Research in Finance, Volume 24

RESEARCH IN FINANCE VOLUME 24 RESEARCH IN FINANCE EDITED BY ANDREW H. CHEN Edwin L. Cox School of Business, Southern...

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RESEARCH IN FINANCE VOLUME 24

RESEARCH IN FINANCE

EDITED BY

ANDREW H. CHEN Edwin L. Cox School of Business, Southern Methodist University, TX, USA

United Kingdom – North America – Japan India – Malaysia – China

JAI Press is an imprint of Emerald Group Publishing Limited Howard House, Wagon Lane, Bingley BD16 1WA, UK First edition 2008 Copyright r 2008 Emerald Group Publishing Limited Reprints and permission service Contact: [email protected] No part of this book may be reproduced, stored in a retrieval system, transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying issued in the UK by The Copyright Licensing Agency and in the USA by The Copyright Clearance Center. No responsibility is accepted for the accuracy of information contained in the text, illustrations or advertisements. The opinions expressed in these chapters are not necessarily those of the Editor or the publisher. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-7623-1377-8 ISSN: 0196-3821 (Series)

Awarded in recognition of Emerald’s production department’s adherence to quality systems and processes when preparing scholarly journals for print

LIST OF CONTRIBUTORS Mukesh Bajaj

LECG LLC and Haas School of Business, UC Berkeley, CA, USA

Melanie Cao

Schulich School of Business, York University, Toronto, Ontario, Canada

Andrew H. Chen

Cox School of Business, Southern Methodist University, Dallas, TX, USA

C. Sherman Cheung

DeGroote School of Business, McMaster University, Hamilton, Ontario, Canada

Wan-Jiun Paul Chiou

Department of Finance, John Grove College of Business, Shippensburg University, Shippensburg, PA, USA

Sun Eae Chun

Graduate School of International Studies, Chang-Ang University, Seoul, Korea

Mary Daly

Economic Research Department, Federal Reserve Bank of San Francisco, San Francisco, CA, USA

Li Hao

Citigroup Global Markets Asia Limited, Citibank Plaza, Hong Kong

William Hillison

College of Business, Florida State University, Tallahassee, FL, USA

John Krainer


Clarence C. Y. Kwan


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LIST OF CONTRIBUTORS

Bun Song Lee

College of Business, Northwestern State University, Natchitoches, LA, USA

Jin-Ping Lee

Department of Finance, Feng Chia University, Taichung, Taiwan

Donald Lien

International Business Program, University of Texas – San Antonio, San Antonio, TX, USA

Jose A. Lopez


David Marlett

Brantley Risk and Insurance Center, College of Business, Appalachian State University, Boone, NC, USA

Sumon C. Mazumdar

LECG LLC and Haas School of Business, UC Berkeley, CA, USA

Peter C. Miu


T. J. O’Neill

School of Finance and Applied Statistics, The Australian National University, Canberra, Australia

Carl Pacini

Department of Accounting and Finance, College of Business, Florida Gulf Coast, University, Ft. Myers, FL, USA

J. Penm

School of Finance and Applied Statistics, The Australian National University, Canberra, Australia

Gordon S. Roberts

Schulich School of Business, York University, Toronto, Ontario, Canada

Mark Schaub

Northwestern State University, Natchitoches, LA, USA

C. W. Sealey

The Belk College of Business Administration, University of North Carolina at Charlotte, Charlotte, NC, USA

List of Contributors

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R. D. Terrell

National Graduate School of Management, The Australian National University, Canberra, Australia

Jason Wei

Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario, Canada

Mei Zhang

Shanghai Finance University, Shanghai, China

INTRODUCTION A total of 12 chapters in this volume represent some current research on important topics in finance and economics. Bajaj et al. demonstrate through a time series analysis that the IPO underwriting spreads seem to be competitive, in contrast to the findings of Chen and Ritter (2000). Sealey argues that it is necessary for the regulator and deposit insurer to be an integral part to mitigate the moral hazard problem in bank regulation. Lee develops a multi-period pricing model to examine the impact of forbearance and potential moral hazard behavior on the cost of deposit insurance. Hao and Roberts show that lead lenders have significant positive influence on loan yield spreads. Daly et al. show that coincident indicators developed to track a state’s gross outputs have significant influence on state-level aggregate bank performance. Some recent studies in global investments are included in this volume. For example, Chiou’s empirical results show that investors in the countries of civic-law origin tend to benefit more from global investments than the ones in the common-law states. Schaub et al. examine investor overreaction and seasonality in the stock markets of Korea, Hong Kong and Japan and find little to no reversals following days of excessive increase, but all three indices reversed 35–45% following days of excessive decline. The contributions to this volume also examine asset allocation of hedge funds, incentive stocks and options, board size and firm performance, impact of higher oil prices on stock market returns and futures hedging effectiveness. For example, Cheung et al. show that a mean-Gini approach is more appropriate than that of mean-variance in asset allocation decisions for hedge funds. Cao and Wei demonstrate that employees’ partial hedge can reduce the vesting requirements on stock ownership and incentive options and undermine the incentive effects. Pacini et al. document that, in the post-Financial Services Modernization Act of 2000, there is a significant inverse relation between the publicly traded property-liability insurer performance and board size. O’Neill et al. find that higher oil prices in the recent years have adversely affected the stock market returns in the U.S.A.,

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INTRODUCTION

UK and France, but positively affected that in Canada and Australia. Finally, Lien and Zhang show that alternative settlement specifications in futures contracts directly affect the futures prices as well as the liquidity risks on futures hedging. Andrew H. Chen Series Editor

COMPETITION IN IPO UNDERWRITING: TIME SERIES EVIDENCE Mukesh Bajaj, Andrew H. Chen and Sumon C. Mazumdar ABSTRACT Chen and Ritter (2000) documented that underwriter spreads for recent US initial public offerings (IPOs) in $20 million range as well as much larger IPOs in the $80 million range are clustered at 7%. This observation has led to a Department of Justice (DOJ) enquiry into potential price fixing by underwriters. We demonstrate through a times series analysis that IPOs have tripled in size and become much riskier over time. A pooled data analysis can therefore mask evidence of competition in the market. We find that spread clustering is not a recent phenomenon. Over time, clustering at 7% has increased as clustering above 7% has declined. IPO spreads have declined significantly over time as the firms going public more recently are riskier, underwriting efforts have increased and recent IPOs are much larger than IPOs in the past. Controlling for time trends, larger IPOs have lower average spreads. The market for underwriting IPOs seems to be competitive with entry of new firms during the hot markets.

Research in Finance, Volume 24, 1–25 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00201-8

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1. INTRODUCTION A firm’s costs of going public entails three types of costs: (a) direct issuing costs which are fixed and largely independent of the underwriter; (b) the underpricing associated with the (positive) first day returns observed relative to offer price; and (c) the ‘‘spread’’ paid to underwriters.1 The issuer’s objective is to minimize the underpricing and spread costs associated with its initial public offering (IPO) of its common equity. More concerted effort by the underwriter or the choice of underwriters could reduce the underpricing costs associated with the offering. For instance, banks that specialize in underwriting firms from certain industries, or bulge bracket investment banks with greater reputation may provide greater certification value for the firm’s IPO and hence reduce its underpricing costs.2 In return, such banks could be expected to demand a higher spread as compensation. The spread could also be a function of the risk associated with the security and the size of the offering among other factors.3 Yet, according to Chen and Ritter (2000) by the late 1990s, the underwriting spread paid for all firm commitment IPOs in the US, regardless of offering size and choice of underwriter was almost exclusively clustered at exactly 7% for over 90% of ‘‘mid-size’’ issues. In contrast, in the early 1980s, only about a quarter of the spreads for such IPOs were at exactly 7%. The observation that the spread paid for IPOs of $20 million was exactly the same as the spread paid for offerings four times as large ($80 million) lead to speculation in some quarters that such a ‘‘seven percent solution’’ was indicative of collusion (or price-fixing) by underwriters. Chen and Ritter (2000) themselves characterized their result as consistent with a ‘‘strategic pricing equilibrium.’’ The US Department of Justice (DOJ) launched an investigation into the ‘‘alleged conspiracy among securities underwriters to fix underwriting fees.’’ A class action lawsuit was brought against 27 investment banks for not competing on price. The lawsuit and the DOJ inquiry were subsequently dropped following a judge’s ruling in favor of the defendants.4 Other non-collusion explanations for the ‘‘seven percent solution’’ have been offered recently in the literature. The 7% spread is arguably consistent with efficient contract theory where underwriters compete in pricing 7% IPOs based on their reputation, placement services, and underpricing that complement the 7% spread (Hansen, 2001).5 The seemingly fixed 7% spread could have emerged as a solution to a double-sided matching mechanism between firms and underwriters in which firms and underwriters pick each other based on criteria other than price (Fernando, Gatchev, & Spindt, 2002).6 Barondes, Butler, and Sanger (2000) found that the

Competition in IPO Underwriting: Time Series Evidence

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probability of receiving an offer price that exceeds the initially estimated offer price is significantly correlated with the gross spread. These authors conclude that the degree of marketing service the issuer receives is a function of the compensation it paid to underwriters. Clustering alone does not necessarily imply lack of competition. Price clustering has been documented earlier in other incontestably competitive financial markets, including AMEX, NYSE, the London Stock Exchange, the London gold market, and the international foreign exchange market.7 Such clustering is believed to be greater the more difficult it is to value the underlying asset.8 Also, other things being equal, for high-priced assets, the price grid tends to be coarser. For example, prices of houses are seldom negotiated in increments of $1. Thus, any conclusions from comparisons of the degree of price clustering over a long time period must directly examine changes in IPO market conditions, especially in the risk and size of IPOs as well as the level of underwriting efforts undertaken. However, a detailed time series analysis of IPOs’ characteristics and their associated spreads has hitherto not been undertaken in the literature.9 We address issues regarding competitiveness of IPO underwriting activities and clustering of underwriting spreads by focusing on time series analysis of several characteristics of IPOs and their underwriting spreads. Our main results are summarized below: 1. In general, for the entire period, from 1980 to 1998, we find that (a) relatively smaller IPOs tend to be riskier; and (b) underwriting spreads tend to be more clustered for riskier IPOs. 2. The median size of an IPO has tripled in the last two decades. 3. Recent IPOs have involved considerably more risky firms (as measured by post-IPO price volatility). These results indicate that a comparison of the degree of clustering in spreads at 7% for $20 million to $80 million IPOs over a two-decade period can lead to a biased conclusion for two reasons. First, keeping issue size constant over this period can lead to comparison of larger IPOs from early years to smaller IPOs of the more recent years. This can mask a decline in average spread over time as well as a negative relationship between the spread and issue size. Second, it would be reasonable to expect that recent IPOs’ spreads would be more clustered since these offerings have been riskier. Additionally, we find that: 4. The increased clustering of spreads at 7% is not explained by an increase in spread clusters lower than 7% but because of a reduction in clustering above 7%.

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5. Over time, IPO spreads have declined significantly while more risky firms are going public and underwriting efforts, as measured by number of co-managers, have increased. 6. Unlike Chen and Ritter (2000), we do find that average spread declines with increase in issue size. 7. We also document that the market has never been concentrated and that there is entry of lead underwriters when the number of IPOs is large. Overall, like Hansen (2001), we find that the IPO underwriting market is quite competitive. In Section 2, we describe our IPO dataset, which is similar to that of Chen and Ritter (2000) except that we do not delete IPOs with proceeds less than $20 million. We also discuss some time trends in the IPO market from 1980 to 1998. In particular, we find that market has never been concentrated, with new entry occurring during periods of increased demand for underwriting services. Section 3 provides some size and volatility trends in the IPO market between 1980 and 1998. Specifically, we note that issues’ average issue size and issues’ aftermarket volatility has increased significantly over time. We document these results and discuss the implications of our time series in Section 4. Section 5 concludes the chapter.

2. SAMPLE DESCRIPTION Our dataset consists of 5,805 firm commitment IPOs from 1980 to 1998 included in the New Issues database of the Securities Data Company (SDC). We exclude closed-end funds, American depository Receipts (ADRs), real estate investment trusts (REITs), and unit offerings. All proceeds reported exclude underwriter warrants and over-allotment options and are expressed in 1997 purchasing power terms adjusted using the US GDP implicit price deflator. Table 1 summarizes the number of offerings by year, the average gross spread, direct issuance costs, and underpricing costs. While the number of offerings has varied annually between 1980 and 1998, it has generally trended up. The average gross spread has declined over the same period, from 8.31% in 1980 to 6.94% in 1998. IPO underpricing has increased significantly over the same period after a decline in the second half of the 1980s. Interestingly, IPO underpricing has generally been greater in ‘‘hot’’ IPO markets: Table 1 indicates that, in general, as the number of IPOs increased so did the underpricing. According to Hansen (2001) such


Table 1.

Gross Spread, Other Direct Expenses, Underpricing and Book Managers by Year.

Year Number Gross Other Direct Underpricing Total of Spread Expenses (%)c Expense Offerings (%)a (%)b (%)d

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

100 239 80 511 210 206 441 310 115 110 108 274 386 475 363 431 683 477 286

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8.31 8.21 7.97 7.61 7.84 7.54 7.36 7.34 7.23 7.12 7.13 6.97 7.04 7.04 7.18 7.02 7.03 6.88 6.94

5.33 4.62 4.84 4.14 5.51 4.18 4.11 4.43 4.53 3.48 3.11 3.16 3.53 3.23 4.05 3.36 3.58 3.68 4.16

18.12 8.54 12.07 9.77 3.17 5.93 5.53 4.61 4.62 8.04 9.97 11.24 10.18 11.89 8.50 19.72 15.19 12.77 21.25

30.59 21.37 24.26 20.92 16.72 13.07 16.59 16.16 16.63 19.49 20.21 21.84 21.20 22.00 20.36 30.59 25.33 23.12 34.44

Number Herfindahl Index of Book for the IPO Managers Underwriting Business 48 88 48 117 85 66 103 87 46 39 39 55 86 105 111 93 118 124 94

467.72 523.34 773.55 474.30 412.16 745.13 568.91 808.36 906.56 1368.67 1292.56 859.60 827.16 632.51 564.39 940.11 844.39 504.33 1073.91

Our dataset consists of 5,805 firm commitment IPOs from 1980 to 1998 included in the New Issues database of the SDC. We exclude closed-end funds, ADRs, REITs, and unit offerings. All proceeds reported exclude underwriter warrants and over-allotment options and are expressed in 1997 purchasing power terms adjusted using the US GDP implicit price deflator. a Gross spread is the gross spread as a percentage of total proceeds, including management fee, underwriting fee, selling concession, and reallowance fee (SDC variable: GPCT). b Other expenses are expenses including registration fee and printing, legal and auditing costs, as a percentage of total proceeds (SDC variable: EXPAMT). c Underpricing is measured by the (positive) first day returns observed relative to offer price. d Total expense is the sum of ‘‘Gross Spread (%)’’ and ‘‘Other Direct Expenses (%)’’.

underpricing varies by issues and across underwriters and is a form of non-price competition. The relationship between the level of underpricing and IPO volume has been analyzed thoroughly by Lowry and Schwert (2002). Table 1 also presents the number of book managers involved with IPOs during a specific year and the corresponding Hirschman-Herfindahl Index (HHI) that measures the concentration in the IPO-underwriting industry.

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The HHI is computed as follows. We first identified the ‘‘book’’ or syndicate manager for each IPO for a given year.10 Each IPO’s proceeds were attributed entirely to its book manager. Each book manager’s share of the aggregate IPO market for that year was then calculated as its total proceeds divided by the total proceeds of all IPOs that year.11 The HHI for the IPOunderwriting business, which captures the degree of concentration in this business, was then computed as the sum of the square of each manager’s market share (expressed as a percentage).12 The 1992 DOJ and Federal Trade Commission Horizontal Merger Guidelines categorize a market as ‘‘unconcentrated’’ when its HHI is below 1000, ‘‘moderately concentrated’’ when its HHI is between 1000 and 1800, and ‘‘highly concentrated’’ when its HHI exceeds 1800. During 1980–1998, the HHI for the IPO-underwriting business never exceeded the highly concentrated threshold of 1400. In fact, the HHI would be considered indicative of a moderately concentrated business in only three of the 19 years studied, viz., 1989, 1990, and 1998. The IPO market was unconcentrated in 16 of the 19 years studied. Interestingly, industry concentration did not coincide with hot IPO markets. Instead, the moderately concentrated HHI levels between 1986 and 1993 occurred when the IPO markets slumped and there were fewer IPOs to be distributed among the established players. The market was unconcentrated, or had a larger number of underwriter firms participating as book managers in hot IPO markets. This is further evidence of the competitive nature of this business since it suggests that market entry was relatively easy in lucrative times and new underwriters entered the business in response to increase in demand. Table 2 provides details of certain time-trend analyses concerning three attributes of the IPO market (HHI, the number of IPOs, and the number of book managers) over the 1980–1998 period. As Table 2 indicates, all three attributes of the IPO market have increased over this period. However, only the increase in the number of IPOs over time is statistically significant at the 95% confidence level. Chen and Ritter (2000) find evidence that the gross underwriting spreads of ‘‘moderately sized offerings,’’ which they define to be in the $20 million–$80 million range (in inflation-adjusted dollars) are clustered at 7%. They argue that the 7% spread is above competitive levels and consistent with ‘‘strategic pricing’’ by investment bankers.13 These authors posit that investment bankers use non-price competition, such as the implicit promise of favorable analyst coverage and buy recommendations, as a means of product differentiation, instead of relying on price competition. Chen and Ritter (2000, p. 1106) do say, however, that ideally a test of price


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Table 2. Time-Trend Analyses (1980–1998 Period): Correlation of Time and Attributes of IPO Market (Number of IPO Offerings, HHI, and Number of Book Managers). Coefficient (t-Stat)

IPO Offerings

HHI

Number of Managers

Intercept

30806.62 (2.4774) 15.64 (2.502)

34714.42 (1.603) 17.84 (1.6384)

4147.56) (1.8615 2.13 (1.8982)

Year R2 Adjusted R2 Observations

0.2691 0.2261 19

0.1364 0.0856 19

0.1749 0.1263 19

Indicates statistical significance at 95% confidence level.

competition in underwriting should examine whether the gross spreads equaled costs, including the opportunity cost of capital employed. However, in the absence of such proprietary data14 these authors limit themselves to considering whether gross spreads vary with issue size as they would be expected to do in the presence of fixed underwriting costs and competition among underwriters. When information pertaining to costs, which is required to directly examine whether there are scale economies in underwriting and whether spreads are set at a competitive level, is unavailable a natural question arises: Is an issue’s size the only relevant economic variable that might explain gross spreads, as Chen and Ritter (2000) postulate? We argue that the additional economic variables, such as the IPO’s volatility and the degree of underpricing, may in fact affect the gross spreads charged in a competitive market. Since these relevant variables may change over time, in the following section we examine time series trends in various factors that would be relevant in examining whether the observed clustering of spreads indicates a non-competitive market.15

3. TRENDS IN IPO CHARACTERISTICS 3.1. Median Issue Size Has More than Tripled between 1980 and 1998 and the Average Issue Size Has Increased More than Five-Fold Table 3 examines the size of IPOs (measured by the IPO’s gross proceeds) on an annual basis over the 1980–1998 period. For each year, various

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Table 3. Year

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

Inflation Adjusted Proceeds by Year (In Millions of Dollars).

Number Mean

100 239 80 511 210 206 441 310 115 110 108 274 386 475 363 431 683 477 286

20.62 18.29 21.63 34.23 18.26 38.01 48.05 51.63 42.40 56.30 44.30 58.94 57.46 63.85 44.30 62.94 66.01 70.79 109.64

Standard Deviation

75th Percentile

Median

25.45 21.97 23.98 51.66 22.04 91.71 125.53 134.33 63.30 122.19 60.67 88.22 86.02 132.39 59.95 98.86 153.58 105.55 325.62

22.83 21.47 24.16 37.77 20.87 33.15 41.97 43.32 52.30 46.37 48.20 56.55 56.66 59.12 44.69 60.86 61.92 70.00 80.09

13.25 11.56 11.61 18.88 11.67 17.00 18.99 23.13 20.89 28.61 29.34 32.95 32.00 32.48 26.62 36.02 35.69 37.20 42.62

25th Percentile Percentile Percentile for $80 for median Percentile for $20 $20 MM– MM MM $80 MM IPO 7.52 7.10 6.90 9.06 6.27 9.17 11.01 10.66 12.69 16.65 18.50 19.95 17.89 18.95 14.79 23.08 20.74 23.60 23.79

70.00% 72.80% 68.75% 51.86% 73.81% 55.83% 51.02% 45.81% 46.96% 35.45% 29.63% 25.18% 29.79% 26.95% 37.74% 19.72% 22.25% 19.50% 21.33%

96.00% 98.33% 95.00% 91.78% 98.10% 90.78% 87.76% 88.71% 87.83% 84.55% 88.89% 82.85% 82.12% 82.32% 88.71% 82.37% 82.43% 79.04% 74.83%

83.00% 85.36% 81.25% 71.82% 85.24% 73.30% 69.39% 66.77% 66.96% 60.00% 59.26% 54.01% 55.96% 54.32% 62.81% 51.04% 52.27% 49.27% 47.90%

inflation-adjusted statistics are presented concerning a specific year’s IPO proceeds (all figures are in 1997 dollars). First, the mean and standard deviation of the proceeds are given, followed by three percentile values: the 75th, median (50th), and the 25th percentile cutoffs (in millions of 1997 dollars). It is apparent from Table 3 that the average IPO proceeds in 1998 were significantly larger in 1998 compared to 1980, even after accounting for inflation. For example, the median inflation-adjusted size of an IPO more than tripled from $13.25 million in 1980 to $42.6 million in 1998. The mean issue has increased even more, by more than five-fold, from $20.62 million in 1980 to $109.64 million in 1998. These data show that it is impossible to give durable definitions to terms such as ‘‘small IPO’’ or ‘‘large IPO’’ based on inflation-adjusted proceed amounts. Consider, for example, Chen and Ritter’s (2000) use of the $20 million–$80 million proceed range to define ‘‘moderate size IPO.’’ Table 3 indicates that in 1980 a $20 million IPO would have been in the 70% percentile of all IPOs during that year. However, by 1998, a $20 million IPO would have exceeded only 21% of all IPOs in 1998. Similarly, IPOs at the


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upper bound ($80 million) of Chen and Ritter’s (2000) definition of ‘‘moderately sized’’ IPOs were not moderately sized at all relative to other deals in 1980. In fact, only 4% of the IPOs issued in 1980 had larger proceeds. In contrast, more than 25% of the total IPOs issued in 1998 would have exceeded $80 million. Further, the last column indicates that while 83% of all IPOs issued in 1980 belonged to the $20 million–$80 million range, only 47.9% of all IPOs issued in 1998 belonged to the same proceed range. Clearly, any analysis of ‘‘competitive’’ behavior that focused on this fixed proceed range for every year from 1980 to 1998 would in effect be comparing the larger IPOs (from the 70th–96th percentile proceed range) of 1980 with moderate-sized IPOs (in the 21st–75th percentile proceed range) of 1998. Inferences drawn from such an analysis could be biased if the size of an IPO is correlated with other characteristics that determine the spread.

3.2. Post-IPO Stock Volatility is Negatively Related to Issue Size and Has Increased Over Time Two interesting results emerge from our examination of the volatility of IPOs in the aftermarket.16 First, as shown in Table 4 Panel A, within a given year there is a inverse relationship between the IPO’s absolute size and the average aftermarket return volatility except for three of the 19 years in our sample.17 The average aftermarket return volatility for the smallest issues (less than $20 million) exceeded that of the largest issues for each year of the sample. Similarly, as shown in Table 4 Panel B, within a given year there is also an inverse relationship between the IPO’s relative size (or quartile ranking) and the average aftermarket return volatility except for one year (1983). In short, our analysis reveals that in a given year, the average aftermarket return volatility is typically smaller for IPOs that are larger in absolute as well as relative terms. Second, our analysis reveals that the average aftermarket return volatility for all IPO issues, regardless of size (absolute or relative), has trended upwards between 1980 and 1998. Table 4 Panels A and B also report the results of time-trend analyses. Adjusting for IPO proceeds’ absolute size, Table 4 Panel A indicates that IPOs’ average aftermarket return volatility has increased over the period. This upward trend over time is most noticeable for IPOs with absolute proceeds in the $20 million–$80 million range. The average after-market return volatility of IPOs with proceeds in this range increased from 3.07% in 1980 to 6.31% in 1998 – an increase of

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Table 4.

Average Volatility by Year as Function of Proceeds.

Panel A: Categorized by absolute size Year

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

Number of Offerings

103 244 83 515 214 209 444 313 118 113 111 277 389 478 366 434 686 480 289

Proceed Category o $20 MM

$20 MM–$80 MM

W $80 MM

All

3.78% 3.32% 3.40% 2.95% 2.73% 2.98% 3.69% 5.13% 3.18% 3.87% 4.45% 4.75% 4.75% 4.80% 4.30% 4.73% 5.27% 5.04% 5.93%

3.07% 2.96% 2.64% 2.82% 2.70% 2.56% 3.13% 4.34% 2.70% 3.28% 4.20% 4.10% 3.96% 3.72% 3.40% 4.29% 4.30% 4.25% 6.31%

2.64% 2.52% 3.37% 2.84% 1.90% 2.57% 2.57% 3.34% 2.04% 2.18% 2.46% 2.62% 2.69% 2.46% 2.32% 2.90% 2.93% 3.27% 4.79%

3.52% 3.21% 3.22% 2.89% 2.71% 2.67% 3.37% 4.58% 2.85% 3.31% 4.03% 3.99% 3.96% 3.77% 3.63% 4.13% 4.25% 4.21% 5.85%

Panel B: Categorized by relative size Year

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994

Number of Offerings

103 244 83 515 214 209 444 313 118 113 111 277 389 478 366

Proceed Quartile(s) Q1

Q2, Q3

Q4

All

4.27% 3.65% 3.87% 3.32% 2.84% 2.91% 3.85% 5.25% 3.41% 3.74% 4.23% 4.75% 4.84% 4.83% 4.40%

3.45% 3.12% 3.21% 2.66% 2.69% 3.03% 3.36% 4.78% 2.82% 3.61% 4.51% 4.18% 4.06% 3.83% 3.72%

2.91% 2.95% 2.71% 3.01% 2.65% 2.48% 2.87% 3.58% 2.36% 2.29% 3.04% 2.91% 2.96% 2.67% 2.71%

3.52% 3.21% 3.22% 2.89% 2.71% 2.67% 3.37% 4.58% 2.85% 3.31% 4.03% 3.99% 3.96% 3.77% 3.63%


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Table 4. (Continued ) Panel B: Categorized by relative size Year

Number of Offerings

1995 1996 1997 1998

434 686 480 289

Proceed Quartile(s) Q1

Q2, Q3

Q4

All

4.69% 5.23% 4.90% 6.20%

4.35% 4.38% 4.34% 6.23%

3.13% 3.10% 3.22% 4.72%

4.13% 4.25% 4.21% 5.85%

Panel C: Time-trend analyses (1980–1998 period) – correlation of time and volatility by relative proceed size quartiles Coefficient (t-Stat) Intercept Time R2 Adjusted R2 Observations

Q1

Q2, Q3

Q4

All

2.1698 (4.1893) 0.0011 (4.2718)

2.1957 (4.2435) 0.0011 (4.3171)

0.7595 (1.8602) 0.0004 (1.9327)

1.8591 (3.9457) 0.001 (4.024)

0.5177 0.4893 19

0.5230 0.4949 19

0.1801 0.1319 19

0.4878 0.4577 19

Note: The table above shows the results of a univariate regression where the dependant variable is average after market return volatiltity in a given year as reported in Table 4B and the independent variable is the given year. Indicates statistical significance at 95% confidence level.

105% in the average volatility. Similarly, adjusting for IPO proceeds’ relative size, Table 4 Panel B indicates that IPOs’ average aftermarket return volatility has increased significantly over the 1980–1998 period. This upward trend over time is most significant for IPOs with proceeds in the second and third quartiles in a given year. The average after-market return volatility of IPOs with proceeds in this range increased from 3.45% in 1980 to 6.23% in 1998 – an increase of 80.5% in the average volatility. Table 4 Panel C indicates the average after market volatility of all quartiles, except Q4, is positively correlated with time in a statistically significant manner at the 95% confidence level. In short, the results presented in this section indicate that any analysis of underwriting spreads should account for inter-temporal changes in the IPO market. Market conditions such as the demand for equity capital and the

12

MUKESH BAJAJ ET AL.

concomitant increase in issue size as well as higher equity volatility must be factored into any analysis of competitive pricing. We do so in the next section.

4. IPO UNDERWRITING SPREADS 4.1. Average Gross Underwriting Spreads Have Declined Keeping Issues’ Relative Size Constant Table 5, Panels A and B describe the gross spread distributions for the ‘‘relatively small,’’ and ‘‘relatively large’’ IPOs, respectively (defined as the bottom and top quartiles, respectively, of IPO proceeds for a given year). The gross spread has declined for relatively small and large IPOs between 1980 and 1998. For example, the average gross spread charged for relatively small IPOs (in the bottom quintile of IPO proceeds in a given year) declined from 9.61% in 1980 to 7.97% in 1998. The average spread for the largest IPOs declined from 6.97% to 5.87% over this period.18 The time-trend analysis reported in Panel C of Table 5 confirms the statistical significance of this downward trend in spreads. In particular it indicates that while the spreads declined in a statistically significant manner over time for both relatively small and relatively large IPOs (in the first and fourth quartiles, respectively) the downward trend is statistically more significant and larger in magnitude for relatively small IPOs compared to relatively large IPOs. Moreover, comparing the data reported in Table 5 Panel A to that of Table 5 Panel B for the same year, reveals that spreads are generally inversely related to the IPOs’ size. For instance, in 1980 the median gross spread for relatively small IPOs was 10%. In contrast, the median gross spread for relatively large IPOs was 7.14% in the same year – a difference of 2.857%. Such a difference persists across each year in our sample, albeit decreasing over time. In 1998, the median gross spread for relatively large IPOs was only 0.075% smaller than the median gross spread for relatively small IPOs. The trend lines fitted to the data for the 1980–1988 and the 1989–1998 periods shown in Fig. 1 Panels A and B confirm this negative relationship between IPO spreads and proceeds.

4.2. Spread Clustering Has Shifted to Lower Spreads Over Time Our analysis adjusts for the inter-temporal shift in magnitude of IPOs. The average IPO proceeds have increased significantly in the 1989–1998 period


Table 5.

13

Gross Spread by Year.

Year Number of Issues

Mean Gross Spread

Standard Maximum 75th Deviation Percentile

Median

25th Minimum Percentile

Panel A: Relatively 1980 25 1981 59 1982 19 1983 124 1984 53 1985 51 1986 110 1987 77 1988 28 1989 27 1990 27 1991 69 1992 97 1993 120 1994 89 1995 107 1996 170 1997 119 1998 71

small IPOs 9.61 9.54 9.04 9.16 8.88 8.72 8.39 8.56 8.42 8.11 8.01 7.55 7.84 7.83 8.37 7.98 7.90 7.74 7.97

(proceed quartile 1) 0.92 11.40 0.86 11.50 0.85 10.00 1.16 17.00 1.05 10.00 1.06 10.00 1.11 10.00 1.14 10.00 1.09 10.00 1.19 10.00 1.22 10.00 1.02 10.00 1.15 10.14 1.14 10.00 1.29 10.00 1.21 10.20 1.32 15.00 1.16 10.00 1.26 10.00

10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 9.76 9.31 9.00 7.50 8.50 8.50 10.00 9.00 8.50 8.00 9.25

10.00 10.00 9.00 9.05 9.00 8.57 8.00 8.00 8.00 7.50 7.50 7.00 7.14 7.07 8.00 7.50 7.00 7.00 7.00

9.00 9.00 8.44 8.00 8.00 8.00 7.50 7.56 7.61 7.00 7.00 7.00 7.00 7.00 7.00 7.00 7.00 7.00 7.00

8.00 7.00 7.50 6.66 7.00 7.00 6.00 6.73 7.00 6.75 6.00 6.00 6.57 6.00 6.18 6.36 6.50 5.18 6.99

Panel B: Relatively large IPOs 1980 25 6.97 1981 59 7.08 1982 20 6.95 1983 128 6.65 1984 52 6.98 1985 51 6.62 1986 111 6.55 1987 77 6.41 1988 29 6.40 1989 27 6.33 1990 27 6.45 1991 69 6.32 1992 97 6.31 1993 120 6.31 1994 91 6.37 1995 108 6.19 1996 170 6.25 1997 120 5.94 1998 71 5.87

(proceed quartile 4) 0.64 8.00 0.41 8.00 0.59 7.90 0.48 7.49 0.39 7.74 0.51 7.65 0.62 8.00 0.72 7.33 0.60 7.25 0.67 7.00 0.61 7.03 0.63 7.00 0.64 7.03 0.69 7.50 0.75 7.04 0.90 7.03 1.05 7.03 1.37 7.06 1.27 7.00

7.25 7.27 7.23 7.00 7.14 6.99 7.00 7.00 6.89 7.00 7.00 6.90 7.00 7.00 7.00 7.00 7.00 7.00 7.00

7.14 7.14 7.03 6.78 7.00 6.77 6.72 6.76 6.51 6.46 6.67 6.55 6.47 6.50 6.73 6.48 6.74 6.50 6.25

6.70 6.96 6.98 6.47 6.92 6.36 6.18 5.87 6.00 5.78 5.75 5.71 5.77 5.73 6.00 5.55 6.00 5.26 5.25

5.00 5.87 5.00 5.00 5.83 5.24 4.71 4.25 5.02 5.00 5.00 5.00 5.00 4.00 3.35 2.80 2.25 1.50 1.13

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MUKESH BAJAJ ET AL.

Table 5.

(Continued )

Panel C: Time-trend analyses (1980–1998 period) – correlation of time and median gross spread for relatively small (quartile 1) and relatively large (quartile 4) IPOs Coefficient (t-Stat)

Small (Q1)

Large (Q4)

Intercept

323.236 (8.629) 0.158 (8.415)

78.091 (6.283) 0.036 (5.745)

0.806 0.795 19

0.660 0.640 19

Year R2 Adjusted R2 Observations


compared to the 1980–1988 period. As Table 3 indicated, the mean (median) IPO (inflation-adjusted) proceeds have steadily increased from $20.62 million ($13.25 million) in 1980 to $109.64 million ($42.62 million) by 1998. Thus, before any observed spread clustering is considered indicative of collusion it is necessary to examine the manner in which such spread clusters may have moved over time. If underwriters were acting in a collusive manner then one would expect to see spreads being clustered at higher levels over time. In contrast, as Fig. 1 (Panels A and B), which plot the spread– proceed relationships for the two subperiods in our sample (1980–1988 and 1989–1998), indicate the level at which spreads appear to be clustered have declined over time, suggesting increasing competition among underwriters over time. In the 1980–1998 period, the predominant clusters appear to be at 10% and 8%. Clusters at 9, 8.5, 7.5, and 7% spread levels are also noticeable. Clusters at below-7% spreads are not apparent during this early period. In the later period (Fig. 1 Panel B), the two most prominent clusters are at 10% and 7%. The clustering at 7% has become more pronounced in the midrange of proceeds relative to the early period. This increased prominence does not result from a general dispersal of the cloud that obscured this cluster in the early period. Instead the increased prominence results primarily from a dispersal of the above-7% portion of that cloud. All of the above-7% clusters identified above from the early period are still visible in the late period. However, this late period shows evidence of below-7% clusters that were not apparent in the early period. There are clusters visible at 6.5, 6, 5.5, 5, and even 4.5%.


15

Panel A: Gross Spread vs. Proceeds (Issues from 1980 - 1988) 12.00

Gross Spread (%)

11.00 10.00 9.00

y = -0.9503Ln(x) + 10.349 R2 = 0.5631

8.00 7.00 6.00 5.00 4.00 0

10

20

30

40

50

60

70

80

90

100 110 120

Constant Dollar Proceeds ($MM) Panel B: Gross Spread vs. Proceeds (Issues from 1989 - 1998) 12.00

Gross Spread (%)

11.00 10.00 9.00

y = -0.7619Ln(x) + 9.747 R2 = 0.4505

8.00 7.00 6.00 5.00 4.00 0

20

40 60 80 Constant Dollar Proceeds ($MM)

100

120

Fig. 1. The Relationship between Gross Spread (%) and Constant Dollar Proceeds ($ millions) in IPOs Completed between (A) 1980 and 1988; and (B) 1989 and 1998.

4.3. Clustering Behavior Varies by Issues’ Relative Size We assigned gross spreads to one of three categories: less than 7%, exactly equal to 7%, or greater than 7%.19 We then examined the fraction of each year’s IPOs which had gross spreads smaller than 7%, equal to 7%, and greater than 7%, respectively, as a function of their relative-size classification.20

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MUKESH BAJAJ ET AL.

Initially, the majority of IPOs in each of the three relative-size groups had spreads greater than 7%. However, over time, the spreads for the majority of IPOs in each of the three relative-size groups declined as shown in Table 6. This spread migration first occurred for large IPOs, then for midsize IPOs, and most recently for small IPOs. The spread migration of the majority of small and midsize IPOs increased clustering in the exactly7%-spread category. The spreads of the majority of large IPOs dropped below 7%, so that their spreads are now predominantly less than 7%. A relatively small IPO (belonging to the first quartile) was unlikely to have a spread less than 7% even during the early years in our sample. There was not a single year between 1980 and 1998, when more than 5% of relatively small IPOs charged spreads below 7% (see Table 6). Between 1980 and 1990, it was much more likely for a relatively small IPO to have a spread greater than 7% than one exactly equal to 7%. Over 70% of small IPOs had gross spreads greater than 7% during this period. This fraction of above-7% spreads has declined since 1990. Even so, until 1995, with the exception of 1991, it was more likely for a relatively small IPO to have a spread above 7% than to have either a spread that was exactly equal to or less than 7%. For the last three years studied, however, it was actually more common for a small IPO to have a spread exactly equal to 7% than to have a spread above 7%. Even in these past three years, the fraction of small IPOs with spreads of exactly 7% has been no larger than 61%. Midsized IPOs (belonging to the second and third quartiles of IPOs in a given year) were more likely to having gross spreads below 7% compared to the relatively small IPOs. In general, by mid-1980s, more than 10% of midsized IPOs had spreads below 7% (see Table 6). However, in every year, a below-7% spread was the least likely possibility for a midsized IPO. Like the small IPOs, the majority of midsized IPOs were initially charged spreads greater than 7%. The fraction of midsized IPOs with spreads greater than 7% declined more quickly for midsized IPOs than for small IPOs. By 1987, and ever since, it has been more common for a midsize IPO to have an exactly-7% spread than have spreads either greater or less than 7%. This clustering of spreads for midsize IPOs has become almost complete. In 1980, 98% of midsized IPOs had spreads greater than 7%; in 1998, over 96% of midsize IPOs have spreads of exactly 7%. The majority of relatively large IPOs were also initially charged gross spreads greater than 7%. However, the popularity of above-7% spreads lasted a much shorter time for these largest IPOs. From 1983 to 1998, it was more common for a large IPO to have a spread less than 7% than a spread equal to or higher than 7%. The only exception to this trend occurred in

Year

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

The Frequency Distribution of IPOs Each Year with Gross Spreads of Less than, Equal to, or Greater than 7% (1980–1998).

Gross Spread Less than 7%

Gross Spread Equal to 7%

Gross Spread Greater than 7%

Small IPOs (%)

Mid-Sized IPOs (%)

Large IPOs (%)

Small IPOs (%)

Mid-Sized IPOs (%)

Large IPOs (%)

Small IPOs (%)

Mid-Sized IPOs (%)

Large IPOs (%)

0.00 0.00 0.00 1.61 0.00 0.00 0.91 3.90 0.00 3.70 3.70 1.45 2.06 4.17 1.12 0.93 2.94 0.84 0.00

2.00 4.13 2.44 17.37 0.95 10.58 17.27 15.38 10.34 3.57 5.56 5.88 5.73 3.40 2.73 3.70 3.80 5.88 3.47

32.00 23.73 20.00 65.63 28.85 68.63 68.47 64.94 75.86 66.67 70.37 76.81 70.10 68.33 58.24 66.67 60.00 64.17 69.01

0.00 3.39 0.00 1.61 7.55 7.84 10.91 5.19 7.14 22.22 25.93 63.77 46.39 46.67 31.46 46.73 50.59 60.50 53.52

0.00 2.48 7.32 26.64 20.00 22.12 29.09 44.87 67.24 85.71 87.04 89.71 88.54 92.77 92.90 95.83 94.44 93.28 96.53

8.00 20.34 35.00 24.22 44.23 25.49 21.62 29.87 20.69 33.33 29.63 23.19 29.90 30.83 41.76 33.33 40.00 35.00 30.99

100.00 96.61 100.00 96.77 92.45 92.16 88.18 90.91 92.86 74.07 70.37 34.78 51.55 49.17 67.42 52.34 46.47 38.66 46.48

98.00 93.39 90.24 55.98 79.05 67.31 53.64 39.74 22.41 10.71 7.41 4.41 5.73 3.83 4.37 0.46 1.75 0.84 0.00

60.00 55.93 45.00 10.16 26.92 5.88 9.91 5.19 3.45 0.00 0.00 0.00 0.00 0.83 0.00 0.00 0.00 0.83 0.00

17

‘‘Small’’, ‘‘Mid-Sized’’, and ‘‘Large’’ IPOs are defined to be all IPOs in the first, or the second and third, or fourth quartiles by constant dollar proceeds of all IPOs in the specified year, respectively. The percentage shown in each cell indicates the fraction of similar-sized IPOs in the specific year with gross spreads of less than, equal to or greater than 7%. Thus, adding the three percentages reported for all ‘‘small IPOs’’ across the same row (i.e., holding the IPO Year constant) adds up to 100%. Similarly, the three percentages reported for all mid-sized IPOs across the same row (i.e., holding the IPO Year constant) adds up to 100% and the three percentages reported for all large IPOs across the same row (i.e., holding the IPO Year constant) adds up to 100%.


Table 6.

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MUKESH BAJAJ ET AL.

1984, when clustering at 7% was the most common category. Despite the dominance of below-7% spreads through 1998, clustering at 7% has not completely disappeared. Since 1981 at least 20% of all large IPOs in the year had spreads of exactly 7%. In contrast, above-7% spreads have largely disappeared for large IPOs. Only two such deals appear in our sample between 1990 and 1998. This analysis reveals that relative size is a useful concept to help discuss the shifts in gross-spread categorization of IPOs. In particular, once we divided the IPOs into three relative size groups, it is apparent that their clustering behavior over time has been significantly different.

4.4. IPO Underwriting Spreads are Negatively Related to IPO Size In this subsection, we focus on the main claim made by Chen and Ritter (2000). These authors observe that by the mid-1990s, underwriting spread paid for all firm commitment IPOs in the US, regardless of offering size and choice of underwriter was almost exclusively clustered at exactly 7% for over 90% of ‘‘mid-size’’ issues. Such clustering of spreads is considered indicative of possible collusion among underwriters or consistent with a ‘‘strategic pricing equilibrium’’ (Chen & Ritter, 2000). Our analysis provides evidence to the contrary. Regressing the Underwriter’s Gross Spread (as a percentage) against the natural logarithm of the IPO’s ‘‘constant’’ (inflation adjusted) dollar proceed (IPO Size) reveals a statistically significant negative correlation between spreads and proceeds in both the subperiods in our sample [the earlier period (1980–1988) and the later period (1989–1998)]. This result suggests that, in general, over the entire range of observed IPO proceeds, percentage underwriting spreads do decline with IPO proceeds. This finding is consistent with the hypothesis that underwriters’ information production costs include a fixed cost, and there are economies of scale in such costs (i.e., the fixed component of information gathering cost declines as percentage of IPO proceeds as IPO proceeds increase) and percentage spreads decline concomitantly, as they are expected to in a competitive underwriting market. We also conducted a piecewise linear regression over each of the two subperiods, as described in Morck, Shleifer, and Vishny (1988), to further examine the impact of economies of scale on underwriting spreads. In order to motivate the empirical results of this regression let us consider a simple analytical model. Suppose underwriters’ total spreads are a (linear) function of total information production costs, which include a fixed and


19

a variable component. Let us denote such total costs, TC=a+bQ, where a, b, and Q denote the fixed cost, the per proceed dollar variable cost, and the total proceeds from an IPO, respectively. The average cost per IPO proceeds dollar can then be expressed as AC = a/Q+b. Differentiating AC with respect to Q, indicates the percentage spread is a decreasing function of Q,21 and twice differentiating AC with respect to Q indicates that the negative relationship between spread and proceeds decreases as Q, the proceeds (or IPO Size) increases.22 That is, economies of scale eventually become insignificant for the largest IPOs. In our piecewise linear regression, we regressed IPO Size against Gross Spread, controlling for the IPO’s relative (decile-based) size. Our piecewise linear regression may be expressed formally as: S ¼ a þ b 1 X 1 þ b 2 X 2 þ b 3 X 3 þ b 4 X 4 þ b5 X 5 þ b6 X 6 þ b7 X 7 þ b8 X 8 þ b9 X 9 þ b10 X 10 where S and X denote the Gross Spread and the IPO Size, respectively, and X1, y, X10 are transformations of the proceeds into 10 decile-based categories as defined below. ( X if X oD1 X1 ¼ D1 if X D1 8 if X oD1 > : D D if X D 2 1 2 8 0 if X oD 2 > < X 3 ¼ X D2 if D2 X D3 > : D D if X D 3 2 3 .. .

8 if X oD8 > : D D if X D 9 8 9 ( 0 if X oD9 X 10 ¼ X D9 if X D9 where the upper bound of the first through the ninth proceeds deciles are denoted by D1, y, D9.

20

MUKESH BAJAJ ET AL.

Our piecewise linear regression results shown in Table 7 are consistent with such a model in both subperiods. The estimated coefficients of the transformed IPO relative size variables X1, y, X10 are generally negative and statistically significant in both the 1980–1988 and the 1989–1998

Table 7. Piecewise Regression Results (Gross Spread against IPO Relative Size) and Decile Characteristics. Independent Variables

Panel A: ‘‘Early’’ Intercept X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 R2 Adjusted R2 Observations Panel B: ‘‘Later’’ Intercept X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 R2 Adjusted R2 Observations

Coefficient

t-Statistic

period (1980–1988) 10.801 56.576 0.351 7.881 0.147 2.936 0.269 5.518 0.160 5.205 0.068 2.473 0.016 0.701 0.036 2.175 0.003 0.264 0.013 2.500 0.007 3.142

Decile Charateristics Mean spread (%)

Mean proceeds ($MM)

Upper bound of proceeds decile ($MM)

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

9.43 8.81 8.42 7.80 7.47 7.32 7.17 7.04 6.93 6.61

3.90 6.27 8.29 10.97 14.36 18.12 23.12 30.23 43.53 77.72

5.25 7.27 9.33 12.59 16.14 20.42 26.42 35.07 53.67 119.04

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

9.05 7.40 7.09 7.01 7.02 6.96 6.97 6.93 6.87 6.56

6.74 13.20 18.42 23.39 28.55 33.55 39.74 48.61 63.25 93.25

9.75 16.07 20.77 25.68 31.05 36.27 43.87 54.57 74.53 120.00

0.6181 0.6162 2,112 Period (1989–1998) 11.345 114.19 0.349 (26.72) 0.137 (14.14) 0.005 (0.41) 0.013 (1.02) 0.004 0.38 0.012 (1.04) 0.000 (0.04) 0.000 0.07 0.010 (3.31) 0.010 (5.33) 0.6277 0.6265 3,217



21

subperiods. That is, the spread–proceeds relationship is negative (indicative of economies of scale) for IPOs that are of similar size (within the same decile). Importantly, our piecewise linear regression confirms that the negative relationship between spread and proceeds is larger and statistically more significant for relatively smaller IPOs compared to larger IPOs as the benefits of economies of scale decline after IPO size exceed a certain threshold. This analysis reveals why a comparison of the spread charged on a typical IPO in the early period, which was relatively small, to a typical IPO in the later period, which was relatively large, may be potentially misleading. In the former instance, the percentage spread charged would be largely based on the fixed component of the underwriter’s information gathering costs. Thus, small changes in proceeds would result in significant changes in such average information gathering costs and the resultant spread determined in a competitive equilibrium. Fig. 2, lines A and B plot the estimated piecewise linear regression coefficients against the ‘‘constant’’ (inflation adjusted) dollar IPO proceed for the early and later subperiods (1980–1988 and 1989–1998, respectively). Both lines have steep negative slopes initially (for smaller IPOs), indicating that the gross spread declines significantly as small IPOs get marginally

11.000

Predicted Gross Spread (%)

10.500 10.000 9.500 9.000 8.500 8.000

Line A: EarlyPeriod

7.500 7.000 6.500 6.000 0.00

Line B: Later Period

20.00

40.00

60.00

80.00

100.00

120.00

Constant Dollar Proceeds ($MM)

Fig. 2.

Predicted Values of Piecewise Regression (1980–1988 ‘‘Early’’ Period vs. 1989–1998 ‘‘Later’’ Period).

22

MUKESH BAJAJ ET AL.

larger. Line A continues to be negatively sloped across all IPOs made during the early period. Line B, which plots the spread–proceeds relationship for the later period, when IPOs were typically larger, flatten out after IPO proceeds reach a critical size. This result is consistent with he model described above because the percentage spread charged would be largely based on the variable component of the underwriter’s information gathering costs for larger IPOs. Hence, a marginal increase in IPO size (for large IPOs) would not result in significant changes in such average information gathering costs or in the resultant spread determined in a competitive equilibrium. Thus, Chen and Ritter’s (2000) analysis’ failure to identify a strong negative correlation between spreads charged and IPO proceeds is not surprising given their focus on IPOs in the mid-1990s, when IPOs were generally large.

5. CONCLUSIONS Integrity of the IPO market has recently been questioned in several respects, including whether the gross spread charged by underwriters for IPOs of common shares in the US is fixed at a non-competitive level. The possibility of anticompetitive price fixing was fueled by certain findings by Chen and Ritter (2000). First, these authors found that almost all recent US firm commitment IPOs between $20 million and $80 million in proceeds have been charged an underwriting spread of exactly 7%, while in the early 1980s only 25% of IPOs faced such clustering at exactly 7%. Second, they did not find expected negative relationship between issue size and spread. Our time series evidence reveals that the median size of an IPO has tripled in the last two decades and recent IPOs have involved considerably more risky firms. We also find that smaller IPOs tend to be riskier and underwriting spreads tend to be higher and more clustered for riskier IPOs. Therefore, given the changes in size and risk of IPOs over the last two decades, pooled data can mask evidence of competition in the market. We find that spreads were clustered even in earlier periods, and more significantly, such clustering was at levels greater than 7%. Over time, clustering at 7% has increased as clustering above 7% has declined. IPO spreads have declined significantly over time as the firms going public are now riskier, underwriting efforts have increased and IPOs are much larger today than in the past. Controlling for time trends, larger IPOs have lower average spreads. There is entry of new firms during the hot markets.


23

Overall, we conclude from the weight of evidence that the market for underwriting IPOs seems to be competitive.

NOTES 1. The spread is measured as a percentage of the offer price that is retained by the underwriter. A 5% spread implies that the underwriter retains 5% of the gross proceeds raised through an IPO. The underwriters’ spread typically consists of three components: a management fee that is generally split between the lead and co-lead underwriters; an underwriting fee that is split across all members of the underwriting syndicate; and a selling concession (Draho, 2004). 2. See Ljungqvist and Wilhelm (2003), and Draho (2004) for a discussion of these issues. 3. This is consistent with extant empirical research. Lee, Lochhead, Ritter, and Zhao (1996) found that (a) spreads were inversely related to offering size in a pooled cross-sectional and time series sample of IPOs and holding the offering size constant, average IPO spreads for IPOs were generally higher than spreads paid for offering safer securities [secondary equity offerings (SEOs) or straight debt]. In a similar vein, Bajaj, Mazumdar, and Sarin (2002) found that the spreads paid for preferred stock offerings were generally between the spreads paid for IPOs and straight debt offerings. Preferred stockholders’ claim on the firm’s cash flows is senior to that of common equity but subordinate to that of debt holders. Hence, the risk associated with preferred stock lies is bounded by the risk associated with common equity and straight debt. 4. See Draho (2004) and ‘‘IPO firms face probe of 7% fee – U.S. Antitrust group questions a standard.’’ The Wall Street Journal, May 3, 1999, p. C1. For references to various stories concerning the pricing fixing allegation and the DOJ enquiry see Hansen (2001). 5. According to Chen and Ritter (2000) 7% is above the spread level that would prevail in a competitive market because of two main reasons. One, the expected economies of scale in underwriting costs should lead to a negative relationship between the spread and firm size in this range, which they fail to find. Two, average underwriting spreads are higher in the US than in many foreign countries. Hansen (2001) argues that 7% is below the competitive price level, predicted from an empirical relationship between spread and their determinants for the non-7% IPOs. He also argues that foreign IPOs do not necessarily provide a good pricing benchmark for US IPOs. 6. They find that higher quality firms pick more reputable underwriters, as predicted by their double-sided matching characterization of non-pricing competition. 7. For references see Grossman, Miller, Cone, Fischel, and Ross (1997). 8. Grossman et al. (1997) construct a ‘‘competitive theory of clustering’’ and predict that clustering should be higher (i.e., the unit of trade would be coarser) when the value of assets is unknown and precise valuation is difficult or costly. Harris (1989) finds that stock market price clustering was greater following in the highvolatility aftermath of the 1987 crash than it was the previous week even though the overall price level was lower. Gwilym, Clare, and Thomas (1998) show that price

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clustering increased with derivatives’ volatility on the London International Financial Futures and Options Exchange (LIFFE). 9. Hansen (2001) for instance considers pooled time series cross-sectional data on IPOs from the 1980s and compares these data to similar pooled data from the 1990s. 10. The book manager works with the company to prepare the new issue and register it with the Securities Exchange Commission. The book manager also often organizes the syndicate to spread the issue’s risk across members (Source: NASD Regulations Glossary, www.nasdr.com). 11. This methodology was also used by Dunbar (2000). 12. For example, if there were only two lead managers in a given year, one with a 60% market share and the other with 40%, the HHI would be 5100 (which equals 602+402). The maximum value the HHI can attain would correspond to a monopolist, i.e., a single manager with 100% market share; this HHI would be 10000. 13. In strategic pricing, individual underwriters realize that if they undercut their competitors by charging a lower spread to obtain a deals today then competitors would respond in kind in the future thereby reducing the present value of profits. It is therefore in the self-interest of each investment banker to charge a spread greater than the competitive level at which, by definition, underwriters would earn no economic profits. The Chen and Ritter (2000) argument is based on Dutta and Madhavan’s (1997) model of a non-cooperative game used to explain high bid–ask spreads on Nasdaq stocks. 14. Another problem with using cost information according to Chen and Ritter (2000) is that costs may be endogenous. That is, higher spreads may induce underwriters to offer additional services to obtain business, thereby increasing costs. 15. Chen and Ritter (2000) argue that the relationship between gross spreads and underpricing is weak according to their unreported regressions. 16. We measure volatility by the standard deviation of the first 250 daily returns subsequent to the issuance of the IPO. This daily volatility is multiplied by the square root of 250 (the number of trading days in the year) to represent annualized volatility as a percentage. 17. In 1982, 1983, and 1987, the average volatility of issues in the $20 million–$80 million range were slightly lower than the average volatility of issues greater than $80 million range. 18. The data for the spread and issue size relationship for mid-sized IPOs (which belong to the second and third quartiles of IPOs each year sorted by issue proceeds) have not been reported in Table 4. However, this relationship too is qualitatively similar: the average spread of midsize IPOs declined 8.32% in 1980 to 6.96% in 1998. 19. We considered an IPO’s spread as being in the 7%-spread category if its underwriters’ discount was within a half penny on either side of the discount that would yield a spread of exactly 7%. This definition responds to (a) the existence of issue prices exactly 7% of which yields a fractional-penny discount, and (b) the common industry practice throughout this period of quoting integer-penny discounts. This differs from Chen and Ritter’s methodology: they would not, for example, consider a $0.94 or $0.95 discount on an issue price of $13.50 as a 7% spread, because an exact 7% discount would be the fractional-penny discount of $0.945.


25

20. ‘‘Small’’, ‘‘mid-sized’’, and ‘‘large’’ IPOs in a given year were defined as the IPOs that belonged to the first, second and third, or fourth proceeds quartiles, respectively. 21. This partial derivative of AC with respect to Q is @AC=@Q ¼ ða=Q2 Þ. 22. This second partial derivative equals 2ða=Q3 Þ.

ACKNOWLEDGMENTS The authors are grateful to seminar participants at the 2003 European Finance Association meetings and Qin Lei for their comments on an earlier draft and to Nikolai Caswell for his excellent research assistance.

REFERENCES Bajaj, M., Mazumdar, S., & Sarin, A. (2002). Cost of issuing preferred stock: An empirical analysis. Journal of Financial Research, XXV(4), 577–592. Barondes, R. R., Butler, A. W., & Sanger, G. C. (2000). IPO spreads: You get what you pay for. Unpublished manuscript. University of Missouri-Columbia, Rice University and Louisiana State University. Chen, H., & Ritter, J. R. (2000). The seven percent solution. Journal of Finance, 55, 1105–1131. Draho, J. (2004). The IPO decision: Why and how companies go public? Edward Elgar, Cheltenham, UK and Northampton, MA, USA. Dunbar, C. G. (2000). Factors affecting investment bank initial public offering market share. Journal of Financial Economics, 55, 3–41. Dutta, P., & Madhavan, A. (1997). Competition and collusion in dealer markets. Journal of Finance, 52, 245–276. Fernando, C. S., Gatchev, V. A., & Spindt, P. A. (2002). The long-term relationship between firms and underwriters: The seven percent solution revisited. Unpublished Manuscript. University of Michigan and Tulane University. Grossman, S. J., Miller, M. H., Cone, K. R., Fischel, D. R., & Ross, D. J. (1997). Clustering and competition in asset markets. The Journal of Law and Economics, 40(1), 23–60. Gwilym, O. A., Clare, A., & Thomas, S. (1998). Extreme price clustering in the London equity index futures and options market. Journal of Banking and Finance, 22, 1193–1206. Hansen, R. S. (2001). Do investment banks compete in IPOs? The advent of the ‘‘7% plus contract’’. Journal of Financial Economics, 59, 313–346. Harris, L. (1989). S&P 500 cash stock price volatilities. Journal of Finance, 44, 1155–1176. Lee, I., Lochhead, S., Ritter, J. R., & Zhao, Q. (1996). The costs of raising capital. Journal of Financial Research, XIX(1), 59–74. Lowry, M., & Schwert, G. W. (2002). IPO market cycles: Bubbles or sequential learning. Journal of Finance, 57, 1170–1200. Morck, R., Shleifer, A., & Vishny, R. W. (1988). Management ownership and market valuation: An empirical analysis. Journal of Financial Economics, 20, 293–315.

CAN DELEGATING BANK REGULATION TO MARKET FORCES REALLY WORK? C. W. Sealey ABSTRACT A major theme in the literature on bank regulation is that greater reliance on market forces can mitigate the moral hazard problem inherent in government sponsored deposit insurance. Specific proposals to impose greater market discipline on banks include minimum requirements on (1) uninsured subordinated debt financing (either fixed-term or with optiontype features), and (2) private coinsurance on deposits. Both proposals amount to delegating the responsibility for bank regulation to various private sector claimholders. The results suggest that such delegation (with or without claims that include option-type features) may be ineffective in lowering bank risk, at least within the present regulatory and institutional framework. Alternative mechanisms exist that can mitigate the moral hazard problem; however, it may be necessary for the regulator/deposit insurer to be an integral part of the solution.

The unprecedented deposit insurance losses in the United States during the 1980s and early 1990s were the result of numerous factors.1 Prominent among those factors were (1) an unwillingness by regulators to close

Research in Finance, Volume 24, 27–56 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00202-X

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troubled institutions in a prompt manner (capital forbearance),2 and (2) excessive risk-taking by banks resulting from moral hazard (risk shifting).3 A number of academics and regulators have argued that both of the above problems could be either eliminated or significantly mitigated through a combination of regulatory reforms and greater reliance on market discipline.4 In response, bank regulatory practices and procedures have undergone important changes, both legally and operationally. Specifically, to force regulators to close seriously troubled institutions, prompt corrective action is now required by law. Moreover, measures such as risk-adjusted deposit insurance have been implemented to increase market discipline. Additional proposals have been put forth to increase market discipline on bank risk-taking activities, most of which are intended to work in relation to regulatory reforms that prohibit or severely restrict the practice of forbearance. Two proposals that have figured prominently in the literature, but have yet to be implemented, would require banks to (1) increase their dependence on uninsured private sector debt financing, such as subordinated debentures (with or without option features); and (2) obtain coinsurance from the private sector on at least a portion of their insured deposits. In essence, the policy of relying on market discipline to constrain bank risk-taking amounts to delegating, at least partially, the responsibility for bank regulation to various uninsured private sector claimholders. Since a bank’s asset quality is private information, and claimholders do not have inherent knowledge of this quality, delegation can be successful only if private sector claimholders have proper incentives to produce information and exert discipline on banks. Moreover, even if proper incentives exist, claimholders may not possess the means to control the bank’s actions. Hence, control – legal or contractual – must be considered an integral part of any delegation mechanism. A number of conjectures have been put forth in the literature concerning the efficacy of market discipline as a tool to control bank risk-taking. For example, Baer (1990) notes that ‘‘Market participants do not necessarily have better information. However, they have better incentives to make use of the information they do have.’’ Also, according to Avery, Belton, and Goldberg (1988, p. 598), ‘‘y one might expect that the discipline exercised by holders of bank subordinated debt should be compatible to that of the Federal Deposit Insurance Corporation (FDIC) and consistent with the objectives of government regulation and prudential supervision.’’ In spite of these and other conjectures, there appear to be no specific models in the literature to show how, why, or under what conditions private sector

Can Delegating Bank Regulation to Market Forces Really Work?

