.0335*** 3.69

0.0056 0.04

any panel and the signs of the coefficients are even positive in some cases. This is inconsistent with the US evidence in Pa´stor and Stambaugh (2003) and the results for developed markets in Liang and Wei (2006). Consistent with the recent findings of Hou, Karolyi, and Kho (2006), the log of market capitalization is not priced, while book-to-market ratio is strongly priced in all specifications and in all regions considered. The market beta is not priced in any specification in Table 3. The economic significance of liquidity risk is comparable to that in Acharya and Pedersen (2005) in the US market. Table 2 shows that the difference of liquidity risks

0.0517** 2.52

ln(B/M)

0.0067 1.45 0.0075 1.18

0.0404 0.79

ln(MV)

between the top- and bottom-decile portfolios, b10 4,D b1 4,D , sorted on pre-ranking beta b4,D , is 0.055. 4,D Combining this with the estimated coefficient of b of 0.010 in the overall world market (Panel A), the total 4,D annual impact from b is 0.66%. Similarly, I obtain 2,D 3,D annual 0.78% and 0.09% for b and b , respectively. Aggregating all effects from these three liquidity risks produces a total annual effect of 1.53% for the overall world market. The magnitude is larger than what Acharya and Pedersen (2005) find for the US market, viz., a total 1.1%. For emerging markets, the total annual contribution of liquidity risks is 5.58%, which is more than thrice the effect for the overall world market. This is consistent with


my conjecture that liquidity risks could be more important in international financial markets than in the US. In Section 7, I present additional evidence of the economic significance of liquidity risks by showing that trading based on liquidity risk generates material trading alphas in the factor model regressions. To gain more insight into the results in Table 3, I perform cross-sectional regressions over six different geographic regions: Developed Asia (Australia, Hong Kong, Japan, and Singapore), Developed Europe (Austria, Belgium, Denmark, Finland, France, Germany, Italy, Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, and the UK), Emerging Asia (China, India, Indonesia, South Korea, Malaysia, Pakistan, Philippines, Taiwan, and Thailand), Emerging Europe/Middle East/Africa (Greece, Israel, Poland, Portugal, South Africa, and Turkey), North America (Canada and the US), and Latin America (Brazil, Chile, and Mexico). Based on the results in Table 3, which show the significant pricing of liquidity risk in emerging markets, I show results only for emerging market subregions in Table 4. For precision of the estimates, I

147

require at least 30 stocks to be available in a cross section for each month. b4,D is significantly priced in Emerging Asia (coefficient of 0.04 with a t-value of 2.77) and in Emerging Europe/Middle East/Africa (coefficient of 0.04 with a tvalue of 2.20). However, this is not the case for Latin America. This finding implies that the pricing of b4,D in emerging markets in Table 3 is mostly driven by emerging-market countries in Asia, Europe, Middle East, and Africa. In Emerging Asia, the commonality beta is also priced with a premium of 0.070 and a t-value of 2.99, which is highly significant at the conventional 1% level. The liquidity net beta is highly significant in Panels A and B, largely due to the significant pricing of b4,D. The local commonality beta also contributes to the pricing of the liquidity net beta in Panel A. However, b1,D and b3,D are not priced in any panel. In all specifications shown in Table 4, the cross-sectional regression tests are unable to reject the null hypothesis of a zero liquidity premium against the alternative hypothesis of a positive premium.

Table 4 Cross-sectional regressions of local liquidity risk by geographic region. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to either local market returns or the innovations in local market illiquidity. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into ten equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the ten portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is computed by Eq. (4). Cross-sectional regressions with country dummies are performed for each month over Emerging Asia (Panel A), Emerging Europe, the Middle East, and Africa (Panel B), and Latin America (Panel C). The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 106. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Intercept

ZR

Panel A: Emerging Asia 0.0019 0.0170 0.38 3.78 0.0047 0.0182 1.08 3.83 0.0111** 0.0141 2.00 3.43 0.0059 0.0153 1.22 3.71

Beta 1

0.0017 0.20 0.0025 0.29 0.0052 0.60 0.0040 0.45

Panel B: Emerging Europe/Middle East/Africa 0.0047 0.0059 0.0420*** 3.23 0.90 0.49 0.0416*** 0.0032 0.0050 3.18 0.61 0.41 0.0407*** 0.0026 0.0034 3.10 0.51 0.27 0.0426*** 0.0042 0.0051 3.28 0.81 0.42 Panel C: Latin America 0.0026 0.0194** 2.35 0.44 ** 0.0187 0.0014 2.25 0.25 0.0181** 0.0053 2.19 1.01 0.0194** 0.0040 2.33 0.71

0.0089 0.86 0.0087 0.84 0.0072 0.70 0.0085 0.81

Beta 2

Beta 3

Beta 4

Beta 5

ln(MV)

ln(B/M)

0.0339*** 3.03

0.1478 0.24 0.2749 0.46 0.2012 0.34 0.1490 0.24

0.0056*** 6.01 0.0056*** 5.96 0.0057*** 6.08 0.0056*** 6.01

0.0296** 2.41

0.6322 0.87 0.6835 0.93 0.6161 0.84 0.6159 0.85

0.0077*** 8.05 0.0077*** 8.02 0.0078*** 8.12 0.0078*** 8.11

0.0073 0.99

0.2974 0.65 0.2216 0.49 0.2599 0.57 0.2990 0.65

0.0038*** 2.72 0.0038*** 2.71 0.0036** 2.57 0.0037*** 2.62

0.0699*** 2.99 0.0128 0.31 0.0402*** 2.77

0.0148 0.74 0.0455 1.09 0.0386** 2.20

0.0275 1.55 0.0142 0.30 0.0043 0.44

148


In sum, I find strong evidence that investors demand compensation for holding stocks for which liquidity is sensitive to fluctuations in local market return. I also find that the sensitivity of stock liquidity to local market liquidity is priced in emerging markets. However, I cannot find evidence that the expected liquidity, local market risks, and b3,D are significantly related to cross-sectional differences in asset prices.

5.2. Empirical results for global liquidity risks With the superscript D replaced by W (world), the LCAPM in Eqs. (2) and (3) shows that, under the

assumption of fully integrated world financial markets, only global returns and illiquidity matter, while those of local markets do not. Table 5 shows results of the crosssectional regression tests based on the assumption of fully integrated world financial markets. The liquidity net beta is priced in Panels A, B, and C, after controlling for size and book-to-market, while the market beta is not priced in any specification in the table. b4,W drives the pricing of the liquidity net beta in the overall world market (Panel A) and in developed markets (Panel B). The driver is b2,W in emerging markets (Panel C). Specifically, b4,W is priced with a coefficient of 0.008 (a t-value of 2.69) after controlling for size and book-tomarket in the overall world market. For developed

Table 5 Cross-sectional regressions of global liquidity risk. For each individual stock i, pre-ranking beta k (k=1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to either global market returns or the innovations in global market illiquidity. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the five-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into ten equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the ten portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is defined in a manner similar to Eq. (4). Cross-sectional regressions with country dummies are performed for each month over all the sample countries (Panel A), developed markets (Panel B), emerging markets (Panel C) and the US (Panel D). The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 106. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Intercept

ZR

Beta 1

Panel A: All countries 0.0092 0.0020 1.44 0.89 0.0096 0.0017 1.52 0.73 0.0104* 0.0015 1.66 0.66 0.0092 0.0018 1.44 0.79

0.0030 0.69 0.0031 0.72 0.0028 0.68 0.0030 0.71

Panel B: Developed markets 0.0003 0.0084** 2.57 0.11 0.0086** 0.0004 2.58 0.15 0.0082** 0.0001 2.51 0.03 0.0088*** 0.0001 2.69 0.03

0.0029 0.65 0.0031 0.68 0.0025 0.58 0.0030 0.66

Panel C: Emerging markets 0.0104 0.0096 1.43 2.89 0.0104 0.0099 1.44 2.95 0.0116 0.0090 1.61 2.71 0.0107 0.0094 1.47 2.85

0.0034 0.60 0.0034 0.60 0.0038 0.66 0.0035 0.61

Panel D: US 0.0094*** 3.24 0.0079** 2.35 0.0089*** 2.96 0.0096*** 3.38

0.0057 1.09 0.0063 1.17 0.0050 1.02 0.0063 1.16

0.0008 0.15 0.0004 0.08 0.0007 0.13 0.0002 0.04

Beta 2

Beta 3

Beta 4

Beta 5

ln(MV)

ln(B/M)

0.0087*** 2.62

0.0340 0.52 0.0303 0.46 0.0320 0.48 0.0317 0.48

0.0050*** 8.91 0.0050*** 8.91 0.0050*** 8.91 0.0050*** 8.91

0.0074* 1.80

0.0319 0.50 0.0268 0.41 0.0326 0.50 0.0301 0.46

0.0044*** 6.72 0.0044*** 6.72 0.0045*** 6.73 0.0044*** 6.72

0.0105** 2.15

0.5867 1.11 0.5744 1.08 0.6020 1.14 0.5929 1.12

0.0061*** 8.39 0.0061*** 8.40 0.0062*** 8.47 0.0061*** 8.38

0.0488 1.64

0.0700 0.81 0.0888 0.99 0.0774 0.89 0.0859 0.96

0.0038*** 3.97 0.0038*** 3.94 0.0038*** 4.00 0.0038*** 3.98

0.0124 1.09 0.0259 1.05 0.0081*** 2.69

0.0082 0.62 0.0505 1.41 0.0072* 1.96

0.0653*** 2.69 0.0083 0.25 0.0075 1.53

0.0801 1.06 0.1005* 1.67 0.0194 0.84


markets, b4,W is significant at the 10% level with a coefficient of 0.007, but it is not priced in emerging markets. Although I find weak evidence of pricing of b3,W in the US, it is priced in neither developed nor emerging markets. Consistent with previous research on the integration of financial markets in developed countries (Wheatley, 1988; Korajczyk and Viallet, 1989; Chan, Karolyi, and Stulz, 1992), analyses in this subsection provide some evidence on the integration of developed markets from the perspective of liquidity. Considering that liquidity could be a global phenomenon, as shown in topical examples such as the Asian financial crisis, the meltdown of LongTerm Capital Management, and the ongoing subprime mortgage crisis, it is intuitively appealing that liquidity risks are related to asset pricing in the global context. One potential problem with the analyses in this subsection arises from the fact that global factors encompass local factors by construction. I resolve this problem in Section 5.3 by investigating the pricing of global liquidity risk when global factors are independent of local factors in a given country. 5.3. Do US markets drive global liquidity risk? The finding of the pricing of global liquidity risk in Section 5.2 raises an interesting question as to whether the US market, which is allegedly the largest financial market in the world, is a driving force in the pricing of global liquidity risk. In this subsection, I compare the pricing of liquidity risks with respect to US factors with the pricing of liquidity risks with respect to global aggregates that are independent of both local and US factors. To differentiate the US market from the rest of the world, I decompose global factors into two groups: US factors and the ‘‘nonlocal and non-US global’’ factors that are net of both local and US factors. The nonlocal & nonUS global factors are obtained in a manner similar to Jorion and Schwartz (1986). First, I obtain the nonlocal global factors for country j by orthogonalizing the global factors to the local factors of country j. That is, I obtain nonlocal global return of country i, RðWDÞ , from the i,t residuals of a regression of global market returns on local ðWDÞ market return. Ci,t is obtained in a similar way. Subsequently, I regress these nonlocal global factors on the US factors to obtain the nonlocal & non-US global ðWDÞUS factors, RðWDÞUS and Ci,t , from the residuals. I i,t compute betas by Eq. (3) but with respect to these factors as well as US factors. In Eq. (8), the superscripts (W D) US and US of each beta indicate that the beta is computed with respect to the nonlocal & non-US global factors and the US factors, respectively. All betas have a common denominator of a variance, Var Rt W Ct W . Finally, I test the LCAPM in Eq. (8) using all stocks in the sample excluding those from the US US

EðRi,t Rf ,t Þ ¼ EðCi,t Þ þ l

ðWDÞUS

þl

1,US

ð bi

1,ðWDÞUS

ð bi

3,ðWDÞUS

bi

2,US

þ bi

4,US

bi

Þ

2,ðWDÞUS

þ bi

4,ðWDÞUS

bi

3,US

bi

Þ

ð8Þ

149

The time series averages of the estimated premiums in the cross-sectional regressions are shown in Table 6. The liquidity risk that arises from the covariance of illiquidity with the US market return significantly affects the 4,US expected returns: b is priced at the 1% significance level in the overall world market (a coefficient of 0.007) and at the 5% level in developed markets (a coefficient of 0.008). However, the liquidity risk with respect to nonlocal & non-US global factors is not statistically significant or is significant with the wrong sign. That is, under the columns labeled ‘‘nonlocal & non-US global,’’ all 4,ðWDÞUS significant b s have positive signs. This finding shows that the US market plays a key role in the pricing of global liquidity risk, implying that global investors who need to rebalance their portfolios seek compensation for holding stocks whose liquidity plummets in a US market 4,US downturn. A significant b contributes to significant pricing of the liquidity net beta in the overall world market (Panel A) and in developed markets (Panel B). No significant results are found for emerging markets and for different types of liquidity risks. [Interestingly, the global commonality risk, which is significant in Table 5, is no longer significant in Table 6. This is because the earlier finding is largely due to the pricing of commonality risk with respect to the local market illiquidity, which is infused into global illiquidity in the aggregation process. By extracting the local aggregate of illiquidity from the global aggregate of illiquidity via the orthogonalization process, the pricing of local commonality risk is distinguished from that of global commonality risk. Table 7 also shows that the commonality risk is significantly priced only in local markets. The exercise in this subsection that distinguishes the effect of global liquidity risk on asset pricing from that of local liquidity risk shows the importance of the US market relative to that of the rest of the world. Global liquidity risk with respect to the US market is shown to be important in developed markets, while this is not the case in emerging markets. In Section 6, I further investigate which variables, other than the developedand emerging-market categories, help to explain the differences in the pricing of local and global liquidity risk with respect to the US market across countries. 5.4. Asset pricing of liquidity risk under a mildly segmented world financial market This subsection examines the LCAPM under the assumption that the degree of integration of world financial markets is mild in the sense that the degree lies somewhere between full segmentation and full integration (Errunza and Losq, 1985; Bekaert and Harvey, 1995). Because local and global liquidity risks are jointly tested under this assumption, the analysis in this subsection provides an opportunity to examine the relative importance of local and global risk. My prior is that the importance of global risk is higher in countries with a high degree of integration, and local risks are more important in countries that are segmented. Tables 7 and 8 summarize results of the cross-sectional regression tests of the model in Eq. (6), which is formed

150


Table 6 Cross-sectional regressions of global liquidity risk: US versus non-US. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to the returns and the innovations in illiquidity of either the US market or the ‘‘nonlocal & non-US’’ global market. Nonlocal & non-US factors are obtained by orthogonalizing global aggregates against the local and the US markets. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have preranking beta k of year t. Then, at the beginning of year t, stocks are sorted into 10 equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is defined in a manner similar to Eq. (4). Cross-sectional regressions with country dummies are performed for each month over all the sample countries (Panel A), developed countries (Panel B), and emerging markets (Panel C). The US stocks are dropped from the test. The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 106. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. US Intercept

ZR

Panel A: All countries 0.0024 0.0125* 1.81 1.06 0.0131* 0.0022 1.88 0.96 0.0126* 0.0022 1.82 0.99 0.0126* 0.0025 1.81 1.12

Beta 1

Beta 2

(excluding US) 0.0019 0.42 0.0020 0.0069 0.45 0.57 0.0018 0.42 0.0020 0.45

Panel B: Developed markets (excluding US) 0.0132*** 0.0004 0.0034 4.24 0.16 0.75 0.0137*** 0.0001 0.0034 0.0176 4.23 0.05 0.77 1.21 0.0138*** 0.0001 0.0032 3.77 0.04 0.72 0.0135*** 0.0004 0.0033 4.31 0.16 0.74 Panel C: Emerging markets 0.0098 0.0097 0.0031 1.21 2.86 0.48 0.0115 0.0103 0.0026 1.40 2.91 0.41 0.0107 0.0099 0.0028 1.32 2.97 0.44 0.0114 0.0105 0.0025 1.36 3.01 0.39

Beta 3

Nonlocal & non-US global Beta 4

Beta 5

Beta 1

0.0062*** 2.61

0.0031 0.50 0.0031 0.51 0.0031 0.50 0.0029 0.48

0.0152 0.56 ***

0.0065 2.70

0.0066** 2.26

0.0265 0.82 0.0077** 2.54 0.0026 0.54

0.0042 0.16 0.0103 0.32 0.0018 0.35

under the assumption of a mildly segmented world financial market. Based on the earlier results showing that the US plays a key role in the pricing of global liquidity risk, I test global liquidity risks with respect to US factors instead of global liquidity risks with respect to nonlocal global factors. Hence, betas in Eq. (6) with the superscript (W D) are replaced by betas formed with k,US respect to the US market, b . I drop US stocks from the tests. Again, based on the earlier results, I omit the results 3,D 3,US on b and b from the tables to save space. In Table 7, the liquidity net betas with respect to local and US factors are both priced at the 5% level with premiums of 0.002 (t-value of 2.42) and 0.005 (t-value of 2.24), respectively, in the overall world market. This is supportive of the assumption of a mild degree of world market integration. By examining developed and emerging markets separately, it emerges that the global liquidity net beta is significant in developed markets,

0.0027 0.33 0.0027 0.32 0.0028 0.33 0.0026 0.31 0.0035 0.47 0.0034 0.46 0.0030 0.40 0.0028 0.36

Beta 2

Beta 3

Beta 4

Beta 5

ln(MV)

ln(B/M)

0.0043 1.03

0.0792 0.96 0.0738 0.90 0.0749 0.91 0.0780 0.94

0.0052*** 9.22 0.0053*** 9.26 0.0052*** 9.22 0.0053*** 9.26

0.0015 0.30

0.0801 1.00 0.0752 0.94 0.0782 0.98 0.0794 0.98

0.0046*** 6.72 0.0046*** 6.73 0.0046*** 6.70 0.0046*** 6.72

0.0095 1.33

0.6225 1.20 0.6816 1.28 0.5838 1.16 0.6321 1.21

0.0064*** 8.25 0.0065*** 8.35 0.0064*** 8.30 0.0065*** 8.31

0.0034 0.51 0.0102 0.58 0.0098** 2.20

0.0036 0.51 0.0172 0.90 0.0037 0.73

0.0072 0.54 0.0064 0.28 0.0284** 2.49

but not in emerging markets. On the contrary, the local liquidity net beta is highly significant in emerging markets. This is not the case in developed markets. Generally, global liquidity risks are not priced in emerging markets and local liquidity risks are not priced in developed markets. This finding is consistent with the previous results and implies that the level of financial market integration is relatively higher in developed markets than in emerging markets. This implication is also consistent with Bekaert, Harvey, and Lundblad (2007), which shows that the level of integration of financial markets in emerging countries is relatively low. It is notable that the local commonality beta is significant at the 1% level (a premium of 0.004 with a t-value of 2.74) in the overall world market (Panel A), which is not the case in the context of a fully segmented world market (Table 3). This could arise from dropping US stocks, for which the local commonality risk is not priced, thereby increasing the


151

Table 7 Cross-sectional regressions of local liquidity risk and liquidity risk with respect to the US market. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to the returns and the innovations in illiquidity of either local market or the US market. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into ten equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is defined in a manner similar to Eq. (4). Cross-sectional regressions with country dummies are performed for each month over all the sample countries (Panel A), developed countries (Panel B), and emerging markets (Panel C). The US stocks are dropped from the test. The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 106. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Local Intercept

ZR

Panel A: All countries 0.0129* 0.0032 1.92 1.49 0.0125* 0.0031 1.86 1.40 0.0128* 0.0022 1.92 1.00 0.0126* 0.0028 1.88 1.31

Beta 1

Beta 2

Beta 3

(excluding US) 0.0004 0.48 0.0005 0.0044*** 0.57 2.74 0.0006 0.0003 0.70 0.08 0.0006 0.62

Panel B: Developed markets (excluding US) 0.0137*** 0.0007 0.0006 4.41 0.32 0.39 0.0134*** 0.0007 0.0006 0.0033 4.09 0.31 0.42 1.39 0.0128*** 0.0001 0.0007 0.0012 3.87 0.06 0.47 0.17 0.0141*** 0.0006 0.0007 4.53 0.25 0.44 Panel C: Emerging markets 0.0116 0.0122 0.0001 1.59 3.58 0.08 0.0112 0.0126 0.0002 0.0066*** 1.54 3.53 0.23 2.87 0.0113 0.0100 0.0004 1.56 3.08 0.46 0.0111 0.0112 0.0003 1.52 3.45 0.37

US Beta 4

Beta 5

Beta 1

Beta 2

Beta 3

Beta 4

Beta 5

ln(MV)

ln(B/M)

0.0023** 2.42

0.0033 0.0053** 0.89 2.24 0.0034 0.0084 0.92 0.69 0.0035 0.0138 0.94 0.51 0.0033 0.0060** 0.90 2.53

0.0904 1.16 0.0867 1.10 0.0839 1.06 0.0891 1.14

0.0051*** 9.73 0.0051*** 9.74 0.0051*** 9.74 0.0051*** 9.72

0.0012 0.89

0.0049 0.0058** 1.24 1.98 0.0049 0.0228 1.26 1.57 0.0050 0.0194 1.28 0.62 0.0050 0.0071** 1.27 2.41

0.0910 1.34 0.0884 1.28 0.0857 1.23 0.0891 1.30

0.0045*** 7.01 0.0045*** 7.04 0.0045*** 7.07 0.0045*** 7.03

0.5658 1.10 0.6489 1.25 0.5681 1.11 0.5519 1.07

0.0062*** 8.52 0.0062*** 8.52 0.0062*** 8.59 0.0062*** 8.54

0.0027** 2.08

0.0013 0.72 0.0035*** 3.25

0.0007 0.17 0.0041*** 2.87

contribution of the priced local commonality risk of emerging markets in the overall cross section. Table 8, which presents empirical results by geographic subregion, shows that the pricing of the local commonality beta in emerging markets largely arises from Developed Asia (Panel A), Emerging Asia (Panel C), and Latin America (Panel E). Consistent with the results in Table 3, Table 7 shows 4,D that the local liquidity risk of b is priced in the overall world market (a coefficient of 0.003 and a t-value of 2.08) and in emerging markets (a coefficient of 0.004 and a t-value of 2.87). Table 8 shows that the 4,D significant pricing of b arises mostly from Emerging Asia (Panel C). This implies that investors request compensation for holding stocks whose liquidity is sensitive to the fluctuation of local, not the US, market returns in emerging market countries. In contrast with emerging markets, global liquidity risk seems more important than local liquidity risk in developed markets. 4,US In Panel B of Table 7, b is significant at the 5%

0.0009 0.20 0.0008 0.18 0.0009 0.19 0.0011 0.25

0.0011 0.22 0.0022 0.08 0.0170 0.51 0.0026 0.50

level with a coefficient of 0.007 in developed markets, 4,D but the local liquidity risk b is not significant. Table 8 shows that Developed Europe contributes most to the 4,US pricing of b in developed markets. Evidence in this subsection of the pricing of global liquidity risk implies that developed countries have close financial link with the US market. 5.5. Robustness tests The goal of this subsection is to evaluate the robustness of the empirical results described in the previous subsections in Section 5. First, I use local currency returns instead of US dollar returns in the cross-sectional regressions. Second, I discuss the crosssectional test results based on the country-by-country analysis. Third, I present the results of cross-sectional regressions using characteristic-based portfolios as test assets.

152


Table 8 Cross-sectional regressions of local liquidity risk and liquidity risk with respect to the US market by geographic region. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to the returns and the innovations in illiquidity of either local market or the US market. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into 10 equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is defined in a manner similar to Eq. (4). Cross-sectional regressions with country dummies are performed for each month over Developed Asia (Panel A), Developed Europe (Panel B), Emerging Asia (Panel C), Emerging Europe, the Middle East, and Africa (Panel D), and Latin America (Panel E). The US stocks are dropped from the test. The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 106. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Local Intercept

ZR

Panel A: Developed Asia 0.0095 0.0011 1.14 0.35 0.0116 0.0002 1.38 0.07 0.0102 0.0012 1.25 0.37

Beta 1

0.0005 0.32 0.0005 0.30 0.0006 0.35

Panel B: Developed Europe 0.0136*** 0.0033 0.0019 3.99 1.23 0.88 0.0130*** 0.0031 0.0019 3.70 1.13 0.86 0.0138*** 0.0032 0.0019 4.05 1.18 0.83 Panel C: Emerging Asia 0.0003 0.0176 0.06 3.98 0.0033 0.0187 0.63 3.99 0.0029 0.0161 0.52 3.92

0.0000 0.03 0.0001 0.12 0.0003 0.34

Beta 2

0.0019 0.73 0.0019 0.71 0.0020 0.73

Beta 4

Beta 5

Beta 1

0.0007 0.47

0.0029 0.75 0.0029 0.75 0.0030 0.77

0.0046* 1.71 0.0004 0.22 0.0010 0.53 0.0011 0.39 0.0014 0.64 0.0036*** 3.09 0.0075*** 3.00 0.0044*** 2.73

Panel D: Emerging Europe/Middle East/Africa 0.0303 0.0049 0.0006 1.34 0.89 0.33 0.0224 0.0035 0.0008 0.0075 0.92 0.64 0.41 0.95 0.0371* 0.0042 0.0006 1.68 0.78 0.31 Panel E: Latin America 0.0190** 0.0014 2.08 0.24 0.0193** 0.0002 2.06 0.04 0.0191** 0.0031 2.09 0.55

US

0.0057 1.38

0.0075 1.44 0.0016 0.86

0.0091* 1.77 0.0004 0.17

5.5.1. Local currency returns Table 9 shows the pricing of liquidity risk under the assumption of mildly segmented world markets, with returns, illiquidity, and betas based on local currency. The results in this table are similar to the results in Table 7, which are based on US dollar returns. That is, evidence of priced local and global liquidity risks is maintained. 5.5.2. Country-by-country analysis Under the assumption of a mildly segmented world financial market, I perform the cross-sectional tests

0.0015 0.47 0.0015 0.47 0.0016 0.51 0.0022 0.44 0.0021 0.41 0.0023 0.46 0.0027 0.36 0.0004 0.05 0.0047 0.63 0.0019 0.24 0.0028 0.37 0.0018 0.23

Beta 2

Beta 4

Beta 5

ln(MV)

ln(B/M)

0.0068 0.84

0.1081 1.09 0.1093 1.09 0.1061 1.07

0.0064*** 8.03 0.0064*** 8.05 0.0064*** 8.06

0.0046* 1.66

0.0450 0.79 0.0399 0.70 0.0442 0.77

0.0026*** 3.72 0.0026*** 3.71 0.0026*** 3.73

0.0057 0.85

0.2137 0.36 0.3375 0.58 0.1938 0.33

0.0057*** 6.09 0.0058*** 6.10 0.0057*** 6.09

0.0016 0.22

0.6501 0.85 0.7665 0.95 0.6105 0.80

0.0077*** 8.12 0.0076*** 7.84 0.0078*** 8.19

0.0067 0.63

0.2795 0.65 0.2034 0.46 0.2626 0.60

0.0037*** 2.63 0.0037*** 2.71 0.0035** 2.46

0.0539 1.10 0.0110 1.42

0.0020 0.15 0.0049* 1.74

0.0510 1.19 0.0110 1.53

0.0648 1.62 0.0062 0.78

0.0040 0.08 0.0069 0.64

separately for each of the 37 countries (excluding the US) that have sufficient numbers of stocks.12 Similarly to Section 5.4, I jointly test local liquidity risk and liquidity risk formed with respect to US market returns and illiquidity using returns, illiquidity, and betas based on local currencies.

12 Results for the country-by-country analysis are available upon request.

Table 9 Cross-sectional regressions of liquidity risk based on local currency. For each individual stock i, pre-ranking beta k (k= 1,y,4) of year t is estimated using the monthly returns (in local currency) and innovations in illiquidity over the years t 5 to t 1 with respect to the returns (in local currency) and the innovations in illiquidity of either local market or the US market. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have pre-ranking beta k of year t. Then, at the beginning of year t, stocks are sorted into 10 equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. With all four betas obtained by repeating this procedure, the liquidity net beta, beta 5, is defined in a manner similar to Eq. (4). Cross-sectional regressions with country dummies are performed for each month over all the sample countries (Panel A), developed countries (Panel B), and emerging markets (Panel C). The US stocks are dropped from the test. The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. The coefficient of ln(MV) is multiplied by 103. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively.

Intercept

ZR

Beta 1

Panel A: All countries (excluding US) 0.0223 *** 0.0053 0.0000 4.20 2.24 0.01 0.0225*** 0.0054 0.0001 4.26 2.22 0.08 0.0235*** 0.0047 0.0001 4.44 1.99 0.17 0.0225*** 0.0050 0.0001 4.25 2.13 0.15 Panel B: Developed markets (excluding US) 0.0144*** 0.0022 0.0002 3.83 0.85 0.17 0.0145*** 0.0022 0.0002 3.74 0.85 0.18 0.0138*** 0.0020 0.0003 3.70 0.77 0.25 0.0147*** 0.0021 0.0003 3.90 0.82 0.21 Panel C: Emerging markets 0.0274*** 0.0143 4.09 4.16 0.0284*** 0.0150 4.28 4.20 0.0285*** 0.0124 4.34 -3.79 0.0277*** 0.0134 4.14 4.09

0.0004 0.54 0.0004 0.45 0.0002 0.20 0.0002 0.22

Beta 2

Beta 3

US Beta 4

Beta 5

Beta 1

0.0017** 2.22

0.0024 0.79 0.0025 0.81 0.0025 0.82 0.0025 0.81

0.0035** 2.54 0.0006 0.15 0.0020* 1.72 0.0007 0.66 0.0022 1.17 0.0019 0.31 0.0007 0.47 0.0032*** 3.17 0.0062*** 2.95 0.0007 0.17 0.0038*** 2.83

0.0042 1.25 0.0042 1.26 0.0043 1.29 0.0042 1.28 0.0032 0.87 0.0030 0.84 0.0031 0.85 0.0031 0.87

Beta 2

Beta 3

Beta 4

Beta 5

ln(MV)

ln(B/M)

0.0037* 1.79

0.4363 0.97 0.4715 1.04 0.4919 1.09 0.4493 1.00

0.0048*** 8.50 0.0048*** 8.49 0.0048*** 8.49 0.0048*** 8.50

0.0047* 1.80

0.2255 0.48 0.2446 0.51 0.2745 0.57 0.2366 0.50

0.0043*** 6.40 0.0043*** 6.40 0.0043*** 6.38 0.0043*** 6.38

0.0001 0.03

1.4778** 2.46 1.5645** 2.59 1.4957** 2.52 1.4697** 2.46

0.0055*** 7.14 0.0055*** 7.13 0.0055*** 7.21 0.0055*** 7.21

0.0113 1.03 0.0012 0.05 0.0043** 2.02

0.0235* 1.81 0.0001 0.00 0.0055** 2.12

0.0081 0.35 0.0082 0.29 0.0002 0.04


Local

153

154


Country-by-country analyses reveal substantial variations across countries in the pricing of liquidity risk. Out of the 37 countries considered, the local liquidity net beta is priced for five countries (Canada, Hong Kong, India, Pakistan, and South Africa), and the global liquidity net beta is significant for six countries (Canada, France, Greece, Netherlands, Poland, and Portugal). 4,D Local liquidity risk of b is negative in 30 countries and significantly negative in six countries (Canada, Hong Kong, India, Pakistan, South Africa, and Switzerland). Twenty-two 4,US countries have negative coefficients for b and, for six of them (Canada, Greece, Italy, Netherlands, Poland, and Sweden), the beta is also significant at least at the 10% level. The local commonality beta is priced with a positive sign at the 1% significance level (Hong Kong and India), at the 5% level (Italy and Singapore), or at the 10% level (Pakistan). But no significant pricing is found of the global 2,US commonality risk b in countries other than Turkey. Country-by-country analysis yields some evidence of the pricing of local and global liquidity risk. Nevertheless, the pervasiveness of the effect of liquidity risk on asset pricing in the overall world financial market seems unclear at the country-level analysis. It is likely that the low quality of international stock-level data (Ince and Porter, 2006; Bekaert, Harvey, and Lundblad, 2007) and the relatively short sample period could have reduced the power of the test for many countries considered in this subsection. On the contrary, the regional-level analyses in the earlier subsections seem to provide a relatively clearer picture of the pervasive effect of liquidity risk on asset pricing in international financial markets. 5.5.3. Portfolio-level analysis In the literature on asset pricing, it is not uncommon to use portfolios as test assets that are sorted on firm characteristics such as size and book-to-market. The use of portfolios as test assets is particularly popular when the reduction of noise in the estimated loadings is an important issue. In addition, it could mitigate the potential dominating influence of a few countries that have large numbers of sample stocks on cross-sectional regressions that are performed over stocks from multiple countries. However, empirical results of portfolio-based tests could be sensitive to the characteristic that is used to sort stocks (Brennan, Chordia, and Subrahmanyam, 1998; Berk, 2000). Nevertheless, given the popularity of using portfolios as test assets in the literature, I show in this subsection the results of cross-sectional tests in relation to portfolios based on size, book-to-market, and illiquidity. For each year, I sort stocks into 10 or 25 equally weighted portfolios within a country on the basis of previous year-end market capitalization, previous year-end book-to-market ratio, or previous year-average illiquidity. If the total number of stocks in a country in Table 1 is between 100 and 300, the stocks are sorted into 10 portfolios. If the number is larger than 300, the country has 25 portfolios.13 Market returns and illiquidity are 13 Stocks from Austria, Belgium, Brazil, Chile, Denmark, Finland, Indonesia, Israel, Mexico, Netherlands, New Zealand, Norway, Pakistan,

obtained as value-weighted aggregates of returns and illiquidity, respectively, at the local and global market levels. The betas of year t are estimated using portfolio returns (in US dollars) and innovations in illiquidity over the years t 5 to t 1. Consistent with the case of individual stock-level tests, innovations in illiquidity are obtained from AR(1) filtering of the first-differences of portfolio illiquidity. In this exercise, local risks are based on the LCAPM of fully segmented world markets, and global risks are obtained on the basis of the model of fully integrated world financial markets. Given the market beta as well as liquidity betas, cross-sectional regressions with country dummies are performed for each month over portfolios across countries. Tables A1 and A2 in the Appendix separately report time series averages of the coefficient of local and global risks for three different portfolios. To save space, I do not report t-values, but the significance of the coefficients are indicated by asterisks. Consistent with earlier results, the 4,D local liquidity risk of b is significantly priced in both the overall world market and emerging markets regardless of portfolios used in the tests Table A1. In particular, the emerging-market results look fairly strong. However, contrary to the case of results based on individual stocks, the significant coefficients of the local commonality betas are all negative. Some evidence shows that b3,Dis priced when book-to-market portfolios are used as test assets (Panel B), but this is not the case when other test assets are used. Turning to global liquidity risk (Table A2), there is some evidence that b4,W is priced (Panels B and C) in the overall world market. This finding is consistent with the earlier result. However, regional analysis shows that the pricing of b4,W is somewhat sensitive to the selected test assets. The results based on size portfolios and book-to-market portfolios show that b4,W is priced in emerging markets but not in developed markets. On the contrary, the results based on illiquidity portfolios in Panel C show the opposite. Overall, portfolio-level analyses provide some evidence to further support the earlier results. However, some results appear to be sensitive to the choice of the firm characteristic used to sort stocks into portfolios. 6. What drives the relative importance of local and global liquidity risks in asset pricing? Given the findings in the earlier sections, it would be interesting to see what drives the relative importance of local and global liquidity risks. The results in Section 5 show that the categorization of financial markets as developed and emerging markets plays a role in this regard. In this section, I examine the effect of country-level proxies for transparency, political risk, and (footnote continued) Philippines, Poland, Portugal, Spain, and Turkey are sorted into 10 portfolios in each country. The countries with 25 portfolios are Australia, Canada, China, France, Germany, Greece, Hong Kong, India, Italy, Japan, Malaysia, Singapore, South Africa, South Korea, Sweden, Switzerland, Taiwan, Thailand, the UK, and the US. Switzerland has 299 stocks but is included in the 25 portfolio group.


155

global investment flows on the pricing of local and global liquidity risks. My prior expectation is that the relative importance of global liquidity risk is higher in countries with high transparency, low political risk, and large crossborder investments. It is because global investors could be more prevalent in such countries (Chan, Covrig, and Ng, 2005; Gelos and Wei, 2005) and their global rebalancing of portfolios could have an effect on the pricing of liquidity risk. Based on the assumption of mildly segmented world financial markets and the earlier finding that the US market drives the pricing of global liquidity risk, I jointly test both local risk and risk with respect to the US market in the regressions. I focus only on 4,S the commonality beta and b (S= D or S= US), both of which are shown to be priced in Section 5. In this section, I use stocks from the 37 countries (excluding the US) that are used in the preceding cross-sectional regressions. I employ two measures of transparency. One is the index of accounting standards from La Porta, Lopez-deSilanes, Shleifer, and Vishny (1998), which is constructed based on the coverage of items in companies’ 1990 annual reports. Out of the 37 countries considered, four countries do not have this variable and hence are dropped from the test (China, Indonesia, Pakistan, and Poland). The index varies from 36 (Portugal) to 83 (Sweden) in the sample, with higher values indicating higher accounting standards. The other measure of transparency is the index of credibility of disclosure from Bushman, Piotroski, and Smith (2004), which is the percentage of firms in a country that are audited by the big five accounting firms. This variable has a value of one, two, three, or four if the percentage falls in the range of 0–25%, 25–50%, 50–75%, or 75–100%, respectively. Stocks from three countries in our sample are dropped due to lack of this variable (China, Indonesia, and Poland). I use the index of expropriation risk from La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998) as a proxy for political risk. This measure assesses the threat of outright confiscation or forced nationalization. The scale ranges from zero to ten, with higher values indicating smaller risk of expropriation. For 35 countries in the sample (excluding China and Poland) for which the variable is available, the index ranges from 5.22 (Philippines) to 9.98 (Netherlands and Switzerland). I also consider measures of cross-border investment flows. The first measure is the market value of US stock holdings (in millions of US dollars, as of June 30, 2007) held by foreign investors. I obtain these data for all 37 countries from the website of the Department of US Treasury.14 I also use the market value of stock holdings (in billions of US dollars, as of December 2005) in a country held by US institutions. I collect these data for 23 countries from Ferreira and Matos (2008), who originally obtain the data for 27 countries from the FactSet/LionShare database.15 According to Griffin,

Nardari, and Stulz (2004), investment flows are sometimes ‘‘pushed’’ by the US market returns and ‘‘pulled’’ by local market returns. Variables for cross-border holdings could shed some lights on how shifts in investment flows triggered by changes in the US or local market returns affect the pricing of liquidity risk. To examine the effect of each country-level proxy on the pricing of liquidity risk, I perform cross-sectional regressions of the expected returns on the set of explanatory variables: liquidity level, market risk, liquidity risk, and the two interaction terms incorporating the country-level proxy, X. The two interaction terms are liquidity risk and liquidity level, both of which are interacted with X. I also include size and book-to-market to control for firm characteristics. 4,US The interaction terms of b and X are significant for all five country-specific variables considered in Table 10, 4,US showing that the global liquidity risk of b is significantly priced in countries with high accounting standards, high credibility of disclosure, low political risk, a large amount of holdings of US stocks, and a large amount of stocks held by US institutions. For example, the coefficient 4,US for b is positive, 0.040, when the index of credibility of disclosure is unity (the lowest transparency). However, it is negative, 0.023, as specified in the LCAPM, when the index is 4 (the highest transparency). On the contrary, the 4,D local liquidity risk ofb is significantly priced in countries with lower transparency. These results are consistent with the prior expectation that global liquidity risk is important in countries with high transparency, low political risk, and large cross-border investments, because global investors, who request compensation for bearing liquidity risk, could be more prevalent in such countries. However, in opaque countries where global investors are uncommon, local liquidity risk is shown to be more important than global liquidity risk. The table also reports empirical results for commonality risk. The significant pricing of local commonality risk shows that stocks that become more liquid in low local market liquidity are valued by investors in opaque markets. This provides additional insight to Karolyi, Lee, and van Dijk (2009), who show that the commonality in liquidity is greater in opaque countries than in transparent countries. However, global commonality risk with respect to the US market is important in countries with large cross-border investments into and from the US. This highlights the importance of US market liquidity, which could be more pronounced when there are sizable US-related cross-border investments. Taken together, global liquidity risk is more important than local liquidity risk in countries that are more open, that is, in countries with high transparency, low political risk, and large cross-border investment flows. However, in countries with the contrary properties, and hence where global investors are rare, the importance of local liquidity risk increases.

14 The website is http://www.treas.gov/tic/shl2007r.pdf. I use Table 22 in the document. 15 These 23 countries are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, India, Italy,

(footnote continued) Japan, Netherlands, Norway, Poland, Portugal, Singapore, South Africa, Spain, Sweden, Switzerland, and the UK.

Intercept

ZR

ZR*X

Beta 1

Beta 2

Beta 2*X

X = Accounting standards 0.0034 0.0828 0.0012*** 0.63 3.15 3.05 0.0036 0.0418 0.0006* 0.72 1.82 1.86

0.0003 0.45 0.0001 0.14

0.0543** 2.11

0.0007* 1.96

X = Credibility of disclosure 0.0044 0.0476 0.0124*** 0.90 2.87 2.81 0.0042 0.0133 0.0033 0.89 0.68 0.66

0.0009 1.03 0.0001 0.14

0.0332** 2.05

X = Risk of expropriation 0.0047 0.0269 1.00 0.99 0.0045 0.0007 0.96 0.02

0.0003 0.43 0.0000 0.02

0.0208 0.91

0.0024 0.85 0.0004 0.13

X = Foreign portfolio holdings of US stocks 0.0083* 0.0039 0.0001 0.0000 1.95 0.82 0.26 0.02 0.0078* 0.0041 0.0002 0.0002 1.81 0.93 0.94 0.23 X = Amount of stocks held by US institutions 0.0078* 0.0027 0.0850 0.0001 1.97 0.62 0.42 0.08 0.0069* 0.0010 0.0949 0.0002 1.93 0.22 0.48 0.20

US Beta 4

0.0493* 1.69

Beta 2

Beta 2*X

0.3061 1.37

0.0040 1.22

0.0008* 1.74

0.0114* 1.81 0.0113* 1.79

0.1739 0.88

0.0059** 2.02

0.0135** 2.14 0.0118* 1.88

0.0386 0.11

0.0024 1.26

0.0106* 1.86 0.0108* 1.79

0.0211 0.34

0.0010** 2.15

0.0049 0.86 0.0065 1.06

0.0991 1.58

0.0001** 2.14

0.0044 0.81 0.0077 1.35

0.0021 0.84 0.0202 1.27 0.0011** 2.11 0.0014 0.34

0.0175*** 2.76

Beta 1

0.0092** 2.03 0.0158* 1.66

0.0060 1.05

Beta 4*X

0.0002*** 2.69 0.0091 1.60

Beta 4

0.0641 1.36

Beta 4*X

ln(MV)

ln(B/M)

N

0.0057*** 6.00 0.0056*** 5.57

15,290

0.0011* 1.69

0.0513 0.65 0.0394 0.50

0.0058*** 6.90 0.0056*** 5.87

15,369

0.0209** 2.42

0.0424 0.55 0.0377 0.49

0.0056*** 5.83 0.0055*** 5.62

15,460

0.0199*** 2.83

0.0338 0.45 0.0398 0.53

0.0055*** 5.75 0.0055*** 5.53

16,643

0.0019*** 2.82

0.0314 0.42 0.0146 0.20

0.0050*** 6.68 0.0045*** 5.80

12,263

0.0002** 2.37

0.0409 0.56 0.0127 0.18

0.0432 0.87 0.0609** 2.21 0.0024 0.06 0.1716*** 2.81 0.0067** 2.05 0.0035 0.41 0.0014*** 2.72 0.0136 1.45

15,290

15,369

15,460

16,643

12,263


Local

156

Table 10 Cross-sectional regressions of liquidity risk interacted with country-specific variable. For each individual stock i, pre-ranking beta k (k =1,y,4) of year t is estimated using the monthly returns and innovations in illiquidity over the years t 5 to t 1 with respect to the returns and the innovations in illiquidity of either local market or the US market. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity over the 5-year window. The 5-year window starts at either January 1988 or the first month in which stocks are present in the sample. Stocks should have at least 36 monthly returns and innovations in illiquidity within the given window to have preranking beta k of year t. Then, at the beginning of year t, stocks are sorted into 10 equally weighted portfolios in a given country based on the pre-ranking beta k of year t. Beta k is estimated for each of the 10 portfolios over the sample period (post-ranking beta). The post-ranking beta k of portfolio p is assigned to an individual stock i, which belongs to portfolio p in a given year. Cross-sectional regressions are performed for each month over the sample countries. The US stocks are dropped from the test. The table shows the averages of the estimated coefficients together with the t-values in italics. ZR is the previous month’s average zero-return proportion. The interaction variable X is as follows. The index of accounting standards denotes the coverage of items in companies’ 1990 annual reports (La Porta, Lopez-de-Silanes, Shleifer, and Vishny, 1998). The index of credibility of disclosure denotes the percentage of firms in the country that are audited by the big five accounting firms (Bushman, Piotroski, and Smith, 2004). The index of expropriation risk measures the threat of outright confiscation or forced nationalization by the state (La Porta, Lopez-de-Silanes, Shleifer, and Vishny, 1998), with a higher value indicating lower risk. Foreign portfolio holdings of US stocks is the market value of US stocks (in millions of US dollars) held by foreign investors as of June 30, 2007 (epartment of Treasury). Amount of stocks held by US institutions is the market value of stock holdings (in billions of US dollars) in a country held by US institutions (Ferreira and Matos, 2008). Ln(MV) is the log of the market capitalization in US dollars, and ln(B/M) is the log of the book-to-market ratio at the end of the previous year. N is the number of stocks included in the regression. The coefficient of ln(MV) is multiplied by 106. All the coefficients of the interaction terms of Foreign portfolio holdings of US stocks and the coefficient of ZR interacted with amount of stocks held by US institutions are multiplied by 104. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively.