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claimholders have incentives to product information and monitor banks in order to exert market discipline. Instead, as pointed out by Bliss and Flannery (2000, p. 1), belief in the efficacy of market discipline has become an ‘‘... article of faith among financial economist.’’ While there exist substantial empirical research into the disciplinary effects of uninsured debt financing on bank risk-taking, the results have been inconclusive at best.5 In fact, Bliss and Flannery, based on their recent empirical investigation into the issue, conclude that there is no strong evidence that private sector claimholders, especially bond holders, exert beneficial influences on the managerial actions of banks. They further conclude that ‘‘Market influence remains, for the moment, more a matter of faith than of empirical evidence.’’ The purpose of this chapter is to develop a specific model, under conditions of moral hazard, where the regulator and/or bank claimholders can exert market discipline on bank behavior by producing information and monitoring, but only by expending resources and thus incurring costs. The model is designed to investigate the relative incentives of different claimholders to produce costly information and exert market discipline on banks’ risk-taking decisions. The results of the model should help shed light on the feasibility of delegating the regulatory function to market forces. The results presented here can be classified into three general categories. First, as a benchmark, we assume that all claimholders, both private and government, have identical monitoring technology and enforcement powers. The results suggest that, given current institutional arrangements and regulatory practices, the quality of bank assets may not be improved by relying on market discipline imposed on banks by private sector claimholders, at least using the amounts of subordinated debt and private coinsurance advocated elsewhere.6 Specifically, the results suggest that the various private sector claimholders of a bank choose optimal levels of information production and monitoring based on their potential losses in the event of insolvency. If the regulator has the greatest potential losses, then private sector claimholders have less incentive to monitor than the regulator, or vice versa.7 Second, even if private sector claimholders lack the legal authority of a government regulator, the addition of various option features to the subordinated debt of banks has been suggested in the literature as a means of giving such claimholders recourse against risk shifting. Thus, private sector claimholders may be induced to produce information and/or take actions that are allowable under the contractual provisions of their claims. The results suggest, however, that the addition of option features to bank

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debt does not necessarily improve asset quality. Puttable subordinated debt may result in suboptimal risk choices by the bank when compared to straight debt. Convertible subordinated debt does better, but does not achieve a first-best allocation. Third, we show that alternative mechanisms exist involving option-type claims that may solve the moral hazard problem and achieve the first-best outcome. The important aspect of these mechanisms, however, is that they may depend on the involvement of the regulator and thus are not examples of market discipline per se. For example, we show that a security, which we call deposit linked options (DLO), could be designed by the regulator to be superior to subordinated fixed claims held by the private sector, irrespective of any option features that these private sector claims may involve. DLO give the regulator an option to receive bank equity (or an equivalent value in cash) on a pre-specified portion of the bank’s total return. By optimally designing the features of this instrument, we show that the moral hazard problem can be solved, and the first-best outcome can be achieved. Such a solution also increases overall social welfare because it does not involve monitoring the quality of the bank, which represents a dead-weight cost in equilibrium.8 The remainder of the chapter is organized as follows: the first section proposes a simple model of delegated monitoring where various private sector claimholders can produce information and directly monitor the bank. Section 2 presents, as a benchmark for purposes of comparison, the firstbest asset quality chosen by a hypothetical social planner and the secondbest quality chosen by a bank that maximizes shareholder wealth. Section 3 examines the incentives of claimholders to expend resources on information production and monitoring, derives the optimal monitoring level for each class of claimholder, and compares these optimal monitoring levels. Section 4 considers monitoring using subordinated debt embedded with options-type features. Section 5 shows that alternative mechanisms exist that the regulator could use to mitigate the moral hazard problem. Section 6 concludes the chapter.

1. THE MODEL 1.1. The Setup for the Bank In this section, we develop a simple model of bank regulation under moral hazard that may involve direct monitoring of the bank by any one of its


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different classes of claimholders. At t=0, the bank contributes its own equity capital E, takes in deposits worth D, and issues subordinated debt with a face value B, where deposit claims are strictly senior to subordinated debt claims. For simplicity, we assume that the bank invests its total funds in a single risky asset, A, and chooses the quality of this asset, q 2 ð0; 1Þ. The bank’s managers are assumed to make decisions in the interest of shareholders. The regulator insures a portion, aR, of the bank’s deposits, where 0oaR 1, and may mandate a minimum requirement on regulatory capital, which is computed as the sum of equity and subordinated debt.9 The remaining fraction of deposits, aC ð1 aR Þ, is insured by a private insurance firm (henceforth, referred to as the coinsurer). Let pR and pC denote the insurance premiums, per dollar of deposits, charged by the regulator and the coinsurer, respectively. These insurance premiums may or may not be equal, and the regulator may or may not charge a risk-adjusted premium. The return on the bank’s asset (principle plus interest) is realized at t ¼ 1, and depends, in the first instance, on the quality of the asset, q, chosen ex ante by bank management. The asset may have a successful outcome with probability q, or an unsuccessful outcome with probability (1q). If the outcome is successful, referred to here as State 1, the bank’s return is RðqÞ þ e~ , where e~ is asset-specific noise that is unique to the bank and Eð~eÞ ¼ 0. In State 1, the asset’s return is sufficiently high to more than payoff both depositors and subordinated debtholders, i.e., RðqÞ þ e~4D þ B. Finally, let the expected return in State 1, where the expectation is taken with respect to e~, be denoted simply as R(q). Let R2 denote the return on the bank’s asset if the outcome is unsuccessful. This unsuccessful outcome is hereafter referred to as State 2. In this state, R2 may or may not be sufficient to cover all of the bank’s fixed claims, but in any event leaves shareholders with nothing, i.e., D þ B R2 and either D 0 or D 0. In State 2, we assume that the bank is declared insolvent by the regulator, its asset is liquidated, and its return is shared pro rata among the insuring agents (regulator and coinsurer). If any excess funds are available after depositors are paid in full, the excess is used to pay subordinated debt holders. Specifically, if R2 D, the regulator receives an aR fraction of the liquidation value and the coinsurer receives an aC fraction. The regulator and coinsurer then pay depositors in full, incurring losses. If R2 4D, the regulator and coinsurer incur no losses and any residual is paid to subordinated debtholders.10

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The return function, R(q), is assumed to be such that R0 ðqÞo0, while qR(q) is increasing and concave in q, assuring the existence of a socially optimal (first-best) level of quality, qFB, for the bank’s asset. From the distribution of returns described above, it follows that a higher quality level, i.e., a higher q, increases the likelihood of the good state, State 1, while at the same time decreasing the magnitude of returns in that state. Thus, a bank interested in shifting risk will choose a lower quality asset than it would do otherwise but achieves a higher payoff if success occurs. For expositional ease, the bank is assumed to capture all the surplus from the loan returns.11 All parties are assumed to be risk neutral, and the risk-free rate of return is zero. Finally, the basic postulate of common knowledge is adopted meaning that all participants in the model understand the structure of the decision problem that they face. This understanding includes the objectives and rationality of participants, the range of possible payoffs for all actions that participants can take, a participant’s knowledge that other participants have this knowledge, and so on.12 The bank’s choice of q is private information, and cannot be observed, even ex post. The presence of the borrower-specific noise, e~, ensures that q cannot be inferred from the ex post realization of returns. This gives rise to a moral hazard problem in that the bank may have an incentive to choose a level of asset quality that may be suboptimal from a social or regulatory point of view. In the process, the bank may take advantage of the holders of its fixed claims as well as the deposit insurer. Nevertheless, the bank’s choice of quality may be monitored and controlled, as described below.

1.2. The Monitoring Technology The delegation of the bank monitoring function to the private sector can take one of two forms. First, the regulator can contract with, and compensate, a private sector agent to perform the information production and monitoring function.13 Second, the regulator can set requirements on banks to maintain a minimum level of regulatory capital composed of certain private sector claims and then rely on the holders of those claims to produce information and monitor in a manner that is hopefully consistent with its own goals. In the latter case, the incentive to produce information and monitor is determined by the contractual provisions of the claims, in conjunction with whatever regulatory framework exists. It is the second case that is modeled in this chapter, since it is most consistent with proposals for greater reliance on market discipline.


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We model monitoring within two separate frameworks, referred to here as direct and indirect monitoring. For either type of monitoring to be worthwhile, the monitor must have the ability to undertake actions, based on the information gathered, in order to mitigate the bank’s incentive to take risk. Otherwise, even if the monitor can observe the bank’s risk perfectly, the bank can (and will) simply ignore the dictates of the monitor if the latter has no recourse. Recourse is provided by the contractual provisions of the bank’s private sector claims that specify the actions available to the monitor if the bank is discovered to be shifting risk. Under direct monitoring, the claims issued by the bank are assumed to be straight vanilla claims (either fixed-term uninsured debt or coinsurance), but include covenants that give the holder enforcement options that are equivalent to those of the regulator, thus putting private sector claimholders and the regulator on an equal footing. These options could take several forms, but in essence involve the power to issue cease and desist orders to banks. Under indirect monitoring, private sector claims are assumed to lack such direct regulatory powers, but the claims may be fashioned to have option-type features of a financial nature that can be exercised on the basis of information produced, or other signals received, by the claimholders. These provisions then act as the means of recourse for the monitor. For both direct and indirect monitoring, information is gathered about the riskiness of the bank’s portfolio through the use of a technology that is assumed to be available to all the claimholders of the bank. Moreover, the technology is assumed to be employed by classes of claimholders as a whole rather than by individuals. The issue of small groups of claimholders acting alone is abstracted from here by assuming that the various classes of claims are held by small groups of agents capable of acting in unison. If the class of claims has a diverse ownership, the issue of delegated monitoring may become one more step removed, as in Diamond (1984), where a class of claimholders may find it necessary to delegate monitoring to still another party.14 The monitoring technology is assumed to be stochastic, but simple. Let mi denote the level of information production and monitoring by the ith monitor, and let d denote the probability that this monitoring will reveal the bank’s true quality up to a minimum quality level, q, where q ¼ f ðmi Þ, f 0 ðmi Þ40, and f 00 ðmi Þo0. The parameter d is a measure of the noise in the monitoring technology, where a higher d corresponds to less noise. One interpretation of this monitoring process, the interpretation which we adopt here, is that, with probability d, an examination or audit of the bank identifies loan portfolios of quality less than the minimum level, q, which is determined by the monitoring level mi. A higher level of q is achieved with a

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higher level of mi, i.e., greater resources are committed to the monitoring process. With probability (1d), the monitor observes nothing and the bank is free to make asset substitutions in order to shift risk. Since the monitoring of bank compliance requires resources, the monitoring process is costly. Let C(mi) be the cost of monitoring, which is assumed to have the following properties: C(0)=0, C(1)-N, C 0 ðmi Þ40, and C 00 ðmi Þ40. In words, greater levels of monitoring requires greater commitment of resources on the part of the monitor, and the efficiency of the monitoring process declines on the margin.

2. THE BANK’S QUALITY DECISION WITH NO MONITORING First, we examine the benchmark case when the bank is not monitored at all. With no monitoring, the bank chooses the ex ante quality level, q, to maximize the expected payoff to equity holders, where the expected net payoff is given by pE ðqÞ ¼ ½RðqÞ D Bq DðaR pR þ aC pC Þ E The first-order condition,15 which yields the second-best quality level, qSB, is SB @½q RðqSB Þ ðD þ BÞ ¼ 0 (1) @qSB By contrast, a social planner would maximize expected social surplus,16 which is assumed to be given by pP ðqÞ ¼ ½qRðqÞ þ ð1 qÞR2 A The first-best (socially optimal) solution implies, @½qFB RðqFB Þ R2 ¼ 0 @qFB

(2)

Since ðD þ BÞ R2 by earlier assumptions about returns, it follows from Eqs. (1) and (2) that the second-best solution in the case of no monitoring under moral hazard, qSB , is such that qSB qFB . Thus, as expected, the bank has an incentive to choose a lower level of loan quality than is socially optimal, as long as R2 is sufficiently low so that equity holders can benefit from risk shifting to other claimholders. This suboptimal behavior is caused by the bank’s incentive to shift risk to the holders of fixed claims against the bank, e.g., the deposit insurer and the holders of subordinated debt.


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3. THE BANK’S QUALITY DECISION WITH DIRECT MONITORING As discussed above, the monitor’s success in controlling bank risk depends on (1) the amount of (costly) resources invested in information production and monitoring, and (2) the recourse available to the monitor in the event the bank is caught engaging in risk-shifting behavior. In this section, we deal with the case of direct monitoring where the bank’s financial claims are of the straight vanilla type, but the monitor possesses recourse equivalent to regulatory powers. In order to keep the comparisons valid, it is assumed that each class of claimholder, including the regulator, has access to the same monitoring technology, as well as the same regulatory powers.17 Formally, under the direct monitoring case, for a given level of monitoring, mi, the bank’s feasible set of quality choices becomes ½q; 1Þ ð0; 1Þ. This implies that monitoring sets a lower bound of q for the bank’s choice of quality, with higher monitoring levels leading to higher quality choices by the bank. If the bank attempts to choose a quality level below q, then the monitor can resort to ‘‘cease-and-desist’’ orders or take other actions to force the bank to choose better quality. Furthermore, consistent with discussions elsewhere concerning the inability of pricing, per se, to solve the moral hazard problem,18 we abstract from much of the pricing issues here in order to focus on the incentives of different claimholders to monitor the bank. This assumption is easily justifiable since pricing and monitoring are interdependent (substitute) decisions for claimholders; thus, given any pricing regime, the claimholder can choose a monitoring level to optimize. As noted above, when claimholder i chooses a monitoring level, mi, with probability d the monitor is able to observe the bank’s choice of quality and control the minimum quality level, q. Hence, the bank’s optimal choice of ex ante quality is given by q ðmi Þ 2 arg max pE ðqÞ ¼ d½ðRðqÞ D BÞq DðaR pR þ aC pC Þ q2½q;1Þ

þ ð1 dÞ½ðRðqSB Þ D BÞqSB SB DðaR pSB R þ aC pC Þ E

ð3Þ

It follows that q ðmi Þ ¼ q ¼ f ðmi Þ when the bank is monitored, where mi is such that f 1 ðqSB Þomi of 1 ðqFB Þ.19 On the other hand, with probability ð1 dÞ the monitor will learn nothing about loan quality, and hence the bank will choose the second-best quality, qSB. In the analysis that follows,

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q ðmi Þ represents the reaction function of the bank in response to a level of monitoring, mi, carried out by claimholder i. 3.1. Socially Optimal Monitoring Before proceeding to the monitoring incentives of the various claimholders, it is illustrative to first consider the socially optimal monitoring level. The social planner will choose mP to maximize the expected social surplus, pP ðmP Þ ¼ d½q ðmP ÞRðq ðmP ÞÞ þ ð1 q ðmP ÞÞR2 þ ð1 dÞ½qSB RðqSB Þ þ ð1 qSB ÞR2 A CðmP Þ The first-order condition gives @q ðmP Þ @½q ðmP ÞRðq ðmP ÞÞ d R2 C 0 ðmP Þ ¼ 0 @mP @q ðmP Þ

ð4Þ

(5)

The information production level, mP, that solves (5), is the socially optimal level of information production given the objective function in (4).20 3.2. The Regulator’s Problem For a given deposit insurance premium, pR ,21 the regulator chooses its optimal level of monitoring, mR, in order to maximize, subject to a breakeven constraint, its expected payoff is given by22 pR ðmR Þ ¼ d½aR pR D aR ½D R2 ð1 q ðmR ÞÞ 1fR2 oDg þ ð1 dÞ½aR pR D aR ½D R2 ð1 qSB Þ 1fR2 oDg CðmR Þ where

ð6Þ

1fR2 oDg

1 if R2 oD 0 elsewhere:

Since the regulator’s objective is to minimize cost, it is not the same as that of the social planner. The first-order condition for optimal, cost minimizing information production, and monitoring for the regulator is @q ðmR Þ daR (7) ½ðD R2 Þ 1fR2 oDg C 0 ðmR Þ ¼ 0 @mR


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3.3. The Subordinated Debtholder’s Problem Subordinated debtholders choose their level of monitoring, mB, to maximize their expected payoff, is given by pB ðmB Þ ¼ d½Bq ðmB Þ þ ðR2 DÞð1 q ðmB ÞÞ 1fR2 Dg þ ð1 dÞ½BqSB þ ðR2 DÞð1 qSB ðmB ÞÞ 1fR2 Dg B CðmB Þ where

1fR2 Dg

1 if R2 D 0 elsewhere:

The first-order condition is @q ðmB Þ d ½B ðR2 DÞ 1fR2 Dg C 0 ðmB Þ ¼ 0 @mB

(8)

3.4. The Private Coinsurer’s Problem The private coinsurer chooses its level of monitoring, mC, in order to maximize its expected payoff, which is given by pC ðmC Þ ¼ d½aC pC D aC ðD R2 Þð1 q ðmC ÞÞ 1fR2 oDg þ ð1 dÞ½aC pC D aC ðD R2 Þð1 qSB Þ 1fR2 oDg CðmC Þ where 1fR2 oDg is defined above. The first-order condition for optimal information production is @q ðmC Þ daC (9) ½ðD R2 Þ 1fR2 oDg C 0 ðmC Þ ¼ 0 @mC

3.5. A Comparison of Optimal Monitoring Levels We are now in a position to compare the optimal monitoring levels of the regulator with those of the subordinated debtholder, the private coinsurer, and the social planner. Proposition 1. In general, the optimal monitoring levels of various claimholders do not coincide, either with that of the social planner, the

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regulator, or with each other. The optimal monitoring levels, fmR ; mB ; mC g, are such that the following relationships hold: 1. mR mB ; iff 2. mR mB ; iff and 3. mR mC ; iff 4. mR mC ; iff

aR ½ðD R2 Þ 1fR2 oDg ½B ðR2 DÞ 1fR2 Dg , aR ½ðD R2 Þ 1fR2 oDg ½B ðR2 DÞ 1fR2 Dg , aR aC , aR aC .

Proof. The proof follows from a comparison of the first-order conditions (7), (8), and (9). 3.5.1. Discussion of Comparisons First, note that specific comparisons of the monitoring level of the social planner with that of the regulator, subordinated debtholder, and private coinsurer are, in general, not possible (except in the special case where the monitoring level is zero) since the latter three have fixed, debt-like claims against the bank’s assets, whereas the social planner maximizes total social surplus. Depending on the values of the various parameters in the model, the regulator or private sector claimholders may optimally monitor either more or less than the social planner. In general, conditions (1) and (2) in Proposition 1 suggest that the incentive for a claimholder to monitor is dependent on the expected losses of the claimholder conditional on the event that the bank becomes insolvent. If these conditional losses are equal in size, then the optimal level of monitoring by the various claimholders will also be the same. If not, then their optimal monitoring levels depend on the relative sizes of their claims when failure occurs. Specifically, in parts (1) and (2) of the Proposition, the term aR ½ðD R2 Þ 1fR2 oDg is the loss incurred by the regulator if the bank fails. This value may vary anywhere from zero to the total value of insured deposits, D, depending on the liquidation value of the bank’s assets and the value of aR. The term ½B ðR2 DÞ 1fR2 Dg is the loss to subordinated debtholders if failure occurs, which may vary from zero to the total value of subordinated debt, B. Note that when 1fR2 oDg ¼ 1, then 1fR2 Dg ¼ 0, and vice versa. The sizes of these two claims determines the relative incentive to monitor. For part (3) and (4) of the Proposition, since the regulator and the coinsurer have identical losses except for the fraction of deposits insured, their incentives depend on the sizes of their respective fractions.


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A number of factors influence the conditional expected losses to claimholders. Considering the regulator first, the regulator has a greater incentive to produce information and monitor the greater the proportion of deposits insured by the regulator, aR and the lower the residual value of the bank in liquidation, R2.23 For subordinated debtholders, the incentive to produce information and monitor increases as the amount subordinated debt outstanding for the bank increases, and decreases as the expected recovery in liquidation increases. Two additional points are of interest concerning the above results. First, since with rational expectations each class of claimholder is aware of the incentives of the others, the claimholder with the greatest potential loss in the bank’s insolvency will engage in all monitoring activities. The remaining claimholder groups will rationally refrain from information production and monitoring since such an activity would be a needless and costly duplication of the efforts by another stakeholder. In other words, the claimholder with the greatest stake in the bank’s solvency will monitor the bank and other claimholders will act as free riders. Second, the above results are based on the assumption that the regulator acts to minimize losses. As pointed out earlier, the regulator may have an objective function that also includes certain social welfare concerns, such as financial stability. Although, the FDIC Improvement Act of 1991 makes cost minimization an important consideration of the FDIC, cost minimization may be ignored, for example, if the failure of a given bank has the potential for a systemic impact on financial system stability. If such social benefits, which are positive externalities, are included in the regulator’s objective function, the regulator should have an even greater incentive to produce information and monitor. If this is the case, other things equal, the relative incentives for subordinated debtholders and private sector coinsurers would decrease.

4. THE BANK’S QUALITY DECISION IN THE ABSENCE OF DIRECT MONITORING The previous section considers direct monitoring as a means of alleviating the moral hazard problem inherent in bank regulation.24 Under the direct monitoring scenario, private sector claimholders have the power to enforce, based on their investment in monitoring, minimum quality levels on the bank. It may be questionable, however, whether lawmakers and/or regulators would be willing to delegate sufficient regulatory powers to

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private sector claimholders to allow them to directly enforce quality and thus function effectively as direct monitors. Without some means of recourse in response to bank decision-making, there is little incentive for private sector claimholders to perform the delegated monitoring function in the absence of direct payments as compensation. In this section, we examine redesigned private sector claims that incorporate option-type features, and claimholders have recourse only by exercising the contractual options associated with their claims.25 In the first case, puttable subordinated debt, involves indirect monitoring and is perhaps more consistent with the spirit of market discipline as discussed in the literature, since it allows private sector claimholders to use their information to act unilaterally – while remaining, of course, within the legal and contractual framework of their claims. In the second case, convertible subordinated debt, private sector claimholders have no monitoring role since their option is exercisable, ex post, on observable returns.

4.1. Indirect Monitoring and Puttable Subordinated Debt When subordinated debt contains option-type features, the holders of these claims may have an incentive to produce information, and undertake unilateral actions (exercise their option) based on what they find. Under this scenario, monitoring is indirect since debtholders have no direct enforcement powers. Thus, debtholders lack the authority to force the bank to make a particular quality choice; however, they may produce information and undertake unilateral actions such as exercising their option which may be costly to the bank. One variant of such an instrument is subordinated debt with an imbedded put option feature.26 The holders of puttable subordinated debt could exercise their option to put the debt back to the bank for immediate repayment at par if they have reason to believe the bank is shifting risk. To model the case of puttable subordinated debt, we assume for simplicity that the regulator insures all deposits (i.e., aR ¼ 1Þ and charges an insurance premium of pR per dollar of insured deposits, which is paid in advance. Whether the premium is risk adjusted or not is immaterial to the results. The setup of the monitoring technology is similar to that used in the previous section. The holders of subordinated debt can expend resources on information production and monitoring. The level of information production by subordinated debtholders is denoted, as before, by mB. With


41

probability d, the information produced reveals the bank’s true quality up to a minimum quality level, q, where q ¼ f ðmB Þ, and information production is subject to the same cost conditions outlined earlier. With probability ð1 dÞ, the information produced reveals nothing about bank quality, giving debtholders no justification to put their debt and leaving the bank free to engage in risk-shifting behavior. At t ¼ 0, the bank obtains financing consisting of equity, deposits, and puttable subordinated debt, and chooses an asset with a quality level q*. Simultaneously, subordinated debtholders choose an optimal monitoring level, mB, which may reveal the bank’s true quality up to a minimum level of q ¼ f ðmB Þ. If monitoring reveals that the bank’s true quality, q*, is less than q, then the holders of subordinated debt exercise their option and put the debt back to the bank for full payment at par before the t ¼ 1 cashflows are realized.27 If, on the other hand, q q, then the debtholders do nothing.28 Finally, if monitoring reveals no information, subordinated debtholders have no basis to put back the debt and thus do nothing. Therefore, subordinated debtholders can put back the debt if and only if their monitoring reveals that the bank has chosen a level of quality less than q. In the event the debt is put back to the bank, the capital requirement by the regulator implies that the bank must raise the amount B in alternative financing from capital markets before the final cashflows are realized. This could be achieved through an equity offering or, alternatively, by issuing low-quality junior (i.e., junk) debt. For simplicity, assume that the bank issues junior debt, and incurs an additional cost of r per dollar.29 Like subordinated debt, the junior bonds would be repaid in full only in State 1. Moreover, for simplicity, we also assume that in State 2, R2 oD, i.e., if the bank fails, uninsured debtholders receive nothing. As noted above, we assume that the regulator uses a fixed pricing policy for deposit insurance. 4.1.1. The Bank’s Problem The bank chooses its optimal ex ante level of quality, q*, to maximize its expected payoff, which is given by pE ðq jmB Þ ¼ d½ðRðq Þ D BÞq 1fq qg þ d½ðRðq Þ D Bð1 þ rÞÞq 1fq o qg þ ð1 dÞ½ðRðqSB Þ D BÞqSB pR D E

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where 1

fq qg

1 if q q 0 elsewhere

; and 1

fq o qg

1 if q o q 0 elsewhere:

The first-order condition for the bank is @½q Rðq Þ ðD þ BÞ Br 1fq o qg ¼ 0 @q

(10)

4.1.2. The Subordinated Debtholder’s Problem The holders of puttable subordinated debt choose their monitoring level, mB, so as to maximize their expected payoff, which is pB ðmB jqÞ ¼ d½B 1fqo qg þ Bq 1fqqg þ ð1 dÞBqSB B CðmB Þ Their first-order condition is, @q dB 1fqqg C 0 ðmB Þ ¼ 0 @mB

(11)

4.1.3. Comparing Optimal Monitoring Levels The issue is whether subordinated debt with an imbedded put option can induce the bank to choose higher quality ex ante if information production and monitoring reveal that the bank is shifting risk. A comparison of the first-order conditions above lead to the following result: Proposition 2. Puttable subordinated debt does not improve the bank’s choice of quality compared with the direct monitoring case. In fact, the bank’s optimal quality choice, when subordinated debt is puttable and monitoring is indirect, is inferior to the quality decision when straight subordinated debt is used with direct monitoring. To verify this statement, note that the Nash equilibrium to this game is a pair, fq ; mB g, that solves equations (10) and (11). Examining (10) first, note that the bank’s quality decision does not improve as debtholders increase their monitoring activities. Moreover, if r40, then the bank’s equilibrium quality choice, q*, is actually lower than the second-best quality chosen under the no monitoring case. To see this, compare the first-order conditions in (1) and (10). Furthermore, from (11), it is evident that the


43

equilibrium level of monitoring by subordinated debtholders is zero. Thus, in equilibrium puttable subordinated debt becomes equivalent to high-yield financing and is priced according to second-best quality. The reason that puttable subordinated debt does not lead to better risktaking by the bank is because it does not involve sufficient penalties to the bank for bad behavior and monitoring is costly to debtholders. Simply allowing debtholders to put the debt back to the bank on the basis of a noisy signal of poor quality is not sufficient. First, since the monitoring is noisy, the bank can choose poor quality and may not be caught. Second, even if caught and subordinated debtholders choose to put back their debt, the bank may be able to switch over to an alternative source of funds, e.g., highyield financing.30 Although more expensive, such financing is a fixed-debt claim, payable in full only in the good state, and, in any event, priced to reflect the bank’s true risk in the first place.31 Third, even if the bank is caught and looses the benefit of shifting risk to debtholders, the bank may still be able to shift risk to the deposit insurer, and since the deposit insurer is likely to be a much bigger stakeholder in the bank, shifting risk to the deposit insurer is much more attractive financially.32 Proposals put forth in the literature on puttable subordinated debt as a means of imposing market discipline on banks rely on debtholders to monitor a bank’s risk and signal the regulator about poor quality by putting the debt back to the bank. Presumably, the regulator would then step in and take actions to restrain risk. The results in Eq. (11) suggest, however, that the prospect of regulatory intervention provides no additional incentives for the holders of puttable subordinated debt to produce information and monitor. Thus, the results in Proposition 2 continue to hold: debtholders have no incentive to produce information and monitor, and cannot provide an informed signal about bank quality by putting their debt. Under these circumstances, if the regulator is to take an informed action, it must assume the role of information producer and monitor and puttable debt is redundant.

4.2. Convertible Subordinated Debt: A Case of No Monitoring In this section, we analyze another variant of the subordinated debt contract (i.e., convertibility) that is designed to change the bank’s risk-taking behavior without resorting to costly monitoring methods. Green (1984) has shown, in the context of corporate finance, that warrants and convertible debt can alleviate the shifting of risk from stockholders to bondholders. This notion has since been applied to banking regulation by John, John, and

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Senbet (1991), who argue that taxing a bank’s profits in the good states may induce the bank to choose better risks ex ante, a result that is isomorphic to a convertible-type claim. In the case of subordinated debt, an interesting question is whether making the bank’s subordinated debt convertible to equity can similarly solve the risk-shifting problem. To examine this issue, let the subordinated debtholders have the option to convert their debt, B, into a g fraction of the equity of the bank. The subordinated debtholders do not need to engage in any costly monitoring of the bank’s ex ante choice of quality since the option to convert is based on observable bank returns. Conversion occurs at the option of subordinated debtholders, and they choose to convert their debt if and only if g½RðqÞ D B. Therefore, conversion takes place only in State 1. The ex ante expected payoff to the subordinated debtholders is pB ¼ q maxfg½RðqÞ D; Bg B The payoff to the bank’s shareholders in State 1 is Minfð1 gÞ½RðqÞ D; RðqÞ D Bg Shareholder’s expected payoff is pE ¼ q minfð1 gÞ½RðqÞ D; RðqÞ D Bg pR D E ¼ qð1 gÞ½RðqÞ D 1fCg þ q½1 1fCg ½RðqÞ D B DpR E where

1fCg

1 if g½RðqÞ D4B 0 elsewhere:

The bank’s optimal quality solution is given by the first-order condition, @½qRðqÞ @½qRðqÞ ðD þ BÞ þ B g D 1fCg ¼ 0 @q @q The following result can be derived from the above: Proposition 3. The optimal convertible subordinated debt contract involves a conversion factor g such that g

B Rðq Þ

D

; where q is s:t:

Furthermore, qFB 4q 4qSB .

@½q Rðq Þ D ¼ 0. @q


45

That is, while an optimally designed convertible debt contract may induce a better quality choice than straight subordinated debt with no monitoring, it still does not achieve first-best. The reason is that risk shifting to the deposit insurer remains a problem. Unless the size of the convertible subordinated debt is large relative to deposit claims, such debt cannot be viewed as a substitute for monitoring by the regulator/deposit insurer. In fact, as long as the size of the subordinated debt, convertible or not, is small, it is problematic whether market discipline will result in an appreciable improvement in the quality of banks’ portfolios.

5. AN ALTERNATIVE MECHANISM: SOLVING THE MORAL HAZARD PROBLEM In previous sections, we show that reliance on market discipline imposed by private sector claimholders may not solve, or even mitigate, the bank’s moral hazard problem arising from deposit insurance. In this section, we present an example of an alternative contracting mechanism, which we call deposit linked options (DLO), that can solve the moral hazard problem, provided the instrument is optimally designed.33 For the sake of simplicity, we modify the earlier model as follows: First, to keep the comparisons valid, the regulator sets the same equity capital requirement, E, as before. Second, we assume that there is no coinsurer and all deposits are insured by the regulator. Third, the regulator does not require the bank to sell subordinated debt; thus, the bank must take in more deposits than previously to compensate for the absence of such debt financing. Finally, the bank’s State 2 return is assumed to be insufficient to fully repay depositors, i.e., R2 oD. Deposits can be repaid fully by the bank only in State 1; however, depositors, being fully insured, always receive the full value of their deposits irrespective of the bank’s return. As payment for deposit insurance, the regulator may charge the bank a deposit insurance premium, pR, per dollar of deposits, which may or may not be actuarially fair. In addition, the bank is required to issue a (call) option, exercisable at the discretion of the regulator, that gives the regulator the right to a share of the banks ex post equity value (in the form of a cash payment) if the options are in-the-money. Let CDLO denote the expected option payoff34 to the regulator at t ¼ 1, which can be written as C DLO ¼ maxfl½RðqÞ ð1 ZÞD ZD; 0g

(12)

where 0oZ 1 and 0 l 1 are constants that are set by the regulator.35 In effect, the regulator receives an option with an exercise price that is a

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portion, Z, of the banks deposits and an expected payoff that is a function of q, l, Z, and D. The DLO contract has two distinguishing features. First, its exercise price and payoff are related to deposits. Under present, and even proposed, institutional and regulatory arrangements, deposits are, and will likely remain, the only sufficiently large source of funding for the bank on which to base such a contract. The DLO contract is likely to necessitate the involvement of the regulator/deposit insurer, and thus cannot be viewed as an example of market discipline per se. Second, as shown below, there are optimal values for Z and l that make information production unnecessary in order to mitigate the moral hazard problem and achieve a first-best solution. Given the above features, the regulator optimally exercises the DLO if and only if l½RðqÞ ð1 ZÞD ZD 0. Define 1 if l½RðqÞ ð1 ZÞD ZD 0 1fDLOg 0 otherwise: The ex ante expected payoff to the regulator is pR ¼ q maxfl½RðqÞ ð1 ZÞD ZD; 0g þ ð1 qÞðR2 DÞ þ pR D The expected payoff to the bank’s stockholders can be written as pE ¼ q½RðqÞ D C DLO pR D E

(13)

Substituting (12) into (13) and simplifying yields the expected payoff to bank equity holders, which is pE ¼ qð1 lÞ½RðqÞ ð1 ZÞD 1fDLOg þ q½1 1fDLOg ½RðqÞ D pR D E The solution that maximizes shareholder value is given by the first-order condition, @½qRðqÞ @½qRðqÞ D l ð1 ZÞD ZD 1fDLOg ¼ 0 @q @q which leads to the following result: Proposition 4. The optimal, DLO contract consists of the regulator setting values for l* and Z* as following: 1. l ZD=Rðq Þ ð1 ZÞD , and 2. Z ¼ ½D R2 =D .


47

The values l* and Z* in turn induce the bank to choose an optimal quality level, q*, such that @½q Rðq Þ=@q ð1 ZÞD ¼ 0. Furthermore, the bank’s optimal quality, q , achieves the first-best level of quality, i.e., q* ¼ qFB. To understand why DLO may be successful at alleviating the moral hazard problem, it is useful to recall why uninsured subordinated claims may not work. The regulator pays private sector claimholders nothing for their efforts, while perhaps at the same time having a considerably greater stake in the bank’s success. In other words, reliance on market discipline, if successful, in effect makes the regulator a free rider. If the chief beneficiary of private sector monitoring is the regulator, private sector claimholders may be unwilling to invest resources in information production and monitoring because their claims are too small to make such an expenditure worthwhile. Thus, the usual free rider outcome results in under investment on the part of claimholders with less at stake. In the case of puttable subordinated debt, the problem is somewhat different. If the bank is monitored and detected to be risk shifting, the likely penalty is that the bank must go to the bond market and pay a price for debt that merely reflects the risk that the bank was taking in the first place. And, because of noise in the monitoring process, there is a positive probability that the bank will be able to shift risk and not be detected. Moreover, the benefits from shifting risk to the deposit insurer can be high, since the insurer may have a large stake in the bank’s failure. Finally, with convertible subordinated debt, the problem is alleviated to some extent, but not completely. The reason is that, if subordinated debt is a relatively small source of funding for the bank, the conversion feature of the debt is not likely to provide a sufficient penalty to the bank to offset the benefits of shifting risk to the deposit insurer. Now, consider DLO. Of the debt instruments discussed in previous sections, DLO are most similar to convertible subordinated debt. The DLO contract works better than convertible debt, however, because it is linked to deposits, which are a larger source of the bank’s financing.36 For the DLO contract, the greater the amount the regulator has at stake in the bank (as measured by its expected loss if the bank becomes insolvent), the greater is the value of the regulator’s option in the event of risk shifting. If the DLO is in-the-money, it is sufficiently costly to the bank that risk shifting does not pay. Thus, risk shifting is no longer value enhancing to shareholders and the bank chooses the first-best quality level.37 Moreover, an examination of Eq. (12) reveals another important feature of the DLO contract; namely, if the contract is designed optimally, as shown in Proposition 4, then, in equilibrium where the bank chooses first-best

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quality, the DLO is not expected to be exercised since it is expected to be exactly at-the-money at t ¼ 1.38 It is also important to note that DLO are not likely to result from a market solution to the risk-shifting problem, and thus is not likely to be an example of market discipline. A bank would not voluntarily issue such options since it is much more lucrative to shift risk to the deposit insurer. Unless the DLO were to be a precondition for deposit insurance or otherwise part of a regulatory requirement, they would likely not be created. Finally, it is interesting that the DLO contract is, in principle, similar to an ex post deposit insurance pricing scheme.39 For example, for an optimally designed DLO contract, the regulator could set the ex ante deposit insurance premium such that the premium plus the value of the option would allow the regulator to break even, thus being equivalent to riskadjusted deposit insurance. Even though our DLO mechanism is in the spirit of proposals by other researchers that advocate ex post deposit insurance premiums, an advantage of the model is that we formalize how ex post premiums might be set in order to mitigate the moral hazard problem and achieve a first-best solution to risk-taking behavior on the part of banks.40 At the same time, however, the DLO mechanism could be subject to the same criticisms as other proposals that seek to base deposit insurance premiums on ex post performance. In other words, since the ex post premiums, i.e., payments by banks to the regulator when the options are exercised, would be proportional to ex post performance above a certain level, they could be viewed as a penalty for good performance and superior management rather than part of an actuarially fair, ex ante contract. On the other hand, since in equilibrium DLO are not expected to be exercised, they might avoid some of this criticism. Because of asset-specific risk, however, there is always a positive probability that the DLO will be in-themoney and exercised by the regulator. Thus, the scheme probably cannot avoid all criticism of this kind.

6. CONCLUSIONS A number of policy proposals have been put forth in recent years with the purpose of enhancing market discipline on bank decision-making. The underlying presumption is that traditional government regulators are either unable or unwilling to provide effective regulatory control over bank risk. Market discipline has been promoted as an effective substitute to traditional regulation based on the conjecture that it will induce banks to choose higher


49

quality. What is often overlooked is that reliance on market discipline is not costless. Private sector claimholders must expend resources on information production and monitoring, whereas the chief beneficiary of these efforts may be the regulator/deposit insurer. In this chapter, we develop a model of market discipline where the regulator could implicitly delegate the responsibility for bank regulation to various private sector claimholders, such as subordinated debtholders and coinsurers. The model is designed to investigate the relative incentives that may exist for the regulator and the private sector claimholders to produce information and monitor. The main result of the model is as follows: If the banking system remains in its present form with high leverage, substantial insured deposit financing, and significant losses to the deposit insurer in the event of insolvency, then the successful delegation of the regulatory function to private sector claimholders via market discipline may not be feasible. This result holds for both the direct and indirect monitoring cases. The principal reason is that the regulator remains the most vulnerable in the event of insolvency, and if the regulator acts to protect its own financial interest – which it must do, at least to some degree, by law – then in equilibrium other claimholders, knowing the regulators position, simply become free riders on the efforts of the regulator. Nevertheless, direct delegated monitoring may be successful if private sector claimholders and the regulator at least have roughly the same expected losses in the event of insolvency. In the case of private sector coinsurance, achieving roughly the same potential losses in the event of insolvency may not be desirable, since having such a large fraction of deposits insured by the private sector could lead to financial catastrophe in the event of a systemic problem. In the case of subordinated debt, a large requirement on such financing might fundamentally alter the product mix of the banking industry and perhaps hamper the efficiency, liquidity, and cost of the payments mechanism. The results do show, however, that there are, at least in principle, alternative mechanisms that have the potential to solve the moral hazard problem. A feature of such mechanisms is that they may not involve market discipline, per se, since they require the regulator to be closely involved. The reason is that only the regulator (deposit insurer) may have a sufficiently large stake in the bank to have the incentive to solve the moral hazard problem. One example of an alternative mechanism is DLO, where the regulator has an option to share in the banks end-of-period equity value. This type of contract can be optimally designed to penalize banks if they choose to shift risk. An additional feature of this claim is that information production is not necessary to solve the moral hazard problem. But, it is

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isomorphic to ex post deposit insurance pricing and, as such, is subject to similar criticisms. An important caveat when interpreting the results is that we compare the incentives of various private sector claimholders with a regulator who acts to minimize costs. In principle, current legislation is aimed at encouraging the deposit insurer to act in such a manner. In reality, however, the regulator may lack incentives to monitor and/or sanction banks that make poor quality decisions, or the regulator may have an altogether different objective function based on self-interest. Hence, the ability of private sector claimholders to free ride on the efforts of the regulator may be hampered if the regulator’s efforts are not effective in the first place. In this case, the overall benefit of reliance on market discipline may be greater than the model suggests, but would still be characterized by under investment in information production and monitoring by the private sector. What the results do suggest, however, is that it is perhaps better to formulate policies that induce the regulator to act in the desired way rather than attempting to pass the buck for bank regulation to claimholders that have much less at stake.

ACKNOWLEDGMENTS The author is grateful to S. Nagarajan for helpful comments on earlier versions of the chapter. All remaining errors are of course the author’s sole responsibility.

NOTES 1. A comprehensive discussion of these problems can be found in Benston, Eisenbeis, Horvitz, Kane, and Kaufman (1986), among others. 2. The regulator may have its own self-interested goals that conflict with its regulatory mission. For example, see Kane (1987, 1989) and Boot and Thakor (1993) on this issue. 3. Models that deal specifically with moral hazard and/or adverse selection are John et al. (1991), Chan, Greenbaum, and Thakor (1992), Campbell, Chan, and Marino (1992), Giammarino, Lewis, and Sappington (1993), and Nagarajan and Sealey (1995, 1998). 4. For discussions of the rationale for greater market discipline, see, Benston et al. (1986), Wall (1989), Evanoff (1991), and Congressional Budget Office (1992).


51

5. See, for example, Baer and Brewer (1986), Avery et al. (1988), Hannan and Hanweck (1988), James (1988, 1990), Gilbert (1990), Gorton and Santomero (1990), Ellis and Flannery (1992), and Bliss and Flannery (2000). 6. For example, Evanoff (1991) advocates a subordinated debt requirement of four percent of bank assets, Benston et al. (1986) mention an amount equal to three to five percent of deposits, and an FDIC proposal suggests approximately three percent of assets. Furthermore, the FDIC Improvement Act of 1991 authorizes regulatory authorities to seek private sector coinsurance on up to ten percent of insured deposits. 7. We assume the regulator (deposit insurer) produces information and monitors banks with the goal of minimizing costs. This assumption is common in the literature and is consistent with the FDIC’s legislative mandate of minimizing losses to the deposit insurance fund. Thus, the regulator is distinguished from a social planner in that the latter is concerned with the socially optimal allocation. More is said concerning this issue, and its possible effects on the results, later in the chapter. 8. DLO contracts do require monitoring the cashflows of a bank, but this is a far less demanding task than monitoring the quality of the loan portfolio. Existing criminal penalties against fraud provide strong (although not perfect) incentives for banks to report financial statements truthfully. 9. It is well-known that the regulator can solve most of a bank’s incentive problems by mandating a very high capital requirement (Campbell et al., 1992). Such a requirement, however, would result in a fundamental change in the services provided by banks, and as Campbell, Chan, and Marino point out, such a change may not be desirable because of the social value of the liquidity services provided by banks. Since our aim is to focus on the delegated monitoring of banks, we do not address the regulator’s optimal capital requirement for banks, which has been addressed elsewhere in the literature (e.g., Nagarajan and Sealey, 1995, 1998). 10. Experience from in the 1980s suggests that prompt action to close failing institutions can result in significantly lower losses, while delayed closure can increase losses. Thus, R2 may be a function of the regulator’s closure policy. Treatment of the optimal closure policy is beyond the scope of the present chapter; thus, for simplicity, closure policy is taken as given. 11. The results continue to hold as along as the bank captures a positive share of the profits (see Chan et al., 1992). 12. Since banks specialize in making loans that are not informationally transparent, the postulate of common knowledge may seem somewhat strong in the case of the payoff function on bank assets, R(q). In our model, asset quality, as measured by q, is the only parameter of the return function that is unobservable by participants other than the bank. Nevertheless, since asset quality is at the heart of the moral hazard problem, we believe our model incorporates the major element of the opaque nature of bank assets. 13. The case where an agent is explicitly compensated for monitoring the bank is modeled by Campbell et al. (1992). 14. One interpretation of an entire class of claimholders monitoring the bank is that these claims (e.g. subordinated debt) are closely held, and hence there are no free-rider problems within the same class of claimholders. In general, if the claims are widely held, then free-riding within a class of claims becomes a problem, and it may

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become necessary for the claimholders themselves to delegate the monitoring function. In Diamond (1984), e.g., lenders (depositors) delegate the task of monitoring borrowers to banks. 15. Throughout the chapter, the focus is on the first-order conditions. It is easy to verify that the second-order conditions are satisfied, given our assumptions about the bank’s returns. 16. Here, we assume that the social planner considers social surplus to be composed only of the expected monetary returns to all bank claimholders. In the case of banks, one might argue that society in general benefits from high-quality bank portfolios through the positive externalities of financial system stability. Although difficult to quantify, if such externalities were included, the social surplus generated by high quality would increase and the first-best quality chosen by the social planner would be higher than the level implied by the first-order condition in Eq. (2). 17. Note that the assumption that other claimholders of a bank have the same regulatory powers as, say, the FDIC, is in reality very strong. This assumption is relaxed in later sections. 18. See, for example, Nagarajan and Sealey (1998) for a formal discussion of this issue. 19. Note that the cases f 1 ðqSB Þ4mi and f 1 ðqFB Þomi do not arise: The former achieves nothing, whereas the latter is suboptimal for the monitor, given that monitoring is costly. 20. As noted earlier, social surplus, as defined here, excludes any externalities that might accrue from financial system stability, etc. If these added benefits were included in the social planner’s objective function, then the socially optimal level of information production and monitoring would be greater than that implied by Eq. (5). 21. The deposit insurance premium set by the regulator is taken as fixed, since we wish to focus on the incentives to monitor. If the regulator can charge a large enough premium to break-even irrespective of quality, then monitoring becomes irrelevant if the regulator’s only concern is to minimize losses. 22. Analogous to the social planner, the regulator may have an objective function that is broader than strict cost minimization, such as the social welfare benefits from financial stability, etc. Most often in the literature, however, the regulator/deposit insurer is modeled with the objective of cost minimization. See, e.g., Acharya and Dreyfus (1988), Nagarajan and Sealey (1996, 1998), among others. If positive externalities were included in the regulator’s objective function, then the benefits of information production and monitoring for the regulator would be greater than that implied by Eq. (6), and the regulator would optimally monitor more than the level implied by Eq. (7). As Saunders (2000, p. 414) points out, however, ‘‘y the FDIC Improvement Act generally confirms cost minimization as an important objective defining FDIC’s policies.’’ 23. Book values play an important role in the closure decisions of regulators. If book value significantly overstates market value, the FDIC may experience large losses in the event of failure. This problem is compounded by the practicality that audits can occur only discretely. Thus, book values may appear to ‘‘jump’’ significantly downward at the time of failure when in actuality this is only an acknowledgment of a more continuous process that has been underway for some


53

time. See Cooperstein, Pennacchi, and Redburn (1995) for empirical evidence that book values overstate market values as banks approach failure, at least for the 1980s and early 1990s. 24. Direct monitoring may be feasible if the bank’s private sector claims are privately held by a small group of investors, as in the case of privately placed subordinated debt or a single insurer or single consortium of insurers. Direct monitoring is less feasible, however, when the bank’s claims are diffused and widely held, as in the case of publicly placed debt. 25. What we refer to as indirect monitoring is similar in spirit to a number of policy proposals to use subordinated debt as a source of market discipline on banks. See, for example, Wall (1989) and Evanoff (1991). We do not attempt, however, to model their specific proposals. 26. Wall (1989) appears to be the first to discuss puttable subordinated debt as a means of imposing market discipline on banks. In his framework, the regulator retains primary responsibility for preventing banks from investing in overly risky portfolios. The role of subordinated debtholders is, at least in part, to signal the regulator about the market’s assessment of bank risk if they put their debt back to the bank. We model the case of puttable subordinated debt somewhat differently. In our model, market discipline is imposed on banks by the threat that subordinated debtholders will exercise their put option if banks are caught shifting risk. Thus, our model does not directly correspond to Wall’s setup, although, as discussed at the end of this section, our results may have implications for the viability of puttable subordinated debt as a vehicle for informing the regulator of bank risk. 27. If the subordinated debtholders demand compensation for the monitoring costs they incur, then the bank may have to offer a premium. This possibility does not change the results presented here. 28. As before, it should be clear that the bank will not choose a quality level greater than q, unless q oqSB , and no monitor will choose a monitoring level where q oqSB . Thus, the bank’s choice of quality, q , is such that qSB q q. 29. In our risk-neutral world with a discount rate of zero, in equilibrium the bank expects puttable subordinated debt to be priced to yield an expected return of zero based on an equilibrium monitoring level, mB , and corresponding quality level q ¼ ðmB Þ. If information production reveals that quality is less than q, then the bank is attempting to shift risk and debtholders put the debt back to the bank. When the bank resorts to the high yield market, the ‘‘junk’’ bondholders price their issues based on second-best quality. Although their expected return will be zero as well, equity holders must pay higher borrowing costs relative to subordinated debt financing (plus any additional flotation costs). Note that if r ¼ 1, the bank is credit-rationed, and may not be able to raise additional funds. 30. To avoid this problem, the regulator may require that the bank attempt to raise new equity instead of issuing high-yield (junk) bonds. However, due to the well-known debt-overhang problem (Myers, 1977), investors will not subscribe to such an equity issue, as the first cashflows are sure to be paid out to the fixed claimholder, i.e., the deposit insurer. Puttable subordinated debt does no better if the bank faces credit rationing and is unable to raise additional funds. In this case, the bank could be closed and assets sold, but such a strategy is unlikely to generate

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sufficient funds to pay the subordinated debt holders after depositors and the deposit insurer have been paid. 31. If subordinated debt is put back to the bank by its holders, rational expectations implies that market participants then know that the bank has chosen secondbest quality. Suppliers of new debt would charge a rate commensurate with that level of risk. If, for whatever reason, the bank cannot obtain financing at any rate, then the bank would face a situation of credit rationing and could be forced to liquidate. 32. There is at least one scenario where the bank could shift risk to the deposit insurer and subordinated debtholders would have no incentive to put their debt. Suppose the bank has the ability to manipulate returns in such a way as to produce a mean preserving spread in the return distribution. If R2 D, this change in spread would leave subordinated debtholders equally well off, and would shift risk to the deposit insurer. We are grateful to an anonymous referee for pointing out this possibility. 33. The solution discussed in this section is in the spirit of John et al. (1991) and Green (1984). 34. The expected payoff on the option refers to the expectation taken over the random variable e~, where Eð~eÞ ¼ 0. 35. As will be evident later in this section, Z ¼ 0 and l ¼ 0 are not possible optimal solutions for the model. In the former case, deposit insurance is redundant, and in the latter the DLO is always worthless. 36. Moreover, compared to deposits, subordinated debt is likely to continue to be a small portion of bank financing under any reasonable proposal concerning requirements on subordinated debt. 37. As noted earlier, if the social planner’s objective function includes externalities such as financial stability, the first-best asset quality would be higher than that given in Eq. (2). In such a case, the DLO contract would not yield first best but would still yield better quality than puttable or convertible subordinated debt. 38. Because of asset-specific risk, e~, the DLO could be in the money in spite of the bank choosing first-best quality. 39. The authors are grateful to an anonymous referee for pointing out that partially convertible deposits are in the same class of contracts as ex post deposit insurance premiums. The imposition of ex post premiums are suggested by Benston et al. (1986) and Kane (1987), among others, as a means of mitigating the moral hazard problem associated with deposit insurance. 40. Nagarajan and Sealey (1998) also develop a formal model of ex post deposit insurance premiums. Their framework, however, is somewhat different from that presented here and involves ex post premiums that are based on the performance of the bank relative to the market.

REFERENCES Acharya, S., & Dreyfus, J. F. (1988). Optimal bank reorganization policies and the pricing of federal deposit insurance. Journal of Finance, 44, 1313–1334.


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Avery, R. B., Belton, T. M., & Goldberg, M. A. (1988). Market discipline in regulating bank risk: New evidence from the capital markets. Journal of Money, Credit and Banking, 20, 597–610. Baer, H. (1990). What we know about the deposit insurance problem. Chicago Fed Letter (July). Baer, H., & Brewer, E. (1986). ‘‘Uninsured deposits as a source of market discipline: Some new evidence,’’ Economic Perspectives. Federal Reserve Bank of Chicago (September/ October), 23–31. Benston, G. J., Eisenbeis, R., Horvitz, P., Kane, E., & Kaufman, G. (1986). Perspectives on safe and sound banking: Past, present, and future. Cambridge: MIT Press. Bliss, R. R., & Flannery, M. J. (2000). Market discipline in the governance of U.S. bank holding companies. Proceedings of the annual conference on bank structure and competition, Federal Reserve Bank of Chicago, Chicago, IL. Boot, A., & Thakor, A. (1993). Self-interested bank regulation. American Economic Review, 83, 206–212. Campbell, T., Chan, Y.-S., & Marino, A. (1992). An incentive based theory of bank regulation. Journal of Financial Intermediation, 2, 255–276. Chan, Y., Greenbaum, S. I., & Thakor, A. (1992). Is fairly priced deposit insurance possible? Journal of Finance, 47, 227–245. Congressional Budget Office. (1992). Reforming federal deposit insurance. Congress of the United States (September). Cooperstein, R. L., Pennacchi, G. G., & Redburn, F. S. (1995). The aggregate cost of deposit insurance: A multiperiod analysis. Journal of Financial Intermediation, 4, 242–271. Diamond, D. (1984). Financial intermediation and delegated monitoring. Review of Economic Studies, 51, 393–414. Ellis, D. M., & Flannery, M. J. (1992). Risk premia in large CD rates: Time series evidence on market discipline. Journal of Monetary Economics, 27, 481–502. Evanoff, D. D. (1991). Subordinated debt: The overlooked solution for banking. Chicago Fed Letter (May). Giammarino, R., Lewis, T., & Sappington, D. (1993). An incentive approach to bank regulation. Journal of Finance, 48, 1523–1542. Gilbert, R. A. (1990). Market discipline of bank risk: Theory and evidence. Federal Reserve Bank of St. Louis, Review, 72(January/February), 3–18. Gorton, G., & Santomero, A. (1990). Market discipline and bank subordinated debt. Journal of Money, Credit and Banking, 22, 119–128. Green, R. (1984). Investment incentives, debt and warrants. Journal of Financial Economics, 13, 115–136. Hannan, T. H., & Hanweck, G. A. (1988). Bank insolvency risk and the market for large certificates of deposit. Journal of Money, Credit and Banking, 20, 203–211. James, C. M. (1988). The use of loan sales and standby letters of credit by commercial banks. Journal of Monetary Economics, 22, 325–346. James, C. M. (1990). Heterogeneous creditors and the market value of bank LDC loan portfolios. Journal of Monetary Economics, 25, 611–627. John, K., John, T. A., & Senbet, L. (1991). Risk-shifting incentives of depository institutions: A new perspective on federal deposit insurance reform. Journal of Banking and Finance, 15, 895–915. Kane, E. J. (1987). No room for weak links in the chain of deposit-insurance reform. Journal of Financial Services Research, 1, 77–111.

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Kane, E. J. (1989). Changing incentives facing financial-services regulators. Journal of Financial Services Research, 3, 265–274. Myers, S. (1977). Determinants of corporate borrowing. Journal of Financial Economics, 3, 147–175. Nagarajan, S., & Sealey, C. W. (1995). Forbearance, deposit insurance pricing, and incentive compatible bank regulation. Journal of Banking and Finance, 19, 1109–1130. Nagarajan, S., & Sealey, C. W. (1998). State-contingent bank regulation and the fair pricing of deposit insurance. Journal of Banking and Finance, 22, 1139–1156. Saunders, A. (2000). Financial institutions management: A modern perspective (3rd ed.). Irwin: McGraw-Hill. Wall, L. D. (1989). A plan for reducing future deposit insurance losses: Puttable subordinated debt. Economic Review, 74(July/August), 2–17.

INTERNAL MODEL-BASED CAPITAL STANDARD AND THE COST OF DEPOSIT INSURANCE Jin-Ping Lee ABSTRACT The new Basel Accord (known as Basel II) attempts to introduce more risk-sensitive capital requirements. We propose a multiperiod deposit insurance pricing model that incorporates specific regulatory capital requirements and the possibility of capital forbearance and moral hazard. We estimate the cost of deposit insurance under alternative regulation regimes based on the building block approach of the 1988 Basel Accord (known as Basel I) and internal model-based (IMB) capital regulation. In contrast to the building block of Basel I, Basel II’s IMB capital regulation links more closely the capital requirement to a bank’s actual risk. We develop a multiperiod pricing model while incorporating the effects of capital forbearance and moral hazard. The fairly-priced premium rates are computed by assuming that a bank’s asset value follows a GARCH process. In contrast to previous studies based on the building block capital standard, we find that forbearance and the potential moral hazard behavior will not increase the cost of deposit insurance in the scheme of Basel II’s IMB capital regulation.


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1. INTRODUCTION The objectives of the Basel Capital Accord, adopted in 1988 by the Basel Committee on Banking Supervision, are to promote soundness and stability in the international banking system. The accord sets forth a framework for measuring capital adequacy and a minimum standard to be achieved by banks in the adopting countries. The Basel Accord requires a bank to have available as ‘‘regulatory capital’’ at least 8% of the value of it risk-weighted assets and assets equivalent to off-balance-sheet exposures. The bank capital ratio and whether that ratio meets the 8% minimum have become important indicators for an institution’s financial strength. The 1988 Basel Capital Accord, now familiarly known as Basel I, was a major step forward in capital regulation. However, it is too simple to address the activities of complex banking organizations. The limited differentiation among degrees of risks has created incentives for banks to gain the system through regulatory capital arbitrage. A bank engaging in capital arbitrage may, as a result, hold too little capital for the assets it retains, even though it meets the capital requirement of the Basel rule. Extensive literature, for example Kim and Santomero (1988), Gennotte and Pyle (1991), Rochet (1992), and Blum (1999), has argued that uniform capital requirements can induce banks to increase risk-taking which results in higher probability of default. Regulators have recognized such a problem and there have been important steps taken toward enhanced risk sensitiveness of capital requirements since the release of Basel I. For instance, an amendment to the Basel I incorporated the market risk into the banking regulation framework in 1996. It offers banks the opportunity to compute the minimum capital requirements by using a value-at-risk approach. In 2004, the Basel committee finalized a comprehensive revision to the Basel Accord, also called Basel II. The focus of the reform has been in strengthening the regulatory capital for active banking organizations through minimum capital requirements that are more sensitive to an institution’s risk profile and reinforces incentive for strong risk management.1 The newly proposed internal model-based (denoted as the IMB approach, hereafter) capital standard allows regulatory capital requirements to be more closely aligned with the economic capital allocations that bank managers set for operational purposes.2 The goal of banking regulation is to provide a safe-and-sound banking industry that will protect depositors and promotes good investment policies among banks. However, the prudent regulation may create two types of distortions: excessive risk-taking by managers and implicit taxes that exhaust the entire surplus.3 For many years, deposit insurance has been the

Internal Model-Based Capital Standard and the Cost of Deposit Insurance

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most effective method for stabilizing the banking system. It has been argued in the literature that deposit insurance has a social cost of moral hazard. Bhattacharya, Boot, and Thakor (1998) discussed regulatory measures presented in the literature to reduce moral hazard. Crouhy, Galai, and Mark (2001) found that deposit insurance is not priced according to a bank’s individual risk and the potential for moral hazard and also argued that the optimal capital requirement could reduce moral hazard. The cost of deposit insurance is equivalent to the value of a put option written by the insuring agent. Therefore, the contingent claim analysis can be used to derive the value of deposit insurance. A partial list of studies that have applied contingent claim analysis to value deposit insurance includes Merton (1977, 1978), Pennacchi (1987a, 1987b), Ronn and Verma (1986), McCulloch (1985), Allen and Saunders (1993), Duan, Moreau, and Sealey (1995), Duan and Yu (1994, 1999), Falkenhein and Pennacchi (2003), and Lee, Lee, and Yu (2005). Much of this stream of deposit insurance pricing research has attempted to reflect the policy parameters of capital requirements, closure rules, or capital forbearance in the model. However, in the traditional single-period deposit insurance pricing model, the capital requirement has only a limited meaning, because at most, it determines the initial capital position of a bank. Since the bank is assumed to be liquidated at the end of the coverage period, the close condition is solely based on the solvency condition, and not the capital standard. Duan and Yu (1994, 1999) and Cooperstein, Pennacchi, and Redburn (1995) set up a multiperiod framework to measure the effect of the capital standard on the cost of deposit insurance. However, the capital standard specified in these studies was based on the 1988 Basel Capital Accord and did not explicitly take into account the relationship between the bank’s individual risk and the capital requirement. Kupiec (2004) analyzed how the capital constraint set up by the VaR (value-at-risk) measure for bank risk affects the bank’s capital allocation. Dangl and Lehar (2004) analyzed the impact of risksensitive capital requirements on a bank’s optimal risk-taking behavior. These studies focused on analyzing how the new Basel Capital Accord affects banks’ risk-taking behaviors, but they did not explicitly consider how the new accord impacts regulators’ closure policy and the cost of deposit insurance. Chen, Ju, Mazumdar, and Verma (2006) proposed a disaggregated approach to demonstrate that deposit insurance premia and capital requirements will be significantly miscalculated while ignoring truncated nature of loan payoffs. This study intends to compare how deposit insurance guarantees may differ between capital requirements based on the 1988 Basel Accord

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and the new Basel Accord. We develop a model to value the cost of deposit insurance under the cases of Basel I’s building block approach and Basel II’s IMB (VaR) approach while considering the adequate empirical specification for the bank’s asset value process.4 We also investigate how the interaction between the capital requirements for alternative regulations and a bank’s potential risk-taking behaviors affects the cost of deposit insurance.

2. THE MODEL The risk-based premium for a bank can conceptually be viewed as a put option. The intrinsic cost of the deposit insurance critically depends on the dynamics of a bank’s asset return, the insolvency resolution, and the closure policy. In this study we include the effects of a delayed closure and its induced moral hazard behavior on the cost of deposit insurance. Their effects can be analyzed in a multiperiod setting. These effects are specified in the following sections.

2.1. The Dynamic of Bank Asset Return Merton (1977) modeled the deposit insurance as a put option and achieved a close-form solution for the risk-based premium while assuming that a bank’s asset value is governed by a geometric Brownian motion (GBM). The traditional analyses for deposit insurance valuations were mostly conducted within the GBM assumption for a bank’s asset value even though under different model specifications.5 However, a large body of empirical studies has demonstrated that financial asset returns exhibit fat-tail and volatility clustering features, which contradict the traditional assumption for the constant volatility of the bank asset value. In this study we follow Duan and Yu (1999) to assume that the bank asset return is governed by a GARCH(1,1) process. We consider a discrete time set-up, the dynamics of bank asset return from time t to t+Dt is denoted by Rt+Dt; that is Rt+Dt=ln (A(t+Dt))/A(t), where A(t) is the value of the bank assets at time t, which can be written as follows: 1 (1) RtþDt ¼ r þ lstþDt s2tþDt þ stþDt tþDt 2 s2tþDt ¼ b0 þ b1 s2t þ b2 s2t 2t

(2)


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where r is the risk-free rate of interest; l the unit risk premium embedded in the bank asset return; et+Dt, conditional on the time t information, a standard normal random variable with respect to the physical probability measure governing the actual return system; the settings of b0>0, b1Z0, and b2Z0 ensure that conditional volatility stays positive; b1+b2o1 is specified to ensure covariance stationarity of the dynamic of bank asset return. Following the GARCH option pricing theory developed by Duan (1995), the dynamic of bank asset return can be locally risk-neutralized as follows: 1 RtþDt ¼ r s2tþDt þ stþDt xtþDt 2

(3)

s2tþDt ¼ b0 þ b1 s2t þ b2 s2t ðxt lÞ2

(4)

where xt=et+l is a standard normal random variable, conditional on time t information, with respect to the risk-neutralized probability measure.

2.2. Insolvency Resolution and Insurance Payoffs We assume that the bank asset value is subject to be reset at the time of audit. Since the majority of bank failures are resolved through either purchase-and-assumption or the government-assisted merger method, in the event of failure resolution the insuring agent typically arranges for a reorganization of the failed bank and continues to provide deposit insurance coverage. This adjustment resets the assets of the failed bank to the leverage required under the capital requirement. For this perspective, the deposit insurance contract is automatically renewed and it can be viewed as a stream of single-period put options with occasional asset value resets. In addition to the asset value reset for the resolution of a failed bank, the other asset value reset comes from the distribution of cash dividends. Since the equity holders of profitable banks may withdraw excessive capital, a ceiling is placed on a bank asset value. When audits on the bank are assumed to be conducted periodically at time ti, i=1,2, y, the asset value adjustment mechanism at auditing time ti is 8 rti q Derti ; if A > ti qu De < u rti if qu Derti A (5) Ati ¼ Ati ; ti rDe > : q Derti ; otherwise l

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where A ti denotes the value of the bank assets before the adjustment at auditing time ti. The parameters ql and qu(1rqloqu) are set to be the lower and upper bounds for the asset value. Parameter ql reflects the capital standard set by the regulatory authority, whereas parameter qu, a threshold level of the asset-to-debt ratio, determines the extent to which the equity holders of profitable banks are willing to leave to the capital with the banks. The initial face value of total interest-bearing bank deposits is denoted by D. Since the deposits are insured, the interest rate applicable is assumed to be the risk-free rate of return, r. Parameter r(0oroql) is used to model the capital forbearance. When ro1, the bank, if insolvent, will not be forced to face an immediate intervention as long as it remains within the capital forbearance range. An insolvent bank is able to function normally since the insuring agent guarantees the performance of its deposit liabilities. An insured bank faces a failure resolution only when its asset value falls below rDerti . Although parameter r alters the condition for triggering an asset adjustment, the adjustment will fully restore the asset value to the level dictated by the capital standard.6 In the traditional single-period setting, the decision for early closure or capital forbearance is actually irrelevant, because banks are assumed to be liquidated at the end of the period anyway. The typical adjustment made to the deposit insurance payoff in the single-period setting is somewhat artificial and inconsistent with the reality. A multiperiod deposit insurance coverage exposes the insuring agent to a stream of put option-like liabilities. We assume that the payment and auditing times coincide, and thus the random liability or the put option payoff at auditing time ti, denoted by P(ti), can be described as follows: ( rti 0; if A ti minðr; 1ÞDe Pðti Þ ¼ (6) Derti Ati ; otherwise At the termination date, i.e. T=tn, r must be set at one. Therefore, the last liability facing the insuring agent can be written as follows: Pðtn Þ ¼ MaxfDertn Atn ; 0g

(7)

which is a familiar expression for the put option payoff.

2.3. Capital Standards Bank regulations, such as capital standard, regulatory prompt corrective action, and capital forbearance, are important in order to value the


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cost of deposit insurance. Previous single-period models, such as Merton (1977), Ronn and Verma (1986), Pennacchi (1987a, 1987b), and Duan, Moreau, and Sealey (1995), did not explicitly explore the effect of bank regulations on the bank’s risk-taking behavior and the cost of deposit insurance. Nagarajan and Sealey (1995) discussed the interaction between the regulator’s incentive and the closure rule on a problem bank. Galloway, Lee, and Roden (1997) proposed that the insuring agent typically arranges reorganization for a failing bank and then continues to provide deposit insurance coverage. However, how the Basel II’s IMB approach affects the bank capital requirement and the cost of deposit insurance is still an open question. In contrast to the description of Basel II not significantly changing overall capital requirements, the Federal Deposit Insurance Corporation (FDIC) in the U.S. expects large percentage reductions in risk-based capital requirements. In addition, the FDIC expects the risk-based capital requirements for Basel II’s IMB capital regulation would be far below the level needed for current prompt corrective action (PCA) proposals and will weaken the current PCA framework. In this study we propose to measure the costs of deposit insurance for the capital standards set by the 1988 Basel Accord and Basel II, respectively. We also present the effects of capital forbearance and moral hazard on the cost of deposit insurance for the alternative capital standards. Under the building block of the 1988 Basel Accord, tiers 1 and 2 capital should exceed 8% of the risk-adjusted asset value amount. The capital standard can be translated into ql=1.087. This standard mandates banks to hold capital as a safety cushion in order to ensure bank solvency. To link the capital requirement to the risk of a bank’s assets, the accord assigns assets to different risk buckets and specifies bucket-specific capital requirements. Whereas capital requirements are homogeneous to the same within each of these buckets, the economic risk of assets assigned to the same bucket may vary substantially. This opens the opportunity for regulatory capital arbitrage. For this reason, the Basel Committee proposed the IMB approach to link minimum capital requirements to the bank’s actual risk closely. We analyze the IMB capital regulation by using VaR measures of banks’ risk exposures. The capital requirements based on the VaR approach are conceptually different from the building block approach of the 1988 Basel Capital Accord, since it includes not only the exposure to risk factors, but also the volatility of risk factors. We assume that the capital requirement developed by the IMB approach is solely based on VaR. Our setting for the bank asset returns implies that they arePuncorrelated across days, and hence the n-period bank asset return, Rn ¼ n0 Rt , will be governed by a normal

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distribution with a variance: b0 1 ðb1 þ b2 Þn1 ðn 1Þ ðb1 þ b2 Þ Cn ¼ 1 ðb1 þ b2 Þ 1 ðb1 þ b2 Þ n 1 ðb1 þ b2 Þ 2 þ s 1 ðb1 þ b2 Þ 0

(8)

In the IMB regime, capital regulation demands that the difference between the bank’s asset value and the bank’s liabilities must be at least as high as the VaR, for a specific time horizon (e.g. nDt horizon) and confidence level (e.g. w%). At auditing time ti, the w% VaR for the bank can be written as follows: pffiffiffiffiffiffi VaRn ðw%Þ ¼ Dti F1 ðw%Þ Cn (9) where Dti denotes the value of bank deposits at time ti; and F1(w%) refers to the w percentile of standard normal distribution. In other words, the bank is allowed to operate next period if A ti VaRn ðw%Þ. For Basel II’s IMB approach the parameter value for ql can be calculated by the following equation: ql ¼

Derti 1 VaRn ðw%Þ

(10)

2.4. Moral Hazard Kane (1986, 2001) and Kaufman (1987) argued that capital forbearance induces a failing bank to adopt risk-shifting portfolio strategies – a situation in the literature known as moral hazard. In addition to capital regulation on the problem bank, the possibility of capital forbearance and the potential moral hazard behavior are also incorporated in our pricing model. We formalize such risk-taking behavior by the outcomes of a bank’s asset value, which is classified into three categories.7 When the bank asset value is greater than the capital standard at auditing time, the bank functions normally and its portfolio’s risk characteristics remain unchanged. If the bank asset value slides below the capital standard, but is tolerated by the regulatory authority, then moral hazard occurs and the bank is assumed to increase its portfolio risk. Once the problem bank breaks the threshold level at which the insuring agent can no longer forbear, the insuring agent steps in


65

to reorganize the bank. We follow Duan and Yu (1999) to model the risktaking behavior by increasing the value of b0. This action increases the stationary standard deviation of its asset portfolio by 100w%, i.e. b0(ti)=(1+o2)b0(ti1). Specifically, the adjustment can be described as follows: 8 rti b ðt Þ; if A > ti ql De < 0 i1 rti b0 ðti Þ ¼ ð1 þ o2 Þb0 ðti1 Þ; if ql Derti 4A (11) ti r De > : b ðt Þ; otherwise 0 0 where b0(.) is indexed by time to reflect its time-varying nature.

2.5. Fairly-Priced Premium The fairly-priced premium rate is a risk-based rate that equates the present value of the whole stream of deposit insurance liabilities with the present value of the total insurance levies at that premium rate. We assume a hypothetical constant premium rate over the coverage period and the insuring agent guarantees the deposit coverage up to time T, i.e. tn. The n-period fairlypriced premium rate, denoted by dn, can be computed as follows: dn ¼

n 1 X erti E 0 ½Pðti Þ nD 0

(12)

where E 0 ð:Þ denotes the expectation taken at time 0 with respect to the dynamics specified in (3) and (4). The fairly-priced premium rate is, of course, a theoretical entity. This premium rate nevertheless serves as a convenient measure for the intrinsic value of the deposit insurance coverage. The model’s analytic aspect is now fully specified, and a numerical analysis will be conducted in the next section.

3. NUMERICAL ANALYSIS 3.1. Parameter Values The basic unit of time is assumed to be one business day (i.e. Dt=1 day) and auditing takes place once a year (i.e. titi1= 250 days). We use

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the parameter values estimated by Duan and Yu (1999) and set b0=7.254 107, b1=0.931771, b2=0.037339, and l=0.027647. Parameter qu, which is set to reflect the threshold level at which the bank’s equity holders will withdraw excess capital, is assumed to be 1.15. Parameter ql is set at 1.087 for the building block approach. Recall that the parameter value for ql is consistent with the 8% capital standard under the 1988 Basel Accord. For Basel II’s IMB approach the parameter value for ql depends on the amount of risk that the bank bears. The value of ql can be calculated by Eq. (10). At the time of auditing, the values of b0, b1, and b2 are not observable. However, a path of the bank’s asset returns for the last year can be observed, and hence the values of the parameters can be estimated by the path of observed asset returns. Once the values of b0, b1, and b2 being estimated, the value for ql specified by the Basel II’s IMB approach can be computed through Eqs. (8)–(10). In order to measure the impact of the bank’s initial capital position on the cost of deposit insurance, three values of the asset-to-liability ratio (A/D) are examined: 1.09, 1.11, and 1.13. The risk-free rate of interest is assumed to be 6% per annum. The simulations are run on a daily basis with 5,000 paths.

3.2. Premium for the Building Block Approach For the building block approach, fairly-priced premium rates are simulated by the framework of Duan and Yu (1999). Table 1 presents the premium rates corresponding to different coverage horizons. The upper panel of Table 1 shows the premium rates without considering the effects of capital forbearance and moral hazard. That is the case where the capital standard is strictly enforced by the regulatory authority. The lower panel presents the premium rates when the effects of capital forbearance and moral hazard are taken into account. The capital forbearance parameter r is set at 0.97 and the risk-taking intensity parameter w is assumed to be 0.2. As expected, the premium rate decreases with the bank’s initial capital position (A/D) for both cases where the effects of capital forbearance and moral hazard are and are not taken into account. In the case of a low initial asset-to-liability ratio, we observe that the increase in the coverage horizon reduces the fairly-priced premium rate. However, the reverse is present in the case of a bank with a relative high initial capital-to-liability ratio. This is because the longer coverage horizon is, the more the bank with low initial asset-to-liability ratio is likely to become insolvent and be resolved by the


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Table 1. The Fairly-Priced Deposit Insurance Premium Rate (in Basis Points) under the Building Block Capital Standard. Without forbearance and moral hazard A/D 1.09 dT=1 57.05 dT=2 47.89 43.95 dT=3 dT=4 41.11 dT=5 39.76 38.64 dT=6 dT=7 38.24 With forbearance and moral hazard 57.05 dT=1 dT=2 79.65 dT=3 91.53 96.10 dT=4 dT=5 100.91 dT=6 106.12 111.04 dT=7

1.11 35.71 35.06 35.08 34.37 34.35 34.13 34.45

1.13 21.49 26.18 28.88 29.65 30.56 30.96 31.74

35.17 61.12 75.64 83.45 90.21 96.83 103.30

21.49 46.90 63.09 72.55 81.71 89.27 95.97

This table is based on the following parameter values: qu=1.15, ql=1.087, b0=7.254 107, b1=0.931771, b2=0.037339, and l=0.027647.

methods of either purchase-and-assumption or the government-assisted merger. The new capital injection on the resolution of a failed bank could reduce the cost of deposit insurance. If the capital standard is not strictly enforced, then the insured bank effectively faces a looser capital requirement which is likely to encourage the bank to conduct risk-taking behavior. The lower panel of Table 1 offers the premium rates computed for the case when the effects of capital forbearance and moral hazard are taken into account while the forbearance parameter r is set at 0.97. It is clearer to show the effects of capital forbearance and moral hazard under the building block capital standard by using Fig. 1 to trace out the premium rates presented in Table 1. In Fig. 1, the upper (lower) plane portrays the premium rates for the case where capital forbearance and moral hazard are (not) taken into account. We observe that the forbearance-induced moral hazard raises the premium rate. We also observe that the premium difference increases with the coverage horizon but decreases with the bank’s capital position. These results are similar to those of Duan and Yu (1994, 1999) in which the bank asset returns are assumed to be governed by GBM and the GARCH process, respectively.

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Fig. 1. Deposit Insurance Premium Rates (in Basis Points) under the Building Block Capital Standard with vs. without Forbearance and Moral Hazard.

3.3. Premium for the Basel II’s IMB Approach Capital forbearance and moral hazard drive up the premium rate in a regime where the capital requirement is set by the 1988 Basel Accord. However, in the regime where the capital standard is specified by Basel II’s IMB approach, whether the forbearance-induced moral hazard will increase the cost of deposit insurance is not clear. Table 2 reports the premium rates computed in the case where the capital standard is set by Basel II’s IMB approach. The upper panel of Table 2 presents the premium rates computed in the case where the effect of forbearance-induced moral hazard is not taken into account. Similar to the building block approach, the premium


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Table 2. The Fairly-Priced Deposit Insurance Premium Rate (in Basis Points) under the Basel II’s IMB Capital Standard. Without forbearance and moral hazard A/D 1.09 dT=1 57.05 dT=2 47.96 45.21 dT=3 dT=4 43.58 dT=5 42.69 42.31 dT=6 dT=7 42.18

1.11 35.72 29.98 28.72 27.66 27.16 26.78 26.64

1.13 21.49 18.96 18.14 18.42 18.13 17.93 17.83

With forbearance and moral hazard 57.05 dT=1 dT=2 37.50 dT=3 29.98 26.25 dT=4 dT=5 23.51 dT=6 22.01 21.07 dT=7

35.72 24.84 21.40 19.66 18.62 18.31 18.08

21.49 17.51 17.13 16.10 15.55 15.31 15.72

This table is based on the following parameter values: qu=1.15, ql=1.087, b0=7.254 107, b1=0.931771, b2=0.037339, and l=0.027647.

rate decreases with the bank’s initial capital position and whether the increase in the coverage horizon will drive up the premium rate depends on the bank’s initial capital position. We also observe that the premium rates computed in the case of the capital requirement set by Basel II’ IMB approach are lower than that computed under the building block approach except for the case of the bank with a lower initial capital position. For instance, the premium rate computed by Basel II’s IMB approach is lower by the amount of about eight basis points than that computed by the building block approach in the case where the bank’s initial capital position is set at 1.11 and the coverage horizon is set at 7 years. However, the premium rate computed by Basel II’s IMB approach is higher by the amount of about four basis points than that computed by the building block approach in the case where the bank’s initial capital position is set at 1.09 and the coverage horizon is set at 7 years. The lower panel of Table 2 reports the premium rates computed when the effect of forbearance-induced moral hazard is taken into account. In order to show the effects of capital forbearance and moral hazard under the Basel II’s IMB capital standard, the premium rates in Table 2 are further

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presented in Fig. 2. The lower (upper) plane portrays the premium rates for the case where the effects of capital forbearance and moral hazard are (not) taken into account. In contrast to the results of the building block approach, we observe that the forbearance-induced moral hazard does not increase the premium rate in the case where the capital standard is set by Basel II’s IMB approach. This is because the failing bank if forborne by the regulatory authority for taking a more risky portfolio will increase the level of capital requirement and there is a possibility for intervention at the next auditing date. This result implies that the capital standard specified by Basel II’s IMB approach can be used to prevent the failing bank from taking on more risky behavior. In contrast to the literature concluding that the

Fig. 2. Deposit Insurance Premium Rates (in Basis Points) under the Basel II’s IMB Capital Standard with vs. without Forbearance and Moral Hazard.


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forbearance-induced moral hazard will drive up the cost of deposit insurance, our study indicates that the capital standard set by Basel II’s IMB approach can reduce the incentive of the failing bank to take up more risky behavior.

4. CONCLUSION In this study we develop a multiperiod deposit insurance pricing model to explicitly consider the effects of alternative capital standards, the possibility of capital forbearance, and potential moral hazard behavior. Our model also takes into account the effect of the econometric specification that has been proven to be very useful in modeling the financial time series. First, we consider the case of the 1988 Basel Accord and achieve a result similar to early studies: (1) the cost of deposit insurance decreases with the bank’s capital position and (2) capital forbearance and moral hazard increase the premium rate. Next, we compute the premium rates in the case where the capital standard is set by the Basel II’s IMB approach. Similar to the result of the building block approach of the 1988 Basel Accord, the premium rate decreases with the bank’s capital position. However, in contrast to the result of the building block approach, capital forbearance and the potential moral hazard behavior do not increase the premium rate in which the capital requirement is set by Basel II’s IMB approach. This result concludes that the capital requirement based upon the Basel II’s IMB approach can effectively reduce the forbearance-induced moral hazard and the cost of deposit insurance.

NOTES 1. Gordy (2000) and Crouhy et al. (2001) argued that the internal models proposed in the literature for computing the optimal economic capital are indeed very sophisticated. 2. Jones (2000) noted that alignment promises to reduce regulatory compliance costs and minimize the credit and markets distortions associated with capital regulation. 3. See Dewatripont and Tirole (1994) and Bhattacharya and Thakor (1993). 4. A large body of empirical studies has conclusively demonstrated that financial asset returns exhibit many robust features such as fat-tailed return distribution, volatility clustering, and leverage effects (see for example, the review article by Bollerslev, Chou, & Kroner, 1992). Duan and Yu (1999) argued that the empirical regularity is incompatible with the Black–Sholes model, the use of such a modeling

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framework for deposit insurance analysis is at best questionable, and specified the GARCH process to a bank’s asset value. 5. For example, Merton (1978) and Pennacchi (1987a) considered a stochastic auditing, while Ronn and Verma (1986) and Duan and Yu (1994) incorporated capital forbearance and moral hazard. 6. The asset reset mechanism largely follows that of Duan and Yu (1994, 1999). 7. Empirical evidence of risk-taking activities can be found in Galloway et al. (1997) among others.

ACKNOWLEDGMENTS The author thanks the helpful comments of Andrew Chen, Min-Teh Yu, and seminar participants at the 2006 FMA European Conference. This research is supported by the National Science Council of R.O.C. (Grant No.: NSC94-2416-H-035-007).

REFERENCES Allen, L., & Saunders, A. (1993). Forbearance and valuation of deposit insurance as a callable put. Journal of Banking and Finance, 17, 629–643. Bhattacharya, S., Boot, A. W., & Thakor, A. V. (1998). The economics of bank regulation. Journal of Money Credit and Banking, 30, 745–770. Bhattacharya, S., & Thakor, A. V. (1993). Contemporary banking theory. Journal of Financial Intermediation, 3, 2–50. Blum, J. (1999). Do capital adequacy requirements reduce risks in banking? Journal of Banking and Finance, 23, 755–771. Bollerslev, T., Chou, R., & Kroner, K. (1992). ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics, 52, 5–59. Chen, A. H., Ju, N., Mazumdar, S. C., & Verma, A. (2006). Correlated default risks and bank regulations. Journal of Money, Credit, and Banking, 38, 375–398. Cooperstein, R., Pennacchi, G., & Redburn, F. (1995). The aggregate cost of deposit insurance: A multiperiod system. Journal of Financial Intermediation, 4, 242–271. Crouhy, M., Galai, D., & Mark, R. (2001). Risk management. McGraw-Hill. Dangl, T., & Lehar, A. (2004). Value-at-risk vs. building block regulation in banking. Journal of Financial Intermediation, 13, 96–131. Dewatripont, M., & Tirole, J. (1994). The prudential regulation of banks. MIT Press. Duan, J.-C. (1995). The GARCH option pricing model. Mathematical Finance, 5, 13–32. Duan, J.-C., Moreau, A., & Sealey, C. W. (1995). Deposit insurance and bank interest rate risk: Pricing and regulatory implications. Journal of Banking and Finance, 19, 1091–1108. Duan, J.-C., & Yu, M.-T. (1994). Forbearance and pricing deposit insurance in a multiperiod framework. Journal of Risk and Insurance, 61, 575–591. Duan, J.-C., & Yu, M.-T. (1999). Capital standard, forbearance and deposit insurance coverage under GARCH. Journal of Banking and Finance, 23, 1691–1706.


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Falkenhein, M., & Pennacchi, G. (2003). The cost of deposit insurance for private held banks: A market comparable approach. Journal of Financial Service Research, 24, 121–148. Galloway, T. M., Lee, W. B., & Roden, D. M. (1997). Banks’ changing incentives and opportunities for risk taking. Journal of Banking and Finance, 21, 509–527. Gennotte, G., & Pyle, D. (1991). Capital control and bank risk. Journal of Banking and Finance, 15, 805–824. Gordy, M. B. (2000). A comparative anatomy of credit risk model. Journal of Banking and Finance, 24, 119–149. Jones, D. (2000). Emerging problems with Basel Capital Accord: Regulatory capital arbitrage and related issues. Journal of Banking and Finance, 24, 35–58. Kane, E. J. (1986). Appearance and reality in deposit insurance: The case for reform. Journal of Banking and Finance, 10, 175–188. Kane, E. J. (2001). Dynamic inconsistency of capital forbearance: Long-run vs. short-run effects of too-big-to-fail policymaking. Pacific-Basin Finance Journal, 9, 281–300. Kaufman, G. (1987). Bank capital forbearance and public policy. Contemporary Policy Issues, 5, 84–91. Kim, D., & Santomero, A. (1988). Risk in banking and capital regulation. Journal of Finance, 43, 1219–1233. Kupiec, P. H. (2004). Internal model-based capital regulation and bank risk-taking incentive. Journal of Derivative, 11, 33–42. Lee, S.-C., Lee, J.-P., & Yu, M.-T. (2005). Bank capital forbearance and valuation of deposit insurance. Canadian Journal of Administrative Sciences, 22, 220–229. McCulloch, J. H. (1985). Interest-risk sensitive deposit insurance premia. Journal of Banking and Finance, 9, 137–156. Merton, R. (1977). An analytic derivation of the cost of deposit insurance and loan guarantee. Journal of Banking and Finance, 1, 3–11. Merton, R. (1978). On the cost of deposit insurance when there are surveillance costs. Journal of Business, 51, 439–452. Nagarajan, S., & Sealey, C. W. (1995). Forbearance, prompt closure, and incentive compatible bank regulation. Journal of Banking and Finance, 19, 1109–1130. Pennacchi, G. (1987a). Alternative forms of deposit insurance: Pricing and bank incentive issues. Journal of Banking and Finance, 11, 291–312. Pennacchi, G. (1987b). A reexamination of the over- (or under-) pricing of deposit insurance. Journal of Money, Credit and Banking, 19, 340–360. Rochet, J. C. (1992). Capital requirements and behavior of commercial banks. European Economic Review, 36, 1137–1170. Ronn, E., & Verma, A. (1986). Pricing risk-adjusted deposit insurance: An option-based model. Journal of Finance, 41, 871–895.

LEAD LENDERS AND LOAN PRICING Li Hao and Gordon S. Roberts ABSTRACT Prior research suggests that given the legal environment in the U.S., smaller syndicates with fewer lead banks should represent ‘‘best practices’’ to promote efficient monitoring and ease of renegotiation. Such syndicates should be associated with lower loan spreads. Controlling for other influences on loan pricing, we conduct tests of this proposition drawing on data from DealScan, Compustat and Federal Reserve Call Reports for U.S. loans between 1988 and 1999. Consistent with our hypothesis, the number of lead lenders is shown to have a significant positive influence on loan yield spreads.

1. INTRODUCTION Does it matter how many banking relationships a firm has? A number of studies document how banking relationships evolve over the life cycle of a typical borrowing firm (Petersen & Rajan, 1994; Houston & James, 2001; Harhoff & Korting, 1998) or vary across countries with different legal systems (Ongena & Smith, 2000). Preece and Mullineaux (1996) switch the focus of investigation from the firm to the loan contract. They hold that loans from single lenders and smaller Research in Finance, Volume 24, 75–101 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00204-3

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syndicates reduce servicing costs through more efficient monitoring and easier renegotiation if the borrower experiences financial distress and they report higher abnormal announcement returns for such loans. Aintablian and Roberts (2000) support this result reporting lower abnormal returns for syndicated (as opposed to single-lender) loans. In related research, Gasbarro, Le, Schwebach, and Zumwalt (2004) reinforce the importance of flexibility and report positive announcement effects for credit lines but not for term loans which are more difficult to renegotiate. Focusing directly on syndicate size and concentration, Lee and Mullineaux (2004) again emphasize facilitating renegotiation and monitoring as key considerations in setting syndicate structures. The number of lenders also depends on the borrower’s environment. Megginson, Poulsen, and Sinkey (1995) determine that, in the 1980s, loans to less developed countries produced negative announcement effects. Esty and Megginson (2003) investigate syndicate structure for an international sample of syndicated project loans. In settings with higher legal and enforcement risks, loan syndicates with large numbers of lenders can deter strategic default on the part of the borrower. For countries with strong legal rights and enforcement, they find that banks concentrate on their roles as ‘‘monitors and providers of low cost re-contracting’’ suggesting smaller, more concentrated syndicates. Esty and Megginson (2003) measure concentration in terms of both the total number of banks and the number of lead, or arranging banks. They focus on lead banks as the most important providers of monitoring and re-contracting services. For syndicated loans to U.S. borrowers, the implication of these prior studies is that smaller syndicates with fewer lead banks represent ‘‘best practices’’ to promote monitoring efficiency and flexibility in restructuring. While earlier research developed this implication from announcement effects and syndicate structure it should also be reflected in loan pricing. The contribution of this chapter is to test the hypothesis that smaller syndicates, with fewer lead banks are associated with lower loan spreads and fees. Consistent with Esty and Megginson (2003), we establish that the number of lead banks is a significant variable in loan pricing. Controlling for other influences on pricing, our tests find a positive relationship between the number of lead lenders and loan yield spreads suggesting that, in the U.S. context, the presence of multiple lenders is associated with higher costs arising from duplication of monitoring and complex renegotiation processes. We conduct additional tests to isolate the impacts of monitoring duplication and renegotiation costs as competing reasons for borrowers paying higher costs in U.S. syndicates with greater numbers of lead banks.

Lead Lenders and Loan Pricing

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Our results point to monitoring duplication arising from free riders joining larger syndicates as the principal explanatory factor. The remainder of the chapter is organized as follows. In the next section, we discuss proxies for bank, borrower and non-price loan characteristics. The central hypotheses tested in this study are also discussed in Section 2. Section 3 describes the data and the empirical approach we use. Our empirical tests and robustness checks are reported in Section 4. Section 5 concludes the chapter.

2. BANK, BORROWER, NON-PRICE LOAN CHARACTERISTICS This chapter examines how the number of lead banks impacts loan yield spreads controlling for borrower characteristics and non-price loan features. We discuss the variables and measures for each dimension in turn. 2.1. Proxies for Bank Characteristics: Number of Lead Lenders We define as lead lenders those banks that have lending relationships with borrowers and retain administrative, monitoring, or contract enforcement responsibilities. The number of lead lenders is specified in each loan facility, and is different from the current number of banking relationships the borrower maintains. In our sample, 66% of the syndicated loans have two or more lead banks.1 It is expected that the presence of multiple lead lenders affects the lenders’ monitoring effectiveness increasing the possibility of free riders (Lee & Mullineaux, 2004).2 Considering the duplication of monitoring, sharing of benefits and complexity of the negotiation process, including more lead lenders in a given loan contract is expected to result in higher loan rates.3

2.2. Bank Size This study employs a measure of relative size (defined as the ratio of bank size to borrower size) as a proxy for bank bargaining power vis-a`-vis the borrower. Given its monopoly of borrower information, a bank may ‘‘hold up’’ the borrower by threatening liquidation and the larger the bank relative to the borrower, the greater its potential power to do so. Following the logic in Coleman, Esho, and Sharpe (2004), it is expected that the relative size ratio is positively related to loan yield spreads.

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Bank size and borrower size are measured as the natural logarithms of their total assets. In this study, we assign each lead bank a weight based on its portion of the shares held by lead banks in each loan facility. Each lead bank’s total assets is then multiplied by its weight, and the sum of all the lead banks’ weighted assets is used to calculate bank size for each loan facility. Our measure represents a refinement by including all lead banks in the calculation.

2.3. Bank Monitoring Power Bank monitoring power can be measured in a variety of ways. Billett, Flannery, and Garfinkel (1995) employ bank credit rating as a proxy for monitoring effectiveness. They argue that high quality banks attempt to maintain their credit ratings because higher credit ratings are associated with larger bank profits resulting from effectiveness in monitoring corporate borrowers. Coleman et al. (2004) develop monitoring proxies which measure the labor input into the monitoring process.4 In the present research, we choose loan loss provisions as our monitoring quality proxy. Johnson (1997) argues that a change in these provisions indicates a shift in management’s assessment of loan portfolio quality and/ or a change in monitoring and screening abilities. Bank management is thought to have superior information about default risks in its loan portfolios compared to investors and other stakeholders. Therefore, we assume that decisions on the level of loan loss provisions convey information about the quality of bank monitoring activities. As discussed above, monitoring and information production, two main advantages of bank debt relative to public debt, provide banks with an information monopoly which might be used to extract higher rents from borrowers according to Rajan’s (1992) ‘‘hold-up’’ theory. In other words, bank lenders’ monitoring power is positively related to loan yield spreads. As the proxy for bank lenders’ monitoring power, loan loss provisions are negatively associated with the intensity of bank monitoring activities. The loan loss provision is thus expected to be inversely related to loan yield spreads; the higher the loan loss provisions, the lower the loan yield spreads.

2.4. Bank Risk As a proxy for bank liquidity risk, Hubbard, Kuttner, and Palia (2002) choose the capital–assets ratio, arguing that a riskier bank will have a lower


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capital–assets ratio and charge a higher premium. They find that the cost of borrowing from low-capital banks is higher than that of borrowing from well-capitalized banks, even after controlling for borrower risk and information costs. Following the argument in Hubbard et al. (2002), in this study we also use the capital–assets ratio (equity capital/total assets) to measure bank liquidity risk. We presume that banks with higher capital– assets ratios have less liquidity risk, and charge lower premia. This suggests that a bank’s capital–assets ratio is negatively related to loan yield spreads.

2.5. Proxies for Borrower and Loan Characteristics Recognizing the important influences of borrower characteristics such as leverage, firm size and firm solvency, on firms’ investment decisions, we include borrower leverage (debt/assets), borrower size (natural logarithm of total assets) and borrower current ratio (current assets/current liabilities) to measure borrower effects on loan yield spreads.5 These borrower variables serve as proxies for borrower risk and information costs. One would expect that borrower size is negatively related to loan yield spreads since smaller firms are assumed to have higher risk due to higher information costs, and larger firms are likely to be more diversified, which implies lower expected bankruptcy costs and lower risk. This is consistent with the findings of Petersen and Rajan (1994), who posit that adverse selection and moral hazard have more influence on small and young corporate borrowers. Similarly, Sufi (2006) finds that when the borrower is more informationally opaque, syndicates are more concentrated and reports weak evidence that spreads are higher. We include book-value measures of leverage (debt/assets) as the proxy for borrower risk. As borrowers with higher leverage ratios likely have higher risk, borrower leverage is expected to be positively related to loan yield spreads. To control for the effects of non-price loan characteristics on the determinants of loan yield spreads, we include the facility amount size, term facility maturity, a dummy variable indicating the loan’s secured status and a dummy variable indicating whether the loan is syndicated. If the loan is underwritten by a syndicate, it is more likely to be successfully distributed and associated with lower risk. This is equivalent to a reduction in syndication risk for the originating bank(s) and a reduction in the firmspecific risk associated with individual loans. Therefore, the syndicated loan indicator dummy variable is expected to be negatively related to loan yield spreads.

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Table 1.

Hypothesized Signs of Variables Explaining Loan Spreads.

Variables

Borrower characteristics Borrower solvency Asymmetric information Credit quality Bank characteristics Bank risk Bank monitoring Bank liquidity risk Monitoring duplicate/ Renegotiation flexibility Non-price loan characteristics Controls

Characteristics Proxies

Expected Sign

Realized Sign

Current ratio Borrower size Leverage

ve ve +ve

ve ve +ve

Relative size Loan loss provision Capital asset ratio Number of lead lenders

+ve ve ve +ve

ve ve ve +ve

Maturity Facility size Loan distribution Secured

ve ve ve +ve

ve ve ve +ve

We include borrower current ratio (current assets/current liabilities), borrower size (the natural logarithm of total assets) and leverage (debt/assets), which serve as proxies for two groups of borrower characteristics: borrower risk and information costs. Relative size is defined as the ratio of bank size to borrower size. Loan loss provisions indicate changes in management’s assessment of loan portfolio quality and/or a change in monitoring and screening abilities. We use the capital–assets ratio (equity capital/total assets) to measure bank liquidity risk. We define as lead lenders those banks that have lending relationships with borrowers and retain administrative, monitoring, or contract enforcement responsibilities. The number of lead lenders is specified in each loan facility (contract). Maturity is the term facility maturity. Facility size is the natural logarithm of the amount term facility size. Loan distribution is a dummy variable which equals 1 (0 otherwise) if the loan is underwritten by a syndicate of banks. Secured is a dummy variable which equals 1 (0 otherwise) if the loan is secured.

Prior studies have documented that loans with longer maturities are associated with firms with higher credit quality (Gottesman & Roberts, 2004). Because borrowers with lower credit quality are limited to shortermaturity loans, greater maturity is negatively related to loan yield spreads. In the same vein, borrowers required to pledge collateral are also associated with higher risk (Berger & Udell, 1990; Harhoff & Korting, 1998). Accordingly, secured status is likely to be positively related to loan yield spreads (Gottesman & Roberts, 2007). Loan size is viewed as an important determinant of loan yield spreads. Larger loans are more likely to be associated with large borrowers, for whom more information is available. The presence of more information about these


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firms tends to reduce lenders’ costs of monitoring, and for this reason, large borrowers are charged lower loan yield spreads. As a result, a negative relationship between the size of the loan and loan yield spread is expected. A summary of the model and the expected signs of the estimated coefficients are provided in Table 1. Although we estimate a model treating the explanatory variables as exogenous, some loan variables are likely to be endogenous. We address this issue in robustness checks where we re-estimate the model in a simultaneous equations framework. The results suggest that the main findings of the estimated bank effects on loan yield spreads are robust to the simultaneous equations framework. Thus, the results do not appear to be driven by specification error in the single-equation Ordinary Least Squares (OLS) framework.

3. DATA Our main data sources are the DealScan database, Compustat and U.S. Federal Reserve Call Reports. Supplied by the Loan Pricing Corporation (LPC), the DealScan database includes borrower identity and location; lender identity, lenders’ shares and roles;6 loan purpose, type, amount and contract date; and price, as well as a number of non-price terms.7 The DealScan database provides relatively little detail on the borrower’s and the lender’s financial positions. Financial variables reflecting borrower characteristics can be obtained from Compustat, while lender characteristics are available in the Call Reports provided by the U.S. Federal Reserve. These are the regulatory filings that all commercial banks with insured deposits submit each quarter. The Call Reports include detailed information on the composition of bank balance sheets and some additional data on off-balance-sheet items. We use the date of the facility to match the annual report data of banks and borrowers with the year-end data immediately preceding the facility date. We obtain loan data for 1988–1999 from the DealScan, bank data for 1987–1998 from the Call Reports, and borrower data for 1987–1998 from Compustat. As for lender type, we include bank lenders only and exclude other types of lenders such as insurance companies, mutual funds, etc. We begin with an extraction of the DealScan database which contains data on 65,380 loan facilities originated by U.S. banks. Following our theoretical discussion, we require that the borrower’s country of origin be the U.S. and delete observations with missing borrower names and/or borrower tickers. We also exclude loan facilities without lenders’ names or a

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loan facility active date. We are left with 19,082 loan facilities after applying these filters. Using the names of the borrowers and locations recorded in DealScan, we match the loan data with firm data from Compustat. In total, 10,839 loan facilities are successfully matched. Next, we use the names of lead banks in DealScan to link matched loan and borrower information with bank-level information in Federal Reserve Call Reports which supply many financial, structural and geographical variables for bank lenders. As stated earlier, for syndicated loans, we assume that the lead bank’s characteristics have the greatest effects on the determination of loan contract terms because the responsibilities for bargaining, monitoring and screening are placed on the lead banks.8 For loans with multiple lead banks, we assign each a weight according to its portion of the total shares held by lead banks. After matching with bank data, 1,869 loan facilities with usable information remain. A large number of observations are lost in the process of linking the loan information with bank-level data because many bank names could not be found in Call Reports. Finally, we drop 17 observations identified as outliers because the logarithm of borrower total assets is less than zero. The remaining sample data consist of 1,852 loan facilities associated with 95 banks and 740 firms.9 Each firm, on average, has more than two loan facilities in this sample. Since DealScan covers the loan syndication market, in our final sample 72% of loan facilities are syndicated loans and 28% are sole-lender loans. For comparison’s sake, in the full DealScan sample 80% of loan facilities are syndicated loans and 20% are sole-lender loans. Table 2 provides a description of all the explanatory and dependent variables used in the cross-sectional analysis of the effects of bank, borrower and non-price loan characteristics on loan yield spreads. We begin by documenting the summary statistics of selected key variables in Table 3. As shown in Table 3, the loan yield spread (RATEAISD), measured by rate all-in-spread drawn, is on average 178 basis points above the benchmark London interbank offering rate (LIBOR).10 In DealScan, all-in-spread drawn is expressed as a spread over LIBOR which takes into account both one-time and recurring fees associated with the loan. The all-in-spread drawn is thus defined as the coupon spread, plus any annual fee, plus any up-front fee divided by the maturity of the loan. For loans not based on LIBOR, the LPC converts the coupon spread into LIBOR terms by adding or subtracting a constant differential reflecting the historical averages of the relevant spreads. In this sample, the average maturity of the loan facilities is 3.62 years, and the mean loan facility size is $0.27 billion.


Table 2.

Description of Dependent and Explanatory Variables.

Variable Loan spreads

Current ratio Borrower size Leverage Tax assets ratio Relative size ratio Loan loss provision Capital asset ratio Number of lead lenders Maturity Facility size Loan distribution Secured

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Description Rates all-in-spread drawn, defined as the basis point coupon spread over LIBOR plus the annual fee and plus the upfront fee spread over the duration of the revolver Borrowers’ current assets over current liabilities Natural logarithm of borrower total assets Borrower’s total debts over total assets Borrower’s total income taxes over total assets Natural logarithm of bank total assets over natural logarithm of borrower total assets Provision for loan and lease loss Bank’s equity capital over total assets The number of lead banks in each term facility The term facility maturity The natural logarithm of the amount term facility size A dummy variable equal to 1 (0 otherwise) if the loan is underwritten by a syndicate of banks A dummy variable equal to 1 (0 otherwise) if the loan is secured

This table provides a description of all the explanatory variables and dependent variable used in the cross-sectional analysis of the effects of bank, borrower and other loan characteristics on loan yield spreads.

Bank lenders in this sample have average total assets of $32 billion, total loans (net of unearned income) of $21.6 billion and total deposits of $22.6 billion, with a cash/assets ratio of 8%. Meanwhile, the borrowers have mean total assets of $2.9 billion and mean sales of $1.9 billion.11 Table 4 contains a matrix of Pearson correlation coefficients among the dependent and explanatory variables which reveal some simple relationships among the variables.12 The relative size ratio is positively correlated with loan yield spreads. Both loan loss provisions and capital–assets ratios are negatively correlated with loan yield spreads. This is consistent with the idea that banks with intensive monitoring power and lower risk extract a higher spread for their monitoring and lending activities.

4. EMPIRICAL RESULTS Table 5 presents regression results on the relationships between loan yield spreads and the number of lead banks along with other bank characteristics,

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Table 3.

Descriptive Statistics for Dependent and Explanatory Variables.

Variable Loan spreads Current ratio Borrower size ($billion) Leverage Relative size ratio Loan loss provision Capital asset ratio Number of lead lenders Maturity (year) Facility size ($billion) Loan distribution Secured

Number

Mean

SD

1,690 1,523 1,852 1,819 1,848 1,852 1,848 1,852 1,753 1,852 1,843 1,235

178.1 2.169 2.900 0.320 1.884 156.8 0.073 3.103 3.620 0.270 0.723 0.741

114.9 1.796 12.91 0.262 1.428 379.1 0.019 3.454 2.340 0.630 0.448 0.438

Minimum 15.00 0.100 0.001 0.000 0.411 104.0 0.034 1.000 0.080 0.00001 0.000 0.000

Maximum 755.0 40.67 257.4 2.137 47.72 2507.0 0.266 28.00 20.00 7.000 1.000 1.000

This table presents summary statistics of the explanatory and dependent variables. The loan agreements were originated during the period January 1988–December 1999. Loan spreads are rates all-in-spread drawn, expressed as a spread over LIBOR which take into accounts both one-time and recurring fees associated with the loan. Borrower current ratio is defined as the ratio of current assets over current liabilities; borrower size is the natural logarithm of total assets; leverage is defined as the ratio of debt over assets. Loan loss provision is a measure of bank loan quality. The number of lead lenders is specified in each loan facility (contract). Maturity is the term facility maturity. The facility size shown in this table is measured in billion dollars. Loan distribution is a dummy variable which equals 1 (0 otherwise) if the loan is underwritten by a syndicate of banks. Secured is a dummy variable which equals 1 (0 otherwise) if the loan is secured.

borrower characteristics and non-price loan features. We compute White’s (1980) standard errors to account for heteroskedaticity.13 As shown in Table 5, Regression 1 reports the results without considering the effects of bank characteristics, while the variables reflecting bank characteristics are included in Regression 2. The pure effects of non-price loan characteristics on loan pricing are examined in Regression 3. Bank effects and non-price loan characteristics are incorporated in Regression 4. It is clear that the regression equations as a whole are significant based on the F-values. Comparing the adjusted R2 in these four regressions demonstrates that the inclusion of the number of lead lenders along with other bank characteristics among the explanatory variables in Regressions 2 and 4 somewhat improves the entire model’s explanatory power. Moreover, most of the coefficients of variables reflecting bank characteristics are statistically significant. We next discuss in detail the effects of bank, borrower and non-price loan characteristics on the determinants of loan yield spreads based on the regressions in Table 5.

Loan spreads Current ratio Borrower size Leverage Relative size ratio Loan loss provision Capital asset ratio The number of lead lender Maturity Facility size Loan distribution Secured

Loan Spreads

Current Ratio

1 0.066** 0.636 0.023 0.316 0.059 0.116 0.385 0.195 0.644 0.515 0.482

1 0.212 0.318 0.062 0.103 0.106 0.206 0.045 0.199 0.183 0.069

Borrower Size

1 0.138 0.566 0.055 0.101 0.632 0.201 0.829 0.604 0.385

Correlation Matrix: Full Sample. Leverage

1 0.049 0.057 0.058 0.206 0.122 0.219 0.209 0.032

Relative Size Ratio

1 0.112 0.033 0.296 0.153 0.444 0.369 0.170

Loan Loss Provision

1 0.055 0.135 0.022 0.037 0.048 0.019

Capital Asset Ratio

1 0.061 0.051 0.116 0.083 0.082

The Number Maturity of Lead Lenders

1 0.171 0.653 0.378 0.224

1 0.299 0.320 0.064

Facility Size

1 0.721 0.312

Loan Secured Distribution

1 0.195


Table 4.

1

This table shows the correlation matrix of key variables in this study. Loan spreads is the rates all-in-spread drawn. In DealScan, all-in-spread is expressed as a spread over LIBOR which takes into accounts both one-time and recurring fees associated with the loan. Current ratio is borrowers’ current assets over current liabilities. Borrower size is the natural logarithm of borrower total assets. Borrower’s total debts over total assets are the leverage ratio employed in this chapter. Relative size ratio is the natural logarithm of bank total assets over natural logarithm of borrower total assets. Loan loss provision is a measure of bank loan quality. Bank’s equity capital over total assets is the capital asset ratio. The variable, the number of lead lenders, is defined as the number of lead banks in each term facility. Maturity is the term facility maturity. The natural logarithm of the amount term facility size is the facility size. Loan distribution is a dummy variable equal to 1 (0 otherwise) if the loan is underwritten by a syndicate of banks. Secured is a dummy variable equal to 1 (0 otherwise) if the loan is secured. , , indicate significance at 1, 5 and 10% levels, respectively.

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Table 5.


OLS Estimations of the Determinants of Loan Yield Spread: Full Sample.

Variable

Regression 1

Regression 2

Regression 3

Regression 4

Intercept

287.48 (20.85)

348.87 (18.30)

247.88 (32.81)

274.18 (21.94)

4.78 ( 2.57) 12.33 ( 4.11) 13.69 (1.26)

4.02 ( 2.19) 20.61 ( 6.19) 4.30 (0.40)

Borrower characteristics Current ratio Borrower size Leverage Bank characteristics Relative size ratio

4.36 ( 2.49) 0.03 ( 3.89) 230.21 ( 1.74) 8.00 (5.25)

Loan loss provision Capital asset ratio Number of lead lenders Non-price loan characteristics Maturity Facility size Loan distribution Secured Adjusted R2 Number of observations F value PrWF

0.21 ( 1.83) 14.66 ( 5.21) 33.01 ( 3.85) 89.3 (12.87)

0.25 ( 2.19) 18.43 ( 6.38) 20.56 ( 2.39) 86.42 (12.74)

0.5099 952 142.47 o.0001

0.5373 948 101.07 o.0001

0.8 (0.51) 0.02 ( 4.10) 317.49 ( 2.46) 4.24 (3.34) 0.19 ( 1.89) 22.26 ( 12.85) 38.14 ( 4.89) 87.55 (15.09)

0.19 ( 1.90) 27.09 ( 12.30) 29.25 ( 3.71) 86.44 (15.04)

0.5051 1144 292.93 o.0001

0.5205 1140 155.69 o.0001

This table shows the estimates of the effects of bank, borrower and other loan characteristics on loan yield spread. The dependent variable is loan yield spread which is the rate all-in-spread drawn in DealScan database, expressed as a spread over LIBOR which takes into accounts both one-time and recurring fees associated with the loan. , , indicate significance at 1, 5 and 10% levels, respectively. t-statistics are calculated using White’s heteroskedasticity-consistent standard errors. Sample sizes for these regressions vary on the basis of the availability of all explanatory variables for each regression.


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4.1. Number of Lead Lenders As shown in Table 5, the coefficient of the number of lead lenders is significantly positive and relatively large in magnitude. In economic terms, a one standard deviation increase in the number of lead lenders comes with a 22 basis points (11%) increase in loan yield spreads. This supports our principal hypothesis that syndicates with greater numbers of lead banks are moving away from best practices.14 As discussed earlier, syndicates with more lead banks may be associated with inefficient duplication of monitoring and loss of flexibility in renegotiation. To differentiate between these two explanations, we conduct further tests using bond ratings to partition our sample by ex ante default risk as a predictor of the probability of future renegotiation.15 We then examine whether the coefficient for the impact of the number of lead lenders on spreads is larger for non-investment-grade borrowers which we expect are associated with a higher probability of financial distress and thus higher expected renegotiation costs. To capture borrower default risk and subsequent potential renegotiation, we employ Moody’s credit ratings on borrowers’ senior debt available from DealScan. We classify borrowers into three categories: investment grade (rating of BBB or higher), high yield (below BBB) and not rated and run regressions for each group separately. In untabled results, the significant positive relationship between the number of lead lenders and loan yield spreads holds across all three subgroups. There is, however, no statistical significance attached to the differences between coefficients on number of lead lenders comparing investment grade vs. high yield vs. unrated loans. These further tests offer no support for the hypothesis that increased renegotiation costs associated with a larger number of lead lenders explains the positive link between this variable and loan spreads. As a result, we leave it for future research to distinguish between renegotiation costs and free riding as explanations for our conclusion that syndicates with fewer lead banks represent best practices. 4.2. Other Bank Effects The coefficient of the relative size ratio (bank over borrower size) is significantly negative in Regression 2. This result is inconsistent with our prediction that larger banks have market power. As discussed earlier, this divergence might arise because our sample contains relatively large borrowers and small banks so that market power may not be evident.16

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As shown in Table 5, the coefficient of bank loan loss provisions is significantly negative as expected. A one standard deviation decrease in bank loan loss provisions leads to a 12 basis points (6%) increase in loan yield spreads. The results are consistent with the argument that banks with low levels of loan loss provisions have superior monitoring power and thus charge higher spreads. The significantly negative coefficient of the bank lenders’ capital–assets ratio supports the contention that a more risky bank with a lower capital– assets ratio will charge a higher premium. A one standard deviation decrease in bank lenders’ capital–assets ratios is associated with a 4 basis points increase in loan yield spreads. We also run the regressions with alternative proxies for bank risk, loan deposit ratio and cash assets ratio (not reported), and obtain very similar results.17 This result is consistent with our expectation and also with the findings in Hubbard et al. (2002) and Coleman et al. (2004).

4.3. Borrower and Loan Effects As shown in Table 5, the coefficient of the current ratio is significantly negative, consistent with our expectation and findings in prior studies. Since a borrower’s current ratio is regarded as a proxy for borrower risk, the higher the current ratio, the lower the probability the borrower has shortterm solvency or liquidity problems. The significant negative coefficient of borrower size is also consistent with our hypothesis. It is costly for banks to monitor and screen these more opaque smaller firms and, therefore, smaller corporate borrowers are usually charged higher loan yield spreads.18 Further results from Table 5 that deserve mention are the coefficients of the loan characteristics variables. The statistically significant relationship between loan yield spreads and term facility maturity is consistent with findings in Strahan (1999) and Dennis, Nandy, and Sharpe (2000). The negative sign of the coefficient of maturity suggests that maturity is inversely related to loan yield spreads, as loans with longer maturity are more likely associated with borrowers with higher credit quality (Gottesman & Roberts, 2004). The negative relationship between loan yield spreads and facility size is in line with findings in Angbazo, Mei, and Saunders (1998). Borrowers in larger loans are more likely to be large firms which are assumed to have lower levels of risk.


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The coefficient of loan distribution, a dummy variable equal to 1 if the loan is underwritten by a syndicate of banks, is negative. Loan syndication lowers the risk of an unsuccessful distribution of loans and yield spreads are lower. As expected based on Table 1, a positive relationship between secured status and loan yield spreads is obtained consistent with findings in Angbazo et al. (1998), Dennis et al. (2000), and Gottesman and Roberts (2007).

4.4. Robustness Checks This section discusses results from several robustness checks of our original results. 4.4.1. Term Loans vs. Revolvers In our tests so far, we pool term loans, revolvers and other types of loan agreements together. This approach could be subjected to criticism because different types of loans have different properties. For example, unlike term loans, revolvers offer the borrower the right (but not the obligation) to draw down, repay and redraw all or part of the loan at its discretion (Rhodes, 2000). A revolver facility provides an ongoing line of credit that may be drawn down, repaid and re-borrowed many times over the life of the facility. Because the expected size of the loan to be drawn down is often variable depending on the borrower’s future circumstances, revolvers are more likely to be associated with quantity risk (take-down risk) which could lead to higher required yield spreads (Ho & Saunders, 1983). To address these differences between unique features for revolvers, we separately re-estimate the model for three subsamples containing term loans, revolvers and other types of loan agreements, as shown in Table 6.19 From Table 6, it is clear that the results in the revolvers subsample are similar to the original findings as shown in Table 5. In contrast, the coefficient for the number of lenders and that for monitoring skill (loan loss provision) lose significance in the term loan regression. Besides the basic differences between revolvers and other types of credit loans, the difference in sample size could also be a reason for the weak regression results for the term loan and other types of loan subsamples: the sample sizes for the latter two are much smaller than that of the revolver subsample. 4.4.2. Simultaneous Equation Model In exploring the determination of loan pricing, ordinary least squares are widely employed (for example, Qian & Strahan, 2004; Degryse &

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Table 6.


OLS Estimations of the Determinants of Loan Yield Spread: Subsamples.

Variable

Intercept Borrower characteristics Current ratio Borrower size Leverage Bank characteristics Relative size ratio Loan loss provision Capital asset ratio Number of lead lenders Non-price loan characteristics Maturity Facility size Loan distribution Secured Adjusted R2 Number of observations F value PrWF

Term Loans

Revolvers

Others

Regression 1

Regression 2

Regression 3

555.42 (7.78)

353.27 (16.38)

251.03 (3.63)

5.65 ( 1.27) 45.36 ( 4.74) 12.30 ( 0.50)

4.94 ( 2.26) 21.79 ( 5.59) 13.95 (1.12)

5.83 ( 1.10) 3.35 (0.24) 39.75 ( 1.04)

36.97 ( 3.12) 0.02 ( 0.99) 76.56 ( 0.21) 4.25 (1.19)

3.74 ( 2.14) 0.02 ( 3.06) 210.05 ( 1.32) 8.82 (4.89)

1.31 ( 0.17) 0.0006 (0.02) 214.78 ( 0.44) 6.57 (1.28)

0.81 ( 2.84) 1.39 ( 0.21) 27.58 ( 1.33) 78.44 (3.76)

0.29 ( 1.86) 19.15 ( 4.95) 17.01 ( 1.68) 75.15 (9.79)

0.11 (0.20) 27.54 ( 2.77) 65.24 ( 2.26) 147.89 (6.65)

0.4276 221 16.01 o.0001

0.5372 623 66.52 o.0001

0.6883 104 21.87 o.0001

This table presents the estimates of the effects of bank, borrower and other loan characteristics on loan yield spread in three subsamples, term loans, revolvers and others. The dependent variable is loan yield spread which is the rate all-in-spread drawn in DealScan database, expressed as a spread over LIBOR which takes into accounts both one-time and recurring fees associated with the loan. , , indicate significance at 1, 5 and 10% levels, respectively. t-statistics are calculated using White’s heteroskedasticity-consistent standard errors.


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Ongena, 2005, among others). On the other hand, applying the singleequation OLS technique can be subjected to criticism. Brick, Kane, and Palia (2004) show an important correlation between loan interest rates, collateral and fees in the examination of the joint impact of borrower–lender relationships on those loan terms. Moreover, Dennis et al. (2000) model maturity, secured status and pricing within a simultaneous decision framework and point out important interrelationships among those contract terms. Dennis et al. (2000) document significant bidirectional relationships between maturity and secured status and a unidirectional relationship from both maturity and secured status to loan pricing (all-in-spread). Accordingly, Coleman et al. (2004) employ both OLS and reduced form regressions to investigate the effects of bank characteristics on loan pricing and maturity. To explore the sensitivity of our results to the single-equation OLS framework and its specifications, we re-estimate the model in a reduced form, simultaneous equations framework similar in spirit to the empirical approach in Coleman et al. (2004).20 In both the maturity equation and secured status equation, we include bank, borrower and non-price loan characteristics. These results are provided in Table 7 which also repeats our single-equation OLS estimate for yield spread (Regression 2 from Table 5) for ease of comparison. A good place to begin in assessing robustness is with a comparison of the two yield spread regressions. The main message of this chapter is that increasing the number of lead lenders leads to higher spreads and this conclusion is reinforced by observing that the coefficient for this variable in the reduced form, yield spread regression is similar to its OLS counterpart in magnitude, sign and significance level. Put another way, our main result is robust to replacing maturity and security with their fitted values in the reduced form formulation. A second important result is that lead lenders with stronger monitoring abilities (lower loan loss provisions) are able to charge higher spreads. Again, this result is robust with the coefficients on loan loss provision similar in magnitude, sign and significance across the two yield spread regressions in Table 7. Continuing our robustness comparison reveals that seven of the eight borrower and bank characteristics variables are also comparable in magnitude, sign and significance. The one exception is the capital–assets ratio which is significantly negative in the OLS regression but fails to achieve significance in the reduced form version. Turning to the set of variables for non-price loan characteristics, we see that facility size, loan distribution and the secured dummy are again comparable in the same three respects. The only divergence in this category of variables arises with maturity which is

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Table 7.

The Determinants of Loan Yield Spreads: Single-Equation OLS vs. Reduced Form.

Variable

Intercept Borrower characteristics Current ratio Borrower size Leverage

Single-Equation OLS Yield spread

Yield spread

348.87 (18.30) 4.02 ( 2.19) 20.61 ( 6.19) 4.30 (0.40)

339.22 (17.36) 4.80 ( 2.40) 20.91 ( 5.99) 3.41 (0.31)

Tax asset ratio Intangible ratio Bank characteristics Relative size ratio Loan loss provision Capital asset ratio Number of lead lenders Non-price loan characteristics Maturity Facility size Loan distribution Secured Adjusted R2 Number of observations F value PrWF

4.36 ( 2.49) 0.03 ( 3.89) 230.21 ( 1.74) 8.00 (5.25)

3.34 ( 2.00) 0.02 ( 2.98) 180.85 ( 1.22) 9.12 (5.64)

0.25 ( 2.19) 18.43 ( 6.38) 20.56 ( 2.39) 86.42 (12.74)

0.1 ( 0.81) 20.45 ( 6.41) 13.43 ( 1.50) 85.25 (11.93)

0.5373 948 101.07 o.0001

0.5636 754 89.54 o.0001

Reduced Form Maturity

Secured status

21.21 (4.03) 0.85 (1.44) 3.28 ( 3.28) 7.33 (2.26) 5.82 (0.30)

1.2 (13.29) 0.009 (0.86) 0.13 ( 7.70) 0.2 (3.60)

0.72 ( 1.45) 0.004 (1.7) 103.74 (2.37) 0.95 (1.98)

0.06 (4.52) 0.01 ( 1.35) 0.000006 ( 0.17) 0.80 (1.06) 0.01 ( 1.21)

3.95 (4.20) 15.46 (5.96)

0.03 (1.61) 0.05 (1.12)

0.2363 754 24.33 o.0001

0.2048 754 20.42 o.0001

This table shows the estimates of the effects of bank, borrower and other loan characteristics on loan yield spread in both single-equation OLS framework and reduced form framework. The dependent variable is loan yield spread which is the rate all-in-spread drawn in DealScan database, expressed as a spread over LIBOR which takes into accounts both one-time and recurring fees associated with the loan. , , indicate significance at 1, 5 and 10% levels, respectively. t-statistics are calculated using White’s heteroskedasticity-consistent standard errors.


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negative and significant in the OLS equation but not significant in the reduced form version. The endogeneity of maturity is likely the cause here. Overall, our comparisons of the two yield spread regressions in Table 7, suggest that our main findings are robust to the reduced form framework. The results do not appear to be driven by specification error in the singleequation OLS framework. 4.4.3. Alternative Measures of Lender Numbers The central focus of this chapter is on the role of the number of lead lenders. To explore the sensitivity of our original results to alternative lender number measures, we rerun the models employing total number of lenders and the number of participant banks (not counting lead lenders). As shown in Table 8, Regression 1 provides the results from the original model in Table 5. Regression 2 shows the effects of total number of lenders on the setting of loan yield spreads. This significantly positive relation between total number of lenders and loan yield spreads is similar in spirit to the association between the number of lead lenders and loan yield spreads. Moreover, as shown in Regression 3 of Table 8, the coefficient of the number of participants is also significantly positive. Notably, Regression 4 presents results which incorporate the effects of both the number of lead lenders and the number of participants on loan yield spreads. As seen in Regression 4, the coefficient of the number of participants becomes much less significant relative to that in Regression 3 when both the number of lead lenders and the number of participants are included in the model as explanatory variables. It is clear that the effects of lead lenders on loan yield spreads are significant and dominate the effects of participants on loan yield spreads.21 This is supportive of the important roles played by lead lenders who maintain the responsibilities of monitoring, administrative activities and loan enforcement, while participating lenders simply provide credit for borrowers; this is consistent with our expectation that lead lenders account for most of the effects that total number of lenders has on loan yield spreads. 4.4.4. Multiple Loan Facilities Our final robustness check introduces a control for cross-sectional correlation possibly introduced by our treatment of each loan facility within a deal as a separate loan. Such correlation could arise because independent control variables for borrower and lender characteristics are typically the same when a number of facilities are initiated on the same day. To test for any biases introduced in this way, we create a subsample of

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Table 8.

Robustness Check: The Number of Lead Lenders vs. Other Lender Variables.

Variable

Regression 1

Regression 2

Regression 3

Regression 4

Intercept

348.87 (18.30)

359.06 (18.45)

354.70 (18.11)

357.00 (18.31)

4.02 ( 2.19) 20.61 ( 6.19) 4.30 (0.40)

4.27 ( 2.33) 21.81 ( 6.42) 9.37 (0.88)

4.52 ( 2.46) 20.16 ( 5.97) 12.78 (1.19)

4.10 ( 2.24) 21.94 ( 6.46) 6.51 (0.60)

4.36 ( 2.49) 0.03 ( 3.89) 230.21 ( 1.74) 8.00 (5.25)

4.72 ( 2.69) 0.03 ( 3.88) 233.69 ( 1.67)

4.48 ( 2.54) 0.03 ( 4.12) 247.03 ( 1.75)

4.67 ( 2.67) 0.03 ( 3.81) 228.12 ( 1.63) 6.13 (3.40)

Borrower characteristics Current ratio Borrower size Leverage Bank characteristics Relative size ratio Loan loss provision Capital asset ratio Number of lead lenders Number of total lenders

3.44 (5.37)

Number of participants Non-price loan characteristics Maturity Facility size Loan distribution Secured Adjusted R2 Number of observations F value PrWF

4.02 (4.43) 0.25 ( 2.19) 18.43 ( 6.38) 20.56 ( 2.39) 86.42 (12.74)

0.24 ( 2.13) 18.00 ( 6.29) 17.46 ( 2.00) 84.54 (12.45)

0.5373 948 101.07 o.0001

0.5379 948 101.31 o.0001

2.08 (1.94)

0.19 ( 1.89) 22.26 ( 12.85) 38.14 ( 4.89) 87.55 (15.09)

0.25 ( 2.22) 18.63 ( 6.46) 17.75 ( 2.03) 85.22 (12.53)

0.5334 948 99.54 o.0001

0.5387 948 93.24 o.0001

This table shows the estimates of the effects of bank, borrower and other loan characteristics on loan yield spread with different proxies of syndicate structure. The dependent variable is loan yield spread which is the rate all-in-spread drawn in DealScan database, expressed as a spread over LIBOR which takes into accounts both one-time and recurring fees associated with the loan. , , indicate significance at 1, 5 and 10% levels, respectively. t-statistics are calculated using White’s heteroskedasticity-consistent standard errors. Sample sizes for these regressions vary on the basis of the availability of all explanatory variables for each regression.