7. Asset pricing of liquidity risk: factor model regressions In addition to a cross-sectional regression framework in which I have presented empirical results so far, the factor model regressions have been used in the previous literature to show the pricing of liquidity risk (Pa´stor and Stambaugh, 2003; Sadka, 2006). In this section, I show how much trading alpha can be generated by trading on the basis of local or global liquidity risk. Using stocks from the 37 countries (excluding the US) that are used in the cross-sectional tests, I perform factor model regressions for the liquidity risks that are shown to be priced in the preceding sections.16 In each year t, a stock is ranked into one of ten groups in a given country on the basis of its pre-ranking beta, which is estimated over the years t 5 to t 1. Subsequently, stocks with the same rank are combined to form 10 equally weighted portfolios across countries in the regions specified in the first column of Table 11. The US dollar-return, in excess of the risk-free rate Rft, of portfolio p (p= 1,y,10), Rkp,t , is regressed on global factors as specified in the following factor models: k

k

W Rkp,t Rf ,t ¼ a1,k p þ dp ðRt Rf ,t Þ þ xp,t

ð9Þ

and M,k W S,k H,k k Rkp,t Rf ,t ¼ a3,k p þ jp ðRt Rf ,t Þ þ jp SMBt þ jp HMLt þ Zp,t

ð10Þ The superscript k indicates that the portfolio is sorted on pre-ranking beta k (k=1,y,4). The Fama and French factors of SMB (small cap minus big) and HML (high book-tomarket minus low) are formed in the global context as in Griffin (2002). A difficulty arises, however, in the use of the factor model in the global financial market because, unlike the US, there is as yet no commonly accepted global factor model.17 In addition, as Griffin (2002) shows, the Fama and French factors per se are local, not global. However, given the popularity of factor model regression, I use global factors as well as US factors, which are obtained from K. French’s data library, in the regressions. The results using the US factors are generally stronger than those using global factors in the sense that the former generally produce higher alphas with higher levels of significance than the latter. In Table 11, however, I report the more conservative results, which are based on global factor models. Table 11 shows the estimated intercepts (alphas) from the regression of each of the 10 portfolios formed based on local commonality risk (Panel A), liquidity risk from the covariance of illiquidity with local market return (Panel B), and liquidity risk from the covariance of illiquidity with US market return (Panel C). Rows labeled ‘‘Global onefactor alpha’’ and ‘‘Global three-factor alpha’’ signify that the 16 The assumption on the degree of world market integration does not affect the results of the factor model regressions because only the rank, which is not affected by the assumption, of each beta matters in the sorting of stocks. 17 The exception is an unpublished work of Hou, Karolyi, and Kho (2006), which suggests a global factor model that is based on global market return, cash flow to price ratio, and momentum.

157

intercepts are from the models in Eqs. (9) and (10), respectively. The last column of the table (labeled ‘‘10-1’’) shows the difference in the estimated intercepts that are obtained from the regressions of the portfolios with the highest beta (p=10) and of those with the lowest beta (p=1). Henceforth, I call this difference the ‘‘10-1 spread.’’ Economically, the 10-1 spread denotes the excess return relative to the given factors that can be earned by simultaneously taking a long position in the highest-decile portfolio and a short position in the lowest-decile portfolio. Panel A of Table 11 shows the intercepts of portfolios based on local commonality risk. The 10–1 spread produces significant monthly excess returns of 0.39% and 0.24% from the one-factor model and the three-factor model, respectively. On an annual basis, these returns are approximately 4.72% and 2.87%, respectively. The alphas in general are monotonically increasing from the lowestbeta portfolio to the highest-beta portfolio. In emerging markets, the 10–1 spread is 0.58% for the one-factor alpha and 0.55% for the three-factor alpha. The numbers are annual 7.23%, and 6.87%, respectively, and are highly significant both statistically and economically. In Panel B, the portfolios are formed based on the local 4,D liquidity risk of b . The 1–10 spread, which is formed by going long the lowest-decile portfolio and shorting the highest-decile portfolio, is 0.24% (annual 2.87%) over all countries in the one-factor model, and it is highly significant at the 1% level (t-value of 2.81). Consistent with the preceding results for emerging markets, the 1–10 spreads from the one-factor model and the three-factor model are 0.55% and 0.62%, respectively, and are highly significant at the conventional 1% level in emerging markets. These returns are annual 6.39% and 7.12%, respectively. Again, there are monotonic patterns of the alphas along with the portfolios. The results of the one-factor model in the first two panels show that an annual excess return of 7.59% (=4.72+2.87%), which is highly significant both statistically and economically, can be obtained in the overall world market by trading on the basis of both the local common4,D ality risk and b . If the regression is performed only for stocks from emerging markets, the sum of the one-factor alphas obtained from trading based on these liquidity risks has the much higher value of 13.62%. Regarding global liquidity risk with respect to US market (Panel C), a significant 1–10 spread of 0.15% (annual 1.75%) emerges from the one-factor model, which is significant at the 5% level. However, this spread is not significant in the three-factor models. In an unreported result, I find that the trading alpha is 0.17%, which is highly significant at the 1% level, when the US three factors are used in the factor model. In developed markets, where a significant pricing of global liquidity risk is shown in the previous cross-sectional analysis, the 1–10 spread from the one-factor model is 0.14%, which is significant at the 10% level. When the US factors are used, the 1–10 spread from the one-factor model and the three-factor model are 0.159% and 0.161%, respectively, both of which are significant at the 5% level (unreported). In this section, I present in a factor model regression framework supporting evidence of the pricing of liquidity risk by showing that trading based on liquidity risk

158


Table 11 Factor model regressions of liquidity risk. In each year t, a stock is ranked into one of 10 groups in a given country on the basis of its pre-ranking beta k (k= 1,y,4) of year t, which is estimated over the years t 5 to t 1. Subsequently, stocks with the same rank are combined to form 10 equally weighted portfolios across countries in the regions specified in the first column of the table. Each portfolio return (in US dollars) in excess of the risk-free rate is regressed on global factors as specified in the following factor models: k k W Rkp,t Rf ,t ¼ a1,k p þ dp Rt Rf ,t þ xp,t

ð9Þ

and M,k

Rkp,t Rf ,t ¼ a3,k p þ fp

S,k H,k k RW t Rf ,t þ fp SMBt þ fp HMLt þ Zp,t :

ð10Þ

The SMB (small cap minus big) and HML (high book-to-market minus low) are formed in the global context as in Griffin (2002). The table shows the estimated alphas with the t-values in italics from the regression of each of the 10 portfolios that are formed based on local commonality risk (Panel A), liquidity risk from the covariance of illiquidity with local market return (Panel B), and liquidity risk from the covariance of illiquidity with US market returns (Panel C). The US stocks are dropped from the test. Rows labeled ‘‘Global one-factor alpha’’ and ‘‘Global three-factor alpha’’ denote that the intercepts are from the models in Eqs. (9) and (10), respectively. The last column of the table (labeled ‘‘10–1’’) shows the difference in the estimated intercepts that are obtained from the regressions of the portfolios with the highest beta (p = 10) and of those with the lowest beta (p= 1). *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Region

1 (small)

2

3

4

5

6

7

8

9

10 (large)

10–1

0.581** 2.35 0.515** 2.43

0.612** 2.42 0.520** 2.42

0.706*** 2.77 0.432** 2.00

0.651** 2.48 0.517** 2.30

0.696*** 2.60 0.512** 2.30

0.829*** 3.08 0.395* 1.76

0.929*** 3.42 0.256 1.10

0.385*** 5.02 0.235*** 3.00

0.891** 2.20 0.702* 1.91

0.953** 2.37 0.658* 1.83

1.070*** 2.65 0.551 1.52

0.992** 2.44 0.689* 1.91

1.032** 2.58 0.607* 1.71

1.270*** 3.15 0.339 0.94

1.430*** 3.51 0.119 0.32

0.582*** 4.58 0.554*** 3.87

0.622** 2.45 0.543** 2.57

0.602 ** 2.34 0.536** 2.44

0.620** 2.52 0.457** 2.16

0.641*** 2.66 0.435** 2.13

0.658*** 2.67 0.402* 1.86

0.610** 2.48 0.456** 2.13

0.660*** 2.62 0.462** 2.14

0.241*** 2.81 0.138 1.60

1.404*** 1.275*** 1.123*** 1.073*** 0.937** 3.35 3.19 2.80 2.67 2.28 Global three-factor alpha 0.165 0.250 0.508 0.531 0.780** 0.43 0.68 1.42 1.47 2.16 Panel C: Portfolios sorted on global liquidity risk with respect to US market, beta 4 All countries (excluding US) Global one-factor alpha 0.850*** 0.729*** 0.626** 0.671*** 0.614** 3.11 2.85 2.38 2.68 2.49 Global three-factor alpha 0.369 0.400* 0.541** 0.439** 0.482** 1.60 1.83 2.41 2.05 2.29

0.978** 2.43 0.631* 1.75

0.960** 2.39 0.633* 1.77

0.852** 2.18 0.711** 2.00

0.909** 2.35 0.600* 1.70

0.853** 2.07 0.780** 2.09

0.551*** 3.56 0.615*** 3.58

0.625*** 2.62 0.439** 2.16

0.558** 2.27 0.505** 2.36

0.684*** 2.69 0.435** 1.99

0.683*** 2.67 0.463** 2.14

0.702*** 2.71 0.447** 2.02

0.147** 2.44 0.078 1.19

0.448* 1.87 0.347 1.47

0.386 1.54 0.439* 1.78

0.555** 2.18 0.285 1.13

0.512** 1.97 0.396 1.58

0.518* 1.97 0.426* 1.69

0.142* 1.88 0.080 1.00

Panel A: Portfolios sorted on local liquidity risk, beta 2 All countries (excluding US) 0.563** 0.634*** Global one-factor alpha 0.545** 2.28 2.40 2.62 Global three-factor alpha 0.491** 0.441** 0.436** 2.35 2.14 2.10 Emerging markets Global one-factor alpha 0.848** 0.868** 0.975** 2.20 2.17 2.48 Global three-factor alpha 0.673* 0.691* 0.592* 1.93 1.89 1.66 Panel B: Portfolios sorted on local liquidity risk, beta 4 All countries (excluding US) Global one factor alpha 0.901*** 0.747*** 0.683*** 3.24 2.82 2.62 Global three-factor alpha 0.323 0.418* 0.487** 1.38 1.85 2.21 Emerging markets Global one-factor alpha

Developed markets (excluding US) Global one-factor alpha 0.660** 2.34 Global three-factor alpha 0.346 1.28

0.506* 1.95 0.414* 1.66

0.435 1.64 0.496* 1.94

0.498** 1.98 0.354 1.43

generates material trading alphas that are significant both statistically and economically.

8. Conclusion This paper empirically investigates an equilibrium asset pricing relation with liquidity, as specified in the LCAPM of Acharya and Pedersen (2005), using a large sample of assets covering 30,000 stocks from 50 countries around the world for the period of 1988–2007.

0.457* 1.86 0.389 1.63

The empirical evidence presented in this paper is supportive of the LCAPM in that liquidity risks are priced independently of market risk in international financial markets, even after controlling for liquidity level, size, and book-to-market. Specifically, it is shown that a security’s required return depends on the covariance of its own liquidity with the aggregate local market liquidity, as well as on the covariance of its own liquidity with local and global market returns. These findings imply that liquidity is an important concern when investors rebalance their portfolios in the face of down markets or illiquid


markets. Therefore, the findings have implications for international portfolio diversification, because liquidity risk is another dimension to consider in addition to traditional market risk.

159

By providing evidence that expected returns of stocks from around the world are affected by the covariance of liquidity with US market returns, I also show that the US market is a driving force of global liquidity risk.

Table A1 Cross-sectional regressions of local liquidity risk at the portfolio level. Each year, stocks are sorted into 10 or 25 equally weighted portfolios within a country on the basis of the previous year-end market capitalization, the previous year-end book-to-market ratio (B/M), and the previous year-average illiquidity. If the total number of stocks in a country shown in Table 1 is between 100 and 300, the stocks are sorted into 10 portfolios. If the number is larger than 300, the country has 25 portfolios. Market return and illiquidity are the value-weighted averages of the returns and illiquidity, which are aggregated at the local market level. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of the illiquidity. Each beta k (k= 1,y,4) of year t is estimated using the portfolio returns (in US dollars) and innovations in illiquidity over the years t 5 to t 1. The liquidity net beta, beta 5, is computed by Eq. (4). Local risks are obtained on the basis of the liquidity-adjusted capital asset pricing model of fully segmented world financial markets. Given the market beta as well as three liquidity betas, crosssectional regressions with country dummies are performed for each month. The table shows the averages of the estimated coefficients. ZR is the previous month’s average zero-return proportion. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Region

Intercept

ZR

Beta 1

Beta 2

Panel A: Size portfolios All countries 0.0049 0.0030 0.0044 0.0042 Developed 0.0060 0.0058 0.0067 0.0066 Emerging 0.0118* 0.0074 0.0114* 0.0107 US 0.0179*** 0.0131*** 0.0174*** 0.0171***

0.0224*** 0.0236*** 0.0227*** 0.0231*** 0.0208*** 0.0212*** 0.0219*** 0.0215*** 0.0292*** 0.0312*** 0.0271*** 0.0296*** 0.0242** 0.0264** 0.0223* 0.0218*

0.0029 0.0025 0.0022 0.0024 0.0096*** 0.0091*** 0.0093*** 0.0095*** 0.0081** 0.0076* 0.0095** 0.0094** 0.0102** 0.0079* 0.0109** 0.0106**

0.0068**

Panel B: B/M portfolios All countries 0.0041 0.0043 0.0038 0.0034 Developed 0.0053 0.0040 0.0055 0.0048 Emerging 0.0047 0.0033 0.0046 0.0049 US 0.0069 0.0064 0.0057 0.0060

0.0266*** 0.0269*** 0.0264*** 0.0267*** 0.0230*** 0.0236*** 0.0230*** 0.0233*** 0.0286*** 0.0291*** 0.0277*** 0.0280*** 0.0980*** 0.0758*** 0.0905*** 0.0873***

0.0025 0.0021 0.0020 0.0019 0.0029 0.0032 0.0034 0.0033 0.0149*** 0.0138*** 0.0148*** 0.0136*** 0.0078 0.0121** 0.0057 0.0069

Panel C: Illiquidity portfolios All countries 0.0123* 0.0105* 0.0112* 0.0113* Developed 0.0125*** 0.0105*** 0.0112*** 0.0105*** Emerging 0.0135** 0.0128* 0.0135** 0.0144** US 0.0249*** 0.0188*** 0.0200*** 0.0184***

0.0168*** 0.0171*** 0.0160*** 0.0168*** 0.0142*** 0.0150*** 0.0148*** 0.0155*** 0.0209*** 0.0218*** 0.0179*** 0.0192*** 0.0071 0.0003 0.0002 0.0030

0.0072*** 0.0074*** 0.0076*** 0.0076*** 0.0066** 0.0068** 0.0069** 0.0070** 0.0125*** 0.0117*** 0.0117*** 0.0128*** 0.0127** 0.0068 0.0108** 0.0095*

Beta 3

Beta 4

Beta 5

0.0051 0.0034* 0.0007 0.0067* 0.0096 0.0017 0.0021 0.0050 0.0215 0.0202*** 0.0079** 0.1400** 0.0268 0.0165* 0.0116 0.0060** 0.0131** 0.0071*** 0.0050*** 0.0079*** 0.0003 0.0040*** 0.0015 0.0017 0.0287*** 0.0159*** 0.0137*** 0.0349 0.1331*** 0.0281*** 0.0293*** 0.0117*** 0.0053 0.0050** 0.0008 0.0201*** 0.0061 0.0011 0.0034** 0.0103 0.0007 0.0153*** 0.0118*** 0.2630*** 0.0839** 0.0286** 0.0297***

160


Table A2 Cross-sectional regressions of global liquidity risk at the portfolio level. Each year, stocks are sorted into 10 or 25 equally weighted portfolios within a country on the basis of the previous year-end market capitalization, the previous year-end book-to-market ratio (B/M), and the previous year-average illiquidity. If the total number of stocks in a country shown in Table 1 is between 100 and 300, the stocks are sorted into 10 portfolios. If the number is larger than 300, the country has 25 portfolios. Market return and illiquidity are the value-weighted averages of the returns and illiquidity which are aggregated at the global level. The innovations in illiquidity are obtained from AR(1) filtering of the first-differences of illiquidity. Each beta k (k= 1,y,4) of year t is estimated using portfolio returns (in US dollars) and innovations in illiquidity over the years t 5 to t 1. The liquidity net beta, beta 5, is defined in a manner similar to Eq. (4). Global risks are obtained on the basis of the liquidity-adjusted capital asset pricing model of fully integrated world financial markets. Given the market beta as well as three liquidity betas, crosssectional regressions with country dummies are performed for each month. The table shows the averages of the estimated coefficients. ZR is the previous month’s average zero-return proportion. ZR is tested against the alternative hypothesis of positive coefficients, while the others are two-tailed tests. *, **, and *** denote significance at the 10%, 5%, and 1% level, respectively. Region

Intercept

ZR

Beta 1

Beta 2

Panel A: Size portfolios All countries 0.0080 0.0085 0.0081 0.0082 Developed 0.0011 0.0018 0.0010 0.0011 Emerging 0.0094 0.0094 0.0094 0.0093 US 0.0079 0.0082 0.0103* 0.0100*

0.0224*** 0.0223*** 0.0225*** 0.0226*** 0.0199*** 0.0193*** 0.0201*** 0.0202*** 0.0304*** 0.0310*** 0.0311*** 0.0313*** 0.0348** 0.0312** 0.0272** 0.0280**

0.0018 0.0014 0.0019 0.0018 0.0020 0.0023 0.0020 0.0020 0.0042** 0.0036* 0.0042** 0.0041** 0.0087 0.0098 0.0105 0.0102

0.0069

Panel B: B/M portfolios All countries 0.0063 0.0060 0.0065 0.0064 Developed 0.0049 0.0036 0.0044 0.0042 Emerging 0.0035 0.0039 0.0041 0.0042 US 0.0026 0.0045 0.0002 0.0003

0.0268*** 0.0265*** 0.0265*** 0.0264*** 0.0230*** 0.0227*** 0.0233*** 0.0234*** 0.0297*** 0.0294*** 0.0292*** 0.0292*** 0.0896*** 0.0892*** 0.0774*** 0.0791***

0.0014 0.0017 0.0015 0.0015 0.0038** 0.0040** 0.0036** 0.0036** 0.0013 0.0007 0.0008 0.0008 0.0012 0.0023 0.0003 0.0002

0.0052

Panel C: Illiquidity portfolios All countries 0.0096 0.0095 0.0097 0.0097 Developed 0.0090** 0.0071* 0.0077** 0.0073** Emerging 0.0098 0.0098 0.0100 0.0100 US 0.0160** 0.0176*** 0.0168** 0.0172***

0.0173*** 0.0187*** 0.0179*** 0.0182*** 0.0150*** 0.0164*** 0.0157*** 0.0160*** 0.0203*** 0.0222*** 0.0212*** 0.0217*** 0.0060 0.0023 0.0030 0.0017

0.0040** 0.0042*** 0.0042*** 0.0042*** 0.0042* 0.0046** 0.0043** 0.0043** 0.0063*** 0.0061*** 0.0063*** 0.0065*** 0.0052 0.0071 0.0070 0.0077

0.0280***

Furthermore, the empirical results presented in this paper show that the world price of liquidity risk is more important than its local counterpart in countries where

Beta 3

Beta 4

Beta 5

0.0097 0.0014 0.0012 0.0009 0.0086 0.0000 0.0001 0.0143 0.0208 0.0029* 0.0028 0.0095 0.0580 0.0160** 0.0134*

0.0187** 0.0023*** 0.0019** 0.0085 0.0245*** 0.0001 0.0003 0.0018 0.0140 0.0031* 0.0030* 0.0088 0.0140 0.0263*** 0.0243***

0.0008 0.0025** 0.0011 0.0319*** 0.0143 0.0031** 0.0013 0.0276*** 0.0024 0.0021 0.0010 0.0502 0.0356 0.0199** 0.0183**

more global investors are present—specifically, in developed countries and in countries with high transparency, low political risk, and large cross-border investment


flows. This finding sheds some lights on the importance of global investment and on the relatively high degree of integration in these countries. An important limitation of this study is that only the unconditional version of the global LCAPM has been tested. An interesting extension would be to test the conditional version of the LCAPM, in which liquidity risks vary over time in a way that depends on predetermined information variables. Such an extension could allow for investigation of the determinants of the time-varying liquidity risk premium in international financial markets. Based on the results in this paper, it is plausible that the economic variables that affect US market returns would also influence time-varying liquidity risk in world financial markets. 9. Appendix A Cross-sectional regressions of local liquidity risk at the portfolio level is shown in Table A1 and cross-sectional regressions of global liquidity risk at the portfolio level is shown in Table A2. References Acharya, V.V., Pedersen, L.H., 2005. Asset pricing with liquidity risk. Journal of Financial Economics 77, 375–410. Amihud, Y., 2002. Illiquidity and stock returns: cross-section and timeseries effects. Journal of Financial Markets 5, 31–56. Amihud, Y., Mendelson, H., 1986. Asset pricing and the bid-ask spread. Journal of Financial Economics 17, 223–249. Bekaert, G., Harvey, C.R., 1995. Time-varying world market integration. Journal of Finance 50, 403–444. Bekaert, G., Harvey, C.R., Lundblad, C., 2007. Liquidity and expected returns: lessons from emerging markets. Review of Financial Studies 20, 1783–1831. Berk, J.B., 2000. Sorting out sorts. Journal of Finance 55, 407–427. Brennan, M.J., Chordia, T., Subrahmanyam, A., 1998. Alternative factor specifications, security characteristics, and the cross-section of expected stock returns. Journal of Financial Economics 49, 345–373. Brennan, M.J., Subrahmanyam, A., 1996. Market microstructure and asset pricing: on the compensation for illiquidity in stock returns. Journal of Financial Economics 41, 441–464. Brockman, P., Chung, D.Y., 2003. Investor protection and firm liquidity. Journal of Finance 58, 921–937. Brockman, P., Chung, D.Y., Pe´rignon, C., 2009. Commonality in liquidity: a global perspective. Journal of Financial and Quantitative Analysis 44, 851–882. Brunnermeier, M.K., Pedersen, L.H., 2009. Market liquidity and funding liquidity. Review of Financial Studies 22, 2201–2238. Bushman, R.M., Piotroski, J.D., Smith, A.J., 2004. What determines corporate transparency? Journal of Accounting Research 42, 207–252 Chan, K., Covrig, V., Ng, L., 2005. What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide. Journal of Finance 60, 1495–1534. Chan, K.C., Karolyi, G.A., Stulz, R.M., 1992. Global financial markets and the risk premium on U.S. equity. Journal of Financial Economics 32, 137–167. Chiyachantana, C.N., Jain, P.K., Jiang, C., Wood, R.A., 2004. International evidence on institutional trading behavior and price impact. Journal of Finance 59, 869–898. Chordia, T., Roll, R., Subrahmanyam, A., 2000. Commonality in liquidity. Journal of Financial Economics 56, 3–28. Coughenour, J.F., Saad, M.M., 2004. Common market makers and commonality in liquidity. Journal of Financial Economics 73, 37–69. Eleswarapu, V.R., Venkataraman, K., 2006. The impact of legal and political institutions on equity trading costs: a cross-country analysis. Review of Financial Studies 19, 1081–1111. Errunza, V., Losq, E., 1985. International asset pricing under mild segmentation: theory and test. Journal of Finance 40, 105–124.

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Disagreement and return predictability of stock portfolios$ Jialin Yu Department of Finance and Economics, Graduate School of Business, Columbia University, 421 Uris Hall, 3022 Broadway, New York, NY 10027, USA


abstract

Article history: Received 27 February 2009 Received in revised form 23 November 2009 Accepted 7 March 2010 Available online 7 August 2010

This paper provides evidence that portfolio disagreement measured bottom-up from individual-stock analyst forecast dispersions has a number of asset pricing implications. For the market portfolio, market disagreement mean-reverts and is negatively related to ex post expected market return. Contemporaneously, an increase in market disagreement manifests as a drop in discount rate. For book-to-market sorted portfolios, the value premium is stronger among high disagreement stocks. The underperformance by high disagreement stocks is stronger among growth stocks. Growth stocks are more sensitive to variations in disagreement relative to value stocks. These findings are consistent with asset pricing theory incorporating belief dispersion. & 2010 Elsevier Ltd All rights reserved.

JEL classification: G12 Keywords: Disagreement Equity premium Discount rate Value premium

1. Introduction This paper analyzes the asset pricing implications of disagreement for a portfolio of assets. The idea that disagreement can matter for equilibrium asset price and expected return is shown in Miller (1977)—if pessimists face short-sales constraints, the price of an asset reflects the valuation of optimists. One implication is that greater disagreement is associated with higher price and lower

$ I thank Andrew Ang, Rachel A.J. Campbell (discussant), Douglas Diamond, Michael Gallmeyer, Larry Glosten, Robert Hodrick, Harrison Hong (discussant), Narasimhan Jegadeesh (discussant), Jong-Wook Kim (discussant), Paul Tetlock, Rossen Valkanov, Wei Xiong, Hongjun Yan (discussant), Motohiro Yogo, Kathy Yuan (discussant), Hong Zhang (discussant), and seminar participants at the 18th Annual Conference on Financial Economics and Accounting, Asian FA and NFA International conference, Columbia University, CUNY Baruch College, CUNY Graduate Center, European Finance Association annual meeting, Fordham University, NBER Behavioral Finance meeting, NYU Stern Five-Star Conference on Research in Finance, Princeton University, SAC Capital Advisors, the Tenth Texas Finance Festival, University of Alberta Banff conference for helpful comments. E-mail address: [email protected] URL: http://www0.gsb.columbia.edu/faculty/jyu

0304-405X/$ - see front matter & 2010 Elsevier Ltd All rights reserved. doi:10.1016/j.jfineco.2010.08.004

subsequent return.1 This prediction is supported by the cross-sectional evidence in Chen, Hong, and Stein (2002) and Diether, Malloy, and Scherbina (2002). The mechanism in Miller (1977) has a direct corollary for portfolios: greater portfolio disagreement is associated with lower subsequent portfolio return. This prediction is under-explored, with the exception of Park (2005) who finds supportive evidence for the market portfolio by measuring market disagreement top-down using analyst forecast dispersion of Standard & Poor’s (S&P) 500 index annual earnings-per-share (EPS). It is not so straightforward, however, to gauge disagreement for a portfolio of assets. Portfolio disagreement can alternatively be constructed bottom-up by aggregating disagreements regarding the individual assets in the portfolio. Bottom-up measure of disagreement likely offers a better signal-to-noise ratio than the top-down measure. Bottom-up disagreement is constructed using thousands of individual-stock forecasts while there are, on average,

1 See also Harrison and Kreps (1978), Harris and Raviv (1993), and Scheinkman and Xiong (2003). Hong and Stein (2007) provide a recent review of this literature.

J. Yu / Journal of Financial Economics 99 (2011) 162–183

only 20 or so analysts in the sample covering S&P 500 EPS. The analysts’ effort likely mirrors investors’ focus on stock picking. Some individual-stock disagreements may not be reflected in the top-down disagreement but can be discerned from the bottom-up disagreement. For example, investors may agree on the future prospect of the market. In this case, there may appear to be little disagreement from the top-down measure. However, still waters run deep. Investors may disagree on which stocks will lead/lag the market; hence, strong disagreement may exist and can be discerned from the bottom up, which may make the bottom-up disagreement a better proxy of the belief dispersion within the market. Using the Institutional Brokers’ Estimate System (I/B/E/S) database on analyst forecast, this paper finds that the ex post market return is negatively related to the bottom-up disagreement, consistent with Miller (1977). The bottom-up disagreement works substantially better than the top-down disagreement. The result holds for a variety of bottom-up disagreement constructions, from value-weighting to equal-weighting of individual-stock forecast dispersions, and from using long-term EPS growth rate forecasts to near-term fiscal period EPS forecasts.2 For example, a one-standard-deviation increase in the bottom-up disagreement measured from value-weighted individual-stock long-term EPS growth rate forecast dispersions is associated with a statistically and economically significant drop in the expected one-year market return of 6.6% (e.g., from 9% to 2.4%). The horizon for the low ex post return is consistent with the speed of mean reversion in disagreement. This paper finds that disagreement mean-reverts slowly. Shocks to the disagreement have a half-life of about one year and largely mean-revert within three years. Consistent with the speed of mean reversion, the return implications are found to be stronger for one-year to three-year return horizons. The effect of disagreement is robust to controlling for a host of alternative hypotheses, including all the variables reviewed in Campbell and Thompson (2008) and Goyal and Welch (2008), which are found by earlier studies to correlate with market return. The paper also tests a pillar of the disagreement model—positive contemporaneous correlation between portfolio return and shocks to disagreement. That is, price becomes higher when there is more disagreement, which is the source of the low ex post return. This indeed holds for the market portfolio. Further, shocks to disagreement are found to correlate more with discount-rate news than with cash-flow news in the Campbell and Shiller (1989) return decomposition. Higher disagreement manifests as lower discount rate. Discount-rate news and cash-flow

2 When using forecasts for individual-stock annual or quarterly EPS, the effect of company guidance of annual or quarterly earnings should be accounted for (see Section 4). Annual or quarterly EPS forecasts also requires scaling, which may introduce variations unrelated to disagreement (Qu, Starks, and Yan, 2004; Cen, Wei, and Zhang, 2007). Therefore, in the following discussions, this paper features forecasts on long-term EPS growth rate. Because the top-down forecasts are typically made for value-weighted market benchmarks, this paper features value-weighted bottom-up disagreement to facilitate comparison.

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news have distinct implications for asset pricing. A number of studies have relied on the discount-rate variation to address asset-pricing challenges. Fama and French (1988a), Campbell and Shiller (1989), and Campbell and Vuolteenaho (2004) use the discount-rate effect to address the time-varying equity premium and the value premium. However, it is unclear what drives the variations in discount rate. Fama and French (1988a, p. 5) point out, ‘‘The interesting economic question, motivated but unresolved by our results, is whether the predictability of returns implied by such temporary price components is driven by rational economic behavior yor by animal spirits.’’ Campbell and Vuolteenaho (2004) echo that their paper is ‘‘silent on what is the ultimate source of variation in the market’s discount rate’’ (p. 1270) and conjecture that ‘‘it is possible that our discount-rate news is simply news about investor sentiment’’ (p. 1261). The relation between disagreement and discount-rate news adds to our understanding of discount-rate variations. This relation, together with the empirical finding in Campbell and Vuolteenaho (2004) that growth stocks are more sensitive to the discount-rate news than value stocks, predicts the mean reversion of disagreement affects growth stocks more than value stocks. Consistently, this paper finds that a one-standard-deviation increase in disagreement is associated with a drop in ex post one-year growth (or value) stock return by 8.17% (or 2.58%). Consequently, there is evidence of time-varying expected Fama and French (1993) high-minus-low (HML) book-to-market portfolio return associated with disagreement. Another implication of the Miller (1977) model that is empirically under-explored is the interaction between disagreement and the optimism of the marginal investor. The negative relation between the ex post return and belief standard deviation should be twice as large if the marginal investor’s belief is two standard deviations above fundamental instead of one standard deviation above fundamental. The marginal investor is not directly observable. Nonetheless, this restriction yields a number of testable implications if there exists a set of test assets whose marginal investors have different optimism. This paper uses portfolios sorted on the book-to-market ratio as test assets. Low book-to-market stocks (growth stocks) historically have lower returns than high book-to-market stocks (value stocks). There is some evidence that growth stock investors are overly optimistic.3 Assuming the marginal investors in growth stocks are more optimistic, the interaction between marginal investor and disagreement implies: (i) high disagreement stocks have low return and the effect is stronger for growth stocks; (ii) growth stocks have low return and the effect is stronger for high disagreement stocks; (iii) contemporaneously, growth stock returns are more positively correlated with variations in disagreement than value stocks; (iv) ex post, growth stock returns are more negatively correlated with disagreement than value 3 See Lakonishok, Shleifer, and Vishny (1994) and La Porta (1996). The risk-based explanation of the value premium is not the focus of this paper, though the finding that disagreement relates to discount-rate news also has implications for the risk of value/growth stocks.

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stocks. These predictions are all confirmed in the data, thus lending further support to the disagreement mechanism and adding to our understanding of the value premium. This finding also provides a potential explanation to the sensitivity of growth stock return to discount-rate news found in Campbell and Vuolteenaho (2004).4 The bottom-up approach to measuring portfolio disagreement helps here because analysts rarely provide top-down forecasts for customized portfolios. Taken together, the evidence on equity premium, discount rate, and value premium provides strong support for the hypothesis that disagreement matters for the equilibrium price and expected return in the stock market. It is likely promising to explore the implications of disagreement for other markets. The conditions of disagreement and short-sales constraint likely hold for houses, art, or tulip bulbs with various shapes, etc. The distinction between top-down and bottom-up disagreement will also likely be important. For example, does measuring disagreement top-down capture adequately the belief dispersion in the national housing market if homebuyers tend to focus on the local housing market condition? These questions are left for future work. This paper is organized as follows. Section 2 discusses the bottom-up measure of disagreement. The relation between disagreement and ex post market return is tested in Section 3. Section 4 compares the bottom-up and top-down approaches. The relation between disagreement, discount-rate news, and time-varying value premium is examined in Section 5. Section 6 analyzes the interaction between disagreement and marginal investor optimism using portfolios sorted by book-to-market ratio. Section 7 performs robustness checks. Section 8 concludes. 2. Bottom-up measure of portfolio disagreement This paper uses analyst forecasts of the earnings-pershare (EPS) long-term growth rate (LTG) as the main proxy for investors’ beliefs regarding the future prospects of individual stocks. The data are provided by the I/B/E/S database. This measure is used in a number of studies (e.g., Moeller, Schlingemann, and Stulz, 2007). The longterm forecast has several advantages. First, it features prominently in valuation models. Second, it is less affected by a firm’s earnings guidance relative to shortterm forecasts (see Section 4). Because the long-term forecast is an expected growth rate, it is directly comparable across firms or across time. Analyst forecasts from December 1981 through December 2005 are used in this study. For each firm i in each month t, the average and the standard deviation of analyst forecasts of EPS LTG are obtained from the unadjusted I/B/E/S summary database and denoted as 4 The effect from disagreement complements the finding in Campbell, Polk, and Vuolteenaho (2010) that some of the cross-sectional variations in stock return sensitivity to discount-rate news are associated with the cross-sectional variations in the sensitivity of the stock fundamental to discount-rate news.

mi,t and si,t , respectively.5 Monthly stock closing prices and shares outstanding are obtained from the Center for Research in Security Prices (CRSP). Only common stocks (CRSP item SHRCD= 10 or 11) listed on the NYSE/Amex/ Nasdaq are included. Let MKTCAPi,t denote the market capitalization of stock i at the end of month t. The portfolio disagreement, measured bottom-up, is the cross-sectional value-weighted average of individualstock disagreement, , X X st ¼ MKTCAPi,t si,t MKTCAPi,t : ð1Þ i

i

The cross-sectional value-weighted average of individualstock average forecast is , X X mt ¼ MKTCAPi,t mi,t MKTCAPi,t : i

i

Unless otherwise stated, Sections 3–5 study the disagreement of the market portfolio and Section 6 studies the disagreement of book-to-market sorted portfolios. Fig. 1 plots the time series of st for the market portfolio. Table 1 provides summary statistics. Both mi,t and si,t are in percentages. The time-series average of s is 3.23% and the time-series average of m is 14.23%. On average, analysts expect the EPS of a typical stock to grow at 14.23% per year and the forecast standard deviation is 3.23%.6 3. Disagreement and time-varying equity premium 3.1. Mean reversion of disagreement To study the relation between disagreement and return, this section begins by analyzing the mean reversion property of disagreement. In the Miller (1977) model, if disagreement does not vary, it has only a level effect on prices but does not generate time-varying expected returns. Therefore, this section runs the following regression:

st ¼ a þ b stlag þ et :

ð2Þ

The lag ranges from one month to three years. The results are reported in Table 2. Disagreement is positively autocorrelated. At the one-month lag, the auto-correlation 5 Diether, Malloy, and Scherbina (2002) find that the I/B/E/S summary file closely tracks the summary statistics constructed from the I/B/E/S detailed file. mi,t and si,t are winsorized at 1% and 99% levels to account for potential outliers or data errors. Due to the large number of firms involved in the data construction, the result is insensitive to winsorizing. The pairwise correlation between winsorized and nonwinsorized disagreement is 0.982 for the market portfolio and the results in this paper are essentially the same using the non-winsorized variables. 6 It is shown that analyst forecasts may be biased (e.g., De Bondt and Thaler, 1990; Chan, Karceski, and Lakonishok, 2003). But it is unclear that a bias in the mean will affect the forecast standard deviation and its time-series variation in a systematic way. As shown in La Porta (1996), I/B/E/S coverage is tilted towards big stocks, though the performance of stocks in I/B/E/S is not statistically different from stocks in CRSP. The lack of small stock coverage in I/B/E/S has minimal impact on s because of value weight.


165

4.5

Disagreement (%)

4

3.5

3

2.5

1985

1990

1995 Year

2000

2005

Fig. 1. Time series of disagreement. This figure plots the monthly disagreement s, which is the cross-sectional value-weighted average of analyst forecast standard deviations of long-term EPS growth rate. The sample period is December 1981–December 2005.

Table 1 Summary statistics. Panel A reports summary statistics for s and m. s (m) is the cross-sectional value-weighted average of analyst forecast standard deviation (average forecast) of individual-stock long-term EPS growth rate. The analysts’ forecast standard deviations and average forecasts are winsorized at the 1% and 99% levels to construct s and m. s and m are in percentages. Panel B reports summary statistics for various portfolio returns. RM t,t + h is the market return measured by the CRSP value-weighted return (including distributions) in excess of linked one-month T-bill rate from month t to t+ h. NDR and NCF are the discount-rate and cash-flow news from the return decomposition in Campbell and Vuolteenaho (2004). For each variable, the sample period, number of observations (# obs), time-series average (avg), standard deviation (std dev), minimum (min), and maximum (max) are reported. Sample period t

# Obs

Avg

Std dev

Min

Max

Panel A: Proxies of beliefs (%) st 1981.12–2005.12 mt 1981.12–2005.12

289 289

3.23 14.23

0.38 1.76

2.70 12.37

4.42 20.82

Panel B: Market portfolio return ( 100) RM 1981.12–2005.12 t,t + 1 RM 1981.12–2005.12 t,t + 6 RM 1981.12–2005.12 t,t + 12 RM 1981.12–2004.12 t,t + 24 M Rt,t + 36 1981.12–2003.12 DR Nt 1,t 1981.12–2001.12 CF Nt 1,t 1981.12–2001.12

289 289 289 277 265 241 241

0.68 4.37 9.17 18.64 30.93 0.42 0.13

4.41 11.09 16.32 23.60 33.16 4.83 2.21

23.13 27.97 34.71 48.73 52.48 17.20 10.55

12.43 37.60 58.36 65.59 106.04 21.18 5.48

coefficient is 0.93 and highly statistically significant. The auto-correlation gradually decays over longer lags. The speed of decay is roughly in line with an autoregressive model with order one (AR(1)).7 At the one-year horizon, the regression slope is 0.54, which implies that the half-life of a shock to disagreement is about one year. The slope estimate is close to zero at the three-year horizon, at which point shocks to disagreement have largely reverted. Also reported in Table 2 is the mean of disagreement implied by the regression estimates (i.e., implied mean= a=ð1bÞ). The implied mean is around 3.2%, consistent with the sample average in Table 1.

7 The Bayes information criterion (BIC) also suggests that the autoregressive order of disagreement is one. The BIC result is unreported for brevity.

Table 2 Mean reversion of disagreement. This table reports the regression results of: st ¼ a þ b stlag þ et , where s is the cross-sectional value-weighted average of individualstock disagreements (measured by analyst forecast standard deviations of long-term EPS growth rate). The lag ranges from one month to three years. Also reported is the mean of s implied by the regression estimates, i.e., implied mean = a=ð1bÞ. The t-statistics in parentheses are adjusted for auto-correlation of 36 monthly lags using Newey and West (1987). The sample period is December 1981–December 2005.

Lag (in months)

stlag t-stat Constant t-stat Implied mean of s

(1) 1

(2) 6

(3) 12

(4) 24

(5) 36

0.930 (34.40) 0.225 (2.65) 3.20

0.751 (12.04) 0.807 (3.92) 3.24

0.540 (5.96) 1.473 (4.85) 3.20

0.193 (1.46) 2.556 (5.22) 3.17

0.041 (0.24) 3.039 (4.85) 3.17

166


Ex post one−year excess market return

0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1 −0.2 Observations Nonparametric mean estimate Pointwise 95% confidence band

−0.3 −0.4 2.6

2.8

3

3.2

3.4 3.6 3.8 4 Disagreement (%)

4.2

4.4

Fig. 2. Disagreement and ex post market return. This figure shows the scatterplot of disagreement s and ex post one-year CRSP value-weighted market return in excess of the risk-free rate. s is measured by the cross-sectional value-weighted average of analyst forecast standard deviations of long-term EPS growth rate. Also plotted is a local polynomial nonparametric estimate (Fan and Gijbels, 1996) of the expected ex post one-year excess return conditioning on s (implemented by the LOWESS procedure in the software package Stata using the default bandwidth). The 95% pointwise confidence band adjusts for the correlation of overlapping annual returns using the Newey and West (1987) standard error with 12 lags. The sample is monthly and spans December 1981–December 2005.

The evidence suggests that disagreement slowly mean-reverts. Only a small fraction of shocks to disagreement decay within one month. Shocks have a half-life of about a year and more than 80% mean-revert in two years. The remaining 20% largely reverts in the third year. This finding indicates that the effect of disagreement on returns is likely stronger for the one- and two-year return horizons, which is confirmed in the subsequent sections. 3.2. Disagreement and ex post market return Monthly data on market returns (NYSE/Amex/Nasdaq value-weighted index returns including distributions), individual-stock returns, and Treasury bill (T-bill) rates from 1981 to the end of 2006 are obtained from CRSP. Let RM denote the market return in excess of the T-bill rate. Table 1 shows that RM averages to 9.17% per year with a standard deviation of 16.32% in the sample. Fig. 2 shows a scatterplot of ex post one-year market return against disagreement. A negative relation is visible, which is confirmed by a nonparametric estimate of the expected return conditioning on disagreement. The upper 95% confidence interval for observations with the highest disagreement indicates a 5.64% annual return, which is below the lower 95% confidence interval for the return of observations with the lowest disagreement (10.4% annual return). Observations with low disagreements tend to have positive returns; observations with high disagreements tend to have negative returns (though more volatile). Further, the negative relation between return and disagreement is approximately linear, which motivates the following linear regression: RM t,t þ h ¼ a þ b st þ et ,

ð3Þ

where RM t,t + h is the excess market return from month t to t+h.8 The horizon h ranges from one month to three years. The results are in Panel A of Table 3. The coefficient of disagreement is negative for all return horizons. Disagreement has the least explanatory power at the one-month horizon, consistent with Table 2 that little disagreement mean-reverts within one month. At the one-year horizon, the coefficient of disagreement is 0.174 and is statistically significant (t-stat = 2.59). The economic magnitude is large—a one-standard-deviation increase in disagreement is associated with a 6.6% reduction in ex post one-year market return (e.g., 9% to 2.4%). To put the economic magnitude in perspective, the mean and the standard deviation of the one-year market return during the sample period are 9% and 16%, respectively. The effect of disagreement in Panel A roughly doubles going from a one-year to two-year return horizon and further increases slightly for the three-year return horizon. The results are consistent with the mean reversion speed of disagreement. Next, the regression controls for the expected level of EPS long-term growth rate (m) and the price-earnings ratio (PE), RM t,t þ h ¼ a þ b st þ g mt þ d PEt þ et :

ð4Þ

The rationale for these controls is that high disagreement may coexist with expectations of high growth rate and high valuation ratios. Since a measure like PE is an imperfect indicator of overvaluation, it is useful to see if disagreement provides incremental explanatory power. 8 All the regressions in this paper have been re-run using raw market return instead of excess return over the risk-free rate. The results are similar and therefore unreported.