Table 9.

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OLS Estimations of the Determinants of Loan Yield Spread: The Main Facility.

Variable

Regression 1

Regression 2

Regression 3

Regression 4

Intercept

296.12 (19.35)

353.75 (18.35)

260.85 (27.82)

292.02 (20.25)

4.4 ( 2.09) 12.74 ( 3.28) 21.93 (1.76)

3.88 ( 1.87) 19.61 ( 5.06) 15.23 (1.28)

Borrower characteristics Current ratio Borrower size Leverage Bank characteristics Relative size ratio

3.4 ( 4.83) 0.02 ( 3.34) 194.43 ( 1.27) 10.40 (6.19)

Loan loss provision Capital asset ratio Number of lead lenders Non-price loan characteristics Maturity Facility size Loan distribution Secured Adjusted R2 Number of observations F value PrWF

0.23 ( 1.31) 16.48 ( 3.71) 32.61 ( 2.86) 83.51 (11.03)

0.3 ( 1.79) 23.47 ( 5.22) 16.35 ( 1.41) 80.14 (10.86)

0.5212 616 96.64 o.0001

0.5529 614 69.93 o.0001

0.06 ( 0.04) 0.02 ( 3.56) 271.34 ( 1.88) 7.91 (5.36) 0.24 ( 1.67) 24.27 ( 9.50) 34.64 ( 3.34) 81.68 (12.81) 0.5098 751 195.96 o.0001

0.28 ( 1.99) 33.49 ( 10.51) 18.6 ( 1.73) 80.01 (12.80) 0.5312 749 106.95 o.0001

This table shows the estimates of the effects of bank, borrower and other loan characteristics on loan yield spread using the subsample which contains the largest loan facility for each loan deal. The dependent variable is loan yield spread which is the rate all-in-spread drawn in DealScan, expressed as a spread over LIBOR which takes into accounts both one-time and recurring fees associated with the loan. , , indicate significance at 1, 5 and 10% levels, respectively. tstatistics are calculated using heteroskedasticity-consistent standard errors. Sample sizes for these regressions vary on the basis of the availability of all explanatory variables for each regression.

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facilities each of which represents the largest facility in a separate loan deal. As this subsample is free of cross-sectional correlation by construction, we can test for robustness by using it to rerun the regressions in Table 5. As shown in Table 9, the principal findings, positive and highly significant coefficients for the number of lenders are replicated in this robustness check. All of the other variables have the same signs as in corresponding Table 5 regressions. In three cases in Table 9 (maturity in Regression 1 and the capital–assets ratio and loan distribution in Regression 2), the coefficients lose the statistical significance they attained in the original regressions likely due to reduction in sample size. In one case (leverage in Regression 1), statistical significance is attained where it did not exist previously. Overall, the robustness check suggests that no serious bias was introduced into our original tests by including multiple facilities in the same deal.

5. CONCLUSIONS Efficient monitoring and ease of renegotiation are two of the special roles of banks in lending to large, U.S. borrowers in syndicated loans. Prior research by Esty and Megginson (2003), among others, suggests that given the legal environment in the U.S., smaller syndicates with fewer lead banks should represent ‘‘best practices.’’ If this is correct, such syndicates should be associated with lower loan spreads. Controlling for other influences on loan pricing, we conduct tests of this proposition drawing on data from DealScan, Compustat and Federal Reserve Call Reports for U.S. loans between 1988 and 1999. Consistent with our hypothesis, the number of lead lenders is shown to have a significant positive influence on loan yield spreads for two reasons. First, a larger number of lead lenders reduces monitoring efficiency by introducing free riders who collect fees, but rely on other lenders’ monitoring efforts. Second, should the borrower later experience financial distress, the additional lead lenders are likely to complicate the renegotiation of the lending agreement. We conduct tests aimed at determining which of these two explanations is foremost in our data but fail to obtain significant results leaving this issue for future research. Our results broaden available evidence on syndicate design. The tests here focus exclusively on U.S. domestic loans. Future research could examine the relationship of loan pricing and the number of lead lenders for international loans to borrowers in environments characterized by high legal and enforcement risks. For such loans, increasing the number of lead


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lenders could serve to mitigate the risk of strategic default reducing yield spreads.

NOTES 1. Our study includes only domestic loans by U.S. banks. We exclude foreign loans because we seek to test the pricing implications of ‘‘best practices’’ for an environment with a strong legal system and good enforcement. 2. Lee and Mullineaux (2004) show that this is also true of the total number of lenders as certain types of renegotiations require unanimity of all syndicate members. 3. Francois and Missioner-Piera (2005) make an opposing argument for costs measured in terms of loan fees only. They find that lower fees are associated with larger numbers of lead banks consistent with economies of specialization. Our cost measure includes both fees and spreads. 4. Assuming that staff abilities in monitoring activities are reflected in their salaries, salary expense share will mirror the resources invested in monitoring activity and the competence of bank staff. To control for possible differences in efficiency across banks, Coleman et al. (2004) estimate a fitted version as their proxy for monitoring effort. Similarly, they estimate fitted non-performing loans and loan charge-off ratios to control for influences other than monitoring. 5. The primary proxy for borrower leverage is the ratio of total debt (long-term debt plus debt in current liabilities) to borrower total assets (book value) (Hubbard et al., 2002; Johnson, 2003). 6. From the DealScan database, the lender role is divided into the following types: Participant, Advisor Only, Secondary Investor, Subparticipants, Technical Agent, Collateral Agent, Co-agent, Co-arranger, Co-manager, Co-lead Manager, Co-Syndications Agent, Administration Agent, Agent, Arranger, Documentation Agent, Lead Bank, Lead Manager, Manager, Managing Agent, Sole Lender, Sr. Lender Manager, Sr. Managing Agent and Syndications Agent. In selecting our sample of lead banks, we eliminate the first six categories. 7. In DealScan, some of the ‘‘deals’’ involve more than one loan ‘‘facility’’ originated by the same borrower on a given date. In this study, we conduct our analysis at the facility-level, treating each facility as a separate loan. In cases where deals involve the same group of lenders in all facilities, our approach has the potential to introduce cross-sectional correlation because many of the lender independent variables do not change across facilities. 8. Dennis and Mullineaux (2000) document that the agent bank negotiates and drafts all the loan documents; participants can provide comments and suggestions but are not generally involved in the negotiations with the borrower. In some transactions, agent roles (origination, loan administration, collateral administration) are divided among several institutions. Fees are split in the case of multiple agents. Angbazo et al. (1998) state that lead banks retain primary administrative, monitoring and contract enforcement responsibilities. Banks acting as managers perform administrative oversight duties although their share ownerships in the syndicated loan are on average smaller than lead banks. Participants do not perform special

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functions other than being signatories to the original loans. We exclude banks whose lender role in a syndicated loan is that of participant, advisor only, secondary investor, subparticipants, technical agent, or collateral agent in syndicated loans. 9. Only eight of the loans represent project finance. 10. Other studies using the ‘‘all-in-spread drawn’’ to measure loan yield spreads include Angbazo et al. (1998), Hubbard et al. (2002), and Dennis et al. (2000). Loans are frequently priced off the prime rate, 6-month LIBOR and 6-month Certificate of deposit (CD) rates. 11. In some important respect our sample is comparable to that in Coleman et al. (2004) drawn from Securities Data Company (SDC). The average facility amount in our sample ($270 million) is roughly comparable to the average of $363 million in the Coleman et al. (2004) sample. Further, the majority of the loans in both samples are syndicated. 12. To detect multicollinearity, we apply the variance inflation factor (VIF) which can be expressed as VIF=1/(1 R2). A general rule is that the VIF should not exceed 10 (Belsley, Kuh, & Welsch, 1980). In this study, we use each explanatory variable as the dependent variable to run a regression and obtain the R2 and VIF. None of the VIFs we obtained exceed 10. 13. Although we employ OLS regressions, it can be argued that a Tobit model is more appropriate given that loan yield spreads are non-negative (truncated at zero). In results not reported here, we replicate our findings in Table 5 using Tobit. We are indebted to the referee for raising this point. 14. Our results run contrary to the negative relationship between a number of lead lenders and fees under the lender-specialization hypothesis of Francois and Missioner-Piera (2005). One possible explanation is that cost measured in terms of fees only (as in their paper) bears a different relationship to the number of lead lenders than does all-in-spread drawn used here. To investigate, we conduct univariate tests dividing our sample in deciles by the number of lenders and calculating mean spreads for each decile. In these univariate tests, we replicate the negative relationship between costs and the number of lead lenders found by Francois and Missionier-Piera thus ruling out differences in the cost measure as the reason for differing findings. Moving to a second explanation, we note that the number of lead lenders takes on a positive coefficient in our regressions when we include borrower and bank characteristics established as important in explaining spreads in prior research but excluded in their paper. Future research will address the robustness of their results. 15. We also examine ex post default risk by creating a subsample of loans to firms that were subsequently delisted in the Center for Research in Securities Prices (CRSP). Of the 740 firms in our sample, only 37 were delisted, and of these, information is available on only 27. Due to this small sample size, we must leave such an ex post investigation for future research. 16. The coefficient of the relative size ratio loses significance in Regression 4 in Table 5. Our argument focusing on the issue of size may be too narrow. An alternative interpretation for the negative relation between the relative size ratio and loan yield spreads can be inferred from the following. Empirical studies of the U.S. banking industry document the significant effects of a bank’s size on its lending business. Larger banks are more likely to lend to medium and large companies,


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assuming these borrowers have less firm-specific risk. Given that banks prefer lending to big borrowers, if a big bank lends to a small borrower then one would expect that the small borrower must have high credit quality and strong bargaining power in order to borrow from the bank. As a result, we presume that those small borrowers who borrow from big banks are associated with a lower risk premium, and thus the relationship between the relative size ratio (lender size over borrower size) and loan yield spreads is negative. 17. The cash assets ratio is used in Kashyap, Rajan, and Stein (2002) to measure bank liquid-assets. 18. The variance inflation factor (VIF) for this case indicates that, multicollinearity between borrower size and relative size is not a severe problem here. As a further check, in view of the correlation between these two explanatory variables, we replace borrower size (logarithm of borrower total assets) with firm size (logarithm of borrower total sales) and obtain similar empirical results (not reported). 19. A term loan is for a specific amount which is to be repaid in full by an agreed date. A revolver is also available for a specific amount of money for an agreed period of time, but unlike the term loan, it offers the borrower the right (but not the obligation) to draw down, repay and redraw all or part of the loan at their discretion (Rhodes, 2000). 20. In the recursive model of this study, both maturity and secured status are included in the loan yield spread equation as explanatory variables, while loan yield spread is not included in the maturity and secured status equations. 21. The number of participants could be endogenous and dependent on pricing causing a problem with the interpretation here. Lee and Mullineaux (2004) conduct related tests treating syndicate size, in turn, as both exogenous and endogenous. Their results are robust to the exogeneity assumption.

ACKNOWLEDGEMENTS The authors thank Melanie Cao, Lawrence Kryzanowski, John Smithin, and Yisong Tian for their valuable suggestions and comments. In addition, this chapter has benefited from comments received from seminar participants at York University, the Tenth Annual Conference of the Multinational Finance Society and the Northern Finance Association Meeting. Financial support for this research came from the Social Sciences and Humanities Research Council of Canada.

REFERENCES Aintablian, S., & Roberts, G. S. (2000). A note on market response to corporate loan announcements in Canada. Journal of Banking and Finance, 24(3), 381–393.

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Angbazo, L., Mei, J., & Saunders, A. (1998). Credit spreads in the market for highly leveraged transaction loans. Journal of Banking and Finance, 22, 1249–1282. Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. New York: Wiley. Berger, A., & Udell, G. (1990). Collateral, loan quality and bank risk. Journal of Monetary Economics, 25(January), 21–42. Billett, M., Flannery, M., & Garfinkel, J. (1995). The effect of lender identity on a borrowing firm’s equity return. Journal of Finance, 50(2), 699–718. Brick, I. E., Kane, E. J., & Palia, D. (2004). Evidence of jointness in the terms of relationship lending. Working Paper. Rutgers University and Boston College. Coleman, A. D. F, Esho, N., & Sharpe, I. G. (2004). Does bank monitoring influence loan contract terms? Working Paper. School of Banking and Finance, University of New South Wales, Australia. Degryse, H., & Ongena, S. (2005). Distance, lending relationships, and competition. Journal of Finance, 60(1), 231–266. Dennis, S., Nandy, D., & Sharpe, I. G. (2000). The determinants of contract terms in bank revolving credit agreements. Journal Financial and Quantitative Analysis, 35(1), 87–110. Dennis, S. A., & Mullineaux, D. J. (2000). Syndicated loans. Journal of Financial Intermediation, 9, 404–426. Esty, B., & Megginson, W. (2003). Creditor rights, enforcement, and debt ownership structure: Evidence from the global syndicated loan market. Journal of Financial and Quantitative Analysis, 38(1), 37–59. Francois, P., & Missioner-Piera, F. (2005). The agency structure of loan syndicates. Working Paper. HEC Montreal. Gasbarro, D., Le, K. S., Schwebach, R. G., & Zumwalt, J. K. (2004). Syndicated loan announcements and borrower value. Journal of Financial Research, 27(1), 133–141. Gottesman, A. A., & Roberts, G. S. (2004). Maturity and corporate loan pricing. Financial Review, 39(1), 55–77. Gottesman, A. A., & Roberts, G. S. (2007). Loan rates and collateral. Financial Review, 42(3), 401–427. Harhoff, D., & Korting, T. (1998). Lending relationships in Germany: Empirical results from survey data. CEPR Discussion Paper no. 1917. Ho, T., & Saunders, A. (1983). Fixed-rate loan commitments, takedown risk, and the dynamics of hedging with futures. Journal of Financial and Quantitative Analysis, 18(4), 499–516. Houston, J. F., & James, C. M. (2001). Do relationships have limits? Banking relationships, financial constraints, and investment. Journal of Business, 74(3), 347–374. Hubbard, R. G., Kuttner, K. N., & Palia, D. N. (2002). Are there ‘‘bank effect’’ in borrowers’ costs of funds? Evidence from a matched sample of borrowers and banks. Journal of Business, 75(4), 559–581. Johnson, S. (1997). The effect of bank reputation on the value of bank loan agreements. Journal of Accounting, Auditing and Finance, 24, 83–100. Johnson, S. A. (2003). Debt maturity and the effects of growth opportunities and liquidity risk on leverage. The Review of Financial Studies, 16(1), 209–236. Kashyap, A., Rajan, R., & Stein, J. (2002). Banks as liquidity providers: An explanation for the coexistence of lending and deposit taking. Journal of Finance, 57(1), 33–73. Lee, S. W., & Mullineaux, D. J. (2004). Monitoring, financial distress, and the structure of commercial lending syndicates. Financial Management, 33(3), 107–130.


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Megginson, W. L., Poulsen, A. B., & Sinkey, J. F. (1995). Syndicated loan announcements and the market value of the banking firm. Journal of Money, Credit and Banking, 27, 457–475. Ongena, S., & Smith, D. C. (2000). What determines the number of bank relationships? Crosscountry evidence. Journal of Financial Intermediation, 9, 26–56. Petersen, M. A., & Rajan, R. G. (1994). The benefits of lending relationships: Evidence from small business data. Journal of Finance, 49(1), 3–37. Preece, D., & Mullineaux, D. J. (1996). Monitoring, loan renegotiability, and firm value: The role of lending syndicates. Journal of Banking and Finance, 20(3), 577–593. Qian, J., & Strahan, P. E. (2004). How law and institutions shape financial contracts: The case of bank loans. Working Paper. Boston College. Rajan, R. G. (1992). Insiders and outsiders: The choice between informed and arm’s-length debt. Journal of Finance, 47(4), 1367–1400. Rhodes, T. (2000). Syndicated lending practice and documentation (3rd ed.). Euromoney Books. Strahan, P. E. (1999). Borrower risk and the price and nonprice terms of bank loans. Working Paper. Department of Finance, Boston College. Sufi, A. (2006). Information asymmetry and financing arrangements: Evidence from syndicated loans. Journal of Finance, 62(2), 629–668. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct rest for heteroskedasticity. Econometrica, 48(4), 817–838.

REGIONAL ECONOMIC CONDITIONS AND AGGREGATE BANK PERFORMANCE Mary Daly, John Krainer and Jose A. Lopez ABSTRACT The idea that a bank’s overall performance is influenced by the regional economy in which it operates is intuitive and broadly consistent with historical bank performance. Yet, micro-level research on the topic has borne mixed results, failing to find a consistent link between various measures of bank performance and regional economic variables. This chapter attempts to reconcile the intuition with the micro-level data by aggregating bank performance, as measured by nonperforming loans, up to the state level. This level of aggregation reduces the influence of idiosyncratic bank effects sufficiently so as to examine more clearly the influence of state-level economic variables. We show that regional variables, such as employment growth and changes in real estate prices, are not particularly useful for predicting changes in bank performance, but that coincident indicators developed to track a state’s gross output are quite useful. We find that these coincident indicators have a statistically significant and economically important influence on state-level, aggregate bank performance. In addition, the coincident indicators potentially contribute to the out-of-sample forecasts of the relative riskiness of state-level bank portfolios, which should be of interest to bankers and bank supervisors. Research in Finance, Volume 24, 103–127 r 2008 Published by Emerald Group Publishing Limited ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00205-5

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1. INTRODUCTION It is intuitive that commercial banks should be affected by the economic conditions in the regions in which they operate. The vast majority of banks in the United States are small and specialize in making loans to individual retail consumers and small businesses. The ability of these customers to repay their loans should be more closely tied to regional economic conditions, to the extent that these conditions differ from those prevailing at the national level. In fact, comparisons of state output growth and movements in nonperforming loans, as shown in Fig. 1 for California, suggest a relationship between bank performance and regional economic conditions. More broadly, regions in close proximity to one another can display quite different patterns in standard measures of both bank asset quality and bank performance over time. As shown in Figs. 2 and 3, the nonperforming loan ratios and return on assets for banks in Arizona,

16

Economic Growth and Nonperforming Loans in California

14 12 10

Nonperforming loans/ total loans

8 6 4 2

Year over year % change in GSP

0 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Fig. 1. Comparison of Annual Growth Rates of California Gross State Product and Year-end Aggregated Ratios of Nonperforming Loans to Total Loans for Banks Headquartered in California. Note: The growth rates are the year-over-year changes in logged California GSP, as reported by the Bureau of Economic Analysis. The bank nonperforming loans and total loans were generated from the FFIEC Consolidated Reports of Condition (i.e., the Call Reports). Individual bank values were aggregated across all banks headquartered in California.

Regional Economic Conditions and Aggregate Bank Performance

12%

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Nonperforming Loans to Total Loans for Banks Headquartered in Contiguous States AZ CA OR

10% 8% 6% 4% 2% 0% 1982

1985

1988

1991

1994

1997

2000

Source: FFIEC Consolidated Reports of Condition

Fig. 2. Year-end Ratios of Aggregated Nonperforming Loans to Total Loans of State Headquartered Banks. Note: The bank’s nonperforming loans and total loans were generated from the FFIEC Consolidated Reports of Condition (i.e., the Call Reports). Individual bank values were aggregated across all banks headquartered in the states of Arizona (AZ), California (CA), and Oregon (OR).

California, and Oregon, which are relatively close in geographic terms, have behaved quite differently over the past 20 years. Despite this intuition, establishing the precise nature of the relationship between regional economic conditions and individual bank performance has proven difficult. Overall, the literature paints a mixed picture of the importance, size, and timing of the impact of regional economic variables in models of bank performance. Furthermore, even in the most promising analyses, the inclusion of regional economic indicators does little to improve out-of-sample forecasts of bank performance. This chapter attempts to reconcile the intuition and the micro-level evidence by stepping back from the usual analysis of performance measures for individual banks and aggregating these measures up to the state level. That is, we assess whether changes in state-level economic variables are useful predictors of state-level banking conditions, which we measure as nonperforming loans. Aggregation of banking data to the state level holds promise along two dimensions. First, the aggregation should reduce the influence of idiosyncratic bank effects on the empirical results, as per the analysis of equity portfolios based on firm size in the finance literature, and thus permit a clearer analysis of well-defined state-level economic indicators

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4% 3% 2%

Return on Assets for Banks Headquartered in Contiguous States (4-quarter average) AZ CA OR

1% 0% -1% -2% -3% 1983

1986 1989 1992 1995 1998 2001 Source : FFIEC Consolidated Reports of Condition

Fig. 3. Year-end Return on Asset Ratios of State Headquartered Banks. Note: Bank’s return on asset is defined as the ratio of earnings to total assets using data from the FFIEC Consolidated Reports of Condition (i.e., the Call Reports). Individual bank values were aggregated across all banks headquartered in the states of Arizona (AZ), California (CA), and Oregon (OR).

on bank performance. Second, the potential usefulness of this relationship for bank portfolio risk management and for supervisory purposes should remain intact; that is, the trade-off between improved understanding of economic factors on regional banking systems and less information on their effect on individual banks should be a reasonable one. For consistent state-level economic indicators, we use the composite regional indexes developed by Crone (1994, 1999, 2004), based on the work by Stock and Watson (1989). Our regression results confirm the common findings that the links between state-level economic variables and individual bank performance measures are weak. However, when we aggregate the nonperforming loan data up to the state level, we find a stronger relationship between local economic performance and bank performance as measured in two ways. First, we find evidence that the state-level coincident indicators Granger-cause state-level nonperforming loan ratios. We also find that the cross-state variance in annual growth rates of the coincident indicators Granger-causes the cross-state variance in nonperforming loan ratios across states, but the reverse does not hold. Second, we focus on the usefulness of this relationship for out-of-sample forecasting, which is both a strong test of our reduced-form model’s


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accuracy and an important element for policy applications by bankers and supervisors. Using a linear probability model of whether individual banks were expected to have a high level of nonperforming loans, we generate forecasted rankings of state-level nonperforming loan ratios. We find that inclusion of the composite state-level indicators in the forecasting model does little to improve forecasts of state-level bank risk, but it also does not measurably worsen the results. We argue that the coincident indicator should still be considered useful in this setting, especially since it is available at a higher frequency and on a closer to real-time basis than most regional economic series. In conclusion, our results suggest that the impact of regional economic conditions on regional bank performance can be detected after aggregating the data up to the state level. Although our results apply only to relative rankings of state-level banking performance, these rankings should be useful to supervisors as early warning systems that signal the likelihood of deterioration in a state’s banking conditions. The chapter proceeds as follows. Section 2 reviews the literature on establishing the empirical link between bank performance and the local economies they operate in. Section 3 describes the data and state-level coincident indicators used in the study. Section 4 presents our analysis of the weak relationship between these variables and nonperforming loans at the individual bank level. In Section 5, we present our analysis of the stronger relationship between state-level economic indicators and state-level bank performance measures. In Section 6, we conduct the out-of-sample forecasting exercise based on relative rankings of expected state-level nonperforming loan ratios, and Section 7 concludes.

2. LITERATURE REVIEW While it is intuitive that local economic conditions should affect bank health and performance, a large literature on the topic has shown the empirical relationship to be elusive.1 On the positive side, Calomiris and Mason (2000) found that several county- and state-level economic indicators impacted bank survival rates during the Great Depression. In a more current setting, Avery and Gordy (1998) found that one-half of the change in bank loan performance between 1984 and 1995 could be explained with a collection of state-level economic variables. Berger, Bonime, Covitz, and Hancock (2000) found evidence that aggregate state- and regional-level variables were

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important contributors to the persistence in firm-level performance (i.e., return on assets) observed in the U.S. banking industry. But by and large, the statistical link between local economic variables and bank condition fades away when (a) economic variables are disaggregated to common local banking market definitions, and (b) when the variables are used for forecasting purposes. Zimmerman (1996) as well as Meyer and Yeager (2001) provide evidence on this first point. Both papers focused on the performance of small banks in the hopes of identifying institutions that would be most vulnerable to economic shocks (i.e., least able to diversify their asset portfolio) and could easily be linked to a distinct local economy. Zimmerman (1996) looked at the performance of California community banks and found that banks operating in southern California performed significantly worse than their counterparts in northern California between 1990 and 1994. However, he could not find a local economic variable to explain these differences. Meyer and Yeager (2001) examined the impact of county- and state-level economic variables on various performance ratios for a sample of small rural banks.2 They found that the county-level variables significantly impacted bank performance, but only in the absence of the state-level variables. In terms of forecasting, Nuxoll, O’Keefe, and Samolyk (2003) used statelevel economic variables, such as the unemployment rate, growth in personal income, and the amount of failed business liabilities, in order to predict bank failures and bank asset quality. Their basic result was that economic variables add little information to the forecasts of these bank-specific variables. Jordan and Rosengren (2002) investigated whether forecasts of regional economic variables had an impact on the supervisory CAMELS ratings assigned to banks.3 They found that contemporaneous measures of regional economic conditions did not add explanatory information over the bank-specific variables already used in bank surveillance models. However, one-year-ahead forecasts of these variables were found to be both economically and statistically significant in improving the predictive power of the surveillance models that assess bank performance in four quarters. Furthermore, they found that these effects were more pronounced during difficult regional economic periods. An important caveat to this analysis and to our data set is that bank deregulation in the U.S. has led to consolidation and to banks’ geographic expansion.4 As noted by Morgan and Samolyk (2003) in their study of bank geographic diversification, U.S. banks have not only become bigger during the course of the 1990s, but they have also become wider by expanding their operations across multiple banking markets. Using a geographic


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diversification index based on deposits, the authors found important differences across bank size categories and over time. We address this concern only in terms of constructing the regional variables corresponding to the interstate banks in our sample (see the discussion in the following section).

3. DATA 3.1. Regional Coincident Indicator As discussed earlier, a single measure of regional economic conditions is hard to come by. Here, we rely on a unique measure of state economic activity that combines a number of individual regional variables into a single index. This coincident indicator is potentially helpful in two ways. First, it closely matches real gross state product (GSP), which is considered a good measure of overall performance of a state’s economy. However, unlike GSP, which is produced with a substantial lag and at an annual frequency, the index can be produced quarterly at the same frequency as our banking data and maintained contemporaneously. In addition to tracking GSP, the index also captures the interactions between other state-level variables such as employment growth and personal income, again allowing these interactions to vary across states. Simply stated, the index proxies for a set of unobservable state-level economic factors that may affect the credit quality of bank loan portfolios as measured by nonperforming loans. We use a coincident indicator developed by Crone (1994, 1999, 2004).5 Crone’s regional index builds on the work of Stock and Watson (1989), who developed a coincident index for the national economy. The state indexes are produced at a monthly frequency and cover the period from January 1979 to November 2006.6 As constructed by Crone (2004), the coincident indicators for the 50 states include three monthly indicators – nonagricultural employment, the unemployment rate, and average hours worked in manufacturing – and one quarterly indicator – real wage and salary disbursements – of regional economic conditions. To ensure consistency, the following criteria are applied. (1) The indexes are constructed from the same set of indicators for each state. (2) The timing of the index is benchmarked to employment in each state. (3) The trend for the index corresponds to GSP for each state.

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6.0

GSP growth (%)

5.0

4.0

3.0

2.0

1.0

0.0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

CI growth (%)

Fig. 4. Correlation of Average Year-over-year Growth Rates of Gross State Product and Coincident Indicators. Note: The growth in gross state product (GSP) is calculated as annual averages of year-over-year changes in logged GSP over the period from 1986 to 2000 for each of the 50 states, as reported by the Bureau of Economic Analysis. The growth in the state-level coincident indicators is calculated as annual averages of year-over-year changes in logged indexes as generated by Crone (2004). The correlation between these 50 data points is 0.89.

Fig. 4 shows a scatter plot of average annual growth between 1986 and 2000 in GSP and the coincident indicator growth for the 50 states. The coincident indicators for each state are aggregated to the annual frequency for comparison with GSP. As the figure shows, the coincident indicator tracks GSP quite well with a correlation coefficient of 0.89.

3.2. Other Regional Indicators By and large, the literature on bank performance and regional economic conditions has relied on several regional indicators, including house price appreciation, employment growth, personal income growth, and the unemployment rate. To tie this paper to previous work in the area and to


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evaluate the usefulness of composite measures relative to others, these variables are included in our analysis. House price appreciation by state is measured using data from the Office of Federal Housing Enterprise Oversight (OFHEO), which produces an index of home prices by state on a quarterly basis. These indices are used to compute year-over-year growth rates for house prices in each state. The personal income data come from the Bureau of Economic Analysis and are released quarterly. Again, the quarterly levels are used to compute year-over-year growth rates. Data on employment and unemployment come from the Bureau of Labor Statistics. As these data are released monthly, our analysis includes year-over-year changes in these variables at a quarterly frequency.

3.3. Bank-Specific Regional Indicators A key challenge in this analysis is the problem of correctly identifying the regional economy for an individual bank. An obvious choice is to simply define the state of headquarters as the bank’s region. Such a choice was more accurate before the advent of cross-state banking laws in the early 1980s and the Riegle-Neal Act of 1994 that opened up the entire country to bank branches, and is probably still reasonable for the case of small banks (see Meyer & Yeager, 2001). For the sample used in this analysis, however, a more complete measure of banks’ regions of operation is required. For this chapter, a bank’s regional economy is defined as a weighted average of the states it operates in, where the weight on any given state corresponds to the share of the bank’s total deposits that originate from that state. The bank-specific weights are constructed based on the branch-level data available from the Summary of Deposits (SOD) data collected and maintained by the Federal Deposit Insurance Corporation (FDIC). The SOD database contains deposit data for more than 85,000 branches/offices of FDIC-insured institutions. SOD information is required for each insured office located in any state, the District of Columbia, the Commonwealth of Puerto Rico, or any U.S. territory or possession such as Guam or the U.S. Virgin Islands, without regard to the location of the main office. For SOD purposes, a branch/office is any location, or facility, of a financial institution, including its main office, where deposit accounts are opened, deposits are accepted, checks paid, and loans granted. Some branches include, but are not limited to, brick and mortar locations, detached or attached drive-in facilities, seasonal offices, offices on military bases or government installations, paying/receiving stations or units, and Internet

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and Phone Banking locations where a customer can open accounts, make deposits, and borrow money. This definition of a branch should very accurately gauge the cross-state activities of a bank.7 All the regional variables and the coincident indicator are weighted by the deposit shares to define bank-specific regional economic conditions. Data are collected annually; hence, the bank-specific weights are updated only once every four quarters.

3.4. Banking Variables The banking data are collected from the quarterly Consolidated Reports of Condition (i.e., the Call Reports) that commercial banks file with their bank regulators. The data set consists of all commercial banks with domestic charters between 1983.Q3 and 2006.Q3. As is well documented in the literature, changes in regulation and competitive pressures spurred a remarkable degree of consolidation in the banking industry. At the beginning of the period, there were 10,775 unique bank entities in the banking database, and by the end of the sample period, this number had dwindled to 7,429 banks. Bank condition is measured here as the ratio of total nonperforming loans to total loans and nonperforming loans are defined as loans past due 30 days or more (but still accruing interest) as well as non-accruing loans. Bank-level control variables include the natural log of assets to control for the many differences between large and small banks and the shares of the loan portfolio assigned to commercial and industrial (C&I) lending, consumer lending, residential mortgage lending, and nonresidential real estate lending. The banking variables are summarized in Table 1.

4. TRADITIONAL MICRO-LEVEL VIEW 4.1. In-Sample Importance of Regional Variables The literature on the impact of regional economic performance on bank conditions relies on a basic model specification that regresses an individual bank’s performance variable on a set of bank-specific variables and regional indicators. This type of model is followed in this chapter.8 The estimated model takes the following form: yijt ¼ a þ gyijt1 þ bxit4 þ yzjt4 þ ijt ,

(1)


Table 1.

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Descriptive Statistics for the Banking Control Variables.

Log(assets) NPL/Total loans C&I/Total loans Consumer/Total loans Residential RE/Total loans Nonresidential RE/ Total loans

Mean

Median

25th 75th Percentile Percentile

11.146 0.034 0.190 0.155 0.289

10.976 0.026 0.160 0.138 0.261

10.277 0.013 0.098 0.080 0.148

0.230

0.213

0.131

SD

Min.

Max.

11.776 0.046 0.249 0.215 0.401

1.334 0.032 0.132 0.099 0.183

7.077 0.000 0.000 0.000 0.000

20.893 0.895 1.000 0.500 1.000

0.308

0.137

0.000

1.000

Notes: This table provides descriptive statistics of the bank control variables used in the regression analysis. The sample period is from 1983.Q3 to 2006.Q3. The 983,388 observations in the sample correspond to 18,797 unique banks. All of these variables were generated from the FFIEC Consolidated Reports of Condition (the Call Reports). Log(assets) refers to the natural log of bank’s total assets. Nonperforming to total loans is the ratio of bank nonperforming loans to total loans. The four control variables for bank portfolio composition were normalized using total bank loans. Commercial and industrial (C&I) loans refer to business lending. Consumer loans refer to all personal loans, except mortgages. Residential real estate (RE) lending refers to mortgages. Nonresidential RE lending refers to commercial RE lending.

where yijt is the nonperforming loan ratio for bank i operating in region j at quarter t; a a common intercept term; yijt1 a lagged value of the dependent variable included to account for its persistence; xit4 a vector of bankspecific variables lagged by four quarters; and zjt4 a vector of region-specific variables, including the coincident indicator, also lagged four quarters. The explanatory variables are lagged four quarters under the assumption that changes in bank characteristics and regional economic condition will take several quarters to appear in the performance variable. All regressions are estimated with state dummies and robust standard errors to account for the non-independence of multiple observations on the same bank over time. Note that the five specifications of the model used throughout the chapter are: (i) bank-specific variables only; (ii) bank-specific variables plus regional variables excluding the coincident indicator; (iii) bank-specific variables and all regional variables; (iv) bank-specific variables and just the coincident indicator; and (v) all the prior variables plus the coincident indicator interacted with the bank’s portfolio shares.

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4.2. All Banks The regression results for all banks are reported in Table 2. The findings point to a strong impact associated with the inclusion of the lagged value of the nonperforming loan ratio in all of the specifications. Invariably, the coefficient on the lagged dependent variable is approximately 0.82 and is statistically significant. Also, consistent with many other studies in banking, the size control is statistically significant. Larger banks tend to have lower nonperforming loan ratios than smaller banks. The inclusion of economic variables (see column (ii) of Table 2) shows that individual state-level variables are clearly statistically significant. The coefficients on the change in house prices, personal income, and the employment variables all have the predicted signs and are statistically significant. However, the counterintuitive positive sign on GDP is an example of some of the difficulties researchers have had in pinning down the influence of economic conditions on bank condition. We also observe positive coefficient estimates when we substitute state-level output (GSP) for aggregate GDP. We would expect positive changes in this variable to be associated with decreasing problem loan ratios, all else being held equal. In column (iii) of Table 2, the coincident indicator is added to the model along with the other regional variables. All coefficients on the observable economic variables remain statistically significant, although their magnitudes are somewhat diminished. This is particularly true for the employment growth variable, which declines in importance by half. The coefficient on the year-over-year change in the coincident indicator, meanwhile, is estimated to be 0.0304, which has one of the largest magnitudes of any of the coefficients on the regional economic variables (other than the coefficient on GDP, which has the counterintuitive sign). The more parsimonious specification includes only the control variables and the coincident indicator is shown in column (iv) of the table. Again, the estimated coefficient on the coincident indicator is sizeable and statistically significant. Column (v) of Table 2 shows a specification of the model that includes interactions of the coincident indicator growth variable with the composition of the bank’s loan portfolio. The interaction terms are meant to examine whether banks with particular loan concentrations are more or less susceptible to regional shocks. The findings indicate that the largest impact of the coincident indicator is for banks with large concentrations of commercial (i.e., C&I) loans and nonresidential real estate loans. This result seems consistent with both the greater volatility in the commercial lending

Table 2. Impact of Lagged Bank Control and Regional Variables on Bank NPL Ratios.

Coeff.

(ii) t-stat.

Coeff.

(iii) t-stat.

Coeff.

(iv) t-stat.

Coeff.

(v) t-stat.

Coeff.

t-stat.

Log (assets) 0.0006 23.35 0.0005 17.68 0.0004 17.47 0.0006 23.70 0.0004 17.50 Consumer/Total loans 0.0027 6.63 0.0011 2.74 0.0012 2.97 0.0031 7.49 0.0023 4.09 C&I/Total loans 0.0047 12.28 0.0036 9.15 0.0036 9.01 0.0047 12.29 0.0066 11.62 Residential real estate/Total loans 0.0036 13.01 0.0026 9.17 0.0026 9.19 0.0039 13.75 0.0015 4.25 Nonresidential/Total loans 0.0028 8.48 0.0013 3.92 0.0014 4.19 0.0031 9.23 0.0008 1.70 0.8286 233.14 0.8184 207.25 0.8174 205.16 0.8276 230.57 0.8173 205.59 (Nonperforming/Total loans)t1 – – 0.0426 32.31 0.0477 34.36 – – 0.0477 34.35 GDP growtht4 House price growtht4 – – 0.0032 5.22 0.0025 4.29 – – 0.0024 4.09 Personal income growtht4 – – 0.0013 1.62 0.0032 4.02 – – 0.0032 3.96 Employment growtht4 – – 0.0364 24.24 0.0075 4.06 – – 0.0080 4.24 – – 0.0005 21.53 0.0005 22.11 – – 0.0005 21.56 Unemployment ratet4 Coincident indicator growtht4 – – – – 0.0304 20.44 0.0127 14.95 0.0166 2.97 CIt4 Residential real estate/Total loans – – – – – – – – 0.0320 5.31 CIt4 Nonresidential/Total loans – – – – – – – – 0.0660 8.37 – – – – – – – – 0.0303 3.28 CIt4 Consumer/Total loans CIt4 C&I/Total loans – – – – – – – – 0.0850 9.24 Constant 0.0183 7.95 0.0103 4.64 0.0093 4.27 0.0186 8.14 0.0074 3.42 F-value Adj. R2

2,736 0.70

3,727 0.70

3,769 0.70

2,767 0.70

3,609 0.70

115

Notes: The table presents regression results for all banks over the sample period from 1983.Q3 to 2006.Q3, which includes 613,993 observations. The regression model is yijt ¼ a þ gyijt1 þ bxit4 þ yzjt4 þ ijt ; SEQ CHAPTER where yijt is the nonperforming loan ratio for bank i operating in region j at quarter t; a a common intercept term; yijt1 a lagged value of the dependent variable included to account for its persistence; xit4 a vector of bank-specific variables lagged by four quarters; and zjt4 a vector of region-specific variables, including the coincident indicator, also lagged four quarters. The five model specifications are (i) bank-specific variables only; (ii) bank-specific variables plus regional variables excluding the coincident indicator; (iii) bank-specific variables and all regional variables; (iv) bank-specific variables and just the coincident indicator; and (v) all the prior variables plus the coincident indicator interacted with the bank’s portfolio shares. All regressions are estimated with state dummies and robust standard errors to account for the non-independence of multiple observations on the same bank over time. The estimated coefficients, corresponding t-statistics and F-statistics, and adjusted R2 values are reported for each of the five specifications examined.


(i)

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sectors and the ability of banks to more easily diversify their risk on consumer and residential loans, such as through securitization.9

4.3. Interstate and Intrastate Banks Given the national deregulation of interstate banking that occurred during the 1990s, we chose to extend the analysis by examining interstate banks (i.e., banks with deposits located in multiple states) and intrastate banks (i.e., banks with deposits located in only one state) separately. The results are presented in Tables 3 and 4. Note that the sample sizes are quite different across the two samples with the intrastate sample being much larger. With some minor exceptions, the coefficient values and statistical significance of the explanatory variables across the two samples are very similar. Notably, for the fourth specification using just the coincident indicator, both samples exhibit a decline in NPL ratios when regional conditions improve. That said, there is an interesting difference between the intrastate and interstate regressions that appears in the interaction terms included in the fifth specification. As shown in Table 3, the interactions between loan shares and the coincident indicator have smaller coefficients or are insignificant altogether for the sample of interstate banks. However, as shown in Table 4 for the sample of intrastate banks, the growth in the coincident indicator significantly improves the NPL ratio of banks with higher exposures to C&I lending, nonresidential real estate lending, and residential real estate lending. This finding suggests that the geographic diversification by interstate banks may translate into diversification of lending risks away from state-level factors. In summary, the results from our reduced-form models point to a possible link between regional indicators and bank performance. The linkage appears most robust for the coincident indicator measure of regional economic performance. This is consistent with other work showing positive and consistent results for GSP variables and more mixed results for other regional indicators. The results from the inter- and intrastate banks suggest that regional conditions have some explanatory power for both types of entities, although interstate banks appear more able to diversify away lending risks than intrastate banks. That said, the results fall short of economic importance, and regional information can be said to have little explanatory power in our regressions.

Table 3.

Impact of Lagged Bank Control and Regional Variables on Interstate NPL Ratios.

Log (assets) Consumer/Total loans C&I/Total loans Residential real estate/Total loans Nonresidential/Total loans (Nonperforming/Total loans)t1 GDP growtht4 House price growtht4 Personal income growtht4 Employment growtht4 Unemployment ratet4 Coincident indicator growtht4 CIt4 Residential real estate/Total loans CIt4 Nonresidential/Total loans CIt4 Consumer/Total loans CIt4 C&I/Total loans Constant F-value Adj. R2

(ii)

(iii)

(iv)

(v)

Coeff.

t-stat.

Coeff.

t-stat.

Coeff.

t-stat.

Coeff.

t-stat.

Coeff.

t-stat.

0.0002 0.0003 0.0001 0.0034 0.0006 0.8450 – – – – – – – – y – 0.0071

2.75 0.24 0.08 4.18 0.66 61.78 – – – – – – – – y – 5.35

0.0001 0.0003 0.0006 0.0036 0.0005 0.8369 0.0213 0.0015 0.0026 0.0251 0.0001 – – – y – 0.0062

2.59 0.18 0.42 3.91 0.53 60.41 5.57 0.78 0.63 4.52 1.71 – – – – – 4.48

0.0001 0.0005 0.0005 0.0034 0.0006 0.8361 0.0223 0.0011 0.0019 0.0132 0.0001 0.0112 – – – – 0.0062

2.53 0.28 0.37 3.73 0.54 60.16 5.84 0.57 0.47 2.04 1.80 2.77 – – – – 4.45

0.0001 0.0005 0.0001 0.0036 0.0008 0.8418 – – – – – 0.0131 – – – – 0.0079

3.01 0.34 0.10 4.35 0.79 61.22 – – – – – 4.63 – – – – 5.73

0.0001 0.0032 0.0012 0.0042 0.0013 0.8358 0.0219 0.0011 0.0018 0.0118 0.0001 0.0448 0.0267 0.0263 0.0883 0.0250 0.0071

2.51 1.67 0.70 3.84 0.95 60.43 5.79 0.56 0.45 1.77 1.79 2.16 1.42 1.02 2.67 0.83 4.56

1,305 1,305

1,044 0.7431

1,021 0.7432

1,250 0.7427

886 0.7434

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Notes: The table presents regression results for interstate banks over the sample period from 1983.Q3 to 2006.Q3, which includes 20,449 observations. The regression model is yijt ¼ a þ gyijt1 þ bxit4 þ yzjt4 þ ijt ; SEQ CHAPTER where yijt is the nonperforming loan ratio for bank i operating in region j at quarter t; a a common intercept term; yijt1 a lagged value of the dependent variable included to account for its persistence; xit4 a vector of bank-specific variables lagged by four quarters; and zjt4 a vector of region-specific variables, including the coincident indicator, also lagged four quarters. The five model specifications are (i) bank-specific variables only; (ii) bank-specific variables plus regional variables excluding the coincident indicator; (iii) bank-specific variables and all regional variables; (iv) bank-specific variables and just the coincident indicator; and (v) all the prior variables plus the coincident indicator interacted with the bank’s portfolio shares. All regressions are estimated with state dummies and robust standard errors to account for the non-independence of multiple observations on the same bank over time. The estimated coefficients, corresponding t-statistics and F-statistics, and adjusted R2 values are reported for each of the five specifications examined.


(i)

Table 4. Impact of Lagged Bank Control and Regional Variables on Intrastate NPL Ratios.

Coeff.

(ii) t-stat.

Coeff.

(iii) t-stat.

Coeff.

(iv) t-stat.

Coeff.

118

(i)

(v) t-stat.

Coeff.

t-stat.

Log (assets) 0.0004 10.96 0.0003 10.22 0.0003 9.77 0.0004 11.33 0.0003 9.67 Consumer/Total loans 0.0068 15.04 0.0049 11.15 0.0049 11.26 0.0072 15.67 0.0052 8.34 C&I/Total loans 0.0065 17.92 0.0052 12.88 0.0052 12.95 0.0066 17.88 0.0078 13.11 Residential real estate/Total loans 0.0001 0.49 0.0010 3.78 0.0008 3.02 0.0002 0.98 0.0005 1.52 Nonresidential/Total loans 0.0013 4.29 0.0008 2.57 0.0008 2.64 0.0012 4.11 0.0026 5.53 0.8241 172.59 0.8149 154.74 0.8140 153.07 0.8206 167.09 0.8136 153.31 (Nonperforming/Total loans)t1 – – 0.0197 13.88 0.0236 15.81 – – 0.0232 15.48 GDP growtht4 House price growtht4 – – 0.0086 13.79 0.0070 11.41 – – 0.0069 11.10 Personal income growtht4 – – 0.0012 1.32 0.0001 0.08 – – 0.0002 0.24 Employment growtht4 – – 0.0271 16.62 0.0007 0.33 – – 0.0020 0.84 – – 0.0004 14.38 0.0004 14.26 – – 0.0004 14.01 Unemployment ratet4 Coincident indicator growtht4 – – – – 0.0288 17.35 0.0255 24.42 0.0035 0.60 CIt4 Residential real estate/Total loans – – – – – – – – 0.0075 1.20 CIt4 Nonresidential/Total loans – – – – – – – – 0.0536 6.18 – – – – – – – – 0.0084 0.76 CIt4 Consumer/Total loans CIt4 C&I/Total loans – – – – – – – – 0.0816 7.83 Constant 0.0070 16.28 0.0058 13.97 0.0056 13.67 0.0081 17.87 0.0045 10.11 10,805 0.6926

9,806 0.6939

9,345 0.6941

11,465 0.6932

7,247 0.6943

Notes: The table presents regression results for interstate banks over the sample period from 1983.Q3 to 2006.Q3, which includes 489,265 observations. The regression model is yijt ¼ a þ gyijt1 þ bxit4 þ yzjt4 þ ijt ; SEQ CHAPTER where yijt is the nonperforming loan ratio for bank i operating in region j at quarter t; a a common intercept term; yijt1 a lagged value of the dependent variable included to account for its persistence; xit4 a vector of bank-specific variables lagged by four quarters; and zjt4 a vector of region-specific variables, including the coincident indicator, also lagged four quarters. The five model specifications are (i) bank-specific variables only; (ii) bank-specific variables plus regional variables excluding the coincident indicator; (iii) bank-specific variables and all regional variables; (iv) bank-specific variables and just the coincident indicator; and (v) all the prior variables plus the coincident indicator interacted with the bank’s portfolio shares. All regressions are estimated with state dummies and robust standard errors to account for the non-independence of multiple observations on the same bank over time. The estimated coefficients, corresponding t-statistics and F-statistics, and adjusted R2 values are reported for each of the five specifications examined.

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F-value Adj. R2


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5. AGGREGATE EVIDENCE OF A RELATIONSHIP Before examining further the micro-level evidence of a relationship between bank conditions and regional economic performance, it is useful to pin down their association in the aggregate data. We do this simply by testing whether annual growth in the state-level coincident indicators Grangercauses the nonperforming loan ratio aggregated to the state-level. Looking across states, we also test whether the variance in states’ annual growth rates of the coincident indicators Granger-causes the variance of cross-state nonperforming loan ratios. We use eight lags of both the dependent and independent variables in these tests and report the results in Table 5. The results in the top panel provide mixed evidence of the importance of regional indicators in predicting banking condition at the state level, with growth in the coincident indicator Granger-causing the nonperforming loan ratio in 19 states at the 5% significance level. Importantly, there is less evidence that the relationship works the other way; that is, nonperforming loan ratios Granger-caused growth in just 10 states. A much clearer picture emerges for the relationship in the bottom panel between the cross-state variance in CI growth and NPL ratios. The variance in annual growth of the coincident indicator across states Granger-causes the variance in nonperforming loan ratios across states, but the reverse does not hold. There is no evidence of feedback from nonperforming loans to regional economic growth. These results suggest a role for regional indicators in models of bank condition, especially in modeling differences across states over time. Based on these findings, we turn to estimating a reduced-form model of bank performance at the state level that includes bank-specific variables and regional economic conditions. The results also support our research strategy, namely that we move away from forecasting individual bank performance or even absolute bank risk by state, turning to relative rankings by state as our goal.

6. FORECASTS OF RELATIVE STATE RANKINGS OF BANK CONDITION The evidence presented so far provides little hope for using regional information to explain fluctuations in individual bank performance. However, this outcome need not imply that regional variables cannot be

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Table 5. Granger Causality Tests between Annual Coincident Indicator Growth Rates and Nonperforming Loan Ratios at the State level. The Coincident Indicator Does Not Granger Cause Nonperforming Loans F-stat. Top panel: results by state AK 5.30 AL 1.05 AR 1.76 AZ 1.00 CA 1.77 CO 0.45 CT 1.94 DE 2.35 FL 1.15 GA 1.79 HI 1.05 IA 2.05 ID 3.01 IL 2.67 IN 0.98 KS 1.63 KY 2.05 LA 3.88 MA 2.37 MD 6.47 ME 2.62 MI 1.65 MN 0.62 MO 2.43 MS 1.51 MT 1.61 NC 1.75 ND 2.48 NE 3.17 NH 0.63 NJ 1.00 NM 0.95 NV 0.52 NY 1.25 OH 3.51 OK 2.07 OR 2.06 PA 0.88 RI 0.40

Nonperforming Loans Does Not Granger Cause the Coincident Indicator

Probability

F-stat.

Probability

0.00 0.41 0.10 0.44 0.10 0.89 0.07 0.03 0.35 0.09 0.41 0.05 0.01 0.01 0.46 0.13 0.05 0.00 0.03 0.00 0.01 0.13 0.76 0.02 0.17 0.14 0.10 0.02 0.00 0.75 0.45 0.48 0.84 0.28 0.00 0.05 0.05 0.54 0.92

3.69 0.71 1.05 1.87 0.87 0.94 1.56 2.21 2.04 0.77 2.31 2.24 0.38 1.51 0.81 0.74 1.87 0.58 1.35 1.38 0.93 0.93 0.46 0.52 0.68 1.58 1.39 0.48 0.82 0.45 1.17 1.50 1.37 0.59 2.19 1.24 0.75 0.62 2.71

0.00 0.68 0.41 0.08 0.55 0.49 0.15 0.04 0.05 0.63 0.03 0.04 0.93 0.17 0.59 0.65 0.08 0.79 0.24 0.22 0.50 0.50 0.88 0.84 0.71 0.15 0.22 0.87 0.59 0.88 0.33 0.18 0.23 0.78 0.04 0.29 0.64 0.75 0.01


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Table 5. (Continued ) The Coincident Indicator Does Not Granger Cause Nonperforming Loans

SC SD TN TX UT VA VT WA WI WV WY

Nonperforming Loans Does Not Granger Cause the Coincident Indicator

F-stat.

Probability

F-stat.

Probability

1.87 1.41 1.92 1.57 1.85 1.61 2.17 1.29 2.35 3.79 5.85

0.08 0.21 0.07 0.15 0.08 0.14 0.04 0.27 0.03 0.00 0.00

0.48 0.97 0.80 0.60 1.55 0.65 0.94 0.86 2.41 2.26 6.51

0.86 0.47 0.61 0.77 0.16 0.73 0.49 0.55 0.02 0.03 0.00

0.00

0.75

0.65

Bottom panel: variance across states 5.68

Notes: The top panel presents Granger-causality tests between annual coincident indicator (CI) growth rates at the state level and nonperforming loans (NPL) ratios aggregated up to the state level. The annual CI growth rates are calculated as the year-over-year growth rate in the individual states’ coincident indicator as of the fourth quarter of the year. The state-level NPL ratios are calculated as the ratio of the sum of individual banks’ NPL quantities to the sum of their total loans, both aggregated up to the state level using weights based on deposit ratios calculated from the Summary of Deposits. The bottom panel presents Granger-causality tests between the within-year, cross-sectional variances of CI growth rates and state-level NPL ratios. The period examined is from 1983 to 2002. The tests are based on eight lags of each variable. The resulting F-test statistics and their corresponding p-values are presented. The results that reject the null hypothesis at the 5% significance level.

used to understand broader trends in banking sector conditions. To examine this alternative perspective, we focus on forecasting the relative rankings of bank risk, measured as nonperforming loan ratios, by state. Such rankings should be useful to both bankers, who are potentially managing loans to borrowers across the country, and to bank supervisors, who monitor the condition of banks nationwide. Although these rankings abstract from the absolute level of bank risk in a state, they retain a useful amount of relative risk across states at a point in time and across time. Our forecasting exercise proceeds as follows. First, we modify the modeling framework from the earlier part of the paper and estimate a linear probability model of whether or not a bank’s NPL ratio exceeds a

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predetermined level. The new dependent variable is a binary variable equal to one if a bank NPL ratio is greater than 5.4%, which corresponds to the 80th percentile of the empirical distribution of NPL ratios in our data set. Second, we break the full sample into three sub-periods and estimate the models for each sub-period absent the last year. We use the fitted models for each period to forecast the value of the linear probability model for each bank in each sub-period’s out-of-sample year; that is, the four quarters of 1989, the four quarters of 1995, and the first three quarters of 2006, respectively. Note that, in this exercise, we restrict the analysis to the sample of banks with operations in a single state. We denote the forecasted value for bank i headquartered in state j at quarter t+1, conditional on the information available at time t, as y^ ijtþ1 .10 For our linear probability model, the actual numerical values of y^ ijtþ1 are not especially meaningful to the analysis. However, the cardinal ordering of these numerical values allows us to generate state-level risk rankings based on nonperforming loan ratios. To generate state-level ratios of nonperforming loans to total loans, we aggregate across banks in each state at each point in our forecasting periods. That is, the NPL ratio for state j at quarter t+1, denoted as d jtþ1 is calculated as: NPL X Lijtþ1 d NPLjtþ1 ¼ y^ ijtþ1 , Ljtþ1 i2j where Lijt+1 is the total loans for bank i headquartered in state j at quarter t+1 and Ljt+1 the total loans across all banks headquartered in state j at quarter t+1. We construct the actual state problem loan ratios, denoted as NPLjt+1 using the same formula as above, but replacing the y^ ijtþ1 values with the observed NPL ratios for the individual banks. One complication that arises is that the strong economy since the late 1990s has resulted in a sharp reduction in the number of problem loan banks. To guard against the possibility of forecasts of negative probabilities from the linear model, we transform all probability forecasts using the logit transformation, ^ ijtþ1 Þ=ð1 þ expðy^ ijtþ1 ÞÞ. y^ tran ijtþ1 ¼ expðy We generate four sets of forecasted state rankings based on the specifications (i) through (iv) used in Section 4. We assess the accuracy of these forecasted state rankings by examining the extent to which they reproduce the actual rankings of state-level NPL ratios. The degree of forecast accuracy is measured using the Spearman rank correlation test,


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which tests the null hypothesis that the actual and the forecasted rankings are independent. If we reject the null hypothesis, then the model generating the forecasts is accurately characterizing the underlying economic relationships. Please note that all of these correlation coefficients, as presented in Table 6, are significant at the 5% level, except for the forecasts for 2006. The most likely reason for the lack of significance for the 2006 forecasts is the large degree of consolidation that occurred in the U.S. banking system between 1995 and 2006. To consider the importance of the regional indicators, we look to see whether the forecasted rankings are different, depending on the inclusion of the coincident indicator in the forecasting model. The findings show that regional variables do little to improve forecasts of state-level bank risk;

Table 6.

Spearman Rank Correlations between Actual and Forecasted State-level Problem Loan Ratios for Intrastate Banks.

Quarter

(i)

(ii)

(iii)

(iv)

1989.Q1 1989.Q2 1989.Q3 1989.Q4

0.9386 0.9088 0.8709 0.8773

0.9462 0.9264 0.9091 0.8949

0.9443 0.9054 0.8801 0.8897

0.9343 0.8999 0.8507 0.8656

1995.Q1 1995.Q2 1995.Q3 1995.Q4

0.8742 0.8501 0.8599 0.8337

0.8350 0.8036 0.7742 0.7454

0.8443 0.8005 0.8492 0.8939

0.8522 0.8160 0.8752 0.9075

2006.Q1 2006.Q2 2006.Q3

0.3266 0.2404 0.2059

0.2906 0.1755 0.1283

0.2357 0.1517 0.1020

0.2859 0.2284 0.1920

Notes: The forecasted state-level NPL ratios are constructed as the weighted average of a state’s individual banks’ fitted values from a simple linear probability model of whether their NPL ratios are above 5.4%, the full sample’s 80th percentile. The weights are the individual bank’s total loans to the total loans for all the state’s banks. The actual state-level NPL ratios are constructed as the ratio of the aggregated values across a state of non-performing loans and total loans. The results are compared using the Spearman rank correlation test, which tests the null hypothesis that the actual and the forecasted rankings are independent. The columns correspond to four model specifications: (i) bank-specific variables only; (ii) bank-specific variables plus regional variables excluding the coincident indicator; (iii) bank-specific variables and all regional variables; and (iv) bank-specific variables and just the coincident indicator. The out-of-sample results are for each quarter of the final year of each sub-period. Statistically significant.

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i.e., the correlations in column (iv) are not measurably different from those in column (i) for any of the out-of-sample forecast quarters. However, it is also true that the coincident indicator never does measurably worse than the models that incorporate actual regional variables. This seems to be the general message. Out of sample, a series such as the coincident indicator that collects the trend common to a variety of regional indicators is just as accurate as the original series themselves. Hence, the coincident indicator may still be considered useful, especially since it is available at a higher frequency and on a closer to real-time basis than most regional economic series.

7. CONCLUSION In summary, our work points to a clear link between bank conditions, measured by nonperforming loan ratios, and state-level coincident indicators and other regional variables. The statistical significance and economic relevance of the coincident indicator remains stable across sub-samples of inter- and intra-state banks. In general, the coincident indicator performs at least as well as employment growth and outperforms other measures of regional conditions. Moreover, it appears to capture important and tractable interactions among the included regional variables that would otherwise be relegated to the state fixed effect or the residual.

NOTES 1. The term ‘‘local’’ economic conditions refers broadly to the county or state in which a bank is headquartered. For this study, the economic variables summarizing local economic conditions will be at the state level, but it is still reasonable to assume that they capture certain national developments. For example, Carlino and DeFina (1998, 1999) found that regions, such as New England and the Southeast, and states exhibit different degrees of sensitivity to national monetary policy changes. 2. The authors limited their bank sample to small rural banks (i.e., those with less than $300 million in assets located outside of a metropolitan statistical area) in the Eighth District of the Federal Reserve System. The four bank performance ratios that they examined were the ratio of nonperforming loans to total loans, the ratio of net loan losses to total loans, the ratio of other real estate owned to total assets, and adjusted return on assets (i.e., net income plus provisions divided by total assets). The county and state variables used were unemployment rates, employment growth, personal income growth, and per capita personal income growth. Note that they used a Tobit regression for the first and third bank variables.


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3. Their dependent variable reflecting bank performance is the supervisory CAMELS ratings. The bank-specific variables included in their regressions were the logarithm of total assets, lagged CAMELS ratings, the ratio of capital to total assets, the ratio of nonperforming loans to total assets, the ratio of net income to total assets, the ratio of liquid assets to total assets, the ratio of C&I lending to total assets, the ratio of CRE lending to total assets, the ratio of residential real estate lending to total assets, the ratio of other real estate owned to total assets, the ratio of long-term deposits to total assets, and the ratio of 30-day past-due loans to total assets. The state-level regional economic variables they used were payroll employment growth, residential house price appreciation, and total personal income growth. 4. See the chapters by Jayaratne and Strahan (1996) and Morgan, Rime, and Strahan (2004) for research on the impact of banking deregulation on local economic variables. 5. Crone (1994) originally constructed his state indexes based on four monthly data series – the total number of jobs in nonagricultural establishments, real retail sales, average weekly hours in manufacturing, and the unemployment rate. 6. These series have been made publicly available by the Federal Reserve Bank of Philadelphia at http://www.phil.frb.org/econ/stateindexes/index.html 7. For SOD purposes, the FDIC collects deposit balances for commercial and savings banks as of June 30 each year. For insured commercial banks and FDICsupervised savings banks, the definition of deposit is the same as in the Consolidated Report of Condition. The definition relates to domestic deposits held, or accepted, by the reporting bank in its main office and in any branch located in any State, the District of Columbia, the Commonwealth of Puerto Rico, or any U.S. territory or possession which include but are not limited to Guam and the U.S. Virgin Islands. 8. An alternative specification would be to do the estimation in two stages, in which the first stage regresses the bank performance variable on bank-specific variables and 50 state dummies for each quarter, and the second stage regresses the state dummies on regional economic indicators (see Card & Krueger, 1992; Hanushek, Rivkin, & Taylor, 1996). 9. The analysis in Table 2 was repeated including bank fixed effects. Except the growth in personal income, all coefficients on the economic variables have the same expected signs and are statistically significant at conventional levels. 10. Note that y^ ijtþ1 is neither an indicator variable, like our dependent variable, nor is it a true probability, since its support is not limited to the unit interval. Instead, y^ ijtþ1 is a relative value that indicates proximity to the 5.4% nonperforming loan ratio that we selected; that is, higher values of y^ ijtþ1 indicate that bank i is more likely to be above the threshold, while lower values of y^ ijtþ1 indicate that the bank is more likely to be below the threshold.

ACKNOWLEDGMENTS The views expressed in this chapter are those of the authors and not necessarily those of the Federal Reserve Bank of San Francisco or the Federal Reserve System. We thank seminar participants at the Conference

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on the Use of Composite Indices in Regional Economic Analysis, the Federal Reserve System conferences on banking and regional studies as well as Robert Avery, Fred Furlong, Andy Haughwout, Robert Hunt, Simon Kwan, Leonard Nakamura, Marc Saidenberg, James Stock, and Rob Valletta for helpful comments. We thank Liz Laderman for sharing the SOD data with us, Anita Todd for editorial assistance, and Jackie Yuen and Ashley Maurier for excellent research assistance.