167

Table 3 Disagreement and time-varying equity premium. Panel A reports the regression results of ex post market return in excess of the risk-free rate on s. Panel B repeats the regression in Panel A, controlling for m and PE (price-earnings ratio). s (m) is the value-weighted average of analyst forecast standard deviation (average forecast) of individual-stock longterm EPS growth rate. PE is constructed monthly from the S&P composite index and its earnings, both of which are from Robert Shiller’s Web site. Panel C repeats the regression in Panel A, controlling for PE using non-overlapping returns. Panel D reports the Hodrick (1992) t-statistics for the regression in pffiffiffi Panel A except that the market return is in log scale following Hodrick (1992). Panel D also reports the Valkanov (2003) t= T statistic and p-value for the regression R-square. Panel E regresses one-month ex post excess market return, also in log scale, on lagged h-month average (denoted MA(h)) of s. Panel E estimates the magnitude of the Stambaugh (1999) bias via a simulation where the ‘‘true’’ coefficients are set to the regression estimates. Panel E reports the p-value of the lagged average of s by comparing the t-statistic in the actual regression to the distribution of the t-statistics in a second simulation which is identical to the first simulation except that the ‘‘true’’ coefficient is set to zero. Panel E also reports the Campbell and Yogo (2006) Bonferroni Q-test confidence interval (C.I.) for the lagged average of s. Panels F and G report the regression results of ex post excess market return on s, controlling for a host of other variables reviewed in Campbell and Thompson (2008) and Goyal and Welch (2008) that correlate with ex post market return. Panel F controls for these other variables one-by-one. */**/*** indicate statistical significance at the 90%/95%/99% levels. Panel G controls for all of these variables in one regression. The first (second) adjusted R-square in Panel G is for the regression of ex post market return on all the controls with (without) s. CAY is measured quarterly in Panel F and is converted to monthly in Panel G using the last available quarterly observation. The other variables are measured monthly. For brevity, only the coefficient of s is shown in Panels F and G. The t-statistics in Panels A–B and F–G are adjusted for auto-correlation using Newey and West (1987), with the number of lags being equal to the return horizons. The t-statistics in Panels C and E are adjusted for heteroskedasticity (White, 1980). The sample period is December 1981–December 2005. Return horizon (in months)

1

6

12

24

36

0.061 (1.51) 0.240 (1.94) 4.0%

0.174 (2.59) 0.654 (3.16) 16.2%

0.351 (2.92) 1.317 (3.48) 32.8%

0.443 (2.12) 1.734 (2.70) 27.4%

0.163 (2.82) 0.004 (0.24) 0.007 (2.03)

0.280 (2.69) 0.017 (0.53) 0.007 (1.37)

0.335 (1.73) 0.023 (0.44) 0.012 (1.50)

0.061 (1.23) 0.003 (1.77) 49

0.127 (2.06) 0.005 (1.41) 25

0.281 (1.92) 0.008 (1.97) 12

0.704 (2.68) 0.003 (0.22) 8

pffiffiffi Panel D: Hodrick (1992) t-statistics and Valkanov (2003) t= T statistics s 0.007 0.064 Hodrick (1992) t-stat (0.04) (1.59) pffiffiffi 0.057 0.234 t OLS = T pffiffiffi 0.374 0.112 p-value of t OLS = T

0.174 (2.16) 0.492

0.321 (2.21) 0.770

0.378 (2.03) 0.725

Panel A: Ex post excess market return on disagreement s s 0.006 t-stat (0.88) Constant 0.027 t-stat (1.21) Adj R2 0.1%

Panel B: Controlling for expected long-term growth rate m and price-earnings ratio PE s 0.000 0.041 t-stat (0.00) (0.95) m 0.002 0.003 t-stat (0.65) (0.29) PE 0.000 0.003 t-stat (1.19) (1.73) Panel C: Non-overlapping return regressions

s t-stat PE t-stat Number of observations

R2 p-value of R2

0.004 (0.58) 0.001 (1.83) 289

0.3% 0.327

5.2% 0.092

0.018

0.006

0.018

19.6% 0.012

37.4% 0.004

34.6% 0.014

Panel E: Non-overlapping return regressions using Hodrick (1992) specification 0.0067 0.0118 MA(h)of s t-stat (0.96) (1.59) Adj R2 0.0% 0.6% Stambaugh (1999) bias 0.0008 0.0011 p-value of s 0.350 0.121 Campbell and Yogo (2006) 90% C.I. Lower 0.0165 0.0247 Upper 0.0070 0.0007

0.0189 (2.40) 1.9% 0.0013 0.018

0.0218 (2.40) 2.0% 0.0023 0.019

0.0186 (1.81) 1.0% 0.0028 0.074

0.0310 0.0051

0.0349 0.0062

0.0338 0.0001

Panel F: Coefficients of disagreement s, controlling one-by-one for other return predictors PE 0.004 0.048 CAY (quarterly) 0.012 0.056 DP 0.006 0.058 SMOOTHEP 0.007 0.068** BM 0.006 0.063* SHORTYIELD 0.006 0.064* LONGYIELD 0.006 0.064* TERMSPREAD 0.006 0.059 DFSPREAD 0.009 0.085*** INFLATION 0.006 0.061 EQUITYSHARE 0.006 0.074**

0.152*** 0.166** 0.168*** 0.190*** 0.179*** 0.185*** 0.184*** 0.169*** 0.226*** 0.173*** 0.207***

0.323*** 0.285** 0.344*** 0.372*** 0.358*** 0.361*** 0.366*** 0.337*** 0.402*** 0.350*** 0.415***

0.394*** 0.233 0.433*** 0.481*** 0.457*** 0.467** 0.472*** 0.419** 0.523*** 0.441** 0.572***

168


Table 3 (continued ) Return horizon (in months)

1

6

Panel G: Coefficients of disagreement s, controlling for other return predictors together s 0.004 0.064 t-stat (0.45) (1.66) All other variables Adj R2 4.1% 22.1% Adj R2 without s 4.4% 20.1%

The results are shown in Panel B of Table 3. The economic and statistical significances of disagreement remain similar. The level of the expected growth rate has essentially no effect on return, consistent with the explanation that the aggregate market has incorporated the level of expected future growth.9 The market return is negatively associated with PE. The effect of PE is statistically significant for the one-year return horizon, and is marginally significant for the other horizons. This raises the question of whether the effect of disagreement is robust to controlling for alternative mechanisms that affect the equity premium. Before investigating this, some econometric issues related to the baseline specification (3) are addressed in Sections 3.3 and 3.4.

3.3. Long-horizon return regression The return horizons in regression (3) range from one month to three years. An econometric issue arises because observations of long-horizon returns overlap, which potentially biases the test towards rejecting the null hypothesis of zero explanatory power (e.g., Richardson and Stock, 1989; Hodrick, 1992). Newey and West (1987) t-statistics have been used to account for the overlapping returns. Additional econometric tests are now applied to ensure valid inference. When the return horizon is h, the simplest way to avoid overlapping returns is to use only observations sampled at time t ¼ 0,h,2h,3h, . . .. In this case, the return from time 0 to h does not overlap with the return from time h to 2h. The result using this simple non-overlapping specification is in Panel C of Table 3, which also controls for PE, found earlier to correlate with returns. Returns of all horizons remain negatively correlated with disagreement and the relation is statistically significant for the one- to threeyear horizons. However, this simple non-overlapping specification is not ideal. The problem is that very few observations are left in the long-horizon regressions and the inference depends on the small sample performance of the asymptotic distribution. This problem results from a loss of information in the simple specification. Because only observations at time 0,h,2h,yare used, in-between information on disagreement is discarded. Two methods are used to address this problem. The first method, studied in the rest of this section, uses the overlapping return specification in (3) but applies asymptotic distributions in 9 This time-series result differs but is not inconsistent with the cross-sectional result in La Porta (1996), who finds that stocks with rosy analyst expectations tend to do poorly afterwards.

12

24

36

0.261 (6.27) 38.9% 21.7%

0.438 (7.56) 58.6% 34.4%

0.412 (6.72) 65.4% 54.3%

Hodrick (1992) and Valkanov (2003) that are specifically designed for the overlapping regression setup. The second method, studied in Section 3.4, uses a non-overlapping return specification in Hodrick (1992) that does not result in a loss of information. Following Hodrick (1992) and Valkanov (2003), the rest of this section and Section 3.4 use log excess return (denoted by lower case rM) as dependent variable although similar results are obtained using simple excess return RM.10 Panel D of Table 3 shows the results using the standard error in Hodrick (1992, Eq. (8)), which is shown by Ang and Bekaert (2007) to perform well in small samples. The statistical significance is consistent with that from the Newey and West (1987) standard error in Panel A. pffiffiffi Valkanov (2003) constructs a t= T test statistic from dividing the ordinary least squares (OLS) t-statistic by the square root of the sample length. The test allows for persistent right-hand-side regressors. Valkanov (2003) propffiffiffi vides asymptotic distributions for the t= T statistic and for the OLS R-square. The results are shown in Panel D of Table 3.11 The negative relation between disagreement and ex post market return is statistically significant for all return horizons of one to three years. Under the null hypothesis of no effect from disagreement, the probability of observing the high regression R-square by chance is less than 2%. 3.4. Non-overlapping return regression This section uses an alternative specification that uses non-overlapping returns and involves no loss of information. Specifically, Hodrick (1992) suggests the following specification: ! h1 X M 1 rt,t þ 1 ¼ a þ b h stt þ et , ð5Þ t¼0

which regresses the one-month return on the lagged h-month average of disagreement.12 The regression results are in Panel E of Table 3. There is a negative 10 The log excess market return is defined as logð1 þ market returnÞlogð1 þ T-bill returnÞ, which is the log market return when T-bill instead of cash is used as numeraire. 11 The asymptotic distributions in Valkanov (2003) can be obtained by simulation and depend on a nuisance parameter c. Following Valkanov (2003), c is set to 19.41 using the procedure in Stock (1991). The other parameters used in the Valkanov (2003) test are d ¼ 0:1619, number of simulation sample paths = 10,000, and the step size in discretizing the continuous-time stochastic processes = 1/10,000. 12 The intuition is that the slope coefficient of regressing h-horizon return rM on disagreement st is derived from t,t + h M covðrt,t þ 1 þ rtMþ 1,t þ 2 þ þ rtMþ h1,t þ h , st Þ which, for stationary series, is M equivalent to covðrt,t þ 1 , st þ st1 þ þ sth þ 1 Þ.


relation between disagreement and ex post return and the effect is stronger using the lagged one-year or two-year average of disagreement. The adjusted R-squares are lower than those in Panel A because the dependent variable is the one-month return. Stambaugh (1999) discusses a regression bias that arises when return is regressed on a lagged regressor and innovations to the regressor and return are correlated. Unlike dividend yield studied in Stambaugh (1999), disagreement does not mechanically relate to the market return. Nonetheless, a simulation is conducted in Panel E of Table 3 to measure the potential magnitude of the bias.13 The bias is small relative to the actual estimate (e.g., the estimated bias is 0.0013 compared to the coefficient of 0.0189 in the actual one-year regression). This panel also shows the p-value for the null hypothesis that disagreement has no effect by comparing the t-statistic in the actual regression (5) to the percentiles of the t-statistics in a second simulation.14 The p-value from simulation is consistent with the t-statistic in the actual regression. Panel E of Table 3 further constructs a Campbell and Yogo (2006) Bonferroni Q-test confidence interval for the coefficient of disagreement in (5). The test is motivated by the uniformly most powerful test and allows broad dynamics of the regressor (e.g., a finite-order autoregressive process with the largest root less than, equal to, or even greater than one). Only 90% confidence intervals are shown because Campbell and Yogo (2005, 2006) tabulate for one-sided tests of 5% p-value.15 The confidence intervals are consistent with the t-statistics in Panel E.16

3.5. Alternative hypotheses Motivated by the finding in (4), this section studies whether the effect of disagreement is driven by alternative mechanisms that affect the equity premium. Specifically, this section controls for a host of other variables that correlate 13 The simulation is similar to those in Kothari and Shanken (1997), Lewellen (2004), and Ang and Bekaert (2007). In the simulation, the ‘‘true’’ coefficients are set to the estimates of (5). Disagreement is assumed to follow an AR(1) process with coefficients given by column 1 of Table 2. The error terms are drawn with replacement from the joint empirical distribution of the two residuals in the regression (5) and in the regression in column 1 of Table 2. 10,000 simulated samples are drawn. The bias is measured by the difference between the average simulation estimate of disagreement in regression (5) and the ‘‘true’’ coefficient. 14 This second simulation is identical to the first simulation except that the ‘‘true’’ coefficient is set to zero. 15 Following Campbell and Yogo (2005), the autoregressive order of the regressor is determined by the Bayes information criterion when computing the confidence interval. 16 The intuition for why the t-statistics perform well is that the disagreement does not mechanically relate to returns. For example, in the one-year regression, the Campbell and Yogo (2006) d (defined as the correlation between innovations to return and innovations to disagreement) is only 0.165. This contrasts with the dividend-price ratio, which has close to perfect correlation with return (Campbell and Yogo, 2006, Table 4). According to Campbell and Yogo (2006, Table 1), with such a low d, the conventional t-statistics are valid unless the auto-correlation coefficient of disagreement is above 0.993. From column 1 of Table 2 in this paper, the actual auto-correlation in the sample is only 0.93.

169

with ex post market return, which are reviewed in Campbell and Thompson (2008) and Goyal and Welch (2008). These variables include the price-earnings ratio PE, consumptionwealth ratio CAY, dividend-price ratio DP, smoothed earnings-price ratio SMOOTHEP, book-to-market ratio BM, short-term interest rate SHORTYIELD, long-term bond yield LONGYIELD, the term spread between long- and short-term Treasury yields TERMSPREAD, the default spread between corporate and Treasury bond yields DFSPREAD, the lagged rate of inflation INFLATION, and the equity share of new issues EQUITYSHARE.17 Quarterly data on CAY are obtained from Martin Lettau’s Web site. Monthly data for the other variables can be obtained from the Web site of Amit Goyal. First, these variables are added one-by-one into regression (3). The regressions are monthly except for CAY (quarterly). Panel F of Table 3 shows the results. The coefficients of disagreement are negative across the return horizons and the additional control variables.18 The estimates are in line with those in Panel A of Table 3 and are statistically significant for all regressions involving the one- and two-year return horizons and for most three-year regressions. Next, all of the control variables are added into the regression.19 RM t,t þ h ¼ b0 þ b1 st þ b2 PEt þ b3 CAY t þ b4 DP t þ b5 SMOOTHEP t þ b6 BM t þ b7 LONGYIELDt þ b8 TERMSPREADt þ b9 DFSPREADt þ b10 INFLATIONt þ b11 EQUITYSHAREt þ et :

ð6Þ

The results are in Panel G of Table 3. The coefficient of interest is b1 . It remains statistically and economically significant at the one-year to three-year horizons. Panel G provides two adjusted R-squares. The first R-square is for the regression specification (6). The second R-square is for a regression that is otherwise identical to (6) except that disagreement is omitted. Due to the econometric issues associated with overlapping regressions (see Section 3.3), these R-squares cannot be compared across different return horizons. Instead, they illustrate, for a given return horizon, the effect of adding one extra regressor of disagreement. This also applies to the other tables in this paper that use overlapping regressions. In Panel G of Table 3, there is substantial improvement in regression fit when disagreement is included. For example, when including all the 17 A partial list of references for these variables includes Rozeff (1984), Fama and French (1988a), and Campbell and Shiller (1988, 1989) on the dividend-price ratio, the earnings-price ratio and its smoothed version; Kothari and Shanken (1997) and Pontiff and Schall (1998) on the book-to-market ratio; Keim and Stambaugh (1986), Campbell (1987), Fama and French (1989), and Hodrick (1992) on interest rates of Treasury and corporate debt securities; Fama and Schwert (1977) and Fama (1981) on inflation; Baker and Wurgler (2000) on the equity share of new issues; Lettau and Ludvigson (2001) on the level of consumption in relation to wealth. 18 The coefficients of the other control variables are in line with earlier studies. Judging by the regression R-square in a separate univariate regression of market return on these control variables oneby-one, price-earnings ratio has the most explanatory power in the sample followed by dividend-price ratio. These results are unreported for brevity. 19 In this regression, CAY is converted into monthly data using the last available quarterly value. SHORTYIELD is omitted because of multicollinearity with LONGYIELD and TERMSPREAD.

170


Table 4 Compare top-down and bottom-up disagreement measures. NG Panel A reports the pairwise correlation coefficients among sTD , sNG . sTD is the disagreement measured top-down by the analyst forecast ANN , and s standard deviation of S&P 500 earnings scaled by the most recent realized S&P 500 earnings. sNG (sNG ANN ) is measured bottom-up as the cross-sectional value-weighted average of analyst forecast standard deviation of individual-stock long-term EPS growth rate (individual-stock annual EPS), using only firms that issue no quarterly or annual guidelines. Panels B, C, D, and E report the regression results of ex post S&P 500 returns in excess of the risk-free NG rate on sTD , sNG , and all three disagreement measures together, respectively. The t-statistics are adjusted for auto-correlation using Newey and ANN , s West (1987), with the number of lags being equal to the return horizons. The sample period is January 1982–July 2001. Panel A: Correlation matrix

sTD

sNG ANN

sNG

sTD sNG ANN sNG

1 0.447

1

0.270

0.381

1

Return horizon (in months)

1

6

12

24

36

1.703 (2.27) 4.2%

4.942 (3.42) 14.1%

6.238 (2.55) 11.3%

14.594

17.255

(5.27) 41.2%

(3.56) 29.3%

Panel D: Ex post market return on bottom-up disagreement measure from long-term forecasts 0.001 0.052 0.157 sNG t-stat (0.26) (2.25) (5.02) 2 Adj R 0.4% 6.1% 27.2%

0.319 (5.67) 42.1%

0.407 (4.55) 35.0%

Panel E: Ex post market return on all three disagreement measures 0.509 sNG ANN

Panel B: Ex post market return on top-down disagreement measure sTD 0.227 0.921 t-stat (1.51) (1.88) 2 Adj R 0.6% 2.5%

Panel C: Ex post market return on bottom-up disagreement measure from annual EPS forecasts 0.495 3.748 6.892 sNG ANN t-stat Adj R2

t-stat

sNG t-stat

sTD t-stat

(2.02) 1.2%

(1.54) 0.004 (0.64) 0.125 (0.70)

(4.52) 15.6%

(4.05) 24.3%

3.428

4.702

8.852

9.284

(3.16) 0.018 (0.84) 0.082 (0.16)

(2.63) 0.108 (3.46) 0.259 (0.39)

(4.72) 0.224 (6.26) 1.103 (1.05)

(1.67) 0.308 (4.14) 1.699 (1.19)

4. Compare bottom-up and top-down disagreement measures

year y is set to a weighted average of the forecast dispersions for the fiscal years y and y+1 (the weight for year y+1 increases linearly from 3/12 in March to 11/12 in November). This section constructs the top-down measure in the same way and denotes it sTD .20 Panel B of Table 4 shows the regression results of ex post S&P 500 return in excess of the risk-free rate on the top-down disagreement sTD . The regression covers January 1982–July 2001, the sample period in Park (2005).21 There is a negative relation between S&P 500 return and disagreement, confirming Park

This paper constructs portfolio disagreement bottom-up using individual-stock disagreements. Park (2005) measures disagreement of the market portfolio top-down using analyst forecasts of S&P 500 earnings. This section compares these disagreement measures. Specifically, Park (2005) takes the I/B/E/S analyst forecasts of annual S&P 500 earnings and uses the forecast standard deviation scaled by the most recent realized S&P 500 earnings to measure market disagreement. To prevent the mechanical drop in dispersion of annual forecasts as the fiscal year-end becomes closer, Park (2005) uses a rolling measure of disagreement— disagreement in December of year y 1, January and February of year y is set to the forecast dispersion for the fiscal year y while disagreement in March to November of

20 Analyst forecast standard deviation of the S&P 500 earnings for the second nearest fiscal year is missing for three months in the early part of the sample period, due to insufficient analyst coverage. It is unclear how Park (2005) incorporates the missing data in the rolling measure of market disagreement. The current section sets these three observations of market disagreement to missing. Nonetheless, the regression results are similar to those reported in Park (2005). 21 The sTD series is not extended further beyond July 2001 because analysts switched to forecasting S&P 500 operating EPS instead of reported EPS shortly afterwards. This paper has also tried several methods to link the dispersion series from reported EPS and the dispersion series from operating EPS, including linking the two raw series directly, adding or multiplying a constant to the raw series to remove the discontinuities at the link point, and varying the time of the link point. The results are similar, and the bottom-up disagreement still performs better.

controls but no disagreement, the R-square in the one-year regression is 21.7% compared to 38.9% when disagreement is added. The two- and three-year results are similar. Substantial improvement in R-square when disagreement is added is similarly observed in the regressions in Panel F of Table 3 where the other control variables are included one-by-one. These results are unreported for brevity.


171

Bottom−up disagreement Ex post 1yr S&P500 ret

−0.4 4 −0.2 3.5 0 3

0.2

Ex post 1yr S&P 500 return

Bottom−up disagreement (%)

4.5

0.4

2.5

1985

1990

1995 Year

2000

2005

Top−down disagreement Ex post 1yr S&P500 ret

−0.4 −0.2 0.1 0 0.2

0.05

Ex post 1yr S&P 500 return

Top−down disagreement

0.15

0.4 0 1985

1990

1995 Year

2000

2005

Fig. 3. Compare top-down and bottom-up disagreement measures. The first plot shows the time series of bottom-up disagreement s and ex post oneyear S&P 500 return in excess of the risk-free rate. s is the cross-sectional value-weighted average of analyst forecast standard deviations of long-term EPS growth rate. For each month t, the plot shows the disagreement st and the ex post S&P 500 return from t to t +12. To facilitate comparison, the S&P 500 return is plotted upside down. The sample period is December 1981–December 2005. The second plot shows the same ex post one-year S&P 500 excess return against the top-down disagreement sTD , which is measured by the analyst forecast standard deviation of S&P 500 earnings scaled by the most recent realized S&P 500 earnings. The sample period of the second plot is January 1982–July 2001, which is the sample period in Park (2005).

(2005), though the top-down disagreement has less explanatory power than the bottom-up disagreement in Panel A of Table 3.22 To visualize the correlation between ex post return and the top-down and bottom-up disagreement measures, Fig. 3 shows the time-series plot of ex post one-year excess S&P 500 return alongside each of the two disagreement measures, respectively. Since the correlation is negative, the S&P 500 return is plotted upside down to facilitate comparison. The first plot in Fig. 3 uses the bottom-up disagreement s. A positive relation between s

22 The result in Panel A of Table 3 is similar (somewhat stronger) when restricted to the sample period of Park (2005). To facilitate comparison, the dependent variable in Table 4 is S&P 500 return used by Park (2005). Nonetheless, the results in this section are similar if CRSP value-weighted return is used. The results are also similar if real S&P 500 return is used instead of S&P 500 return in excess of the risk-free rate.

and the (inverted) S&P 500 return can be seen. For example, a number of spikes and subsequent drops in the (inverted) return matches the spikes and drops in s such as those around years 1983, 1987, 1989, the dot-com era, etc. There are many reasons that can potentially affect the equity premium, which may make the plot noisy. Nonetheless, the relation between the bottom-up disagreement and return is visually less noisy than the relation between the top-down disagreement and return shown in the second plot of Fig. 3, confirming the formal regression results. The disagreement measures s and sTD differ in (i) s is constructed bottom-up while sTD is constructed top-down; (ii) s uses forecasts of EPS long-term growth rate while sTD employs annual EPS forecasts. To see the relative contribution of (i) and (ii), this section constructs a third disagreement measure bottom-up using forecasts of individual-stock annual EPS. Specifically, let sANN denote the month t i,t

172


standard deviation of analyst forecasts of annual EPS for stock i. To prevent the mechanical drop in forecast standard deviation when the fiscal year-end is near, a weighted average of the nearest and the second nearest fiscal year EPS forecast standard deviations are used to construct sANN in i,t the same way as Park (2005) to facilitate comparison. Recall the top-down disagreement sTD in Park (2005) is S&P 500 forecast dispersion scaled by the most recent S&P 500 EPS. The bottom-up measure of market disagreement using annual EPS forecasts, denoted by sANN,t , is constructed by replacing the dispersion in market EPS (the numerator in qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ANN 2 sTD ) with i ðsi,t si,t Þ , where si,t is the number of shares outstanding for firm i at time t.23 This parallels the top-down measure in Park (2005) except that the disagreement regarding market EPS is inferred bottom-up using individual-stock disagreement over annual EPS. Since sTD and sANN both use annual forecasts, comparing them shows the effect of top-down versus bottom-up approaches. Because sANN and s both use bottom-up construction, comparing them shows the effect of using annual forecasts versus longterm forecasts. It is important, however, to note the effect of earnings guidance prior to using disagreement measures based on individual-stock annual EPS forecasts. Fig. 4 shows the number of firms issuing annual or quarterly earnings guidelines. The First Call database collects data on company-issued guidelines since August 1990, which may be a subset of actual guidance since companies may have guided prior to 1990 or through channels outside First Call coverage. Nonetheless, there are a lot of observed guidelines. In recent years, there are more than 1,500 firms issuing annual EPS guidelines and over 2,000 firms issuing quarterly EPS guidelines. Such guidelines will likely affect forecast dispersion because low forecast dispersion may reflect superior earnings guidance instead of genuinely low disagreement. To see the effect of guidance, the second plot in Fig. 4 shows the time series of bottom-up disagreement sANN from annual EPS forecasts, separately for the set of firms that issue guidelines and for the rest of the firms. The ‘‘disagreement’’ of those firms that guide declines almost monotonically throughout the sample to about half a cent per $1 earnings near the end of the sample period. Although the guidance of a firm may also be informative for other firms that do not guide (e.g., firms in the same industry), the measured disagreement for firms that do not guide

23 This assumes the forecasts for different firms are uncorrelated because, letting xi denote the next annual EPS forecast for firm i, the forecast variance of market earnings VarðSi si xi Þ ¼ Si ðsi sANN Þ2 if xi are i uncorrelated with xj for iaj. There are likely market- or industry-wide factors that drive the EPS of many firms and generate correlation, but measuring forecast correlation across firms is difficult because an analyst does not usually cover many firms. A random pair of firms often has no analyst covering both firms. However, the result in this section is similar if the bottom-up disagreement sANN,t is measured instead by P ANN replacing the numerator of sTD with (which amounts to i si,t si,t assuming EPS forecasts for different stocks are perfectly correlated). The bottom-up measures constructed from these two alternative assumptions on forecast correlation have a pairwise correlation coefficient of 0.791. Therefore, forecast correlation across firms does not appear to influence the results in this section.

exhibits substantial fluctuations over time. Therefore, the rest of this section focuses on the bottom-up disagreement constructed from annual EPS forecasts of those firms that issue no earnings guidelines, denoted by sNG ANN . Although the earnings guidance does not appear to substantially affect the bottom-up disagreement s constructed from long-term EPS growth rate (s for firms that guide/do not guide have a correlation of 0.622 and their plots are both similar to Fig. 1), the rest of this section focuses on s constructed for the set of firms that do not guide, denoted sNG , for the ease of comparison. The results are similar if s measured from all firms is used. Panel A of Table 4 shows that the top-down disagreeNG ment sTD and the two bottom-up measures sNG ANN and s are positively correlated with the correlation coefficient ranging from 0.270 (between bottom-up sNG from longterm forecasts and top-down sTD from annual forecasts) to 0.447 (between sNG ANN and sTD which both use annual forecasts). All the correlation coefficients are statistically significant at the 99% level. Panels C and D of Table 4 show the regression results of ex post S&P 500 excess return on NG sNG ANN and s , respectively. The ex post returns are NG NG negatively related to sNG . sNG have ANN and s ANN and s similar explanatory power, though sNG is somewhat ANN stronger for short-horizon returns while sNG is stronger at the longer horizons. This is consistent with Panel E of Table 4, which regresses ex post S&P 500 excess return on all three disagreement measures. The top-down measure sTD is no longer statistically significant. Similar to the univariate regression, sNG ANN is stronger at the short horizon. Dispersion from annual forecasts may tilt more towards those disagreements that will be resolved sooner (e.g., when the annual report is released) than dispersion from long-term forecasts. Consistently, sNG affects longerhorizon returns more. NG Overall, sNG perform similarly and both ANN and s perform better than the top-down measure sTD . This suggests that the improvement comes more from topdown versus bottom-up construction than from annual versus long-term forecasts. Why does the bottom-up approach do better? There are a number of explanations. First, the bottom-up approach likely has a better signalto-noise ratio. Fig. 5 shows the time-series plots of the number of firms with non-missing stock-level disagreement, along with the average number of analysts following each stock. The sample contains a large number of firms. There are more than 700 stocks in the early part of the sample and around 2,000 stocks towards the end of the sample. The average number of analysts per firm is stable at around five to seven analysts per firm. Therefore, the bottom-up disagreement constructed at any given time uses thousands of forecasts. This is far more than the top-down approach, where, on average, only 23 analysts cover the next year’s S&P 500 earnings. Even fewer analysts cover the subsequent years’ S&P 500 earnings. There are often more analysts covering a single large stock than the S&P 500. One caveat is that when the bottom-up disagreement is constructed out of annual forecasts, one needs to control for the practice of earnings guidance. Interestingly, the top-down approach does not immediately appear to be affected by earnings guidance—Fig. 3


173

2500 Firms with annual EPS guidelines Firms with quarterly EPS guidelines

Number of firms

2000

1500

1000

500

0 1990

1992

1994

1996 Year

1998

2000

2002

Disagreement from annual forecasts

0.07 0.06

Firms with no guidelines Firms with guidelines

0.05 0.04 0.03 0.02 0.01 0 1985

1990 Year

1995

2000

Fig. 4. Earnings guidance and annual forecasts. The first plot shows the time series of the number of firms issuing annual or quarterly EPS guidelines in a given year. The First Call database collects data on company issued guidelines since August 1990. The second plot shows the disagreement measured bottom-up using individual-stock annual EPS forecasts during the sample period January 1982–July 2001, separately for the set of firms that issue guidelines and for the rest of the firms. A firm is considered to issue guidelines as long as it has at least one observation of either annual or quarterly EPS guidelines in the First Call database.

does not show any monotonic drop in top-down disagreement even when Fig. 4 reveals an increasing number of guidelines. This is likely because some market strategists forecast index earnings top-down by treating an index as though it were an individual entity while other analysts forecast bottom-up by averaging EPS forecasts of companies comprising the index. For example, Standard & Poor’s Web site provides both types of forecasts for the S&P 500. The presence of top-down index earnings forecasts may make the top-down disagreement less affected by individual firm guidance. The earnings guidance may even lead to apparently larger top-down disagreement if the bottom-up index earnings forecasts are guided away from the top-down index earnings forecasts, which may not represent genuine variations of belief dispersion in the market.

Further, bottom-up and top-down disagreement measures are not identical in theory. For ease of illustration, assume for now that there are n firms each with a weight of 1/n in the market. Assume an investor’s belief regarding firm i’s earning ei is random with mean e. This investor’s belief regarding the market is n1 Si ei -e when there are many firms. This holds by the law of large numbers under fairly general conditions, including but not restricted to the case when ei is homoskedastic and i.i.d. across firms. In this case, there is no disagreement regarding the market earnings in the top-down sense since all investors believe market earnings to be e. However, there is disagreement measured bottom-up since investors may disagree over individual stocks unless all ei are degenerate random variables. Therefore, there can be disagreement even if the top-down disagreement measure is zero.


Number of firms Number of analysts per firm

Number of firms

2500

9

2000 7 1500 5 1000 3

500

1985

1990

1995

2000

Average number of analysts per firm

174

2005

Year Fig. 5. Number of firms and number of analysts. This figure shows the monthly number of firms covered by at least two analysts (left vertical axis) so that forecast standard deviation can be computed, along with the average number of analysts covering each firm (right vertical axis).

On the contrary, if there is no bottom-up disagreement, there is no top-down disagreement (apart from measurement errors). Mathematically, the bottom-up disagreement differs from the top-down disagreement because the average of the standard deviation (i.e., the average of individual-stock disagreement) differs from the standard deviation of the average (i.e., the disagreement over the market). If investors focus on picking individual stocks, as suggested by the analysts’ focus on individual stocks, the bottom-up disagreement likely reflects the belief dispersion better than the top-down disagreement measures. This section shows that the choice between annual EPS forecasts and long-term EPS forecasts is less important. Nonetheless, this paper features bottom-up disagreement constructed from long-term forecasts in the discussion. As discussed previously, long-term forecasts face less complication introduced by the annual and quarterly earnings guidelines.24 Standard deviation from annual EPS forecasts requires scaling, which may introduce variations unrelated to disagreement (Qu, Starks, and Yan, 2004; Cen, Wei, and Zhang, 2007). As pointed out by Moeller, Schlingemann, and Stulz (2007), because the long-term forecast is an expected growth rate, it is directly comparable across firms or across time. 5. Disagreement, discount rate, and time-varying value premium An important pillar of the Miller (1977) model is the positive contemporaneous correlation between portfolio return and shocks to disagreement. That is, price becomes 24 Specifically, sNG ANN identifies firm guidance using information in the entire First Call sample. If a firm’s decision to guide does not depend on market return, this will not bias the return regressions. Alternatively, this paper has identified firm guidance using only a firm’s past guidance information. The return regression results are still statistically significant but less so compared to using sNG ANN (e.g., the t-stat in the one-year return regression is 1.97 compared to 4.05 in Panel C of Table 4). A firm that prefers to guide may do so via a channel not covered by First Call or before First Call initiates coverage, which can introduce more noise when guidance is measured with less information.

higher when there is more disagreement, which is the source of the low ex post return. Campbell and Shiller (1989) decompose return into discount-rate news and cash-flow news, which have distinct implications for asset pricing. A number of studies have relied on the discountrate variation to address asset-pricing challenges. For example, Fama and French (1988a), Campbell and Shiller (1989), and Campbell and Vuolteenaho (2004) use the discount-rate effect to address the time-varying equity premium and the value premium. However, it is unclear what drives the variations in discount rate. Does variation in disagreement correlate contemporaneously with discount-rate news or cash-flow news? This is studied in the following regression: DR CF st sth ¼ a þ b Nth,t þ g Nth,t þ et ,

ð7Þ

where s is the market disagreement measured bottom-up in (1). Monthly data on discount-rate news NDR and cash-flow news NCF are obtained from the return decomposition in Campbell and Vuolteenaho (2004) (data are downloaded from the Web site of the American Economic Review). The sample period for the discount-rate and CF cash-flow news is 1981 to the end of 2001. NDR t h,t (Nt h,t) is the discount-rate news (cash-flow news) from month t h to t, constructed as the sum of the monthly discountDR rate news NDR t h,t h + 1,y,Nt 1,t (monthly cash-flow news CF CF Nt h,t h + 1,y,Nt 1,t). h ranges from six months to three years.25 The regression results are presented in Panel A of Table 5. An increase in disagreement is associated with a contemporaneous drop in the discount rate. The relation is statistically significant for all horizons. In contrast, the

25 The one-month horizon is excluded because, at this frequency, the measured change in disagreement does not entirely coincide with the return. This is because analyst disagreement is measured using the latest available forecasts prior to the month-end and the return is measured using prices at the month-end. This issue is less pronounced for longer horizons. Nonetheless, the regression has been repeated for the one-month horizon and the result is similar. This result is unreported for brevity.


175

Table 5 Disagreement and time-varying value premium. DR CF Panel A reports the regression results of st sth ¼ a þ b Nth,t þ g Nth,t þ et , where s is the cross-sectional value-weighted average of analyst forecast CF standard deviation of individual-stock long-term EPS growth rate. NDR t h,t (Nt h,t) is the discount-rate news (cash-flow news) from month t h to t constructed as the sum of the monthly discount-rate news (cash-flow news) from the return decomposition in Campbell and Vuolteenaho (2004). Panel B regresses the value-weighted portfolio returns (in excess of the risk-free rate) of low or high book-to-market stocks (denoted by RL or RH, respectively) L from month t h to t on contemporaneous changes of s: RLth,t ðor RH or RH th,t Þ ¼ a þ b ðst sth Þ þ et . Panel C regresses ex post returns R

on s: RLt,t þ h ðorRH t,t þ h Þ ¼ a þ b st þ et . Panel D regresses ex post Fama and French (1993) HML (high-minus-low book-to-market portfolio) returns on s: HMLt,t þ h ¼ a þ b st þ et , where HMLt,t + h is the linked monthly HML return from month t to t+ h. The HML returns are downloaded from Kenneth French’s Web site. Panel E repeats the regression in Panel D, controlling for LOGBMH LOGBML. LOGBMH (or LOGBML) is the log of the value-weighted book-to-market ratio for the value (or growth) stock portfolio. The t-statistics are from Newey and West (1987) with h lags. The sample period is December 1981–December 2005. h

6

Panel A: Disagreement s and discount-rate news NDR 0.926 t h,t t-stat (2.91) NCF 1.476 t h,t t-stat (1.81)

12

24

36

1.419 (4.54) 0.268 (0.30)

1.253 (3.07) 0.665 (0.80)

1.094 (3.19) 1.294 (1.47)

0.373 (4.55)

0.495 (4.60)

0.021 (0.20)

0.083 (0.57)

6

12

24

36

0.080 (1.81) 5.9%

0.215 (3.07) 20.8%

0.450 (3.72) 39.3%

0.608 (2.88) 37.3%

0.008 (0.24) 0.3%

0.068 (1.29) 2.2%

0.160 (2.53) 7.7%

0.240 (1.87) 9.5%

0.070 (1.63) 0.200 (1.51) 8.2%

0.178 (2.39) 0.519 (2.22) 22.3%

0.315 (3.40) 0.904 (2.93) 34.0%

0.335 (3.61) 0.927 (2.99) 36.9%

0.157 (2.47) 0.118 (1.56) 25.8%

0.284 (3.59) 0.169 (1.52) 37.4%

0.294 (3.72) 0.223 (2.59) 42.8%

Panel B: Contemporaneous book-to-market portfolio returns on changes in s Low B/M stocks st sth 0.151 0.298 t-stat (2.65) (6.23) High B/M stocks st sth 0.001 0.063 t-stat (0.01) (0.88) Return horizon (in months)

1

Panel C: Ex post book-to-market portfolio returns on s Low B/M stocks s 0.008 t-stat (1.05) Adj R2 0.0% High B/M stocks s 0.002 t-stat (0.32) Adj R2 0.3% Panel D: Ex post HML returns on s

s t-stat Constant t-stat Adj R2

0.008 (1.08) 0.021 (0.92) 0.5%

Panel E: Ex post HML returns on s, controlling for the difference in book-to-market ratios s 0.005 0.057 t-stat (0.81) (1.57) LOGBM H LOGBM L 0.014 0.073 t-stat (1.48) (1.38) Adj R2 1.3% 11.3%

estimates for cash-flow news flip signs depending on the horizon and none of them are statistically significant. Campbell and Vuolteenaho (2004) find empirically that growth stocks have higher discount-rate beta than value stocks after the 1960s. This, together with the finding in regression (7), suggests that the growth and value stock returns may have different sensitivities to contemporaneous variations in disagreement. This prediction is tested below. Following Fama and French (1993), growth and value portfolios are formed at the end of June each year. Growth/value stocks are defined as those with the lowest/highest 30% book-to-market ratio using NYSE breakpoints. Book-to-market ratios are constructed as in Daniel and Titman (2006) and firms

with negative book values are excluded. Let RLt h,t (or RH t h,t) denote the value-weighted portfolio returns of low (or high) book-to-market stocks from month t h to t in excess of the linked one-month T-bill rate. The following time-series regression is run separately for growth and value portfolios: RLth,t ðor RH th,t Þ ¼ a þ b ðst sth Þ þ et : The return horizon h ranges from six month to three years. The results are in Panel B of Table 5. Contemporaneously, growth stock returns are positively correlated with shocks to disagreement. The correlation is statistically significant for all return horizons. In contrast,

176


the correlations for value stocks, though positive, are smaller and less statistically significant.26 Having found that growth stocks go up more when disagreement is on the way up, then when disagreement reaches a peak and subsequently mean-reverts, the same sensitivity implies growth stocks go down more than value stocks (i.e., the negative relation between disagreement and ex post return should be stronger for growth stocks than for value stocks). To examine this, ex post growth (value) portfolio returns are regressed on disagreement: RLt,t þ h ðor RH t,t þ h Þ ¼ a þ b st þ et :

ð8Þ

Panel C of Table 5 shows the results. Consistent with the prediction, both growth and value stock returns correlate negatively with disagreement, and the effect is stronger for growth stocks. A one-standard-deviation increase in disagreement is associated with a reduction in ex post one-year growth (value) stock return by 8.17% (2.58%). The difference in growth/value stocks’ sensitivities to disagreement implies that disagreement has explanatory power for the time-series variations in the Fama and French (1993) HML (high-minus-low book-to-market portfolio) return. To test this prediction, the HML returns (downloaded from Kenneth French’s Web site) are regressed on disagreement: HMLt,t þ h ¼ a þ b st þ et ,

ð9Þ

where HMLt,t + h refers to the linked HML return from month t to t +h. The results are presented in Panel D of Table 5. The coefficient of disagreement is positive and statistically significant for return horizons from one to three years. Disagreement alone accounts for 22.3% of the one-year HML return variations. The next regression further controls for the book-to-market ratio of value stocks relative to growth stocks: HMLt,t þ h ¼ a þ b st þ g ðLOGBMH LOGBML Þ þ et ,

the marginal investor. To see this, assume that the average belief of a stock is mi and the belief dispersion is si . Assume the marginal investor’s valuation of stock i is mi þ bi si . When bi =0, the marginal investor’s belief is the average belief. When bi 4 0 (bi o 0), the marginal investor is more optimistic (pessimistic) than the average belief. When there is disagreement, the marginal investor can be overly optimistic for two reasons: (i) the average belief mi is overly optimistic (e.g., Lakonishok, Shleifer, and Vishny, 1994; La Porta, 1996); (ii) bi 4 0; or both. To simplify illustration, the discussion in this section assumes the average belief is correct and focuses on the effect due to bi. The effect due to mi being overly optimistic will be analyzed in Section 7. The marginal investor is generally unobservable. However, assuming the availability of a set of assets with different optimism bi, the following implications are testable. Testable implications. In this setting, a stock is more overvalued if bi si is higher. Therefore, 1. Given bi 4 0, high disagreement stocks have lower expected returns than low disagreement stocks. This effect is stronger for stocks with higher optimism bi. 2. Given si , the expected return of stocks with higher optimism bi is lower. This effect is stronger for high disagreement stocks. 3. Contemporaneously, the returns of stocks with high optimism bi are more positively correlated with variations in disagreement. 4. Ex post, returns of stocks with high optimism bi are more negatively correlated with disagreement. To test these implications, this paper uses portfolios sorted on the book-to-market (B/M) ratio as test assets by making the following assumption. The empirical findings form a joint test of this assumption and the disagreement mechanism.

ð10Þ

where LOGBMH (or LOGBML) refers to the log of the valueweighted book-to-market ratio for the value (or growth) stock portfolio. The results are presented in Panel E of Table 5. Even after controlling for book-to-market ratios, the disagreement has a statistically and economically significant effect on ex post HML return. The coefficient of disagreement in the one-year return regression is 0.157 (t-stat = 2.47). A one-standard-deviation increase in disagreement is associated with an increase of 5.97% (e.g., 2% to 7.97%) in ex post one-year HML return. 6. Disagreement of book-to-market sorted portfolios The Miller (1977) model gives rich implications based on the interaction between disagreement and the optimism of 26 The difference between value and growth stocks is statistically significant. This conclusion is based on a pooled regression of growth and value stock returns on changes in s, a dummy variable that equals one (zero) for the growth (value) stock portfolio, and their interactions. The coefficient in front of the interactive term is statistically significant at the 95% level for all return horizons. This result is unreported for brevity.

Assumption. Low book-to-market stocks (growth stocks) have higher optimism bi than high book-to-market stocks (value stocks). Further, for the lowest book-to-market portfolio, bi 40. The B/M ratio is constructed in the same way as in Section 5. Stocks are sorted into quintile portfolios based on the B/M ratio. Panel A of Table 6 shows summary statistics of the five portfolios. On average, the low B/M portfolios (growth stock portfolios) have more stocks, larger market capitalization, more analyst coverage, and lower return. Panel C1 of Table 6 shows, for portfolios double sorted by individual-stock B/M ratio and disagreement, the annual return alphas relative to the market factor. Consistent with Testable Implication 1, high disagreement stocks have lower return alpha than low disagreement stocks, and the underperformance is more pronounced for growth stocks. For example, within the top growth stock quintile, high disagreement stocks have an annual return alpha of 4.42% compared to low disagreement stocks whose alpha is 2.80%, a difference of 7.22% (t-stat =2.17). The underperformance of high disagreement stocks diminishes monotonically for portfolios with higher B/M ratios. Within the

Table 6 Disagreement of book-to-market sorted portfolios. Panel A shows the time-series average of the number of stocks, the average market capitalization (in millions US dollars), the average number of analysts covering a stock, and the value-weighted portfolio return for each of the book-to-market (B/M) quintile portfolios. The B/M portfolios are formed at the end of June each year using NYSE breakpoints. Disagreement for each B/M portfolio (denoted by sðiÞ for i= 1,2,y,5) is constructed as the value-weighted average of analyst forecast standard deviation of individual-stock long-term EPS growth rate using only stocks in the corresponding B/M portfolio. Panel B shows the pairwise correlation coefficients of sðiÞ among the five B/M portfolios. Panels C1 and C2 show the ex post value-weighted portfolio return alphas relative to the market factor (measured by the CRSP valueweighted return) for portfolios sorted independently by individual-stock B/M and disagreement. In Panel C1, the ‘‘3–1’’ return is constructed within each B/M quintile as the return difference between the high and low disagreement portfolios. The diff-in-diff portfolio return is the difference of the ‘‘3–1’’ return between the top and bottom B/M quintiles. Alphas for only the diff-in-diff portfolio are reported in Panel C2. Panel D shows, for each of the B/M portfolios i= 1,2,y,5, the estimates of b in the regression: Rth,t ðiÞ ¼ a þ b ðst ðiÞsth ðiÞÞ þ et . Rt h,t(i) denotes the value-weighted return from t h to t of B/M portfolio i in excess of the risk-free rate. Panel E shows, for each B/M portfolio, the estimates of b in the regression: Rt,t þ h ðiÞ ¼ a þ b st ðiÞþ et . The t-statistics in parentheses are from Newey and West (1987) with the number of lags being equal to the return horizons. The sample period is December 1981–December 2005. 2

3

4

5 (High B/M)

459 4596 6.8 0.74

343 2896 6.0 0.80

291 2075 5.7 0.88

232 1888 5.7 0.91

175 1665 5.1 1.02

Panel B: Correlation matrix of disagreement of B/M portfolios 1 (Low B/M) 1 2 0.555 3 0.465 4 0.208 5 (High B/M) 0.090

1 0.564 0.229 0.132

1 0.299 0.214

1 0.550

1

Panel A: Summary statistics of B/M portfolios Number of stocks Market capitalization (M$) Analysts per stock Monthly return (%)

Panel C1: Ex post annual return alpha (100) relative to the market Disagreement

1 (Low B/M) 2 3 4 5 (High B/M) 5–1 t-stat

1 (Low)

2

3 (High)

3–1

t-stat

2.80 5.60 5.99 5.69 7.11 4.31 (1.63)

0.77 1.76 3.62 3.14 6.63 7.41 (2.06)

4.42 1.16 2.06 4.37 6.84 11.27 (2.15)

7.22 6.76 3.93 1.31 0.26 6.96 (1.97)

(2.17) (2.61) (1.70) (0.69) (0.13)


1 (Low B/M)

Panel C2: Ex post return alpha (100) relative to the market for other return horizons Months

1

6

12

24

36

Alpha (diff-in-diff portfolio) t-stat

0.47 (1.30)

3.70 (1.89)

6.96 (1.97)

17.56 (3.28)

20.71 (3.02)

177


(2.50) (3.55) (1.66) (1.44) (2.65) (2.84) 24

0.173 0.152 0.062 0.038 0.047 0.219 0.062 0.067 0.033 0.026 0.023 0.085

(1.42) (2.74) (2.01) (1.37) (1.33) (2.01)

12 6

(2.12) (4.41) (2.16) (1.07) (1.39) (2.64)

0.342 0.261 0.067 0.018 0.072 0.415

(2.36) (4.21) (1.35) (0.60) (2.10) (2.82)

0.501 0.328 0.159 0.057 0.106 0.607

36

0.368 0.181 0.179 0.074 0.100 0.468 0.286 0.156 0.059 0.044 0.061 0.347

(0.01) (1.98) (1.24) (0.76) (1.16) (0.47) 0.000 0.010 0.007 0.003 0.004 0.004

1 h (in months)

Panel E: Ex post B/M portfolio returns on portfolio disagreement

top value quintile, the alpha spread between the high and low disagreement stocks is only 0.26% per year, which is statistically insignificant. The difference between the extreme value and growth quintiles is 6.96% per year (t-stat =1.97). The monotonic patterns across portfolios are similar for other return horizons. The results are statistically significant at the 95% level for the return horizons of one to three years, and significant at the 90% level for the return horizon of six months (Panel C2 of Table 6). The results using raw portfolio returns are similar though noisier because the high disagreement stocks tend to have high market beta. The results are also similar when controlling the SMB size factor and the UMD momentum factor. These results are unreported for brevity. I do not control for the Fama and French (1993) HML factor when computing the return alphas because this section studies portfolios sorted by B/M ratio. Consistent with Testable Implication 2, Panel C1 shows that, among high disagreement stocks, the value stocks have an annual alpha of 6.84% compared to growth stocks whose annual alpha is 4.42%, a difference of 11.27% (t-stat = 2.15). This outperformance by value stocks diminishes monotonically for portfolios with lower disagreement. Among the portfolio of stocks with the lowest disagreement, the alpha spread between value and growth stocks is only 4.31% per year (t-stat =1.63). Panels D and E of Table 6 provide evidence supportive of Testable Implications 3 and 4 regarding the contemporaneous and ex post relation between return and disagreement of growth/value stock portfolios. For each book-to-market sorted portfolio, disagreement is constructed bottom-up using long-term EPS growth rate forecasts. The bottom-up approach facilitates the study of such portfolio disagreement because analysts rarely produce top-down estimates for customized portfolios. Let st ðiÞ for i= 1,2,y,5 denote the disagreement of each of the five B/M portfolios in month t. Panel B shows the correlation matrix of the five portfolio disagreements. They are positively correlated, though the correlation diminishes for portfolios that are further apart in terms of the B/M ratio. Panel D conducts the following regression for each of the five B/M portfolios: Rth,t ðiÞ ¼ a þ b ðst ðiÞsth ðiÞÞ þ et :

1 (Low B/M) 2 3 4 5 (High B/M) 5–1

0.167 0.108 0.076 0.009 0.017 0.185 0.099 0.023 0.014 0.011 0.000 0.098 1 (Low B/M) 2 3 4 5 (High B/M) 5–1

(2.09) (0.80) (0.70) (0.78) (0.03) (2.08)

12 6 h (in months)

Panel D: Contemporaneous B/M portfolio returns on changes in portfolio disagreement

Table 6 (continued )

(2.65) (2.06) (2.41) (0.43) (0.94) (2.84)

24

(2.53) (2.01) (1.78) (1.70) (2.42) (2.73)

36

(2.52) (2.32) (3.49) (2.99) (2.26) (2.56)

178

sth,t ðiÞ denotes the value-weighted return from t h to t in excess of the linked T-bill rate for each B/M portfolio i= 1,2,y,5. The results in Panel D show that the growth stock returns are more positively related to the contemporaneous changes in portfolio disagreement.27 The difference between growth and value stocks is statistically significant and holds across various return horizons, consistent with Testable Implication 3. 27 There is some suggestive evidence in Panels D and E of Table 6 that value stocks may even have pessimists (bi o 0) as the marginal investor so that the value stocks’ contemporaneous return drops when disagreement increases and ex post return is high following high disagreement. However, this interpretation is subject to the caveat that it is unclear what the benchmark relation is in these two panels. Therefore, this paper focuses on the difference between growth and value portfolios.