REFERENCES Avery, R., & Gordy, M. (1998). Loan growth, economic activity, and bank performance. Manuscript, Board of Governors of the Federal Reserve System. Berger, A. N., Bonime, S. D., Covitz, D. M., & Hancock, D. (2000). Why are bank profits so persistent? The roles of product market competition, informational opacity and regional/ macroeconomic shocks. Journal of Banking and Finance, 24, 1203–1235. Calomiris, C. W., & Mason, J. R. (2000). Causes of U.S. bank distress during the depression. NBER Working Paper no. 7919. Card, D., & Krueger, A. (1992). School quality and black-white relative earnings: A direct assessment. The Quarterly Journal of Economics, 107(1), 151–200. Carlino, G., & DeFina, R. (1998). The differential regional effects of monetary policy. Review of Economics and Statistics, 80, 572–587. Carlino, G., & DeFina, R. (1999). The differential regional effects of monetary policy: Evidence from the U.S. states. Journal of Regional Science, 39, 339–358. Crone, T. M. (1994). New indexes track the state of the states. Federal Reserve Bank of Philadelphia Business Review (January/February), 19–31. Crone, T. M. (1999). Using state indexes to define economic regions in the United States. Working Paper no. 1999-19. Federal Reserve Bank of Philadelphia. Crone, T. M. (2004). Consistent economic indexes for the 50 States. Working Paper no. 2004–09. Federal Reserve Bank of Philadelphia. Hanushek, E., Rivkin, S., & Taylor, L. (1996). Aggregation and the estimated effects of school resources. The Review of Economics and Statistics, 78(4), 611–627. Jayaratne, J., & Strahan, P. E. (1996). The finance-growth nexus: Evidence from bank branch deregulation. Quarterly Journal of Economics, 111, 639–670. Jordan, J. S., & Rosengren, E. S. (2002). Economic deterioration and bank health. Manuscript, Federal Reserve Bank of Boston. Meyer, A. P., & Yeager, T. J. (2001). Are small rural banks vulnerable to local economic downturns? Federal Reserve Bank of St Louis Review, 83(2), 25–38. Morgan, D. P., Rime, B., & Strahan, P. E. (2004). Bank integration and business volatility. Quarterly Journal of Economics, 119, 1555–1584. Morgan, D. P., & Samolyk, K. (2003). Geographic diversification in banking and its implications for bank portfolio choice and performance. Manuscript, Research and Market Analysis Group, Federal Reserve Bank of New York.


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Nuxoll, D. A., O’Keefe, J., & Samolyk, K. (2003). Do local economic data improve off-site bank monitoring models? FDIC Banking Review, 15(2), 39–53. Stock, J. H., & Watson, M. W. (1989). New indexes of coincident and leading economic indicators. NBER Macroeconomics Annual (9), 351–394. Zimmerman, G. (1996). Factors influencing community bank performance in California. Federal Reserve Bank of San Francisco Economic Review (1), 26–42.

WHO BENEFITS MORE FROM GLOBAL DIVERSIFICATION? AN OVER-TIME PERSPECTIVE Wan-Jiun Paul Chiou ABSTRACT This chapter investigates the relative magnitude of the benefits of global diversification from the viewpoint of domestic investors in various countries by forming time-rolling efficient frontiers. To enhance feasibility of asset allocation strategies, the constraints of short-sales and over-weighting investments are taken into account. The empirical results suggest that local investors in less developed countries, particularly in Latin America, East Asia, and Southern Europe, comparatively benefit more from global diversification. Investors in the countries of civic-law origin tend to benefit more from global investment than the ones in the common-law states. Although the global market has become more integrated over the past decades, diversification benefits for domestic investors declined but did not vanish. The results of this chapter are useful for asset management professionals to determine target markets to promote the sales of international funds.


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1. INTRODUCTION This chapter is to empirically examine the relative magnitude of global diversification benefits for domestic investors in countries at different developmental stages, in various regions, and of dissimilar legal origins by forming efficient frontiers over time. Previous researches investigate the strategies of optimal portfolio allocation and confirm the benefits of global diversification for domestic investors in developed countries, particularly those in the United States.1 However, the comparison of the benefits of global diversification for local investors in different countries was not yet explored. Moreover, since the world financial market has increasingly integrated, it is natural to examine how the relative size of diversification benefits for local investors changed over time. To enhance the feasibility of strategies, the impact of disproportional asset allocation on the global optimal portfolio is taken into account in this chapter. The answers to the above issues provide critical insights to financial professionals. The countries in which domestic investors receive comparatively higher benefits from global investment represent potential target markets for the asset management industry because of local investors’ stronger incentive for overseas diversification. The analyses of global diversification benefits discussed in this chapter are different from previous studies in three dimensions. First, differing from previous studies that focus on the strategies and gains from the viewpoint of the U.S. investor, this chapter emphasizes the global diversification benefits to domestic investors in various countries. For local investors in developing countries with less investment selections, global diversification may be more important than for the investors in developed countries. To reduce the bias caused by the departure from normality of parameters, the non-parametric Mann–Whitney test is implemented to test the cross-national difference in the global diversification benefits. Second, the infeasibility of strategies caused by over-weighting (OW) investment in small markets is considered when the benefits of diversification are computed. Previous researches document that the benefits of global diversification are not completely eroded by short-sale (SS) constraints.2 However, when investors determine the asset allocation, they generally consider the relative magnitude of market values since it associates to the liquidity of portfolio. It is well-known that investors may not necessarily allocate assets internationally by completely following the optimal efficient frontier proposed by Markowitz (1952) due to the lack of investibility in certain nations.3 If the weights on small markets are too large, the strategies

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merely with the constraints of non-negative weights are not practicable. The efficient frontiers with the constraints of short-sales and over-weighting investments allow international investors to generate more feasible strategies. Third, this chapter examines the dynamics in diversification gains and the variation of portfolio weighting. In past decades, the correlations in the international market increased, and the domestic expected returns in most countries declined (Bekaert & Harvey, 2003; Bekaert, Harvey, & Ng, 2005). The former has a negative effect, while the latter has a positive impact on the global diversification benefits to domestic investors. Given the mixed influences discussed above, the long-term trend of international diversification benefits is not clear a priori. Consequently, a thorough empirical investigation is desired. The time series analysis of potential gains helps to determine whether international diversification still benefits domestic investors when the world capital market is increasingly integrated. To appropriately estimate the gains of international diversification from the perspective of local investors, two straightforward measures are utilized. The first one is the increase in risk-adjusted premium by substituting the local portfolio as the maximum Sharpe ratio (MSR) portfolio (MSRP) on the international efficient frontier.4 This gauge is to reflect the motivation of investors who wish to maximize the mean-variance efficiency of their portfolios. The second one is the reduction in the standard deviation by replacing the domestic portfolio as the international minimum variance portfolio (MVP). This measurement is to correspond to investors’ demand to decrease portfolio risk via global diversification. This chapter investigates the relative economic value of global diversification for domestic investors in countries at different developmental stages and in various regions. The advantages of international diversification between two major legal origins are also compared. La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998) and Stulz and Williamson (2003) find that the legal origin of a country’s law system helps explain the degree of investor protection in that state. It is widely regarded that the so-called Anglo-Saxon model, or common-law system, is more appropriate for protecting the rights of investors than the civic-law system. As the capital flows become more international, the design of protection of investor rights is an important factor for investors determining global asset allocation. The empirical results suggest that domestic investors in emerging markets, particularly in Latin America, East Asia, and Southern Europe, comparatively benefit more from global diversification than those in developed countries. Investors in the countries of civic-law origin enjoy relatively greater benefits from global diversification than the ones in the states of common-law origin.

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This result holds under more restrictive investment restrictions on weights. On average, the global diversification benefits slightly decrease as the world financial market became more integrated after the late 1980s. The time series analyses of portfolio weights show that the installation of over-weighting investment constraints and enhance feasibility of asset allocation strategies. The chapter is organized as follows. Section 2 reviews the literature on the benefits of international diversification. Section 3 describes how we estimate the benefits of global diversification under various investment constraints. The data used in this study are described in Section 4. Section 5 reports the major empirical results of the over-time international comparison of diversification benefits. The examinations of globally diversifying portfolio weights are reported in Section 6. Section 7 presents the conclusions and discusses relevant issues.

2. LITERATURE REVIEWS Previous empirical evidence confirms the improvement of the mean-variance efficiency of a portfolio by diversifying internationally. Bekaert and Urias (1996), De Roon, Nijman, and Werker (2001), Harvey (1995), and Li, Sarkar, and Wang (2003) suggest that U.S. investors benefit from improved investment performance by including emerging markets into a portfolio that is originally constructed of stocks from developed countries. Cosset and Suret (1995) find that including securities from high-political-risk countries into the portfolio can increase mean-variance efficiency. The constraints on international investment challenge, but do not entirely extinguish, the benefits brought by global diversification. Harvey (1995), Li et al. (2003), and Pa´stor and Stambaugh (2000) confirm the benefits of international diversification even when short-sales are not allowed. Considering geographical restrictions, De Roon et al. (2001) find that investors in East Asia and Latin America still can generate benefits from diversifying their portfolios by investing in other countries in Latin America. Jagannathan and Ma (2003) investigate the impacts of imposing short-sales and upper-bound investment constraints on mean-variance efficiency and portfolio risk. Errunza, Hogan, and Hung (1999) find that U.S. investors can utilize domestically traded American Depositary Receipts (ADRs) to duplicate the benefits of international diversification. The degree of international market integration is one of the important factors that are associated with the effectiveness of international diversification. Bekaert and Harvey (1995), Bekaert et al. (2005), De Jong and De Roon (2005), and Errunza, Losq, and Padmanabhan (1992) suggest that the


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world market is mildly segmented and that the degree of global market integration varies throughout time.5 The integration of international financial markets, in general, has gradually increased, but the emerging markets are still more segmented than are developed countries. On the other hand, although Campbell, Lettau, Malkiel, and Xu (2001) find that stock price movements are becoming more synchronized, this does not necessarily imply the disappearance of the benefits of diversification. Statman and Scheid (2005) suggest that the cross-sectional dispersion for asset returns affects the effectiveness of diversification. The institutional and cultural heterogeneities among countries are key factors in explaining a non-synchronous movement of security prices among markets. Beck, Demirgu¨c- -Kunt, and Levine (2003) and Demirgu¨c- -Kunt and Maksimovic (1998) suggest that the international differences of financial markets can be explained by natural endowments. Stulz and Williamson (2003) indicate that the liberalization and development of financial markets relate to the cultural background, such as major religion and language. Bekaert and Harvey (2003) report the major characteristics of emerging markets and their chronological innovations since the late 1970s. Finally, Beck et al. (2003), Demirgu¨c- -Kunt and Maksimovic (1998), La Porta et al. (1998), and Stulz and Williamson (2003) find that the legal origin is associated with the development of the financial market. The differences in cultural background, natural endowments, institutional systems, and legal tradition deter integration of international financial markets so that investors may generate gains from overseas diversification. In sum, previous studies document the benefits of global diversification with constraints such as short-sales. The increase in correlations of international financial markets does not completely eliminate the benefits because of the dispersion of returns among countries. The difference of cultures, natural endowments, and institutional systems among markets cause the dispersion of returns among markets. The gap of understanding regarding the cross-nation comparisons on the benefits of constrained international diversifications needs to be filled.

3. MEASURES OF THE GLOBAL DIVERSIFICATION BENEFITS The maximum increase in risk-adjusted performance and the greatest reduction in volatility brought by the optimal global portfolios are used to estimate the benefits of diversification for domestic investors. To enhance the

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feasibility of asset allocation, the constraints such as short-sale and overweighting investment are taken into account. The time series of diversification benefits with various weighting restrictions are obtained by the time-rolling international efficient frontiers formed by the monthly returns in five years. Suppose a representative investor would like to minimize the volatility of her portfolio, given the same return, by allocating funds among international markets. The investment opportunities can be characterized as a vector of multivariate Gaussian stochastic returns of N international assets: RT ¼ ½r1 ; r2 ; . . . ; rN

(1)

The expected returns in excess of the risk-free interest rate and the variance–covariance of asset returns can be expressed as a vector lT ¼ ½m1 ; m2 ; . . . ; mN and a positive definite matrix V, respectively. Let S be the set of all real vectors wT ¼ ½w1 ; w2 ; . . . ; wN that define the weight of each asset such that wT 1 ¼ w1 þ w2 þ . . . þ wN ¼ 1, where 1 is an N vector of ones. Suppose the best predictors of expected returns, variances, and covariances among assets are their past averages. This non-risk-loving investor thus follows the method of Markowitz (1952) to form the global efficient frontier by using the monthly returns in the previous five years. Combining the objective function and restrictions, the determination of optimal portfolio is then expressed as a Lagrangian: 1 minfw;f;Zg X ¼ wT Vw þ fðmp wT lÞ þ Zð1 wT 1Þ 2

(2)

where mp denotes the expected return on the portfolio, and the shadow prices f and Z are two positive constants. The quadratic programming solution for asset spanning, wp, can be obtained by the first-order conditions of Eq. (2). The negative portfolio weights, i.e., short-selling assets, are permitted in this setting. The subset Pk is defined as the array of achievable portfolio weights with various investment constraints. If there are no restrictions on asset allocation, then P0=S. To make the optimal portfolio more realistic, various investment constraints are added. It is well known that short-selling is not allowed for foreign investors in many countries, particularly in less developed nations.6 The restriction of non-negative weights is incorporated in the system of Lagrangian in Eq. (2). Since the incentives of international diversification are not only to seek higher yields but also to reduce volatility, an investor who desires to maximize risk-adjusted performance will select


the MSRP on the efficient frontier. The MSR is n o MSR ¼ maxfwp g ðwTp lÞ=ðwTp Vwp ÞwTp 2 P1

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(3)

where P1 ¼ fwp 2 S : 0 wi 1; i ¼ 1; 2; . . . ; Ng. One should not have a problem constructing the portfolio that yields the highest risk-adjusted premium on the international efficient frontier by allocating capital according to the weights of the MSRP. Furthermore, the over-weighting investment constraints are taken into consideration. Specifically, the investor considers the relative magnitude of market capitalization in each country when determining global asset allocation. The subset of portfolio weights PJ with constraints SS+OW(U) can be described as PJ ¼ wp 2 S : 0 wi UwðCapÞi 1; i ¼ 1; 2; . . . ; N ; U41 (4) where w(Cap)i is the proportion of the market value of each country i in the world, and U is any real number greater than 1.7 Differing from Jagannathan and Ma (2003), in this chapter, the upper bound is explicitly determined by the share of market value in the world. Therefore, the MSR on the constrained international efficient frontiers is n o MSRJ ¼ maxfwp g ðwTp lÞ=ðwTp Vwp Þ1=2 wTp 2 PJ

(5)

There are three reasons that international investors need to consider the unattainability of short-sale and excessive investments. First, when making decisions regarding the fund allocations in international assets, investors not only consider the profitability but also take into account marketability of investment targets. The centralization of funds in the minor markets may cause the illiquidity of a portfolio. Second, the excessive foreign capital inand out-flows in small markets may trigger volatility in asset values, which may generate dramatic changes of mean-variance efficiencies and correlations among international financial markets. Finally, in many countries, foreign investors are prohibited to short-sell and to hold more than a certain proportion of company shares.8 It is particularly true in most developing countries. A large percentage of foreign capital allocation on the investing vehicles in those small markets may be impractical from legal and institutional aspects. Accordingly, the strategies that consider boundaries of weights are more realistic.

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Differing from studies by De Roon et al. (2001), Li et al. (2003), and Wang (1998) that utilize the change of raw return to measure benefits, we use the increase in risk-adjusted premiums. For a local investor in any country, the increment of unit-risk-return brought by international diversification is di;J ¼ MSRJ SRi

(6)

where SR is the Sharpe ratio for country is domestic portfolio and J denotes the various investment constraints. The other measurement for the benefits of diversification is the greatest reduction in volatility as a result of global diversification. Elton and Gruber (1995) suggest that investors may seek to minimize the variance of a portfolio because of the lack of predictability of expected returns. In this case, one may want to invest in the MVP. The weighting of the MVP can be characterized as n h io wMVP;J ¼ wp : minfwp g wTp Vwp wTp 2 PJ (7) where PJ can be various domains of portfolio weights on the efficient frontiers. Following the methodologies suggested by Li et al. (2003), the maximum decline in volatility by diversifying internationally with various investment constraints is h i1=2 i;J ¼ 1 wTMVP;J VwMVP;J =V i (8) In this study, the global efficient frontiers and the Sharpe ratio are estimated by using monthly returns in five years. The time series of di,J and ei,J for domestic investors with various investment constraints can be generated by rolling over the asset returns in the next periods. The weightings for the MSRP and the MVP in each period are also calculated.

4. DATA This study utilizes the U.S. dollar-denominated monthly returns of the Morgan Stanley Capital International (MSCI) indices for 21 developed countries and 13 developing countries from January 1988 to December 2005. The data of market values are obtained from the World Federation of Exchanges. Table 1 lists the countries, their average growth rates for market

Country

countries 14.81 15.14 12.72 14.96 13.09 10.16 14.28 19.11 24.37 13.13 9.60 14.97 16.12 15.04 5.36 10.24 20.00 8.14 13.62 14.39 10.75

Cap Weight (%)

Mean Return

2.08 0.33 0.78 3.83 2.41 3.15 0.48 2.48 0.54 4.20 7.89 2.72 0.29 2.06 11.80 1.23 0.49 0.10 0.66 1.14 43.88

0.113 0.087 0.081 0.107 0.124 0.096 0.137 0.105 0.114 0.111 0.093 0.125 0.099 0.077 0.009 0.117 0.116 0.067 0.084 0.136 0.114

Legal Origin

Common Civil Civil Common Civil Civil Civil Civil Civil Civil Common Common Common Civil Civil Civil Civil Common Common Civil Common

Region

Oceania C/W Europe C/W Europe N. America C/W Europe C/W Europe C/W Europe C/W Europe N. Europe C/W Europe C/W Europe E. Asia C/W Europe S. Europe E. Asia C/W Europe N. Europe Oceania E. Asia N. Europe N. America

Sharpe Ratio Median

Std. dev.

Max

Time

0.001 0.091 0.020 0.024 0.117 0.046 0.060 0.005 0.081 0.057 0.025 0.002 0.002 0.010 0.089 0.122 0.015 0.034 0.023 0.013 0.114

0.069 0.134 0.127 0.093 0.151 0.111 0.093 0.116 0.162 0.091 0.133 0.115 0.140 0.083 0.060 0.158 0.090 0.136 0.107 0.128 0.171

0.201 0.392 0.376 0.219 0.411 0.309 0.312 0.295 0.375 0.254 0.291 0.251 0.372 0.179 0.048 0.360 0.241 0.254 0.223 0.341 0.393

Dec-05 Dec-05 Aug-98 Sep-00 Mar-98 Jul-98 Apr-98 Aug-98 Jan-93 Jan-00 Mar-98 Sep-94 May-98 Apr-98 Jul-97 Jun-98 Jan-98 Nov-05 Feb-96 Mar-00 Jan-00

Min

0.122 0.172 0.196 0.169 0.197 0.199 0.142 0.145 0.261 0.139 0.293 0.145 0.200 0.163 0.240 0.213 0.183 0.249 0.190 0.139 0.147

Time

Oct-01 Jun-00 Apr-03 Aug-94 Apr-03 Apr-03 Apr-03 Aug-93 Apr-00 Apr-03 Apr-03 Oct-02 Mar-03 Apr-03 Sep-98 Apr-03 Oct-02 Dec-00 Sep-98 Oct-02 Apr-05

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Panel A: Developed Australia Austria Belgium Canada Switzerland Germany Denmark Spain Finland France UK Hong Kong Ireland Italy Japan Netherlands Norway New Zealand Singapore Sweden USA

Cap Growth (%)

Capitalization and Performance of Markets.


Table 1.

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Table 1. (Continued ) Country

Cap Growth (%)

Panel B: Emerging markets Argentina 7.48 Brazil 19.78 Chile 12.48 Greece 22.19 Indonesia 15.84 Korea, S. 15.72 Malaysia 5.37 Mexico 4.28 Philippines 7.62 Portugal 16.08 Thailand 6.11 Turkey 24.10 Taiwan 12.74

Cap Weight (%)

Mean Return

0.12 1.23 0.35 0.37 0.21 1.85 0.47 0.62 0.10 0.17 0.32 0.42 1.23

0.185 0.193 0.182 0.133 0.082 0.077 0.064 0.223 0.223 0.045 0.060 0.129 0.062

Legal Origin

Civil Civil Civil Civil Civil Civil Common Civil Civil Civil Common Civil Civil

Region

L. America L. America L. America S. Europe E. Asia E. Asia E. Asia L. America E. Asia C/W Europe E. Asia S. Europe E. Asia

Sharpe Ratio Median

Std. dev.

Max

Time

0.019 0.024 0.046 0.009 0.064 0.042 0.013 0.045 0.104 0.041 0.002 0.004 0.040

0.101 0.089 0.173 0.105 0.108 0.079 0.126 0.133 0.171 0.127 0.141 0.064 0.065

0.165 0.230 0.368 0.229 0.149 0.206 0.233 0.437 0.266 0.283 0.213 0.143 0.122

Mar-94 Jul-97 Nov-94 Oct-99 Dec-05 Dec-05 Jan-94 Feb-94 Oct-95 May-98 Jan-94 Jan-94 Sep-97

Min

0.235 0.181 0.217 0.180 0.279 0.239 0.272 0.131 0.269 0.242 0.273 0.136 0.174

Time

Jun-02 Oct-02 Oct-02 Jul-95 Oct-98 Jan-98 Nov-98 Feb-99 Nov-01 May-03 Sep-98 Feb-95 Oct-02

WAN-JIUN PAUL CHIOU

Notes: The growth rate of capitalization during the period of 1992:12–2005:12 and the world capitalization weight as of the end of 2005 in each country are reported. The mean of raw return for each market from 1988:01 to 2005:12 is annualized. The legal origin variables are obtained from La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998). The mean, median, standard deviation, maximum, and minimum of the time series of the monthly Sharpe ratio for each market are also presented.


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values from 1992 to 2005, legal origins, and the percentages of world market capitalization as of the end of 1992, 1999, and 2005. The legal origin variables are obtained from La Porta et al. (1998). The value-weighted average growth rate of market capitalization for all countries during the sample period is 10.6%. For our sample, the countries of the largest growth in market value were Finland, Turkey, Greece, Norway, Brazil, and Spain. On the other hand, Mexico, Japan, Malaysia, and Thailand are of the lowest growth rates. The variation within each group of countries at different developmental stages and in various areas is considerable. Over the sample period, the stock markets in developed countries consistently represent more than 90% of world equity market value. The countries are grouped into seven geographical regions: Central/ Western Europe, Northern Europe, Southern Europe, East Asia, North America, Latin America, and Oceania. Market capitalization is weighted heavily on three major continents: North America, Europe, and East Asia. The relative sizes of equity markets among countries fluctuated over the period. As of the end of 2005, the seven largest markets by country are the U.S., Japan, U.K., France, Canada, Germany, and Hong Kong. Overall, they account for about four-fifths of equity market values in the world. Among them, the U.S. market continuously is of the largest capitalization during the sample period, though the proportion of market value varied over time. On the other hand, the capitalization of the emerging markets is relatively small. As of the end of 2005, Brazil, Korea, and Taiwan are the only developing countries with a world capitalization share greater than 1%. Table 1 also presents summary statistics of the annualized return and monthly Sharpe ratio for each country. For our sample, the raw return of stock markets in developing countries, in general, is higher than the stock markets in developed countries. However, the cross-region difference in returns among emerging markets is considerable. The stock prices in Latin America outperformed the ones in other areas, while the countries in East Asia performed worse than the rest of the world. Owing to its long-term economic recession, Japan is the country of lowest return during the sample period. In addition, the Sharpe ratios in developed countries, on average, are higher than the ones in the emerging markets. The countries of the maximum mean-variance efficient domestic portfolio are the U.S., Switzerland, the Netherlands, and Finland. It is consistent with the previous findings that the mean-variance efficiency of equity prices in emerging markets is lower due to their higher volatility. The medians of monthly Sharpe ratios for three developed countries (Austria, Japan, and

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New Zealand) and eight developing countries (Argentina, Indonesia, Korea, Philippines, Portugal, Thailand, Turkey, and Taiwan) are negative. The time variation in risk-adjusted performance in each stock market is also presented. The averages of the standard deviation of Sharpe ratio for the developed countries and emerging markets are 0.118 and 0.114, respectively. Compared to the medians of Sharpe ratio, the range of the unit-risk return of each market during the sample period is considerable. Among each group of countries categorized by developmental stages or geographical regions, the periods for the highest and lowest Sharpe ratios disperse significantly. For the developed countries, the maximum domestic Sharpe ratio most likely occurred in three years: 1994, 1998, and 2005. For most emerging markets, the greatest Sharpe ratios came about before 1998. For all countries, the years with the large number of minimum Sharpe ratios are 1998, 2002, and 2003. The local investors in most emerging markets generated the worst risk-adjusted performance in 1998 and the ones in developed countries get the lowest in 2002 and 2003. This is because the emerging markets lost a great deal of value in the financial crises while the evaporation of high-tech bubbles after 2000 and an economic recession caused by the terrorist attack against the U.S. in 2001 had a great impact on the equity markets’ performance in the developed countries. Overall, the risk-adjusted performances of stock prices demonstrate diverse movements among markets. The non-synchronism of mean-variance efficiency across countries implies the potential gains to domestic investors by diversifying their portfolios globally. For instance, in Table 1, there are 10 markets of the best riskadjusted performance and six markets of the worst in 1998. Similarly, four countries had the highest Sharpe ratio and three countries had the lowest in 2000. This suggests that the cross-market performances differ drastically within the same year, and local investors may avoid loss in their home markets by allocating their funds optimally in other countries. Table 2 shows the means of the unconditional correlation coefficients of each country with all other markets and with countries grouped by regions in two sub-periods. The developed countries, in general, demonstrate higher correlations with the other markets than the emerging markets. Most countries also have the highest coefficients of correlation with the other countries of the same region and with the ones in North America. The magnitudes of correlations increase over time, however, the phenomena that the emerging markets are less correlated with other countries can be constantly observed in the two sample periods. The fact that most markets are less correlated with the countries from other regions indicates possible diversification benefits from

World Average

1988–1996

1997– 2005

1988– 1996

1997– 2005

0.55 0.43 0.45 0.56 0.51 0.57 0.50 0.57 0.40 0.59 0.56 0.47 0.48 0.49 0.38 0.58 0.54 0.48 0.47 0.55 0.56

0.14 0.07 0.06 0.13 0.02 0.01 0.01 0.22 0.12 0.10 0.06 0.17 0.09 0.05 0.06 0.02 0.14 0.06 0.15 0.13 0.19

0.58 0.39 0.32 0.61 0.40 0.52 0.47 0.56 0.37 0.50 0.51 0.55 0.43 0.46 0.34 0.49 0.58 0.44 0.55 0.52 0.57

North America

1988– 1996

0.43 0.17 0.41 0.65 0.39 0.33 0.27 0.40 0.33 0.40 0.51 0.49 0.40 0.29 0.26 0.51 0.41 0.28 0.48 0.44 0.65

East Asia

Central/Western Europe

Northern Europe

Southern Europe

1988– 1996

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

0.66 0.41 0.48 0.79 0.58 0.71 0.65 0.66 0.60 0.72 0.70 0.57 0.58 0.56 0.50 0.68 0.66 0.51 0.57 0.71 0.79

0.25 0.30 0.26 0.34 0.25 0.26 0.20 0.29 0.27 0.24 0.29 0.41 0.33 0.25 0.21 0.30 0.24 0.22 0.52 0.31 0.29

0.53 0.31 0.23 0.47 0.33 0.36 0.31 0.38 0.25 0.35 0.38 0.54 0.32 0.26 0.40 0.38 0.39 0.48 0.57 0.39 0.45

0.29 0.42 0.51 0.33 0.50 0.58 0.49 0.51 0.32 0.53 0.54 0.34 0.51 0.38 0.40 0.61 0.46 0.27 0.44 0.50 0.39

0.54 0.56 0.68 0.58 0.69 0.73 0.65 0.71 0.46 0.76 0.70 0.40 0.61 0.66 0.36 0.76 0.63 0.48 0.37 0.66 0.62

0.43 0.34 0.35 0.39 0.38 0.42 0.45 0.55 0.55 0.35 0.54 0.35 0.50 0.40 0.38 0.51 0.55 0.39 0.45 0.57 0.40

0.57 0.39 0.47 0.67 0.55 0.69 0.59 0.63 0.55 0.73 0.63 0.43 0.51 0.59 0.40 0.65 0.54 0.47 0.42 0.65 0.65

0.04 0.34 0.16 0.02 0.17 0.19 0.15 0.18 0.03 0.17 0.10 0.10 0.22 0.15 0.06 0.16 0.10 0.12 0.17 0.19 0.00

1997– 2005

0.40 0.34 0.37 0.45 0.40 0.52 0.38 0.51 0.43 0.53 0.48 0.26 0.43 0.49 0.24 0.47 0.49 0.39 0.31 0.53 0.46

Oceania

1988– 1996

0.66 0.22 0.15 0.42 0.27 0.22 0.19 0.42 0.38 0.23 0.45 0.30 0.34 0.19 0.26 0.39 0.38 0.66 0.37 0.47 0.29

1997– 2005

0.70 0.52 0.42 0.63 0.52 0.54 0.46 0.58 0.41 0.55 0.57 0.55 0.53 0.46 0.52 0.55 0.61 0.70 0.60 0.55 0.54

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Panel A: Developed countries AUS 0.28 AUT 0.31 BEL 0.32 CAN 0.31 CHE 0.32 DEU 0.35 DNK 0.30 ESP 0.39 FIN 0.28 FRA 0.33 GBR 0.38 HKG 0.33 IRL 0.37 ITA 0.28 JPN 0.27 NLD 0.40 NOR 0.34 NZL 0.25 SGP 0.40 SWE 0.38 USA 0.32

Latin America

Coefficients of Correlation among Markets.


Table 2.

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Table 2. (Continued ) World Average

1988–1996

Panel B: Emerging markets ARG 0.06 BRA 0.10 CHL 0.08 GRC 0.19 IDN 0.14 KOR 0.15 MAL 0.33 MEX 0.16 PHL 0.27 PRT 0.28 THL 0.28 TUR 0.09 TWN 0.15

1997– 2005

0.36 0.52 0.51 0.39 0.34 0.38 0.34 0.52 0.37 0.46 0.41 0.38 0.40

Latin America

1988– 1996

0.18 0.12 0.14 0.09 0.05 0.06 0.10 0.22 0.15 0.09 0.17 0.06 0.14

North America

East Asia

Central/Western Europe

Northern Europe

Southern Europe

Oceania

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

1988– 1996

1997– 2005

0.57 0.67 0.66 0.38 0.36 0.33 0.38 0.65 0.41 0.36 0.42 0.48 0.54

0.16 0.08 0.14 0.06 0.20 0.19 0.41 0.25 0.34 0.20 0.36 0.05 0.12

0.42 0.63 0.61 0.40 0.35 0.42 0.36 0.69 0.43 0.50 0.46 0.52 0.49

0.05 0.08 0.14 0.11 0.20 0.22 0.46 0.21 0.39 0.18 0.41 0.11 0.25

0.33 0.42 0.50 0.23 0.48 0.45 0.49 0.48 0.51 0.26 0.57 0.25 0.47

0.02 0.08 0.04 0.29 0.11 0.13 0.33 0.12 0.24 0.40 0.26 0.11 0.13

0.31 0.56 0.46 0.50 0.26 0.32 0.26 0.48 0.29 0.64 0.31 0.38 0.32

0.02 0.22 0.08 0.18 0.14 0.23 0.37 0.20 0.20 0.32 0.21 0.03 0.14

0.36 0.53 0.52 0.45 0.25 0.39 0.26 0.55 0.26 0.57 0.31 0.51 0.36

0.14 0.16 0.01 0.35 0.13 0.07 0.16 0.00 0.16 0.41 0.21 0.35 0.05

0.36 0.41 0.48 0.33 0.19 0.27 0.20 0.45 0.20 0.40 0.18 0.33 0.28

0.17 0.13 0.03 0.15 0.20 0.16 0.30 0.14 0.29 0.28 0.20 0.01 0.06

0.37 0.54 0.56 0.38 0.42 0.53 0.36 0.57 0.48 0.42 0.62 0.41 0.45

Note: The averages of unconditional coefficients of correlation of each country with other countries of different regions during two periods, 1988:01–1996:12 and 1997:01–2005:12, are reported.

WAN-JIUN PAUL CHIOU


143

inter-continent investments. In addition, the stock markets in the rest of the world tend to have considerable price co-movements with the markets in North America, particularly the United States. The cross-temporal comparison of correlation also provides an evidence of enhancement of integration of the international financial market. The means of correlation of each market with all other countries in the second period is persistently greater than the ones in the first period. In the first period, some markets are negatively correlated or almost uncorrelated with certain areas. The enhancement of correlation is particularly considerable for the emerging markets with the countries that are in the different regions. All means of correlation coefficient in the second period are increasing and positive. This supports the enhancement of integration of the international financial market over the past two decades. Because of the chronological deviation of mean-variance efficiency and correlations among markets, the shape and size of efficient frontiers vary drastically over time. Fig. 1 exhibits the efficient frontiers of the global portfolio at the end of each year from 1993 to 2005. The movement of efficient frontiers does not follow certain direction. The efficient frontier little by little shifted to the northwest from 1993 to 1994 then progressing in an adverse path from 1994 to 1997. The position of optimal portfolios did not change significantly during 1998–2001. For our sample, the possible investment sets in 2002 and 2003 were the smallest and moved toward the northwest in 2004 and

Monthly Expected Return

0.05 0.04 94

0.03

93 01

00

96

99 98

0.02

97

02

03

05 04

0.01 95

0.00 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

-0.01 Monthly St. Dev.

Fig. 1. Unconstrained Efficient Frontiers: 1993–2005. Notes: The unconstrained global efficient frontiers at the beginning of each year from 1993 to 2005 are presented. The efficient frontiers are constructed by the previous 60 monthly returns.

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2005. The above revolution of mean-variance efficient portfolio is affected by the business cycle of the world economy. Since the returns and risks are timevarying, the inter-temporal comparison of diversification benefits should be based upon incremental values, such as d and e. The above findings regarding the dynamics of international market returns highlight the desire of over-time analysis on the strategies and benefits of international diversification. The non-synchronous movement of risk-adjusted returns among international markets suggests that the local investors have a chance to improve the mean-variance efficiency of their portfolios by investing in foreign assets. Since the return vector and variance–covariance matrix show a noticeable time variation, it is appropriate for investors to keep rebalancing the weighting for the optimal portfolios. Although, intuitively, the enhancement of global capital market integration causes the shrinkage of diversification benefits, it remains unclear whether international diversification is still desired by domestic investors. Furthermore, most previous studies incorporate only a small number of emerging markets to determine the benefits and strategies of diversification for investors in developed countries. They also did not consider the impact of over-weighting investment constraints. This study portrays the over-time relative economic size in diversification benefits across country while taking into account the more feasible strategies of a wider coverage of international equity markets.

5. EMPIRICAL RESULTS In the first sub-section, the long-term average global diversification benefits are presented. The trends of economic sizes of benefits provide evidence of integration of the global financial market. The absolute value and comparative magnitudes of global diversification benefits across countries over the testing period are reported in the second sub-section.

5.1. Long-Term Trends of Diversification Benefits In Fig. 2, each Sharpe ratio curve is formed by the returns during 1988:01– 2005:12 with various weighting constraints. The global diversification with any level of investment restrictions is preferable to holding merely a domestic U.S. portfolio. The Sharpe ratio curve with short-sale constraints is the most meanvariance efficient one. When the over-weighting constraints are added, the

Who Benefits More from Global Diversification? 0.70

145

Short-sales (SS) SS + OW(10) SS + OW(5) SS + OW(3) US

0.60

Sharpe Ratio

0.50 0.40 US

0.30 0.20 0.10 0.00 0.00

0.05

0.10

0.15

0.20 St. Dev.

0.25

0.30

0.35

0.40

Fig. 2. Sharpe Ratio on Constrained Efficient Frontiers. Notes: This graph demonstrates the curves of annualized risk-adjusted premium on global efficient frontiers of under various investment constraints as well as the U.S. domestic portfolio during 1988:01–2005:12. The investment constraints include short-sale (SS) and over-weighting (OW) investment. The number in parentheses denotes the upper limit of times of proportion of domestic market value to world capitalization.

benefits of international diversification decrease. The Sharpe ratio curves move southeast when the weighting constraints become increasingly restrictive (from 10 to 5 to 3). The U.S. portfolio still lies on the southeast in the graph. Fig. 3 demonstrates the time series of average global diversification benefits with various portfolio-weighting boundaries. In Panel A, the time series of d with various investment constraints fluctuate considerably over time. The benefits under various trading constraints move in the same direction but are not proportional in size. Unlike the significant impact of adding investment weights on mean-variance efficiency, Panel B demonstrates moderate temporal alteration in the cross-country averages of e. In addition, the diversification benefits with the most restrictive constraints, i.e., dSS+OW(3) and eSS+OW(3), are the least volatile over the testing period than those of less constrained asset allocation. When the Sharpe ratio benefits of no-short-selling portfolio are high, the divergences of diversification benefits among the optimal strategy under various constraints expand. This suggests that the effectiveness of the less restrictive diversifying strategies seems to be more sensitive to the change of market returns. Meanwhile, the more constrained portfolios eliminate uncertainty in asset

146

0.60 0.50

WAN-JIUN PAUL CHIOU Panel A: Increase in Mean- Variance Efficiency SS + O W (3) SS + O W (5) SS + O W (10) SS

0.40 0.30 0.20 0.10 0.00 Jan-93

Jan-95

Jan-97

Jan-99

Jan-01

Jan-03

Jan-05

Jan-03

Jan-05

Panel B: Decrease in Standard Deviation

0.07

SS SS+OW(10) SS+OW(5) SS+OW(3)

0.06 0.05 0.04 0.03 0.02 0.01 0.00 Jan-93

Jan-95

Jan-97

Jan-99

Jan-01

Fig. 3. Over-Time Average Global Diversification Benefits. Notes: The mean of global diversification benefits for all countries under various investment constraints are presented. Panel A demonstrates the increase in mean-variance efficiency brought by global MSRP (d). Panel B shows the decrease in standard deviation brought by the global MVP (e).

allocations since a certain portion of weighting shifts to other second-best alternatives, which generally are larger markets of second-best meanvariance efficiency. The inter-temporal evaluation of diversification benefits seemingly supports integration of the international financial market. In Panels A and B, the increase in risk-return and the decrease in volatility brought by the global diversification slightly shrink. This trend is particularly evident when more constrained upper boundaries of weighting are considered. This indicates that as the international markets become more integrated, the


147

gains of international diversification decrease. Though the improvement of mean-variance efficiency and reduction in portfolio volatility for the domestic investors are quite volatile, the persistently positive values suggest that diversifying globally is still desired by domestic investors in a more integrated international capital market.

5.2. Over-Time International Comparison of Diversification Benefits Table 3 reports the summary of time series of the global diversification benefits for different groups of countries. In Panel A, the local investors, on average, can increase by 0.314 of monthly risk-return and decrease by 0.05 of standard deviation by global diversification during the sample period. When the portfolio weights are increasingly restricted, the benefits generated from global investment gradually diminish but are not entirely eradicated. This is consistent with the finding in Fig. 3. The results in Panel A suggest that the benefits of international diversification to local investors in emerging markets, in general, are greater than for those in developed countries. When short-selling is forbidden, the average median for upsurge in risk-adjusted premium, d, and the average reduction in portfolio volatility, e, for the portfolios of emerging markets are 0.339 and 0.086, respectively, which are greater than the ones for developed countries of 0.277 and 0.029. This result holds for the various scenarios of increasingly restrictive investment constraints. The diversification benefits for investors in developed countries are eroded by adding investment restrictions less than the ones in emerging markets, especially d. Fig. 4 shows the temporal variation in the average global diversification benefits for domestic investors in developed countries and emerging markets under short-sale constraints graphically. In Panel A, the values of meanvariance benefits to local investors in developed countries are larger only before 1995. After that, however, investors in emerging markets enjoyed the greater d than the ones in developed countries, especially during 1997 and 2002. Panel B shows that the investors in emerging markets consistently benefit greater decrease in risk (e) than the investors in developed countries. In general, the diversification benefits to investors in emerging markets demonstrate more substantial time variation than the ones in developed countries. The global diversification benefits to investors in various areas are presented in Panel B of Table 3. The local investors in East Asia, Southern Europe, and Oceania enjoy relatively superior increments in risk-adjusted

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WAN-JIUN PAUL CHIOU

Table 3.

Summary of Time Series of Global Diversification Benefits.

Panel A: Countries at different developmental stages All Countries

Developed Countries

Emerging Markets

0.3143 0.1033

0.2765 0.0943

0.3393 0.1200

0.0502 0.0054

0.0294 0.0026

0.0861 0.0116

0.1955 0.0925

0.1755 0.0765

0.2068 0.1317

0.0497 0.0055

0.0283 0.0027

0.0852 0.0117

0.1594 0.1015

0.1513 0.0812

0.1722 0.1440

0.0490 0.0053

0.0275 0.0025

0.0846 0.0115

0.1476 0.1092

0.1316 0.0872

0.1506 0.1527

0.0478 0.0052

0.0258 0.0026

0.0837 0.0113

SS d Median Std. dev. e Median Std. dev. SS+OW(10) d Median Std. dev. e Median Std. dev. SS+OW(5) d Median Std. dev. e Median Std. dev. SS+OW(3) d Median Std. dev. e Median Std. dev.

Panel B: Countries in different regions L. America E. Asia S. Europe C/W Europe N. Europe N. America Oceania SS d Median Std. dev. e Median Std. dev.

0.2672 0.0958

0.3409 0.1227

0.3209 0.1290

0.2600 0.1060

0.2144 0.1424

0.2094 0.1378

0.3281 0.1466

0.0765 0.0218

0.0641 0.0167

0.0803 0.0094

0.0226 0.0052

0.0478 0.0067

0.0162 0.0054

0.0278 0.0041


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Table 3. (Continued ) Panel B: Countries in different regions L. America E. Asia S. Europe C/W Europe N. Europe N. America Oceania SS+OW(10) d Median Std. dev. e Median Std. dev. SS+OW(5) d Median Std. dev. e Median Std. dev. SS+OW(3) d Median Std. dev. e Median Std. dev.

0.1406 0.1492

0.2071 0.1536

0.2329 0.1135

0.1969 0.0698

0.1787 0.0898

0.1496 0.0773

0.2577 0.1549

0.0756 0.0217

0.0619 0.0169

0.0795 0.0094

0.0214 0.0050

0.0473 0.0068

0.0149 0.0055

0.0264 0.0044

0.1291 0.1629

0.1759 0.1662

0.1803 0.1151

0.1579 0.0708

0.1526 0.0868

0.1371 0.0698

0.2258 0.1655

0.0747 0.0217

0.0609 0.0168

0.0792 0.0092

0.0205 0.0049

0.0467 0.0066

0.0143 0.0052

0.0256 0.0044

0.1206 0.1722

0.1693 0.1750

0.1526 0.1180

0.1357 0.0755

0.1347 0.0880

0.1305 0.0680

0.2062 0.1743

0.0727 0.0218

0.0601 0.0165

0.0779 0.0092

0.0190 0.0051

0.0461 0.0063

0.0132 0.0048

0.0243 0.0046

Panel C: Countries of different legal origins

SS d Median Std. dev. e Median Std. dev. SS+OW(10) d Median Std. dev. e Median Std. dev.

Civil Law

Common Law

0.3135 0.0955

0.3069 0.0959

0.0533 0.0068

0.0338 0.0075

0.1953 0.0913

0.2035 0.1005

0.0526 0.0067

0.0328 0.0079

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Table 3. (Continued ) Panel C: Countries of different legal origins

SS+OW(5) d Median Std. dev. e Median Std. dev. SS+OW(3) d Median Std. dev. e Median Std. dev.

Civil Law

Common Law

0.1573 0.0991

0.1622 0.1115

0.0518 0.0065

0.0322 0.0078

0.1371 0.1062

0.1423 0.1201

0.0504 0.0065

0.0314 0.0075

Notes: The median and standard deviation of benefits of international diversification in different groups of countries are reported. The countries are classified by developmental stages, geographic region, and legal origins. The upper and lower boundaries of portfolio weights such as short-sales (SS) and over-weighting investment (OW) are taken into account.

premium by implementing global diversification than the rest of the world. For home investors in regions of emerging markets, such as Latin America, East Asia, and Southern Europe, the primary benefit of incorporating overseas stocks in their portfolios is to reduce risk. The benefits of international diversification for investors in Central/Western Europe and North America are relatively slight compared to the rest of the world. Even so, the risk premium for North American investors increases by 0.131 while the risk decreases by 0.013 per month via implementing global diversification under the constraints of short-sales plus three-times over-weighting investments. Panel C reports the advantages of international diversification between countries of various legal origins. The difference in d between developed countries and emerging markets is insignificant. On the other hand, local investors in the countries of civic-law origin experienced greater reductions in portfolio volatility. A possible explanation is that, in general, investors are better protected from expropriation by insiders of businesses or governments under the common-law system. The greater reduction in risk


0.60

Panel A: Increase in Mean-Variance Efficiency

δ

0.50

151

Developed Countries Emerging Markets All Countries

0.40 0.30 0.20 0.10 0.00 1-Jan-1993 0.12 ε 0.10

1-Jan-1995

1-Jan-1997

1-Jan-1999

1-Jan-2001

1-Jan-2003

1-Jan-2005

1-Jan-2003

1-Jan-2005

Panel B: Decrease in Standard Deviation Developed Countries Emerging Markets All Countries

EM

0.08 0.06

All Countries

0.04 DC

0.02 0.00 1-Jan-1993

1-Jan-1995

1-Jan-1997

1-Jan-1999

1-Jan-2001

Fig. 4. Over-Time Difference in Global Diversification Benefits. Notes: The mean of short-sale constrained global diversification benefits for all countries, developed countries, and emerging markets are presented. Panel A demonstrates the increase in mean-variance efficiency brought by global MSRP (d). Panel B shows the decrease in standard deviation brought by the global MVP (e).

for investors in civic-law states indicates that the global asset allocation lessens the uncertainties of domestic portfolios explicitly caused by legal systems at their home countries. Table 4 reports the summary of time series of the Mann–Whitney test of international difference in global diversification benefits to domestic investors, d and e, between the countries at different development stages, in various regions, and of different legal origins. The values presented in

152

Table 4.

Summary of Time Series of Mann–Whitney Test of Difference in Diversification Benefits. Developmental Stages

SS d Median Std. dev. pW 1.96 (%) po1.96 (%) e Median Std. dev. pW 1.96 (%) po1.96 (%)

Legal Origins

Emerging market

L. America

E. Asia

S. Europe

C/W Europe

N. Europe

N. America

Oceania

Civil law

0.7088 1.7706 48.46 2.56

0.0267 1.3963 23.45 19.87

0.7222 2.1241 39.10 2.56

0.3339 1.1818 12.18 0.00

0.4233 2.0449 10.26 23.72

0.7590 1.1229 0.00 2.56

0.6587 0.9309 0.00 14.49

0.5123 1.1858 1.28 9.62

0.3780 0.9630 1.28 0.00

4.1640 0.2108 100.00 0.00

1.8174 0.3610 41.67 0.00

2.2055 0.7484 71.15 0.00

1.2751 0.3351 2.56 0.00

2.8898 0.7090 0.00 79.49

0.4554 0.3880 0.00 0.00

1.6102 0.4170 0.00 40.38

0.8051 0.2683 0.00 0.00

1.3607 0.6811 32.69 0.00

0.7088 1.7706 48.46 2.56

0.0267 1.3963 23.45 19.87

0.7222 2.1241 39.10 2.56

0.3339 1.1818 12.18 0.00

0.4233 2.0449 10.26 23.72

0.7590 1.1229 0.00 2.56

0.6587 0.9309 0.00 14.49

0.5123 1.1858 1.28 9.62

0.3780 0.9630 1.28 0.00

4.1640 0.2108 100.00 0.00

1.8174 0.3610 41.67 0.00

2.2055 0.7484 71.15 0.00

1.2751 0.3351 2.56 0.00

2.8898 0.7090 0.00 79.49

0.4554 0.3880 0.00 0.00

1.6102 0.4170 0.00 40.38

0.8051 0.2683 0.00 0.00

1.3607 0.6811 32.69 0.00

WAN-JIUN PAUL CHIOU

SS+OW(10) d Median Std. dev. pW 1.96 (%) po1.96 (%) e Median Std. dev. pW 1.96 (%) po1.96 (%)

Regions


0.7088 1.7706 48.46 2.56

0.0267 1.3963 23.45 19.87

0.7222 2.1241 39.10 2.56

0.3339 1.1818 12.18 0.00

0.4233 2.0449 10.26 23.72

0.7590 1.1229 0.00 2.56

0.6587 0.9309 0.00 14.49

0.5123 1.1858 1.28 9.62

0.3780 0.9630 1.28 0.00

4.1640 0.2108 100.00 0.00

1.8174 0.3610 41.67 0.00

2.2055 0.7484 71.15 0.00

1.2751 0.3351 2.56 0.00

2.8898 0.7090 0.00 79.49

0.4554 0.3880 0.00 0.00

1.6102 0.4170 0.00 40.38

0.8051 0.2683 0.00 0.00

1.3607 0.6811 32.69 0.00

0.7088 1.7706 48.46 2.56

0.0267 1.3963 23.45 19.87

0.7222 2.1241 39.10 2.56

0.3339 1.1818 12.18 0.00

0.4233 2.0449 10.26 23.72

0.7590 1.1229 0.00 2.56

0.6587 0.9309 0.00 14.49

0.5123 1.1858 1.28 9.62

0.3780 0.9630 1.28 0.00

4.1640 0.2108 100.00 0.00

1.8174 0.3610 41.67 0.00

2.2055 0.7484 71.15 0.00

1.2751 0.3351 2.56 0.00

2.8898 0.7090 0.00 79.49

0.4554 0.3880 0.00 0.00

1.6102 0.4170 0.00 40.38

0.8051 0.2683 0.00 0.00

1.3607 0.6811 32.69 0.00



Notes: The summary of time series of Mann–Whitney test of difference in diversification benefits, d and e, between the countries at different development stages, in various regions, and of different legal origins is reported. The proportions of months that the tested group of countries is significantly different from the rest of countries in the world during the sample period are presented.

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Table 3 represent the average of economic benefits of global diversification but do not indicate the relative magnitude between various factions of countries. The null hypothesis is that there is no statistically significant difference for the benefits of diversification among the countries of the tested group and the rest of the world. Since there is no sound theory supporting Gaussian distribution of diversification benefits among markets, the nonparametric Mann–Whitney test is implemented. The proportions of months that the tested group of countries is statistically significantly higher, pW1.96, and lower, po1.96, than the rest of countries in the world during the testing period are presented. For the test of difference in d between countries at various developmental stages, the medians of Mann–Whitney statistics suggest investors in emerging markets obtain moderately higher improvement of risk-return than the ones in developed countries. On the other hand, the risk-reduction benefits to investors in emerging markets are higher than the ones in developed countries at a statistically significant level. This result holds for the various scenarios of investment constraints. To assist visualization of the chronological change, Fig. 5 demonstrates the time series of Mann–Whitney statistics testing the difference in short-sale constrained global diversification benefits between emerging markets and developed countries. For the increase in risk-return, the proportion of the

Increase in Mean-Variance Efficiency () Decrease in Volatility () 4.50

2.50 1.96

0.50 Jan-93

Jan-95

Jan-97

Jan-99

Jan-01

Jan-03

Jan-05

-1.50 -1.96

-3.50

Fig. 5. Time Series of Mann–Whitney Statistics on Global Diversification Benefits. Notes: The time series of Mann–Whitney statistics testing the difference in short-sale constrained global diversification benefits between emerging markets and developed countries is demonstrated. The null hypothesis is there is no difference in global diversification benefits for investors in emerging markets and developed countries. The benefits are measured by the increase in mean-variance efficiency brought by global MSRP (d) and the decrease in volatility brought by the global MVP (e).


155

testing period of Mann–Whitney statistics higher than 1.96 is significantly greater than the one lower than 1.96. Specifically, investors in developing countries obtained superior mean-variance efficiency benefits during 1997 and 2002. On the other hand, investors in emerging markets persistently generate significantly higher reduction in volatility via global diversification. In Table 4, the comparative sizes of advantages from investing internationally vary from region to region. The local investors in Latin America and East Asia enjoy relatively superior increments in risk-adjusted premium and greater shrinkages in volatility. For investors in Southern Europe and Oceania, the statistics of the Mann–Whitney test suggest that benefit of incorporating overseas stocks in their portfolios is not so statistically significant like the average numbers presented in Table 3. The benefits of global diversification for investors in the areas of more industrial countries are relatively minor. The better/worse relationships among continents with more restrictive weighting boundaries are similar to the ones merely with short-sale constraints. The results of the Mann–Whitney test also suggest that the benefits of risk-adjusted return to domestic investors in the countries of civic-law origin are slightly greater. However, this superiority only exists in a small proportion of the testing period. On the other hand, the investors in common-law states receive significantly less benefits of volatility reduction in about one-third of the sample period. This suggests that local investors in the states of civic-law origin, in general, enjoy greater benefits from global diversification.

6. CONSTRAINTS OF WEIGHTING AND FEASIBILITY OF STRATEGIES Table 5 shows the weights of each group of countries for the MSRPs under various investment constraints. The mean, standard deviation, maximum of weight, and proportion of non-zero-weight months during the testing period are reported. The average weight and number of selected markets in each year demonstrate the change of constituents in the optimal portfolios. Panel A shows the weighting distribution when only short-sale is prohibited. Compared to the mean in each group, the high standard deviation suggests a considerable time variation of weights. As exhibited in Panels B, C, and D, when the over-weighting investment restrictions are added and more constrained, the variation in shares on the optimal global asset allocation for each group of countries decreases. In addition, the maximum values of

156

Table 5. MSRP Weights. Weight EM

Number

LA

EA

C/W EU

N EU

S EU

NA

OC

EM

DC

0.6859 0.3668 1.0000 95.51

0.1755 0.2769 0.8774 48.72

0.1282 0.2586 1.0000 50.64

0.3350 0.3062 1.0000 78.21

0.1773 0.3006 1.0000 51.92

0.0114 0.0280 0.1441 23.72

0.1703 0.2290 0.8518 48.08

0.0024 0.0124 0.0803 5.13

1.75

2.47

6.00

7.00

0.1714 0.1430 0.4415 0.7309 0.9262 0.9950 0.9484 0.9833 1.0000 0.9085 0.0378 0.6659 0.9653

0.6799 0.7789 0.4867 0.1332 0.0388 0.0044 0.0000 0.0000 0.0000 0.0222 0.0296 0.1073 0.0000

0.1078 0.0472 0.0773 0.1359 0.0345 0.0000 0.0000 0.0000 0.0000 0.0693 0.9326 0.2268 0.0346

0.1693 0.1388 0.3777 0.4832 0.4271 0.6808 0.1913 0.0855 0.2439 0.0026 0.0000 0.6172 0.9370

0.0000 0.0000 0.0007 0.0293 0.1085 0.0491 0.0874 0.4207 0.6722 0.9059 0.0306 0.0006 0.0000

0.0431 0.0351 0.0000 0.0000 0.0005 0.0006 0.0516 0.0167 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0577 0.2181 0.3905 0.2652 0.6697 0.4770 0.0839 0.0000 0.0071 0.0452 0.0000

0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0029 0.0283

5.42 3.83 2.42 3.08 2.42 0.33 0.67 0.42 0.00 0.33 1.75 1.58 0.50

1.83 1.58 2.25 2.83 4.00 5.17 4.25 3.42 2.42 1.08 0.42 1.50 1.42

Panel B: SS+OW(10) constraints Mean 0.1208 0.8792 Std. dev. 0.1000 0.1000 Max 0.3314 1.0000 Non-zero (%) 86.54 100.00

0.0505 0.0418 0.1322 69.23

0.1322 0.1336 0.4450 64.10

0.2833 0.1824 0.9166 92.31

0.0506 0.0426 0.1446 74.36

0.0086 0.0141 0.0456 33.33

0.4323 0.2328 0.9369 92.95

0.0425 0.0754 0.1827 28.85

3.92

5.63

10.00

11.00

0.0793 0.0955

0.3003 0.3228

0.2269 0.3015

0.0000 0.0000

0.0348 0.0273

0.3588 0.2530

0.0000 0.0000

8.50 8.00

4.92 5.00

Panel A: Short-sales constraints Mean 0.3141 Std. dev. 0.3668 Max 1.0000 Non-zero (%) 67.31 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

1993 1994

0.8286 0.8570 0.5585 0.2691 0.0738 0.0050 0.0516 0.0167 0.0000 0.0915 0.9622 0.3341 0.0347

0.1841 0.2050

0.8159 0.7950

WAN-JIUN PAUL CHIOU

DC

0.9008 0.8904 0.9183 0.9879 0.9821 0.9856 0.9910 0.9252 0.7718 0.7084 0.7578

0.0789 0.0600 0.0442 0.0062 0.0000 0.0000 0.0079 0.0276 0.0505 0.1185 0.0876

0.2138 0.1319 0.0360 0.0000 0.0000 0.0000 0.0000 0.0472 0.3074 0.2043 0.1546

0.2881 0.3139 0.3251 0.3995 0.1227 0.1864 0.2364 0.5394 0.1424 0.1888 0.4123

0.0008 0.0229 0.0770 0.0705 0.0920 0.1286 0.0699 0.0631 0.0646 0.0378 0.0310

0.0000 0.0000 0.0015 0.0037 0.0163 0.0144 0.0012 0.0000 0.0026 0.0104 0.0000

0.4184 0.4663 0.5162 0.5201 0.7691 0.6706 0.6847 0.3081 0.2630 0.2593 0.1318

0.0000 0.0051 0.0000 0.0000 0.0000 0.0000 0.0000 0.0146 0.1695 0.1811 0.1827

5.17 4.42 2.75 1.00 0.75 0.67 0.25 1.17 4.83 6.83 6.58

4.67 6.08 5.83 7.75 4.92 4.67 3.67 2.67 5.67 8.00 9.33

Panel C: SS+OW(5) constraints Mean 0.0782 0.9218 Std. dev. 0.0579 0.0579 Max 0.2251 1.0000 Non-zero (%) 91.03 100.00

0.0328 0.0246 0.0675 73.08

0.0985 0.1113 0.6717 65.38

0.2666 0.1727 0.7051 94.87

0.0328 0.0279 0.0878 74.36

0.0057 0.0082 0.0228 37.82

0.5409 0.2387 0.9684 100.00

0.0227 0.0386 0.0914 36.54

4.60

7.28

10.00

14.00

0.0454 0.0555 0.0545 0.0398 0.0312 0.0086 0.0000 0.0000 0.0039 0.0217 0.0365 0.0638 0.0654

0.1680 0.1735 0.1564 0.1414 0.0323 0.0000 0.0000 0.0000 0.0000 0.0350 0.2800 0.1526 0.1409

0.2006 0.2250 0.1518 0.1686 0.2231 0.3166 0.1403 0.2317 0.2021 0.3566 0.1942 0.5022 0.5535

0.0000 0.0000 0.0029 0.0129 0.0516 0.0602 0.0517 0.0678 0.0343 0.0316 0.0435 0.0539 0.0155

0.0205 0.0159 0.0000 0.0000 0.0021 0.0046 0.0088 0.0094 0.0013 0.0000 0.0019 0.0065 0.0038

0.5655 0.5292 0.6341 0.6328 0.6575 0.6100 0.7992 0.6911 0.7584 0.5408 0.3545 0.1297 0.1297

0.0000 0.0009 0.0004 0.0045 0.0023 0.0000 0.0000 0.0000 0.0000 0.0144 0.0893 0.0914 0.0914

9.42 8.75 6.42 5.00 3.25 1.83 0.75 0.75 0.50 1.67 5.42 8.00 8.00

6.33 6.75 5.17 7.08 8.33 9.50 5.50 5.33 4.25 4.42 8.00 11.17 12.75

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

0.0992 0.1096 0.0817 0.0121 0.0179 0.0144 0.0091 0.0748 0.2282 0.2916 0.2422

0.1138 0.1166 0.0844 0.0775 0.0627 0.0182 0.0096 0.0096 0.0064 0.0567 0.1318 0.1707 0.1586

0.8861 0.8834 0.9156 0.9225 0.9373 0.9818 0.9904 0.9904 0.9936 0.9433 0.8682 0.8293 0.8414


1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

157

158

Table 5. (Continued ) Weight EM

DC

Panel D: SS+OW(3) constraints Mean 0.0525 0.9475 Std. dev. 0.0378 0.0378 Max 0.1351 1.0000 Non-zero (%) 92.95 100.00 0.0720 0.0741 0.0674 0.0580 0.0448 0.0138 0.0058 0.0078 0.0049 0.0340 0.0835 0.1097 0.1064

0.9280 0.9259 0.9326 0.9420 0.9552 0.9862 0.9942 0.9922 0.9951 0.9660 0.9165 0.8903 0.8936

LA

EA

C/W EU

N EU

S EU

NA

OC

EM

DC

0.0208 0.0155 0.0403 73.08

0.0853 0.1079 0.4514 65.38

0.2371 0.1815 0.7048 94.87

0.0228 0.0178 0.0527 76.92

0.0042 0.0053 0.0137 44.87

0.6157 0.2611 0.9811 100.00

0.0142 0.0233 0.0548 41.03

5.01

8.24

13.00

16.00

0.0314 0.0358 0.0362 0.0244 0.0191 0.0070 0.0000 0.0000 0.0024 0.0130 0.0233 0.0383 0.0394

0.0986 0.1045 0.1082 0.1064 0.0292 0.0000 0.0000 0.0000 0.0000 0.0210 0.2044 0.2853 0.1509

0.1731 0.1858 0.0915 0.1206 0.1776 0.2706 0.1351 0.2000 0.1954 0.2139 0.1624 0.4991 0.6570

0.0000 0.0000 0.0057 0.0136 0.0405 0.0416 0.0312 0.0434 0.0228 0.0189 0.0281 0.0400 0.0103

0.0113 0.0108 0.0000 0.0000 0.0028 0.0038 0.0053 0.0068 0.0015 0.0000 0.0012 0.0047 0.0061

0.6856 0.6563 0.7579 0.7320 0.7284 0.6771 0.8285 0.7498 0.7780 0.7245 0.5269 0.0778 0.0815

0.0000 0.0068 0.0005 0.0030 0.0025 0.0000 0.0000 0.0000 0.0000 0.0086 0.0536 0.0548 0.0548

9.75 8.92 7.00 5.50 3.75 1.92 0.75 1.17 0.67 1.67 5.58 8.75 9.75

6.83 7.50 5.58 7.92 9.58 10.58 5.42 5.67 4.92 4.42 8.83 14.58 15.25

Notes: The summaries of the MSRP weights and number of selected countries with various investment constraints for emerging markets (EM), indices of Latin America (LA), North America (NA), East Asia (EA), Central/Western Europe (C/W EU), Northern Europe (N EU), Southern Europe (S EU), and Oceania (OC), are reported. Non-zero is the percentage of months during sample period that the weight is greater than zero. The mean of weights for each year is also reported.