To examine Testable Implication 4, Panel E of Table 6 conducts, for each B/M portfolio i= 1,2,y,5, the following regression: Rt,t þ h ðiÞ ¼ a þ b st ðiÞ þ et : Consistent with Testable Implication 4, the results in Panel E show that the ex post growth portfolio returns are more negatively related to portfolio disagreement.28 Taken together, the results show an interesting link between disagreement and the value/growth stock returns. Evidence in this section suggests that, controlling for disagreement, the marginal investor in growth stocks displays more optimism (in the sense of higher bi). This translates into a number of cross-sectional and timeseries predictions regarding growth/value stock returns, which are supported by the data. The results also provide a potential explanation to the finding in Campbell and Vuolteenaho (2004) that growth stocks are more sensitive to discount-rate news. This is because an increase in disagreement is associated with higher stock price (which can manifest as lower discount rate), and the effect is stronger for growth stocks (higher bi) than value stocks.

7. Robustness checks The scatterplot and the nonparametric estimate in Fig. 2, along with Fig. 3, indicate that the effect of disagreement on market return is not driven by just a few observations. To further confirm that it is not driven entirely by the dot-com era, a subsample analysis is conducted by dividing the sample period into two. The first subsample spans December 1981–December 1993, a total of 145 monthly observations. The second subsample starts from January 1994 and ends in December 2005, a total of 144 monthly observations. Regression (6) is run separately for each subsample. The results are in Panel A of Table 7. In both subsamples, there is a statistically and economically significant negative relation between market return and disagreement for the one- to three-year horizons. The effect of disagreement is similar in the subsamples for the one-year return and is somewhat stronger for the two- and three-year returns in the latter sample.29 Other subsample classifications such as before/ after year 1990 give similar results. A subsample analysis is also conducted for the HML return regression (10). The effect of disagreement on HML return is statistically and economically significant for both subsamples, though somewhat stronger in the more recent subsample. These results are unreported for brevity. 28 Similar to Fig. 2, I have checked the scatterplots of ex post return on portfolio disagreement for each of the B/M portfolios and the results in Panel E of Table 6 do not appear driven by just a few observations. I have also repeated the analysis for portfolios constructed by a double sort on B/M ratio and market capitalization. The result is similar except that it is somewhat noisier for small stocks, consistent with Panel B of Table 7. These results are unreported for brevity. 29 I have repeated the subsample analysis by including the controls one-by-one using only those control variables that are statistically significant in the regressions in Panel F of Table 3 and the results are similar. These results are unreported for brevity.

179

Panel B of Table 7 studies the effect of disagreement for size-sorted portfolios. Similarly, ex post size portfolio returns are negatively related to portfolio disagreement and the effect is stronger for the return horizons of one to three years. The statistical significance is stronger for large stocks, likely because they tend to have more analyst coverage, hence better measurement of disagreement. For example, a large stock may sometimes be followed by over 30 analysts. In contrast, some of the small stocks in the sample may have only two or three analysts. Also, when a single arbitrageur cannot undo the mispricing of a large stock, the synchronization problem among arbitrageurs (Abreu and Brunnermeier, 2002, 2003; Brunnermeier and Nagel, 2004) may create limits to arbitrage or even amplify the mispricing. High turnover can reflect disagreement (e.g., Scheinkman and Xiong, 2003; Baker and Stein, 2004). This paper has constructed disagreement using turnover (note that top-down and bottom-up turnovers coincide), and finds that turnover correlates negatively with ex post return. To the extent that turnover can be a proxy for disagreement, this is supportive evidence for the disagreement mechanism. However, turnover may have other interpretations (e.g., Amihud, Mendelson, and Pedersen, 2005). Therefore, Panel C of Table 7 controls for turnover when regressing market return on disagreement. The effect of disagreement remains statistically significant and is similar in magnitude to that in Panel A of Table 3. Compared to the regression with turnover alone (unreported), adding disagreement substantially increases explanatory power measured by the adjusted R-squares. De Bondt and Thaler (1985) and Fama and French (1988b) show that the stock market exhibits negative autocorrelation at long horizons. Panel D of Table 7 controls for lagged market return when regressing ex post market return on disagreement, and the effect of disagreement remains similar to that in Table 3. Panel E of Table 7 measures disagreement bottom-up using quarterly EPS forecasts (constructed in the same way as sNG ANN in Section 4 except that the standard deviation of annual EPS forecasts for a stock is replaced with the standard deviation of quarterly EPS forecasts times four). To overcome the mechanical drop in forecast standard deviation when a fiscal quarter-end becomes closer, a rolling mechanism similar to that in Section 4 is used. Specifically, the forecast standard deviation in December is measured using forecasts for the fiscal quarter ending in March next year. The forecast standard deviation in January is a weighted average with 2/3 weight on forecast standard deviation for the March quarter and 1/3 weight for the June quarter. In February, 2/3 weight is on the June quarter and only 1/3 weight is on the March quarter. In March, the entire weight is shifted to the June quarter (similarly for other months). Quarterly forecasts may incur noise relating more to the seasonal fluctuations rather than the long-run prospect of a company. Nonetheless, the results in this panel are similar (though somewhat stronger for short-horizon returns and weaker for longhorizon returns) relative to the results using longerhorizon forecasts.

180

Table 7 Robustness checks. Panel A conducts subsample analysis for the regression in Panel G of Table 3. Panel B shows, for each size portfolio, the regression results of ex post value-weighted portfolio return in excess of the risk-free rate on portfolio disagreement. The size portfolios are constructed monthly. Big/medium/small stocks are defined as those with the highest 30%/middle 40%/lowest 30% market capitalization using NYSE breakpoints. The portfolio disagreements are constructed as the value-weighted average of analyst forecast standard deviation of long-term EPS growth rate using stocks in each size portfolio. Panel C repeats the regression in Panel A of Table 3, controlling for the average monthly turnover in the past year. Following Baker and Stein (2004), turnover is stochastically detrended by subtracting the average turnover in the previous five years from it and the regression controls for the dividend-price ratio DP and the equity share of new issues EQUITYSHARE. Panel D regresses ex post h-month excess market return RM t,t + h on st , NG controlling for lagged h-month market return RM t h,t. Panel E repeats the regression in Panel A of Table 3 except that the disagreement sQTR is constructed bottom-up from the analyst forecasts of quarterly EPS, using firms that issue no annual or quarterly EPS guidelines. Panel F repeats the regression in Panel A of Table 3 except that the disagreement is measured by the equal-weighted average of individual-stock analyst disagreements over the long-term EPS growth rate, sEW . Panel G repeats the regression in Panel A of Table 3, controlling for the idiosyncratic risk in Goyal and Santa-Clara (2003). Panels H1 and H2 repeat Panels C1 and C2 of Table 6 except that the disagreement portfolio is sorted conditioning on the idiosyncratic volatility in Ang, Hodrick, Xing, and Zhang (2006). Panel I repeats the regressions in Panel E of Table 6, controlling for the cross-sectional value-weighted average of individual-stock idiosyncratic volatility for stocks in each book-to-market sorted portfolio. The t-statistics in parentheses are from Newey and West (1987), with the number of lags being equal to the return horizons. The sample period is January 1982–July 2001 in Panel E, and is December 1981–December 2005 in other panels. Return horizon (in months)

6

12

24

36

0.018 (1.47)

0.043 (1.09)

0.156 (3.16)

0.239 (3.87)

0.206 (3.88)

0.003 (0.16)

0.015 (0.24)

0.162 (2.50)

0.366 (3.84)

0.396 (6.26)

Panel B: Ex post size portfolio returns on portfolio disagreement 1 (Big) 0.005 (0.74) 2 0.005 (0.70) 3 (Small) 0.000 (0.05)

0.057 (1.35) 0.045 (1.94) 0.010 (0.37)

0.165 (2.35) 0.090 (2.61) 0.034 (0.82)

0.360 (2.76) 0.116 (2.53) 0.048 (1.16)

0.481 (2.11) 0.121 (2.03) 0.037 (0.54)

0.001 (0.18)

0.034 (0.81)

0.145 (2.27)

0.351 (3.36)

0.517 (2.69)

0.006 (0.90)

0.061 (1.51)

0.174 (2.53)

0.360 (3.16)

0.438 (2.32)

Panel E: Disagreement measured bottom-up using quarterly EPS forecasts 0.588 sNG QTR

2.461

4.466

8.165

9.553

(3.40) 11.5%

(2.89) 17.4%

(2.49) 18.9%

(1.75) 13.0%

0.055 (2.95) 9.0%

0.117 (3.22) 19.3%

0.194 (2.55) 26.5%

0.257 (2.45) 24.2%

0.059 (1.47)

0.167 (2.70)

0.332 (3.61)

0.405 (2.50)

Panel A: Subsample analysis December 1981–December 1993

s t-stat January 1994–December 2005

s t-stat

Panel C: Controlling for turnover

s t-stat Panel D: Controlling for lagged market return

s t-stat

t-stat Adj R2

(2.66) 3.1%

Panel F: Equal-weighted average of individual-stock long-term forecast dispersions 0.007 sEW t-stat (1.36) Adj R2 0.5% Panel G: Controlling for idiosyncratic risk

s t-stat

0.006 (0.89)


1

Panel H1: Ex post annual return alpha (100) relative to the market, SMB (size), and UMD (momentum) when disagreement is sorted conditional on idiosyncratic volatility Disagreement

1 (Low B/M) 2 3 4 5 (High B/M) 5–1 t-stat

1 (Low)

2

3 (High)

3–1

t-stat

2.32 5.63 7.05 7.35 9.78 7.46 (3.69)

0.94 2.01 5.98 6.48 7.64 8.58 (3.39)

5.47 0.10 3.45 6.11 9.98 15.46 (3.09)

7.79 5.73 3.60 1.24 0.21 8.00 (1.97)

(2.31) (2.74) (1.71) (0.70) (0.11)

Panel H2: Ex post return alpha (100) relative to the market, SMB, and UMD for other return horizons when disagreement is sorted conditional on idiosyncratic volatility 1

6

12

24

36

Alpha (diff-in-diff portfolio) t-stat

0.33 (0.98)

3.78 (1.71)

8.00 (1.97)

25.38 (4.21)

40.69 (4.36)

Panel I: Ex post B/M portfolio returns on portfolio disagreement, controlling for idiosyncratic volatility h (in months)

1

1 (Low B/M) 2 3 4 5 (High B/M) 5–1

0.005 0.014 0.010 0.003 0.004 0.001

6 (0.60) (2.23) (1.60) (0.72) (1.26) (0.08)

0.044 0.080 0.042 0.026 0.024 0.068

12 (1.12) (2.73) (2.46) (1.36) (1.42) (1.82)

0.148 0.152 0.066 0.040 0.051 0.198

24 (1.96) (3.95) (2.13) (1.13) (1.58) (2.55)

0.270 0.221 0.041 0.021 0.076 0.347

36 (1.98) (3.17) (0.89) (0.71) (2.34) (2.47)

0.381 0.229 0.115 0.062 0.117 0.498

(1.93) (2.01) (1.34) (1.83) (2.53) (2.25)


Months

181

182


The construction of bottom-up disagreement features value-weighting of individual-stock disagreements so far, which facilitates comparison with top-down disagreement because analysts typically make top-down forecasts for value-weighted market benchmarks. Because small stocks tend to have less analyst coverage compared to big stocks, value-weighting also helps reduce the measurement error of disagreement associated with small stocks. A concern with value-weighting is that it may potentially accentuate the unusual disagreement dynamics of a few big stocks. This unlikely drives the results because, while it is possible that the measured disagreement is pushed too high by a few big stocks, it is also possible that the measured disagreement is pushed too low. On average, it actually tends to bias against finding a relation between disagreement and return, from results on measurement error in the regression literature. Nonetheless, a direct check using equal-weighted individual-stock disagreements is helpful to guard against such a concern. Therefore, Panel F of Table 7 repeats the regression (3) except that the disagreement is constructed using the equalweighted individual-stock long-term EPS forecast dispersions and the results are similar to those in Table 3. In addition, results similar to Table 4 and Panel E of Table 7 are obtained from equal-weighted individual-stock annual and quarterly EPS forecast dispersions (unreported for brevity). Therefore, the results are unlikely driven by the weighting scheme of individual-stock disagreements. I have also used disagreement in log scale, a binary measure of disagreement (high versus low), disagreement constructed without first winsorizing individual-stock disagreements, and disagreement constructed using only stocks covered by at least five analysts. The results are largely similar and are unreported for brevity. High disagreement may be associated with high uncertainty and volatility.30 Goyal and Santa-Clara (2003) find that the equity premium is affected by the average stock variance, which is controlled for in Panel G of Table 7. The effect of disagreement remains similar. This paper has also replaced the average stock variance in Goyal and Santa-Clara (2003) with average idiosyncratic volatility, where the idiosyncratic volatility is estimated from the residual of stock return relative to the Fama and French (1993) three-factor model (see Ang, Hodrick, Xing, and Zhang, 2006, 2009), the effect of disagreement remains similar. Controlling other variables such as the market return volatility and skewness, or the Baker and Wurgler (2007) sentiment index yields similar results (unreported for brevity). Panel H of Table 7 repeats Panel C of Table 6, except that the disagreement portfolios are sorted conditioning on idiosyncratic volatility in Ang, Hodrick, Xing, and Zhang (2006). Specifically, stocks are first sorted into three portfolios of high/mid/low idiosyncratic volatility. Stocks within each idiosyncratic volatility portfolio are further sorted into three portfolios of high/mid/low

30 Pastor and Veronesi (2003, 2006) study the effect of uncertainty on stock valuation, though their models do not focus on expected stock return.

disagreement. The three high disagreement portfolios with high/mid/low idiosyncratic volatilities are then combined to form the final high disagreement portfolio. The mid/low disagreement portfolios are constructed similarly. Panels H1 and H2 show that the results after controlling for idiosyncratic volatility remain similar to Panels C1 and C2 of Table 6. The result is also similar if stocks are first sorted into decile portfolios of idiosyncratic volatility to give a finer control. Panel I of Table 7 repeats Panel E of Table 6, controlling for the valueweighted average of individual-stock idiosyncratic volatility for each B/M portfolio. The results are similar. In particular, the ‘‘5–1’’ coefficient for the control of idiosyncratic volatility is insignificant (unreported). Therefore, idiosyncratic volatility does not appear to drive the difference in growth/value stock return sensitivity to disagreement. Overly optimistic average belief can also contribute to overvaluation (i.e., when mi in Section 6 is above the fundamental). For example, Lakonishok, Shleifer, and Vishny (1994) and La Porta (1996) find supportive evidence of expectation errors. To account for potential errors related to the average forecast, this paper has repeated Panels H1, H2, and I of Table 7 replacing the idiosyncratic volatility with the average analyst forecast. The results are similar and unreported for brevity.

8. Conclusion This paper studies the asset pricing implications of disagreement, with a focus on its implications for stock portfolios. It shows that measuring portfolio disagreement from the bottom-up gives strong support for asset pricing theories incorporating disagreement such as Miller (1977). For the market portfolio, the ex post expected return is low following high disagreement and the horizon for low return is consistent with the speed of mean reversion in disagreement. Contemporaneously, variations in disagreement correlate positively with market return. In particular, an increase in disagreement manifests as a drop in discount rate. In the cross-section, this paper finds interesting implications from the interaction between disagreement and investor optimism, using book-to-market sorted portfolios as test assets. High disagreement stocks underperform low disagreement stocks, and the effect is stronger for growth stocks. The value premium is stronger among high disagreement stocks. Growth stocks are more sensitive to variations in portfolio disagreement than value stocks. These findings show that disagreement matters for important asset pricing issues including the equity premium, discount rate, and the value premium. It will be interesting in future work to see if the contrast between bottom-up and top-down disagreement applies to other markets. Such distinction may also apply in a corporate context (e.g., a corporation with multiple subsidiaries) which can generate potential implications for mergers and acquisitions or spin-offs. One may question whether disagreement will disappear after sufficiently long periods of learning. Acemoglu,


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Does access to external finance improve productivity? Evidence from a natural experiment$ Alexander W. Butler a,n, Jess Cornaggia b a b

Jones Graduate School of Business, Rice University, 6100 S Main St, MS-531, Houston, TX 77005, USA Kelley School of Business, Indiana University, 1309 E 10th St, #370A, Bloomington, IN 47405, USA


abstract

Article history: Received 16 July 2008 Received in revised form 19 December 2008 Accepted 26 February 2009 Available online 19 August 2010

We study the relation between access to finance and productivity. Our contribution to the literature is a clean identification of a causal effect of access to finance on productivity. Specifically, we exploit an exogenous shift in demand for a product to expose how producers adapt their productivity in the presence of varying levels of access to finance. We use a triple differences testing approach and find that production increases the most over the sample period in areas with relatively strong access to finance, even in comparison with a control group. This result is statistically significant and robust to a variety of controls, alternative variables, and tests. The causal effect of access to finance on productivity that we find speaks to the larger role of finance in economic growth. & 2010 Published by Elsevier B.V.

Keywords: Access to finance Economic growth JEL classifications: G21 G32 D24

1. Introduction Does finance cause economic growth? The literature addressing the question of whether finance creates growth (e.g., Hicks, 1969) or follows growth (e.g., Robinson, 1952) is vast, and dates back at least as far as Schumpeter (1912). Because finance and growth are endogenously determined,

$ The paper was completed while we were at the University of Texas at Dallas. We are grateful for helpful comments from Bo Becker, Mitchell Berlin, Lee Ann Butler, Gerry Gay, Radha Gopalan, Gustavo Grullon, Debarshi Nandy, Andy Naranjo, Valery Polkovnichenko, David Robinson, Phil Strahan, Masahiro Watanabe, James Weston, Harold Zhang, audience members at the 2008 Western Finance Association annual meetings, and seminar participants at Baylor University, Commodity Futures Trading Commission, Federal Deposit Insurance Corporation, Massachusetts Institute of Technology-Sloan, University of Florida, University of Oklahoma, Purdue University, Rice University, Stanford Graduate School of Business, University of Texas at Dallas, Wayne State University, and World Bank. Special thanks go to Weston Rose of Deere & Company and Caitlin Boyle of King Corn for help in acquiring information about corn production. Any errors are our own. n Corresponding author. Tel.:/fax: + 1 713 348 6341. E-mail address: [email protected] (A.W. Butler).

0304-405X/$ - see front matter & 2010 Published by Elsevier B.V. doi:10.1016/j.jfineco.2010.08.009

one of the biggest hurdles facing empirical work in this area is clean identification of the direction of causality. Little exists in the way of clearly exogenous variation in finance for researchers to exploit. Further, what the precise channels are through which any finance-to-growth effect operates remain unclear. This paper examines the impact of access to finance on productivity as a candidate explanation to help bridge the gap, and we use a natural experiment created by a government mandate to achieve identification in our tests. In the United States, the Energy Policy Act of 2005 mandated that renewable fuel additives in gasoline nearly double to 7.5 billion gallons by 2012. This act, combined with rising crude oil prices at the time and federal biofuel tax credits, created an exogenous shift in demand for US corn, the main ingredient in US ethanol production. We use these events as a natural experiment to examine the finance-growth nexus: whether access to finance is a critical component for encouraging economic growth and productivity. We use county-level data on crops, weather, and finance in midwestern states (the primary cornproducing region in the United States known colloquially as the ‘‘corn belt’’) during 2000–2006 to study the

A.W. Butler, J. Cornaggia / Journal of Financial Economics 99 (2011) 184–203

productivity response of farmers to the shift in demand for corn that the Energy Policy Act of 2005 created. Consistent with the view that finance affects growth, we find a large shift in corn productivity in response to the ethanol-induced shift in demand and that this productivity improvement is most pronounced in counties with high levels of bank deposits. We use a triple differences (differences-in-differences-in-differences, DIDID) testing procedure. The first difference is the response of productivity to greater versus lesser access to external finance. The second difference is the response of productivity to a shift in demand. The third difference is the response of productivity for the commodity with increased demand (corn) versus a control crop that had no shift in demand (soybeans). Our main variable of interest is the interaction of these three: productivity response for corn (relative to soybeans) during the ethanol boom (relative to the pre-ethanol mandate period) across varying levels of access to finance. To construct our tests, we need an appropriate measure of productivity for the farming industry. Farmers and economists (e.g., Feder, 1985, among many others) commonly view crop yields as a relevant measure of farming productivity. Crop yield is output per unit of land, specifically, the harvested number of bushels of a crop per acre planted in that crop. These data are available for each crop by county on an annual basis. The advantages of our proxy for productivity compared with, say, total factor productivity are that it is easily measured, need not be estimated like a total factor productivity measure, and is specific to the industry we study. We also need an appropriate empirical measure of access to finance. In similar spirit to Becker (2007), we use a measure based on aggregate county-level bank deposits. Becker (2007) shows that local bank deposit supply has a positive and significant effect on local economic outcomes through the loans that the banks make. What is particularly useful for our study is Becker’s result that the market for bank capital is segmented geographically. That is, at the metropolitan statistical area (MSA) and zip code levels, local deposits (and hence loan supply) affect local economic outcomes. Becker’s result is consonant with Petersen and Rajan (2002), who find that the median distance between small businesses and their banks in recent years is only about five miles. For comparison, the size of the median county in our sample is 416 square miles, or about 20 miles by 20 miles. Given the highly localized nature of bank lending, our access to finance measure is, arguably, a good one. Nonetheless, we examine a number of alternative measures of access to finance and find similar results. The magnitude of our results suggests that the effect of access to finance on growth is economically nontrivial. A simple two-way sort demonstrates that, in response to the shift in demand for corn, corn yields in the midwestern United States have increased by 10.4 bushels per acre more in counties with high bank deposits than in counties with low bank deposits over the sample period in comparison with the control crop. To provide some perspective, the standard deviation of corn yields across counties in Iowa, the state producing the most corn, was only 8.8 bushels per acre in 2006.

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Our DIDID procedure allows us to dismiss many alternative hypotheses. Our results indicate that the increase in productivity is restricted to corn, which experienced a large demand shift, but not our control crop (soybeans); productivity is greater during the ethanol boom period compared with before the ethanol boom period; the increase in productivity occurs in areas (counties) that have substantial access to finance, but not those that have less financial development. Thus, a competing alternative hypothesis must relate to corn only, to the ethanol boom period only, and to the financeheavy counties only. This rules out, among other things, general trends in farm productivity. There are other determinants of crop yields besides access to finance. Soil fertility and weather are two obvious things that affect agriculture. We control directly for weather with precipitation and temperature variables and control indirectly for soil fertility and other unobservables with state or county fixed effects. One potential concern is that of reverse causality. If a county experiences high crop yields, this leads to more wealth for the farmers in the county, who could then deposit their wealth in local banks. In this case, finance and productivity are linked, but finance follows (not facilitates) productivity. We use additional tests to help rule out this alternative explanation. First, we use the number of bank branches in a given county as an alternative measure of access to finance. Although in the long run bank branches could migrate to where there is economic prosperity, in the short run the number of bank branches should be insensitive to changes in crop yields, yet be indicative of greater access to finance. Second, we use an instrumental variables approach with either lagged measures of access to finance or demographic variables serving as instruments for current access to finance. This instrumental variables approach forces the exogenous portion of access to finance to explain productivity. These alternative approaches leave all of our main conclusions unchanged. Our results are robust to a variety of additional changes in our baseline tests including changes in our measure of access to finance, our control crop, our productivity benchmark, our event defining the natural experiment (the sudden switch from sugar to high fructose corn syrup by major soft drink manufacturers in 1985, which we use in conjunction with a different measure of access to finance based on bank branching deregulation (as in Jayaratne and Strahan, 1996), general trends in farm productivity, and unobservable time invariant factors such as stable demographic characteristics that would be absorbed by state or county fixed effects specifications. Our paper connects the literature on determinants of economic growth with that on how corporate financing constraints affect investment decisions. The financial constraints literature shows that the financing frictions and the costs of external finance can have substantial impacts on firms’ operating decisions such as investment timing and allocations in real assets (Whited, 1992, 2006; Chava and Roberts, 2008). And, like Bakke and Whited (2008), we examine how financing frictions affect real economic outcomes. While their paper looks at corporate

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Table 1 Crop details. This table specifies the variety of each crop we study in the paper. This table also contains information quantifying recent US harvests of each crop measured and the time of year that each crop is planted and harvested. Harvest amounts, as well as planting and harvest seasons information, come from the United States Department of Agriculture. Crop

Variety

2002 harvested acres (millions)

2007 harvested acres (millions)

Planting season

Harvest season

Corn Soybeans

Yellow-kernelled (field corn) Yellow

68.2 72.4

85.4 63.3

Spring Late spring

Fall Fall

operating decisions, such as employment and investment, we examine the ultimate outcomes, in the form of changes in productivity, of operating decisions. Finance and growth papers similar to ours include Gatti and Love (2006), who study the relation between access to credit and total factor productivity in a sample of Bulgarian firms. Our findings and theirs are consistent, but one of the important differences is that we study a developed economy, which sets our paper apart from the vast majority of papers in the finance and growth literature (for example, Djankov and Hoekman, 1999; Maurel, 2001). We also employ a testing procedure that resolves the problem of endogeneity between access to finance and productivity, and we use an unambiguous measure of productivity, instead of estimated measures such as total factor productivity. The rest of the paper is organized as follows. Section 2 has institutional details to provide background information on the research setting. Section 3 describes the analytic framework from which we approach the relation between access to finance and productivity. Section 4 discusses our data and describes their basic properties. Section 5 describes our methods for testing the relation between access to finance and productivity, and it gives results. Section 6 discusses robustness tests for these results, and Section 7 concludes. 2. Institutional detail This section contains institutional details on corn and soybeans crops, ownership of American farms, and ethanol production. 2.1. Corn and soybeans Corn, soybeans, and other crops are bought and sold on midwestern US agricultural spot markets. According to the 2002 Census of Agriculture conducted by the National Agricultural Statistics Service (NASS), a division of the United States Department of Agriculture (USDA), corn and soybeans are the two largest planted cash crops in the United States, with harvests of 68.2 million acres and 72.4 million acres, respectively. Table 1 contains basic information regarding these crops. In recent years, soybeans were the largest harvested crop in the United States. By 2007, however, corn supplanted soybeans as the largest harvested cash crop in the United States. Despite the change of status between corn and soybeans as the most widely harvested crop, they remain the two largest harvested crops, overall.

Corn comes in two main varieties: sweet corn and yellow-kernelled corn (i.e., field corn). Yellow-kernelled corn is an actively traded commodity; sweet corn is not. Yellow-kernelled corn is the main ingredient in ethanol production in the United States, and thus it is the focus of this paper. Soybeans effectively come in only one variety: yellow soybeans. 2.2. Ownership of American farms A statistical brief published by the Bureau of the Census states: ‘‘People own most farmland. Some 2.6 million owners are individuals or families, and they own more than two-thirds of all farm acreage. Fewer than 32,500 non-family-held corporations own farmland, and they own less than 5 percent of all U.S. farmland.’’1 Securities and Exchange Commission filings by large American food processing companies (e.g., ConAgra and Archer Daniels Midland) bear this out. Rather than being actively involved in growing crops, these companies are downstream from the actual farming operations, and use harvested crops as inputs to their operations. 2.3. Institutional detail: ethanol According to a 2007 report from the Economic Research Service, a division of the USDA, the demand for ethanol in the United States has surged due to a number of complementary forces.2 First, market conditions for crude oil have changed. Crude oil prices averaged $20 per barrel in the 1990s but rapidly grew to a record $59 per barrel in 2006. As crude oil becomes more expensive, ethanol becomes more attractive as an alternative fuel source. Second, the Energy Policy Act of 2005 mandated that renewable fuel additives in gasoline (ethanol is a principal renewable fuel) reach 7.5 billion gallons by 2012. Further, this new legislation provides no liability protection for the gasoline additive methyl tertiary butyl ether (MTBE). Many states have recently banned MTBE, a suspected carcinogen that can contaminate aquifers of drinking water. Without liability protection, ethanol becomes an increasingly attractive substitute. Third, new tax laws provide further incentives for biofuels. Tax credits of 51 cents per gallon of ethanol blended with gasoline are available to US gasoline manufacturers under the current federal tax law. Imported ethanol faces a tariff 1

Source: http://www.census.gov/apsd/www/statbrief/sb93_10.pdf. Source: Paul C. Wescott, Economic Research Service (http://www. ers.usda.gov/Publications/FDS/2007/05May/FDS07D01/fds07D01.pdf). 2


of 54 cents per gallon (with the exception of duty-free status for certain Central American and Caribbean countries on up to 7% of the US market for imported ethanol). Hahn (2008) discusses economic and political issues affecting ethanol production. The ethanol production industry in the midwestern US is not heavily concentrated. Our snapshot of ethanol production capacity data for 2006 includes information for 120 ethanol plants in the midwestern United States. Sixty-seven of those plants are owned by limited liability corporations (LLCs) or limited partnerships (LPs), suggesting that small companies own a large percentage of the plants. Most of the remaining plants are owned by corporations, although we cannot determine the size of many of the corporations because they are not publicly traded. As of April 2006, the 67 plants owned by LLCs or LPs have a combined ethanol production capacity of 3,713 million gallons of ethanol per year. The remaining plants have a combined production capacity of 4,737 million gallons of ethanol per year. 3. Hypothesis development Our analysis focuses on how a producer’s budget at time t is a function of her ability to borrow against future cash flows and the present value of her future production. A producer’s budget increases with her ability to borrow against future cash flows, and a producer can enhance her productivity by taking advantage of this expanded budget. In our empirical tests, we capture cross-sectional variation in ability to borrow against future cash flows with county-level bank deposits. The relation between budget and bank deposits follows because, when bank deposits are high, the banks holding them will have more funds to provide as loans (i.e., access to finance increases), as in Becker (2007). A producer’s budget further increases with the present value of future production. This effect follows because lenders favorably view expected increases in production. That is, a producer is able to borrow greater amounts when the value of her future productivity is expected to be high. Our empirical tests center on the idea that the ethanol boom increased the present value of future cash flows to growing corn and that the ability to borrow against these future cash flows varies cross-sectionally county by county depending on the accessibility of finance. Although the available data are too coarse to allow us to scrutinize individual farms’ specific uses of an expanded budget—that is, we do not know if corn farmers use their larger budgets for increased capital expenditures, for labor costs, or for buying more land—we can test the idea that the availability of external finance could allow producers in an area to improve their productivity in response to a shift in demand for their product. 4. Data Our data are on an annual frequency and are made up of county-level variables from the 12 states of the midwestern United States (Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, South Dakota, and Wisconsin) from 2000 to 2006.

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According to our calculations from USDA data, these 12 states account for about 88% of all US corn production.

4.1. Independent variables The first independent variable of interest is the ethanol boom period dummy. We select 2005 as the starting year of the ethanol boom. The ethanol boom period dummy is equal to one in 2005 and 2006 and zero in previous years. If farmers correctly anticipated the enactment of the Energy Policy Act of 2005, then such foresight would bias against finding our results. The second independent variable of interest is access to finance. In similar spirit to Becker (2007), we use county-level bank deposits to proxy for access to finance. Bank deposits data come from the Federal Deposit Insurance Corporation (FDIC) website (http://www2.fdic.gov/sod/index.asp). We sum all bank deposits held by banks within a given county insured by the FDIC each year. Noting that many banks rely heavily on deposit financing, Becker (2007) shows a positive effect of local deposit supply on loan supply, and hence local economic activity. We expect better access to finance in counties with high levels of bank deposits. We also expect banks with more deposits to make more loans. This appears to be the case in our sample. Because we are interested particularly in agricultural loans, we compute the correlation between deposits and loans to finance agricultural production from 2000 to 2006. The data we use are bank-level loan and deposit data from the Reports of Condition and Income (Call Reports) published by the FDIC. The correlations between deposits and loans to finance agricultural production are positive and statistically significant. For all banks in the United States the correlation is 0.52; for the subsample of unit banks in the midwestern United States the correlation is 0.65. We are particularly interested in unit banks because they tend to be small and local, and farmers tend to borrow from them.3 The bottom line is that banks with more deposits make more agricultural loans, which is a key insight for understanding the channel through which local bank deposits affect local farming outcomes. Our baseline measure of access to finance is a poorfinance county dummy variable (Low Deposits) equal to one if the level of bank deposits in a given county falls into the bottom quintile of all county-level bank deposits for a given year and zero otherwise. Although other sources of external finance are available to farmers (e.g., federal farm loans programs), commercial banks provide the majority of non-real estate farm loans (Cramer, Jensen, and Southgate, 2001, and our own calculations from USDA data). The presence of other sources of finance works against our findings by making local bank finance less important to local economic outcomes. Fig. 1 shows the change of relative densities of bank deposits across the midwestern United States from 2000 to 2006. 3 Koo, Duncan, and Taylor (1998) find that local commercial bank financing is the greatest source of credit used by farmers in the United States. Specifically, 63% of farmers use local commercial bank financing. Only 4% of farmers use nonlocal commercial bank financing.

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Fig. 1. Changes of county-level bank deposits. This figure shows the change of relative density of bank deposits within counties in the midwestern United States from 2000 to 2006. Darker shading indicates greater growth in bank deposits.

Fig. 2. Changes of county-level corn yields. This figure shows the change of relative density of corn yields produced by counties in the midwestern United States from 2000 to 2006. Darker shading indicates relatively greater growth in corn yields.

4.2. Dependent variables Our primary dependent variable is crop yield, measured in bushels per acre, which proxies for productivity. Bushel sizes vary somewhat by crop, but they are typically around 50 harvested pounds of a given crop. Crop yields data come from the NASS. Figs. 2 and 3 show the changes of concentrations of corn and soybeans yields across the midwestern United States from 2000 to 2006.

4.3. Control variables We collect county-level ethanol production capacity as of April 2006, measured in millions of gallons produced per year. Ethanol production capacity data come from the Renewable Fuels Association (RFA) website (www.etha nolrfa.org/industry/locations/). We have two measures of

ethanol production capacity: ethanol production capacity in place, and ethanol production capacity under construction or planned for expansion. Fig. 4 shows a map of ethanol production capacity as of 2006 plotted over county-level changes in corn yields. We sum at the county level across ethanol plants in the county to determine the ethanol production capacity in place and under construction or planned for expansion. A total of 110 counties in our sample have ethanol production capacity in place, under construction, or planned for expansion as of 2006. Ethanol producers could choose to build their plants in counties with high corn yields in an effort to minimize transportation costs. Therefore, we expect to see a positive relation between yields and whether or not a county has an ethanol production facility. Not surprisingly, temperature and precipitation play an important role in the production of corn and soybeans


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Fig. 3. Changes of county-level soybean yields. This figure shows the change of relative density of soybean yields produced by counties in the midwestern United States from 2000 to 2006. Darker shading indicates relatively greater growth in soybean yields.

Fig. 4. Ethanol production capacity plotted over changes of corn yields. County-level ethanol production capacity data are represented by pie charts. Black slices represent in-place ethanol production capacity as of April 2006, and white slices represent ethanol production capacity planned for expansion. Pie size represents current plus future ethanol production capacity. Layered underneath the ethanol production capacity data are relative densities of changes of corn yields produced by counties in the midwestern United States from 2000 to 2006. Darker shading indicates relatively greater growth in corn yields.

(see Thompson, 1986; Carlson, Todey, and Taylor, 1996). We control for meteorological conditions in our multivariate regressions by including growing degree days and inches of precipitation (and, as a robustness test, their squared terms to allow for nonlinearities). We collect daily observations for both of these variables from Weather Underground (www.weatherunderground.com), a web-based commercial weather service. We consider the growing seasons listed in Table 1 and sum both of these variables from May 1 through October 31 for each year. Growing degree days (GDD) is a typical measure of temperature relevant for agriculture and is defined as D X T þ Tmin,d GDD ¼ Tbase ,0 , max max,d ð1Þ 2 d¼1

where D equals the total number of days from May 1 through October 31, Tmax,d equals the maximum temperature for a given day, measured in degrees Fahrenheit, Tmin,d equals the minimum temperature for a given day, measured in degrees Fahrenheit, and Tbase equals the base temperature of 50 degrees Fahrenheit. Weather stations are distributed sporadically across counties in the midwestern United States. Some counties have one or more weather stations, but most have none. We pick four weather stations for each state that are approximately evenly distributed geographically, and we assign the data from the weather stations to the closest counties. This approach assumes that meteorological conditions within regional clusters of counties do not have significant variation. This is probably a safe

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Table 2 Summary statistics. Panel A presents pooled summary statistics for county-year-crop observations. We examine counties in the 12 midwestern states each year from 2000 to 2006 with nonzero yields of corn and soybeans. Individual crop yields are measured in bushels per acre. Crop yields data come from the National Agricultural Statistics Service, which is affiliated with the United States Department of Agriculture. Deposits represents the sum of all deposits held within banks insured by the Federal Deposit Insurance Corporation (FDIC) for a given county and a given year, measured in millions of dollars. Branches represents a count of all bank branches insured by the FDIC for a given county and a given year. Deposits and branches data come from the FDIC’s website. Population Density is equal to the county population for a given year divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given county-year, measured in thousands of dollars per person. Population, unemployment, and per capita income data come from the US Census Bureau’s website. Precipitation and GDD represent the inches of precipitation and number of growing degree days in an associated crop’s region from May through October of a given year, respectively. Meteorological data come from weatherunderground.com. Panel B presents summary statistics for standard deviations of crop yields at the county level. For example, N is the number of counties growing a particular crop any year from 2000 to 2006, Mean is the average standard deviation of counties’ crop yields from 2000 to 2006, and so forth. Variable

N

Mean

Standard Deviation

Minimum

25%

Median

75%

Maximum

Panel A Corn Yield Soybeans Yield Deposits Branches Pop. Density Unemployment Per Capita Income Precipitation GDD

6,723 6,323 13,594 13,594 12,918 13,594 13,594 12,975 12,975

130.2 38.9 1,064 23.6 261.3 4.8 26.2 25.0 2,836

34.5 10.1 5,677 57.5 1,242.7 1.6 4.6 21.5 587

0 2.9 0.8 0 0.9 1.8 8.9 2.5 1,267

109.3 32.0 151 7 29.0 3.6 23.1 16.1 2,434

135.4 40.0 300 11 72.2 4.6 25.7 20.7 2,833

155.1 46.9 638 21 175.1 5.7 28.6 27.3 3,219

220.0 67.0 180,338 1,616 32,789.8 13.1 52.5 227.5 4,289

982 929

19.8 6.5

7.3 2.1

15.0 5.2

18.5 6.4

23.8 7.8

46.6 14.6

Panel B SD of Counties’ Corn Yields SD of Counties’ Soybean Yields

assumption because the midwestern states exhibit little variation in topography and geology, especially within each state.4 We control for population density, because it could be related to deposits (urban areas are likely to have more financial institutions). Population density could also directly correlate with crop yields. For example, counties with higher levels of urbanization could be less suitable for agricultural growth (due to poorer air quality or less arable land) or because, when population density increases, residents urbanize land less suitable for agriculture, increasing yields per planted acre. We use the US Census Bureau (http:// www.census.gov/main/www/access.html) estimates of county populations each year from 2000 to 2006 and calculate population density by dividing the estimate of a county’s population for a given year by the county’s square mileage. Local economic conditions could be correlated with crop yields. We control for local economic conditions with two additional variables: county-level unemployment rates and county-level per capita income. Data on unemployment and per capita income are available from the US Census Bureau (http://www.census.gov/support/DataDownload. htm). Both of these measures are available on an annual basis from 2000 to 2006. We also control for whether a county had an ethanol plant in place in 2006 or had an ethanol plant under construction or planned for expansion. Ethanol production capacity and access to finance could be correlated. The county-level data for corn and soybeans in the midwestern United States from 2000 to 2006 give 12,849

4 For a whimsical piece of evidence supporting this claim, see Fonstad, Pugnatch, and Vogt (2003).

0 0

county-year-crop observations. Table 2 provides summary statistics for our independent, dependent, and control variables. Panel A presents pooled summary statistics for county-year-crop observations. The maximum values for deposits and population density come from Cook County, Illinois, which contains the city of Chicago. Panel B presents summary statistics for standard deviations of county-level crop yields. This information is useful for interpreting the economic magnitudes of the forthcoming regression results. We present correlations among key variables in Table 3. 5. Methods and results This section describes our baseline econometric methods and the main results of the paper. 5.1. Agricultural lending in the corn-heavy counties We motivate our baseline tests by comparing agricultural lending in the top corn-producing counties in the midwestern United States with agricultural lending in the rest of the country. The idea here is to determine whether the share of agricultural loans in total loans has increased in counties experiencing the greatest growth in corn yields. We begin by calculating the change in average corn yield in all midwestern counties from 2000 to 2006. We rank these changes and focus on the one hundred counties exhibiting the greatest gains in corn yields over this time period. We randomly select one unit bank for each of these one hundred counties, and calculate the bank’s ratio of its loans to finance agricultural production to total loans, which we call simply an agriculture loan ratio, for


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Table 3 Correlation matrix. This table presents pairwise correlations of county-year observations. We examine all counties in the 12 midwestern states each year from 2000 to 2006 and report information on corn and soybeans. Individual crop yields are measured in bushels per acre. Crop yields data come from the National Agricultural Statistics Service, which is affiliated with the United States Department of Agriculture. Deposits represents the sum of all deposits held within banks insured by the Federal Deposit Insurance Corporation (FDIC) for a given county and a given year, measured in thousands of dollars. Branches represents a count of all bank branches insured by the FDIC for a given county and a given year. Deposits and branches data come from the FDIC’s website. Population Density is equal to the county population for a given year divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given county-year, measured in thousands of dollars per person. Population, unemployment, and per capita income data come from the US Census Bureau’s website. GDD and Precipitation represent the number of growing degree days, and inches of precipitation in an associated crop’s region from May through October of a given year, respectively. Meteorological data come from weatherunderground.com. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively.

Corn Yield Soybeans Yield Deposits Branches Population Density Unemployment Per Capita Income Precipitation

GDD

Corn Yield

0.028nn 0.062nnn 0.014 0.017 0.106nnn 0.014 0.130nnn 0.097nnn

0.779nnn 0.021n 0.042nnn 0.069nnn 0.037nnn 0.187nnn 0.082nnn

Soybeans Yield

0.007 0.004 0.012 0.077nnn 0.162nnn 0.101nnn

Deposits

Branches

0.941nnn 0.012 0.044nnn 0.271nnn 0.021n

0.008 0.008nnn 0.386nnn 0.016

the first and last years of the sample period (2000 and 2006). We then match our randomly selected unit bank with a matching unit bank outside the midwestern United States. For the year 2000, we classify all unit banks outside the midwestern United States into ten bins based on total assets (bank size) and then subdivide each of the ten bins into ten additional bins by total loans to finance agricultural production (agricultural specialization of the bank). Therefore, we have one hundred bins. We determine which of the one hundred bins each of the unit banks from our top-one hundred-corn-growth counties would be in and then choose as the best match in that bin the unit bank that minimizes the sum of squared percentage differences in total assets and total loans to finance agricultural production. We compare the sample and matched banks’ agriculture loan ratio from 2000 to 2006. We find that this ratio declines by 0.014 for the non-midwestern matched banks from 2000 to 2006 (perhaps due to an increase in real estate lending). However, the agriculture loan ratio increases by 0.013 for unit banks residing in the top-one hundred-corn-growth counties. Both the increase in agriculture loan ratio for our midwestern banks and the decrease in the same for the nonmidwestern matched banks are statistically significant at the 5% level. Table 4 displays these results. For the sake of comparison, the average standard deviation of the ratio of the agriculture loan ratio for all banks in the United States from 2000 to 2006 was 0.011, so these differences are economically meaningful as well. 5.2. Differences-in-differences-in-differences: two-way sorts We sort crop yields into 35 groups. First, we split the sample by year into seven groups (i.e., the data for each year from 2000 to 2006 become a group). Within each year, we then form five quintiles based on the county-level bank deposits. That is, we place yields coming from counties with the lowest quintile of bank

Population Density

0.046nnn 0.290nnn 0.009

Unemployment

Per Capita Income

0.228nnn 0.021nn

0.026nnn

Table 4 Univariate tests of agricultural lending as a fraction of total loans. This table presents the mean ratio of loans to finance agricultural production to total loans from 2000 to 2006. We compute this ratio for one hundred unit banks in the midwestern United States residing in counties experiencing the greatest growth in corn yields over our sample period and matching banks outside the midwestern United States with similar levels of agricultural loans and total assets as of 2000. We use nn to represent significance at the 5% level based on two-tailed t-tests. Year

Top-one hundredcorn-growth counties

2000 mean 2006 mean

0.174 0.187

Difference

0.013nn

Matched counties outside the midwest 0.221 0.207 0.014nn

deposits in the first group, yields coming from counties with the next-lowest quintile of bank deposits in the second group, and so forth, until we finish by placing yields coming from counties with the highest quintile of bank deposits in the fifth and final group. Then we average the yields. This procedure creates a seven-by-five matrix of average yields. We calculate the first difference by subtracting the average yield of the low bank deposits group of a given year from the average yield of the high bank deposits group for the same year. We perform a two-tailed t-test to determine if the difference is statistically significant. We perform this procedure for each year, from 2000 through 2006. The first difference demonstrates whether, for a given year, the average yield from a county with relatively high access to finance is higher than the average yield from a county with relatively low access to finance. We calculate the second difference by subtracting the first difference for 2000 from the first difference for 2006. We perform a two-tailed t-test to determine if the second difference is statistically significant. This second difference demonstrates whether the gap in productivity between counties with high access to finance and low

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access to finance is simultaneously expanding with the increased demand for corn. We calculate the third difference after repeating this entire process for a control crop (soybeans). By comparing the second difference of corn with that of soybeans, we produce a third difference. This third difference allows us to assess whether the increasing gap found by the second difference is unique to corn or simply a by-product of an economy-wide boom in agricultural productivity. Table 5 gives results for the DIDID approach. Our results show that corn yields in the midwestern United States have increased by 10.4 bushels per acre more in counties with high bank deposits than in counties with low bank deposits over the sample period. To put this in perspective, 10.4 bushels per acre is approximately half of a standard deviation of an average county’s annual corn yield per acre. In contrast, the difference in soybean yields between counties with varying levels of bank deposits shows no significant change over the sample period. These results demonstrate how access to finance can affect productivity when an exogenous increase in demand for a product arises. Corn producers in counties with high levels of bank deposits respond to the exogenous shift in demand for corn by ramping up productivity. However, corn producers in counties with low levels of bank deposits do not increase productivity to the same extent. The demand for soybeans has not experienced a similar exogenous shift. Therefore, as expected, the difference in soybean productivity across counties with low and high levels of bank deposits has remained stable. We show this result graphically in Fig. 5. Table 5 shows an interesting feature of the relation between finance and productivity. The largest interquintile increase in productivity comes between the lowest and second-lowest quintiles. The difference in the mean corn yield between the lowest and

second-lowest quintile is 11.9 bushels, which is almost double the difference between second-lowest and the middle quintile. Differences between other quintiles are even smaller. We interpret this result as evidence that access to finance has a nonlinear influence on productivity. That is, increases in access to finance improve productivity, but decreasingly so. Accordingly, we use a dummy variable (equal to one for countyyear observations in the bottom quintile of bank deposits and zero otherwise) for low access to finance in our regressions that follow. We also use other measures, such as a continuous measure of deposits and number of bank branches, and find similar results. 5.3. Regression specification: differences-in-differences We perform multivariate ordinary least squares (OLS) regressions. Eq. (2) shows our basic regression approach. Subscripts i, t, and k denote county, year, and crop, respectively. Yieldi,t,k ¼ b1 Corn Dummyk Access to Financei,t Ethanol Periodt

þ b2 Corn Dummyk Access to Financei,t þ b3 Corn Dummyk Ethanol Periodt þ b4 Corn Dummyk þ b5 Access to Financei,t Ethanol Periodt þ b6 Access to Financei,t þ b7 Ethanol Periodt þ Controls þ Constantþ ei,t,k

ð2Þ

Ethanol Period is a dummy variable equal to one during the ethanol boom period (2005 and after) and zero otherwise. This variable proxies for the demand for corn, because the ethanol boom period provides an impetus for corn farmers to boost productivity. We do not include year dummy variables to capture time varying trends in corn farming productivity because doing so would introduce collinearity with Ethanol Period. Instead, we

Table 5 Univariate tests of corn and soybean yields using a two-way sort. Each year-deposit quintile bin contains the average corn (top) and soybean (bottom) yield for year and deposit quintiles. Crop yields data come from the National Agricultural Statistics Service’s (NASS) website, which is affiliated with the United States Department of Agriculture (USDA). Difference represents the difference between the average yields associated with the highest and lowest levels of deposits for a given year (right column), or the difference between the average yields associated with the earliest and latest years for a given deposit quintile (bottom row). We use two-tailed t-tests to examine the differences in means. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Year 2000 2001 2002 2003 2004 2005 2006 Mean Difference (2006–2000)

Deposits: low to high 114.6 32.8 117.0 36.0 105.6 32.9 114.5 32.3 134.0 37.0 125.2 40.2 117.2 39.0 118.3 35.7 2.6 6.2nnn

128.6 36.5 127.3 38.6 117.0 37.2 122.8 30.9 148.0 40.8 136.9 42.7 130.5 41.1 130.2 38.3 1.9 4.6nnn

135.9 40.2 134.2 40.1 122.0 38.9 130.5 32.8 154.4 43.4 140.2 44.2 140.4 43.8 136.8 40.5 4.5nn 3.6nnn

Difference (high–low) 138.5 39.7 133.7 40.2 121.1 39.0 137.4 33.8 155.9 44.0 142.8 43.9 146.5 45.1 139.4 40.8 8.0nnn 5.4nnn

134.3 39.1 130.4 39.0 115.2 38.0 138.0 32.2 151.0 42.6 140.8 43.7 147.3 44.9 136.7 39.9 13.0nnn 5.8nnn

19.7nnn 6.2nnn 13.4nnn 3.0nnn 9.6nnn 5.1nnn 23.5nnn 0.1 17.0nnn 5.6nnn 15.6nnn 3.5nnn 30.1nnn 5.9nnn

10.4nnn 0.3


193

Yield (bushels per acre)

160 140 120 100 80 60 40 20 0 2000 High corn

2001

2002

Low corn

2003

2004

High soybeans

2005

2006

Low soybeans

Fig. 5. Average corn and soybean yields in high and low bank deposit quintiles. This figure contains time series plots of four variables measured annually from 2000 to 2006: the average corn yield in counties with bank deposits in the highest quintile, the average corn yield in counties with bank deposits in the lowest quintile, the average soybean yield in counties with bank deposits in the highest quintile, and the average soybean yield in counties with bank deposits in the lowest quintile.

control for time varying mean effects with our agricultural control (soybeans). We also use other measures to control for systemic time variation in productivity. The first OLS regression pools all of the county-yearcrop observations. The dependent variable is crop yield. We separately winsorize corn and soybean yields at 1% and 99% to mitigate the effects of outliers, though this procedure does not materially affect any of our results or conclusions. We regress yields on bank deposits, the ethanol boom period dummy variable, and dummy variables for each crop. We also include a number of interaction terms in the regression. We interact crop dummies with the lowquintile deposits dummy variable and the ethanol boom period dummy variable. We expect this term to be negative and significant for corn, but insignificant for soybeans. We expect a negative relation for corn because corn yields should be lowest in counties with low access to finance (the low-quintile deposits dummy variable equals one), yet particularly so when the demand for corn is high (the ethanol boom period dummy variable equals one) due to increasing interest in ethanol. We expect insignificant coefficients for soybeans because this crop has not experienced an exogenous shift in demand. We include interaction terms for crop dummy variables with the low-quintile deposits dummy variable and for crop dummy variables with the ethanol boom period dummy. For control variables, we include the natural logarithm of population density, the unemployment rate, per capita income, the natural logarithm of inches of precipitation, and the natural logarithm of growing degree days. (If we do not take logged values of these control variables, our main results are all qualitatively unchanged.) To the extent that warmer weather and more rainfall are good for crop yields, we expect positive relations between both growing degree days and crop yields and also between precipitation and crop yields. The relations between weather and crop yields could be nonlinear or non-monotonic or both—e.g., warm weather or precipitation could be beneficial to growing conditions only to a point—so we also run tests with squared terms for our

weather variables for robustness purposes. We do not tabulate results that include these higher-ordered terms, but our main results do not change if we include them.

5.4. Difference-in-differences regression results for corn and for soybeans Our main results appear in Tables 6 and 7. In Table 6 we regress separately corn yields, and then soybeans yields, on the following variables: the low-quintile deposits dummy variable; the ethanol period dummy variable; our population, economic, and weather controls; and, our variable of primary interest, the interaction between the low-quintile deposits dummy variable and the ethanol period dummy variable, which captures whether productivity responded least in counties with low access to finance after the shift in demand for corn created by the ethanol boom. We expect the coefficient on this interaction term to be negative and statistically significant for corn. We perform three separate regressions. The first regression includes no geographical dummy variables, while the second and third regressions include either state or county fixed effects. When we exclude geographical dummy variables, identification comes from both cross-sectional and time series variation. Including state dummy variables removes any unobserved heterogeneity at the state level and forces identification of the regression coefficients through cross-sectional differences at the county level or time series variation within a state or county or both. Including county fixed effects forces identification of the regression coefficients solely through time series variation within a county. In this last specification, time invariant factors such as soil fertility and highly persistent demographic characteristics such as the intelligence and religiosity of the county’s farmers cannot drive our results. Standard errors are robust to heteroskedasticity, and we cluster them at the county level.

194


Table 6 Individual regressions for corn and soybeans. This table presents ordinary least squares regression results based on county-year-crop observations. The regression specification is Yieldi,t = b1 Low Depositsi,t Ethanol Periodt + b2 Low Depositsi,t + b3 Ethanol Periodt + Controls + Constant + ei,t,. The dependent variable is crop yield, measured in bushels per acre. We separately winsorize corn and soybean yields at 1% and 99%. Panel A uses corn yield as the dependent variable, and Panel B uses soybeans yield as the dependent variable. Regression 1 includes no geographical fixed effects; Regression 2 includes state dummy variables; Regression 3 includes county fixed effects. Low Deposits is a dummy variable equal to one if the level of bank deposits in a given county falls into the bottom quintile of all county-level bank deposits for a given year, and zero otherwise. Ethanol Period is an indicator variable equal to one if the yield is harvested during the ethanol boom period (2005 and 2006) and zero otherwise. Ethanol County is a dummy variable equal to one if a given county has an ethanol production facility as of 2006 or has plans to build or expand ethanol production capacity as of 2006. Population Density is equal to the county population for a given year divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given county-year, measured in thousands of dollars per person. Precipitation and GDD represent the inches of precipitation and number of growing degree days in an associated crop’s region from May through October of a given year, respectively. The standard errors are in parentheses. They are robust to heteroskedasticity, and we cluster them at the county level. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Independent variables

(1)

(2)

(3)

Panel A: Determinants of corn yields Low Deposits Ethanol Period 4.196nn (1.639) Low Deposits 6.790nn (2.792) Ethanol Period 6.207nnn (0.960) Ethanol County 13.527nnn (2.497) Ln Population Density 4.282nnn (0.848) Unemployment 2.190nnn (0.469) Per Capita Income 0.002 (0.002) Ln Precipitation 8.041nnn (1.271) Ln GDD 6.878n (3.920) Constant 34.526 (31.935)

5.812nnn (1.542) 0.329 (2.220) 4.304nnn (0.856) 9.482nnn (2.065) 1.163 (0.831) 1.804nnn (0.421) 0.001nnn (0.000) 2.762nnn (0.995) 1.539 (3.711) 90.266nnn (28.861)

8.320nnn (1.582) 4.679nn (2.214) 1.196 (1.322) – (–) 33.914nnn (12.406) 0.059 (0.486) 0.004nnn (0.000) 8.645nnn (0.715) 17.574nnn (3.554) 0.680 (63.108)

N Adjusted R2 State dummies? County fixed effects?

6,608 0.365 Yes No

6,608 0.681 No Yes

0.902n (0.508) 0.114 (0.592) 4.358nnn (0.243) 2.516nnn (0.501) 0.701nnn (0.208) 1.164nnn (0.117) 0.022nnn (0.006) 1.065nnn

1.620nnn (0.475) 2.109nn (0.817) 3.691nnn (0.328) – (–) 3.889 (4.136) 0.919nnn (0.131) 0.053nnn (0.009) 3.401nnn

6,608 0.125 No No

Panel B: Determinants of soybeans yields Low Deposits Ethanol Period 0.536 (0.544) Low Deposits 1.181 (0.800) Ethanol Period 5.365nnn (0.283) Ethanol County 3.586nnn (0.670) Ln Population Density 1.432nnn (0.240) Unemployment 1.137nnn (0.135) Per Capita Income 0.008 (0.006) Ln Precipitation 2.584nnn

Table 6 (continued ) Independent variables

Ln GDD Constant N Adjusted R2 State dummies? County fixed effects?

(1)

(2)

(3)

(0.331) 2.473nn (1.258) 10.976 (9.703)

(0.271) (0.216) 4.443nnn 3.395nnn (1.037) (0.886) 1.544 26.286nnn (7.918) (20.194)

6,241 0.149 No No

6,241 0.419 Yes No

6,241 0.622 No Yes

Table 6 gives results for 6,608 county-year corn yield observations and 6,241 county-year soybean yield observations. The regressions reveal a negative and significant relation between crop yields for both corn and soybeans and the interaction between the low-quintile deposits dummy variable and the ethanol boom period. The magnitude of the deposits-ethanol effect on corn productivity is roughly four to six times larger than it is on soybean productivity, depending upon the regression specification. For example, in the first corn yield regression, the coefficient on the interaction between low-quintile deposits and ethanol is 4.2. This result means that, in response to the ethanol-induced demand shock for corn, counties with good access to finance were able to increase productivity by about four bushels of corn per acre more than corn-growing counties with poor access to finance. The analogous effect in soybean production is a 0.5 bushel differential response to the ethanol boom for counties with relatively good access to finance compared with those with poor access to finance. A visual inspection of these two magnitudes suggests that the effect on corn is much larger. In our specification with county fixed effects, both corn and soybeans productivity show a statistically significant effect of access to finance in response to the ethanol period, though the magnitude is much larger for corn. Our interpretation of this finding is that some economies of scope could exist for soybean production that come from improvements to corn production. For instance, using good access to finance to borrow money to purchase a large piece of farm equipment could have spillover effects to several crops if the equipment is not too specialized. 5.5. Pooled regression results: triple differences To test formally whether the deposits-ethanol effect is stronger for corn than for soybeans, we pool the corn and soybeans data together and allow the intercepts and slope coefficients for Low Deposits, Ethanol Period, and the Low Deposits Ethanol Period interaction to vary by crop. Our interest is in whether the slope coefficient on Low Deposits Ethanol Period is significantly different for corn and soybeans. We test this by examining whether the triple interaction of the corn crop dummy with the lowquintile deposits dummy variable and the ethanol boom period dummy (i.e., Corn Low Deposits Ethanol Period) is significantly different from zero. We include our population and weather controls, as well as state dummy


variables, county fixed effects, or neither state dummy variables nor county fixed effects. Standard errors are robust to heteroskedasticity, and we cluster them at the county level. Table 7 gives results for pooled OLS regressions involving 12,849 county-year-crop observations. The regressions reveal a negative and significant relation between crop yields and the triple interaction term of the corn dummy variable, the low-quintile deposits dummy variable, and the ethanol boom period. Consider the first regression. The coefficient on the triple interaction term is 2.7, which means the change in corn yields, net of change in soybean yields, from before to during the

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ethanol boom is significantly lower in counties with the lowest levels of bank deposits. We interpret this result as follows. Although farmers in all counties might want to increase their productivity in response to the shift in demand for corn, those farmers in counties with little access to finance are less able to respond because they are relatively restricted in their ability to finance a plan for growth. This result is not being driven by unobserved state- or county-level factors (e.g., a favorable business climate in the state or soil fertility), because the result holds with state fixed effects (Regression 2) and with county fixed effects (Regression 3). Furthermore, the magnitude of the

Table 7 Pooled regressions for corn and soybeans. This table presents pooled ordinary least squares regression results based on county-year-crop observations. The regressions specification is Yieldi,t,k = b1Cornk Access to Financei,t Ethanol Periodt + b2 Cornk Access to Financei,t + b3 Cornk Ethanol Periodt + b4 Cornk + b5 Access to Financei,t Ethanol Periodt + b6 Access to Financei,t + b7 Ethanol Periodt + Controls + Constant + ei,t,k. The dependent variable is crop yield, measured in bushels per acre. We separately winsorize corn and soybean yields at 1%. We employ three different measures of Finance in this table. Regressions 1, 2, and 3 use the following measure of access to finance: a dummy variable equal to one if the level of bank deposits in a given county falls into the bottom quintile of all county-level bank deposits for a given year and zero otherwise. Regression 1 has no geographic fixed effects; Regression 2 includes state dummy variables; Regression 3 includes county fixed effects. Regression 4 measures finance with the standardized log of the sum of all deposits held within banks insured by the Federal Deposit Insurance Corporation (FDIC) for a given county and a given year, in thousands of dollars. Regression 5 measures finance by the standardized log number of bank branches insured by the FDIC for a given county and a given year. Corn is a dummy variable equal to one if the given yield is that of a corn crop and zero if the yield is that of a soybean crop. Ethanol Period is an indicator variable equal to one if the yield is harvested during the ethanol boom period and zero otherwise. We define the ethanol boom period as 2005 and later. Ethanol County is a dummy variable equal to one if a given county has an ethanol production facility as of 2006 or has plans to build or expand ethanol production capacity as of 2006. Population Density is equal to the county population for a given year divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given countyyear, measured in thousands of dollars per person. Precipitation and GDD represent the inches of precipitation and number of growing degree days in an associated crop’s region from May through October of a given year, respectively. The standard errors are in parentheses. They are robust to heteroskedasticity, and we cluster them at the county level. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Finance is measured by Low deposits dummy Independent variables Corn Finance Ethanol Period Corn Finance Corn Ethanol Period Corn Finance Ethanol Period Finance Ethanol Period Ethanol County Ln Population Density Unemployment Per Capita Income Ln Precipitation Ln GDD Constant N Adjusted R2 State dummies? County fixed effects?

Ln(Deposits)

Ln(Number of bank branches)

(1) 2.723n (1.414) 14.031nnn (1.950) 2.061nnn (0.485) 94.591nnn (0.682) 1.065n (0.544) 3.121nn (1.268) 4.688nnn (0.519) 8.701nnn (1.547) 2.941nnn (0.538) 1.689nnn (0.298) 0.001 (0.001) 5.539nnn (0.792) 5.078nn (2.563) 29.027 (20.729)

(2) 3.003nn (1.401) 13.846nnn (1.914) 2.054nnn (0.481) 94.728nnn (0.673) 1.897nnn (0.561) 7.081nnn (1.214) 3.229nnn (0.442) 6.097nnn (1.281) 0.860n (0.514) 1.506nnn (0.267) 0.007nnn (0.001) 2.180nnn (0.632) 3.101 (2.374) 3.968 (18.362)

(3) 2.898n (1.490) 12.766nnn (1.920) 1.869nnn (0.497) 95.540nnn (0.671) 3.659nnn (0.758) 10.242nnn (1.791) 0.285 (0.725) – (–) 20.065nnn (7.548) 0.419 (0.285) 0.003nnn (0.001) 6.197nnn (0.429) 7.874nnn (2.099) 62.373 (38.347)

(4) 0.688 (0.520) 4.528nnn (0.712) 1.120nn (0.475) 92.989nnn (0.659) 1.449nnn (0.296) 9.926nnn (2.279) 0.133 (0.703) – (–) 26.697nnn (8.181) 0.305 (0.283) 0.003nnn (0.001) 6.256nnn (0.431) 7.632nnn (2.098) 93.070nn (41.709)

(5) 1.056nn (0.509) 3.739nnn (0.703) 1.385nnn (0.468) 92.931nnn (0.667) 1.288nnn (0.291) 4.484n (2.569) 0.383 (0.696) – (–) 20.982nnn (8.006) 0.428 (0.285) 0.004nnn (0.001) 6.194nnn (0.430) 8.014nnn (2.093) 62.448 (40.456)

12,849 0.787 No No

12,849 0.832 Yes No

12,849 0.890 No Yes

12,849 0.889 No Yes

12,849 0.889 No Yes

196


effect is about the same for each of our geographical fixed effects specifications. To put the magnitude of this result in perspective, consider the second regression, which includes state dummy variables. The coefficient on the triple interaction term is about 3.0 bushels per acre, which is greater than 10% of a standard deviation of an average county’s annual corn yield per acre. As an alternative measure of access to finance, in Regression 4 we substitute for our low-quintile bank deposits dummy variable the natural logarithm of the sum of all deposits held within banks for a given county and a given year. This is a continuous, not discrete, measure. We expect this variable to have a positive relation with productivity. Productivity could be high (low) in areas with high (low) access to finance. The triple interaction term involving the corn dummy variable, bank deposits, and the ethanol boom period dummy is positive but not statistically significant. This result is consistent with our discussion of the nonlinear relation between bank deposits and productivity. Our interpretation of this result is that, in a highly developed economy such as the United States, the marginal impact of access to finance on productivity is greatest where the level of access to finance is lowest. The continuous measure of access to finance, which forces a linear relation upon the data, does not adequately capture this aspect of the relation between access to finance and productivity response to a demand shock. 6. Robustness This section describes additional tests and results which establish the robustness of our main results. 6.1. Bank branches as an alternative measure of access to finance A potential criticism of the baseline regressions is that county-level bank deposits could be endogenous with crop yields due to economic prosperity. That is, if a county experiences high crop yields, this leads to more wealth for the farmers in the county, who could then deposit their wealth in local banks. This wealth can then be redistributed to farmers in the form of loans, who can then use the access to finance to improve productivity further. That is, prosperous and productive farming counties are unlikely to appear in the low deposits group, creating a reverse causality. We address this possibility by substituting the number of bank branches in a given county for the usual low deposits dummy variable as the measure of access to finance in our regressions. Although in the long run bank branches could migrate to where there is economic prosperity, in the short run changing local economic conditions surely have a relatively small impact on changes in the number of local bank branches. That is, the number of bank branches should be insensitive to changes in crop yields, but counties with more bank branches should be able to provide greater access to

finance. Regression 5 in Table 7 reports the results of this regression. Using number of bank branches as our measure of access to finance produces the same qualitative results as our low deposits dummy. We take the natural logarithm of one plus the number of branches and standardize the variable to be zero mean, unit variance. The coefficient on the triple interaction term is about 1.1, which means that a one standard deviation increase in the logged number of county-level bank branches explains more than one additional bushel of corn per acre when the demand for corn is high. In short, using number of bank branches produces the same qualitative results as using the low deposits quintile dummy variable.

6.2. Alternative methods of addressing endogeneity between access to finance and yields We argue that in the short run the number of bank branches should be insensitive to changes in crop yields and, therefore, the number of bank branches provides a measure of access to finance that is relatively immune to reverse causality arguments that say finance follows productivity. However, there could be different views of what constitutes the short run. We further address the concern of endogeneity between access to finance and crop yields in this subsection. We reproduce the results displayed in Panel A of Table 6 using an instrumental variables approach. We use as an instrument for the low deposits dummy variable the lagged value of the low deposits dummy variable. We instrument for both the interaction term and the direct effect. (We also separately instrument for the number of bank branches in a given county with the lagged number of bank branches in a given county, instrumenting for both the interaction term and the direct effect and find similar results.) In turn, we use values lagged one, two, and three years. These instruments satisfy the criteria of good instruments: the instruments are highly correlated with the explanatory variables (correlations for Low Depositst Ethanol Period and Low Depositst k Ethanol Period, Low Depositst and Low Depositst k, Ln Branchest Ethanol Period and Ln Branchest k Ethanol Period, and Ln Branchest and Ln Branchest k are each above 0.900 and are statistically significant at the 1% level), the instruments are unlikely to be correlated with the error term in the second-stage regression equation because it is doubtful that current-year productivity can directly affect access to finance in the previous year, and the instruments should affect only productivity inasmuch as they affect access to finance in the current year. Access to finance measures are likely persistent, meaning a common component remains in each observation over time. This characteristic erodes the validity of the lagged measures of access to finance as instruments for current-year access to finance. We find results similar to those of our baseline regressions, although the magnitudes are somewhat smaller. We find statistically significant negative coefficients on the instrumented low deposits dummy variable


(coefficients range from 0.72 to 2.03, depending on which lag we use as an instrument) and positive and statistically significant coefficients on the instrumented number of bank branches in a given county (coefficients range from 0.29 to 0.52, depending on which lag we use as an instrument). (We do not tabulate these results.) In short, using an instrumental variables approach does not change our main conclusion—that access to finance enables productivity growth. We also use an alternative instrument for access to finance: the number of senior citizens in a given countyyear. Becker (2007) shows the intuitive result that metropolitan statistical areas with a large fraction of seniors have more bank deposits per capita. Unlike Becker (2007), however, we are interested in the level of bank deposits (i.e., deposits not scaled by population), so we use as an instrument the number of seniors in a given county-year instead of the fraction of seniors in a given county-year. We repeat the analyses in Panel A of Table 6 after conducting first-stage regressions in which we instrument for Low Deposits with the number of seniors in a given county-year, and we instrument for Low Deposits Ethanol Period with the number of seniors in a given county-year interacted with Ethanol Period. The first-stage regressions pass Stock and Yogo (2005) F-tests, suggesting the instruments are valid. Although we do not report these results for the sake of conserving space, the second-stage results are in fact stronger and larger in magnitude than the results of our baseline tests. As a concluding remark about reverse causality, we note that fluctuations in corn-based farm revenues do not seem to affect future bank deposits. We find that, for a typical county-year, total corn revenues (estimated by multiplying the average price of corn during the harvest period by production) are a minute percentage of bank deposits in that county. Further, deposits are insensitive to changes in corn revenues. The correlation between corn revenue and the following year’s deposits is less than 1% and is statistically insignificant.

6.3. Explanatory power of deposits in contiguous counties County-level bank deposits, our proxy for access to finance in the baseline regressions, might not be a reasonable measure of access to finance if financial capital is geographically mobile. County-level bank deposits could be capturing a wider, regional effect of access to finance, or capital markets perhaps are not sufficiently segmented for county-level bank deposits to proxy accurately for access to finance. We address this possibility by examining whether access to finance in neighboring areas affects productivity. Specifically, we add to our regression a set of controls for whether the sum of bank deposits in all contiguous counties in our baseline regression framework is in the lowest quintile of the sum of bank deposits in all contiguous counties. (Using the average, not the sum, of contiguous county deposits, or using the level of deposits instead of the bottom-quintile dummy for the computation makes no difference.) We include the low-quintile

197

contiguous county deposits dummy interacted with crop dummy variables and the ethanol boom period dummy, as in the baseline regression. Table 8 presents the results. As expected, low-quintile contiguous counties’ deposits do not explain own-county crop yields. The coefficients on the triple interaction terms involving low-quintile contiguous deposits are not significant for corn yields in any of the three regression specifications. Importantly, however, the triple interaction term involving owncounty bank deposits remains negative and significant for corn. We interpret this result as evidence that countylevel bank deposits are a reasonable measure of access to finance and that, consistent with Becker (2007), capital markets are geographically segmented. 6.4. Access to finance and changes in planted acreage We examine planted acreage as an alternative proxy for productivity. In addition to trying to improve their per-acre output, corn farmers could respond to the ethanol shock by substituting corn acreage for other crops. We substitute planted acreage in a county for crop yields on the left-hand side of the baseline regression. Table 9 presents the regression results. The relation in the baseline regressions—namely, that poor access to finance relates negatively to productivity—continues to hold. Specifically, we see that about three thousand acres of corn went unplanted in counties with bank deposits in the lowest quintile of the pooled average of county-year bank deposits, during the ethanol boom period. 6.5. Tests using bank branching deregulation to measure access to finance Jayaratne and Strahan (1996) demonstrate that financial markets can directly affect economic growth. Their tests exploit the relaxation of bank branch restrictions in the United States. They show that rates of real per capita growth in income and output increased significantly in states after the state allowed intrastate bank branching. We follow Jayaratne and Strahan’s basic approach, and examine crop yields before and after states deregulated their banking systems by allowing mergers and acquisitions through the holding company structure. We use the Jayaratne and Strahan (1996) starting date, 1972, and extend the sample through 2002 (Jayaratne and Strahan’s data end in 1992). We create a state-level dummy variable equal to one in the years following a state’s bank branching deregulation and zero otherwise. Because this time period pre-dates the ethanol boom, we use a different demand shock for identification in our tests. In 1985, major US soft drink manufacturers Coca-Cola and PepsiCo switched the primary sweetener they used in sodas from sugar cane-based glucose to corn-based high fructose corn syrup. The availability of high fructose corn syrup in American foods jumped from 37.2 pounds per capita in 1984 to 45.2 pounds per capita in 1985. This one-year increase of 8.0 pounds per capita is the

198


Table 8 Regressions including deposits in contiguous counties. This table presents pooled ordinary least squares regression results based on county-year-crop observations. The dependent variable is crop yield, measured in bushels per acre. We separately winsorize corn and soybean yields at 1%. Regression 1 has no geographic fixed effects; Regression 2 includes state dummy variables; Regression 3 includes county-fixed effects. Corn is a dummy variable equal to one if the given yield is that of a corn crop and zero if the yield is that of a soybean crop. Low Deposits is a dummy variable equal to one if the level of bank deposits in a given county falls into the bottom quintile of all county-level bank deposits for a given year and zero otherwise. Ethanol County is a dummy variable equal to one if a given county has an ethanol production facility as of 2006 or has plans to build or expand ethanol production capacity as of 2006. Ethanol Period is an indicator variable equal to one if the yield is harvested during the ethanol boom period (2005 or later) and zero otherwise. Population Density is equal to the county population for a given year divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given county-year, measured in thousands of dollars per person. Precipitation and GDD represent the inches of precipitation and number of growing degree days in an associated crop’s region from May through October of a given year, respectively. The standard errors are in parentheses. They are robust to heteroskedasticity, and we cluster them at the county level. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Independent variables

(1)

(2)

(3)

Corn Low Deposits Ethanol Period

2.573n (1.533) 0.800 (1.927) 13.067nnn (2.040) 2.138 (1.653) 2.037nnn (0.501) 94.953nnn (0.690) 4.647nnn (0.505) 8.615nnn (1.516) 1.125nn (0.568) 0.217 (0.700) 2.617nn (1.166) 0.531 (0.819) 2.821nnn (0.548) 1.689nnn (0.298) 0.001 (0.001) 5.361nnn (0.753) 4.860n (2.535) 26.254 (20.629)

2.969nn (1.515) 0.383 (1.889) 12.871nnn (2.024) 2.218 (1.649) 1.987nnn (0.498) 95.097nnn (0.683) 3.198nnn (0.427) 5.996nnn (1.244) 1.953nnn (0.582) 0.017 (0.646) 6.600nnn (1.154) 0.031 (0.865) 0.979n (0.502) 1.513nnn (0.264) 0.007nnn (0.001) 2.096nnn (0.615) 2.990 (2.347) 1.821 (18.220)

3.174nn (1.594) 0.430 (1.915) 11.210nnn (2.058) 3.592nn (1.644) 1.740nnn (0.520) 96.054nnn (0.688) 0.359 (0.711) – (–) 3.222 (0.828) 0.030 (0.851) 9.015nnn (1.816) 3.440nnn (1.180) 18.202nn (7.434) 0.426 (0.281) 0.003nnn (0.001) 6.125nnn (0.420) 7.371nnn (2.093) 59.028 (37.774)

12,849 0.793 No No

12,849 0.837 Yes No

12,849 0.892 No Yes

Corn Low Contiguous Deposits Ethanol Period Corn Low Deposits Corn Low Contiguous Deposits Corn Ethanol Period Corn Ethanol Period Ethanol County Low Deposits Ethanol Period Low Contiguous Deposits Ethanol Period Low Deposits Low Contiguous Deposits Ln Population Density Unemployment Per Capita Income Ln Precipitation Ln GDD Constant N Adjusted R2 State dummies? County fixed effects?

largest since the USDA began recording the availability of high fructose corn syrup for American consumption in 1966. We capture this shift in demand for corn due to the widespread use of high fructose corn syrup with a dummy variable equal to one from 1985 (the year of the switch to high fructose corn syrup) on and zero in the previous years. We then repeat our productivity tests using state-level averages for crop yields, bank branch deregulation as a proxy for access to finance, and CocaCola and PepsiCo’s switch to high fructose corn syrup representing a shift in demand for US corn. Standard errors are robust to heteroskedasticity and clustered at

the state level, our unit of observation for these tests. Table 10 presents the results. The results support both our findings mentioned above and the findings of Jayaratne and Strahan (1996). Corn yields increase by a statistically significant 22.3 bushels per acre in states with deregulated bank branching restrictions when the demand for corn is high because of Coca-Cola and PepsiCo’s switch from sugar glucose to high fructose corn syrup as the primary sweetener in their soft drinks. An important caveat is in order. We do not have weather data going back to this time period, so we do not control for temperature and precipitation as we do in our baseline tests. However, it seems unlikely that these


199

Table 9 Regressions with planted acreage proxying for productivity. This table presents pooled ordinary least squares regression results based on 12,849 countyyear-crop observations. The regression specification is Planted Acreagei,t,k = b1 Cornk Low Depositsi,t Ethanol Periodt + b2 Cornk Low Depositsi,t + b3 Cornk Ethanol Periodt + b4 Cornk + b5 Low Depositsi,t Ethanol Periodt + b6 Low Depositsi,t + b7 Ethanol Periodt + Controls + Constant + ei,t,k. The dependent variable is planted acreage. Regression 1 includes no geographical dummy variables; Regression 2 includes state dummy variables; Regression 3 includes county fixed effects. Corn is a dummy variable equal to one if the given acreage is that of a corn crop and zero if the acreage is that of a soybean crop. Low Deposits is a dummy variable equal to one if the level of bank deposits in a given county falls into the bottom quintile of all county-level bank deposits for a given year and zero otherwise. Ethanol County is a dummy variable equal to one if a given county has an ethanol production facility as of 2006 or has plans to build or expand ethanol production capacity as of 2006. Ethanol Period is an indicator variable equal to one if the acreage is planted during the ethanol boom period and zero otherwise. We define the ethanol boom period as 2005 and later. Population Density is equal to the county population for a given year divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given county-year, measured in thousands of dollars per person. Precipitation and GDD represent the inches of precipitation and number of growing degree days in an associated crop’s region from May through October of a given year, respectively. The standard errors are in parentheses. They are robust to heteroskedasticity, and we cluster them at the county level. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Independent variables Corn Low Deposits Ethanol Period Corn Low Deposits Corn Ethanol Period Corn Low Deposits Ethanol Period Low Deposits Ethanol Period Ethanol County Ln Population Density Unemployment Per Capita Income Ln Precipitation Ln GDD Constant N Adjusted R2 State dummies? County fixed effects?

(1)

(2) nn

(3)

2,852 (1,388) 133 (2,905) 3,528nnn (552) 678 (1,463) 597 (1,504) 41,268nnn (4,810) 2,566nn (1,263) 40,835nnn (5,172) 5,507nnn (1,434) 5,431nnn (832) 1.157nnn (0.356) 6,069nnn (1,874) 6,520 (6,230) 123,510nn (51,399)

3,153 (1,311) 843 (2,872) 3,443nnn (512) 1,076 (1,454) 34 (1,398) 36,650nnn (4,519) 5,262nnn (1,131) 32,658nnn (4,394) 6,230nnn (1,649) 6,200nnn (779) 1.013nnn (0.344) 4,129nn (1,893) 25,010nnn (7,516) 109,501n (59,077)

3,279nnn (1,108) 3,430 (2,911) 3,306nnn (437) 2,760n (1,481) 1,899nn (924) 375 (1,681) 1,596nnn (354) – (–) 20,868nnn (5,809) 86 (97) 0.309nnn (0.113) 407nn (161) 1,756nnn (610) 162,646nnn (24,934)

12,849 0.176 No No

12,849 0.369 Yes No

12,849 0.864 No Yes

omitted variables are correlated with branching deregulation, so our coefficient estimates might not suffer from any severe bias.

6.6. Ethanol production capacity as a function of access to finance So far we show that access to finance can affect productivity growth in response to a demand shock. We now ask whether access to finance has a direct effect on other economic outcomes. Specifically, we ask whether county-level financial development affects the location and size of ethanol plants. We perform a number of regressions involving ethanol production capacity as a function of access to finance. We have a snapshot of data for ethanol production capacity (in place and planned for

nn

future expansion or under construction) for 2006. We begin by regressing our dummy variable Ethanol County (a county that has an ethanol plant in place or planned for future expansion or under construction) on the lowquintile bank deposits dummy variable, the previous year’s corn yield, and population density using a probit model. The second, third, and fourth regressions use the same regressors. However, for these regressions we use the following dependent variables: county-level ethanol production capacity in place, county-level ethanol production capacity planned for future expansion or under construction, and the sum of county-level ethanol production capacity in place with that planned for future expansion or under construction. Panel A of Table 11 presents the regression results. We find a significant relation between ethanol production capacity and access to finance. In all four of our

200


Table 10 Productivity regressions with bank branch deregulation and corn syrup. This table presents pooled ordinary least squares regression results based on 724 state-year-crop observations from 1972 to 2002. The dependent variable is average yield per acre. We separately winsorize corn and soybean yields at 1% and 99%. Deregulation represents a dummy variable equal to one in years following the allowance bank branching via merger and acquisition through the holding company structure and zero otherwise. Corn Syrup represents a dummy variable equal to one in the years following Coca-Cola and PepsiCo’s transition from sugar glucose to high fructose corn syrup and zero otherwise. Coca-Cola and PepsiCo switched to corn syrup in 1985. The standard errors are in parentheses. They are robust to heteroskedasticity. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Independent variables

Average yield (bushels)

Corn Deregulation Corn Syrup

22.260n (11.479) 21.575 (12.436) 17.755nnn (2.936) 63.909nnn (3.461) 10.065n (5.158) 11.637n (5.383) 3.208n (1.757) 42.949nnn (1.757)

Corn Deregulation Corn Corn Syrup Corn Deregulation Corn Syrup Deregulation Corn Syrup Constant N Adjusted R2 Year dummies? State dummies?

724 0.934 Yes Yes

regression specifications we find a significant and negative effect of poor access to finance on ethanol plant location or size. (We find similar results when we use the number of county-level bank branches as the explanatory variable, instead of the low-deposits dummy.) Thus, we provide some support for the idea that finance is related to economic growth and viability by virtue of the ethanol plants built in finance-heavy counties. An important caveat to the results above is that the location or capacity of ethanol production plants, or both, could be endogenous. Plants’ location or size could be chosen based on where access to finance is good, or finance could follow to the areas where ethanol plants are. We address this point by instrumenting for access to finance in 2006 with access to finance in 2004 (the year prior to the ethanol mandates) and using the instrumented measure of access to finance to explain ethanol production capacity under construction or planned for expansion as of 2006. These instruments satisfy the criteria of good instruments: the instruments are highly correlated with the explanatory variables (correlations for Low Deposits2004 and Low Deposits2006 and for Ln Branches2004 and Ln Branches2006 are statistically significant at the 1% level), the instruments are unlikely to be correlated with the error term in the second-stage regression equation because it is doubtful that future ethanol production capacity as of 2006 can directly affect access to finance in 2004, and the instruments should

affect only future ethanol production capacity inasmuch as they affect access to finance in the 2006. We use two measures of access to finance: the lowquintile deposits dummy variable and the number of bank branches in a given county. Panel B of Table 10 presents the regression results. Our results indicate that the exogenous portion of access to finance explains future ethanol production capacity for each measure. For instance, if a county is in the low-deposits quintile, it will on average forgo the opportunity to host over 1.3 million gallons of ethanol production capacity in each of the following years. (The regression coefficient is 0. 300, and e0.300 is about 1.35.) Similarly, for each standard deviation more bank branches that a county has, it can expect to host an additional 1.2 million gallons of ethanol production capacity in each of the following years. (The regression coefficient is 0.156, and e0.156 is about 1.2.) These results provide a tangible example of how access to finance can lead to considerable improvement in economic outcomes.

6.7. Crop prices as an alternative proxy for demand As an alternative to our ethanol period dummy, we use spot market prices for our commodities as a proxy for demand for the crops. Price is not an ideal proxy for demand because changes in price could reflect changes in demand or supply. A visual inspection of a time series of crop prices plotted in Fig. 6 shows a large spike in price for soybeans in late 2004. This price spike was due to supply shocks in the United States and Brazil, the world’s two largest soybean producers.5 Even though price changes could be due to supply or demand changes, we nonetheless proceed with this robustness test using price as an admittedly imperfect proxy for demand shifts. Spot market price data are collected from Bloomberg. In particular, we average the daily spot market prices from September through October (i.e., spot market prices around the time of harvest) for corn and soybeans to proxy for the demand for each crop during a given year. This variable enters our multivariate regressions. Fig. 6 displays spot market prices over time. We use pricing data from spot markets in Illinois. (The choice of the spot market from which we select the pricing data makes little difference in our tests. For example, the price of yellow-kernelled corn harvested in the USDA Northern Illinois region has a correlation of 0.973 with that harvested in the USDA Northeast Iowa region.) We substitute crop prices for the ethanol period dummy throughout the baseline regression equation, including the interaction terms, and add year dummies. We find qualitatively similar results to our main tests. We find corn yields are lowest in counties with poor access to finance (i.e., the counties have bank deposits in the lowest quintile), yet particularly so when the demand for corn is high (i.e., the price of corn is high) due to increasing interest in ethanol. 5 Source: Bruce A. Babcock, Iowa State University, Center for Agricultural and Rural development (http://www.extension.iastate.edu/ AGDM/articles/babcock/BabMay04.html).