WAN-JIUN PAUL CHIOU

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Number


159

weights for developed countries, emerging markets, and each region gradually decline when over-weighting constraints are more restrictive. The import of upper bounds in portfolio weighting drives the distribution more proportional to the size of the market and results in less substantial alteration in asset allocation. The comparison of the components of the optimal portfolio with various constraints indicates that less restrictive strategies may not be feasible. We first investigate the asset allocation in countries of different developmental stages. Shown in Panel A of Table 5, the no-short-selling portfolio weighting in emerging markets not only fluctuates drastically but is also disproportionate to the distribution of the world capital market value. On average, the investors who wish to maximize portfolio mean-variance efficiency should place 31.41% of wealth in emerging markets, which represent merely 7.4% of total market value of all countries at the end of 2005.9 As the overweighting investment constraints are included and more restrictive, which are exhibited in Panels B, C, and D, the average weight on the assets in developing countries decreases, while the probability that securities in other second-best markets are selected in the MSRPs increase. The short-sale constrained strategies heavily distribute funds in emerging markets to maximize risk-return during 1993–1996 and 2003–2004 and allocate almost nothing in 1998 and 2001. On the other hand, the weighting of the portfolios with upper bounds are less volatile and have no overwhelming distribution on emerging markets. We then examine asset allocation in different regions. Panel A of Table 5 shows that overwhelming investments can also be found in small-cap regional portfolios, such as Latin America, Northern Europe, Southern Europe, and Oceania when only short-selling is considered. On the other hand, the weights for areas of large market value, such as North America and Central/Western Europe are zero for a number of periods. The more restrictive over-weighting constraints decrease portfolio weight to other second-best mean-variance efficient markets of larger capitalization. As shown in Panels B, C, and D of Table 5, the weighting of the more constrained MSRPs are not as unbalanced as the one in short-saleforbidden portfolios. For the case of SS+OW(3), the weights are proportional to the relative magnitude of international market capitalization, and assets in each area are more frequently included in the MSRP. Furthermore, in most regions, the time variation of weight for each area is lower than the other three less restrictive scenarios.10 The weights of all regions vary drastically and the overwhelming component for the MSRP in small markets is common over the sample period. The execution of such

160

WAN-JIUN PAUL CHIOU

strategies may cause illiquidity of a portfolio and trigger excessive price volatility when excessive funds flow in and out of those small markets. This eventually changes the relationship of mean-variance efficiency and correlation among markets. As the over-weighting constraints become more limited, the major components of the MSRPs concentrate assets in North America, Central/Western Europe, and East Asia. Their weighting distributions also change less considerably over the sample period than the ones of less constrained portfolios. The number of market indices selected in the basket also authenticates the essentialness of more restricted portfolio strategies. The time series average for no-short-selling asset allocation is 4.2 national indices in the testing period. That implies, overall, that more than 80% of international portfolios are redundant. The inclusion of over-weighting constraints effectively expands the coverage of the optimal portfolio to 9.6 (SS+OW(10)), 11.8 (SS+OW(5)), and 13.3 (SS+OW(3)). Although a certain portion of Sharpe ratio benefits are lost due to the ‘‘compulsorily’’ diversifying international diversifications, the inclusion of upper bounds also increases the invariance of weighting and benefits, as well as expands the assets chosen in the optimal portfolios. A similar conclusion can also be found in the weighting of the MVP. As reported in Panel A of Table 6, when there are no constraints on the upper bounds, the average optimal weight on the emerging markets is disproportional, although the weighting imbalance of the MVP is less than the one of the MSRP with corresponding investment restrictions. In addition, the regional components of the MVP differ from the ones of the MSRP. Geographically, the weights of the MVP on the securities in Latin America and Northern Europe are less than the ones of the MSRP, while the weighting on the assets in Central/Western Europe and North America is heavier. Even though the weightings on East Asian indices are similar, the MVP allocates more funds in developed countries but the MSRP place greater weighting on emerging markets in this area. This phenomenon occurs because the goal to hold the MVP is to generate the least risky investment and the allocations direct to the assets in the countries where the security prices are less volatile. The numbers of countries selected in the MVP are more than the one in the MSRP under the same investment constraints. On average, 2.79 emerging markets and 5.76 developed countries are included in the short-sales constrained MVP within one month. Similar to the transformation of the MSRP, the time variation in weighting decreases and the coverage of selected portfolios expands as the over-weighting investing constraints become more restrictive. The weights

MVP Weights. Weight

EM

DC

Number

EA

C/W EU

N EU

S EU

NA

OC

EM

DC

0.0351 0.0593 0.2311 66.03

0.1365 0.1390 0.5558 100.00

0.5626 0.2364 0.8920 100.00

0.0000 0.0000 0.0000 0.00

0.0075 0.0144 0.0527 28.21

0.2340 0.2379 0.7088 67.95

0.0242 0.0344 0.1345 53.85

2.79

5.76

7.00

9.00

0.6915 0.8166 0.8863 0.8867 0.9084 0.9856 0.9793 0.8853 0.8526 0.8964 0.8892 0.7661 0.8577

0.2109 0.1029 0.0374 0.0158 0.0071 0.0027 0.0000 0.0049 0.0372 0.0060 0.0125 0.0179 0.0351

0.0612 0.0441 0.0562 0.0976 0.0887 0.0444 0.0381 0.0620 0.1191 0.1143 0.1760 0.3725 0.1365

0.2706 0.2242 0.2338 0.3409 0.5226 0.6557 0.8024 0.8365 0.8340 0.8558 0.7224 0.5386 0.5626

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0363 0.0370 0.0202 0.0041 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0075

0.3328 0.5827 0.6434 0.5416 0.3815 0.2964 0.1581 0.0715 0.0000 0.0000 0.0086 0.0213 0.2340

0.0881 0.0091 0.0091 0.0000 0.0000 0.0006 0.0014 0.0252 0.0098 0.0238 0.0805 0.0497 0.0242

6.50 4.42 3.00 2.67 2.00 1.25 1.00 2.08 3.00 2.42 2.75 3.00 2.17

5.67 5.50 6.42 7.50 7.50 6.58 5.08 6.00 4.92 4.33 4.75 5.58 5.00

Panel B: SS+OW(10) constraints Mean 0.0761 0.9239 Std. dev. 0.0481 0.0481 Max 0.1860 1.0000 Non-zero (%) 93.59 100.00

0.0132 0.0128 0.0535 72.44

0.1167 0.0931 0.3857 99.36

0.5159 0.2712 0.9011 100.00

0.0013 0.0061 0.0310 5.77

0.0103 0.0153 0.0456 50.00

0.3055 0.2827 0.7742 75.00

0.0371 0.0422 0.1675 64.10

3.46

7.74

9.00

11.00

0.0423

0.0831

0.1302

0.0004

0.0425

0.6033

0.0982

8.33

8.58

Panel A: Short-sales constraints Mean 0.1423 0.8577 Std. dev. 0.0928 0.0928 Max 0.3310 1.0000 Non-zero (%) 98.08 100.00 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

1993

0.3085 0.1834 0.1137 0.1133 0.0916 0.0144 0.0207 0.1147 0.1474 0.1036 0.1108 0.2339 0.1423

0.1748

0.8252

161

LA


Table 6.

162

Table 6. (Continued ) Weight EM 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

LA

EA

C/W EU

N EU

S EU

NA

OC

EM

DC

0.0230 0.0176 0.0213 0.0212 0.0084 0.0000 0.0019 0.0168 0.0017 0.0059 0.0075 0.0039

0.0549 0.0646 0.1002 0.1019 0.0638 0.0265 0.0392 0.1004 0.0965 0.1703 0.2680 0.3473

0.1128 0.1475 0.2840 0.4106 0.4954 0.7248 0.8238 0.8459 0.8568 0.7132 0.5993 0.5625

0.0000 0.0000 0.0000 0.0000 0.0168 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000

0.0396 0.0208 0.0099 0.0018 0.0022 0.0012 0.0124 0.0032 0.0001 0.0000 0.0000 0.0000

0.7284 0.7267 0.5847 0.4644 0.4135 0.2475 0.1021 0.0044 0.0000 0.0000 0.0262 0.0703

0.0413 0.0228 0.0000 0.0000 0.0000 0.0000 0.0203 0.0293 0.0449 0.1106 0.0990 0.0160

5.42 3.83 3.67 2.75 1.58 0.92 2.83 3.33 2.33 3.25 3.67 3.08

7.83 8.17 8.67 8.67 9.67 7.17 7.25 8.58 6.58 5.75 6.67 7.08

Panel C: SS+OW(5) constraints Mean 0.0562 0.9438 Std. dev. 0.0360 0.0360 Max 0.1387 1.0000 Non-zero (%) 94.23 100.00

0.0077 0.0074 0.0324 72.44

0.1257 0.0923 0.3678 100.00

0.4414 0.2059 0.7110 100.00

0.0017 0.0050 0.0278 14.10

0.0085 0.0086 0.0228 63.46

0.3633 0.2486 0.7644 100.00

0.0515 0.0406 0.0914 70.51

4.09

9.37

9.00

12.00

0.0216 0.0114 0.0113 0.0125 0.0184 0.0074 0.0000

0.0982 0.0585 0.0586 0.0776 0.0810 0.0684 0.0552

0.1373 0.0964 0.1369 0.2771 0.3847 0.4829 0.5903

0.0124 0.0010 0.0000 0.0000 0.0002 0.0091 0.0000

0.0228 0.0228 0.0128 0.0095 0.0064 0.0032 0.0019

0.6163 0.7246 0.7277 0.6234 0.5093 0.4289 0.3447

0.0914 0.0853 0.0527 0.0000 0.0000 0.0000 0.0079

8.67 6.42 4.25 4.42 4.08 1.75 1.00

10.75 9.08 9.17 8.92 9.08 10.25 9.92

0.1300 0.0936 0.0784 0.0870 0.0760 0.0213 0.0048

0.8700 0.9064 0.9216 0.9130 0.9240 0.9787 0.9952

WAN-JIUN PAUL CHIOU

0.8844 0.8985 0.8763 0.8927 0.9787 0.9943 0.9551 0.9400 0.9727 0.9417 0.9227 0.9281

1993 1994 1995 1996 1997 1998 1999

0.1156 0.1015 0.1237 0.1073 0.0213 0.0057 0.0449 0.0600 0.0273 0.0583 0.0773 0.0719

DC

Number

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

0.0872 0.0652 0.0551 0.0695 0.0647 0.0205 0.0051 0.0218 0.0324 0.0167 0.0369 0.0395 0.0265

0.9128 0.9348 0.9449 0.9305 0.9353 0.9795 0.9949 0.9782 0.9676 0.9833 0.9631 0.9605 0.9735

0.0009 0.0048 0.0009 0.0047 0.0038 0.0026

0.0437 0.1201 0.1394 0.2312 0.2727 0.3301

0.6480 0.6520 0.6192 0.6064 0.5734 0.5336

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0110 0.0092 0.0025 0.0071 0.0014 0.0000

0.2245 0.1321 0.1602 0.0625 0.0579 0.1112

0.0719 0.0817 0.0777 0.0881 0.0909 0.0224

2.83 3.42 2.50 4.83 5.33 3.67

9.67 10.17 9.75 9.67 8.00 7.42

0.0056 0.0053 0.0241 77.56

0.1401 0.1006 0.3802 100.00

0.3471 0.1470 0.5994 100.00

0.0020 0.0052 0.0189 15.38

0.0077 0.0045 0.0137 83.33

0.4609 0.1993 0.7905 100.00

0.0366 0.0237 0.0548 75.64

4.76

10.86

9.00

14.00

0.0145 0.0068 0.0070 0.0069 0.0139 0.0045 0.0000 0.0007 0.0060 0.0005 0.0037 0.0064 0.0022

0.0860 0.0491 0.0509 0.0783 0.0840 0.0827 0.0773 0.0681 0.1489 0.1838 0.2740 0.2921 0.3465

0.1435 0.1045 0.1444 0.2229 0.3292 0.4269 0.4699 0.5412 0.5258 0.4387 0.4153 0.4077 0.3418

0.0174 0.0016 0.0000 0.0000 0.0004 0.0058 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000

0.0129 0.0137 0.0077 0.0092 0.0091 0.0051 0.0021 0.0086 0.0080 0.0062 0.0090 0.0085 0.0000

0.6739 0.7713 0.7495 0.6824 0.5633 0.4750 0.4199 0.3296 0.2592 0.3183 0.2434 0.2306 0.2751

0.0518 0.0530 0.0405 0.0002 0.0000 0.0000 0.0308 0.0519 0.0519 0.0526 0.0546 0.0548 0.0344

8.67 7.17 4.92 6.17 5.58 2.50 1.50 3.00 3.58 3.00 5.25 6.08 4.50

12.58 10.50 9.83 9.25 9.83 10.58 12.00 11.25 12.17 11.17 11.00 11.42 9.58


2000 0.0287 0.9713 2001 0.0445 0.9555 2002 0.0216 0.9784 2003 0.0511 0.9489 2004 0.0526 0.9474 2005 0.0407 0.9592 Panel D: SS+OW(3) constraints Mean 0.0416 0.9584 Std. dev. 0.0260 0.0260 Max 0.0994 1.0000 Non-zero (%) 99.36 100.00

Notes: The summaries of the MVP weights and number of selected countries with various investment constraints for emerging markets (EM), indices of Latin America (LA), North America (NA), East Asia (EA), Central/Western Europe (C/W EU), Northern Europe (N EU), Southern Europe (S EU), and Oceania (OC), are reported. Non-zero is the percentage of months during sample period that the weight is greater than zero. The mean of weights for each year is also reported.

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for the emerging markets and the regions of small market values also become less heavy. Adding more restrictive investment constraints decreases diversification benefits but generates some desired attributes in managing asset allocation. First, the coverage of both the MSRP and the MVP expands when the upper bounds are more restrictive. For the most constrained case, the MSRP includes 13.25 countries and the MVP 15.62 countries per month, respectively. Furthermore, the time variation for the weights in the optimal portfolios decreases. This is due to the fact that optimalization with less restrictive constraints is likely to generate the corner solutions, which are sensitive to the relative sizes of mean-variance efficiency among markets. Therefore, the more restrictive diversification benefits are less time-varying since the second-best markets with large capitalization are included. The consideration of over-weighting investing limitations makes the optimal investment strategy more feasible although a part of diversification benefits is sacrificed.

7. CONCLUSIONS This chapter investigates the comparative benefits of international diversification in various countries during the period of 1988–2005. The maximum increase in risk-adjusted return and the greatest reduction in standard deviation by diversifying assets globally are utilized to measure the benefits of diversification. To ensure asset allocation strategies feasible, the diversification gains with short-sales and various over-weighting investment constraints are also calculated. The time series of diversification benefits and the statistics of Mann–Whitney tests are calculated. The values of global diversification slightly diminished during our sample period. The long-term trend of diversification benefits seemingly supports integration of global market since. This is particularly evident when more constrained upper boundaries of weighting are considered. The empirical results also suggest that, in general, investors in emerging markets benefit more than those in developed countries from global diversifications. This finding holds for efficient frontiers under various restrictions for investment weights. The regional investors in Latin America, East Asia, and Southern Europe gain significantly more increase in risk premium. In addition, investors in Latin America and East Asia gain relatively greater decline in volatility than other geographical areas. Finally, the investors in the


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countries of civic-law origin legal systems tend to benefit more from global diversification. Our analyses of the benefits of global diversification add to the existing literature by three contributions. First, the global diversification benefits from the perspective of domestic investors in various countries are assiduously investigated. This comparison is useful for professional asset managers in determining target markets and potential clients. Second, this chapter considers the infeasibility of disproportional asset allocation among international financial markets. The efficient frontiers with the constraints of short-sales and over-weighting investments generate practical strategies for international asset allocation. Third, the time variation in diversification benefits is investigated and shows an evidence of integration of global capital market. The major caveat of this chapter is static models of expected return and volatility in determining the optimal portfolios. Chang, Errunza, Hogan, and Hung (2005) examine the demands of market risk hedge and currency exposure hedge in international asset pricing. Bekaert and Harvey (1995) and Bekaert et al. (2005) document the temporal variation of the integration of international financial markets. Chan, Karceski, and Lakonishok (1999) develop forecasting model for the covariances. Harvey (1995) also documents the predictability of international equity returns. However, the purpose of the current chapter is to investigate the difference of benefits of global diversification among markets with various investment constraints in a long-term. Future researches focusing on the impact of international investment restrictions and diversifying benefits may apply dynamic asset pricing theory or conditional asset pricing models and take into account the demands of hedging to market exposure and exchange rates.

NOTES 1. For more detailed discussion, please see Bekaert and Urias (1996), Cosset and Suret (1995), De Roon et al. (2001), De Santis and Gerard (1997), Fletcher and Marshall (2005), French and Poterba (1991), Harvey (1995), Li et al. (2003), Novomestky (1997), and Obstfeld (1994). 2. For detail, please see De Roon et al. (2001) and Li et al. (2003). 3. The investibility of the stock market is decided by the degrees that foreign investors can trade like the local investors in the domestic markets and liquidity of assets (see Bae, Chan, & Ng, 2004). 4. Li et al. (2003) use the increase in expected return brought by diversification to measure the amount of benefit.

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5. Bekaert, Harvey, and Lundblad (2005) and Stulz and Williamson (2003) suggest that the economic development and integration of global financial market are mutually affected. 6. See De Roon et al. (2001), Harvey (1995), Li et al. (2003), and Pa´stor and Stambaugh (2000). 7. In this chapter, we report the changes of benefits of diversification with overweighting investment constraints by setting L=3, 5, and 10. 8. The limit of foreign ownership is often imposed in the so-called strategic industries, such as banking, energy, utility, and media (see Bae et al., 2004). 9. The weight of capitalization for emerging markets is between 4.19% (2000) and 9.39% (1994) during the sample period. 10. The only exception is North America since the average of weight increases as the investment constraints are increasingly restrictive.

ACKNOWLEDGMENTS The author would like to thank Simon Benninga, Lloyd Blenman, Martin Gruber, Norris Larrymore, Jerry Mason, Sophie Zong, and participants at the Financial Management Association Annual Meeting in Orlando, FL, for helpful comments. The author particularly appreciates the useful suggestions from the editor, Andrew Chen. The usual disclaimer applies.

REFERENCES Bae, K., Chan, K., & Ng, A. (2004). Investibility and return volatility. Journal of Financial Economics, 71, 239–263. Beck, T., Demirgu¨c- -Kunt, A., & Levine, R. (2003). Law, endowments, and finance. Journal of Financial Economics, 70, 137–181. Bekaert, G., & Harvey, C. R. (1995). Time-varying world market integration. Journal of Finance, 50, 403–444. Bekaert, G., & Harvey, C. R. (2003). Emerging markets finance. Journal of Empirical Finance, 10, 3–56. Bekaert, G., Harvey, C. R., & Lundblad, C. (2005). Does financial liberalization spur growth? Journal of Financial Economics, 77, 3–56. Bekaert, G., Harvey, C., & Ng, A. (2005). Market integration and contagion. Journal of Business, 78, 39–70. Bekaert, G., & Urias, M. S. (1996). Diversification, integration and emerging market closed-end funds. Journal of Finance, 51, 835–869. Campbell, J., Lettau, M., Malkiel, B., & Xu, Y. (2001). Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk. Journal of Finance, 56, 1–43. Chan, L. K., Karceski, J., & Lakonishok, J. (1999). On portfolio optimization: Forecasting covariances and choosing the risk model. Review of Financial Studies, 12, 937–974.


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Chang, J., Errunza, V., Hogan, K., & Hung, M. (2005). An intertemporal international asset pricing model: Theory and empirical evidence. European Financial Management, 11, 218–233. Cosset, J., & Suret, J. (1995). Political risk and the benefit of international portfolio diversification. Journal of International Business Studies, 26, 301–318. De Jong, F., & De Roon, F. A. (2005). Time-varying market integration and expected returns in emerging markets. Journal of Financial Economics, 78, 583–613. Demirgu¨c- -Kunt, A., & Maksimovic, V. (1998). Law, finance, and firm growth. Journal of Finance, 53, 2107–2137. De Roon, F. A., Nijman, T. E., & Werker, B. J. (2001). Testing for mean-variance spanning with short sales constraints and transaction costs: The case of emerging markets. Journal of Finance, 56, 721–742. De Santis, G., & Gerard, B. (1997). International asset pricing and portfolio diversification with time-varying risk. Journal of Finance, 52, 1881–1912. Elton, E. J., & Gruber, M. J. (1995). Modern portfolio theory and investment analysis (4th ed.). New York: Wiley. Errunza, V., Hogan, K., & Hung, M. (1999). Can the gains from international diversification be achieved without trading abroad? Journal of Finance, 54, 2075–2107. Errunza, V., Losq, E., & Padmanabhan, P. (1992). Tests of integration, mild segmentation and segmentation hypotheses. Journal of Banking and Finance, 16, 949–972. Fletcher, J., & Marshall, A. (2005). An empirical examination of the benefits of international diversification. Journal of International Financial Markets, Institutions and Money, 15, 455–468. French, K. R., & Poterba, J. M. (1991). Investor diversification and international equity markets. American Economic Review, 81, 222–226. Harvey, C. (1995). Predictable risk and returns in emerging markets. Review of Financial Studies, 8, 773–816. Jagannathan, R., & Ma, T. S. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. Journal of Finance, 58, 1651–1683. La Porta, R., Lopez-de-Silanes, F., Shleifer, A., & Vishny, R. W. (1998). Law and finance. Journal of Political Economy, 106, 1113–1155. Li, K., Sarkar, A., & Wang, Z. (2003). Diversification benefits of emerging markets subject to portfolio constraints. Journal of Empirical Finance, 10, 57–80. Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7, 77–91. Novomestky, F. (1997). A dynamic, globally diversified, index neutral synthetic asset allocation strategy. Management Science, 43, 998–1016. Obstfeld, M. (1994). Risk-taking, global diversification, and growth. American Economic Review, 84, 1310–1329. Pa´stor, L., & Stambaugh, R. (2000). Comparing asset pricing models: An investment perspective. Journal of Financial Economics, 56, 335–381. Statman, M., & Scheid, J. (2005). Global diversification. Journal of Investment Management, 3, 53–63. Stulz, R. M., & Williamson, R. (2003). Culture, openness, and finance. Journal of Financial Economics, 70, 313–349. Wang, Z. (1998). Efficiency loss and constraints on portfolio holdings. Journal of Financial Economics, 48, 359–375.

OVERREACTION AND SEASONALITY IN ASIAN STOCK INDICES: EVIDENCE FROM KOREA, HONG KONG AND JAPAN Mark Schaub, Bun Song Lee and Sun Eae Chun ABSTRACT This chapter examines investor overreaction and seasonality in the stock markets of Korea, Hong Kong and Japan using data for the period of 1985–2004. Evidence suggests little to no reversals following days of excessive increase, but all three indices reversed 35% to 45% following days of excessive decline. Seasonality analysis revealed month-of-the-year effects, day-of-the-week effects, the Friday (weekend) effect and the January effect. The Monday effect was not evident.

1. INTRODUCTION Financial innovations have brought about ways to invest that were not feasible in years gone by. Now index investing allows individuals to hold a portfolio that tracks a major stock market index. Market indices were once the benchmarks for investment performance. With the ability to invest in an index via mutual funds, now investors can ‘‘hold’’ the market rather than try Research in Finance, Volume 24, 169–195 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00207-9

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to ‘‘beat’’ the market after expending a large amount of time and effort along the way. Certain market psychological phenomena have been recorded while investigating how investors react to news. Often, in the face of bad news, companies find investors dumping their stocks. Sometimes investors realize they have driven the price below the true value of the firm and begin to repurchase the equity. The finance literature calls this phenomenon ‘‘investor overreaction.’’ Overreaction has not been limited to individual equities. Some of the worst days in US stock market history have been followed with days of reversal (such as Black Monday in 1989). However, the literature lacks comparative overreaction analysis related to Asian indices. We seek to fill this need via our research of overreaction in the Korean, Hong Kong and Japanese stock markets.1 Our chapter documents evidence of such an overreaction, particularly following days of excessive market index declines in these respective markets. The existence of such a phenomenon may provide investors profit-making opportunities by following a contrarian trading strategy. Day-of-the-week and month-of-the-year effects reveal yet another type of stock market inefficiency called stock market seasonality. In the US, prices tend to be higher in January and lower in December. Also stock indexes tend to perform better on Friday and worse on Monday. These anomalies suggest stock markets do not adhere to the semi-strong form of market efficiency. But, do these patterns apply to Asian markets as well? And did the currency crisis of the late 1990s affect these patterns? Besides examining Asian index overreaction, we seek to prove the existence or non-existence of day-of-the-week effects, namely the Monday and Friday effect, and monthof-the-year effects (the January effect in particular) in Korea, Hong Kong and Japan. In addition, we verify whether the patterns of stock market seasonality are different before, during and after the Asian financial crisis.

2. BACKGROUND 2.1. Overreaction Investor overreaction suggests the presence of psychological impacts on stock prices. Originally stated in the research of De Bondt and Thaler (1985, 1987), the Overreaction Hypothesis documented long-term underperformance by a portfolio of historical ‘‘winners’’ and gains to portfolios

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of historical ‘‘losers.’’ These findings go against the semi-strong form of stock market efficiency. Other studies suggest that investor overreaction to ‘‘news’’ tends to occur in the short-run. These include Howe (1986) and Brown and Harlow (1988) who found that overreaction occurs most often in response to bad news. Ketcher and Jordan (1994) report the day after the initial reaction captures the majority of the stock price reversals. Initially investors react to negative news releases about a firm, driving its price down. Afterwards, normally the next day or two, investors realize they drove the price too low and begin buying the stock back. Cox and Peterson (1994) and Brown, Harlow, and Tinic (1988) report fewer problems and more consistent results in studies of short-term overreaction as opposed to long-term. Some studies have tried to contradict these findings, especially for the long-run results, suggesting long-run market equilibrium changes were not taken into account (see Chan, 1988; Ball & Kothari, 1989). Chen and Sauer (1997) adds to the arguments, claiming overreaction results do not persist over time. Studies of overreaction normally include the price movements of individuals stocks. For instance, Cox and Peterson (1994) find the stock returns of firms that experience 1-day price declines of 10% or more bounce back quickly. Diacogiannis, Patsalis, Tsangarakis, and Tsiritakis (2005) found a similar reaction for stocks traded on the Athens Stock Exchange that encounter an initial decline of 8% or more. Other international results for overreaction studies have been promoted by Mun, Vasconcellos, and Kish (1999) in the French and German markets and by Wang, Burton, and Power (2004) in the Chinese market. Clare and Thomas (1995) test the Overreaction Hypothesis using data from the UK market. Overreaction in derivatives markets, or the lack thereof, has also been documented by Fung, Mok, and Lam (2000) and Brookfield (1993). Most literature on the topic of overreaction examines individual equities. But what about overreaction in the entire market index? Our study differs in that we examine overreaction in the macro-market (indices) rather the micro-market (individual equities) for Asian equities in Korea, Hong Kong and Japan. This analysis was provided for the US market by Nam, Pyun, and Avard (2001) who found overreaction in the NYSE, AMEX and NASDAQ indices. Wong (1997) performed regression analyses for overreaction in Asian stock markets. His data covers only up to the middle of 1995, thus excluding Asian financial crisis effects on overreaction behaviors in Asian stock markets. For example, the Korean stock market hardly experienced

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excessive daily stock declines or gains of more than 5% before the Asian financial crisis. Also, Wong (1997) focused less on immediate stock value reversals, where most overreaction effects are captured, to emphasize longer term (up to 20 days) reactions. Consequently, our study will address important questions Wong’s (1997) study left unanswered.

2.2. Seasonality Seasonal anomalies in stock market returns have been the subject of a considerable amount of academic research. The month-of-the-year and day-of-the-week effects suggest average returns may be higher or lower in particular months or on particular days. The main empirical result for monthly effects suggests higher returns in January than in other months (Jaffe & Westerfield, 1985a; Thaler, 1987; Mills & Coutts, 1995; Cheung & Coutts, 1999). Possible explanations for any effects varying with the month of the year include holidays, the number of working days in the month, seasonality in profits announcements, tax deadlines and other related month-specific events. Although in the 1930s Fields (1931) observed that the US stock market consistently experienced significant negative and positive returns on Mondays and Fridays, respectively, interest in the day-of-the week effect revived during the 1980s. Studies by French (1980), Gibbons and Hess (1981), and Keim and Stambaugh (1984) found the average market return in the US is significantly negative on Monday and significantly positive on Friday. Capital markets of many other countries also experienced similar seasonality to the US market (see Jaffe & Westerfield, 1985a, 1985b; Peiro, 1994; Aggarwal & Tandon, 1994). Possible explanations for the day-of-the-week effect involve examining various kinds of measurement errors; the delay between trading and settlements in stocks and in clearing checks; specialist-related biases; the distinction between trading and non-trading periods; the timing of corporate and government news release; and time zone differences between relevant countries and markets. Studies on the emerging Asian capital markets present a number of important seasonal anomalies similar to those found in the US and other developed stock markets. Nassir and Mohammad (1987) found a positive January effect for the Malaysian stock market from 1970 to 1986. Wong, Hui, and Chang (1992) provided further evidence of a January effect in Malaysia.


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Even though Wong and Ho (1986) found no January effect in the Singapore market from 1975 to 1984, they found strong seasonal patterns where lowest returns occurred on Mondays and highest returns occurred on Fridays. Kim (1988) investigated the South Korean and Japanese market and found the returns for Tuesday were significantly negative and lower than the other days of the week, confirming the results of Jaffe and Westerfield (1985a, 1985b). Aggarwal and Rivoli (1989) confirmed the existence of both a January and Monday effect for Singapore, South Korea, Hong Kong and Taiwan. This chapter examines the month-of-the-year and day-of-the-week effect for the Korean, Hong Kong and Japanese stock markets. Instead of using the usual linear regression method, we employ the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Since the studies of Mandlebrot (1963) and Fama (1965), empirical research has found evidence of volatility clustering and kurtosis in changes in stock prices (Connolly, 1989; de Jong, Kemman, & Kloek, 1992). Poshakwale and Murinde (2001) found that the GARCH model successfully accounted for volatility clustering in returns and therefore is superior to the conventional Ordinary Least Squares (OLS) method. In addition, we seek to determine whether calendar patterns (if any) are due to seasonal variation in market risk using the Generalized Autoregressive Conditional Heteroscedasticity (p, q)-in-Mean (GARCH(p, q)-M) model as proposed by Engle, Lilien, and Robins (1987). Choudhry (2000) used the GARCH model and daily returns of seven emerging Asian stock markets to find the significant presence of the day-ofthe-week effect on stock returns and stock volatility. Kamath, Chakornpipat, and Chatrath (1998) also confirmed similar findings in Thailand by using a GARCH model that allows for varying return volatility. Clare, Ibrahim, and Thomas (1998) used a GARCH-M model to allow for variation in return volatility and still found a strong day-of-the-week effect in the Kuala Lumpur Stock Exchange (KLSE). However, all these studies used data for the period before the Asian financial crisis. Yakob, Beal, and Delpachitra (2005) analyzed seasonality patterns of 10 Asia Pacific countries’ stock markets using regression analysis. However, their study used data for the period after January 2000 in order to avoid the influence of the Asian financial crisis on these stock markets. This was an unfortunate data choice because the comparison of seasonality patterns for Asian markets before and after the Asian crisis should be very meaningful. Holden, Thompson, and Ruangrit (2005) found that patterns of Thailand stock market seasonality varied substantially before, during and after the Asian financial crisis.

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Therefore, our study analyzes the stock market seasonality patterns of Korea, Hong Kong and Japan for the full period of 1985 to 2004. Analysis on subsample periods is also conducted in order to find differences in the pattern of seasonality throughout the time period.

3. ANALYSIS OF OVERREACTION 3.1. Data and Methods 3.1.1. Selection of Sample Dates: Observations with Excessive Losses and Gains This study tests for investor overreaction in the stock markets of Korea, Hong Kong and Japan. Observations were chosen based on days of increase and decrease of 5% or more in the respective stock market indices from 1985 to 2005. Data suggest 42 days of excessive loss in the Korean stock market based on the Kospi, 34 days of excessive loss in the Hong Kong market based on the Hang Seng and 15 days of excessive loss in the Japanese stock market based on the Nikkei. Days of 5% or greater gain amounted to 51 on the Kospi, 31 on the Hang Seng and 18 on the Nikkei. On the basis of the number of days of excessive gain and loss, the Japanese market appears to be less volatile than the others. 3.1.2. Computation of Returns Eq. (1) computes the average return for each sample on day t (ARt) as the simple average of the sum of the returns of each of the n days of excessive loss or gain on day t relative to the sample date. ARt ¼

n 1X xrit n i¼1

(1)

Cumulative average returns as of day s are computed as the summation of the average returns starting at day 1 until day s in Eq. (2), where s ends on day 5. CAR1;s ¼

s X

ARt

(2)

t¼1

Both the daily average returns and the cumulative average returns are tested to determine significance using a Z-score. The respective p-values for these tests are reported.


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3.2. Initial Data Analysis Results of Overreaction The results presented in Table 1 reflect the reactions in the Korean stock market to days of excessive loss and gain. In Panel A, the average of the 42 days of 5% loss or greater amounted to 6.38% and is highly significant. Although there was no initial readjustment the day following the excessive losses, by the 5th day after the initial loss the market had recaptured nearly 40% of the excessive losses. This average correction suggests overreaction by investors on the sampled dates. Panel B of Table 1 presents the sample of days of 5% or more gain on the Kopsi index. On average, days of large gains averaged 6.25%. However, these days were followed by days of further cumulative significant gains rather than loss. This suggests no overreaction in the Korean stock market due to days of excessive gains. On average, investors did not ‘‘take profits’’ following these days of stock market increase.

Table 1. Average Return Performance and Percent Reversal for Days when the Korean Stock Market (Kospi) Returned above or below 5% from 1985 to 2004. CAR (%)

p-Value

Cumulative Percent Reversal (%)

Panel A: Days of 5% or greater loss D0 42 6.38 0.00 D1 42 0.52 0.14 D2 42 0.84 0.06 D3 42 0.70 0.12 D4 42 0.40 0.24 D5 42 1.12 0.01

NA 0.52 0.32 1.02 1.42 2.54

NA 0.14 0.33 0.14 0.10 0.01

NA 0.00 5.02 15.99 22.26 39.81

Panel B: Days of 5% or greater gain D0 51 6.25 0.00 D1 51 0.90 0.01 D2 51 0.11 0.39 D3 51 0.05 0.46 D4 51 0.20 0.31 D5 51 0.78 0.06

NA 0.90 1.01 0.96 1.16 0.38

NA 0.01 0.04 0.09 0.08 0.34

NA 0.00 0.00 0.00 0.00 0.00

Day

OBS

AR (%)

p-Value

Note: Average Returns (AR) and cumulative average returns (CAR) are computed and evaluated based on Eqs. (1 and 2) in the text. The percent reversal is the CAR divided by the AR on the announcement day (D0). Significance is denoted with p-values in bold italics for returns significant at the 10% level or lower. Observations (OBS).

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Table 2. Average Return Performance and Percent Reversal for Days when the Hong Kong Stock Market Index (Hang Seng) Returned above or below 5% from 1985 to 2004. CAR (%)

p-Value



NA 1.88 2.93 1.35 2.35 2.93

NA 0.02 0.01 0.18 0.08 0.01

NA 22.90 35.69 16.44 28.62 35.69


NA 0.17 1.19 0.20 0.43 1.18

NA 0.37 0.09 0.43 0.36 0.11

NA 2.39 14.35 0.00 0.00 0.00

Day

OBS

AR (%)

p-Value

See Note section of Table 1.

Panel A of Table 2 reports the average return performance of the Hong Kong stock market index following days of excessive loss. For the 34 days of 5% or greater loss, the losses averaged a highly significant 8.21% of the index value. On average, approximately 23% of that loss was recaptured the day following the excessive loss and nearly 36% of the loss had been reclaimed by the 5th day following the day of excessive loss. These results suggest overreaction on the days of excessive loss on the Hang Seng market index. Panel B of Table 2 presents the stock index performance following 31 different days of gains of 5% or more. The average excessive gain was 7.11%. However, the Hang Seng shows some weak evidence of overreaction, as by the 2nd day after the large gain investors had sold shares, causing a reversal in the index value amounting to 14% of the excessive gain. After the 2nd day, however, evidence of overreaction disappears. Table 3 presents the results of market overreaction in the Japanese stock market. Panel A shows the Nikkei suffered 15 days of 5% or greater loss from 1985 to 2005. The average loss on these days amounted to 6.28% of the index value. However, within 2 days after the excessive losses, the average correction in the Japanese market caused nearly 50% of the loss to be recaptured. And, by the end of the 5th day after the day of excessive loss, the


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Table 3. Average Return Performance and Percent Reversal for Days when the Japanese Stock Market Index (Nikkei 225) Returned above or below 5% from 1985 to 2004. CAR (%)

p-Value



NA 1.29 3.09 2.18 1.67 2.78

NA 0.03 0.00 0.03 0.11 0.00

NA 20.54 49.20 34.71 26.59 44.27


NA 0.20 0.83 0.10 0.55 0.44

NA 0.35 0.13 0.46 0.31 0.35

NA 2.95 12.26 0.00 0.00 0.00

Day

OBS

AR (%)

p-Value


Nikkei had reclaimed over 44% of the average amount lost on the sample date. This suggests that the Japanese stock markets overreacted on the days of excessive loss – even more so than the Korean and Hong Kong markets. Panel B of Table 3 reports the gains on the 18 days of market increase averaged 6.77%. The 2 days following the days of excessive gain accumulated losses amounting to 12% of the excessive gains, but was not significant. Evidence indicated no overreaction in the Japanese stock markets on days where the Nikkei gained 5% or more. In comparing the stock index reversals after days of excessive loss, Fig. 1 suggests the Korean market was the slowest to correct to the overreaction based on the 1st day following the excessive loss. By the 2nd day, the Japanese market had recaptured more of the excessive loss than the Korean and Hong Kong markets. By the 5th day, all three markets had significantly recovered from the days of excessive loss. The graph suggests that the Korean markets reacted slower than the Hong Kong and Japanese markets after the market index excessive decline. In summary, for both Japan and Hong Kong by the 2nd day the stock markets recaptured as much of the loss as the amount they would recapture by the 5th day. However, for Korea we do not observe such immediate

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Percent Reversal

50.00

Korean Hong Kong Japan

40.00 30.00 20.00 10.00 0.00 1

2

3

4

5

Days Following Excessive Loss

Fig. 1.

Cumulative Percent Reversal of Index Returns after Loss of 5% or More.

reversals as in Japan and Hong Kong. Stock markets for Japan and Hong Kong are far more mature than the Korean stock market. We could conjecture that the more mature stock markets reveal more prompt reversals of excessive losses. 3.3. Regression Analysis Results of Overreaction In order to study whether excessive gains or losses in stock market indices lead to abnormal price patterns in subsequent days, this chapter uses mean-adjusted returns to approximate abnormal returns following Wong (1997). This approach has also been used by Atkins and Dyl (1990), Masulis (1980), and others. We use the 60-day average return just prior to the 10th day before the event date as the mean (denoted as M) used for calculating mean-adjusted returns. The average return computation ends at the 10th day prior to the event date rather than the event date itself to eliminate bias caused from unusual returns shortly before an excessive gain or loss. This chapter focuses on 5-day cumulative abnormal returns (denoted by CAR5t) disregarding 10-day and 20-day cumulative abnormal returns used by Wong (1997) since we are interested in the overreaction in the short term. An excessive gain or loss is defined as a 5% or higher 1-day change in stock market returns as proxied by the relevant indices. When there is an excessive market advance (denoted Advt) or decline (denoted Dect) at t


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(i.e. Advt=1 or Dect=1), the subsequent CAR5t will be: CAR5t ¼

5 X

Rtþj 5 M

j¼1

The CAR5t following excessive gains and losses are respectively estimated with the two following regression models: CAR5t ¼ a þ bAdvt þ et CAR5t ¼ a þ bDect þ et When Advt=1 or Dect=1, CAR5t will be a+b as the error terms are assumed to be normally distributed with the mean equal to zero. White’s (1980) heteroscedasticity-consistent standard errors are used for testing to eliminate heteroskedasticity problems. In addition to the whole sample period regression analysis, two subsample periods of 1985–1996 and 1999–2004 are used. The Asian financial crisis affected the stock market substantially and the stock market recorded greater volatility during the financial crisis period of 1997–1998. This may have distorted the overreaction pattern. Table 4 displays the estimation results for the full sample and two subsample periods for the three countries. As shown in Table 4 for the full sample years, we find significant and positive 5-day cumulative abnormal returns after excessive 1-day gains in Hong Kong and Japan. This suggests subsequent abnormal stock prices gradually move up rather than move downward from the price at time t when there is an excessive gain at t. These findings are inconsistent with the

Table 4.

Regression Results for Abnormal Stock Returns following Excessive 1-Day Gains and Losses. 1985–2004

Korea Hong Kong Japan

1985–1996

1999–2004

Advt

Dect

Advt

Dect

Advt

Dect

0.82 (0.15) 2.18** (0.05) 1.40* (0.06)

3.34*** (0.00) 1.6965 (0.31) 3.68*** (0.00)

–

–

0.47 (0.23) 1.10 (0.26)

1.87 (0.42) 6.32*** (0.00)

0.57 (0.43) 5.27*** (0.06) 5.00*** (0.00)

3.24*** (0.00) 0.38 (0.22) 2.30* (0.09)

Note: *, **, *** significance at 10%, 5% and 1% level based on p-values in parenthesis.

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overreaction hypothesis and provide evidence against the weak-form efficient market hypothesis. There could be several explanations why investors receive better than average returns the first 5 days after a stock market advance. First, the information environment may be very efficient in Hong Kong and Japanese stock markets. Thus, new information can cause excessive gains with the gradual diffusion of this new information leading to predictable price patterns. Second, it may be due to investors’ positivefeedback behavior and/or trend chasing. Finally, subsequent information following large 1-day advances just happened to be ‘‘good’’ news on average during the sample period. In the case of excessive losses, we find significant and positive 5-day cumulative abnormal returns for Korea and Japan, supporting the overreaction hypothesis. The magnitude of CAR5t after excessive losses is generally larger than that after excessive gains in Korea and Japan. For the subsample periods of 1999–2004, significant and positive 5-day cumulative abnormal returns (CAR5t) occur for Hong Kong and Japan after excessive 1-day gains. We also find significant and positive CAR5t for Korea and Japan after an excessive 1-day loss, but not for Hong Kong. This result is somewhat different from the one in the previous section, where the overreaction hypothesis was supported after an excessive loss for all three countries. We found no evidence of overreaction after excessive gains for any of the three countries. However, we found consistent evidence for Korea and Japan revealing overreaction behavior after excessive losses. It is a little puzzling that the Hong Kong stock market does not reveal any significant overreaction behavior after excessive losses in Table 4, whereas Table 2 shows significant overreaction behavior after excessive losses for Hong Kong. This inconsistent result might be due to the fact that Table 2 uses the values of CARt which are computed using the daily returns without any adjustment for the average trend of past daily returns, whereas the values of the dependent variable CAR5t in Table 4 were computed using the mean-adjusted daily returns. If the Hong Kong stock market’s daily returns after excess losses have similar positive values as the average daily returns before excessive losses, then it is possible that Table 4 denies the overreaction hypothesis, whereas Table 2 supports the overreaction hypothesis for Hong Kong. As for the subsample period of 1985–1996, only the Japanese stock market had support for overreaction in the case of an excessive loss. Korea had not experienced any excessive gain or loss before the Asian financial crisis in 1997. This is understandable because the Korean economy had achieved recurring, stable growth during the period of 1985–1996.


181

4. ANALYSIS OF SEASONALITY PATTERNS 4.1. Methodology for Seasonality Analysis The study employs the GARCH(p,q) model of Bollerslev (1986), which specifies the mean and conditional variance of stock returns using the following equations: Mean equation Rt ¼

N X

yi Di þ ei

(3)

i¼1

Conditional variance s2t ¼ a0 þ

p X i¼1

ai s2ti þ

q X

bj e2tj

(4)

j¼1

where Rt is the daily returns at time t; Di a dummy variable that represents each day/month; et the residual error term assumed to be distributed normally with a mean of zero and variance equal to s2t ; a0, a1, bj and yI are parameters to be estimated; s2t is the one-period ahead forecast variance (conditional variance); p the order of last period’s forecast variance (GARCH term); q the order of the squared residual error term from the mean equation (ARCH term). The dummy variable takes the value of one for each day of the week or month of the year and becomes zero otherwise. In order for the GARCH(1,1) model to ensure positive conditional variance, the following must be true: a0 40, ai 0, bj 0 and a þ bo1. Upon finding significant day-of-the-week or month-of-the-year effects in GARCH(1,1), we must further determine whether the significant returns are associated with the systematic risk of the stock market following Clare et al. (1998) and Yakob et al. (2005). In these cases, we employ the GARCHM(1,1) model where the conditional variance term is placed into the mean equation as follows: Rt ¼

N X

yi Di þ dst þ et

(5)

i¼1

where the coefficient of D is the significant dummy variable obtained from Eq. (3), st the standard deviation of the conditional variance, which portrays systematic risk, and d captures the influence of conditional

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volatility on stock returns. If the day-of-the-week and month-of-the-year dummy variables remain significant as explanatory variables after including the systematic risk adjustment, then we may conclude the stock return seasonality to be independent of temporary market volatility.

4.2. Preliminary Analysis of Seasonality Tables 5 and 6 show average returns over the entire sample period of 1985–2004 for preliminary analysis of the day-of-the week effect and the month-of-the-year effect. They include p-values determined using a Z-test to indicate significance. Table 5 reports significant positive returns on Tuesday, Wednesday and Friday for Hong Kong, significant negative returns on Monday and significant positive returns on Wednesday for Japan and no significant returns on any day of the week for Korea. For both Hong Kong and Japan, Wednesday shows significant positive returns. This might reflect some kind of spillovers from the US with the time zone difference. Regarding the month-of-the-year effect, Table 6 reports that the Korean market has a negative significant monthly effect for August and positive significant monthly effects for May, October and December. Hong Kong has positive significant monthly effects for January, April, October and November, while the Japanese market exhibited a significant positive effect for January and a significant negative effect for September. For both Hong Kong and Japan, the January effect is significant. The January effect is also observed in the US. In this regard, we can again confirm that the Korean stock market is significantly less mature than the

Table 5. The Day-of-the-Week Effects for Korea, Hong Kong and Japan: 1985–2004.

Korea Hong Kong Japan

Monday

Tuesday

Wednesday

Thursday

Friday

0.02 (0.40) 0.08 (0.13) 0.09** (0.04)

0.03 (0.30) 0.10** (0.02) 0.03 (0.23)

0.10 (0.44) 0.14*** (0.00) 0.06* (0.08)

0.03 (0.27) 0.01 (0.48) 0.05 (0.13)

0.06 (0.14) 0.17*** (0.00) 0.01 (0.44)



183

Table 6. The Month-of-the-Year Effects for Korea, Hong Kong and Japan: 1985–2004. Period Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec

Korea

Hong Kong

Japan

1.05 (0.30) 0.28 (0.44) 2.39 (0.13) 1.15 (0.25) 2.52* (0.09) 1.03 (0.27) 1.78 (0.13) 4.07*** (0.00) 1.54 (0.26) 5.53*** (0.00) 1.78 (0.18) 4.27* (0.07)

4.31** (0.01) 0.94 (0.25) 0.66 (0.34) 3.29** (0.05) 0.20 (0.45) 1.58 (0.11) 0.53 (0.37) 0.09 (0.48) 1.52 (0.33) 2.27* (0.07) 3.28** (0.03) 0.81 (0.32)

1.72* (0.09) 0.63 (0.29) 1.38 (0.19) 1.46 (0.13) 1.10 (0.19) 0.71 (0.30) 0.39 (0.38) 0.59 (0.37) 2.33** (0.03) 0.60 (0.35) 0.48 (0.38) 0.13 (0.46)


stock markets of Hong Kong and Japan. This makes sense because the January effect has something to do with the tax system. Japan shows significant negative average daily returns for September and Korea shows the same for August. This might be due to Asian Thanksgiving holidays in either late August or early September.

4.3. Regression Analysis Results of Seasonality Tables 7, 8 and 9 present results from the GARCH(1,1) and GARCH(1,1)-M models that investigate the day-of-the-week effect on stock returns for Korea, Hong Kong and Japan respectively. The entire sample period of 1985–2004

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Regression Results for Day-of-the-Week Effect: Korea.

Table 7.

GARCH(1,1) 1985–2004 Mean equation Monday

0.03 (0.52) 0.03 (0.37) 0.11*** (0.00) 0.05 (0.16) 0.07** (0.04)

0.02 (0.63) 0.02 (0.62) 0.11*** (0.01) 0.04 (0.34) 0.07* (0.07)

0.01*** (0.00) 0.11*** (0.00) 0.88*** (0.00)

0.04*** (0.00) 0.16*** (0.00) 0.82*** (0.00)

444.56*** (0.00) 128.70*** (0.00) 42.22* (0.07) 43.79** (0.05) 9813.53

152.78*** (0.00) 111.37*** (0.00) 42.43* (0.07) 44.37** (0.04) 5351.56

Tuesday Wednesday Thursday Friday

Conditional variance a0 a1 b

Jarque-Bera Q(30) Q2(30) ARCH-LM(30) Log-likelihood

1985–1996

GARCH-M(1,1) 1999–2004

0.04 (0.73) 0.18** (0.05) 0.07 (0.54) 0.12 (0.26) 0.14 (0.18)

1985–2004

1985–1996

1999–2004

0.11 (0.30) 0.06 (0.15)

0.06 (0.17)

0.02 (0.58)

0.02 (0.65)

0.04 (0.11) 0.05*** (0.00) 0.94*** (0.00)

0.01*** (0.00) 0.06*** (0.00) 0.89*** (0.00)

0.04*** (0.00) 0.16*** (0.00) 0.83*** (0.00)

0.04 (0.12) 0.05*** (0.00) 0.94*** (0.00)

384.55*** (0.00) 30.46 (0.44) 19.83 (0.92) 19.89 (0.92) 3159.21

442.32*** (0.00) 129.93*** (0.00) 41.40* (0.08) 43.32*** (0.00) 9810.35

153.86*** (0.00) 112.46*** (0.00) 42.84* (0.06) 44.74** (0.04) 5348.53

380.24*** (0.00) 29.94 (0.47) 18.66 (0.95) 18.89 (0.94) 3161.28


is divided into the precrisis period of 1985–1996 and postcrisis period of 1999–2004. These are investigated separately in order to capture the changed pattern of seasonality, if any, after the Asian financial crisis. Coefficients a and b are significant for all three countries over the different sample period, marking the heteroscedasticity of the residual term that is captured by the GARCH(1,1) model. To assess the adequacy of the specification, we looked at Jarque-Bera statistics, ARCH-LM test statistics and (squared) Q-statistics. Highly significant Jarque-Bera statistics for the three countries represent the nonnormality of the residual series, rendering the estimates of the covariance matrix inconsistent. To compensate, we computed the quasi-maximum


185

Table 8. Regression Results for Day-of-the-Week Effect: Hong Kong. GARCH(1,1) 1985–2004 Mean equation Monday

0.16** (0.01) 0.25*** (0.00) 0.14** (0.02) 0.20*** (0.00)

0.12 (0.31)

0.09*** (0.00) 0.14*** (0.00) 0.84*** (0.00)

0.14* (0.09) 0.18*** (0.00) 0.76*** (0.00)

0.02 (0.05) 0.05 (0.00) 0.94 (0.00)

0.09*** (0.00) 0.14*** (0.00) 0.84*** (0.00)

0.14*** (0.00) 0.18*** (0.00) 0.76*** (0.00)

0.02** (0.04) 0.05*** (0.00) 0.94*** (0.00)

6078.04*** (0.00) 104.08*** (0.00) 118.89*** (0.00) 112.62*** (0.00) 8747.58

7250.04*** (0.00) 97.23*** (0.00) 67.34*** (0.00) 66.83*** (0.00) 4989.68

6138.78*** (0.00) 104.47*** (0.00) 118.26*** (0.00) 121.94 (0.85) 8747.36

7378.06*** (0.00) 97.70*** (0.00) 66.00*** (0.00) 65.43*** (0.00) 4989.79

108.53*** (0.00) 22.21 (0.85) 21.68 (0.87) 21.73 (0.86) 2271.52

Conditional variance a0

Q2(30) ARCH-LM(30) Log-likelihood

1999–2004

0.12* (0.01) 0.15*** (0.00) 0.07 (0.15) 0.17*** (0.00)

Friday

Q(30)

1985–1996

0.06 (0.39) 0.11 (0.19) 0.08 (0.29) 0.01 (0.93) 0.15* (0.07)

Thursday

Jarque-Bera

1985–2004

0.02 (0.63) 0.17*** (0.00) 0.26*** (0.00) 0.15*** (0.00) 0.21*** (0.00)

Wednesday

b

1999–2004

0.00 (0.91) 0.14*** (0.00) 0.17*** (0.00) 0.09** (0.02) 0.19*** (0.00)

Tuesday

a1

1985–1996

GARCH-M(1,1)

104.32*** (0.00) 23.03 (0.81) 21.89 (0.86) 21.99 (0.85) 2270.04


likelihood (QML) covariances and standard errors using the methods described by Bollerslev and Wooldridge (1992). If the variance equation is correctly specified, there should be no autoregressive conditional heteroskedasticiy (ARCH) left in the standardized residuals. The ARCH-LM test confirms the absence of the ARCH effect in the residual up to lag 30 for the second subsample of 1999–2004 for Korea and Hong Kong, and for the all the sample groups for Japan. If the mean (variance) equation is correctly specified, (squared) Q-statistics should not be significant. (Squared) Q-statistics with a lag of 30 show the absence of a remaining ARCH effect in the mean (variance) equation for the second subsample of 1999–2004 for Korea and Hong Kong, and for all the sample groups for Japan.

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Table 9. Regression Results for Day-of-the-Week Effect: Japan. GARCH(1,1) 1985–2004 Mean equation Monday

1985–1996

0.04 (0.36) 0.05 (0.20) 0.14*** (0.00) 0.09*** (0.00) 0.06* (0.10)

0.07 (0.23) 0.06 (0.11) 0.18*** (0.00) 0.13*** (0.00) 0.08** (0.04)

Conditional variance 0.02*** a0 (0.00) a1 0.13*** (0.00) b 0.87*** (0.00)

0.03*** (0.00) 0.19*** (0.00) 0.82*** (0.00) 8601.22*** (0.00) 42.56* (0.06) 26.08 (0.67) 26.35 (0.71) 4467.96

Tuesday Wednesday Thursday Friday


9578.94*** (0.00) 39.00 (0.13) 23.21 (0.81) 22.63 (0.83) 8080.70

GARCH-M(1,1) 1999–2004

0.09 (0.34) 0.03 (0.68) 0.03 (0.74) 0.01 (0.89) 0.05 (0.52)

1985–2004

1985–1996

1999–2004

–

0.14*** (0.00) 0.097*** (0.00) 0.05 (0.11)

0.06** (0.05) 0.08* (0.10) 0.03 (0.62)

0.09** (0.02) 0.07*** (0.00) 0.88*** (0.00)

0.02*** (0.00) 0.13*** (0.00) 0.87*** (0.00)

0.03*** (0.00) 0.19*** (0.00) 0.81*** (0.00)

78.14*** (0.00) 18.01 (0.96) 32.85 (0.33) 31.44 (0.39) 2644.84

8782.70*** (0.00) 44.92** (0.04) 25.82 (0.69) 25.17 (0.72) 8086.70

8782.70 (0.00) 44.92 (0.04) 25.82 (0.69) 25.17 (0.72) 4471.08

–

–


Consistent with Choudhry (2000) and Balaban, Bayar, and Kan (2001), the patterns of seasonality differ from one country to another. For the whole sample period, GARCH(1,1) results show the positive significant returns on Wednesday and Friday for Korea, Tuesday, Wednesday, Thursday and Friday for Hong Kong and Wednesday, Thursday and Friday for Japan. No country exhibited statistically significant negative returns on Monday, while all three countries showed the weekend effect.2 The results for the subperiod of 1985–1996 are nearly identical to those for the whole period. Existence of the day-of-the-week effects suggests stock markets produce significantly higher (or lower) returns on one day than on other days.


187

Because the level of risk in stock markets change over time, we need to determine whether our results are due to actual seasonal effects or merely the change in systematic risk in the Asian markets. For this reason, we utilize the GARCH-M(1,1) model to determine whether stock market seasonality is due to the influence of conditional risk. The GARCH-M(1,1) results show that the estimated coefficients (y in Eq. (5)) on Tuesday, Wednesday and Friday for Hong Kong and Wednesday and Thursday for Japan are significant; but not for Korea. This implies the weekly seasonality patterns of Korea are due to the daily variation in equity risk. Comparing the estimation result between the first subsample period of 1985 to 1996 and the second subsample period of 1999 to 2004, the day of week effect presented in the first subsample period disappears in the second, with the exception of the weekend effect for Hong Kong that becomes insignificant in GARCH-M(1,1) results. Results like these might suggest that, after the Asian financial crisis, Asian stock markets became significantly more open to foreign investors. This might have caused some of the day-of-the-week effects normally associated with local culture and tradition to become insignificant. Our results on the day-of-the-week effects are consistent with those obtained by Yakob et al. (2005), who analyzed the seasonality patterns of stock markets for 10 Asia Pacific countries. They did not observe the Monday effect except in Indonesia. Our results also indicate the lack of the Monday effect (i.e. there are no significant negative returns on Monday). It appears that in the Asian stock markets, Monday is not much different from other days of the week. Yakob et al. (2005) also observed the Wednesday effect for Indonesia and the Friday effect for Australia, Indonesia and Taiwan. In our study, the Wednesday effect and the Friday effect were significant for all three countries. We can conclude that although the Monday effect is not a global affair, the Friday effect may be one. Yakob et al. (2005) found no significant evidence for the day-of-the-week effect for Korea, Hong Kong and Japan. We believe this is because they only used the data after 2000. Our study shows that the day-of-the-week effect is significant for 1985–1996, which was before the Asian financial crisis, whereas the effect is not significant for 1999–2004 for all three countries. The reason for the Wednesday effect in Asian stock markets is not clear. We speculate that the Wednesday effect is somewhat related to the spillover from the US over the different time zones. Tables 10, 11 and 12 present the results for the month-of-the-year effect for the three countries respectively. As with the results for the day of the

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Regression Results for Month-of-the-Year Effect: Korea.

Table 10.

GARCH(1,1) 1985–2004

1985–1996

1999–2004

0.07 (0.28) 0.03 (0.66) 0.12** (0.01) 0.03 (0.59) 0.06 (0.21) 0.05 (0.31) 0.08* (0.09) 0.01 (0.89) 0.07 (0.13) 0.09** (0.05) 0.19** (0.01) 0.13* (0.09)

0.03 (0.63) 0.03 (0.67) 0.13** (0.01) 0.02 (0.80) 0.07 (0.18) 0.08 (0.15) 0.10** (0.03) 0.03 (0.67) 0.10** (0.04) 0.07 (0.13) 0.16** (0.05) 0.13 (0.13)

0.16 (0.39) 0.07 (0.69) 0.07 (0.64) 0.25 (0.19) 0.04 (0.85) 0.12 (0.50) 0.11 (0.46) 0.31** (0.05) 0.39* (0.06) 0.20 (0.25) 0.33** (0.04) 0.02 (0.90)

Mean equation January February March April May June July August September October November December

Conditional variance a0 a1 b


GARCH-M(1,1) 1985–2004

1985–1996

0.08* (0.10)

0.09* (0.08)

0.04 (0.36)

0.07 (0.18)

1999–2004

0.07 (0.19)

0.23 (0.17) 0.47** (0.03)

0.06 (0.24) 0.15 (0.06)* 0.09 (0.28)

0.12 (0.17)

0.25 (0.14)

0.01*** (0.00) 0.11*** (0.00) 0.89*** (0.00)

0.04*** (0.00) 0.16*** (0.00) 0.83*** (0.00)

0.04* (0.09) 0.05*** (0.00) 0.94*** (0.00)

0.01*** (0.00) 0.11*** (0.00) 0.89*** (0.00)

0.04*** (0.00) 0.16*** (0.00) 0.83*** (0.00)

0.04* (0.10) 0.05*** (0.00) 0.25 (0.14)

414.44*** (0.00) 126.45*** (0.00) 43.80** (0.05) 45.58** (0.03) 9805.36

141.54*** (0.00) 109.96*** (0.00) 43.85** (0.05) 45.78** (0.03) 5342.96

300.50*** (0.00) 32.47 (0.35) 21.50 (0.87) 21.29 (0.88) 3153.12

410.06*** (0.00) 127.15*** (0.00) 43.12* (0.06) 45.16** (0.04) 9806.74

148.90*** (0.00) 110.64*** (0.00) 44.73** (0.04) 46.67** (0.03) 5345.73

289.38*** (0.00) 31.68 (0.38) 20.47 (0.90) 20.66 (0.90) 3156.00



Table 11.

189

Regression Results for Month-of-the-Year Effect: Hong Kong. GARCH(1,1)

1985–2004 Mean equation January

0.22*** (0.00) 0.26** (0.01) 0.06 (0.45) 0.12 (0.13) 0.26*** (0.00) 0.01 (0.85) 0.21*** (0.00) 0.02 (0.78) 0.08 (0.18) 0.42*** (0.00) 0.07 (0.25) 0.16** (0.02)

0.00 (0.97) 0.03 (0.80) 0.15 (0.23) 0.12 (0.42) 0.03 ().82) 0.04 (0.69) 0.03 (0.77) 0.14 (0.18) 0.08 (0.50) 0.11 (0.46) 0.29*** (0.00) 0.02 (0.85)

0.09*** (0.00) 0.13*** (0.00) 0.84*** (0.00)

0.14** (0.01) 0.18*** (0.00) 0.77*** (0.00)

414.44*** (0.00) 126.45*** (0.00) 43.80** (0.05) 45.58** (0.03) 8741.61

141.54*** (0.00) 109.96*** (0.00) 43.85** (0.03) 45.78** (0.03) 4985.01

March April May June July August September October November December

Conditional variance a0

b

Jarque-Bera Q(30) Q2(30)

ARCH-LM(30) Log-likelihood

1999–2004

0.15** (0.02) 0.20** (0.01) 0.03 (0.58) 0.11 (0.11) 0.20*** (0.00) 0.03 (0.54) 0.17*** (0.00) 0.01 (0.91) 0.04 (0.44) 0.33*** (0.00) 0.15** (0.01) 0.10* (0.08)

February

a1

1985–1996

GARCH-M(1,1)


1985–2004

1985–1996

1999–2004

0.11 (0.11) 0.15 (0.15)

0.15* (0.06) 0.19* (0.06)

0.16** (0.01)

0.19** (0.01)

0.13** (0.02)

0.15** (0.02)

0.29** (0.01) 0.11* (0.08) 0.06 (0.32)

0.36** (0.01)

0.10 (0.18)

0.16** (0.04)

0.02* (0.08) 0.05*** (0.00) 0.95*** (0.00)

0.09*** (0.00) 0.14*** (0.00) 0.84*** (0.00)

0.14** (0.01) 0.18*** (0.00) 0.76*** (0.00)

0.03*** (0.00) 0.08*** (0.00) 0.91*** (0.00)

300.50*** (0.00) 32.47 (0.35) 21.50 (0.87) 21.29 (0.88) 2626.34

416.06*** (0.00) 127.15*** (0.00) 43.12* (0.06) 45.16** (0.04) 8742.33

148.90*** (0.00) 10.64*** (0.00) 44.73** (0.04) 46.67** (0.03) 4985.28

289.38*** (0.00) 31.68 (0.38) 20.47 (0.90) 20.06 (0.90) 4973.99

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Table 12.