201

Table 11 Ethanol production as a function of access to finance. Panel A presents regression results based on 911 county-level observations for 2006. Regression 1 is a probit regression in which the dependent variable is a dummy variable equal to one if a given county has an ethanol plant as of 2006 or has an ethanol plant under construction or planned for expansion. Regressions 2 through 4 are ordinary least squares regressions. The dependent variable of Regression 2 is the log of a given county’s ethanol production capacity in place as of 2006. The dependent variable of Regression 3 is the log of a given county’s ethanol production capacity under construction or planned for expansion as of 2006. The dependent variable of Regression 4 is the log of the sum of a given county’s ethanol production capacity in place as of 2006 and ethanol production capacity under construction or planned for expansion as of 2006. Low Deposits is a dummy variable equal to one if the level of bank deposits in a given county falls into the bottom quintile of all county-level bank deposits for a given year and zero otherwise. Corn Yieldt 1 represents a given county’s corn yield in 2005. Population Density is equal to the county population for 2006 divided by the number of square miles in the county. The standard errors are in parentheses. They are robust to heteroskedasticity. Panel B presents regression results based on 903 county-level observations for 2006. The dependent variable for each regression is the log of a given county’s ethanol production capacity under construction or planned for expansion as of 2006. We instrument for access to finance in two ways and then use the instrumented values to explain the dependent variable. In Regression 1 we instrument for the low deposits dummy variable as of 2006 with the low deposits dummy variable as of 2004. In Regression 2 we instrument for the standardized natural log of the number of bank branches in a given county as of 2006 with the standardized natural log of the number of bank branches in a given county as of 2004. Corn Yieldt 1 represents a given county’s corn yield in 2005. Population Density is equal to the county population for 2006 divided by the number of square miles in the county. Unemployment is equal to the percentage of the working population without employment for a given county-year. Per Capita Income is the average personal income for a given county-year, measured in thousands of dollars per person. The standard errors are in parentheses. They are robust to heteroskedasticity. n, nn, and nnn represent significance at the 10%, 5%, and 1% level, respectively. Independent variables

Dependent variable Ethanol county dummy (1)

Panel A: Ethanol regressed on low deposits dummy variable Low Deposits 0.826nnn (0.232) Corn Yieldt–1 0.009nnn (0.002) Population Density 0.106n (0.061) Unemployment 0.118nn (0.060) Per Capita Income 2.030 10 5 (1.550 10 5) Constant 2.025nnn (0.610) N Pseudo- or adjusted R2

911 0.097

Ln(Production capacity in place) (2)

Ln(Planned capacity) (3)

Ln(Planned plus inplace capacity) (4)

0.292nnn (0.090) 0.003nnn (0.001) 0.047 (0.033) 0.054nn (0.023) 1.060 10 5 (7.640 10 6) 0.004 (0.277)

0.230nnn (0.088) 0.005nnn (0.001) 0.037 (0.027) 0.033 (0.027) 5.120 10 6 (8.330 10 6) 0.171 (0.308)

0.501nnn (0.120) 0.007nnn (0.001) 0.080n (0.041) 0.077nn (0.033) 1.280 10 5 (1.050 10 5) 0.083 (0.387)

911 0.036

911 0.033

911 0.063

Independent variables

(1)

Panel B – Future ethanol production capacity regressed on instrumented access to finance Instrumented Low Deposits Dummy 0.300nn (0.128) Instrumented Ln(Number of Bank Branches) Corn Yieldt–1 Population Density Unemployment Per Capita Income Constant N Adjusted R2

6.8. Regressions on subsamples sorted by farm size The NASS provides data on the average number of acres per farm, per county-year for several states, including four states in our sample: Iowa, Nebraska, Ohio, and Wisconsin. We use this measure as a county-level proxy for typical farm sizes in the county. We partition our sample for these four states into two groups based on

(2)

0.005nnn (0.001) 0.049 (0.038) 0.032 (0.032) 6.010 10 6 (9.870 10 6) 0.127 (0.361)

0.156n (0.084) 0.005nnn (0.001) 0.092 (0.060) 0.027 (0.033) 8.820 10 7 (9.990 10 6) 0.093 (0.419)

903 0.027

903 0.027

the average number of acres per farm, and we run the baseline regressions from Table 6 separately on both subsamples. (Because the farm size measure imposes a large and possibly nonrandom reduction in our sample size, we do not tabulate these results.) We find that the finance-causes-growth effect is significant for small-farm counties, but not for large-farm counties. This intuitive result suggests that the investment decisions of

202


Price (dollars per bushel)

12 10 8 6 4 2

Soybeans

1/3/2007

7/3/2006

1/3/2006

7/3/2005

1/3/2005

7/3/2004

1/3/2004

7/3/2003

1/3/2003

7/3/2002

1/3/2002

7/3/2001

1/3/2001

7/3/2000

1/3/2000

0

Corn

Fig. 6. Crop prices over time. This figure displays daily prices of yellow soybeans and yellow-kernelled corn sold on spot markets in Illinois from January 2000 to June 2007 in dollars per bushel.

smaller firms (farms) are more sensitive to access to external finance than larger firms (farms). Other partitions—by quartile or decile, for instance—give the same results. 6.9. Alternative productivity controls Our baseline regressions in Table 7 use soybeans yields as a control. The purpose of including soybeans yields and creating a triple interaction term is to test whether increases in corn productivity are unique to corn, the crop we argue has recently experienced a demand shock. To establish the robustness of our results, we also use two other productivity benchmarks: national labor productivity growth in the business sector and the average of national soybean and wheat productivity (the two largest cash crops in the US behind corn). Data on labor productivity come from the Bureau of Labor Statistics and data on agricultural productivity come from the NASS. Instead of a triple-interaction term, we regress corn yields on access to finance interacted with the ethanol period dummy variable, and we include either national labor productivity or overall agricultural productivity as a separate explanatory variable. In other words, we repeat the corn-only regressions in Table 6, but with national labor productivity or the average of national soybean and wheat productivity as a control variable. Our results are unchanged. Corn yields are higher in counties with good access to finance during the ethanol period, even after controlling for other productivity benchmarks. 6.10. Regressions with only counties that do not change treatment status In our sample some counties switch from the low-deposit quintile to a higher-deposit quintile (or vice versa) during the sample period. Specifically, 93 of our Midwestern counties do not maintain a constant position in either the low-deposit quintile or higher-deposit quintile throughout the sample period. These switching counties do not meet the requirement that our control and treatment groups be identified before the ethanol shock and independent of the ethanol

shock.6 We repeat all of the regression analysis described in the sections above, excluding observations coming from these counties. Excluding these observations strengthens our findings. In untabulated results, the coefficients of interest grow slightly in economic magnitude and gain statistical significance when we restrict our sample to counties with a constant position in either the low-deposit quintile or a higher-deposit quintile. For example, the coefficient on the triple interaction term in Table 7, Regressions 1, 2, and 3 changes from 2.72 to 3.34, 3.00 to 3.47, and 2.90 to 3.23, respectively. 7. Conclusion This paper examines the effect of access to finance on productivity. We exploit an exogenous shift in demand for US corn to expose county-level productivity responses in the presence of varying levels of access to finance. The exogenous shift in demand for corn is due to a boom in ethanol production, which is a result of a number of complementary forces (rising crude oil prices, the Energy Policy Act of 2005, and new federal tax incentives). We find that counties in the midwestern United States with the lowest levels of bank deposits have been unable to increase their corn yields as much as other counties. This result demonstrates the positive impact of access to finance on productivity. We employ a differences-in-differences-in-differences testing approach. Using soybeans as a control crop, we find that the increase of corn yields in counties with high levels of bank deposits is greater over our sample period than in counties with low levels of bank deposits, even in comparison with the yields of soybeans. Specifically, counties with high levels of bank deposits increased their corn yields by 10.4 bushels per acre (10.4 bushels per acre is approximately half of a standard deviation of an average county’s annual corn yield per acre) more than counties with low levels of bank deposits over the sample period. In contrast, we find no significant difference between the increases of soybean yields 6

We thank the referee for this point.


in counties with high and low levels of bank deposits over the sample period. This result eliminates the concern that we are simply capturing overall growth in agricultural productivity. We augment the differences-in-differences-in-differences test with pooled OLS regressions. We regress crop yields on crop dummy variables, a dummy variable measuring low access to finance, proxies for the demand for corn, variables capturing meteorological conditions, and a host of interaction terms. We find that corn yields have increased in response to the exogenous shift in demand for corn, but particularly so in counties associated with strong access to finance. Said differently, corn yields in counties with poor access to finance have been particularly lower than those in counties with high access to finance following the exogenous shift in demand for corn. Specifically, our main regressions show that corn yields were about 2.7 to 2.9 bushels per acre lower in counties with bank deposits in the lowest quintile during the ethanol boom period. This magnitude is greater than 10% of a standard deviation of an average county’s annual corn yield per acre. This result is consistent with that of the differences-in-differences-indifferences test, and further confirms the positive relation between access to finance and productivity. Our findings show a crucial linkage between finance and economic growth. Many economists believe in a positive relation between finance and economic growth. However, the specific channels through which this relation operates are less clear. Our findings provide concrete evidence that increased productivity is a key channel through which finance causes economic growth. References Bakke, T. E., Whited T. M., 2008. What gives? A study of firms’ reactions to cash shortfalls. Unpublished working paper, University of Wisconsin, Madison, WI. Becker, B., 2007. Geographical segmentation of US capital markets. Journal of Financial Economics 85 (1), 151–178.

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Carlson, R.E., Todey, P.E., Taylor, S.E., 1996. Midwestern corn yield and weather in relation to extremes of the southern oscillation. Journal of Production Agriculture 9 (3), 347–352. Chava, S., Roberts, M.R., 2008. How does financing impact investment? The role of debt covenants. Journal of Finance 63, 2085–2121. Djankov, S., Hoekman, B., 1999. In: Trade Reorientation and Productivity Growth in Bulgarian Enterprises. Policy Research Working Paper Series 1707. The World Bank, Washington, DC. Feder, G., 1985. The relation between farm size and farm productivity. Journal of Development Economics 18, 297–313. Fonstad, M., Pugatch, W., Vogt, B., 2003. Kansas is flatter than a pancake. Annals of Improbable Research 9 (3), 16–18. Gatti, R., Love, I., 2006. In: Does access to credit improve productivity? Evidence from Bulgarian firms. Policy research working paper series 3921. The World Bank, Washington, DC. Hahn, R.W., 2008. Ethanol: law, economics, and politics. Working Paper Series 08-02. Reg-Markets Center. Hicks, J.R., 1969. In: A Theory of Economic History. Calderon Press, Oxford, England. Jayaratne, J., Strahan, P.E., 1996. The finance-growth nexus: evidence from bank branch deregulation. Quarterly Journal of Economics 111 (3), 639–670. Koo, W.W., Duncan, M.R., Taylor, R.D., 1998. In: Analysis of Farm Financing and Risk Management for US Farmers, Agricultural economics report 399. North Dakota State University, Fargo, ND. Maurel, M., 2001. Investment, efficiency, and credit rationing: evidence from Hungarian panel data. Unpublished working paper 403. University of Michigan, William Davidson Institute, Ann Arbor, MI. Petersen, M.A., Rajan, R.G., 2002. Does distance still matter? The information revolution in small business lending. Journal of Finance 57 (6), 2533–2570. Robinson, J., 1952, The generalisation of the general theory. In: The Rate of Interest and Other Essays. MacMillan, London, England, pp. 67–163. Schumpeter, J.A., 1912. The theory of economic development: an inquiry into profits, capital, credit, interest and the business cycle. Dunker & Humboldt, Leipzig, Germany. Stock, J.H., Yogo, M., 2005. In: Andrews, D.W.K., Stock, J.H. (Eds.), Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg. Cambridge University Press, Cambridge, England, pp. 80–108. Thompson, L.M., 1986. Climatic change, weather variability, and corn production. Agronomy Journal 78 (4), 649–653. Whited, T.M., 1992. Debt, liquidity constraints, and corporate investment: evidence from panel data. Journal of Finance 47, 1425–1460. Whited, T.M., 2006. External finance constraints and the intertemporal pattern of intermittent investment. Journal of Financial Economics 81, 467–502.




Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies$ Jun Tu a, Guofu Zhou b, a b

Singapore Management University, Singapore Olin School of Business, Washington University, St. Louis, MO 63130, USA


abstract

Article history: Received 29 June 2009 Received in revised form 3 February 2010 Accepted 7 March 2010 Available online 24 August 2010

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/N rule with one of the four sophisticated strategies—the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pa´stor (2000) rule, and the Kan and Zhou (2007) rule—as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G11 G12 Keywords: Portfolio choice Mean–variance analysis Parameter uncertainty

1. Introduction

$ We are grateful to Yacine Aı¨t-Sahalia, Doron Avramov, Anil Bera, Henry Cao, Winghong Chan (the AFA-NFA discussant), Frans de Roon (the EFA discussant), Arnaud de Servigny, Victor DeMiguel, David Disatnik, Lorenzo Garlappi, Eric Ghysels, William Goetzmann, Yufeng Han, Bruce Hansen, Harrison Hong, Yongmiao Hong, Jing-zhi Huang (the SMUFSC discussant), Ravi Jagannathan, Raymond Kan, Hong Liu, Andrew Lo, Todd Milbourn, L˘uboˇs Pa´stor, Eduardo Schwartz, G. William Schwert (the managing editor), Paolo Zaffaroni, Chu Zhang (the CICF discussant), seminar participants at Tsinghua University and Washington University, and participants at 2008 China International Conference in Finance, 2008 AsianFA-NFA International Conference, 2008 Singapore Management University Finance Summer Camp, 2008 European Finance Association Meetings, 2008 Workshop on Advances in Portfolio Optimization at London Imperial College Business School, and especially to an anonymous referee for insightful and detailed comments that have substantially improvedthe paper. Tu acknowledges financial support for this project from Singapore Management University Research Grant C207/MSS6B006. Corresponding author. Tel.: + 1 314 935 6384. E-mail address: [email protected] (G. Zhou).


Although more than half a century has passed since Markowitz’s (1952) seminal paper, the mean–variance (MV) framework is still the major model used in practice today in asset allocation and active portfolio management despite many other models developed by academics.1 One main reason is that many real-world issues, such as factor exposures and trading constraints, can be accommodated easily within this framework with analytical insights and fast numerical solutions. Another reason is that intertemporal hedging demand is typically found to be small. However, as is the case with any model, the true model parameters are unknown and have to be estimated from the data, resulting in the well-known parameter uncertainty or estimation error problem—the estimated

1 See Grinold and Kahn (1999), Litterman (2003), and Meucci (2005) for practical applications of the mean–variance framework; and see Brandt (2009) for a recent survey of the academic literature.

J. Tu, G. Zhou / Journal of Financial Economics 99 (2011) 204–215

205

optimal portfolio rule is subject to random errors and can thus be substantially different from the true optimal rule. Brown (1976), Bawa and Klein (1976), Bawa, Brown, and Klein (1979), and Jorion (1986) are examples of earlier work that provide sophisticated portfolio rules accounting for parameter uncertainty. Recently, MacKinlay and Pa´stor (2000) and Kan and Zhou (2007) provide more such rules.2 In contrast to the above sophisticated strategies, the naive 1/N diversification rule, which invests equally across N assets of interest, relies on neither any theory nor any data. The rule, attributed to the Talmud by Duchin and Levy (2009), has been known for about 1,500 years, and corresponds to the equal weight portfolio in practice. Brown (1976) seems the first academic study of this rule. Due to estimation errors, Jobson and Korkie (1980) state that ‘‘naive formation rules such as the equal weight rule can outperform the Markowitz rule.’’ Michaud (2008) further notes that ‘‘an equally weighted portfolio may often be substantially closer to the true MV optimality than an optimized portfolio.’’ With similar conclusions, Duchin and Levy (2009) provide an up-to-date comparison of the 1/N rule with the Markowitz rule, and DeMiguel, Garlappi, and Uppal (2009) compare the 1/N rule further with almost all sophisticated extensions of the Markowitz rule. Not only that the naive 1/N investment strategy can perform better than those sophisticated rules recommended from investment theory, but also, as shown elsewhere and below, most of the Markowitz-type rules do not perform well in real data sets and can even lose money on a risk-adjusted basis in many cases. These findings raise a serious doubt on the usefulness of the investment theory. To address this problem, we examine two related questions. First, we ask whether any of the four sophisticated rules, namely, the Markowitz rule as well as its extensions proposed by Jorion (1986), MacKinlay and Pa´stor (2000), and Kan and Zhou (2007), can be combined with the naive 1/N rule to obtain better portfolio rules that can perform consistently well. Second, we explore whether some or all of the combination rules can be sufficiently better so that they can outperform the 1/N rule. Positive answers to these two questions are important, for they will reaffirm the usefulness of the Markowitz theory if the theory-based combination rules can perform consistently well and outperform the nontheory-based 1/N rule. The positive answers are also possible based on both economic and statistical intuitions. Economically, a concave utility investor will prefer a suitable average of good and bad performances to either a good or a bad performance randomly, similar to the diversification over two risky assets. Statistically, a combination rule can be interpreted as a shrinkage estimator with the 1/N rule as the target. As is known in

statistics and in finance (e.g., Jorion, 1986), the shrinkage is a tradeoff between bias and variance. The 1/N rule is biased, but has zero variance. In contrast, a sophisticated rule is usually asymptotically unbiased, but can have sizable variance in small samples. When the 1/N rule is combined with a sophisticated rule, an increase of the weight on the 1/N rule increases the bias, but decreases the variance. The performance of the combination rule depends on the tradeoff between the bias and the variance. Hence, the performance of the combination rule can be improved and maximized by choosing an optimal weight. We find that the four combination rules are substantially better than their sophisticated component rules in almost all scenarios under our study, and some of the combination rules outperform the 1/N rule as well, even when the sample size (T) is as small as 120. For example, when T= 120, in a three-factor model with 25 assets and with the annualized pricing errors spreading evenly between 2% to 2%, for a mean–variance investor with the risk aversion coefficient g ¼ 3, the four sophisticated rules, namely, the Markowitz rule and its extensions of Jorion (1986), MacKinlay and Pa´stor (2000), and Kan and Zhou (2007), have utilities (or risk-adjusted returns) of 81.09%, 7.85%, 1.78%, and 1.61%; two of them are losing money on a risk-adjusted basis. In contrast, their corresponding combination rules have utilities of 3.84%, 5.79%, 1.86%, and 5.09%. Hence, all the combination rules are better than their uncombined counterparts, and three of them improve greatly.3 In comparison with the 1/N rule, which has a utility of 3.85% and is the best rule before implementing combinations, two of the combination rules have significantly higher utilities. When T =240 or gets larger, while the 1/N rule, independent of T, still has the same performance, all the other rules improve and many of them outperform the 1/N rule much more significantly. The methodology of this paper is based on the idea of combining portfolio strategies. Jorion (1986), Kan and Zhou (2007), DeMiguel, Garlappi, and Uppal (2009), and Brandt, Santa-Clara, and Valkanov (2009) have applied similar ideas in various portfolio problems. In contrast to these studies, this paper focuses on the combination of the 1/N rule with the aforementioned Markowitz-type rules, and on reaffirming the value of the investment theory. In addition, from a Bayesian perspective, the idea of combining portfolio strategies is closely related to the Bayesian model averaging approach on portfolio selection, which Pa´stor and Stambaugh (2000) apply to compare various asset pricing models and Avramov (2002) applies to analyze return predictability under model uncertainty. This paper shows, along with these studies, that it is important and valuable to combine portfolio strategies in the presence of estimation errors.

2 Recent Bayesian studies on the parameter uncertainty problem, such as Pa´stor (2000), Pa´stor and Stambaugh (2000), Avramov (2004), ¨ Harvey, Liechty, Liechty, and Muller (2004), Tu and Zhou (2004, forthcoming), and Wang (2005), are reviewed by Fabozzi, Huang, and Zhou (2010), and Avramov and Zhou (forthcoming). We focus here on the classical framework.

3 The MacKinlay and Pa´stor (2000) rule has excellent performance even before implementing any combination. But its combination rule improves little. As discussed later, this is not a problem with the rule itself, but a problem with the lack of a good estimation method for estimating the optimal combination coefficient.

206


The remainder of the paper is organized as follows. Section 2 provides the combination rules. Section 3 compares them with the 1/N rule and with their uncombined counterparts based on both simulated and real data sets. Section 4 concludes. 2. Combining portfolio strategies In this section, we study the combination of the 1/N rule with each of the four sophisticated strategies. For easier understanding, we first briefly illustrate the general idea of combining two portfolio rules and then present in detail the four combination rules in the order of their analytical tractability. 2.1. Combination of two rules We consider the following combination of two portfolio rules: ^ c ¼ ð1dÞwe þ dw, ~ w

ð1Þ

~ is an where we ¼ 1N =N is the constant 1/N rule, w estimated portfolio rule based on the data, and d is the combination coefficient, 0 r d r 1. The 1/N rule here is applied to N risky assets of interest.4 The implied portfolio ^ c at T+ 1 is RpT þ 1 ¼ rfT þ 1 þ w ^ c uRT þ 1 , where rfT + 1 return of w is the return on the riskless asset, and RT + 1 is an N-vector of excess returns on the N risky assets.5 Assume that the excess returns of the N risky assets are independent and identically distributed over time, and have a multivariate normal distribution with mean m and ^ c is covariance matrix S. Then the expected utility of w

g

^ c uSw ^ c w ^ c, ^ c Þ ¼ rfT þ 1 þ muw Uðw 2

ð2Þ

where g is the mean–variance investor’s relative risk aversion coefficient. Our objective is to find an optimal combination coefficient d so that the following expected loss is minimized: ^ c Þ ¼ Uðw ÞE½Uðw ^ c Þ, Lðw , w

ð3Þ

where U(w*) is the expected utility of the true optimal portfolio rule w ¼ S1 m=g. This loss function is standard in the statistical decision theory, and is the criterion that Brown (1976), Frost and Savarino (1986), Stambaugh (1997), Ter Horst, De Roon, and Werker (2006), DeMiguel, Garlappi, and Uppal (2009), among others, use to evaluate portfolio rules. The 1/N rule is chosen as the starting point of our combinations because it is simple, and yet can perform remarkably well when the sample size is small. Moreover, as is well-known in statistics (e.g., Lehmann and Casella, 1998), 1/N is one common choice of a good shrinkage

point for improving the estimation of the mean of a multivariate distribution. However, the 1/N rule makes no use of any sample information, and will always fail to converge to the true optimal rule if it does not happen to be equal to it. In contrast, the combination rule always converges, and is designed to be better than either the 1/N ~ theoretically. rule or w, In practice, though, the true optimal combination coefficient d is unknown. What is feasible is only a combination rule based on an estimated optimal d, whose performance will then generally vary over applications. However, since the estimation errors in estimating the optimal d, which is one single parameter, are usually small, the estimated optimal combination rule can ~ in our later generally improve both the 1/N rule and w analysis.

2.2. Combining with the Markowitz rule The simplest case to start with is to combine the 1/N rule with the standard maximum likelihood (ML) rule or ^ be the the (estimated) Markowitz rule. Let m^ and S sample mean and covariance matrix of RT + 1, then the ML ^ 1 m^ =g. Instead of using w ^ ML ¼ S ^ ML , we rule is given by w use a scaled one: w¼

1 ~ 1 S m^ ,

ð4Þ

g

^ . The scaled w is unbiased and ~ ¼ ðT=ðTN2ÞÞS where S ^ ML . performs slightly better than w According to (1), the combination rule is ^ c ¼ ð1dÞwe þ dw: w

ð5Þ

^ c is (all proofs Then the expected loss associated with w are in the appendices) ^ cÞ ¼ Lðw , w

g 2

2

½ð1dÞ2 p1 þ d p2 ,

where

p1 ¼ ðwe w ÞuSðwe w Þ, p2 ¼ E½ðww ÞuSðww Þ: Note that p1 measures the impact from the bias of the 1/N rule, and p2 measures the impact from the variance of w. Thus, the combination coefficient d determines the tradeoff between the bias and the variance. The optimal choice is easily shown as

d ¼

p1 : p1 þ p2

If the riskless asset is also included, the 1/N rule may be adjusted to we ¼ 1N =ðN þ 1Þ. This, worsening from the earlier 1/N rule slightly, makes an insignificant difference in what follows. 5 Note that the performances of most institutional managers are benchmarked to an index, say the S&P500. Then the return on the S&P500 index portfolio can be viewed as the riskless asset to apply the same framework. For active portfolio management with benchmarks, see Grinold and Kahn (1999), for example.

ð7Þ

Summarizing the result, we have

Proposition 1. If p1 40, then there exists an optimal d , 0 o d o 1, such that ^ c Þ o min½Lðw ,we Þ,Lðw ,wÞ, Lðw , w

4

ð6Þ

ð8Þ

^ c strictly dominates both i.e., the optimal combination rule w the 1/N rule and w. The condition p1 40 is trivially satisfied in practice because the 1/N rule will not be equal to the true optimal rule with probability one. Proposition 1 says that the ^ c indeed provides strict optimal combination rule w


improvements over both the 1/N rule and w.6 Suppose p1 ¼ p2 , then d ¼ 1=2, and the loss of w^ c will be only onehalf of the loss of either the 1/N rule or w. This works exactly like a diversification over two independent and identically distributed risky assets. To estimate d , we only need to estimate p1 and p2 , which can be done as follows: 2

1

2

p^ 1 ¼ we uS^ we we um^ þ 2 y~ , g g p^ 2 ¼

1

g2

2

ðc1 1Þy~ þ

c1 N

g2 T

ð9Þ

,

2

ð10Þ

where y~ is an estimator of y ¼ muS1 m given by Kan and Zhou (2007), and c1 ¼ ðT2ÞðTN2Þ=ððTN1ÞðTN4ÞÞ. The condition of T 4N þ 4 is needed here to ensure the ^ 1 . Summarizing, existence of the second moment of S we have 2

Proposition 2. Assume T 4N þ 4. On the combination of the ^ c ¼ ð1dÞwe þ dw, the estimated optimal 1/N rule with w, w one is ^ CML ¼ ð1d^ Þwe þ d^ w, w

ð11Þ

where d^ ¼ p^ 1 =ðp^ 1 þ p^ 2 Þ with p^ 1 and p^ 2 given by (9) and (10). Proposition 2 provides a simple way to optimally combine the 1/N rule with the unbiased ML rule w. This combination rule is easy to carry out in practice since it is only a given function of the data. However, due to the errors in estimating d , there is no guarantee that the ^ CML , will always be estimated optimal combination rule, w better than either the 1/N rule or w. Nevertheless, in our later simulations, the magnitude of the errors in estimating d , though varying over different scenarios, are ^ CML does improve upon w, and generally small. Hence, w can either outperform the 1/N rule or achieve close performances in most scenarios. Therefore, the combination does provide improvements overall. In addition, as T ^ CML converges to the true optimal goes to infinity, w portfolio rule. 2.3. Combining with the Kan and Zhou (2007) rule

207

where d^ k ¼ ðp^ 1 p^ 13 Þ=ðp^ 1 2p^ 13 þ p^ 3 Þ with p^ 1 given by (9), and p^ 13 and p^ 3 given by 1 2 1 1 p^ 13 ¼ 2 y~ we um^ þ ½Z^ we um^ þð1Z^ Þm^ g we u1N g gc1 g 1 ~ 1 m^ þð1Z^ Þm^ m^ uS ~ 1 1N , ð13Þ ½Z^ m^ uS g

g

p^ 3 ¼

2 N 1 ~2 1 y 2 y~ Z^ : 2 T g g c1

ð14Þ

Proposition 3 provides the estimated optimal combi^ KZ . By nation rule that combines the 1/N rule with w design, it should be better than the 1/N rule if the errors in estimating the true optimal dk are small and if the 1/N rule is not exactly identical to the true optimal portfolio rule. This is indeed often the case in the performance evaluations in Section 3. 2.4. Combining with the Jorion (1986) rule Consider now the combination of the 1/N rule with the ^ PJ , which is motivated from both the Jorion (1986) rule, w shrinkage and Bayesian perspectives. Assume T 4 N þ4 as before. The optimal combination coefficient can be solved ^ PJ , analytically in terms of the moments of w

dj ¼

p1 ðwe w ÞuSE½w^ PJ w p1 2ðwe

^ PJ w þ E½ðw ^ PJ w ÞuSðw ^ PJ w Þ w ÞuSE½w

ð15Þ ^ PJ , the analytical However, due to the complexity of w evaluation of the moments is intractable. In Appendix B, we provide an approximate estimator, d^ j , of dj , so that the estimated optimal combination rule, ^ CPJ ¼ ð1d^ j Þwe þ d^ j w ^ PJ , w

ð16Þ

can be implemented easily in practice. ´stor (2000) rule 2.5. Combining with the MacKinlay and Pa In order to provide a more efficient estimator of the expected returns, MacKinlay and Pa´stor (2000) utilize an extension of the capital asset pricing model (CAPM): Rt ¼ a þ bft þ et ,

Consider now the combination of the 1/N rule with the ^ KZ , which is motivated to Kan and Zhou (2007) rule, w minimize the impact of estimation errors via a three-fund portfolio. With Z^ and m^ g as defined in their paper (as estimators of the squared slope of the asymptote to the minimum-variance frontier and the expected excess return of the global minimum-variance portfolio), we have Proposition 3. Assume T 4 N þ 4. On the combination of ~c¼ the 1/N rule with the Kan and Zhou (2007) rule, w ^ KZ , the estimated optimal one is ð1dk Þwe þ dk w ^ KZ , ^ CKZ ¼ ð1d^ k Þwe þ d^ k w w

:

ð17Þ MP

MP ^ and S be the where ft is a latent factor. Let m^ maximum likelihood estimators of the parameters in their latent factor model (see Appendix C for the details), then the (estimated) MacKinlay and Pa´stor portfolio rule is given by the standard Markowitz formula,

^ MP Þ1 m^ MP =g. To optimally combine the 1/N rule ^ MP ¼ ðS w MP ^ , we need to evaluate the optimal combination with w coefficient:

dm ¼

p1 ðwe w ÞuSE½w^ MP w p1 2ðwe

^ MP w þ E½ðw ^ MP w ÞuSðw ^ MP w Þ w ÞuSE½w

:

ð12Þ

ð18Þ

6 Proposition 1 can be extended to allow any fixed constant rules, and can be adapted to allow biased estimated rules as well.

This requires the evaluation of the expectation terms ^ MP . Since it is difficult to obtain them associated with w analytically, we use a Jackknife approach (e.g., Shao and

208


expected utility, do in general have higher Sharpe ratios than their uncombined components.

Tu, 1996) to obtain an estimator, d^ m , of dm , via ^ E½w

MP

^ E½ðw

^ MP w Þ w Tðw

MP

^ w ÞuSðw

MP

T T1 X ^ MP w Þ, ðw T t ¼ 1 t

3. Performance evaluation

w Þ

~ ðw ^ MP w Þ w ÞuS T T1 X ~ ^ MP ^ MP ½ðw t w ÞuS ðw t w Þ, T t¼1

^ T½ðw

ð19Þ

MP

ð20Þ

^ MP ´ stor rule where w t is the (estimated) MacKinlay and Pa when the t-th observation (t= 1,y,T) is deleted from the data. Then the estimated optimal combination rule is ^ w

CMP

^ MP : ¼ ð1d^ m Þwe þ d^ m w

ð21Þ

With the preparations thus far, it is ready to assess the ^ performances of w and real data sets.

CMP

and other rules in both simulations

2.6. Alternative combinations and criteria Before evaluating the combination rules provided above, we conclude this section by discussing some broader perspectives on the combination methodology.7 First, on various ways of combining, what are the gains with combining more than two rules and with combining two rules not including the 1/N rule? Theoretically, if the true optimal combination coefficients are known, combining more than two rules must dominate combining any subset of them. However, the true optimal combination coefficients are unknown and have to be estimated. As more rules are combined, more combination coefficients need to be estimated and the estimation errors can grow. Hence, combining more than two rules may not improve the performance. In addition, combining two rules not including the 1/N rule is usually not as good as including the 1/N rule, as done by our approach here. Nevertheless, certain optimal estimation methods might be developed to improve the performances of the more general combination approaches, which is an interesting subject for future research. Second, on the objective of combining, what happens if the combination is to maximize a different objective function? The Sharpe ratio is such a natural objective which seems at least as popular as the utilities or riskadjusted returns. When the true parameters are known, maximizing the Sharpe ratio and maximizing the expected utility are equivalent, a well-known fact. However, once the true parameters are unknown, the two are different. In this paper, we focus on maximizing the expected utility as it is easier to solve than maximizing the Sharpe ratio because the latter is to maximize a highly nonlinear function of the portfolio weights and there are no closed-form solutions available in the presence of estimation errors. Interestingly, though, due to their equivalence in the parameter certainty case, the combination strategies of this paper, designed to maximize the 7 We are grateful to an anonymous referee for these and many other insights that help to improve the paper enormously.

In this section, we evaluate the performances of the four combination rules and compare them with their uncombined counterparts and the 1/N rule, based on both simulated data sets (10,000 of them) and real data sets. 3.1. Comparison based on simulated data sets Following MacKinlay and Pa´stor (2000), and DeMiguel, Garlappi, and Uppal (2009), we assume first the CAPM model with an annual excess return of 8% and an annual standard deviation of 16% on the market factor. The factor loadings, b’s, are evenly spread between 0.5 and 1.5. The residual variance-covariance matrix is assumed to be diagonal, with the diagonal elements drawn from a uniform distribution with a support of [0.10, 0.30] so that the cross-sectional average annual idiosyncratic volatility is 20%. In addition, we make two extensions. First, we examine not only a case of the risk aversion coefficient g ¼ 3, but also a case of g ¼ 1. Second, we allow nonzero alphas as well to assess the impact of mispricing on the results. This seems of practical interest because a given one-factor model (or any given K-factor models, in general) may not hold exactly in the real world. Table 1 provides the average expected utilities of the various rules over the simulated data sets without mispricing and with N = 25 assets, where the risk-free rate is set as zero without affecting the relative performances of different rules. Panel A of the table corresponds to the case studied by DeMiguel, Garlappi, and Uppal (2009) with g ¼ 3. The true expected utility is 4.17 (all utility values are annualized and in percentage points), greater than those from the estimated rules as expected due to estimation errors. But the four combination rules all have better performances than their uncombined counterparts, respectively. However, in comparison with the 1/N rule, which achieves a good value of 3.89, the combination rules have lower utility values, 1.68, 1.42, 2.19, and 3.71, when T= 120. Despite the improvements over their estimated uncombined counterparts, the combination rules suffer from estimation errors and still underperform the 1/N rule when T is small. Why does the 1/N rule perform so well in the above case? This is because the assumed data-generating process happens to be in its favor: holding the 1/N portfolio is roughly equivalent to a 100% investment in the true optimal portfolio. To see why, we note first that the betas are evenly spread between 0.5 and 1.5, and so the 1/N portfolio should be close to the factor portfolio. Second, under the assumption of no mispricing, the factor portfolio is on the efficient frontier, and hence, the true optimal portfolio must be proportional to it. The proportion depends on g. With g ¼ 3, the 1/N portfolio happens to be close to the true optimal portfolio, as evidenced by its utility value of 3.89 that is close to the maximum possible. It is therefore difficult for any other rules, which


209

Table 1 Utilities in a one-factor model without mispricing. This table reports the average utilities (annualized and in percentage points) of a mean–variance investor under various investment rules: the true optimal rule, the 1/N rule, the ML rule, the Jorion (1986) rule, the MacKinlay and Pa´stor (2000) rule, the Kan and Zhou (2007) rule, and the four combination rules, with 10,000 sets of sample size T simulated data from a one-factor model with zero mispricing alphas and with N = 25 assets. Panels A and B assume that the risk aversion coefficient g is 3 and 1, respectively. T Rules

120

240

480

960

3000

6000

Panel A: g ¼ 3 True 1/N

4.17 3.89

4.17 3.89

4.17 3.89

4.17 3.89

4.17 3.89

4.17 3.89

85.72 12.85 2.11 2.15

25.81 3.79 3.00 0.00

8.35 0.18 3.44 1.13

1.61 1.55 3.65 1.90

2.42 2.98 3.79 2.97

3.30 3.47 3.83 3.47

^ CML w

1.68

2.95

3.42

3.60

3.81

3.90

^ CPJ w

1.42

2.93

3.46

3.71

3.88

3.86

^ CMP w

2.19

3.05

3.48

3.67

3.80

3.83

^ CKZ w

3.71

3.77

3.81

3.85

3.91

3.95

Panel B: g ¼ 1 True 1/N

12.50 6.63

12.50 6.63

12.50 6.63

12.50 6.63

12.50 6.63

12.50 6.63

257.16 38.55 6.33 6.44

77.42 11.38 9.00 0.01

25.05 0.55 10.31 3.38

4.83 4.66 10.94 5.69

7.25 8.95 11.37 8.92

9.91 10.42 11.48 10.40

^ CML w

1.14

4.79

6.39

7.47

9.50

10.62

^ CPJ w

1.28

5.68

6.97

7.11

7.46

10.34

^ CMP w

6.57

9.16

10.49

11.09

10.95

11.43

^ CKZ w

6.36

6.70

6.99

7.41

8.78

9.97

ML Jorion MacKinlay-Pa´stor Kan-Zhou


are estimated from the data, to outperform the 1/N rule in the above particular case. However, when g ¼ 1, the 1/N rule will no longer be close to the true optimal portfolio. This is also evident from Panel B of Table 1. In this case, the expected utility is 12.50 from holding the true optimal portfolio. In contrast, if the 1/N rule is followed, the expected utility is much lower: 6.63. Note that, although the 1/N rule is not optimal, it still outperforms the other rules when T=120. The reason is that the 1/N rule now still holds correctly the efficient portfolio, though the proportion is incorrect. In contrast, the other rules depend on the estimated weights, which approximate the efficient portfolio ^ CMP and weights with estimation errors. Nevertheless, w CKZ ^ w have close results to the 1/N rule when T= 120, and they do better than it when T Z240. Overall, the combination rules improve the performances in this case as well and they do better in outperforming the 1/N rule than previously. After understanding the sensitivity of the 1/N rule to g, we assume g ¼ 3 as usual in what follows. When there is mispricing, Panel A of Table 2 reports the results where the annualized mispricing alphas are evenly spread between 2% to 2%. The combination rules again generally have better performances than their uncombined counterparts. Now the 1/N rule gets not only the proportion but also the composition of the optimal portfolio incorrect, since the factor portfolio is no longer

on the efficient frontier. In this case, the expected utility of the 1/N rule, 3.89, is not close to but is about 40% less than the expected utility of the true optimal rule, 6.50. Now the combination rules not only improve, they also outperform the 1/N rule more easily than before (Panel A of Table 1). For the interest of comparison, we now study how the rules perform in a three-factor model. We use the same assumptions as before, except now we have three factors, whose means and covariance matrix are calibrated based on the monthly data from July 1963 to August 2007 on the market factor and Fama-French’s (1993) size and book-tomarket portfolios. The asset factor loadings are randomly paired and evenly spread between 0.9 and 1.2 for the market b’s, between 0.3 and 1.4 for the size portfolio b’s, and between 0.5 and 0.9 for the book-to-market portfolio b’s. Panel B of Table 2 provides the results with the same mispricing distribution as before (Panel A of Table 2). Once again, the combination rules are generally better than their estimated uncombined components. Since the 1/N rule is now far away from being the true optimal portfolio, it is outperformed by some of the combination rules even with T= 120. As T increases, the combination rules perform even better. Overall, combination improves performance, and some combination rules can outperform the 1/N rule in general. This suggests that there is indeed value-added through combining rules and

210


Table 2 Utilities in factor models with mispricing. This table reports the average utilities (annualized and in percentage points) of a mean–variance investor under various investment rules: the true optimal rule, the 1/N rule, the ML rule, the Jorion (1986) rule, the MacKinlay and Pa´stor (2000) rule, the Kan and Zhou (2007) rule, and the four combination rules, with N = 25 assets for 10,000 sets of sample size T simulated data from a one-factor model (Panel A) and a three-factor model (Panel B), respectively. The annualized mispricing a’s are assumed to spread evenly between 2% to 2%. The risk aversion coefficient g is 3. T Rules

120

240

480

960

3000

6000

Panel A: One-factor model True 1/N

6.50 3.89

6.50 3.89

6.50 3.89

6.50 3.89

6.50 3.89

6.50 3.89

84.75 12.36 2.34 2.35

23.84 2.99 3.23 0.02

6.18 0.95 3.67 1.64

0.65 3.09 3.88 3.14

4.73 5.06 4.02 5.06

5.62 5.71 4.06 5.71

^ CML w

2.02

3.32

3.91

4.43

5.38

5.82

^ CPJ w

2.27

3.70

4.02

3.92

4.83

5.72

^ CMP w

2.41

3.27

3.71

3.90

4.02

4.04

^ CKZ w

3.84

3.95

4.12

4.41

5.14

5.62

14.60 3.85

14.60 3.85

14.60 3.85

14.60 3.85

14.60 3.85

14.60 3.85

81.09 7.85 1.78 1.61

17.11 2.84 2.66 5.12

1.39 7.65 3.09 7.96

8.52 10.45 3.30 10.45

12.76 12.99 3.44 12.99

13.69 13.75 3.48 13.75

^ CML w

3.84

6.15

8.44

10.63

13.02

13.76

^ CPJ w

5.79

5.36

4.17

9.67

13.02

13.76

^ CMP w

1.86

2.73

3.12

3.30

3.45

3.48

^ CKZ w

5.09

6.06

7.57

9.59

12.56

13.58


Panel B: Three-factor model True 1/N ML Jorion MacKinlay-Pa´stor Kan-Zhou

by using portfolio theory to guide portfolio choice over the use of the naive 1/N diversification.8 3.2. Other properties of the combinations In this subsection, we explore two aspects about the combination rules. First, while the combination rules are designed to maximize the expected utility, we also examine their performances in terms of the Sharpe ratio, and provide the standard errors for both the utilities and Sharpe ratios of the rules over the simulated data sets. Second, we study the estimation errors of the combination coefficients. Table 3 provides in percentage points the Sharpe ratios in the one-factor model. Panel A of the table corresponds to the earlier case studied in Panel A of Table 1. Similar to the case in utilities, the combination rules generally improve the Sharpe ratio substantially, despite that maximizing the expected utility may not maximize the Sharpe ratio simultaneously in the presence of parameter uncertainty as discussed in Section 2.6. Prior to combining, all the estimated rules, except the MacKinlay and Pa´stor rule, have Sharpe ratios less than 5.0 when T= 120. In contrast, the combination rules have Sharpe ratios close to that of the 1/N rule, 13.95, which in turn is close to the 8 The same conclusion holds when the number of assets is 50, or in a model without factor structures. The results are available upon request.

Sharpe ratio of the true optimal rule, 14.43. As discussed earlier on utilities, the reason why the 1/N rule does so well is because it is set roughly equal to the true optimal portfolio in this particular simulation design. When some mispricing is allowed (Panel B of Table 3), generally speaking, the combination rules again improve, and they are better than before.9 So far, the combination rules improve significantly across various simulation models. Hypothetically, this might happen with large standard errors in the utilities across data sets. To address this issue, Table 4 reports the standard errors of all the strategies when the data are drawn from a three-factor model with the annualized mispricing a’s ranging from 2% to 2%, the case corresponding to Panel B of Table 2.10 Both the true and the 1/N rules are data-independent, and so their expected utilities are the same across data sets. For the estimated rules, their expected utilities are data-dependent and vary across data sets with their standard errors ranging from 0.29% to 12.37%, when T=120. The combination rules, in general, have smaller standard errors than their estimated component rules, especially when the sample size is less than 480. Similar results are also true for the standard

9 Similar results hold, though not reported, in the three-factor model as well as in the non-factor model. 10 The results in other simulation models are similar, and are omitted for brevity.


211

Table 3 Sharpe ratios in a one-factor model. This table reports in percentage points the average Sharpe ratios of a mean–variance investor under various investment rules: the true optimal rule, the 1/N rule, the ML rule, the Jorion (1986) rule, the MacKinlay and Pa´stor (2000) rule, the Kan and Zhou (2007) rule, and the four combination rules, with 10,000 sets of sample size T simulated data from a one-factor model with N = 25 assets. Panels A and B assume that the annualized mispricing a’s are zeros or between 2% to 2%, respectively. T Rules

120

240

480

960

3000

6000

Panel A: a ¼ 0 True 1/N

14.43 13.95

14.43 13.95

14.43 13.95

14.43 13.95

14.43 13.95

14.43 13.95


3.88 4.54 12.19 4.97

5.59 6.46 13.51 7.03

7.54 8.40 13.86 8.80

9.54 10.18 13.89 10.27

12.19 12.38 13.89 12.34

13.18 13.24 13.89 13.24

^ CML w

12.04

12.88

13.34

13.53

13.83

13.98

^ CPJ w

10.40

12.36

13.22

13.67

13.94

13.90

^ CMP w

12.07

13.44

13.87

13.90

13.89

13.89

^ CKZ w

13.70

13.79

13.86

13.91

14.00

14.07

Panel B: a in [ 2%, 2%] True 1/N

18.02 13.95

18.02 13.95

18.02 13.95

18.02 13.95

18.02 13.95

18.02 13.95


5.92 5.61 12.70 4.77

8.34 8.03 13.98 7.15

10.94 10.69 14.28 10.09

13.32 13.16 14.30 12.97

16.06 16.03 14.31 16.02

16.97 16.95 14.31 16.95

^ CML w

12.81

13.69

14.30

15.02

16.45

17.09

^ CPJ w

11.64

13.73

14.31

14.12

15.60

16.96

^ CMP w

12.52

13.89

14.26

14.28

14.27

14.25

^ CKZ w

14.02

14.23

14.54

15.04

16.21

16.91

errors of the Sharpe ratios, as reported in Panel B of Table 4. To see how the 1/N rule contributes to the combination strategies, Table 5 reports both the true and the average estimated optimal combination coefficients for the four combination rules, with the data simulated in the same ^ CML and w ^ CKZ . When way as in Table 4. Consider first w ^ CML , denoted T=120, the true optimal coefficient d for w simply by d in the table, is 15.74%, but the average estimated one is 20.56%, biased upward. So the latter uses 79.44% (=1– 20.56%) of the 1/N rule. In contrast, the true optimal d for ^ CKZ , 53.78%, is much larger, and the average estimated value w is 56.18%, slightly biased upward with much less usage of the 1/N rule. The standard error of the estimated d is also CKZ

^ . As T increases, the true optimal d’s relatively smaller for w are increasing as expected. It is of interest to note that the 1/N rule remains to possess a few percentage points in the weighting even when the sample size is 6,000. ^ CPJ and w ^ CMP , the estimates of their optimal On w combination coefficients have larger biases. This is because now we do not have analytical and accurate ^ CML estimation formulas for them, unlike the case for w ^ CKZ . In particular, the bias in estimating the optimal and w

^ CPJ and w ^ CMP should improve. This will performances of w be yet another direction for future research. ^ CMP over w ^ MP Because of the small improvements of w due to the inaccurate estimate of the true optimal combination coefficient, it may make sense to consider a simple naive combination of the MacKinlay and Pa´stor rule with the 1/N rule by using a 50% weight. As it turns out in the next subsection, this naive combination rule can ^ MP and w ^ CMP and can perform well improve over both w consistently across all real data sets in our study for practical sample sizes of 120 or 240. However, the same naive ^ CPJ consistently because the procedure does not improve w ^ CPJ and its true difference (not reported here) between w optimal combination rule (using the true optimal combination coefficient) is, in general, much smaller than that in the case of the MacKinlay and Pa´stor rule. As a result, we consider the naive combination only for the MacKinlay and Pa´stor rule in the next subsection. 3.3. Empirical application Now we apply the various rules to the real data sets, which are those used by DeMiguel, Garlappi, and Uppal (2009),11 as well as the Fama-French 49 industry

^ CMP is quite large, which combination coefficient for w CMP

^ barely improves. explains why the combination rule w Clearly, if better estimation methods are found, the

11 We thank Victor DeMiguel for the data. A detailed description of the data can be found in DeMiguel, Garlappi, and Uppal (2009).

212


Table 4 Standard errors of utilities and Sharpe ratios. This table reports the standard errors (in percentage points) of the utilities (Panel A) and the Sharpe ratios (Panel B) for all the strategies with 10,000 sets of sample size T simulated data from a three-factor model with N = 25 assets. The annualized mispricing a’s are assumed to spread evenly between 2% to 2%. The risk aversion coefficient g is 3. T Rules

120

240

480

960

3000

6000

0 0

0 0

0 0

0 0

0 0

0 0

12.37 3.55 0.75 1.44

3.29 1.26 0.36 0.72

1.24 0.61 0.17 0.50

0.53 0.33 0.09 0.32

0.15 0.13 0.03 0.13

0.08 0.07 0.01 0.07

^ CML w

1.24

0.62

0.47

0.31

0.13

0.07

^ CPJ w

0.49

0.37

0.31

0.70

0.13

0.07

^ CMP w

0.67

0.33

0.16

0.08

0.03

0.01

^ CKZ w

0.29

0.35

0.40

0.36

0.17

0.08

0 0

0 0

0 0

0 0

0 0

Panel A: Standard errors of utilities True 1/N ML Jorion MacKinlay-Pa´stor Kan-Zhou

Panel B: Standard errors of Sharp ratios True 0 1/N 0 ML Jorion MacKinlay-Pa´stor Kan-Zhou

4.02 4.18 6.87 4.51

3.01 2.87 3.54 2.82

2.00 1.84 1.16 1.90

1.19 1.12 0.27 1.16

0.43 0.42 0.04 0.42

0.22 0.22 0.03 0.22

^ CML w

2.44

2.22

1.85

1.12

0.42

0.22

^ CPJ w

2.57

2.25

2.28

3.22

0.43

0.22

^ CMP w

6.36

3.38

0.80

0.07

0.04

0.03

^ CKZ w

1.66

1.88

1.84

1.30

0.45

0.23

Table 5 Combination coefficients. This table reports in percentage points the true optimal combination coefficients, the average estimated optimal combination coefficients and their standard errors (in parentheses) for the four combination strategies. The data are simulated in the same way as in Table 4. T Parameters

120

240

480

960

3000

6000

15.74 20.56

29.93 29.38

47.57 45.16

65.12 63.73

85.60 85.35

92.27 92.20

(10.87)

(13.44)

(12.49)

(7.61)

(2.05)

(0.80)

27.56 35.95

46.65 17.61

65.29 11.52

80.32 87.90

93.90 100.00

97.17 100.00

(12.78)

(16.41)

(29.55)

(32.63)

(0.00)

(0.00)

28.50 97.02

42.54 97.27

56.06 98.03

66.62 99.37

76.25 100.00

78.93 100.00

(1.14)

(0.89)

(0.87)

(0.75)

(0.00)

(0.00)

53.78 56.18

68.09 57.37

79.87 63.49

88.35 72.26

95.81 86.43

97.84 92.27

(6.37)

(7.70)

(7.88)

(6.49)

(3.09)

(1.52)

Panel A: wCML

d d^ Panel B: wCPJ

dj d^ j Panel C: wCMP

dm d^ m Panel D: wCKZ

dk d^ k

portfolios plus the Fama-French three factors and the earlier Fama-French 25 portfolios plus the Fama-French three factors.

Given a sample size of T, we use a rolling estimation approach with two estimation windows of length M= 120 and 240 months, respectively. In each month t, starting


213

Table 6 Certainty-equivalent returns based on the real data sets. This table reports the certainty-equivalent returns (annualized and in percentage points) of a mean–variance investor under various investment rules: the true optimal rule, the 1/N rule, the ML rule, the Jorion (1986) rule, the MacKinlay and Pa´stor (2000) rule, the Kan and Zhou (2007) rule, and the four combination rules. While the in-sample ML rule uses all the data for its estimation, the other estimated rules are based on a rolling sample with an estimation window M = 120 (Panel A) or 240 (Panel B). The real data sets are the five data sets used by DeMiguel, Garlappi, and Uppal (2009), and two additional data sets, the Fama-French 25 size (SMB) and book-to-market portfolios (HML) with the Fama-French three factors and the Fama-French 49 industry portfolios with the Fama-French three factors. The risk aversion coefficient g is 3. Industry portfolios N = 11

Rules Panel A: M= 120 ML (in-sample) 1/N ML Jorion MacKinlay-Pa´stor Kan-Zhou

Inter’l portfolios N =9

Mkt/ SMB/HML N=3

FF1-factor N = 21

FF4-factor N = 24

FF25 3-factor N = 28

Indu49 3-factor N =52

8.42 3.66

7.74 3.26

13.61 4.33

46.04 5.27

54.55 5.92

45.24 5.51

57.67 5.14

38.18 9.21 0.76 3.59

18.30 5.80 0.86 3.42

4.90 9.51 0.20 9.51

100.69 0.82 0.47 20.75

128.59 1.99 0.37 22.01

194.33 20.72 1.02 9.15

1173.78 152.10 1.45 17.77

1.39

0.34

6.39

22.25

26.06

14.62

6.40

^ CPJ w

3.15

1.74

4.52

6.39

11.10

6.77

1.20

^ CMP w

2.21

2.26

2.64

3.31

3.54

3.67

3.57

^ CKZ w

3.02

1.79

8.54

28.97

29.35

19.36

8.51

8.42 5.04 14.30 0.76 2.84 1.89

7.74 0.92 6.94 1.38 0.02 0.17

13.61 3.46 12.08 12.40 0.44 12.21

46.04 4.44 5.10 23.15 2.78 26.60

54.55 4.95 38.63 10.56 2.67 19.61

45.24 5.09 20.80 10.44 3.37 14.08

57.67 5.48 158.40 18.70 4.32 12.43

^ CML w

4.58

0.29

11.96

18.73

18.97

16.70

6.29

^ CPJ w

4.19

0.07

12.40

19.01

8.99

7.38

14.55

^ CMP w

4.11

0.49

2.20

3.71

3.88

4.31

4.95

^ CKZ w

5.40

0.88

11.03

26.84

30.25

20.09

16.28

^ CML w

Panel B: M =240 ML (in-sample) 1/N ML Jorion MacKinlay-Pa´stor Kan-Zhou

from t =M, we use the data in the most recent M months up to month t to compute the various portfolio rules, and apply them to determine the investments in the next month. For instance, let wz,t be the estimated optimal portfolio rule in month t for a given rule ‘z’ and let rt + 1 be the excess return on the risky assets realized in month t +1. The realized excess return on the portfolio is rz,t þ 1 ¼ wuz,t rt þ 1 . We then compute the average value of the T M realized returns, m^ z , and the standard deviation, s^ z . The certainty-equivalent return (CER) is thus given by

g

2 CERz ¼ m^ z s^ z , 2

ð22Þ

which can be interpreted as the risk-free rate of return that an investor is willing to accept instead of adopting the given risky portfolio rule z. Clearly the higher the CER, the better the rule. As before, we set the risk aversion coefficient g to 3. Note that all the CERs have a common term of the average realized risk-free rate, which cancels out in their differences. Hence, as in the case for the expected utilities, we report the CERs by ignoring the riskfree rate term. With the real data, the true optimal rule is unknown. We approximate it by using the ML estimator based on the entire sample. This will be referred to as the in-sample ML rule. Although this rule is not implementable in practice, it is the rule that one would have obtained based

on the ML estimator had he known all the data in advance. Its performance may serve as a useful benchmark to measure how the estimation errors affect the out-ofsample results. Table 6 reports the results. Due to substantially less information in the rolling sample, all rules have CERs (annualized and in percentage points as before) less than half of those from the in-sample ML rule in most cases. The first real data set, the 10 industry portfolios plus the market portfolio, is a good example that highlights the problem of the existing estimated rules. When M= 120, the in-sample ML rule has a CER of 8.42, the 1/N rule has a ^ CPJ , w ^ CMP , and w ^ CKZ have 3.15, decent value of 3.66, and w 2.21, and 3.02. But the others including all the four uncombined estimated rules have negative CERs, ranging from 38.18 to 0.76, that is, they lose money on a riskadjusted basis. For the second real data set, the international portfolios, the 1/N rule remains hard to beat. Unlike the other uncombined estimated rules, the MacKinlay and Pa´stor rule, and three combination rules have positive CERs. For all the remaining five data sets, the four combination rules work well in most cases. Overall, both ^ CMP and w ^ CKZ have positive CERs consistently across all w the seven data sets. This is an obvious improvement over the four uncombined theoretical rules, which can have negative CERs or lose money on a risk-adjusted basis. ^ CMP and When M =240, the results are even better. Both w

214


^ CKZ now still have positive CERs consistently across all w the seven data sets. Moreover, most of the combination rules not only improve, but also outperform the 1/N rule most of the time. In short, when applied to the real data sets, the combination rules generally improve from their uncombined Markowitz-type counterparts and can perform consistently well, and some of them can outperform the 1/N rule in most of the cases.

A.2. Proof of Eq. (10) In many expectation evaluations below, a key is to apply two equalities about the inverse of the sample covariance matrix (e.g., Haff, 1979), i.e., the formulas for ^ 1 S1=2 and E½S1=2 S ^ 1 SS ^ 1 S1=2 . Expanding out E½S1=2 S the quadratic form of p2 into three terms, and applying the formulas to the two terms involving w, we have

p2 ¼

1

g2

2

ðc1 1Þy þ

c1 N

g2 T

:

ð24Þ 2

Then, plugging the estimator for y yields the desired claim.

4. Conclusion The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, due to parameter uncertainty or estimation errors, many studies show that the naive 1/N investment strategy performs much better than those recommended from the theory. Moreover, the existing theory-based portfolio strategies, except that of MacKinlay and Pa´stor (2000), perform poorly when applied to many real data sets used in our study. These findings raise a serious doubt on the usefulness of the investment theory. In this paper, we provide new theory-based portfolio strategies which are the combinations of the naive 1/N rule with the sophisticated theory-based strategies. We find that the combination rules are substantially better than their uncombined counterparts, in general, even when the sample size is small. In addition, some of the combination rules can perform consistently well and outperform the 1/N rule significantly. Overall, our study reaffirms the usefulness of the investment theory and shows that combining portfolio rules can potentially add significant value in portfolio management under estimation errors. Since parameter uncertainty appears in almost every financial decision-making problem, our ideas and results may be applied to various other areas. For example, they may be applied to turn many practical quantitative investing strategies (e.g., Lo and Patel, 2008) into those more robust to estimation errors; they may also be applied to hedge derivatives optimally in the presence of parameter uncertainty; or be applied to make optimal capital structure decisions with unknown investors’ expectations and macroeconomic determinants. While studies of these issues go beyond the scope of this paper, they seem interesting topics for future research.

into this equation

A.3. Proof of Proposition 3 Now, we have ~ cÞ ¼ Lðw , w

g

E½½ð1dÞðwe w Þ 2 ~ ~ ÞuS½ð1dÞðwe w Þ þ dðww Þ, þ dðww KZ

~ denotes w ^ for brevity. Let a ¼ we w and where w ~ b ¼ ww , then the following identity holds: ½ð1dÞa þ dbuS½ð1dÞa þ db 2

¼ ð1dÞ2 auSa þ2dð1dÞauSb þ d buSb: Taking the first-order derivative of this identity, we obtain the optimal choice of d,

d¼

auSaauSE½b : auSa2auSE½b þ E½buSb

ð25Þ

~ It is clear that p1 ¼ auSa. Let p13 ¼ auSE½b ¼ we uSE½w ^ 1 ¼ T S1 = ðTN2Þ, we ~ þ mS1 m. Since E½S we ummuE½w can estimate p13 with p^ 13 as given by (13). Finally, let p3 ¼ E½buSb. Using Eq. (63) of Kan and Zhou (2007), we can estimate p3 with p^ 3 as given by (14). Appendix B. Combining with the Jorion (1986) rule PJ

PJ

^ Þ1 m^ , Eq. (15) follows from (25). To compute E½ðS we rewrite PJ

S^ ¼ dS~ þ DDu,

ð26Þ

where d and D are defined accordingly from (26). Inverting this matrix, we have ~ 1 =dS ~ 1 DDuS ~ 1 =ðd2 þ dDuS ~ 1 DÞ ¼ S ~ 1 =dB, ^ PJ Þ1 ¼ S ðS ð27Þ where B is defined as the second term. Since it is relatively small, we treat it as a constant. Then, we approximately ^ PJ Þ1 m^ PJ as the product of the expectations. evaluate E½ðS Finally, we have from (27) that

Appendix A. Proofs of propositions and equations A.1. Proof of Proposition 1

^ PJ Þ1 SðS ^ PJ Þ1 ¼ S ~ 1 SS ~ 1 SB=dÞ þ ðBuSBÞ: ~ 1 =d2 2ðS ðS

Based on (6), we need only to show

ð28Þ ð23Þ

The first term can be evaluated as in Proposition 3. The second and third terms are trivial. Hence, we can evaluate

satisfies f uðd Þ ¼ 0 and f 00 ðd Þ 40 at d , which are easy to verify. Then the claim follows.

PJu ^ PJ 1 ^ PJ Þ1 m^ PJ by treating S ^ PJ approximately E½m^ ðS Þ SðS PJ and m^ as independent variables.

2

2

f ðdÞ ð1dÞ2 p1 þ d p2 ¼ p1 2dp1 þ d ðp1 þ p2 Þ


Appendix C. Semi-analytical solution to the MacKinlay and Pa´stor (2000) rule Assume

normality

with

varðft Þ ¼ s2f ,

Eðft Þ ¼ 0,

Eðft , et Þ ¼ 0N , and that the covariance matrix of the residuals is s2 IN , with IN as the identity matrix. Moreover, assume that an exact asset pricing relation holds with m ¼ bgf , where gf is the factor risk premium. Then,

S ¼ s2 IN þ ammu, where a ¼ s2f =g2f . The maximum likeMP ^ MP , of m and S, are obtained and S lihood estimator, m^ by maximizing the log-likelihood function over s2 , a and m:

NT T lnð2pÞ lnðjammu þ s2 IN jÞ 2 2 T 1X ðRt mÞuðammu þ s2 IN Þ1 ðRt mÞ: 2t¼1

lnL ¼

ð29Þ

The numerical solution to the optimization problem can be very demanding due to the number of parameters. Fortunately, there is available an almost analytical solution.12 ^ þ m^ m^ u. Since Let U^ ¼ S lnðjammu þ s2 IN jÞ ¼ ðN1Þlnðs2 Þ þ lnðs2 þamumÞ,

ð30Þ

we can minimize f ðm,a, s2 Þ ¼ ðN1Þlnðs2 Þ þ lnðs2 þ amumÞ " # 1 s2 ðmum2m^ umÞamuU^ m þ 2 trðU^ Þ þ s2 þamum s

ð31Þ

to obtain the ML estimator. ^ Q^ u be the spectral decomposition of U^ , where Let Q^ L ^ ¼ Diagðl^ 1 , . . . , l^ N Þ are the eigenvalues in descending L order and the columns of Q^ are the corresponding eigenvectors. Further, let z^ ¼ Q^ um^ . For any c, l^ 1 Z c Z l^ N , it can be shown that pðfÞ ¼

N X i¼1

2

ðl^ i cÞz^ i ¼0 ½1fðl^ cÞ2

ð32Þ

i

has a unique solution, which can be trivially found numerically, in the interval (uN,u1) with ui ¼ 1=ðl^ i cÞ. Then, the following objective function: ! ! 2 N N X X z^ i ^ l i c , gðcÞ ¼ ln c þ ðN1Þln ~ ðcÞðl^ cÞ 1f i¼1

i

i¼1

ð33Þ is well defined, and can be solved easily because it is a one-dimensional problem. Let c* be the solution, then the ML estimator of m is

m^ MP ¼ m~ ¼ Q^ ½IN f~ ðc ÞðL^ c IN Þ1 z^ , and hence, the ML estimators of s2 and a are PN ^ l c c s~ 2 , a~ ¼ s~ 2 ¼ i ¼ 1 i 1: N1 m~ um~

ð34Þ

ð35Þ

Then the MacKinlay and Pa´stor (2000) portfolio rule is obtained easily. 12

We are grateful to Raymond Kan for this semi-analytical solution.

215

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Jump risk, stock returns, and slope of implied volatility smile$ Shu Yan Moore School of Business, University of South Carolina, Columbia, SC 29208, United States


abstract

Article history: Received 15 May 2009 Received in revised form 21 December 2009 Accepted 12 January 2010 Available online 25 August 2010

In the presence of jump risk, expected stock return is a function of the average jump size, which can be proxied by the slope of option implied volatility smile. This implies a negative predictive relation between the slope of implied volatility smile and stock return. For more than four thousand stocks ranked by slope during 1996–2005, the difference between the risk-adjusted average returns of the lowest and highest quintile portfolios is 1.9% per month. Although both the systematic and idiosyncratic components of slope are priced, the idiosyncratic component dominates the systematic component in explaining the return predictability of slope. The findings are robust after controlling for stock characteristics such as size, book-to-market, leverage, volatility, skewness, and volume. Furthermore, the results cannot be explained by alternative measures of steepness of implied volatility smile in previous studies. & 2010 Elsevier B.V. All rights reserved.

JEL classification: G12 Keywords: Jump risk Stock returns Options Implied volatility smile Slope

1. Introduction The finance literature shows extensively that distributions of stock returns are leptokurtic or ‘‘fat-tailed.’’ Fattailed distributions can be caused by jumps, that is, sudden but infrequent movements of large magnitude. Modeling dynamics of jumps in stock prices dates back to Press (1967) and Merton (1976a). Subsequent studies such as Ball and Torous (1983), Jarrow and Rosenfeld (1984), and Jorion (1989) provide convincing support for

$ I thank Michael Brennan, James Doran, Shingo Goto, Anurag Gupta, Markus Leippold, Michael Lemmon, Roger Loh, Francis Longstaff, Steve Mann, Pedro Santa-Clara, Richard Stapleton, Dragon Tang, Sergey Tsyplakov, Grigory Vilkov, Ziwei Xu, Hong Yan, Leon Zelotoy, Donghang Zhang, Jane Zhao, and participants at the China International Conference in Finance in Dalian, Conference on Advances in the Analysis of Hedge Fund Strategies at Imperial College Business School, Melbourne Derivatives Research Group Conference, Panagora Asset Management, Second Singapore International Conference on Finance at National University of Singapore, Southern Finance Association annual meetings, and University of South Carolina for helpful comments. I also would like to thank Anitha Manohar for research assistance. E-mail address: [email protected]


the presence of jumps in stock prices. Another strand of papers, following the approach of Cox and Ross (1976) and Merton (1976b), examines the effects of jumps to option pricing beyond the classical diffusion model of Black and Scholes (1973). Articles such as Ball and Torous (1985), Naik and Lee (1990), Amin and Ng (1993), Bakshi, Cao, and Chen (1997), Bates (2000), Duffe, Pan, and Singleton (2000), Anderson, Benzoni, and Lund (2002), Pan (2002), and Eraker, Johannes, and Polson (2003) demonstrate that incorporating jumps is essential in explaining observed option prices. Despite the overwhelming evidence for jumps, a lack of understanding exists on the relation between jump risk and crosssectional expected stock returns. In this paper, I try to shed some light on the subject by examining two questions: (1) How is the expected return of a stock dependent on jump risk? (2) How can jump risk be measured? To address the first question, I adopt the stochastic discount factor (SDF) framework and present a general and yet parsimonious continuous-time model in which the SDF and stock prices follow correlated jump-diffusion processes. In the absence of arbitrage, there exists an SDF

S. Yan / Journal of Financial Economics 99 (2011) 216–233

that prices all assets. (See, for example, Rubinstein, 1976; Ross, 1978; Harrison and Kreps, 1979; and Cochrane, 2005.) The model contains two types of risk: diffusive risk and jump risk, driven by a Brownian motion and a Poisson process, respectively. The expected excess stock return is dependent on both sources of risk. The diffusive component of the return is determined by the covariance between the Brownian motions driving the SDF and stock processes, a well-known continuous-time analogue of the discrete-time brepresentation. The jump component of the return is captured by the covariance between the Poisson processes driving the SDF and stock processes, the covariance between the jump distributions of the SDF and stock when a systematic jump occurs, and the product of the average jump sizes of the SDF and stock. This decomposition highlights the sources affecting the component of expected stock return that compensates for the jump risk. Applying the jump-diffusion model empirically leads to the second question, that is, how to measure or estimate jump risk. There are a couple of major challenges. First, the SDF is not identified due to market incompleteness in the presence of jumps. (See, for example, Naik and Lee, 1990.) Nonetheless, I argue that, based on existing asset pricing models such as the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) and the consumption based capital asset pricing model (CCAPM) of Breeden (1979), the average jump size of the SDF is positive. This seems to be a small step toward understanding the jump risk, but it generates some strong implications. Specifically, I demonstrate that, for reasonable model parameters, the expected excess stock return is monotonically decreasing in the average stock jump size. Identifying the average stock jump size empirically is the second challenge in implementing the jump-diffusion model. Jumps are rare events and estimating average jump size precisely requires long time series samples, which are often unavailable.1 Even with large samples, jumps could fail to realize due to the peso problem. Exacerbating the problem, jump distributions could be time-varying, causing model misspecification and estimation bias. I finesse these difficulties by using information from the option market. The intuition arises from the groundbreaking work of Merton (1976a), who demonstrates the impact of jumps on option prices. Conversely, from observed option prices, I extract information about the underlying jump distribution. The main advantage of this approach is that options are forward-looking contracts and can provide ex ante measures of jump risk. This mitigates the peso problem and reduces the bias caused by in-sample fitting. To proxy jump risk using option data, I propose the slope of implied volatility smile, defined to be the difference between the fitted implied volatilities of

1 Significant progress has been made in estimating jumps in asset prices. Recent papers include Bates (1996), Bakshi, Cao, and Chen (1997), Anderson, Benzoni, and Lund (2002), Pan (2002), Carr and Wu (2003), Chernov, Gallant, Ghysels, and Tauchen (2003), Eraker, Johannes, and Polson (2003), Ait-Sahalia (2004), and Jiang and Yao (2009).

217

one-month-to-expiration put and call options with deltas equal to 0.5 and 0.5, respectively. Theoretically, I demonstrate that the slope measures the local steepness of the smile for near-the-money near-expiration options. In addition, I prove that the slope is approximately proportional to the average stock jump size. Combining these results with the relation between stock return and average stock jump size, I obtain the main hypothesis of the paper: If stock portfolios are formed by ranking on the slope, then the future returns of low slope portfolios are higher than those of high slope portfolios. My empirical analysis is conducted using the option data on 4,048 stocks from January 1996 to June 2005. At first, I employ two tests, one indirect and one direct, to establish the link between the slope of implied volatility smile and average stock jump size. The indirect test is based on the well-known positive relation between jump and skewness. I also propose a new way of computing skewness by taking into account time-varying jump risk. The direct test is based on the jump identification algorithm of Jiang and Yao (2009), which provides estimates of realized jump sizes. This allows for an examination of the predictive power of slope on future jump sizes using time series regressions. The evidence from both tests strongly support the slope being a proxy of average jump size. Next, I examine the relation between slope and future stock returns by considering five equally weighted quintile portfolios formed by sorting stocks on slope at the end of each month. Confirming my hypothesis, the average portfolio returns in the following month exhibit a monotonic decreasing pattern in slope. The pattern does not change even after I adjust portfolio returns using some popular factor models such as the CAPM, the FamaFrench three-factor model, and the four-factor model of Carhart (1997). The difference between the risk-adjusted (using the four-factor model) average monthly returns of the lowest and highest quintile portfolios is 1.9%. The evidence supports the notion that the jump risk embedded in the slope is priced. However, an important question arises: Which component of the jump risk is priced by the market—the systematic component or the idiosyncratic component? To address this issue empirically, I proxy the market jump risk by the slope of Standard & Poor’s (S&P) 500 index options and decompose the slope of a stock into the systematic and idiosyncratic components. Both components are found to be priced as they can predict stock returns in the same way as the slope. Although neither component is able to explain the slope fully, the idiosyncratic component dominates the systematic component as it captures most variation and return predictability in the slope. Consistent with my findings, Jiang and Yao (2009) estimate realized jumps from stock returns and find stock jumps tend to be idiosyncratic. They also find that stock jumps tend to be positive, consistent with my data of positive average slope. It is a puzzle that the idiosyncratic jump risk is priced and even dominates the systematic jump risk. This could be caused by my specific decomposition of the slope, where some systematic factors other than the market

218


slope are missing. But identifying these missing factors posts a challenge as the risk models considered above and the stock characteristics that I control for in robustness checks do not capture these missing factors. An alternative point of view is that the stock market is inefficient as investors mistakenly undervalue (overvalue) stocks with expected negative (positive) idiosyncratic surprises. But this contradicts my model, which assumes efficient stock and option markets. One possible rational explanation of the puzzle could lie in investors’ ability of identifying and aggregating firm-specific information. An idiosyncratic jump in the price of a stock should be totally driven by firm-specific information shocks. But investors are able to forecast precisely the expected idiosyncratic jump size for the stock. When well-diversified portfolios of stocks of similar expected idiosyncratic jump sizes are formed, a low jump-size portfolio has more bad firmspecific surprises on average than a high jump-size portfolio. A utility-maximizing investor, who is averse to bad surprises, should demand higher rate of return for holding the low jump-size portfolio. In the meantime, the total information shock to the market can be negligible if the idiosyncratic jumps cancel each other. According to this explanation, as long as investors do not like adverse jumps, the idiosyncratic jump risk becomes systematic when it is identified and aggregated. Therefore, the idiosyncratic jump risk is nondiversifiable, in contrast to the fact that the idiosyncratic diffusive risk is diversifiable. This is not surprising because jumps are rare and extreme events. For robustness checks of my findings, I control for a number of stock characteristics such as past return, size, book-to-market, leverage, volatility, idiosyncratic volatility, skewness, co-skewness, option trading volume, stock trading volume, and stock turnover rate.2 None of the control variables is found to explain the return predictability of slope. Although the return predictability is persistent up to six months, it does not show any obvious seasonality. My findings are also robust to various data filter rules. In the literature, jump risk is often argued to be reflected by the over pricing of deep out-of-the-money (OTM) put options. In fact, various measures for steepness of implied volatility smile proposed previously use implied volatilities of deep OTM puts. (See, for example, Toft and Prucyk, 1997; Bollen and Whaley, 2004; and Xing et al., 2010.) One problem of using deep OTM puts is that measurement errors can be significant. In contrast, the slope in this paper uses at-the-money options. Furthermore, my model relates the slope to jump risk while previous studies offer different interpretations.3 2 These variables are motivated by a long list of papers including Banz (1981), Basu (1983), Rosenberg, Reid, and Lanstein (1985), Fama and French (1992), Jegadeesh and Titman (1993), Lakonishok, Shleifer, and Vishny (1994), Harvey and Siddique (2000), Ang, Hodrick, Xing, and Zhang (2006), and Pan and Poteshman (2006). 3 For example, Toft and Prucyk (1997) relate slope to firm leverage; Dennis and Mayhew (2002) and Bakshi, Kapadia, and Madan (2003) draw connection between slope and risk-neutral skewness; Cremers, Driessen, Maenhout, and Weinbaum (2008) examine the relation between slope and credit spread; Bollen and Whaley (2004) show slope

To differentiate my paper from earlier papers, I compare the return predictability of slope against the slope measures that use OTM puts. The evidence suggests that the OTM slope measures are unable to capture the return predictability in the slope, while the slope can explain most return predictability in the OTM slope measures. The paper proceeds as follows. In Section 2, I present the jump-diffusion model and all the theoretical results. Section 3 contains the main empirical analysis. In Section 4, I conduct robustness checks. Section 5 concludes. Technical results are provided in the Appendix. 2. Jump-diffusions and asset pricing In this section, we first present the model of stock returns and then demonstrate the relation between jump size and slope of implied volatility smile. 2.1. Stochastic discount factor and stock returns It is natural to formulate jumps using the continuoustime approach. A stochastic discount factor, M(t), is a positive stochastic process so that MS is a martingale for any stock price process S(t). Specifically, I model M(t) as a jump-diffusion process: dM ¼ ðrf lM mJM Þ dt þ sM dW M þ JM dN M , M

ð1Þ

where WM is a standard Brownian motion and NM is a Poisson process with intensity lM ð Z 0Þ, that is, ProbðdN M ¼ 1Þ ¼ lM dt: JM is the jump size with a displaced lognormal distribution independent over time: lnð1 þ JM Þ N ðlnð1 þ mJM Þ12s2JM , s2JM Þ:

ð2Þ

The lognormal specification of JM ensures positivity of M, which guarantees no arbitrage. WM, NM, and JM are independent of each other. rf is the risk-free interest rate. The term lM mJM adjusts the drift for the average jump size. sM is the instantaneous diffusive standard deviation. This type of model for stock prices was introduced by Merton (1976a). I use one-dimensional Brownian motion and Poisson process for simplicity. The model can be extended to incorporate multi-dimensional Brownian motions and Poisson processes. Similarly, I let the price of the ith stock follow a jump-diffusion process: dSi ¼ ðmi li mJi Þ dt þ si dW i þJi dN i , Si

ð3Þ

where Wi is a standard Brownian motion and Ni is a Poisson process with intensity li . Like JM, Ji has a displaced lognormal distribution independent over time: lnð1 þ Ji Þ N ðlnð1 þ mJi Þ12s2Ji , s2Ji Þ:

ð4Þ

(footnote continued) to be affected by the net buying pressure from public order flow; Xing et al. (2010) argue, based on the model of Easley, O’Hara, and Srinivas (1998), that slope reflects informed investors’ demand of OTM puts in anticipating bad news; and Duan and Wei (2009) find slope to be dependent on the systematic risk proportion in the total risk.


Again, Wi, Ni, and Ji are independent of each other, but they are related to the corresponding components in the SDF. Specifically, I assume that WM and Wi, NM and Ni, and JM and Ji are pairwise correlated with correlation coefficients CorrðdW M ,dW i Þ ¼ ri , CorrðNM ,Ni Þ ¼ Zi , and Corrðlnð1 þ JM Þ,lnð1þ Ji ÞÞ ¼ ci , respectively. Notice that Zi is non-negative, while ri and ci can be negative. Ito’s lemma for jump-diffusions implies the following result. Proposition 1. Given the dynamics of the SDF and stock price in Eqs. (1)–(4), the expected excess stock return can be expressed as pffiffiffiffiffiffiffiffiffiffi mi rf ¼ ri sM si Zi lM li ½ð1 þ mJM Þð1 þ mJi Þeci sJM sJi mJM mJi 1:

ð5Þ

Moreover, the expected excess stock return is (i) decreasing in ri and ci ; (ii) decreasing (increasing) in Zi if Yi ð1 þ mJM Þð1 þ mJi Þ eci sJM sJi mJM mJi 1 4 0 ð o 0Þ; and (iii) decreasing (increasing) in mJi if Fi ð1 þ mJM Þeci sJM sJi 14 0ð o 0Þ. Although various forms of Proposition 1 exist in the literature, it is worthwhile to make several observations. First, in the absence of jumps, Eq. (5) is the wellknown continuous-time analogue of the discrete-time brepresentation of expected stock return. Second, when jumps are present but nonsystematic ðZi ¼ 0Þ, Eq. (5) is the same as that in the case of no jumps. This is exactly what Merton (1976a) argues—that idiosyncratic (diversifiable) jumps do not affect expected stock return. In the presence of systematic jump risk ðZi 4 0Þ, the expected stock return depends on the jump distributions. (i) of Proposition 1 says that stocks whose systematic jumps are more negatively correlated with jumps of the SDF ðci o0Þ earn higher returns ceteris paribus. However, the relation between Zi and expected return and the relation between mJi and expected return depend on the signs of quantities Yi and Fi as defined in (ii) and (iii) of Proposition 1, respectively. For the rest of the paper, I focus on the latter because I can infer mJi from the option data. To explore the effect of mJi on expected stock return, I first consider the special case of uncorrelated jump distributions of the stock and SDF, i.e., ci ¼ 0. The determining quantity Fi in (iii) of Proposition 1 simplifies to mJM . To draw inference, I have to know the sign of mJM , the average jump size of M, which is not explicitly specified in the model. The main problem is the nonuniqueness of the SDF because of market incompleteness. I can, however, resort to some well-known asset pricing models to argue that mJM 40. In the CAPM, M is inversely proportional to the market portfolio. Then the empirical evidence that the average jump size of the market portfolio is negative implies mJM 40. As a second example, the SDF in the consumption-based CAPM is proportional to the intertemporal marginal rate of substitution. For a representative investor with a timeseparable power utility function, jumps in the SDF are negatively related to jumps in the consumption growth.

219

(See, for example, Cochrane, 2005.) Therefore, mJM 4 0 holds if the average jump in consumption is negative. Barro (2006) shows strong evidence supporting this assumption. Given mJM 4 0, Proposition 1 indicates that expected stock return is monotonically decreasing in the average stock jump size. In the case of ci a0, the value of Fi depends on the jump parameters mJM , ci , sJM , and sJi . To get some sense on the sign of Fi , I start with a case in which the CAPM holds, and mJM ¼ 10% and sJM ¼ 15%.4 As a worst scenario against Fi 40, I let ci ¼ 1 and further let sJi ¼ 40%, which is very generous as it is more than two-thirds of the average standard deviation of realized stock returns in the sample. Even for these extreme values of ci and sJi , Fi 40. In general, Fi 40 as long as mJM and sJM are of similar magnitude and the product ci sJi is not too negative, which can be due to either small ci or reasonable magnitude of sJi . It is possible that Fi o 0 for some stocks. But these stocks should be outnumbered by stocks with Fi 40 in well-diversified portfolios. It is important to note that whether the expected stock return is monotonically decreasing in mJi is ultimately an empirical issue. What I estimate from the data is basically the empirical SDF, which could well be different from the theoretical SDFs in models such as the CAPM. I thank the referee for this point.

2.2. Jump size and slope of implied volatility Testing the relation between stock return and average jump size requires estimating mJi . As argued by Merton (1980), the parameters related to the diffusive risk such as si can be accurately estimated by quadratic variation of realized stock returns. But the parameters related to the jump risk such as mJi are difficult to pin down because jumps are rare events and could fail to materialize in the sample. Moreover, the parameter could change over time and historical estimate can be biased. In this paper, I propose a rather simple method to proxy mJi that uses information from the option market. Consider a European call option on the ith stock with strike price K and maturity T. Let qi be the dividend yield and let simp ðK,TÞ denote the Black-Scholes implied i volatility. I define log moneyness of the option to be X lnðKeðrf qi ÞT =Si ð0ÞÞ, which is more convenient to work with than K. The log-transformed definition takes into account time value and leads to cleaner formulae than the conventional definition of moneyness K/S. Without ambiguity, I write the implied volatility as simp ðX,TÞ, which is i referred as the implied volatility smile for fixed T. 4 The values used are consistent with those in the literature. For the same sample period, the estimates of the average market jump size and standard deviation in Santa-Clara and Yan (2010) are 9.8% and 16%, respectively. There are other estimates for different sample periods and using different methods. For example, the estimates in Bakshi, Cao, and Chen (1997) are 5% and 7%, and the estimates in Eraker, Johannes, and Polson (2003) are about 3% and 4%. Despite the differences in estimates, Fi 4 0 holds when these alternative parameter values are used.

220


Proposition 2 summarizes some local properties of the smile at X=0. Proposition 2. For T small, the Black-Scholes implied volatility of the at-the-money European call option satisfies

simp ðX,TÞjX ¼ 0 ¼ si þ OðTÞ i

ð6Þ

and @simp ðX,TÞ i @X

¼

li mJi

X¼0

si

Proposition 3. vi is approximately equal to the diffusive volatility si , and si is approximately proportional to the product of jump intensity and average stock jump size. For constant Li 40, vi si and si Li li mJi :

þ OðTÞ,

ð7Þ

where O(T) means in the same order as T. According to Eq. (6), the at-the-money implied volatility converges to the instantaneous diffusive volatility of stock returns as the maturity approaches zero. This extends the similar result of Ledoit, Santa-Clara, and Yan (2003) for diffusions. The jump risk has no impact on the level of the at-the-money implied volatility. But it affects the local steepness of implied volatility smile near-themoney to the extent, as seen in Eq. (7), that the slope, defined to be the partial derivative of implied volatility in terms of moneyness, is proportional to the average jump size. Technically, the parameters such as li and mJi should be specified under the risk-neutral probability measure. In the Appendix, we discuss the transformation between the objective and risk-neutral probability measures. The proposition also holds for put options. I implicitly assume the model parameters to be constant. It is important to note that Proposition 2 can be extended to general settings in which parameters such as the diffusive volatility, average jump size, and jump intensity are time-varying. The findings of Bakshi, Cao, and Chen (1997), Bates (2000), Pan (2002), and SantaClara and Yan (2010), among others, strongly support these more general specifications. In the Appendix, I present evidence that Proposition 2 holds when the diffusive volatility si follows the square-root process of Heston (1993). To implement Proposition 2, I fix time-to-maturity to be small and consider implied volatility simp ðsimp Þ of the i,put i,call put (call) option on the ith stock with D ¼ 0:5 (0.5). These options are not exactly at-the-money but very close to being at-the-money. Define proxies of volatility (vi) and slope of implied volatility smile (si) by ð0:5Þ þ simp ð0:5ÞÞ vi 0:5ðsimp i,put i,call

ð8Þ

and

ð10Þ

ð11Þ

Comparing Eq. (11) with Eq. (7), si is approximately proportional to the local steepness of the implied volatility smile.5 Combining this observation with the discussion following Proposition 1, I can argue that the expected stock return is decreasing in s. To reduce noises in individual stock returns and increase the power of statistical analysis, I consider stock portfolios and formulate my main empirical hypothesis: For stock portfolios formed by ranking on the slope, the returns of low slope portfolios are higher than the returns of high slope portfolios. One could be concerned about the precision of the approximations of Eqs. (6) and (7) and Eqs. (10) and (11). To examine the impact of errors in these approximations, I conduct Monte-Carlo simulations (see the Appendix). Several interesting results are worth commenting upon. First, the errors in the implied volatility level are small even for maturities beyond one month. However, the errors in the slope are relatively large even for maturities less than a month. This is not surprising given that the slope is the derivative of implied volatility. Second, the errors in the slope tend to be negative and are increasing in T, mJi , and li . Third, the slope is a monotonic increasing function of mJi despite approximation errors. This point is critical and provides the foundation for my empirical analysis in which I rank stocks by the slope. The positive relation between the slope and mJi implies that the errors in the slope should not bias the cross-sectional ranking of stocks in mJi . 3. Empirical analysis In this section, I first discuss the data used in the paper. Then I present evidence that the slope does forecast future stock jump size. Next, the main hypothesis is tested. I further investigate the return predictability of the systematic and idiosyncratic components of slope. 3.1. Data

imp imp i,put ð0:5Þ i,call ð0:5Þ:

si s

s

ð9Þ

One practical problem is that individual equity options are American style and their implied volatilities are not obtained by inverting the Black-Scholes formula. Nonetheless, because the options that I use are short-term and near-the-money contracts, their prices are close to the prices of similar European options because early exercise value is low. For example, Bakshi, Kapadia, and Madan (2003) examine a sample of 30 largest stocks in the S&P 100 index and find the difference between Black-Scholes and American option implied volatilities is small enough to be ignored. In the Appendix, I prove Proposition 3.

At the end (last trading day) of each month during January 1996–June 2005, the option data from the OptionMetrics are matched with stock return data from the Center for Research in Security Prices (CRSP) and accounting data from the Compustat. Monthly frequency is chosen for two reasons. First, it is the frequency considered by most studies on cross-sectional stock 5 To be exact, I should use si/vi as the definition of the slope. But I choose the current version for simplicity. My later robustness checks show qualitatively and quantitatively similar results using this alternative definition.


221

Table 1 Stock summary statistics. This table reports, for January 1996–June 2005, the summary statistics (mean and standard deviation) of the firm accounting and stock return data obtained from the Compustat and the Center for Research in Security Prices, respectively. At the end of each month, I use the firm market capitalization, book-to-market ratio, and leverage observed two quarters ago to define the variables ME (in billions of dollars), BM, and LV, respectively. A stock’s b is estimated by regressing its monthly returns on the returns of the Standard & Poor’s (S&P) 500 index. The second last column shows the sample length (in months) of match stock and option data. The last column reports the total number of stocks in the data set. Monthly returns

Mean Standard deviation

ME

BM

LV

b

Mean

Standard deviation

Skewness

Kurtosis

Sample length

Number of stocks

3.252 13.108

1.036 5.704

2.024 16.617

1.339 1.003

0.010 0.060

0.162 0.083

0.408 0.783

4.367 3.083

47 34

4,048

Table 2 Option implied volatilities. This table reports the mean and standard deviation of fitted implied volatilities of the individual equity options with one month to expiration and fixed deltas obtained from OptionMetrics. For each fitted implied volatility, OptionMetrics calculates a dispersion value, which is essentially a weighted average of standard deviations measuring the accuracy of the fitting procedure at that point. DS is the average dispersion over time and across stocks. Calls

Dcall Mean Standard deviation DS

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.584 0.237 0.028

0.572 0.239 0.028

0.565 0.240 0.027

0.560 0.241 0.024

0.559 0.242 0.023

0.558 0.240 0.022

0.559 0.240 0.014

0.562 0.241 0.014

0.566 0.241 0.014

0.571 0.241 0.014

0.576 0.241 0.014

0.583 0.241 0.016

0.591 0.240 0.020

Puts

Dput

0.80

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

Mean Standard deviation DS

0.593 0.248 0.026

0.584 0.248 0.023

0.576 0.246 0.020

0.571 0.245 0.017

0.569 0.245 0.014

0.569 0.244 0.015

0.569 0.242 0.013

0.572 0.242 0.012

0.576 0.241 0.012

0.582 0.241 0.013

0.590 0.240 0.015

0.600 0.237 0.019

0.613 0.232 0.026

returns. Second, it has the benefit of homogeneity, as the options for estimating implied volatility surface in different months have similar maturities. A stock’s b is estimated by regressing its monthly returns on the returns of the S&P 500 index. I also use stock returns of last four years and use the CRSP value-weighted index as the proxy for the market portfolio and obtain similar results. A stock is excluded if it does not have at least two previous years of return data to estimate market beta. Following the convention of the literature, I use the market capitalization, book-to-market ratio, and leverage of each stock observed two quarters ago to define the variables ME, BM, and LV, respectively. I consider three liquidity measures: OV is the total option trading volume; SV is the total stock trading volume; and TO is the stock turnover rate. The data of the risk-free interest rate, Fama-French factors [RM–Rf, small market capitalization minus big (SMB), and high book-to-market ratio minus low (HML)], and the momentum factor (MOM) are downloaded from Kenneth French’s website. The summary statistics of the stocks are reported in Table 1. The sample contains 4,048 stocks with an average time series length of 47 months. The mean market capitalization is over $3 billion and the mean book-to-market ratio is a bit higher than one. On average, the stock returns are positively skewed and fat-tailed. As individual equity options are American style, OptionMetrics employs an algorithm based on the binomial tree

model of Cox, Ross, and Rubinstein (1979) to compute option implied volatilities. The implied volatility surface is then constructed from estimated implied volatilities with a kernel smoothing technique, which is described in detail in the OptionMetrics data manual. OptionMetrics reports the fitted implied volatilities (of both calls and puts) on a grid of fixed maturities and option deltas. The maturities are one month, two months, three months, six months, and one year, and option deltas are 0.2, 0.25, y, 0.8 for calls and 0.8, 0.75,y, 0.2 for puts. For each fitted implied volatility, OptionMetrics also calculates a dispersion value, which is essentially a weighted average of standard deviations that measures the accuracy of the fitting procedure at that point. Table 2 presents the sample statistics of end-of-month fitted implied volatilities with one month to expiration. Clearly, there is a smile, as the atthe-money implied volatility (with D ¼ 0:5 and 0.5 for call and put, respectively) is on average lower than in-themoney and out-of-the-money implied volatilities. The row for average dispersion (DS) shows increasing estimation errors for options deep in-the-money or out-of-the-money. imp I use vimp put ðDput Þ and vcall ðDcall Þ to denote, respectively, the fitted implied volatilities of put and call options with one month to expiration and deltas equal to Dput and Dcall . Following Eqs. (8) and (9), I define v 0:5ðvimp put ð0:5Þ imp þvimp ð0:5ÞÞ and s vimp put ð0:5Þvcall ð0:5Þ, and report the call

222


Table 3 v and various measures of slope. imp This table reports the mean and standard deviation of v and various measures of slope of implied volatility smile. Let vimp put ðDput Þ and vcall ðDcall Þ denote

the fitted implied volatilities with one month to expiration and option deltas equal to Dput and Dcall , respectively. v is defined by imp imp imp sys v 0:5ðvimp and sidio) are defined to put ð0:5Þ þ vcall ð0:5ÞÞ. s is defined by s vput ð0:5Þvcall ð0:5Þ. The systematic and idiosyncratic components of s (s

be, respectively, the fitted value and residual of the time series regression of s on the slope of the S&P 500 index options for the last 12 months. The slope imp measures using OTM puts are defined as sðDÞ vimp put ðDÞvcall ð0:5Þ, for 0:45 r D r 0:20.

Slope measures using OTM puts

Mean Standard deviation

v

s

0.567 0.243

0.010 0.048

sys

s

0.010 0.033

idio

s

0.000 0.072

s( 0.45)

s( 0.40)

s( 0.35)

s( 0.30)

s( 0.25)

s( 0.20)

0.013 0.047

0.017 0.048

0.023 0.049

0.030 0.050

0.040 0.052

0.054 0.054

summary statistics in Table 3. The average implied volatility v is 56.7%, more than twice of the average implied volatility of the S&P 500 index options (about 20%) for the same period. The slope s is positive on average but shows significant variation as the standard deviation of s across stocks is almost five times of the average slope. Because the slope is a proxy of jump risk with measurement error, a wide range of crosssectional differences in slope alleviates the concern that my subsequent portfolio sorting analysis is affected by measurement errors. Furthermore, s varies significantly over time in terms of (unreported) high standard deviation of change of s, implying time-varying jump risk. Almost all correlations among return, v, and s or changes of these variables are insignificant and not reported for brevity. The exception is the negative correlation between return and change of v, which is consistent with the leverage effect suggested by Black (1976) and Christie (1982). I further decompose s into the systematic and idiosyncratic components, using the slope for the S&P 500 index options, sS&P500, to proxy the market jump risk. Specifically, for the ith stock at the end of month t, I estimate the time series regression of the stock slope on the market slope for the last 12 months: si,k ¼ ai þ bi sS&P500,k þ ei,k ,k ¼ t11, . . . ,t.6 I define the systematic and idiosyncratic idio slopes, ssys i,t and si,t , to be the fitted value and residual of the regression, respectively.7 Clearly, most variation in s is captured by the idiosyncratic component. In addition to s, I examine some other slope measures. Particularly, I consider the measures that use out-of-the-money puts, defined as imp sðDÞ vimp put ðDÞ vcall ð0:5Þ for 0:45r D r0:20. The summary statistics of the alternative slope measures using OTM puts are also presented in Table 3. 3.2. Slope predicting jump size One implication of the theoretical results in Section 2 is that the realized jump size is monotonically increasing in the slope of implied volatility smile. Testing this 6 One year of data is lost to estimating the regression. The regression is not defined if there are not enough (or 12) observations. I also use two years of data to estimate the regression and find similar results. 7 The intercept of the regression is part of the systematic slope in this definition. Alternatively, I can incorporate the intercept into the idiosyncratic slope. Another definition that I consider uses the historical estimate of market b for the decomposition. The results for these alternative approaches are similar to those presented in the paper.