Regression Results for Month-of-the-Year Effect: Japan. GARCH(1,1) 1985–2004

Mean equation January

1985–1996

0.17** (0.02) 0.11** (0.01) 0.20*** (0.00) 0.11** (0.05) 0.09** (0.05) 0.02 (0.72) 0.02 (0.75) 0.01 (0.86) 0.02 (0.66) 0.06 (0.41) 0.11** (0.04) 0.09** (0.04)

0.20** (0.01) 0.14*** (0.00) 0.28** (0.01) 0.15** (0.03) 0.11** (0.03) 0.03 (0.60) 0.02 (0.69) 0.04 (0.36) 0.02 (0.68) 0.11 (0.29) 0.11* (0.08) 0.11 (0.02)**

Conditional variance a0 0.02*** (0.00) a1 0.13*** (0.00) b 0.87*** (0.00)

0.03*** (0.00) 0.19*** (0.00) 0.82*** (0.00)

GARCH-M(1,1) 1999–2004

1985–1996 1999–2004

0.15* (0.06) 0.10** (0.02) 0.20** (0.01) 0.10* (0.08) 0.08* (0.09)

0.16* (0.08) 0.12** (0.01) 0.26** (0.02) 0.11 (0.11) 0.08 (0.14)

0.10* (0.06) 0.09* (0.08)

0.08 (0.22) 0.09 (0.10)

0.02*** (0.00) 0.14*** (0.00) 0.87*** (0.00)

0.03*** (0.00) 0.20*** (0.00) 0.81*** (0.00)

–

8691.97*** 7145.18*** 69.17*** 8806.41*** 7600.00*** (0.00) (0.00) (0.00) (0.00) (0.00) Q(30) 38.06 40.09 19.67 38.27 40.20 (0.15) (0.10) (0.93) (0.14) (0.10) 26.12 31.66 32.29 25.89 30.89 Q2(30) (0.67) (0.38) (0.35) (0.68) (0.42) ARCH-LM(30) 25.41 30.65 30.96 25.35 30.04 (0.70) (0.43) (0.42) (0.71) (0.46) Log-likelihood 8073.14 4459.38 2641.84 8079.67 4464.00

–

February March April May June July August September October November December

Jarque-Bera


0.04 (0.77) 0.02 (0.88) 0.13 (0.39) 0.03 (0.80) 0.05 (0.69) 0.17 (0.11) 0.16 (0.21) 0.05 (0.64) 0.14 (0.32) 0.04 (0.74) 0.12 (0.36) 0.04 (0.69)

1985–2004

0.09** (0.02) 0.07*** (0.00) 0.89*** (0.00)

–


191

week effect, coefficients a and b are significant for all three countries over the three different sample periods, marking the heteroscedasticity of the residual term that is captured by the GARCH(1,1) model. ARCH-LM statistics confirm the absence of the ARCH effect in the residual up to lag 30 for the second subsample of 1999–2004 for Korea and Hong Kong, and for all the three sample groups for Japan. Q-statistics with a lag of 30 for Korea and Hong Kong show that serial correlations traced before the financial crisis has disappeared after the crisis. For the Japanese market, no serial correlation is detected regardless of the sample periods considered. As with the day-of-the-week effect, the month-of-the-year effect is not so prevalent in the Korean stock market. We find positive March and November effects for the whole sample period, a positive March effect for the first subsample period of 1985–1996, and a negative September effect for the second subsample period of 1999–2004 after controlling for the market risk in GARCH-M(1,1). The month-of-the-year effect is found to be more prevalent than the dayof-the-week effect for the Hong Kong and Japanese markets. Regarding the whole sample period, positive significant returns for May, July, October and November for Hong Kong, and for January, February, March, April, May, November and December for Japan are found after controlling for the market risk. For the second subsample period of 1999–2004, the Hong Kong market exhibited a positive significant December effect, while the Japanese market exhibited none. As we found in the preliminary data analysis of seasonality in the previous section, both Japan and Hong Kong have significant positive returns for January, whereas the January effect is not significant in Korea. Yakob et al. (2005) also found significant positive returns on January for Malaysia and Taiwan. Therefore, we could conclude that the January effect may be a global affair. Yakob et al. (2005) also found significant negative returns in September for China, Malaysia and Korea. We speculate that the reason for the September effect is somewhat related to Asian Thanksgiving holidays in September in these Asian countries. As reported above, significant positive returns for November and/or December were observed for all three countries. Yakob et al. (2005) also found significant positive effects in November and/or December for Australia, India and Indonesia. These might be related to year-end financial announcements by corporations and year-end bonus payments by Asian employers.

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5. SUMMARY AND CONCLUSIONS This study provides evidence that investors overreacted on days when the Korean, Hong Kong and Japanese stock markets lost 5% or more value in their indices. This evidence is similar to that of other markets in other countries. Also, the three markets showed little or no evidence of overreaction on days of excessive gain in the market index. We conclude that, as shown in studies of other markets, investors overreact more to bad news than to good news as evidenced by the stock market corrections on the days following excessive stock market declines on the Kospi, the Hang Seng and the Nikkei. Overreaction to excessive loss on stock indices is significantly faster for Hong Kong and Japan where the stock markets are far more mature than the Korean stock market. We feel further research may uncover anomalies, such as those appearing in the US markets. The seasonality patterns of the three countries’ stock markets were analyzed in terms of the day-of-the-week effect and the month-of-the-year effect. The analysis of the day-of-the-week effect revealed that the Monday effect is not significant and the Friday or weekend effect is significant in our three Asian countries. The weekend effect appears to be a global affair. Our three countries’ stock markets have significant positive returns on Wednesday. The reason for the Wednesday effect is not clear. As for the month-of-the-year effect, the January effect was observed in Hong Kong and Japan, but not in Korea. In the Asian stock markets, significant negative returns on September were observed and significant positive returns on November and/or December were observed.

NOTES 1. We selected Korea, Hong Kong and Japan because of the maturity of their stock markets and the importance of their economies among the dynamic East Asian economies. Stock markets of Hong Kong and Japan are far more mature than that of Korea. Therefore, we could anticipate the Korean stock market behaves slightly differently from those of Hong Kong and Japan. Furthermore, while Japan hardly suffered and Hong Kong mildly suffered from the Asian financial crisis that affected some East Asian countries during 1997 to 1999, Korea suffered severely from the Asian crisis. Therefore, we will be able to analyze the effect of the Asian crisis on stock markets by studying these three countries’ stock markets. 2. Until December 1998, the Korean stock market had been on Saturday. Therefore, a positive coefficient on Friday for the Korean market should not be considered to reflect the weekend effect in the strict sense.


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REFERENCES Aggarwal, A., & Tandon, D. (1994). Anomalies or illusions? Evidence from stock markets in eighteen countries. Journal of International Money and Finance, 13, 83–106. Aggarwal, R., & Rivoli, P. (1989). Seasonal and day-of-the week effects in the emerging stock markets. The Financial Review, 24(4), 541–550. Atkins, A. B., & Dyl, E. (1990). Price reversals, bid-ask spreads, and market efficiency. Journal of Financial and Quantitative Analysis, 24, 535–547. Balaban, E., Bayar, A., & Kan, O. B. (2001). Stock returns, seasonality and asymmetric conditional volatility in world equity markets. Applied Economic Letters, 8, 263–268. Ball, R., & Kothari, S. P. (1989). Nonstationary expected returns: Implications for tests of market efficiency and serial correlation in returns. Journal of Financial Economics, 25, 51–74. Bollerslev, T., & Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Economic Review, 11, 143–172. Bollerslev, T. P. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307–327. Brookfield, D. (1993). Traded options, capital gains and the term structure of implied volatilities. Applied Financial Economics, 3, 1–13. Brown, K. C., & Harlow, W. V. (1988). Market overreaction: Magnitude and intensity. Journal of Portfolio Management, 14(2), 6–13. Brown, K. C., Harlow, W. V., & Tinic, S. M. (1988). Risk aversion, uncertain information and market efficiency. Journal of Financial Economics, 22(2), 355–385. Chan, K. C. (1988). On the contrarian investment strategy. Journal of Business, 61, 147–163. Chen, C. R., & Sauer, D. A. (1997). Is stock market overreaction persistent over time? Journal of Business, Finance & Accounting, 24(1), 51–67. Cheung, K. C., & Coutts, J. A. (1999). The January effect and monthly seasonality in the Hang Seng Index: 1985–1997. Applied Economics Letters, 6, 121–123. Choudhry, T. (2000). Day of the week effect in emerging Asian stock markets: Evidence from the GARCH model. Applied Financial Economics, 10, 235–242. Clare, A., & Thomas, S. (1995). The Overreaction Hypothesis and the UK Stockmarket. Journal of Business, Finance & Accounting, 22(7), 961–973. Clare, A. D., Ibrahim, M. S. B., & Thomas, S. H. (1998). The impact of settlement procedures on the day-of-the-week effects: Evidence from the Kuala Lumpur stock exchange. Journal of Business Finance & Accounting, 25, 401–418. Connolly, R. (1989). An examination of the robustness of the weekend effect. Journal of Financial and Quantitative Analysis, 24, 133–169. Cox, D. R., & Peterson, D. R. (1994). Stock returns following large one-day declines: Evidence on short-term reversals and longer-term performance. Journal of Finance, 49(1), 255–267. DeBondt, W., & Thaler, R. (1985). Does the stock market overreact? Journal of Finance, 40(3), 793–805. DeBondt, W., & Thaler, R. (1987). Further evidence on investor overreaction and stock market seasonality. Journal of Finance, 42(3), 557–581. Diacogiannis, G., Patsalis, N., Tsangarakis, N. V., & Tsiritakis, E. D. (2005). Price limits and overreaction in the Athens stock exchange. Applied Financial Economics, 15(1), 53–61.

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Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating time varying risk premia in the term structure: The ARCH-M Model. Econometrica, 66, 1127–1162. Fama, E. (1965). The behaviour of stock market prices. Journal of Business, 38, 34–105. Fields, M. J. (1931). Stock prices: A problem in verification. Journal of Business, 7, 415–418. French, K. (1980). Stock returns and the weekend effect. Journal of Financial Economics, 8, 55–70. Fung, A. K., Mok, D. M. Y., & Lam, K. (2000). Intraday price reversals for index futures in the US and Hong Kong. Journal of Banking & Finance, 24(7), 1179–1201. Gibbons, M., & Hess, P. (1981). Day of the week effects and asset returns. Journal of Business, 54, 579–596. Holden, K., Thompson, J., & Ruangrit, Y. (2005). The Asian crisis and calendar effects on stock returns in Thailand. European Journal of Operational Research, 163, 242–252. Howe, J. (1986). Evidence on stock market overreaction. Financial Analysts Journal, 42, 74–77. Jaffe, J., & Westerfield, R. (1985a). The weekend effect in common stock returns: The international evidence. Journal of Finance, 40, 433–454. Jaffe, J., & Westerfield, R. (1985b). Patterns in Japanese common stock returns: Day of the week and turn of the year effect. Journal of Financial and Quantitative Analysis, 20, 261–272. de Jong, F., Kemman, A., & Kloek, T. (1992). A contribution to event study methodology with an application to the Dutch stock market. Journal of Banking and Finance, 16, 11–36. Kamath, R. R., Chakornpipat, R., & Chatrath, A. (1998). Return distributions and the day-ofthe-week effects in stock exchange of Thailand. Journal of Economics and Finance, 22, 97–106. Keim, D., & Stambaugh, R. (1984). A further investigation of the weekend effect in stock returns. Journal of Finance, 39, 819–834. Ketcher, D. N., & Jordan, B. D. (1994). Short-term price reversals following major price innovations: Additional evidence on market overreaction. Journal of Economics and Business, 46(4), 307–324. Kim, S. (1988). Capitalizing on the weekend effect. Journal of Portfolio Management, 14(3), 59–63. Mandlebrot, B. (1963). The variance of certain speculative prices. Journal of Business, 36, 394–419. Masulis, R. W. (1980). The effects of security structural change on security prices: A study of exchange offer. Journal of Financial Economics, 8, 139–178. Mills, T. C., & Coutts, J. A. (1995). Calendar effects in the London stock exchange FT-SE Indices. European Journal of Finance, 1, 79–94. Mun, J. C., Vasconcellos, G. M., & Kish, R. (1999). Tests of the contrarian investment strategy evidence from the French and German stock markets. International Review of Financial Analysis, 8(3), 215–234. Nam, K., Pyun, C. S., & Avard, S. L. (2001). Asymmetric reverting behavior of short-horizon stock returns: An evidence of stock market overreaction. Journal of Banking & Finance, 25(4), 807–824. Nassir, A. M., & Mohammad, S. (1987). The January effect of stocks traded on the Kuala Lumpur stock exchange: An empirical analysis. Hong Kong Journal of Business Management, 5, 33–50. Peiro, A. (1994). Daily seasonality in stock returns: Further international evidence. Economics Letters, 45, 227–232.


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A MEAN-GINI APPROACH TO ASSET ALLOCATION INVOLVING HEDGE FUNDS C. Sherman Cheung, Clarence C. Y. Kwan and Peter C. Miu ABSTRACT In response to common criticisms on the appropriateness of meanvariance in asset allocation decisions involving hedge funds, we offer a mean-Gini framework as an alternative. The mean-Gini framework does not require the usual normality assumption concerning return distributions. We also evaluate empirically the differences in allocation outcomes between the two frameworks using historical data. The differences turn out to be significant. The evidence thus confirms the inappropriateness of the mean-variance framework and enhances the attractiveness of meanGini for this asset class.

Diversification has long been accepted as a sound practice of investments among academics and practitioners. It can take the form of investments in the same asset type across international markets. A pension fund in this case can hold not only US equities but also international equities. Diversification can also take the form of investments in different asset classes. Hedge funds have emerged as a popular asset class in the last decade or so. As Ibbotson Research in Finance, Volume 24, 197–212 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00208-0

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and Chen (2005) report, about 530 hedge funds, totaling 50 billion dollars, were available in 1990 and, by the end of 2004, the number of hedge funds was over 8,000, with about 1 trillion dollars under management. The attractiveness of hedge funds very often is perceived to be their equity-like returns with bond-like risk. This general acceptance of hedge funds has also created a problem for asset allocation decisions. The mean-variance approach that has revolutionized risk analysis and portfolio management may not work well for hedge funds. Mean-variance analysis is appropriate when returns are normally distributed or investors’ preferences are quadratic. Levy and Markowitz (1979) justify the use of mean-variance by showing that it is a second-order Taylor-series approximation of utility functions. The degree of exactness depends on the degree of non-normality of the return series and the nature of the utility function. Fung and Hsieh (1997) demonstrate that hedge funds display option-like payoff patterns that are not normally distributed. Agarwal and Naik (2004) also show that many equity-oriented hedge funds resemble a short position in a put option on the market index and therefore display significant left-tail risk. They argue that the traditional meanvariance framework tends to underestimate the tail risk. Lo (2005) raises similar distributional issues and argues against the mean-variance framework. While there is widespread doubt about the appropriateness of the mean-variance framework, there seems to be no consensus on an alternative. This chapter serves two purposes. First, we offer mean-Gini as an alternative to the traditional mean-variance approach in asset allocations involving hedge funds. Second, we evaluate the magnitude of errors introduced by the mean-variance approach.

THE GINI COEFFICIENT The Gini coefficient has a long history as a measure of income inequality in the economics literature. It has been introduced into the finance profession as a measure of risk in investments.1 To illustrate, suppose that the return of an investment can be characterized as a random draw from a probability distribution. Suppose also that we take many pairs of random draws from the distribution and observe the magnitude of the difference between each pair. For a widely (narrowly) dispersed distribution, the magnitude of that difference would tend to be large (small). The mean-Gini approach therefore has the simplicity of the mean-variance approach framework in that it uses two summary statistics to characterize the distribution of a risky prospect.

A Mean-Gini Approach to Asset Allocation Involving Hedge Funds

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As shown in Yitzhaki (1982), Shalit and Yitzhaki (1984), and others in the literature, the mean-Gini framework is theoretically more superior than mean-variance in the ranking of risky prospects with different return distributions. The framework provides necessary conditions for establishing first- and second-degree stochastic dominance regardless of the probability distribution of returns. It also provides sufficient conditions for cases where the cumulative distributions intersect at most once (see Shalit and Yitzhaki (1984) for the analytical correspondence between mean-Gini and stochastic dominance).2 The restrictive assumption of quadratic utility function or normally distributed asset returns underlying the mean-variance framework is therefore not required in mean-Gini. Depending on the economic context, the Gini coefficient can be defined in various ways. As a risk measure in investments, it is typically defined as 1 G ¼ Ejz1 z2 j 2 where E stands for the expected value operator. According to this expression, G is half of the expected value of the absolute difference between z1 and z2, a pair of realized returns from a cumulative probability density function F(z), defined over a finite range of z ¼ a to z ¼ b, where bWa. Noting that jz1 z2 j ¼ z1 þ z2 2 minðz1 ; z2 Þ we follow Dorfman (1979) and Shalit and Yitzhaki (1984) to express the Gini coefficient as 1 Eðz1 Þ þ Eðz2 Þ 2E ½minðz1 ; z2 Þ G¼ 2 ¼ EðzÞ E ½minðz1 ; z2 Þ In order to express E ½minðz1 ; z2 Þ in terms of F(z), we can treat minðz1 ; z2 Þ as a random variable y from a cumulative probability density function G(y). Given that Prðz1 yÞ ¼ Prðz2 yÞ ¼ F ð yÞ and Prðz1 4yÞ Prðz2 4yÞ ¼ ½1 F ð yÞ2 we have Pr½minðz1 ; z2 Þ y ¼ 1 ½1 F ð yÞ2

200


which is also G( y). It follows that Z b Z E ½minðz1 ; z2 Þ ¼ ydGð yÞ ¼ 2 y¼a

b

y½1 F ð yÞdF ð yÞ

y¼a

As Z

b

EðzÞ ¼

zdF ðzÞ z¼a

Z

b

E ½F ðzÞ ¼

F ðzÞdF ðzÞ ¼ z¼a

1 2

and Z

b

EðzÞ F ðzÞ E ½F ðzÞ dF ðzÞ ¼ 0

z¼a

the Gini coefficient becomes Z b Z b G¼ zdF ðzÞ 2 z½1 F ðzÞdF ðzÞ z¼a z¼a Z b 1 ¼2 z F ðzÞ dF ðzÞ 2 z¼a ¼ 2Cov½z; F ðzÞ which is twice the covariance between the random variable z and its cumulative probability density function F(z). As Lerman and Yitzhaki (1984) explain, the Gini coefficient is proportional to the covariance between the observed values of the variable z and their ranks when they are sorted in an ascending order. Intuitively, with ranks of 1, 2, y, T being assigned to the T observations of the variable z, the cumulative distribution corresponding to the observed value having a rank of t is t/T. For example, the 25th, 50th, and 75th lowest values of 100 observations correspond to the cumulative probabilities of 0.25, 0.50, and 0.75, respectively. Thus, the Gini coefficient can be computed with ease. To extend the Gini coefficient as a risk measure to portfolios of n assets, let R1, R2, y, Rn be the individual random returns. The return on portfolio p can be written as Rp ¼

n X i¼1

xi Ri


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where x1, x2, y, xn are the portfolio weights (i.e., the proportions of investment funds as allocated to the individual assets) satisfying the condition of n X

xi ¼ 1

i¼1

In the case of no short sales, the additional constraints are xi 0; for

i ¼ 1; 2; . . . ; n

Similarly, the portfolio’s Gini coefficient can be written as Gp ¼ 2Cov Rp ; F ðRp Þ

(1)

where F ðRp Þ is the cumulative probability distribution of the portfolio returns. The idea is that, for any given set of portfolio weights, as the random return of a portfolio is a linear combination of the random returns of individual assets in the portfolio with known probability distributions, the portfolio’s Gini coefficient can be established from the implied probability distribution of portfolio returns. An equivalent form of Eq. (1) is Gp ¼ 2

n X

xi Cov Ri ; F ðRp Þ

(2)

i¼1

As Eq. (2) shows, the portfolio’s Gini coefficient is twice the weighted average of the covariances between the individual asset returns and the portfolio’s cumulative distribution. With F ðRp Þ being a function of x1, x2, y, xn, an analytical search for these portfolio weights that minimize Gp may appear to be a tedious task. However, mean-Gini portfolio construction is still simple by using the currently available spreadsheet tools, such as the Excel SolverTM.

DATA Our reference investor is a US investor such as a pension or endowment fund with investments in US equities, international equities, real estate, emerging markets equities, and US bonds with a view to adding hedge funds to the portfolio. The MSCI US return series, the MSCI EAFE gross return series, MSCI Emerging Markets gross return series, and JP Morgan US Bonds return series are used as proxies for the returns on US equities, international equities, emerging markets, and US bonds, respectively. As for hedge funds, CSFB/Tremont Index and Hedge Fund Research Institute

202


Weighted Composite Index (HFRI) are used as alternative benchmarks for returns on hedge funds.3 These two series are used alternatively later to ensure the robustness of our conclusion. Finally, the All REITs return series from the National Association of Real Estate Investment Trusts (NAREIT) is the proxy for returns on real estate.4 The monthly return series for all major asset classes reported in Panel A of Table 1 cover a period from Table 1.

Summary Statistics of Monthly Total Returns. Mean (%)

Standard Deviation (%)

Skewness

Kurtosis

Jarque–Bera Statistic

Panel A: Performance statistics based on data from January 1994 to August HFRI Hedge Fund 0.936 2.051 0.479 6.019 Index CSFB/Tremont Hedge 0.877 2.296 0.120 5.114 Fund Index MSCI US 0.944 4.354 0.536 3.326 MSCI EAFE 0.590 4.206 0.421 3.318 JP Morgan US Bond 0.531 1.379 0.559 4.014 MSCI Emerging 0.502 6.598 0.814 5.053 Markets National Association 1.123 3.802 0.651 4.893 of Real Estate Investment Trusts (NAREIT) Index

p-value

2005 58.527

0.0000

26.412

0.0000

7.323 4.717 13.303 40.033

0.0257 0.0946 0.0013 0.0000

30.800

0.0000

Panel B: Performance statistics of HFRI hedge fund sub-indices based on data from January 1990 to August 2005 Convertible Arbitrage 0.809 1.026 1.121 4.899 67.984 0.0000 Index Distressed Securities 1.207 1.741 0.653 8.521 253.484 0.0000 Index Emerging Markets 1.312 4.232 0.836 6.991 147.498 0.0000 (total) Equity Hedge Index 1.368 2.544 0.180 4.356 15.500 0.0004 Event-Driven Index 1.165 1.885 1.307 7.704 228.023 0.0000 Fixed Income (total) 0.844 0.981 0.290 7.913 192.722 0.0000 Macro Index 1.257 2.396 0.345 3.535 5.993 0.0500 Merger Arbitrage 0.821 1.221 2.618 14.405 1,240.242 0.0000 Index Equity Market Neutral 0.744 0.903 0.168 3.350 1.853 0.3960 Index Relative Value 0.954 1.039 0.838 13.257 850.665 0.0000 Arbitrage Index


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January 1994 to August 2005. These return data, whose summary statistics are shown in Panel A, will form the inputs to an asset allocation exercise involving six major asset classes later. The HFRI data are available since January 1990. All HFRI sub-indices as reported in Panel B of Table 1 are based on data from January 1990 to August 2005.5 Table 1 reports the descriptive statistics of various asset types. In Panel A, the real estate produces the best returns over our sample period. As expected, bonds produce relatively low returns and the lowest risk. The kurtosis of the normal distribution is 3. Each of the two hedge fund indices and the MSCI Emerging Markets Index has kurtosis well in excess of 3. The Jarque–Bera statistics, which is a test of normality, reject the normal distribution assumption for all asset classes except EAFE. As for the individual hedge fund sub-indices reported in Panel B, the skewness and the kurtosis are far worse than those of non-hedge funds. It is no surprise that the Jarque–Bera statistics reject the normality assumption for all but one of the sub-indices.

METHODOLOGY Our approach is straightforward. For the above reference investor, we construct the optimal allocations to the six asset classes of US equities, international equities, US bonds, hedge funds, emerging markets, and REITs using the mean-Gini framework, as well as the traditional mean-variance framework. We then compare the allocations to the six asset classes under each of the two frameworks to detect if there are any meaningful differences. Since mean-Gini is much more robust with respect to the distributional requirements, any meaningful difference in allocations would cast doubt on the appropriateness of the traditional mean-variance framework. While an individual fund manager may pursue option-like strategies with non-normal payoffs, a portfolio of hedge funds can result in the pooling of offsetting strategies and more normal outcomes. This means that portfolio returns based on the hedge fund indices or sub-indices are likely to be better behaved than the individual returns based on single funds. Differences in asset allocations using indices or sub-indices are therefore less likely to be significant. In other words, our approach may result in more favorable conclusions for the mean-variance framework by using better behaved hedge fund indices. If our approach detects meaningful differences in asset allocations under the two frameworks, investors using individual hedge funds in their portfolios should have more reasons to be wary of the mean-variance framework.

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To determine the optimal allocations under either framework, we need estimates for expected return, standard deviation, and Gini for each of the asset classes. The estimates used in this study are obtained with a rolling sample of 48 monthly observations. The first set of estimates of expected return and risk measures is based on 48 monthly data from January 1994 to December 1997. The next set of estimates involves monthly observations from February 1994 to January 1998. This rolling sample procedure generates 93 sets of risk and return measures for each of the asset classes. Based on each of the 93 sets of risk and return measures, optimal allocations under each of the two frameworks can then be estimated. Specifically, minimize Riskp ¯ p ¼ a required return subject to R n P xi ¼ 1 and i¼1

where Riskp is the portfolio risk measure, such as its portfolio standard ¯ p is the expected value of Rp. deviation or its portfolio Gini coefficient, and R Two cases are considered using each framework. Case 1 involves the optimal portfolios with short sales allowed. Case 2 considers the optimal portfolio disallowing short sales. In Case 2, there are additional constraints that each xi must be non-negative. What the above optimization program does is to produce the risk-return frontier for each of the two cases using each of the 93 sets of estimates of input parameters. To ensure the robustness of our conclusion, we estimate the optimal weights under the two frameworks for three points on the frontier by varying the required return in the constraints. In particular, the optimal weights being examined are associated with three points that are evenly spaced on each frontier. For each set of the 93 estimates of input parameters, we find the difference in returns between the highest return asset and the lowest return asset. One of the three points is the half way between the high and the low returns. The other two points are ¼ below the highest return and ¼ above the lowest return. In other words, 8 1 > > R25 ¼ RL þ ðRH RL Þ > > 4 > > < 1 required return ¼ R50 ¼ RL þ ðRH RL Þ 2 > > > > 3 > > : R75 ¼ RL þ ðRH RL Þ 4


205

where RL and RH are, respectively, the lowest and the highest returns among the assets in each set of input parameters. In order to conserve space, the optimal weights for each asset class under the two frameworks are not reported in this chapter.6 Since the issue here is whether the mean-variance framework will produce optimal weights close to those under the more robust mean-Gini framework, the difference in weights under the two frameworks is computed for each of the 93 sets of input estimates.7 These differences for each asset class are plotted in Fig. 1.8 Each panel in Fig. 1 plots the differences in weights for each asset class for R25, R50, and R75. Table 2 contains summary statistics of Fig. 1 using R25, R50, and R75 as one series. Note that Fig. 1 and Table 2 contain a high percentage of zero differences in optimal weights when short sales are disallowed. Column 7 in Table 2 indicates that quite often more than 50% of differences are zeros when short sales are disallowed. Case 1 allowing short sales is more revealing than Case 2 where short sales are disallowed. In Case 2, the 48-month moving average can result in inferior return characteristics for an asset class. Disallowing short sales will produce a zero optimal weight for the asset under both frameworks. Almost all the zero differences in weights are a result of a zero allocation to a particular asset. It would be meaningless to compare the differences between the two frameworks when a manager places no bet in an asset as often the situation in Case 2. The same manager in Case 1 would simply short the inferior asset. As a result, the manager in Case 1 always takes a position in an asset. Comparisons are more meaningful when the manager always takes a position in each of the two frameworks. Interestingly, Table 2 shows that the HFRI has the highest mean difference in weights of 2.805% among all asset classes. In other words, the mean-variance framework, which ignores the tail risk and other non-normal characteristics, over-weighs HFRI by the most. The mean-Gini framework, which captures the non-normal characteristics, tends to be more cautious in its allocation to hedge funds. The maximum (minimum) difference in weights for hedge funds among the three points on the risk-return frontier with the 93 sets of risk-return inputs each is 43.920% (21.182%). The Wilcoxon signed-rank test indicates that the difference in median is statistically significant at the usual 5% level. This means that the portfolio allocations under the two frameworks are not the same. The results therefore vindicate the common perception that the mean-variance framework is inappropriate for hedge funds. Of the 12 scenarios reported in Fig. 1 and Table 2, the Wilcoxon tests indicate significant differences in allocations between the two frameworks

206

C. SHERMAN CHEUNG ET AL. Panel A: HFRI hedge fund index

Difference in weights 0.5 Allow short sell No short sell

0.4 0.3 0.2 0.1 0 -0.1 -0.2

R25

R50

R75

-0.3 Aug-05 Dec-97

Dec-97

Aug-05 Dec-97

Aug-05

Ending month Panel B: MSCI US


0.4 0.3 0.2 0.1 0 -0.1 -0.2

R25

R50

R75

-0.3 Dec-97

Aug-05 Dec-97

Aug-05 Dec-97

Aug-05

Ending month

Fig. 1.

Differences in Optimal Weights of Different Required Expected Returns.


207

Panel C: MSCI EAFE


0.4 0.3 0.2 0.1 0 -0.1 -0.2

R25

R50

R75

-0.3 Dec-97

Aug-05 Dec-97

Aug-05 Dec-97

Aug-05

Ending month Panel D: JP Morgan US Bond

Difference in weights 0.5

Allow short sell No short sell

0.4 0.3 0.2 0.1 0 -0.1 -0.2

R25

R50

R75

-0.3 Dec-97

Aug-05 Dec-97

Aug-05 Dec-97

Ending month

Fig. 1.

(Continued )

Aug-05

208

C. SHERMAN CHEUNG ET AL. Panel E: MSCI Emerging Markets


0.4 0.3 0.2 0.1 0 -0.1 -0.2

R50

R25 -0.3 Dec-97

R75

Aug-05 Dec-97

Aug-05 Dec-97

Aug-05

Ending month Panel F: NAREIT


0.4 0.3 0.2 0.1 0 -0.1 -0.2

R25

R50

R75

-0.3 Dec-97

Aug-05 Dec-97

Aug-05 Dec-97 Ending month

Fig. 1.

(Continued )

Aug-05


209

Table 2. Summary Statistics of the Differences in Optimal Weights (in %) under the Mean-Variance and Mean-Gini Frameworks (Six-Asset Portfolio) with and without Short-Selling Constraints. Mean

HFRI Hedge Fund Index MSCI US

F NS F NS MSCI EAFE F NS JP Morgan US Bond F NS MSCI Emerging F Markets NS National Association F NS of Real Estate Investment Trusts (NAREIT) Index

2.805 0.776 1.959 0.442 0.970 0.130 1.109 0.679 0.270 0.210 0.977 0.685

Standard Deviation

9.300 4.467 3.415 1.822 1.665 0.811 4.182 3.172 1.336 0.820 2.694 2.023

Max

43.920 8.047 4.535 9.222 7.400 3.749 10.881 17.529 4.837 4.722 2.752 1.707

Min

21.182 26.693 14.342 2.716 2.852 5.035 21.292 6.602 4.437 1.436 12.560 14.535

% of Zero Difference

0.00 52.33 0.00 55.91 0.00 74.91 0.00 27.96 0.00 78.14 0.00 60.22

Wilcoxon Test Statistic

p-value

4.768 0.995 9.134 2.990 8.868 3.336 4.442 1.720 1.745 3.692 4.741 6.354

0.0000 0.3198 0.0000 0.0028 0.0000 0.0009 0.0000 0.0855 0.0809 0.0002 0.0000 0.0000

Notes: F, free to short sell; NS, no short selling; and difference in weights is defined as meanvariance optimal weight minus mean-Gini optimal weight.

for nine scenarios at the 5% level. Given the number of significant differences, it would be unwise to adopt the mean-variance framework as an asset allocation approach.

HEDGE FUNDS As a robustness test and to ensure that hedge funds can account for the differences in weights reported earlier, we also conduct the same asset allocation exercise using the 10 HFRI sub-indices.9 This applies to a situation when a manager has to construct a fund of funds represented by the sub-indices.10 The risk and return estimates for each of the 10 subindices are also obtained using 48-month rolling samples. The optimal weights are obtained for 3 points on each risk-return frontier. The differences in weights are then computed. We consider cases of allowing short sales and disallowing short sales. While it is not possible to short a non-tradable asset like hedge funds, it is still considered here due to the peculiar nature of the historical data mentioned earlier. Using historical data to estimate risk-return inputs can result in inferior performance, which

210


has no bearing with reality. As inputs to a portfolio allocation problem, those assets with inferior characteristics will not be in the portfolio when short sales are disallowed. This in turn renders the task of evaluating the two frameworks impossible. Allowing short sales eliminates this problem and at the same time allows us to examine the appropriateness of the meanvariance framework based on the historical risk characteristics of the assets under consideration. In general, the ex ante expected returns in practice must be positive as pension or endowment funds tend to take long positions in asset classes under consideration. The problem we face here would not be an issue in practical implementations. Among the 20 scenarios reported in Table 3, the Wilcoxon tests indicate significant differences in allocations in 12 situations at 5% level.11 The

Table 3. Summary Statistics of the Differences in Optimal Weights (in %) of Portfolios of 10 HFRI Hedge Fund Sub-Indices under the Mean-Variance and Mean-Gini Frameworks with and without Short-Selling Constraints. Mean

Convertible Arbitrage Index Distressed Securities Index Emerging Markets (total) Equity Hedge Index

F NS F NS F NS F NS Event-Driven Index F NS Fixed Income (total) F NS Macro Index F NS Merger Arbitrage F Index NS Equity Market F Neutral Index NS Relative Value F Arbitrage Index NS

0.780 3.194 1.045 0.159 0.703 0.024 0.584 0.717 0.190 0.266 3.848 0.768 2.371 0.017 1.167 4.856 0.593 2.118 2.265 0.305

Standard Deviation

7.105 7.291 6.568 1.514 1.571 0.494 4.951 1.755 6.263 1.529 15.984 3.703 2.867 0.743 7.991 10.356 6.005 5.435 20.162 3.617

Max

20.987 33.307 15.363 9.191 5.385 2.778 7.895 9.587 26.071 8.596 25.741 8.800 12.793 4.777 29.714 9.526 25.988 33.425 105.954 15.229

Min

25.302 6.534 20.467 6.101 5.976 4.133 23.109 3.243 17.759 9.862 73.170 18.849 7.765 3.548 17.542 45.618 33.799 5.453 41.977 23.901

% of Zero Difference

0.00 54.46 0.00 64.55 0.00 79.81 0.00 63.15 0.00 77.93 0.00 39.67 0.00 73.00 0.00 41.31 0.00 52.11 0.00 57.75

Wilcoxon Test Statistic

p-value

2.112 8.352 2.144 2.565 9.199 1.834 0.560 8.716 0.444 3.119 1.644 2.587 14.596 0.906 1.902 8.466 2.110 6.657 0.502 1.655

0.0347 0.0000 0.0320 0.0103 0.0000 0.0666 0.5752 0.0000 0.6570 0.0018 0.1003 0.0097 0.0000 0.3651 0.0572 0.0000 0.0349 0.0000 0.6158 0.0979

Notes: F, free to short sell; NS, no short selling; and difference in weights is defined as meanvariance optimal weight minus mean-Gini optimal weight.


211

maximum difference can be as high as 105.954% in the case of the relative value arbitrage index. Again, it would be unwise to use the traditional meanvariance framework. Note that the Wilcoxon test points to significant difference in a majority of the scenarios when short sales are disallowed. The inability to short hedge funds, therefore, would not affect our conclusion.

CONCLUSION The results reported in this chapter confirm the skepticism quite often expressed about the mean-variance framework. Further, it offers a viable alternative that is far more robust with respect to distributional requirements. The mean-Gini has all the simplicity of the mean-variance and is relatively easy to implement using electronic spreadsheet tools.

NOTES 1. See, for example, Shalit and Yitzhaki (1984 and 2005) and references provided there. 2. Consider two assets, X and Y. For any given investment outcome, if the accumulated area under the cumulative probability distribution of asset X is less than the accumulated area for asset Y, then asset X dominates asset Y according to second-degree stochastic dominance. Second-order stochastic dominance ensures a risk-averse investor has a greater expected utility from investing in asset X than from investing in asset Y. 3. For descriptions and criticisms of the indices, see Fung and Hsieh (2002). 4. All the MSCI series can be obtained from the MSCI website. The All REIT series can likewise be obtained from the NAREIT website. The JP Morgan series can be obtained from Bloomberg. 5. The Panel A data, which will form a six-asset study later, cannot start earlier because JP Morgan bond series is unavailable from Bloomberg until January 1994. 6. The detailed weights are available upon request. 7. The difference in weights is defined as the optimal weight under the meanvariance framework minus that under the mean-Gini framework. 8. The hedge fund index used in producing Fig. 1 is HFRI. The Tremont index produces similar outcome and therefore not reported here. 9. This part of the study relies on data since January 1990 rather than January 1994, as HFRI data are available since January 1990. The six-asset study reported earlier, however, relies on data starting January 1994 since JP Morgan bond series is unavailable from Bloomberg until January 1994. 10. We also repeat the same exercise using 10 Tremont sub-indices with essentially the same conclusions.

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11. The Tremont sub-indices produce more dramatic differences. Eighteen of the same 20 scenarios are significantly different at the 5% level.

ACKNOWLEDGMENT Financial support from the SSHRC is gratefully acknowledged.

REFERENCES Agarwal, V., & Naik, N. (2004). Risk and portfolio decisions involving hedge funds. Review of Financial Studies, 17, 63–98. Dorfman, R. (1979). A formula for the Gini coefficient. Review of Economics and Statistics, 61, 146–149. Fung, W., & Hsieh, D. A. (1997). Empirical characteristics of trading strategies: The case of hedge funds. Review of Financial Studies, 10, 275–302. Fung, W., & Hsieh, D. A. (2002). Hedge-fund benchmarks: Information content and biases. Financial Analysts Journal, 58, 22–34. Ibbotson, R. G., & Chen, P. (2005). Sources of hedge fund returns: Alphas, betas, and costs. Working Paper no. 05-17. Yale International Center for Finance, pp. 11–28. Lerman, R. I., & Yitzhaki, S. (1984). A note on the calculation and interpretation of the Gini index. Economics Letters, 15, 363–368. Levy, H., & Markowitz, H. (1979). Approximating expected utility by a function of mean and variance. American Economic Review, 69, 308–317. Lo, A. (2005). The dynamics of the hedge fund industry. The Research Foundation of CFA Institute. Shalit, H., & Yitzhaki, S. (1984). Mean-Gini, portfolio theory, and the pricing of risky assets. Journal of Finance, 39, 1449–1468. Shalit, H., & Yitzhaki, S. (2005). The mean-Gini efficient portfolio frontier. Journal of Financial Research, 28, 59–75. Yitzhaki, S. (1982). Stochastic dominance, mean variance, and Gini mean difference. American Economic Review, 72, 178–185.

INCENTIVE STOCKS AND OPTIONS WITH TRADING RESTRICTIONS: NOT AS RESTRICTED AS WE THOUGHT Melanie Cao and Jason Wei ABSTRACT Stock ownership and incentive options are used by companies to retain and motivate employees and managers. These grants usually come with vesting features which require grantees to hold the assets for certain periods. This vesting requirement makes the grantee’s total wealth highly undiversified. As a result, as shown by previous researchers, grantees tend to value these incentive securities below market. In this case, grantees will have a strong desire to hedge away the firm-specific risk. Facing the restrictions of direct hedges such as shorting the firm’s stock, employees may implement a partial hedge by taking positions in an asset highly correlated with the firm’s stock, such as an industry index. In this chapter, we investigate the effects of such a partial hedge. Using the continuoustime, consumption-portfolio framework as a backdrop, we demonstrate that the hedging index can enhance the employee’s optimal portfolio holding and increase his intertemporal utility. Consequently, his private valuations of these grants are higher than that without the partial hedging. However, because the partial hedge makes the employee’s total wealth less sensitive to the firm’s stock price, it will also undermine the incentive Research in Finance, Volume 24, 213–248 Copyright r 2008 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(07)00209-2

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MELANIE CAO AND JASON WEI

effects. Therefore, the presumed incentive effects of these restricted assets should not be taken for granted.

1. INTRODUCTION According to the National Center for Employee Ownership (NCEO), approximately 20 million employees and executives in the U.S. received stock and stock options. The employee ownership was pioneered by high-tech start-up companies as a practical way of retaining and motivating talented employees. Usually, these companies require their employees to continue working for a minimum number of years before the stocks and options are vested. During the vesting period, employees are not allowed to sell their stock or option holdings. Retention is achieved through vesting in that the employee must forgo the holdings if he leaves the company before the stocks and options are vested; long-term motivation is achieved by linking the employee’s personal wealth (i.e., the restricted holdings) to the company’s stock value through ownership. Granting stocks without trading restrictions is equivalent to granting cash bonuses, since the employee can sell the stocks immediately after receiving them. In this case, although the employee values his stock grant exactly as the market does, the long-term incentive is absent and the employee can leave the company without incurring any loss. Granting stocks with an infinite vesting period does not make any sense either since they are worthless to the employee. Clearly, trading restrictions imposed for a modest period (usually 5–10 years) are necessary for both retention and long-term motivation purposes. Such restrictions will make part of the employee’s wealth illiquid and impose an exposure to the company-specific or non-systematic risk. Consequently, a risk-averse employee will value such a restricted asset below its market value, resulting in a discount. Presumably, the exposure to the company-specific risk is the source of incentives, since improving the firm’s overall productivity and profitability by working hard may enhance the stock price, hence the employee’s personal wealth. This incentive mechanism is not without costs though. The holding restriction makes the incentive assets illiquid and imposes an exposure to the firm’s specific risk, which leads to a sub-optimal portfolio for the employee. Therefore, a risk-averse employee will always look for ways to hedge away the firm-specific risk. However, employees are not allowed to use direct hedges such as shorting the firm’s stock or writing tradable options on the firm’s stock. As stated explicitly by the Council of Institutional Investor,

Incentive Stocks and Options with Trading Restrictions

215

grantees are required not to enter into hedging positions (such as swaps, option positions or shorting the company’s stock) that offset the alignment and risk characteristic of equity-based awards.1 The institutional restrictions on direct hedging will cause employees to use a partial hedge. That is, the employee will have a desire to take positions in securities highly correlated with the firm’s stock, such as an industry index. To the best of our knowledge, there are only three studies which examine the impacts of holding restrictions on the private valuation of restricted assets, but none of them examines the consequence of employees’ using a hedging index to undo the trading restrictions. Meulbroek (2001) shows how costly bearing non-systematic risk can be from a diversification perspective; Kahl, Liu and Longstaff (2003) (KLL hereafter) demonstrate how much the employee discounts the restricted stock in a portfolio-selection context; in a similar framework, Ingersoll (2006) focuses on the private valuation of incentive options with different features. This chapter sets out to fill the aforementioned gap in the literature. To this end, we link the literatures on executive compensation and asset valuation with portfolio constraints, and go one step further by introducing a hedging index in the portfolio choice set.2 As mentioned earlier, this hedging index can be considered as an industry index with a high correlation to the restricted stock. The portfolio strategy is optimized in a consumptionportfolio selection framework with respect to the employee’s intertemporal utility. Overall, we find that the hedging index can increase the employee’s private valuation of the restricted assets, and in the case of options, increase the delta or incentive sensitivity. Of course, the total incentive is compromised since the exposure to the company-specific risk is reduced. The specific findings are as follows. With respect to the restricted stock, the hedging index can help improve the employee’s optimal consumption-investment policy and align the employee’s private valuation of the restricted stock with the market’s. The difference between the employee’s private value and the stock’s market value represents the illiquidity discount. As expected, the discount increases with the employee’s degree of risk aversion, the length of the vesting period and the volatility of the restricted stock. However, the discount is reduced when the residual correlation between the restricted stock and the hedging index is high. For example, under typical market conditions, an employee with a risk aversion parameter g ¼ 2 and 50% of his wealth in the firm’s stock to be vested in 10 years would discount the stock by as much as 60% when the hedging index is not used. With the hedging index, the discount is reduced to 46%, a 14% improvement of the private valuation. At the same

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time, the non-systematic risk exposure is reduced by approximately 33%. When the residual correlation is perfect, the discount and the exposure to company-specific risk can be completely eliminated. Therefore, the trading restrictions are not as restrictive as we thought, and the intended effectiveness of incentive stocks cannot be taken for granted. With respect to restricted options, the hedging index can also enhance the employee’s private valuation and reduce the discount, regardless of whether the option is European or has vesting and early exercise features. The degree of value enhancement for options is roughly the same as that for the restricted stocks. Moreover, hedging also improves the incentive sensitivity measured by the option’s delta. Therefore, for options, there appears to be a trade-off between the loss of total incentives (measured by the exposure to company-specific risk) and the gain in incentive sensitivity. That the two effects are in different measures hinders a direct trade-off analysis. Although the continuous-time consumption-portfolio framework is similar to that of KLL (2003) and Ingersoll (2006), the present chapter differs from these two studies in three aspects. First and foremost, we focus on how hedging affects the private valuation and incentive effects. Our emphasis helps shed light on the effectiveness of the trading restrictions. Second, we augment their portfolio choice set by including a hedging index. Specifically, our portfolio choice set includes the market portfolio, a hedging index, the restricted stock and the risk-free asset. Our analysis shows that the inclusion of the hedging index can help improve the employee’s intertemporal utility, increase the private valuation of the incentive stocks and options. Third, we analyze both the incentive stocks and options, while Ingersoll focuses only on options and KLL only on stocks. It is worth noting that we study only a particular aspect of incentive stocks and options. Specifically, we study the consequence of hedging on the part of grantees assuming that the compensation package has already been decided. In this sense, issues such as how to design an optimal compensation package are outside the domain of this chapter. By the same token, our study also abstracts from many contemporary issues that can potentially impact the valuation and incentive effects of executive compensation. Backdating and forward-dating are such examples.3 The rest of the chapter is organized as follows. Section 2 formulates and characterizes the employee’s lifetime consumption-investment decision with an expanded portfolio choice set. We illustrate numerically the extent to which the hedging index enhances the employee’s utility and reduces the exposure to the company-specific risk. Section 3 analyzes and demonstrates how the hedging index can reduce the discount of restricted assets. In-depth


217

analyses are carried out for both the restricted stocks and options. Section 4 provides concluding remarks. Proofs and tables are relegated to the appendix.

2. OPTIMAL CONSUMPTION-PORTFOLIO STRATEGY WITH A HEDGING INDEX 2.1. The Setup Consider a risk-averse employee with a finite lifetime horizon T¯ whose preferenceh is described iby a smooth, time-additive expected utility function: R T¯ ¯ UðcÞ ¼E Uðct ; tÞdt .4 Following the literature, we adopt the constant0

relative-risk-aversion (CRRA) utility function for the employee U ðct ; tÞ ¼ eft

c1g t 1g

(1)

where f W 0 is the rate of time preference and g 1 the coefficient of relative risk aversion. The employee works for a company which grants restricted stocks and options over time for retention and motivation purposes. Similar to Ingersoll (2006), we approximate the ongoing nature of the incentive scheme by assuming that the employee is required to hold a fixed fraction of his total wealth (defined later) in the company’s stock during the vesting period which ¯ 5 By the end of the vesting period, the employee is free to ends at time T T. sell these shares. The assumption of fixed fraction is equivalent to assuming proportional growths in the stock’s value and the total wealth. In the absence of trading restrictions and assuming the continuous-time Capital Asset Pricing Model (CAPM), the employee’s optimal portfolio strategy is to hold the market portfolio and the risk-free asset only. With trading restrictions on the stock, his optimal portfolio strategy is no longer clear-cut. The imposed stock holding will force the employee to bear some non-systematic risk, which cannot be fully offset by the market portfolio. The employee will try to find a hedging asset to reduce this non-systematic risk. The portfolio choice set in KLL (2003) and Ingersoll (2006) includes only the market portfolio, the risk-free asset and the restricted stock. However, with trading restrictions, including other assets in the feasible set will help reduce the non-systematic risk, and as a result, improve the employee’s intertemporal utility. The benefit derived from the additional assets cannot be achieved by simply re-scaling the market portfolio’s weights (Section 2.3 and Table 1 delineate this point). It should be noted that, with

Table 1.

Optimal Portfolio Holdings and Utility Level with or without Index. Index12

Index23

Weights

Weights

r1I.m

0.362 0.345 0.293

0.514 0.486

0.392

Asset 1 Asset 2 Asset 3

Index23.m

Weights

r1I.m

Weights

1.000 0.540 0.460

Optimal Portfolio Holdings xb

xm

0.348

0.652

r1I.m

0.542 0.522 0.478

Portfolio Feasible Set

x1

Ultimate Portfolio Holdings x1

218

M

wnb

Utility Level

wn1

wn2

wn3

0.348

0.236

0.225

0.191

100.00

Panel A: Without trading restriction B, M and Assets 1–3

Panel B: Trading restrictions: x1 ¼ 0.1 (own1 ¼ 0.236) 1: 2: 3: 4:

B, B, B, B,

M and Asset 1 M, Asset 1 and Index12 M, Asset 1 and Index23 M, Asset 1 and Index23.m

0.295 0.311 0.265 0.348

0.605 0.652 0.731 0.375

0.100 0.100 0.100 0.100

0.062 0.095 0.176

0.295 0.311 0.265 0.348

0.319 0.304 0.364 0.236

0.209 0.194 0.202 0.225

0.178 0.191 0.169 0.191

99.36 99.46 99.55 100.00

0.421 0.652 1.047 0.731

0.500 0.500 0.500 0.500

0.311 0.476 0.882

0.079 0.159 0.071 0.348

0.652 0.576 0.879 0.236

0.145 0.073 0.112 0.225

0.123 0.191 0.080 0.191

85.16 87.30 89.29 100.00

Panel C: Trading restrictions: x1 = 0.5 (>wn1 = 0.236) Case Case Case Case

1: 2: 3: 4:

B, B, B, B,

M and Asset 1 M, Asset 1 and Index12 M, Asset 1 and Index23 M, Asset 1 and Index23.m

0.079 0.159 0.071 0.348

Note: Parameter values: f ¼ 0.03, g ¼ 4.0, r ¼ 0.06, m1 ¼ 0.10, m2 ¼ 0.15, m3 ¼ 0.20, s1 ¼ 0.15, s1 ¼ 0.25, s3 ¼ 0.35, r12 ¼ 0.2, r13 ¼ 0.3, r23 ¼ 0.4. To calculate the utility level, the agent’s life horizon is set to be T¯ ¼ 40 and the vesting period is set T ¼ 10. The utility level under no trading restriction is normalized to 100. B, Risk-free bond; M, market portfolio (tangent portfolio of Assets 1, 2 and 3); Index12, tangent portfolio of Assets 1 and 2; Index23, tangent portfolio of Assets 2 and 3; Index23.m, portfolio consisting of Assets 2 and 3 with weights proportional to those in the market portfolio.


Case Case Case Case


219

hedging, the employee’s wealth will be less sensitive to the firm’s stock price, hence compromising the incentive effects. To capture the above setting, the employee’s portfolio choice set is assumed to include a bond B earning the risk-free rate r, the market portfolio M, the restricted asset or the company’s stock S and the hedging index I. The price dynamics are dM ¼ ðmm qm Þdt þ sm dzm ; M dS ¼ ðms qs Þ þ ss dzs ; S dI ¼ ðmI qI Þdt þ sI dzI I where the correlation coefficient matrix of $ z=(zm zs zI)u is 0

1

B S ¼ @ rms rmI

rms 1 rIs

rmI

1

rIs C A 1

and the cum-dividend expected returns, dividend yields and the volatilities are 0 1 0 1 0 1 mm qm sm B m ¼ r þ b ðm rÞ C Bq C Bs C m¼@ s A; q ¼ @ s A and s ¼ @ s A s m mI ¼ r þ bI ðmm rÞ

qI

sI

with bs ¼ rms ðss =sm Þ and bI ¼ rmI ðsI =sm Þ and the non-systematic variances for the stock and the index as v2s ¼ ð1 r2ms Þs2s and v2I ¼ ð1 r2mI Þs2I . With the above elements, the employee chooses an optimal consumption and portfolio policy to maximize his expected lifetime utility subject to the usual budget constraint. The first order conditions yield the following stochastic Euler equation: "Z # T U ct Xt ¼ E dt (2) t U ct where Xt is the current price of an asset with a dividend yield of D, and U ct stands for the partial derivative of the utility function with respect to the consumption ct. Intuitively, given his optimal consumption policy, the employee’s private valuation of any security is the expected present value of

220


the future yields or payoffs, discounted at his own marginal rate of substitution. It is important to emphasize that the employee takes as given the market prices of all securities (which are equilibrium outcomes under no trading restrictions). When he is free to trade any security, his private valuation equals the market’s. When he is restricted in trading some of the securities, however, his private valuation may deviate from the market’s. This does not imply any arbitrage since the employee is a price taker in the market place. In other words, we assume that the number of investors with trading restrictions is so small compared with the total population of investors that they cannot influence the competitive financial market. 2.2. Optimal Consumption-Portfolio Policies: Theoretical Results To determine the employee’s valuation of the restricted stock and options and to determine the amount of residual non-systematic risk, we first need to solve the consumption–investment problem to obtain the marginal rate of substitution. To this end, we define the employee’s total wealth as yBt Bt þ yM t M t þ ySt S t þ yI t I t , where yBt ; yM t ; ySt and yI t are portfolio holdings. Denote the percentages of his total wealth invested in the risky assets as xt=(xmt, xs, xIt)u, then we have xmt ¼

yM t M t ; Wt

xst ¼

yS t S t Wt

and xIt ¼

yI t I t Wt

Similar to Merton (1971), the budget constraint is dW t ct ¼ r þ x0t ðm rÞ dt þ ðxt sÞ0 dzt Wt Wt Given the trading restrictions, the employee’s optimization must be solved for two distinct periods as shown below.6 | ---------------------------------- | -----------------------------------------| T T post-vesting period t vesting period

Since there is no trading restriction during the post-vesting period, the optimal solution is similar to the standard Merton solution (1971). That is xmt ¼

sm ; x ¼ 0; xIt ¼ 0; gsm st

8 TotoT¯ 1g

¯ ct ¼ f ða; t; TÞW t

and

¯ g W t JðW ; t; f Þ ¼ eft f ða; t; TÞ 1g


with sm ¼

mm r ; sm

a¼

f 1g s2 rþ m ; g g 2g

221

¯ ¼ f ða; t; TÞ

a 1

¯ eaðTtÞ

The optimal policy indicates that the holding of the market portfolio is positively related to the market’s Sharpe ratio sm, negatively related to the employee’s risk-aversion parameter g and the volatility of the market portfolio sm. Now we turn to the vesting period. Let xs be the fixed percentage of the employee’s total wealth in the restricted stock. For any xs W 0, the optimality condition implies that this constraint is binding. The employee’s optimal portfolio should hold exactly xs during the vesting period (0otoT ). Unlike KLL (2003) and Ingersoll (2006), we augment the portfolio choice set by including the index due to the employee’s desire to reduce the negative impact of the trading restrictions. Specifically, the employee takes xs as given and optimizes the portfolio holdings of the market and the index. In the appendix ‘‘Proof of Proposition 1’’ provides the solution to this optimization problem. To facilitate the presentation of the optimal solution, we denote the residual or partial correlation between the restricted stock and the index, after controlling for the market impact, as rIs : m ¼ ðrIs rms rmI Þ= qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 r2ms Þð1 r2mI Þ: Proposition 1. When there is no trading limit on the index, the employee’s optimal consumption–investment strategy during the vesting period consists of xmt ¼

sm r rmI rIs xs bs ms ; gsm rms ð1 r2mI Þ

ct ¼ F ðA; t; TÞW t

xst ¼ xs ;

xIt ¼ xs rIs : m

and JðW ; t; F Þ ¼ eft F ðA; t; TÞg

vs xI vI

W 1g t ; 1g

8 0otoT

1 2 2 2 2 where A ¼ a ðg 1ÞO ; O ¼ x2s v2s x2 I vI ¼ xs vs ð1 rIs : m Þ; 2 A F ðA; t; TÞ ¼ 1 þ ðAf ða; T; TÞ1 1ÞeAðTtÞ

Proposition 1 indicates that the optimal position on the index depends on four factors: the size of the restricted holding xs, the partial or residual correlation between the stock and the index rIs . m, the residual variance of the stock vs, and the residual variance of the index vI. The results are generally intuitive. For example, a bigger holding of the restricted stock or a higher residual variance of the stock would call for a bigger holding of the index; a higher residual variance of the index would reduce

222


the holding of the index since the hedging purpose is to reduce the residual variance in the first place. As for the partial correlation, when it is positive, the employee will short the index; if it is negative, a long position on the index is called for. The optimal position could be large if the residual correlation is high and/or the ratio of the non-systematic risk is high. In reality, although the employee could take a long position on the index without any limit, he may face certain shorting restrictions imposed by his broker. To complete the framework, we now consider the optimal consumption–investment policy when the index position is limited. To this end, suppose the employee cannot short more than |xI| (xI o 0) of his total wealth. When this constraint is not binding, i.e., when xI oxnI , the employee’s optimal consumption-portfolio strategy is still the one presented in Proposition 1. Otherwise, the following proposition characterizes the optimal holding (we omit the proof for brevity). Proposition 2. When rIs . m W0 and the shorting restriction on the index is xs.rIs . m vs/vI o xI o 0, the employee’s optimal consumption–investment strategy during the vesting period becomes xmt ¼

sm xs bs xI bI ; gsm

ct ¼ F ðA; t; TÞW t where

and

xst ¼ xs ;

xIt ¼ xI

JðW ; t; F Þ ¼ eft F ðA; t; TÞg

W 1g t ; 1g

8 0otoT

1 A ¼ a ðg 1ÞO; O ¼ x2s v2s þ x2I v2I þ 2rIs : m xs xI vs vI ; 2 A F ðA; t; TÞ ¼ 1 þ Af ða; T; TÞ1 1 eAðTtÞ

It should be stressed that the inclusion of the hedging index unambiguously increases the employee’s intertemporal utility and reduce the exposure to the company-specific risk. Contrary to casual perceptions, adding the index into the optimization does not simply boil down to a re-scaling of the market portfolio’s weight. If the index’s role is trivial, then the optimized weight on the index should be either zero or non-zero but inconsequential to the utility level. In the follow subsection, we use a simple, three-risky-asset setup to show that the introduction of an additional asset does improve the overall consumption-portfolio decision and reduce the exposure to nonsystematic risk.


223

2.3. Non-Trivial Role of the Index Let us consider a simple economy where there are only three risky assets and one risk-free bond in the financial market. Suppose that the risk-free rate is r ¼ 6% and the return characteristics of the three risky assets are given in Table 1. The market portfolio is the tangent portfolio formed with the three risky assets. The weights are 36.2% in Asset 1, 34.5% in Asset 2 and 29.3% in Asset 3. As shown in Panel A of Table 1, under no trading restrictions, an investor with risk aversion g=4 will invest 34.8% in the risk-free bond and 65.2% in the market portfolio. In other words, the investor ultimately holds 34.8% of his wealth in the risk-free bond, 23.6% in Asset 1, 22.5% in Asset 2 and 19.1% in Asset 3. The intertemporal expected utility is calculated via the value function in Proposition 1 and re-scaled to 100. Without loss of generality, let us now impose a trading restriction on Asset 1. To see how the introduction of additional assets (other than the market portfolio) can affect the consumption-portfolio decisions, we examine three indices. Index12 is the tangent portfolio formed with Assets 1 and 2. The index’s weights and residual correlation with Asset 1 (controlling for the market) are given in the top portion of Table 1. Index23 is defined in a similar fashion. Index23.m consists of Assets 2 and 3 whose weights are proportional to those in the market portfolio. Naturally, the residual correlation between Asset 1 and Index23.m is 1.0.7 Panel B of Table 1 presents results for the situation where the imposed holding on Asset 1 is 10%, which is lower than the optimal weight of 23.6% in the market portfolio. Without the hedging index (Case 1), the ultimate weight on Asset 1 is 31.9%, higher than $23.6% (the optimal weight of Asset 1 in the market portfolio), and the utility level is now lower. The holding restriction makes the investor worse-off. The overall weight on Asset 1 is higher than 10%, since the investor is also holding the market portfolio which contains Asset 1. Note that this case corresponds to the simplified portfolio choice set as in KLL (2003) and Ingersoll (2006) where the employee can only optimize his strategy over the risk-free bond and the market portfolio. When we include Index12 into the choice set (Case 2), a short position is taken on this index, and the ultimate weights on all assets are different from those of Case 1. More importantly, the utility level improves. The inclusion of Index23 (Case 3) has similar effects, except that the utility improvement is larger since the residual correlation (0.542) is bigger than that in Case 2 (0.392). Moving on to Case 4 where we add Index23.m into the portfolio choice set, the ultimate portfolio weights are all restored to their optimal level, and so is the utility level.