Table 4 Average skewness of stock returns in slope quintiles. I consider the 585 stocks that have the slope data during the entire period of January 1996–June 2005. For the ith stock, let frti gTt ¼ 1 denote its monthly return series. Define a ranking series {Iit} so that Iit = n if the slope of the stock in month t 1 is ranked in the nth quintile, where n 2 ð1, . . . ,5Þ. Fixing a number n 2 ð1, . . . ,5Þ, I collect observations in frti gTt ¼ 1 with slope ranking equal to n, that is, frtij : Itij ¼ ng. I then calculate the skewness of the subseries frtij : Itij ¼ ng. I consider only subseries of at least 10 observations. So I have (at most) five skewnesses for each stock corresponding to five slope rankings. This table reports the statistics of the skewnesses for the five quintile rankings. The last row shows the number of subseries of stock returns in each quintile ranking. Q1 Mean Standard deviation Maximum Minimum Number of observations

Q2

Q3

Q4

Q5

0.075 0.109 0.187 0.181 0.327 0.062 0.121 0.144 0.157 0.276 2.802 2.923 2.804 3.557 5.614 2.980 2.627 2.528 2.619 2.095 516 541 527 549 491

implication empirically has two difficulties. First, identifying realized jumps generally requires long time series of stock returns, which are unavailable. The second difficulty, closely related to the first one, is that jump distributions could change over time, making identification of jumps even harder. In this section, I employ two different tests, one indirect and one direct, to demonstrate that the slope predicts average jump size. The indirect test is based on the well-known fact that jumps are positively related to skewness. Because the slope is a proxy of average jumps size, high (low) slope should predict high (low) future return skewness. To ensure enough observations in computing sample moments, I consider only the 585 stocks that have the slope data for the whole period. To take into account of time variation in slope and skewness, I propose a new way to compute skewness. Let frti gTt ¼ 1 denote the monthly return series of the ith stock. Define an auxiliary ranking series {Iit} so that Iit = n if the slope of the stock at the end of month t 1 is ranked in the nth quintile, where n 2 ð1, . . . ,5Þ. Fixing a number n 2 ð1, . . . ,5Þ, I collect observations in frti gTt ¼ 1 with slope ranking equal to n, that is, the subseries frtij : Iti j ¼ ng. I then calculate the skewness of the subseries frtij : Iti j ¼ ng. For accurate estimation, I consider only subseries with at least 10 observations. So I have (at most) five skewnesses for each


223

Table 5 Returns of portfolios formed on slope. Panels A–C of this table report, respectively, the statistics for monthly returns of equally weighted quintile portfolios as well as the long-short portfolio Q1–Q5 by long the lowest quintile portfolio and short the highest quintile portfolio, formed on slope and its systematic and idiosyncratic components (s, ssys, and sidio) during January 1996–June 2005. In addition to the unadjusted raw returns, I consider the risk-adjusted returns, obtained from three models: the capital asset pricing model (CAPM), the Fama-French three-factor [RM–Rf, small market capitalization minus big (SMB), and high book-tomarket ratio minus low (HML)] model, and the four-factor model that extends the Fama-French three-factor model by incorporating the momentum factor (MOM). The t-statistics for the average (unadjusted and risk-adjusted) returns of Q1–Q5 are reported in brackets. The standard deviation, Sharpe ratio, skewness, kurtosis, and autocorrelation coefficient are calculated for the unadjusted returns. Risk-adjusted mean Threefactor

Fourfactor

Standard deviation

Sharpe ratio

Skewness

Kurtosis

Autocorrelation coefficient

Panel A: Quintile portfolios formed on s Q1 0.021 0.013 Q2 0.013 0.007 Q3 0.010 0.004 Q4 0.008 0.002 Q5 0.002 0.005 Q1–Q5 0.018 0.018 [8.168] [8.128]

0.008 0.004 0.002 0.001 0.009 0.017 [8.158]

0.012 0.005 0.001 0.001 0.008 0.019 [9.638]

0.080 0.059 0.055 0.059 0.072 0.024

0.225 0.175 0.131 0.089 0.008 0.642

0.003 0.608 0.665 0.586 0.499 2.256

3.978 3.878 3.475 3.357 3.358 13.267

0.115 0.092 0.123 0.112 0.132 0.053

Panel B: Quintile portfolios formed on ssys Q1 0.013 0.008 Q2 0.012 0.008 Q3 0.009 0.004 Q4 0.010 0.005 Q5 0.006 0.000 Q1–Q5 0.007 0.008 [3.248] [3.269]

0.003 0.005 0.001 0.001 0.004 0.007 [3.220]

0.006 0.006 0.002 0.002 0.002 0.009 [3.829]

0.073 0.058 0.057 0.061 0.072 0.023

0.140 0.161 0.102 0.109 0.045 0.174

0.076 0.355 0.631 0.519 0.232 1.860

4.733 3.839 3.899 3.969 3.473 11.369

0.117 0.072 0.103 0.145 0.177 0.028

Panel C: Quintile portfolios formed on sidio Q1 0.018 0.013 Q2 0.011 0.007 Q3 0.009 0.005 Q4 0.007 0.002 Q5 0.003 0.002 Q1–Q5 0.014 0.015 [7.083] [7.322]

0.007 0.004 0.002 0.001 0.007 0.015 [7.238]

0.012 0.004 0.002 0.001 0.005 0.017 [8.415]

0.077 0.059 0.054 0.055 0.069 0.022

0.194 0.138 0.113 0.067 0.006 0.527

0.068 0.567 0.688 0.557 0.516 2.038

4.170 3.961 4.073 3.775 3.767 10.453

0.132 0.133 0.130 0.101 0.151 0.050

Quintile

Unadjusted mean

CAPM

stock corresponding to the five slope rankings, respectively. Table 4 presents the summary statistics of the skewnesses. As expected, the average skewness increases from 0.075 for the lowest quintile (n= 1) to 0.327 for the highest quintile (n =5). A direct t-test confirms that the skewness of quintile one is larger than the skewness of quintile five. So the evidence on future skewness supports that a stock with higher slope is more likely to have larger-size jumps. The second test is based on the jump-identification methodology of Jiang and Oomen (2008) and Jiang and Yao (2009). I follow Jiang and Yao (2009) to estimate realized jump sizes. For the 12-month period ended in month t, I use daily returns to construct their jump test statistic, which asymptotically follows a standard normal distribution. If the null of no jumps is rejected at the 5% critical level, an estimate of the annual jump size for that year is derived, which I call JRt. If the null is not rejected at the 5% critical level, I let the annual jump size in that period be a missing observation. I repeat these steps for the next 12-month period ending in month t+1, and so on. Because the time series JRt is constructed with rolling windows, it is the change of JRt that measures the average realized jump size in month t. To test the predictability of slope on future average jump

size, I run the following time series regression:

DJRt þ 1 ¼ a þbst þ et þ 1 :

ð12Þ

I expect the estimated b to be positive. For precise estimation, I exclude stocks with time series shorter than 24 observations, and I end up with 806 stocks. The average estimate of b is 0.037, the t-statistic for all estimates of b is 2.536, and the average R2 is 0.036. The evidence from the predictive regression again supports the positive relation between the slope and average stock jump size. Having established the slope as a proxy of the average jump size, I are ready to test the main hypothesis that the slope predicts stock returns. 3.3. Predicting returns Stocks are ranked, on the last trading day of a month, in ascending order according to s into quintiles, and five portfolios are formed by equally weighing the stocks within each quintile. On average, a quintile portfolio contains 402 stocks. I then record the realized returns of the portfolios in the next month. Repeating these steps for every month in the sample period generates the time series of monthly returns for the five quintiles. Panel A of Table 5 reports the statistics of the quintile portfolio

224


returns.8 As shown in the first column, the average monthly portfolio return decreases from 2.1% for quintile one to 0.2% for quintile five, which is consistent with the main hypothesis. The average monthly return of the longshort portfolio Q1–Q5, formed by long quintile one and short quintile five, is 1.8% with t-statistic of 8.168. The return of Q1–Q5 is also economically significant even in the presence of transaction costs. On average, the quintile portfolios have a turn-over rate of 73.1% per month. Assuming a 0.5% one-way transaction cost as in Jegadeesh and Titman (1993), the long-short portfolio still generates 1.1% profit per month. The quintile portfolios could have different risk profiles and thus have different returns. I use three different models to adjust for variations in risk: the CAPM, the three-factor model of Fama and French (1993), and the four-factor model of Carhart (1997) that extends the Fama-French three-factor model by incorporating the momentum factor. The results for the three models are similar. For example, for the four-factor model, the risk-adjusted quintile portfolio returns are lower than the unadjusted returns but the decreasing pattern of returns in slope is the same. The risk-adjusted return for the long-short portfolio Q1–Q5 is 1.9%, even a bit higher than the unadjusted return. Therefore, the factor models cannot explain the returns of quintile portfolios formed on slope. Without ambiguity, I use the four-factor model to estimate risk-adjusted returns for the rest of the paper. As another measure of performance, the Sharpe ratios of the quintile portfolios also decrease in slope. The Sharpe ratio of Q1–Q5 is almost three times that of quintile one. There seems no obvious patterns in other return characteristics such as skewness, kurtosis, and autocorrelation coefficient of the portfolio returns except that the skewness is positive and close to zero for quintile one but negative for other quintiles. Panel A of Fig. 1 plots monthly average slopes of the quintile portfolios. Panel B plots risk-adjusted monthly returns of the quintiles, while Panel C plots risk-adjusted monthly returns of the long-short portfolio Q1–Q5. The risk-adjusted return of Q1–Q5 is positive in 95 of 114 months and achieves the maximum in January 2001. For robustness check, I also consider forming equally weighted decile portfolios and find results similar to those for the quintile portfolios. As expected, the average unadjusted and risk-adjusted returns of Q1–Q10 for the decile portfolios are even higher than those of Q1–Q5 for the quintile portfolios. These results are not presented for brevity.

3.4. Systematic versus idiosyncratic jump risks As the slope of implied volatility smile is a measure of total jump risk, it is interesting to ask whether the relation between slope and return is driven by systematic or 8 The holding period of the portfolios starts on the first business day in the next month. As a robustness check, I also allow a one-day delay in starting the portfolio holding period and find essentially the same results.

idiosyncratic jump risk.9 Theoretically, Merton (1976a) assumes stock jump risk diversifiable, while papers such as Bates (1996) and Santa-Clara and Yan (2010) assume market jump risk priced. However, the empirical evidence on this issue is sparse, mainly because of the difficulty of disentangling market and idiosyncratic jump risks. Fortunately, the slope of implied volatility smile allows a natural decomposition into the systematic and idiosyncratic components: ssys and sidio. Panels B and C of Table 5 report the statistics of returns of quintile portfolios formed by sorting stocks on ssys and sidio, respectively. Both components predict (unadjusted and risk-adjusted) portfolio returns, indicating that both components are priced. But the decreasing pattern of portfolio returns for the idiosyncratic component is more pronounced and closer to that for s, while the portfolio returns for the systematic component are much flatter. The average unadjusted return of Q1–Q5 is 1.4% for sidio but only 0.7% for ssys albeit statistically significant. Similar patterns are found when performance is measured in terms of Sharpe ratio. To further examine the contributions of the systematic and idiosyncratic components to the slope, I conduct a double-sort exercise, following the methodology of Fama and French (1992). I initially divide stocks into five quintiles by ranking on one of the two components (ssys or sidio) and then within each component quintile I further divide stocks into five quintiles by ranking on s. If the decreasing pattern of portfolio returns in s becomes less significant within a component quintile, it is evidence that the component explains the return predictability of s. The risk-adjusted returns of 25(=5 5) double-sorted quintile portfolios and long-short portfolio Qs1–Qs5 are reported in Panels A and B of Table 6 for ssys and sidio, respectively. When stocks are sorted on ssys first and then on s, the returns of s quintile portfolios are still decreasing in s in all ssys quintiles. The return of Qs1– Qs5 remains large (1.4% on average) and highly significant. However, the decreasing pattern of returns in s becomes much less pronounced when stocks are first sorted on sidio and then on s. The returns of Qs1–Qs5 for the sidio quintiles are still positive but much smaller (0.9% on average) in magnitude. The results seem intuitive given that ssys accounts for most variation in s. In sum, neither component can explain all the return predictability of s. Between the two components, sidio dominates ssys as it captures more variation and predictability in the slope. 4. Robustness checks In this section, robustness checks are conducted on the findings that the slope predicts stock returns. In particular, I control for a number of variables that have been found to explain cross-sectional stock returns. I further examine persistence, seasonality, and the impact of data filter rules on the results. I also consider alternative definitions of slope and differentiate my findings from those in some previous studies. 9 I thank the referee for raising the issue and pointing out the direction of the analysis.


225

Average slopes of qunitile portfolios 0.6 Q1

0.5

Q2

0.4

Q3

Slope

0.3

Q4

0.2

Q5

0.1 0 −0.1 −0.2 −0.3 January 1996

January

January

January

January

January

January

January

January

January

1997

1998

1999

2000

2001

2002

2003

2004

2005

January 2002

January 2003

January 2004

January 2005

January 2002

January 2003

January 2004

January 2005

Returns of qunitile portfolios 0.1

Return

0.05

0

0.05 −

0.1 −

January 1997

January 1998

January 1999

January 2000

January 2001

Returns of Q1−Q5 0.15

Return

0.1

0.05

0

−0.05 January 1997

January 1998

January 1999

January 2000

January 2001

Fig. 1. Average slopes and returns of quintile portfolios. Panel A plots the monthly average slopes of the quintile portfolios formed on s during January 1996–June 2005. Panel B plots the risk-adjusted (using the four-factor model) monthly returns of these portfolios during February 1996–July 2005. Panel C plots the risk-adjusted returns of the long-short portfolio Q1–Q5 for the same period.

4.1. Control for other explanatory variables The factor models cannot explain the return predictability of slope. But s still could be a proxy of some stock characteristics that are related to stock returns. This paper considers market b, past stock return, past idiosyncratic

stock return, size, book-to-market ratio, leverage, implied volatility, idiosyncratic implied volatility, historic idiosyncratic volatility, skewness, co-skewness, systematic volatility, option volume, stock volume, and stock turnover rate. Past return r is the stock return in the month when stocks are ranked and portfolios are formed, and past

226


Table 6 Double sorts on s, ssys, and sidio. This table reports the average risk-adjusted (using the four-factor model) monthly returns of double-sorted quintile portfolios formed on s, ssys, and sidio. The last column of each panel reports the average risk-adjusted monthly returns (and t-statistics in brackets) of the long-short portfolio Qs1–Qs5. The last row of each panel reports the averages across the quintiles in each column. In Panel A, stocks are sorted on ssys first and then on s. In Panel B, stocks are sorted on sidio first and then on s. Q1s Panel A: Sort on ssys first and then on s sys 0.011 Q1s

Q2s

Q3s

Q4s

Q5s

Q1s – Q5s

0.008

0.003

0.000

0.005

0.016

ssys

0.012

0.004

0.001

0.001

0.001

[4.484] 0.013

sys

0.008

0.003

0.001

0.000

0.007

[4.552] 0.015

sys

0.004

0.000

0.000

0.000

0.005

[5.843] 0.009

Q5s

sys

0.006

0.002

0.004

0.006

0.014

[3.966] 0.020

Average

0.008

0.002

0.000

0.001

0.006

[6.789] 0.014

0.012

0.011

0.006

0.000

0.013

Q2 Q3s Q4s

Panel B: Sort on sidio first and then on s idio 0.014 Qs 1

idio

0.005

0.004

0.002

0.000

0.002

[3.474] 0.008

idio

0.002

0.001

0.001

0.000

0.002

[3.454] 0.004

idio

0.002

0.002

0.001

0.002

0.007

[2.164] 0.005

Q5s

idio

0.002

0.004

0.006

0.008

0.015

[2.191] 0.017

Average

0.004

0.003

0.001

0.001

0.005

[5.485] 0.009

Q2s Q3s Q4s

idiosyncratic return is defined as ridio rbRM , where RM is the return of the S&P 500 index during the month. Because slope is constructed from option implied volatilities, it is natural to examine if the results are driven by v. Recent studies such as Goyal and Santa-Clara (2003) and Ang, Hodrick, Xing, and Zhang (2006) show that idiosyncratic volatilities have explanatory power on crosssectional stock returns. Following Dennis, Mayhew, and Stivers (2006), I define the idiosyncratic implied variance 2 as v2idio v2 b v2M , where vM is the implied volatility of the S&P 500 index option. I also look at the historic idiosyncratic volatility vhist idio, defined to be the standard deviation of the residuals of the aforementioned market regression. Harvey and Siddique (2000) find that conditional (co-)skewness helps explain cross-sectional stock returns. I follow their method to examine two measures of conditional skewness: SK, defined as the total skewness of stock returns during the last two years; and CSK, defined as the coefficient of regressing last two years stock returns on the squares of market returns. Duan and Wei (2009) find that the systematic risk proportion in the total risk determines the risk-neutral skewness, which in turn affects the implied volatility smile as shown by Bakshi, Kapadia, and Madan (2003). Following Duan and Wei (2009), I define the systematic risk proportion to be 2 v2sys b v2M =v2 and refer to it as systematic volatility without ambiguity. The liquidity variables are motivated by studies such as Bollen and Whaley (2004), Ofek, Richardson, and Whitelaw (2004), Pan and Poteshman

(2006), and Cremers and Weinbaum (2010) that document evidence of market microstructure effects on option prices and stock returns. I adopt the cross-sectional regression approach of Fama and MacBeth (1973) as it can examine multiple explanatory variables simultaneously.10 For each month during the sample period, I run the cross-sectional regression of the unadjusted stock returns in the subsequent month on certain explanatory variables. Table 7 reports the time series averages of estimated regression coefficients and t-statistics. First, consider univariate regressions that include either s or one control variable. The coefficient for s is negative and highly significant, confirming the earlier results based on the portfolio sorting approach. Among the control variables, only ln(ME) is significant and the negative coefficient is consistent with the size effect shown in the literature. For bivariate regressions that include s and one control variable, the coefficient on s remains negative and significant, while none of the control variables is significant. Next, consider incorporating multiple control variables. Given the large number of control variables, there are numerous possible

10 I also use the double-sorting methodology to analyze the effectiveness of control variables in explaining the return predictability of slope. The results are similar to those based on the Fama and MacBeth regressions and are not reported for brevity. This approach, however, can consider only one control variable at a time.


227

Table 7 Slope and control variables. This table reports the averages of estimated coefficients (and t-statistics in brackets) of Fama and MacBeth regressions for monthly stock returns on slope and control variables. The control variables include b, lagged return (r), lagged idiosyncratic return (ridio), log size [ln(ME)], book-to-market ratio (BM), leverage (LV), implied volatility (v), idiosyncratic variance (v2idio), historic idiosyncratic volatility (vhist idio), skewness (SK), co-skewness (CSK), systematic risk (v2sys), option trading volume (OV), stock trading volume (SV), and stock turnover rate (TO). In univariate regressions, either s or one control variable is used. In bivariate regressions, s and one control variable are used. In multivariate regressions, s and multiple control variables are used. Bivariate Univariate s

b r ridio ln(ME) BM LV v v2idio vhist idio SK CSK v2sys OV SV TO

0.057 [ 9.804] 0.001 [0.560] 0.009 [ 0.613] 0.014 [ 1.007] 0.005 [ 3.348] 0.004 [ 0.051] 0.000 [ 1.455] 0.009 [ 0.594] 0.011 [ 1.507] 0.021 [0.385] 0.002 [0.952] 0.001 [0.560] 0.004 [ 1.404] 0.000 [ 1.560] 0.000 [ 1.345] 0.000 [0.484]

s

0.061 [ 10.552] 0.056 [ 9.847] 0.060 [ 10.480] 0.055 [ 10.036] 0.059 [ 9.479] 0.060 [ 9.645] 0.054 [ 9.580] 0.060 [ 10.037] 0.059 [ 10.503] 0.057 [ 10.039] 0.061 [ 10.552] 0.062 [ 10.222] 0.057 [ 9.840] 0.057 [ 9.859] 0.057 [ 9.983]

Control

0.001 [0.414] 0.007 [ 0.491] 0.011 [ 0.814] 0.000 [ 0.129] 0.133 [ 0.712] 0.000 [ 0.506] 0.009 [ 0.582] 0.011 [ 1.444] 0.048 [ 0.657] 0.002 [ 1.007] 0.001 [0.414] 0.004 [ 1.384] 0.000 [ 0.156] 0.000 [0.784] 0.000 [0.564]

Multivariate Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.059 [ 10.837] 0.002 [0.647] 0.013 [ 1.076]

0.057 [ 9.500]

0.058 [ 10.172]

0.061 [ 10.701]

0.057 [ 10.090]

0.057 [ 9.469] 0.000 [0.236] 0.025 [ 2.979]

multi-variate regressions. I show only six representative models for brevity. The first five models include either two or three control variables, and the last model contains most of the control variables. Due to collinearity among the control variables, I drop several variables in Model 6. Again, the coefficient on s is significant in all multi-variate regressions. Among the control variables only r is significant and ln(ME) is marginally significant in Model 6. Overall, there is no evidence that any of the control variables can explain the return predictability of slope.

4.2. Persistence, seasonality, and filters Next, I investigate the performance persistence of the quintile portfolios formed on s by considering holding horizons up to six months and report average risk-adjusted monthly portfolio returns in Table 8. Because of overlapping samples, the holding period returns are serially correlated for horizons beyond one month, and I calculate the t-statistics using the Newy and West procedure. The decreasing pattern of portfolio returns in s is still present

0.000 [ 0.186] 0.075 [ 0.331] 0.000 [ 0.671]

0.001 [ 1.701] 0.335 [0.854] 0.000 [ 1.367] 0.012 [ 1.012]

0.003 [ 0.199]

0.041 [ 1.232]

0.019 [ 0.681] 0.001 [ 0.670]

0.002 [ 1.144] 0.001 [0.423]

0.000 [ 0.559] 0.000 [1.102] 0.000 [0.371]

0.000 [ 0.606] 0.000 [1.434] 0.000 [0.683]

but becomes less pronounced as the holding period increases. The return of the long-short portfolio Q1–Q5 goes down to 1% at two-month horizon and becomes as low as 0.5% at six-month horizon, albeit statistically significant. In spite of some degree of persistence, most of the profit generated by the long-short portfolio comes in the first month immediately after the portfolios being formed. It implies that jumps are short-lived and average jump sizes are time-varying. This is exactly what is observed in the data: The slope of a stock changes over time. One could be interested in whether there is any seasonality in the return predictability of s. I conduct the portfolio sorting exercises and Fama and MacBeth regressions for 12 calender months and find no apparent differences across different months. Another concern is that the findings could be driven by the choice of data. To address the issue, I employ a number of different filters to the data and repeat the analysis. First, stocks for which s is too high or too low are excluded to make sure the findings not dominated by extreme values of s. Second, financial firms are excluded. Third, I use only the 585 stocks that have the slope data for the whole period. Finally, I look at

228


Table 8 Different holding period returns of portfolios formed on slope. This table reports the average risk-adjusted (using the four-factor model) monthly returns of the quintile portfolios formed on s for holding periods of one month to six months. The last column reports the average risk-adjusted monthly returns (and t-statistics in brackets) of the long-short portfolio Q1–Q5. For horizons longer than one month, I follow the Newy and West procedure to compute the t-statistics because the returns are serially correlated due to overlapping samples. Q1

Q2

Q3

Q4

Q5

Q1–Q5

One month

0.012

0.005

0.001

0.001

0.008

Two months

0.008

0.004

0.002

0.001

0.003

Three months

0.008

0.004

0.003

0.002

0.001

Four months

0.008

0.005

0.003

0.003

0.002

Five months

0.008

0.005

0.004

0.004

0.002

Six months

0.009

0.005

0.003

0.004

0.004

0.019 [9.638] 0.010 [7.560] 0.007 [6.073] 0.006 [4.765] 0.006 [4.601] 0.005 [3.837]

the subsamples of stocks that either paid dividends (2,821 stocks) or did not pay dividends (1,227 stocks) during the sample period. In sum, the results for different subsamples are similar to those for the full sample. These results are not shown for brevity but are available upon request.

4.3. Alternative definitions of slope In the literature, jump risk is often argued to be reflected by the implied volatilities of deep OTM put options. However, as seen in the data, implied volatilities of deep OTM put options can be noisy and therefore might not provide accurate estimates of jump risk.11 To examine the extent moneyness affects measurement of jump risk, I consider alternative slope measures that use OTM put imp options: sðDÞ ¼ simp put ðDÞscall ð0:5Þ, for D ¼ 0:45, . . . ,0:2. Panel A of Table 9 reports the average risk-adjusted monthly returns of the quintile portfolios formed on sðDÞ s next to those for s. It is interesting to observe similar decreasing portfolio returns for all slope measures. The return of the long-short portfolio Q1–Q5 is always positive and significant, but it becomes relatively lower as D increases. This indicates potential larger measurement errors for slope measures using deeper OTM puts. I further examine the issue by running the Fama and MacBeth regressions and report the results in Panel B of Table 9. For the univariate regressions with either s or one of sðDÞs as the explanatory variable, the coefficient is negative and statistically significant for all slope measures. But the magnitude of the coefficient, together with the t-statistic, decreases as D increases, consistent with the findings in Panel A. For the bivariate regressions with s and one of sðDÞs the explanatory variables, the coefficient on s is on average more than two times the coefficient on sðDÞ. Moreover, the coefficient on s is always significant, and the coefficient on sðDÞ is only significant in two of six 11 I thank the referee for suggesting this robustness analysis. I also consider using implied volatilities of deep in-the-money puts and obtain similar results.

cases. These results suggest that sðDÞs, the slope measures that use OTM puts, cannot explain the return predictability of s, while s can explain most of the return predictability of sðDÞs. I also use the double-sorting method to examine the explanatory power of s and sðDÞs and obtain similar findings. However, OTM put options could contain information beyond that in the at-themoney option. A future research direction is to extract all the information embedded in the implied volatility smile. It is important to note that for a fixed value of D, say 0.2, sðDÞ resembles the skew measure in Xing et al. (2010). Using the ratio of strike price to stock price as moneyness, they define skew as the difference between implied volatilities of out-of-the-money put and at-themoney call options. Xing et al. (2010) find that low skew stocks outperform high skew stocks, similar to the results for sðDÞ. They argue that the skew reflects informed investors’ demand of OTM puts in anticipating bad news about future stock prices. The implication is that the option market leads the stock market and is more efficient in incorporating information. In contrast, I assume efficient stock and option markets, and my slope of implied volatility smile proxies the jump risk. The put option used in defining s is slightly in-the-money. So a high value of s cannot be interpreted as anticipation of bad news. I next look at another measure of slope defined as imp sl simp put ðDÞsput ð0:5Þ, for 0:45 r D r0:2. This is similar to the measure in Bollen and Whaley (2004), which is basically the percentage difference between implied volatilities of out-of-the-money put and at-themoney put with D ¼ 0:25 and 0.5, respectively. It is also similar to the slope variable of Xing et al. (2010), although they use put options with different moneynesses instead of different deltas. For my sample, I do not find return predictability of sl. It is interesting to realize that all the alternative measures of slope considered above capture the global steepness of implied volatility smile because the two options used for the definitions have distinct strike prices. In contrast, my slope s is a local steepness measure as the put and call options that I use are both close to being at-the-money.


229

Table 9 Slope measures using out-of-the-money (OTM) put options. This table examines s and sðDÞs, the slope measures that use OTM put options. Panel A reports the average risk-adjusted (using the four-factor model) monthly returns of the quintile portfolios as well as the long-short portfolio Q1–Q5 formed on s and sðDÞs. The t-statistics for the average returns of Q1–Q5 are reported in brackets. Panel B reports the averages of estimated coefficients (and t-statistics in brackets) of the Fama and MacBeth regressions. The univariate regressions use either s or one sðDÞ, while the bivariate regressions use s and one sðDÞ. Panel A: Portfolio returns Slope measures using OTM puts

Q1 Q2 Q3 Q4 Q5 Q1–Q5

s

s( 0.45)

s( 0.40)

s( 0.35)

s( 0.30)

s( 0.25)

s( 0.20)

0.012 0.005 0.001 0.001 0.008 0.019 [9.638]

0.012 0.003 0.002 0.001 0.008 0.019 [9.654]

0.012 0.003 0.002 0.000 0.007 0.019 [9.371]

0.012 0.004 0.001 0.001 0.007 0.018 [8.960]

0.012 0.003 0.001 0.001 0.005 0.017 [7.716]

0.011 0.003 0.001 0.001 0.005 0.016 [7.390]

0.011 0.003 0.001 0.001 0.004 0.015 [6.602]

Panel B: Fama and MacBeth regressions Bivariate

s s( 0.45) s( 0.4) s( 0.35) s( 0.3) s( 0.25) s( 0.2)

Univariate

s

sðDÞ

0.057 [ 9.804] 0.057 [ 9.586] 0.054 [ 9.445] 0.053 [ 9.397] 0.049 [ 8.987] 0.044 [ 7.825] 0.039 [ 6.118]

0.048 [ 1.983] 0.038 [ 2.567] 0.036 [ 3.133] 0.039 [ 3.798] 0.042 [ 4.380] 0.045 [ 4.887]

0.010 [ 0.411] 0.020 [ 1.400] 0.024 [ 2.057] 0.021 [ 2.033] 0.018 [ 1.764] 0.014 [ 1.353]

The last alternative measure of slope that I consider is essentially s normalized by v, that is, s^ s=v. This is similar to the normalization in Bollen and Whaley (2004). Toft and Prucyk (1997) also use the percentage difference between implied volatilities of call (put) options with strike prices 10% below and 10% above the stock price, respectively. The results for s^ are very similar to those for s and are not reported for brevity.

strategy that long the lowest slope quintile portfolio and short the highest slope quintile portfolio generates monthly profit of 1.9% on a risk-adjusted basis. Interestingly, it is the idiosyncratic component of slope that accounts for most of the return predictability of slope. My findings are robust to a number of stock characteristics that have been found to explain stock returns. The results cannot be explained by other slope measures in the literature.

5. Conclusion

Appendix A

Overwhelming empirical evidence exists for jumps in stock prices. Based on a stylized jump-diffusion model for the SDF and stock price processes, I demonstrate that expected stock return should be monotonically decreasing in average stock jump size. Overcoming the difficulties of estimating jump distributions, I show that the average stock jump size can be proxied by the slope of option implied volatility smile. After empirically establishing the relation between the slope and average future jump size, I test the hypothesis that the slope predicts future stock returns and find strong supporting evidence. Low slope portfolios earn higher returns than high slope portfolios. The trading

I first prove the propositions and then present simulation results. A.1. Proofs

Proof of Proposition 1. I first decompose the Poisson processes into independent components: NM ¼ NC þ N~ M and Ni ¼ NC þ N~ i , where NC, N~ M , and N~ i are independent Poisson processes with intensities lC , l~ M , and l~ i , respectively. Direct calculation shows that CorrðNM ,Ni Þ ¼ pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi lC = lM li . Hence lC ¼ Zi lM li , l~ M ¼ lM lC , and l~ i ¼ li lC . Next, I apply the Itô’s formula for jump-diffusions

230


pffiffiffiffiffiffi

(see, for example, Protter, 2004) to MSi:

F around zero ðFðzÞ ¼ 12 þ z= 2p þ Oðz2 ÞÞ results in

dðMSi Þ ¼ ðmi rf þ ri sM si lM mJM li mJi Þ dt þ sM dW M þ si dW i MSi

pffiffiffi 1 CjX ¼ 0 ¼ pffiffiffiffiffiffi Si ð0Þsi T þ OðTÞ: 2p

þ JM dN M þJi dN i þ JM Ji dN C :

ð13Þ

being a martingale implies mi rf þ ri sM si MSi pffiffiffiffiffiffiffiffiffiffi þ Zi lM li E½JM Ji ¼ 0. I rewrite JM Ji ¼ ð1 þ JM Þð1 þ Ji ÞJM Ji 1. Then direct computation of the above expectation leads to Eq. (5). The monotonicity of excess stock return in (i)–(iii) can be derived by differentiating the right-hand side of Eq. (5) with respect to the corresponding parameters. & Proof of Proposition 2. Under the risk-neutral probability measure, the stock price follows dSi =Si ¼ ðrf qi li mJi Þ dt þ si dW i þJi dN i :12

ð14Þ

The call price (C) is equal to the discounted expected payoff: C ¼ erf T E0 ½ðSi ðTÞKÞ þ , where E0(.) denotes the expectation. For small T, the probability that one jump occurs before T is lT, and the probability of multiple jumps is of order O(T2). So up to the order of T2, the log terminal stock price can be approximated by the mixture of normal distributions: lnSi ðTÞ 8 pffiffiffi 1 2 > > > < lnSi ð0Þ þ rf qi 2si li mJi T þ si T e ¼ pffiffiffi 1 > > > lnSi ð0Þ þ rf qi s2i li mJi T þ si T e þ mJi þ sJi z : 2

w=Prob:1li T , w=Prob:li T

ð15Þ where e and z are independent standard normally distributed variables. The option price can be written as C ¼ I1 þ I2 ,

ð16Þ

where I1 and I2 correspond to the components without and with the jump, respectively. I use the Black-Scholes formula to compute I1 and I2 to get 1 2 0 1 X þ li mJi þ s2i T 6 B C 2 B C pffiffiffi C ¼ Si ð0Þ6 4F@ A si T 13 0 1 X þ li mJi s2i T B C7 2 C7 þ OðTÞ, pffiffiffi eX FB @ A5 si T

ð17Þ

where Fð:Þ is the standard normal distribution function. Letting X= 0 and applying the Taylor expansion of 12

To be rigorous, the jump intensity and jump size distribution have to be modified when I switch the probability measure. Technically, I should use li , mJi , and sJi to denote the jump intensity, average jump size, and jump volatility, respectively, under the risk-neutral probability measure. Because the market is incomplete in the presence of jumps, the transformation between the two probability measures is not unique. Santa-Clara and Yan, 2010, for example, find a transformation for their equilibrium model, which depends on the risk aversion of the representative investor. I abuse the notation here by using the same parameters for two different probability measures. However, ignoring the change of probability measure might not be a serious problem because the same transformation is applied to all stocks. As I consider cross-sectional stock returns, the probability transformation would not change the inference much.

ð18Þ

For the derivative, I differentiate Eq. (16) with respect to X and evaluate at X =0: 1 8 0 1 2 pffiffiffi > > l m þ s T l m T < i J i Ji i B C @C e 2 i C ¼ Si ð0Þ pffiffiffi fB @ A > @X X ¼ 0 s s T i > i : 1 2 0 pffiffiffi 1 li mJi þ s2i T 6 B C 2 B C 6 F 4 @ A s i

139 0 1 2 pffiffiffi > l m þ s T C7> = i J i i B 1 2 C7 þ OðTÞ, pffiffiffifB @ A 5 > si si T > ;

ð19Þ

where fð:Þ is the standard normal density. Applying Taylor approximations for ez, f, and F around zero pffiffiffiffiffiffi (ez =1+ z+ O(z2), fðzÞ ¼ 1= 2pð1z2 =2Þ þ Oðz4 Þ) leads to 2li mJi pffiffiffi @C 1 1 ffiffiffiffiffiffi p þ ¼ S ð0Þ s þ T þ OðTÞ: ð20Þ i i @X X ¼ 0 2 si 8p Next, I compute the option price and the derivative of the option price in terms of moneyness using an alternative method. Let CBS denote the option value derived from the Black-Scholes formula using some ðX,TÞ, so that C ¼ C BS ¼ implied volatility function, simp i qi T X ½Fðd1 Þe Fðd2 Þ, where d1 ¼ ðX þ 12 ðsimp Þ2 TÞ= Si ð0Þe i pffiffiffi pffiffiffi imp imp 2 imp 1 si T and d2 ¼ ðX 2 ðsi Þ TÞ=si T . Letting X= 0 pffiffiffi pffiffiffi T and d2 ¼ 12 simp T ) and using the (so that d1 ¼ 12 simp i i Taylor expansion of F results in pffiffiffi 1 CjX ¼ 0 ¼ pffiffiffiffiffiffi Si ð0Þsimp T þOðTÞ: i 2p

ð21Þ

Þ For the derivative, @C=@X ¼ ð@C BS =@XÞ þ ð@C BS =@simp i ð@simp =@XÞ. Setting X= 0 and applying Taylor approximai tions for F and f results in " ! # pffiffiffi 2@simp @C 1 1 imp i ffiffiffiffiffiffi p þ ¼ S ð0Þ s þ T þOðTÞ: i i @X X ¼ 0 2 @X 8p ð22Þ Comparing Eq. (18) with Eqs. (21) and (20) with Eq. (22), respectively, I derive Eqs. (6) and (7). Proof of Proposition 3. Let Xput and Xcall be the log moneyness of the put and call options. From the BlackScholes formula, Dput ¼ eqi T ½Fðd1,put Þ1 and Dcall ¼ pffiffiffi eqi T Fðd1,call Þ, where d1,put ¼ ðXput þ 12 ðsimp Þ2 TÞ= simp T i,put i,put pffiffiffi imp 2 Þ TÞ= s and d1,call ¼ ðXcall þ 12 ðsimp T . By the fact that i,call i,call

Dput ¼ 0:5 and Dcall ¼ 0:5, then Fðd1,put Þ ¼ 10:5eqi T and Fðd1,call Þ ¼ 0:5eqi T . Using the Taylor approximations of F and eqi T , I get Xput = O(T) and Xcall = O(T). The implied volatilities of the put and call options are therefore close to the instantaneous stock volatility: simp ¼ si þOðTÞ and i,put simp ¼ si þOðTÞ. Combining these two equations proves i,call Eq. (10). To prove Eq. (11), further computations show


Xput ¼ 12 s2i T þ OðT 3=2 Þ and Xcall ¼ 12 s2i T þOðT 3=2 Þ. Take the difference between d1,put and d1,call to get 1 1 Xput þ ðsimp Þ2 T Xcall þ ðsimp Þ2 T pffiffiffiffiffiffi 2 pi,put 2 pi,call 2pð1eqi T Þ: ffiffiffi ffiffiffi imp simp s T T i,put i,call ð23Þ Rewrite the above equation as pffiffiffiffiffiffi q T pffiffiffi 1 imp 2pðe i 1Þsimp Þsimp T T þ ðsi,put simp i,put i,put i,call 2 imp imp ðsi,put si,call ÞXcall : ð24Þ þ imp

Xput Xcall

si,call

imp 3/2 ) and Xcall is By earlier results, simp i,put si,call is of order O(T

can be approximated by vi ¼ of order O(T). simp i,put 0:5ðsimp þ simp i,put Þ up to order O(T). So, I can drop the last i,call two terms in Eq. (24), which are of order O(T2), and have the following approximation: pffiffiffiffiffiffi pffiffiffi Xput Xcall 2pðeqi T 1Þvi T : ð25Þ The value of Eq. (25) is nonzero only when the dividend yield qi is nonzero. If that is the case, I can approximate the slope of the implied volatility smile by pffiffiffi simp simp simp simp @simp ðX,TÞ i,put i,put i,call i pffiffiffiffiffiffii,call ðeqi T 1Þvi T : ¼ @X Xput Xcall p 2 X¼0 ð26Þ Using the approximation vi si and comparing Eq. (26) with Eq. (7), si is proportional to li mJi up to the constant pffiffiffiffiffiffiffiffiffi Li ¼ 2 2pT ðeqi T 1Þ. And this proves Eq. (11). The results depend on the assumption of nonzero dividend yield. However, the traded stock options are American style. Even for non-dividend-paying stocks, the put and call options with D ¼ 0:5 and 0.5 can have different strikes because of early exercise opportunities. I leave generalization to American options for future research. In fact, my empirical results for non-dividend-paying stocks are similar to those for dividend-paying stocks. A.2. Monte-Carlo simulations Monte-Carlo simulations are conducted to examine the approximation errors in Proposition 2. I extend the model to incorporate stochastic volatility because of overwhelming empirical evidence of time-varying volatility. In particular, the return volatility follows the square-root process of Heston (1993): qffiffiffiffiffiffi ð27Þ ds2i ¼ ki ðyi s2i Þ dt þ fi s2i dZ i , where Zi is a standard Brownian motion correlated with Wi and the correlation coefficient is CorrðdW i ,dZ i Þ ¼ zi . Although semi-analytical option pricing formula is available for jump-diffusion model of Eqs. (3), (4), and (27) (see, for example, Pan, 2002), I adopt the simulation approach here to compute option prices because of its simplicity. To simulate paths of stock prices, the Euler scheme is used to discretize the continuous-time model

231

and the time interval Dt is set to one-fifth of a day. I approximate the Poisson process by a Bernoulli process, that is, there is at most one jump during an interval. For the benchmark case, I use the following parameter values: rf =0.06, qi = 0.02, li ¼ 0:5, mJi ¼ 0:1, sJi ¼ 0:1, ki ¼ 0:02, yi ¼ 0:025, fi ¼ 0:025, and zi ¼ 0:25. The initial stock price is S(0) =$40 and the initial volatility is si ð0Þ ¼ 0:5. One million paths of stock prices are generated and the price of an option is calculated by discounting the average payoff. I then invert the Black-Scholes formula to get the option implied volatility. For a particular maturity T, I compute the at-the-money implied volatility for which the moneyness X is zero. I also compute the implied volatility for the option with the same maturity but with strike price $0.001 higher than the strike price of the at-the-money option. I approximate the slope by the ratio between the difference of the two implied volatilities and the difference between the two moneyness values. Four different maturities are considered: one day, one week, one month, and two months. I also consider the effects of changing certain parameter values and report the at-the-money implied volatility and slope in Table A.1. In Panel A, I use different values of average jump size, mJi . The left half of the panel reports the implied volatility. For a fixed value of T, a U-shaped pattern of implied volatility is seen as a function of mJi . The implied volatility is biased upward, that is, higher than the instantaneous diffusive volatility, which is equal to 0.5. The bias is very small for maturity of one day but becomes larger for long maturities. For example, at the two-month horizon and when mJi ¼ 0:2, the implied volatility error is 0.04. As expected, the estimated slope of implied volatility smile shows an increasing pattern in terms of mJi when T is fixed. The rate of increase is highest when T is one day, and it gets smaller as T becomes larger. To get a sense of the accuracy of the approximation, I compare slope with mJi as Eq. (7) suggests that these two quantities should be close because of the choice of li ¼ si ð0Þ ¼ 0:5. When mJi ¼ 0:2 and T is one day, slope is 0.143, so the error is 0.057. For mJi ¼ 0:1, the error is 0.045. The magnitude of error is smaller for negative jump sizes. For example, for mJi ¼ 0:1, the bias is only 0.002. Fixing a value of mJi , the error is increasing with T and becomes significant, particularly for positive values of mJi . Overall, the approximation error is significant when average jump size is positive or when maturity is long, or both. However, it is important to notice that the slope of implied volatility maintains an increasing pattern in terms of mJi . The implication is that high slope stocks have more positive jumps than low slope stocks. This is exactly what is needed to formulate the main hypothesis of the paper. Panel B examines the effect of jump intensity, li . As li increases, the error in implied volatility becomes larger but still relatively small in magnitude. For values of li equal to one and two, compare mJi with half of and quarter of slope. As li increases, the approximation error decreases. Panel C examines the effect of correlation between the stock and volatility processes, zi . The error in implied volatility is not affected by zi , while the error in slope

232


Table A.1 Implied volatility and slope from Monte-Carlo simulations. GB= Black and Scholes’s Geometric Brownian Motion model, SV =Heston’s stochastic volatility model, GB-J =Merton’s jump-diffusion model, SV-J =model with stochastic volatility and jump. @simp ðX,TÞ i @X

simp ðX,TÞjX ¼ 0 i

X¼0

One day

One week

One month

Two months

One day

One week

One month

Two months

0.2 0.1 0.05 0.05 0.1 0.2

0.508 0.504 0.503 0.502 0.503 0.506

0.519 0.509 0.506 0.505 0.507 0.514

0.532 0.515 0.510 0.508 0.511 0.523

0.540 0.519 0.513 0.511 0.515 0.529

0.143 0.055 0.014 0.059 0.098 0.188

0.094 0.027 0.002 0.042 0.068 0.146

0.025 0.011 0.021 0.042 0.054 0.100

0.014 0.029 0.032 0.042 0.052 0.088

Panel B: li 0.5 1

0.504 0.508

0.509 0.517

0.515 0.528

0.519 0.533

0.055 0.129

0.027 0.073

0.011 0.007

0.029 0.024

2

0.516

0.534

0.552

0.562

0.280

0.160

0.035

0.022

Panel C: zi 0.5 0.25 0 0.25 0.5

0.504 0.504 0.504 0.504 0.504

0.509 0.509 0.509 0.509 0.509

0.515 0.515 0.515 0.515 0.515

0.519 0.519 0.519 0.519 0.519

0.053 0.055 0.058 0.060 0.063

0.024 0.027 0.030 0.033 0.036

0.014 0.011 0.008 0.004 0.001

0.032 0.029 0.026 0.023 0.020

Panel D: Model GB SV GB-J SV-J

0.500 0.500 0.504 0.504

0.501 0.501 0.509 0.509

0.502 0.502 0.515 0.515

0.505 0.505 0.520 0.519

0.018 0.020 0.058 0.055

0.017 0.020 0.029 0.027

0.024 0.027 0.007 0.011

0.029 0.032 0.026 0.029

T Panel A: mJi

becomes smaller for higher values of zi although the improvements are small. My most general model includes Poisson jump and stochastic volatility, and I call it the SV-J model. When there is no jump and volatility is constant ðli ¼ 0, fi ¼ 0Þ, it becomes Black and Scholes’s Geometric Brownian motion (GB) model. When volatility is stochastic but there are no jumps ðli ¼ 0Þ, the model becomes Heston’s (SV) model. In the case of constant volatility ðfi ¼ 0Þ, it becomes Merton’s jump-diffusion (GB-J) model. Panel D of Table A.1 reports the implied volatility and slope for these different models. For implied volatility, the approximation error is larger for the models with jumps. But the magnitude of errors is small. When jumps are absent, slope is negative and small. In contrast, for the SV-J and GB-J models, slope is positive at least for short maturities. To summarize, slope is related to jumps and not affected much by stochastic volatility. References Ait-Sahalia, Y., 2004. Disentangling diffusion from jumps. Journal of Financial Economics 74, 487–528. Amin, K., Ng, V.K., 1993. Option valuation with systematic stochastic volatility. Journal of Finance 48, 881–910. Anderson, T., Benzoni, L., Lund, J., 2002. An empirical investigation of continuous-time equity return models. Journal of Finance 57, 1239–1284. Ang, A., Hodrick, R.J., Xing, Y., Zhang, X., 2006. The cross section of volatility and expected returns. Journal of Finance 61, 259–299. Bakshi, G., Cao, C., Chen, Z., 1997. Empirical performance of alternative option pricing models. Journal of Finance 52, 589–667.

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