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The contribution of the additional asset is bigger when the restricted position is larger. To appreciate this point, we repeat the calculations in Panel A by setting the restriction on Asset 1 to 50%, which is higher than the optimal weight of 23.6% in the market portfolio. Panel C shows that the restriction reduces the utility by approximately 15% when the investor can only trade the market portfolio and the risk-free bond. But with the right index (Index23.m) the restriction can be totally undone, and the loss of utility can be completely recovered. This simple exercise clearly demonstrates that, when there are trading restrictions on certain assets, allowing only the market portfolio and the risk-free bond in the portfolio choice set will lead to sub-optimal decisions. Introducing other assets into the choice set will improve the consumptionportfolio decisions and enhance the overall utility level. This is why employees will seek for ways to undo the restrictions. 2.4. Impacts of Trading Restrictions on Optimal Portfolio Choices and Non-Systematic Risk To show how the consumption and investment decisions are affected by the trading restrictions, we examine the optimal consumption dynamics. During the post-vesting period, the consumption evolves according dc 1 1 1 sm ¼ rfþ 1 þ s2m dt þ dzm mc dt þ sc dzm c g 2 g g During the vesting period, the consumption process follows dc 1 sm ¼ mc þ ðg 1ÞO dt þ bs xs sm bI xIt sm dzm þ xs ss dzs þ xIt sI dzI c 2 g ( O ¼ O and xIt ¼ xI with a non-binding index shorting limit where ð3Þ O ¼ O and xIt ¼ xI with a binding index shorting limit

During the post-vesting period, the employee’s consumption uncertainty is completely induced by the market portfolio. During the vesting period, regardless of the index shorting limit, his consumption growth rate and volatility are affected by the uncertainty in the market portfolio, as well as by those in the stock and the index. With a well defined residual correlation between the index and the stock (i.e., |rIs . m|o1), we have O W 0. Given that g 1, the consumption growth rate during the vesting period is higher than that during the post-vesting period. The reason is that the vesting requirement


225

makes part of the employee’s personal wealth illiquid and the employee tends to consume at a lower level. As time approaches the end of the vesting, the employee tends to increase his consumption, resulting in a higher consumption growth rate. The consumption variance during the vesting period can be easily shown as s2m =g þ O and is higher than that of the post-vesting period. The excess consumption variance O reaches to its maximum when the index is excluded and reduces to O when the employee can optimally invest in the index. Given the negative relation between the employee’s intertemporal utility and the consumption volatility, it is clear that the employee obtains the highest utility when the index shorting restriction is absent or non-binding, and the lowest utility when the index is not included in the portfolio choice set. As shown later, this result translates to how much the employee discounts the market value of the restricted securities. Since the optimal consumption rate and the total wealth are linearly related, the process for the total wealth will have the same diffusion terms as the consumption process. In other words, the variance of the wealth process shares exactly the same features as the consumption’s. Specifically, during the post-vesting period, the employee’s portfolio has only market risk in it and he does not bear any non-systematic risk. During the vesting period, the employee’s portfolio has the most amount of non-systematic risk in it when hedging is not in place, and optimal hedging can reduce the non-systematic risk to the lowest possible level, which could be zero if the partial correlation is 1.0. When the residual variance from the stock is reduced, the incentive effect is also compromised. To shed further light on the issue, we now present some numerical results. In order to guide ourselves in choosing parameter values, we empirically estimate correlations and the market’s risk-return profile for the high-tech sector. Specifically, we download daily prices from Yahoo! Finance for three indices (S&P 500, Nasdaq, Nasdaq-100) and seven stocks (Apple, Cisco, IBM, Intel, Microsoft, Oracle and Sun) for the period of January 1, 1995 to December 31, 2004. We take S&P 500 as a proxy for the market portfolio, and Nasdaq or Nasdaq-100 as the hedging index. Table 2 reports the estimates. Several observations are in order. First, the hedging indices are highly correlated with the market, but individual stocks are correlated more with the hedging indices than with the market, suggesting the potential usefulness of the hedge indices in reducing non-systematic risk. Second, for a particular stock, its correlation with the hedging index tends to be much higher than those with other stocks, suggesting that the best candidate as a hedging vehicle is the industry index, not related stocks. Third, the narrow

226


Table 2.

Market Profile for the High-Tech Sector, 1995–2004.

Panel A: Pair-wise correlations

S&P 500 Nasdaq Nasdaq-100 Apple Cisco IBM Intel Microsoft Oracle Sun Average

S&P 500

Nasdaq

Nasdaq-100

Apple

Cisco

IBM

Intel

Microsoft

Oracle

Sun

1.00 0.84 0.82 0.39 0.64 0.58 0.62 0.63 0.53 0.55 0.56

1.00 0.98 0.48 0.79 0.57 0.73 0.71 0.65 0.67 0.66

1.00 0.49 0.81 0.58 0.76 0.73 0.67 0.69 0.68

1.00 0.39 0.32 0.42 0.34 0.32 0.38

1.00 0.49 0.61 0.56 0.54 0.62

1.00 0.48 0.45 0.41 0.45

1.00 0.60 0.48 0.52

1.00 0.46 0.45

1.00 0.48

1.00

Panel B: Partial correlations, returns and standard deviations Partial Correlation with Nasdaq S&P 500 Nasdaq Nasdaq-100 Apple Cisco IBM Intel Microsoft Oracle Sun Average

0.300 0.598 0.190 0.492 0.422 0.439 0.462 0.415

Annualized Return

Annualized STD

0.096 0.105 0.138 0.120 0.228 0.174 0.178 0.205 0.183 0.157 0.178

0.181 0.289 0.359 0.588 0.517 0.343 0.480 0.375 0.581 0.613 0.500

Nasdaq-100

0.322 0.648 0.231 0.565 0.477 0.487 0.495 0.461

Note: This table reports summary statistics for the market (S&P 500), the hedging indices (Nasdaq and Nasdaq-100), and seven stocks in the high-tech sector. Results are based on daily prices from January 1, 1995 to December 31, 2004. Panel A reports pair-wise correlations. The values under ‘‘Average’’ is the average of stocks correlations with the corresponding indices, i.e., the correlations in bold-type. Panel B reports, for each stock, the partial correlations, the annualized return, and the annualized standard deviations. The return and standard deviation averages are for the stocks only, i.e., the numbers in bold-type. Annualization is based on 250 trading days per year.

index, Nasdaq-100, provides higher partial correlations than does the Nasdaq itself. We therefore choose Nasdaq-100 as the hedging index.8 For all the numerical investigations to follow, we will set the parameter values close to the empirical estimates. For the market portfolio (i.e., S&P 500)


227

and the hedging index (i.e., Nasdaq-100), we set mm=0.1, sm=0.2, sI=0.35 and rmI=0.8. For the stock, we choose the average for each parameter: ss=0.5, rIs=0.7 and rms=0.5. The resulting partial correlation rIs . m is 0.577. For some analyses, we also examine alternative values for rms (0.2 and 0.8) and rmI (0.4). Table 3 reports optimal portfolio weights and the residual variance under different parameter combinations. To see a broader range of patterns, we preset the range for the partial correlation by using the correlation between the stock and the index as a fitter. For most cases, the absolute weight on the index is smaller than the given weight on the stock, i.e., jxnI =xs jo1:0. This is so since the market portfolio can also provide partial hedging. As is clear from Proposition 2, when the hedging index is absent (i.e., xI ¼ 0), the market weight is reduced by bsxs from the weight under no trading restrictions. This reduction represents the hedging need due to trading restrictions. It is also interesting to observe that when the stock and the index are highly correlated, the market portfolio weight increases as the weight on the restricted stock increases. Intuitively, the higher correlation and higher weight on the stock create a stronger demand for hedging, and hence the bigger short position in the index has to be offset by holding the market portfolio. Table 3 also reveals that, the bigger the restricted holding, the bigger the residual variance. This means that introducing the trading restrictions will increase the residual variance or non-systematic risk, and hedging via the index cannot fully eliminate the excess variance. Moreover, it is seen that the excess variance is always higher when there is a binding restriction on the index. When the correlations take the typical values from Table 2 and the restricted holding is 50% of the total wealth, the optimal hedging position is approximately 120% of the restricted holding, and the weight on the market portfolio is approximately 70% (shown in the last row of the table). The excess variance is 0.0313, approximately 30% of the total variance (0.1313). Without the hedging index, the excess variance can be calculated as 0.0469. Therefore, the exposure to non-systematic risk is reduced by 33% ðð0:0313 0:0469Þ=0:0469 100% ¼ 33%Þ. One may argue that the incentive effect is reduced by 33%. Finally, other things being equal, the size of the excess variance or the amount of non-systematic risk is inversely related to the residual correlation, rIs . m. When this residual correlation is 1.0, the excess variance vanishes, and the impact of the trading restriction is completely undone. In fact, the same result ensues when the residual correlation is negative one. A perfect correlation between the stock and the index (i.e., |rIs|=1.0) can be obtained

228


Optimal Portfolio Weights and Residual Variance.

Table 3.

Without Trading Restriction xmt

s2w ¼ 0:10

¼ 0:50 With Trading Restriction Index Shorting: Non-Binding Restriction xs=0.5

xs=0.1

xs=0.1

xmt

Binding Restriction

xs=0.5

xI ¼ 0:5xI

xs ¼ 0:5

xmt

O

rms

rmI

rIs

rIs . m

xI =xs

0.2 0.2 0.2 0.2 0.2

0.4 0.4 0.4 0.4 0.4

0.08 0.30 0.53 0.75 0.98

0.00 0.25 0.50 0.75 1.00

0.00 0.38 0.76 1.15 1.53

0.45 0.48 0.50 0.53 0.56

0.25 0.38 0.52 0.65 0.78

0.0024 0.0023 0.0018 0.0011 0.0000

0.0600 0.0563 0.0450 0.0263 0.0000

0.25 0.32 0.38 0.45 0.52

0.0600 0.0572 0.0488 0.0347 0.0150

0.2 0.2 0.2 0.2 0.2

0.8 0.8 0.8 0.8 0.8

0.16 0.31 0.45 0.60 0.75

0.00 0.25 0.50 0.75 1.00

0.00 0.58 1.17 1.75 2.33

0.45 0.53 0.61 0.69 0.78

0.25 0.66 1.07 1.47 1.88

0.0024 0.0023 0.0018 0.0011 0.0000

0.0600 0.0563 0.0450 0.0263 0.0000

0.25 0.45 0.66 0.86 1.07

0.0600 0.0572 0.0488 0.0347 0.0150

0.5 0.5 0.5 0.5 0.5

0.4 0.4 0.4 0.4 0.4

0.20 0.40 0.60 0.80 0.99

0.00 0.25 0.50 0.75 1.00

0.00 0.34 0.67 1.01 1.35

0.38 0.40 0.42 0.45 0.47

0.13 0.01 0.11 0.23 0.35

0.0019 0.0018 0.0014 0.0008 0.0000

0.0469 0.0439 0.0352 0.0205 0.0000

0.13 0.07 0.01 0.05 0.11

0.0469 0.0447 0.0381 0.0271 0.0117

0.5 0.5 0.5 0.5 0.5

0.8 0.8 0.8 0.8 0.8

0.40 0.53 0.66 0.79 0.92

0.00 0.25 0.50 0.75 1.00

0.00 0.52 1.03 1.55 2.06

0.38 0.45 0.52 0.59 0.66

0.13 0.24 0.60 0.96 1.32

0.0019 0.0018 0.0014 0.0008 0.0000

0.0469 0.0439 0.0352 0.0205 0.0000

0.13 0.06 0.24 0.42 0.60

0.0469 0.0447 0.0381 0.0271 0.0117

0.8 0.8 0.8 0.8 0.8

0.4 0.4 0.4 0.4 0.4

0.32 0.46 0.59 0.73 0.87

0.00 0.25 0.50 0.75 1.00

0.00 0.23 0.47 0.70 0.94

0.30 0.32 0.33 0.35 0.37

0.50 0.42 0.34 0.25 0.17

0.0009 0.0008 0.0007 0.0004 0.0000

0.0225 0.0211 0.0169 0.0098 0.0000

0.50 0.46 0.42 0.38 0.34

0.0225 0.0214 0.0183 0.0130 0.0056

0.8 0.8 0.8 0.8 0.8 0.5

0.8 0.8 0.8 0.8 0.8 0.8

0.64 0.73 0.82 0.91 1.00 0.70

0.00 0.25 0.50 0.75 1.00 0.577

0.00 0.36 0.71 1.07 1.43 1.19

0.30 0.35 0.40 0.45 0.50 0.54

0.50 0.25 0.00 0.25 0.50 0.71

0.0009 0.0008 0.0007 0.0004 0.0000 0.0013

0.0225 0.0211 0.0169 0.0098 0.0000 0.0313

0.50 0.38 0.25 0.13 0.00 0.29

0.0225 0.0214 0.0183 0.0130 0.0056 0.0352

O

Note: For each correlation combination, the table reports the residual correlation, rIs . m; the optimal weight on the hedging index as a fraction of the given weight on the restricted stock, xI =xs ; the optimal weight on the market portfolio under different weights on the restricted stock, xmt ; and the residual variance under different weights on the restricted stock, O. The last row of the table is based on average correlation parameters reported in Table 2. The last two columns contain the market portfolio weight and the residual variance when the restriction on the index position is binding. The restriction is set at 50% of the optimal level. Other parameter values: mm ¼ 0.1, g ¼ 0.06, ss ¼ 0.5, sI ¼ 0.35, sm ¼ 0.2 and g ¼ 2.0.


229

even if the correlation between the stock and index is not perfect. For example, we can set rms=0.2, rmI=0.8, and rIs=0.75 to have rIs . m=1, as shown in the table.

3. UNDOING THE HOLDING RESTRICTIONS USING THE HEDGING INDEX 3.1. The State Price Deflator To illustrate the benefit of the hedging index to the employee, we need to determine how he values the restricted security with or without the hedging index. The employee’s private valuation of an incentive security hinges upon his state price deflator U cT =U ct , i.e., the marginal rate of substitution. Given the CRRA utility function, we have U ct ¼ eft cg t . Applying Ito’s lemma, we obtain the following processes for the marginal utility: dU c ¼ ðr gOÞdt ðsm gbs xs sm gbI xIt sm Þdzm Uc gxs ss dzs gxIt sI dzI 8 toT dU c ¼ rdt sm dzm Uc

8 tT

(4)

(5)

where O and xIt are defined in Eq. (3). The processes in (4) and (5) apply to the vesting and post-vesting periods, respectively. Beyond the vesting period, the employee’s state price deflator is determined by the risk-free rate and the Sharpe ratio of the market portfolio and is independent of the risk preference parameters f and g. In this case, the employee’s valuation of any incentive security is equal to the market valuation, and the discount is zero. In other words, the optimal course of action for the employee is to sell the incentive security as soon as it is vested. Within the vesting period, the employee’s valuation will deviate from the market’s since the discount rate is r – gO and the variance of the marginal utility is s2m þ g2 O. In the following section, we will determine precisely how much the employee discounts the restricted stock and how the hedging index can alleviate this discount. 3.2. Private Valuation of the Restricted Stock As mentioned, when the employee faces trading restrictions, his private valuation of an incentive security no longer equals the market’s. Instead, it is

230


determined via the Euler Eq. (2) under the state price deflator (4). Taking the continuous dividend yield into consideration, the employee’s subjective valuation of the restricted stock is computed as S^ t ¼ E t ððU cT Þ=ðU ct Þ eqs ðTtÞ S T Þ. Straightforward, albeit tedious algebra leads to S^ t ¼ St el s ðTtÞ where the illiquidity discount ls is defined as ( ls ¼

l s gðxs x2s Þ v2s ð1 r2Is : m Þ

if the index shorting restriction is not binding

l s þ gv2I ðxI xI ÞðxI xI xI =xs Þ if the index shorting restriction is binding

When the trading restriction on the stock is removed, i.e., when xs=0, there is no need to take a position on the index. The illiquidity discount l ns becomes zero and the employee’s private valuation is equal to the market’s. Also, the private valuation reverts to the market value at the end of the vesting period where t=T. However, when xs a0 or toT, the private value is always lower than the market value due to the employee’s bearing of the company-specific risk. The extent to which the employee discounts the restricted stock depends on the length of the vesting period Tt and the illiquidity discount rate, l ns . The illiquidity discount increases with the degree of risk aversion and the volatility of the company’s stock. However, the discount decreases with the correlation between the company’s stock and the index. The discount reduces to its minimum when the index position is optimized. With an optimal index weight, a perfect residual correlation between the stock and the index (i.e., |rIs . m|=1) can make the illiquidity discount completely vanish. In this case, the inherent non-systematic risk is completely avoided, and the employee’s private valuation of the stock coincides with the market’s, reducing the discount to zero. Admittedly, the incentive effects are also nullified in this case, making the restricted stock equivalent to a delayed cash bonus. An obvious policy implication is that, firms must be sure that there does not exist an effective hedging vehicle for the employee when granting restricted stocks. To gain further insights, we report in Table 4 the private stock value as a fraction of its market value for various parameter combinations. One minus the fraction measures the size of discount in percentage. Under each stock restriction, we examine three scenarios: no hedging (corresponding to KLL, 2003; Ingersoll, 2006), hedging with a binding restriction on the index and optimal hedging.9 The difference in the fractions between the no hedging ðxI ¼ 0Þ column and optimal-hedging ðxI ¼ xnI Þ column measures the reduction of discount due to hedging. Other than the obvious (e.g., a higher risk

g

rms

rIs

Tt

Private Value of the Restricted Stock as a Fraction of its Market Value. xs = 0.1

rls . m

xs = 0.3

xs = 0.5

xI = 0.0

xI ¼ 0:5 xI

xI ¼ xI

xI = 0.0

xI ¼ 0:5 xI

xI ¼ xI

xI = 0.0

xI ¼ 0:5 xI

xI ¼ xI

0.20 0.20 0.20

0.34 0.34 0.34

1 5 10

0.30 0.30 0.30

0.958 0.806 0.649

0.959 0.813 0.661

0.961 0.822 0.675

0.904 0.604 0.365

0.907 0.615 0.378

0.912 0.632 0.400

0.887 0.549 0.301

0.889 0.556 0.309

0.897 0.579 0.336

2 2 2

0.80 0.80 0.80

0.75 0.75 0.75

1 5 10

0.30 0.30 0.30

0.984 0.922 0.850

0.985 0.925 0.856

0.985 0.929 0.863

0.963 0.828 0.685

0.964 0.833 0.694

0.966 0.842 0.709

0.956 0.799 0.638

0.957 0.803 0.644

0.960 0.815 0.664

2 2 2

0.20 0.20 0.20

0.54 0.54 0.54

1 5 10

0.65 0.65 0.65

0.958 0.806 0.649

0.966 0.841 0.708

0.975 0.883 0.779

0.904 0.604 0.365

0.919 0.657 0.431

0.943 0.747 0.559

0.887 0.549 0.301

0.898 0.585 0.342

0.933 0.707 0.500

2 2 2

0.80 0.80 0.80

0.87 0.87 0.87

1 5 10

0.65 0.65 0.65

0.984 0.922 0.850

0.987 0.937 0.878

0.991 0.954 0.911

0.963 0.828 0.685

0.969 0.854 0.730

0.978 0.897 0.804

0.956 0.799 0.638

0.961 0.818 0.669

0.974 0.878 0.771

2 2 2

0.50 0.50 0.50

0.92 0.92 0.92

1 5 10

1.00 1.00 1.00

0.967 0.845 0.714

0.982 0.915 0.837

1.000 1.000 1.000

0.924 0.675 0.455

0.953 0.787 0.620

1.000 1.000 1.000

0.911 0.626 0.392

0.932 0.704 0.495

1.000 1.000 1.000

231

2 2 2


Table 4.

232

Table 4. (Continued ) g

rms

rIs

Tt

xs = 0.1

rls . m xI = 0.0

xI ¼ 0:5

xI

xs = 0.3 xI ¼

xI

xI = 0.0

xI ¼ 0:5

xI

xs = 0.5 xI ¼

xI

xI = 0.0

xI ¼ 0:5 xI

xI ¼ xI

4 4 4

0.50 0.50 0.50

0.92 0.92 0.92

1 5 10

1.00 1.00 1.00

0.935 0.714 0.509

0.965 0.837 0.700

1.000 1.000 1.000

0.854 0.455 0.207

0.909 0.620 0.384

1.000 1.000 1.000

0.829 0.392 0.153

0.869 0.495 0.245

1.000 1.000 1.000

2 2 2

0.50 0.50 0.50

0.70 0.70 0.70

1 5 10

0.577 0.577 0.577

0.967 0.845 0.714

0.972 0.867 0.752

0.978 0.894 0.799

0.924 0.675 0.455

0.934 0.710 0.504

0.949 0.769 0.592

0.911 0.626 0.392

0.918 0.651 0.423

0.939 0.732 0.535

4 4 4

0.50 0.50 0.50

0.70 0.70 0.70

1 5 10

0.577 0.577 0.577

0.935 0.714 0.509

0.945 0.752 0.566

0.956 0.799 0.638

0.854 0.455 0.207

0.872 0.504 0.254

0.900 0.592 0.350

0.829 0.392 0.153

0.842 0.423 0.179

0.882 0.535 0.287


Note: This table reports the implied value of the restricted stock as a fraction of the market value for different combinations of the risk aversion, g, the correlation between the stock and the market, rms, the correlation between the stock and the hedging index, rIs, and the vesting period, T t. For each parameter combination, we examine two levels of the stock’s weight relative to the total wealth. Under each stock weight, we examine three index scenarios: no hedging (xI = 0), hedging with a binding constraint on the index (50% of the optimal weight), and hedging with the optimal weight (xI ¼ 0:5 xI ). The last six rows of the table are based on the average correlation parameters in Table 2. Other parameter inputs: ss = 0.5, sI = 0.35, and rmI = 0.8.


233

aversion and a longer vesting period lead to a deeper discount), the table bears out the previous discussions: when the employee optimally chooses the position on the index, he can always reduce the illiquidity discount. Regardless of whether the stock is more correlated with the index or with the market, as long as the residual correlation rIs . m is not zero, hedging will always enhance the private valuation of the stock and undermine the incentive effect due to the reduced exposure to the company’s non-systematic risk. The higher the residual correlation, the better the index can enhance the private valuation, and the weaker the remaining incentive effects. When the partial correlation is 1.0, the entire discount can be removed. In this case, the incentive effect is also completely nullified. It should be noted that many correlation combinations can lead to a perfect or a very high residual correlation rIs . m. To see this, we can set rms=0.2, rmI=0.7 and rIs=0.84 to have rIs . m=1. Under the typical market conditions (the last two panels of the table), for an employee whose risk-aversion is 2 and who holds 50% of his wealth in the restricted stock, he discounts the holding by approximately 60% (1–0.392) when the vesting period is 10 years. With a hedging index, the discount is approximately 46% (1–0.535), representing a reduction of 14%. On the other hand, as shown in Table 3 and discussed in Section 2.4, the non-systematic risk is reduced by approximately 33% in this case. 3.3. Private Value and Incentive Effects of European Options on Restricted Stocks Similar to the analyses for restricted stocks, we first obtain the marginal valuation of options and then determine how much the employee discounts the options due to trading restrictions. The valuation depends on whether the stock is still being restricted at the time of the option’s exercise. When the option’s maturity To is before the end of the vesting period T, the stock will have a private value at the option’s expiry date, and an adjustment for the remaining vesting period must be made, which amounts to a discount to the stock price. When To W T, the stock attains its market value at the option’s maturity and no adjustment is necessary. In this case, we must use both state price deflators. The valuation under the two cases can be summarized as follows: U cT o l s ðTT o Þ ^ maxðS T o e K; 0Þ ; 8 T o oT CI ¼ Et Uc t U cT o U cT ET maxðST o K; 0Þ ; 8 T o 4T C^ I ¼ E t U ct U cT

234


where K is the exercise price of the option. To facilitate presentation, let CBS be the Black–Scholes call value expressed as C BS ðS t ; T t; K; r; q; sÞ ¼ St eqðTtÞ N½d 1 ðr; qÞ KerðTtÞ N½d 2 ðr; qÞ where d 1 ðr; qÞ ¼

lnðSt =KÞ þ ðr q þ s2 =2ÞðT tÞ pffiffiffiffiffiffiffiffiffiffiffiffi s T t pffiffiffiffiffiffiffiffiffiffiffiffi d 2 ðr; qÞ ¼ d 1 ðr; qÞ s T t

and

Then the employee’s valuation of the European option on the restricted stock is (see appendix, ‘‘Proof of Valuation Formula for European Options’’ for a proof) C^ t ¼ C BS S t el s ðTtÞ ; T o t; K; r gO; qs ; ss ; 8 T o oT (6) T t ; q ; ss ; 8 T o 4T C^ t ¼ C BS St el s ðTtÞ ; T o t; K; r gO To t s It is apparent from the above that restricted European calls are always worth less than their Black–Scholes counterparts. In other words, there is a deadweight loss when granting European options. We showed earlier that the illiquidity discount ls and the excess variance O can both be reduced when the index is in place. Thus, the hedging index will narrow the gap between the private valuation and the market’s. When the residual correlation between the stock and the index is perfect: |rIs . m|=1, the employee’s private valuation of the option is equal to the Black–Scholes value. When studying restricted options, we must realize that there are two dimensions to incentive effects. On the one hand, similar to restricted stocks, incentives are preserved through bearing the non-systematic risk. Therefore, it is also true that when the discount on option values is reduced, incentive effects are also compromised. On the other hand, since options are nonlinear transformation of stocks, incentive effect can also be measured in terms of price sensitivities, viz., how much the private value of the option will increase for a given increase in the stock price. For this sensitivity effect, we follow the literature and examine the option’s delta, i.e., the option’s sensitivity to the stock price. In our case, the delta is S t el s ðTtÞ eqðT o tÞ N½d 1 ðr gO; qs Þ or S t el s ðTtÞ eqðT o tÞ N½d 1 ðr gOðT tÞ=ðT o tÞ; qs Þ; clearly lower than its Black–Scholes counterpart. Thus, introducing the hedging index will not only increase the private valuation of the option, but also improve its delta. The two dimensions of the incentive effects for options present an interesting trade-off when the hedging index is held: the total amount of incentive is


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reduced due to less exposure to the non-systematic risk, but the incentive sensitivity is enhanced due to better valuations. Since the two dimensions are measured differently, it is not clear whether an optimal trade-off exists. To quantify the above observations, we report the option values as a fraction of their Black–Scholes counterparts in Panel A and the option delta’s in Panel B of Table 5. For all calculations, we use the typical parameter values as shown in Table 2. For simplicity, we assume that the option’s maturity coincides with the end of the stock’s vesting period. Again, for each given weight on the restricted stock, xs, we examine three scenarios xI=0, xI ¼ 0:5xnI and xI ¼ xnI . Panel A of Table 5 reveals that the discount on options is generally much bigger than that on the restricted stock (by comparing with Table 4). The deeper discount is primarily due to the non-linear nature of the option’s payoff. Table 5 also reveals that the discount is bigger when (1) the weight on the restricted stock is higher, (2) the option is further out-of-the-money and (3) the option’s time to maturity is longer. More importantly, the hedging index can alleviate the discount substantially. For instance, when g=2, xs=0.5 and T – t=10 years, the discount on the at-the-money option is approximately 84% (10.155) when the employee does not hold the hedging index; but this discount is reduced to 68% (10.315) when the hedging index is optimally held, representing an improvement of 16%. Similar observations can be made regarding delta’s in Panel B of Table 5. Although the delta is lower compared with its Black–Scholes counterpart, holding the hedging index can increase the delta or incentive sensitivity. The results in Table 5 indicate that the hedging index can play an important role in reducing the discount and improving the incentive sensitivity for options. However, it should be realized that the total amount of incentive is compromised since the hedging index reduces the exposure to the stock’s non-systematic risk.

3.4. Options with Early Exercise and Vesting Features In reality, vesting requirements are usually imposed not only on the stock, but also on options. Furthermore, the incentive options are normally granted as American options which can be exercised at anytime after the option is vested. The vesting period is typically 5 years within which no exercise is allowed. To make further investigations, we calculate American option values and delta’s using a 5,000-step binomial tree. The starting price of the tree is

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Table 5.

Value Discount and Incentive Effect (Delta) of European Stock Options.

xs

g ¼ 2.0 xI ¼ 0:5 xI

xI ¼ 0.0

g ¼ 4.0 xI ¼ xI

x1 ¼ 0.0

xI ¼ 0:5 xI

xI ¼ xI

Panel A: Option value (as a fraction of Black–Scholes) K ¼ $115, Tt ¼ 10 years, Black–Scholes ¼ $51.208 0.1 0.3 0.5

0.623 0.277 0.146

0.673 0.340 0.197

0.732 0.438 0.304

0.377 0.057 0.008

0.445 0.095 0.021

0.529 0.170 0.063

K ¼ $100, Tt ¼ 10 years, Black–Scholes ¼ $53.514 0.1 0.3 0.5

0.629 0.287 0.155

0.679 0.349 0.207

0.736 0.447 0.315

0.385 0.061 0.009

0.452 0.100 0.023

0.536 0.178 0.068


0.636 0.297 0.165

0.685 0.360 0.218

0.741 0.458 0.328

0.394 0.067 0.011

0.461 0.107 0.026

0.544 0.187 0.075


0.742 0.435 0.277

0.779 0.498 0.340

0.821 0.584 0.446

0.542 0.162 0.048

0.601 0.224 0.085

0.669 0.319 0.164


0.750 0.451 0.295

0.786 0.513 0.358

0.827 0.597 0.464

0.554 0.175 0.055

0.612 0.238 0.094

0.679 0.335 0.178


0.759 0.469 0.316

0.794 0.529 0.378

0.833 0.612 0.484

0.568 0.190 0.064

0.624 0.254 0.107

0.690 0.353 0.196

Panel B: Option delta K ¼ $115, Tt ¼ 10 years, Black–Scholes ¼ 0.680 0.1 0.3 0.5

0.446 0.222 0.131

0.478 0.265 0.169

0.515 0.332 0.248

0.285 0.054 0.010

0.330 0.085 0.023

0.386 0.144 0.062


Table 5. xs

(Continued )

g ¼ 2.0 xI ¼ 0.0

xI ¼ 0:5 xI

237

g ¼ 4.0 xI ¼ xI

x1 ¼ 0.0

xI ¼ 0:5 xI

xI ¼ xI

K ¼ $100, Tt ¼ 10 years, Black–Scholes ¼ 0.697 0.1 0.3 0.5

0.462 0.235 0.142

0.494 0.278 0.181

0.531 0.346 0.263

0.298 0.060 0.012

0.344 0.092 0.026

0.400 0.154 0.069

0.359 0.101 0.030

0.416 0.166 0.078

0.429 0.187 0.083

0.471 0.255 0.149

0.461 0.210 0.098

0.503 0.282 0.170

0.495 0.236 0.116

0.538 0.313 0.197


0.478 0.249 0.155

0.510 0.293 0.195

0.548 0.363 0.280

0.312 0.066 0.014


0.514 0.332 0.233

0.535 0.371 0.274

0.559 0.424 0.345

0.393 0.143 0.051


0.547 0.362 0.260

0.569 0.402 0.304

0.594 0.457 0.378

0.424 0.162 0.062


0.583 0.396 0.293

0.605 0.436 0.337

0.630 0.493 0.415

0.457 0.186 0.076

Note: The table reports the ratio of the European stock option’s value over its Black–Scholes counterpart (Panel A) and delta of the European stock option (Panel B). For each moneyness and maturity combination, we examine the ratio or value discount and delta for two levels of risk aversion (g ¼ 2, 4), three levels of the stock’s weight relative to the total wealth (xs ¼ 0.1, 0.3, 0.5), and three index scenarios: no hedging (xI ¼ 0), hedging with a binding constraint equal to 50% of the optimal weight ðxI ¼ 0:5 xI Þ, and hedging with the optimal weight ðxI ¼ xI Þ. Other parameter inputs: ss ¼ 0.5, s1 ¼ 0.35, rms ¼ 0.5, rmI ¼ 0.8, rIs ¼ 0.7, rIs . m ¼ 0.577, r ¼ 0.06, qs ¼ 0.02. For simplicity, we assume that the option’s maturity coincides with the stock’s vesting period.

S t el s ðTtÞ where as before, T is the end of vesting period and t is the current time. For simplicity, we assume that the stock’s vesting period coincides with the option’s vesting period. In this case, the effective discount rate is r – gO during the vesting period and r during the post-vesting period. The different

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interest rates lead to two distinct branching probabilities for the two periods. The jump size of the binomial tree remains the same in both periods. Panel A of Table 6 reports the American option value with vesting features as a fraction of its market value calculated in the Black–Scholes’ environment, i.e., the plain vanilla American call option. The table shows several vesting scenarios under various parameter combinations. For comparisons, we also report European values in the last panel. For consistency, in the last panel, we also calculate the percentages using the plain vanilla America option value (i.e., $56.10) as the base. There are several interesting observations. First, American options are always worth more than their European counterparts no matter how long the vesting period is. The difference is larger when the risk aversion and the weight on the restricted stock are high.10 When the vesting period is close to 10 years, the American option is practically a European option. This becomes apparent as the vesting period increases, going from the first panel to the last panel. In addition, the impact of the restricted stock’s weight and the hedging schemes is similar to that for European options as shown in Table 5, namely, partial hedging or optimal hedging can reduce the option discount substantially. Second, other things being equal, a longer vesting period clearly reduces the option’s value, which makes intuitive sense. Interestingly, the incremental impact of vesting is more pronounced when the vesting period is short. For instance, for the parameter combination of xs=0.5, g ¼ 2 and xI ¼ xI , the private value of the restricted option as a percentage of the market value decreases from 90% to 57% (a drop of 33% points) when the vesting period increases from 1 to 5 years; however, the percentage decreases from 57% to 35% (a drop of 22% points) when the vesting period increases from 5 to 9 years. Incidentally, it is well known that the early exercise premium should be zero for American call options if the underlying stock does not pay dividends. In Panel A of Table 6, the unrestricted American call is worth more than its European counterpart ($56.10 versus $53.51) purely due to the dividend yield. However, the substantial difference in option values between different vesting scenarios is obviously not due to dividend yield alone. For instance, for the parameter combination of xs=0.5, g ¼ 2 and xI ¼ xI , the American option value under a vesting period of 9 years is approximately one-third of that under a vesting period of 1 year. When the vesting period is reduced from 9 to 1 year, the free exercise period is increased from 1 to 9 years. The significant improvement in value associated with the longer free exercise period is not purely due to dividend yield. Instead, the premium mainly comes from the opportunity to avoid the trading restrictions.


Table 6.

239

Value Discount and Incentive Effects of Stock Options with Vesting and Early Exercise Features.

xs

g=2.0 xI ¼ 0:5 xI

xI=0.0

g=4.0 xI ¼ xI

xI=0.0

xI ¼ 0:5 xI

xI ¼ xI

Panel A: Option value (as a fraction of Black–Scholes) American option, vesting=1 year (Black–Scholes=$56.10) 0.1 0.3 0.5

0.955 0.890 0.853

0.962 0.905 0.870

0.970 0.925 0.900

0.911 0.790 0.724

0.925 0.817 0.753

0.940 0.855 0.808

American option, vesting=5 years (Black–Scholes=$56.10) 0.1 0.3 0.5

0.789 0.544 0.424

0.819 0.596 0.476

0.853 0.670 0.574

0.621 0.280 0.150

0.671 0.342 0.201

0.729 0.439 0.307

American option, vesting=9 years (Black–Scholes=$56.10) 0.1 0.3 0.5

0.636 0.316 0.186

0.681 0.377 0.238

0.733 0.469 0.345

0.410 0.082 0.017

0.473 0.126 0.036

0.551 0.208 0.092

European option, vesting=10 years (Black–Scholes=$53.51) 0.1 0.3 0.5

0.600 0.273 0.147

0.647 0.333 0.197

0.702 0.427 0.300

0.367 0.058 0.009

0.431 0.096 0.022

0.511 0.169 0.065

Panel B: Option delta American option, vesting=1 year (Black–Scholes=0.749) 0.1 0.3 0.5

0.717 0.675 0.650

0.722 0.683 0.664

0.726 0.695 0.682

0.687 0.606 0.565

0.695 0.622 0.586

0.704 0.649 0.624

American option, vesting=5 years (Black–Scholes=0.749) 0.1 0.3 0.5

0.601 0.437 0.358

0.619 0.471 0.393

0.643 0.524 0.466

0.485 0.243 0.147

0.518 0.288 0.184

0.557 0.362 0.273

American option, vesting=9 years (Black–Scholes=0.749) 0.1 0.3 0.5

0.489 0.269 0.176

0.519 0.312 0.213

0.553 0.378 0.297

0.330 0.082 0.021

0.375 0.118 0.041

0.427 0.184 0.093

240


Table 6. xs

(Continued )

g=2.0 xI=0.0

xI ¼ 0:5 xI

g=4.0 xI ¼ xI

xI=0.0

xI ¼ 0:5 xI

xI ¼ xI

European option, vesting=10 years (Black–Scholes=0.697) 0.1 0.3 0.5

0.462 0.235 0.142

0.494 0.278 0.181

0.531 0.346 0.263

0.298 0.060 0.012

0.344 0.092 0.026

0.400 0.154 0.069

Note: In this table, Panel A reports the value of stock options with vesting and early exercise features as a fraction of the plain vanilla American option value ($56.10). For comparison, we also report European values in the last panel, as a fraction of the same base, $56.10. Panel B reports delta of stock options with vesting and early exercise features. Similarly, we report delta’s for European options in the last panel. For each vesting period, we examine the fractions and delta’s for two levels of risk aversions (g ¼ 2, 4), three levels of the stock’s wealth (xs ¼ 0.1, 0.3, 0.5), and three index scenarios: no hedging (xI = 0), hedging with a binding constraint equal to 50% of the optimal weight ðxI ¼ 0:5 xI Þ, and hedging with the optimal weight ðxI ¼ xI Þ. Other parameter inputs: ss ¼ 0.5, sI ¼ 0.35, rms ¼ 0.5, rmI ¼ 0.8, rIs ¼ 0.7, rIs . m ¼ 0.577, g = 0.06, qs ¼ 0.02, St ¼ 100, K ¼ $100, T – t ¼ 10 years. For American options, we assume that the stock’s vesting period coincides with the options’. The American option values are calculated using a binomial tree with 5000 steps.

To examine the incentive sensitivities, we calculate the option’s delta for each entry in Panel A and report the results in Panel B of Table 6. Similar to restricted European options, restricted American options have delta’s lower than their Black–Scholes counterparts. The difference is exacerbated when the vesting period increases. When the vesting period is equal to the option’s maturity, the American option becomes a European option, and the incentive sensitivity reaches the lowest level. Similar to the value effect in Panel A, the incremental effects of vesting is larger when the vesting period is shorter. More important is the hedging effect of the index. Introducing the index can increase delta or incentive sensitivity, especially when the stock’s weight is large and when the employee is more risk-averse. The upshot is that, like other types of options, options with early exercise and vesting features will also enjoy an improvement in private valuation and incentive sensitivity when employees use a hedging index. Comparing Table 6 with Table 5, we see that the extent to which the private value and incentive sensitivity improves with the introduction of the hedging index is similar for European and American options. For instance, with xs=0.5 and g ¼ 2, the private value of an at-the-money European option improves by approximately 16% (=31.5% – 15.5%), while its delta


241

or incentive sensitivity improves by approximately 0.121 (=0.263 – 0.142). The corresponding quantities for an American option with a 5-year vesting period are 15% (=57.4% – 42.4%) and 0.108 (=0.466 – 0.358). Before concluding the study, we would like to offer a few remarks about the general complications of incentive compensations. Intuitively, the reason that the restricted stocks and options can create incentive effects is because their appreciation in value can directly benefit the employees. The employees are willing to work harder in the hope to enhance the stock’s value and hence their own holdings. The vesting requirement forces the employee to bear nonsystematic or firm-specific risk, which drives a wedge between the private and market valuations of the incentive securities. The firm hopes for stronger efforts from employees during the vesting period as they work hard to enhance the stock’s performance. On the other hand, bearing non-systematic risk is sub-optimal for the employees, and they will have every incentive to undo the restriction or avoid the non-systematic risk. Index hedging is thus a natural course of action for employees. As we have seen, the hedging index will definitely benefit the employee in the form of higher private valuation and higher utility, but it will also compromise the absolute incentive effect, although for options, the incentive sensitivity can also improve. Undoubtedly, the employee’s wealth must be tied to the firm’s fortune in order for incentives to exist. Granting stocks or options without trading restrictions will not create long-term incentives because the employee can convert the securities into cash and leave the company at his wish. Vesting requirements will achieve the purpose of retaining the employees, and hopefully, motivating the employees at the same time. But retaining talents and enhancing incentives are two different aspects of an incentive package. Delayed cash bonus or legal contracting can both achieve retention purposes, but they do not necessarily guarantee a higher incentive. An incentive scheme is effective only when both aspects are properly considered. Presumably, granting company stocks or options with vesting features is aimed at achieving both. However, as we have shown, the employee can use a hedging index to undo the vesting effect. With a hedging index, the trading restrictions will not be as restrictive as they appear.

4. CONCLUSION Incentive stocks and options are granted with vesting requirements and the grantees are prohibited from using direct hedges to offset the firm-specific risk. This chapter studies how private valuation and incentive effects are

242


affected when employees use a partial hedge (e.g., by shorting the industry index) to undo the trading restrictions. The analysis is carried out in a continuous-time consumption-portfolio framework. We show that a hedging index can enhance the employee’s private valuation of the restricted assets and, in the case of options, improve the incentive sensitivity. However, all the improvements are achieved via reducing the exposure to the company’s non-systematic risk. In other words, the absolute incentive is compromised. The main results can be summarized as follows. First, the hedging index can increase the employee’s utility and reduce the value discount of the restricted stock. The optimal amount of the index depends positively on the stock’s volatility, the residual correlation between the stock and the index, and negatively on the index’s volatility, the correlation between the stock and the market. The higher the residual correlation between the stock and the index, the more effective is the index in reducing the discount. When the residual correlation is perfect, the discount can be completely removed. Therefore, the trading restrictions on the incentive stocks may not be as restrictive as we thought. Second, the hedging index can also reduce the discount of stock options, and does so to a similar extent as for restricted stocks. Moreover, the hedging index also improves the delta’s or incentive sensitivities of stock options. The value enhancement and the incentive sensitivity improvement are observed for both restricted European options and options with early exercise and vesting features. Previous studies (e.g., Meulbroek, 2001; Kahl et al., 2003; Ingersoll, 2006) only show how and why employees would value restricted assets below their market values. The conventional wisdom is that, employees’ private valuation of restricted assets is below the market’s since they are exposed to the company’s non-systematic risk, and that the bearing of this non-systematic risk is the source of incentives. In this study, we show that the intended effectiveness of granting restricted assets cannot be taken for granted. Employees do have the incentive and means to undo the restrictions in order to enhance their own utility. With typical parameter values, we show a reduction of approximately 33% in the exposure to non-systematic risk. With the right combination of correlations (between the stock, the market portfolio and the hedging index), the exposure to non-systematic risk can be completely removed. Interestingly, some seemingly benign correlations will do. One such an example is following: the stock’s correlation with the market and the index is 0.2 and 0.84 respectively, while that between the market and the index is 0.7.


243

NOTES 1. For further details, please refer to page 12 of the Council’s discussion paper titled ‘‘Executive Compensation Disclosure: How It Works Now, How It Can Be Improved.’’ The paper can be found at the following web site: http://www.cii.org/ site/files/pdfs/CII/%20pay/%20primer/%20edited.pdf 2. For examples of the incentive literature, see Lambert, Larcker, and Verrecchia (1991), Rubinstein (1995), Aboody (1996), Carpenter (1998, 2000), Hall and Murphy (2000, 2002), Meulbroek (2001), and Lambert and Larcker (2003). For examples of the asset valuation with portfolio constraints, see DeTemple and Sundaresan (1999) and references therein. Recent studies on constrained portfolio selections and asset valuation include Henderson and Hobson (2002), Browne, Milevsky, and Salisbury (2003), KLL (2003), and Ingersoll (2006). 3. To preserve accounting earnings and to reduce tax liabilities, firms usually grant at-the-money options by setting the exercise price equal to the prevailing stock price. If options could be granted in-the-money yet recorded at-the-money, the receiving executive will benefit at the expense of the IRS and the shareholders. Backdating refers to the practice where the effective granting date is chosen which saw the lowest stock price in the recent past; in the case of forward-dating or spring-loading, the effective granting date is purposely postponed in anticipation of a stock price decline based on either inside information or the trend of recent stock price movements. In either case, the end-result, albeit illegal, is to record options at-the-money which in effect are in-the-money. The first, major media exposure of backdating was by Forelle and Bandle (2006) in the Wall Street Journal on March 18, 2006. The Wall Street Journal maintains a webpage (http://www.online.wsj.com/public/resources/documents/ info-optionsscore06-full.html) tracking the companies that are under investigation. As of December 29, 2006, the list contains more than 120 companies. For recent academic studies on this issue, please see Bebchuk, Grinstein, and Peyer (2006), Narayanan and Seyhum (2006), and Narayanan, Schipani, and Seyhum (2007). 4. Since the employee no longer faces trading constraints after the vesting period, the role of bequest is unimportant. We therefore assume a zero bequest function for simplicity. 5. KLL (2003) assume that the employee receives only one grant of the company’s stock. Therefore, the number of the restricted shares is fixed during the vesting period. Such a restriction is realistic for IPO lock-up, but less so for an annual incentive scheme used by most of the companies. 6. For simplicity, we assume that the retirement time coincides with the finite horizon of the utility maximization. 7. There are many other ways in which we can introduce an additional asset into the choice set. For instance, we could introduce a tangent portfolio consisting of Assets 1 and 3. This index will be similar to Index12 in nature. Alternatively, we could include Assets 2 and 3 as individual assets, which will be equivalent to including Index23.m alone. 8. Please note that exchange-traded funds are available for both the S&P 500 index and the Nasdaq-100 index. They are ‘‘Spider’’ and ‘‘QQQ,’’ both traded on the American Stock Exchange. Therefore, the optimal portfolio strategy presented in this chapter can be easily implemented in reality.

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9. To maintain a consistent comparison across all scenarios, in this and subsequent tables, we set the index restriction as 50% of the optimal level. We set the restriction as a fraction of the optimal level so that it is always binding to the same extent across all scenarios. 10. Although the table does not show the absolute option values, the aforementioned observations are apparent from the fractions. The fractions for American options are all higher than those for European options in the last panel.

ACKNOWLEDGEMENTS We thank Werner DeBondt, Jin-Chuan Duan, Adam Gehr, Keith Howe, Raymond Kan, Carl Luft, Moshe Milevsky, Joshph Vu, Alan White and seminar/conference participants at DePaul University, McMaster University, University of Toronto, York University, the 2003 annual meeting of the Northern Finance Association, the 2004 annual meeting of the Financial Management Association and the 2004 University of Waterloo Risk & Insurance conference for helpful comments. We also thank the Editor, Andrew Chen, for useful suggestions. Both authors gratefully acknowledge the financial support from the Social Sciences and Humanities Research Council of Canada.

REFERENCES Aboody, D. (1996). Market valuation of employee stock options. Journal of Accounting and Economics, 22, 357–391. Bebchuk, L., Grinstein, Y., & Peyer, U. (2006). Lucky CEOs. Working Paper. John M. Orlin Center for Law, Economics, and Business, Harvard University. Browne, S., Milevsky, M., & Salisbury, T. (2003). Liquidity premium for illiquid annuities. Working Paper. Columbia University and York University. Carpenter, J. (1998). The exercise and valuation of executive stock options. Journal of Financial Economics, 48, 127–158. Carpenter, J. (2000). Does option compensation increase managerial risk appetite? Journal of Finance, 55, 2311–2331. DeTemple, J., & Sundaresan, S. (1999). Non-traded asset valuation with portfolio constraints: A binomial approach. Review of Financial Studies, 12, 835–872. Forelle, C., & Bandle, J. (2006). The perfect paydate. The Wall Street Journal (March 18), A1. Hall, B., & Murphy, K. (2000). Optimal exercise prices for risk averse executives. American Economic Review, 90, 209–214. Hall, B., & Murphy, K. (2002). Stock options for undiversified executives. Journal of Accounting and Economics, 33(1), 3–42. Henderson, V., & Hobson, D. (2002). Real options with constant relative risk aversion. Journal of Economic Dynamics & Control, 27(2), 329–355. Ingersoll, J. (2006). The subjective and objective evaluation of incentive stock options. Journal of Business, 79(2), 453–487.


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Kahl, M., Liu, J., & Longstaff, F. (2003). Paper millionaires: How valuable is stock to a stockholder who is restricted from selling it? Journal of Financial Economics, 67(3), 385–410. Lambert, R., & Larcker, D. (2003). Stock options, restricted stock, and incentives. Working Paper. The Wharton School, University of Pennsylvania. Lambert, R., Larcker, D., & Verrecchia, R. (1991). Portfolio considerations in valuing executive compensation. Journal of Accounting Research, 29, 129–149. Merton, R. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3, 373–413. Meulbroek, L. (2001). The efficiency of equity-linked compensation: Understanding the full cost of awarding executive stock options. Financial Management, 30(2), 5–44. Narayanan, M., Schipani, C., & Seyhum, H. (2007). The economic impact of backdating of executive stock options. Michigan Law Review, 105(8), 1597–1641. Narayanan, M., & Seyhum, H. (2006). The dating game: Do managers designate option grant dates to increase their compensation. Working Paper. University of Michigan. Rubinstein, M. (1995). On the accounting valuation of employee stock options. Journal of Derivatives, 3, 8–24.

APPENDIX Proof of Proposition 1 In order to determine the optimal consumption, cnt and portfolio holdings, xnmt and xnBt ¼ 1 xnmt xs xIt ; we apply the optimal control rule " JðW ; M; S; I; tÞ ¼ maxx;c E

RT

# UðcðtÞ; tÞdt

t

Cðx; c; W ; M; S; I; tÞ ¼ UðcðtÞ; tÞ þ I½J where I½J is the differential generator of J associated with its control function

I½J ¼

@J @J 1 @2 J @J þ W mW þ MmM W 2 s2W þ @t @W 2 @W 2 @M 1 @2 J @2 J 2 2 WM covðdW=W ; dM=MÞ þ M s þ M 2 @M 2 @W @M @J 1 @2 J 2 2 @2 J þ SmS þ WS covðdW=W ; dS=SÞ S s þ S @S 2 @S 2 @W @S

246


@2 J @J SMrms ss sm þ Im @S@M @I I 1 @2 J 2 2 @2 J WI covðdW=W ; dI=IÞ þ I s þ I 2 @I 2 @W @I @2 J @2 J þ IMrmI sI sm þ ISrIs sI ss @I@M @I@S þ

Now, the bequest function for the employee at time T is J(W, M, S, I, T) ¼ J(W, T). The optimal consumption, cnt and the optimal weights, xnmt , xnlt are solved by maximizing Cðx; c; W ; M; S; I; tÞ: The first order conditions are @C @U @J ¼ ¼0 @c @c @W @C @J @m 1 @2 J @s2 @2 J @covðdW=W ; dM=MÞ W Wþ WM ¼ W2 W þ 2 @xm @W @xm @xm 2 @W @xm @W @M @2 J covðdW=W ; dS=SÞ @2 J @covðdW=W ; dI=IÞ WS WI þ þ ¼0 @W @S @xm @W @I @xm 2 @C @J @m 1 @2 J @2 J @covðdW=W ; dM=MÞ 2 @sW W Wþ WM ¼ W þ @xI @W 2 @W 2 @W @M @xI @xI @xI @2 J covðdW=W ; dS=SÞ @2 J @covðdW=W ; dI=IÞ þ þ ¼0 WS WI @W @S @xI @W @I @xI

(A.1)

ðA:2Þ

ðA:3Þ

together with Cðx ; c ; W ; M; S; I; tÞ ¼ Uðc ðtÞ; tÞ þ I½J ¼ 0

(A.4)

JðW ; M; S; I; TÞ ¼ JðW ; TÞ

(A.5)

Tedious algebra confirms the results in Proposition 1. Proof of Valuation Formula for European Options Let To be the maturity of the option. We first prove the result for the case TooT. In this case, at the time of exercise, the stock is still being restricted. The employee’s value of the non-tradable stock option is therefore given by U cT o max ST o el s ðTT o Þ K; 0 ; 8 T o oT C^ t ¼ E t U ct


247

To compute, we need the joint conditional distribution for the state price deflator and the company’s stock. We have dU c ¼ ðr gOÞdt ðsm gbs xs sm gbI xIt sm Þdzm Uc gxs ss dzs gxIt sI dzI and dS ¼ ðms qs Þdt þ ss dzs S Let t ¼ T o t and define x¼

lnðU cT o =U ct Þ Fu pffiffiffi su t

and

y¼

lnðST o =St Þ Fs pffiffiffi ss t

with s 2 þ g2 O Fu ¼ r gO þ m t s2u ¼ s2m þ g2 O 2 s2s m r þ gO=xs F s ¼ m s qs t r¼ s 2 su ss Then the joint conditional density for x and y is f ðx; yÞ ¼

1 x2 þ 2rxy þ y2 pffiffiffiffiffiffiffiffiffiffiffiffiffi exp 2ð1 r2 Þ 2p 1 r2

It is easy to show that U cT o t S T o f ðx; yÞ ¼ St expðl s tÞ exp Fs þ Fu þ ðs2s þ 2rss su þ s2u Þ 2 U ct pffiffiffi pffiffiffi 1 ð y rsu t ss tÞ2 pffiffiffiffiffiffi exp 2 2p pffiffiffi 1 ðx ry ð1 r2 Þsu tÞ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp 2ð1 r2 Þ 2pð1 r2 Þ

248


Therefore, Z

1

Z

1

U cT o S T o f ðx; yÞdxdy ffi U ct 1 t ¼ St expðl s tÞ exp Fs þ Fu þ ðs2s þ 2rss su þ s2u Þ 2 Z 1 1 w2 pffiffiffiffiffiffi exp dw 2 2p d 1 ðrgO;qs Þ ln KF p s ss t

¼ St expðl s tÞ expðqs tÞN½d 1 ðr gO; qs Þ

where d 1 ð; Þ is defined in the text and stock price takes the value S t expðl s tÞ. Similarly, we have pffiffiffi U cT o t 1 ð y rsu tÞ2 f ðx; yÞ ¼ exp Fu þ s2u pffiffiffiffiffiffi exp 2 U ct 2 2p pffiffiffi 1 ðx ry ð1 r2 Þsu tÞ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp 2ð1 r2 Þ 2pð1 r2 Þ Therefore, Z 1Z 1

U cT o t Kf ðx; yÞdxdy ¼ K exp Fu þ s2u ln KF 2 pffi s U ct ss t Z 1 1 w2 pffiffiffiffiffiffi exp dw 2 2p d 2 ðrgO;qs Þ 1

¼ K expððr gOÞtÞN½d 2 ðr gO; qs Þ Now, for the case TooT, the stock obtains its market value at the time of exercise, but the discounting has to be done in two stages. Specifically, the employee’s value of the non-tradable stock option is given by U cT o U cT l s ðTT o Þ ^ Ct ¼ Et ET maxðS T o e K; 0Þ U ct U cT Following similar procedures as above and using the fact that ! 2 Z 1 1 z A NðA þ BzÞ pffiffiffiffiffiffi exp dz ¼ N pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2p 1 1 þ B2 we obtain the formulas as shown in the text.

BOARD SIZE AND FIRM PERFORMANCE IN THE PROPERTY-LIABILITY INSURANCE INDUSTRY Carl Pacini, William Hillison and David Marlett ABSTRACT Extant research on non-financial service firms indicates that board size is a key determinant of firm performance. Property-liability (P&L) insurers, however, face a different set of agency costs and a more intense regulatory environment than most non-financial firms. Both of these factors were reinforced by the implementation of the Financial Services Modernization Act in 2000. We document a significant inverse relation between publicly traded P&L insurer performance and board size in the post-Financial Services Modernization Act period. Publicly traded P&L insurer performance, measured by market-to-book ratio, return on revenues, and the operating ratio, was enhanced for firms with smaller board sizes in 2000 and 2001. Ironically, we find that publicly traded P&L insurers on average increased board size in 2000 and 2001. In a postFinancial Services Modernization Act environment, board size appears to be related to publicly traded P&L insurer performance, but more research is necessary to develop a complete understanding of its role in P&L insurer corporate governance.


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INTRODUCTION Corporate governance deals with mechanisms by which shareholders of a corporation exercise control over corporate insiders and management so that their interests are protected. The board of directors of an organization is viewed as a key component of corporate governance. We analyze the relation between publicly traded property-liability (P&L) insurer economic performance and board size for the years 1999, 2000, and 2001 for several reasons. First, it is important for regulators, investors, executives, and business owners to understand the impact of board size on corporate policy decision-making and insurer performance. Second, the insurance industry has been forced to cope with the effects of the Financial Services Modernization Act of 1999 (the Gramm-Leach-Bliley Act), a law that deregulated financial services and mandates greater reliance on internal corporate governance to oversee the actions of financial institutions (Macey & O’Hara, 2003). Third, there is no extant research on the relation between board size and publicly traded P&L insurer performance. Although existing research addresses the roles of board size and other corporate governance variables in non-financial services firm performance, the P&L insurance industry faces both a different set of agency costs and a more intense regulatory scheme than most non-financial firms. These two factors may amplify any corporate governance problems faced by P&L insurers. The focus on a single industry both improves internal validity and minimizes interindustry differences that affect how certain corporate governance variables interact with environmental contingencies (Finkelstein & D’Aveni, 1994). Owing to the complex interrelationships in corporate governance, numerous variables are introduced to control for confounding issues such as board activity, firm size, leverage, board independence, insider ownership, and prior firm performance. Other control variables related to insurer performance are also considered including distribution channel, concentration ratio, and reinsurance (retention) ratio. Knowledge gained from this study should prove useful to regulators, investors, creditors, policyholders, and others who rely on the P&L insurance industry to manage risk subsequent to the Financial Services Modernization Act. The remainder of this chapter is organized as follows. The next section reviews the theory and literature on board size. This is followed by our main hypothesis and discussion of control variables. The sample selection, methods, and results section is presented next followed by our conclusions, limitations, and avenues for future research.

Board Size and Firm Performance in Property-Liability Insurance

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THEORY AND LITERATURE REVIEW Corporate governance serves to separate ownership and control and thus mitigate agency problems stemming from the inability to write complete contracts for all possible future contingencies (Hart, 1995). The potential conflict between managers and shareholders manifests itself in management’s propensity to expand its span of control by ‘‘empire building’’ at owners’ expense and to make unduly conservative investments in order to maintain the safety of their earnings and tenure (John & Senbet, 1998). Problems resulting from the lack of adequate corporate governance are magnified in the P&L insurance industry because of the lower degree of hostile takeovers, the higher degree of financial leverage, the distinctive character of ownership structure, and the nature of the assets and liabilities (Booth, Cornett, & Tehranian, 2002; Macey & O’Hara, 2003). The promulgation of the Financial Services Modernization Act provides additional motivation for P&L insurers to reconsider corporate governance issues. The channels for efficiency gains for firms with high-quality corporate governance are improved managerial performance and reduced cost of external capital (John & Senbet, 1998). One mechanism that is central to corporate governance is the board of directors. The empirical literature provides substantial evidence that boards play an important monitoring role. Researchers have identified a number of determinants of board effectiveness. One key determinant is board size. However, both theory and evidence are inconsistent on whether larger or smaller board size is linked to improved corporate performance. Resource dependence theory suggests that larger boards are associated with higher levels of firm performance. Theory predicts that by becoming larger and more diverse, boards help to link their organizations to their external environment and obtain critical resources, including prestige and legitimacy (Goodstein, Gautam, & Boeker, 1994). Provan (1980) documents that board size is associated with a firm’s ability to gain critical resources such as budget enhancements and external funding. Increased board size also gives rise to a larger pool of expertise and counsel for entity decision-making. One study suggests that larger boards may enhance corporate governance by reducing CEO domination and making it harder for the CEO to build consensus for decision-making that is not aligned with shareholder interests (Singh & Harianto, 1989). Larger boards also encourage a wide range of views on corporate policy choices. Increased board size, however, also carries potential disadvantages. While a board’s capacity for monitoring increases as more directors are added, the

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benefit may be outweighed by the incremental cost of poorer communication and decision-making associated with larger groups (John & Senbet, 1998). For example, larger groups are less cohesive and experience lower participation (Kidwell & Bennett, 1993). In a meta-analysis that supports the effectiveness of smaller board size, Evans and Dion (1991) document a positive association between group cohesion and performance. Judge and Zeithaml (1992) indicate that larger boards were less likely to participate in strategic decision-making. Lipton and Lorsch (1992) contend that the reduced cohesion and the lower participation level of larger boards discourage directors from speaking out, especially to criticize management, and inhibit independent directors from asserting leadership. Larger board size may also decrease the ability of the board to control management thereby increasing agency problems (Eisenberg, Sundgren, & Wells, 1998). Larger boards are more likely to develop factions and coalitions that lead to group conflict. Moreover, factionalism is exacerbated as a board’s tasks become more complex and ambiguous (Goodstein et al., 1994). Larger boards are also harder to coordinate because of a greater number of potential interactions among board members. Thus, CEOs may gain the advantage in interacting with a larger board through tactics such as coalition building, selective channeling of information, and absolute control over the agenda (Alexander, Fennell, & Halpern, 1993). The relation between board size and publicly traded P&L insurer performance is an empirical question, and to date the evidence is mixed and limited to firms outside the insurance industry. Chaganti, Mahajan, and Sharma (1985) examine the relation between firm performance and board size by comparing 21 pairs of failed and non-failed retailing firms. The results suggest that the non-failed firms tended to have larger boards. Bhagat and Black (2002) find no significant relation between board size and non-financial firm performance in a study of 934 U.S. firms over the 1985–1995 period. Yermack (1996) conducts an investigation of the relation between board size and financial performance on a sample of 452 firms (excluding banks, insurers, and utilities) across eight years (1984–1991). He finds an inverse relation between firm performance and board size. Investors’ valuation of companies declines steadily over a range of board sizes between five and eleven. Beyond 11, no relation appears to exist between board size and market valuation. Eisenberg et al. (1998) document a negative relation between firm profitability and board size for a sample of about 900 small- and mediumsized Finnish firms. The research confirms that a board-size effect exists among boards smaller than those tested by Yermack (1996). Conyon and


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Peck (1998) show a negative relation between firm performance and board size across several European countries. In summary, the empirical results concerning a relation between board size and firm performance are inconsistent. Thus, we evaluate this key corporate governance attribute in publicly traded P&L insurers and the attendant expectation that board size is related to shareholder-management issues and will result in measurable effects in firm performance.

HYPOTHESES DEVELOPMENT, ALTERNATIVE EXPLANATIONS, AND CONTROL VARIABLES As noted above, the association between board size and publicly traded P&L insurer performance is not a priori clear. Although resource dependence theory suggests that a larger board enhances insurer performance, agency theory suggests numerous disadvantages related to larger boards. Limited empirical studies (none involving P&L insurers) have yielded mixed results. Hence, the association, if any, between insurance firm performance and board size is unclear. This reasoning leads to the following null hypothesis: H0. No relation exists between publicly traded P&L insurer performance and the size of the board of directors. The alternative hypothesis is that board size, measured as the number of directors on the board, is related to insurer performance. We use three insurance firm performance measures to enhance the robustness and sensitivity of our analyses. One measure used is the market-to-book ratio (MBR) and is computed by dividing an insurer’s market value of equity plus total liabilities by the book value of total assets. This ratio is a market-based valuation measure capturing multiple dimensions of firm performance. Unlike short-run measures such as current earnings, the MBR represents a comprehensive equilibrium measure capturing both risk and return dimensions (Jose, Lancaster, & Stevens, 1996). MBR is also viewed as a measure of the contribution of a firm’s total assets, including intangible assets such as organizational capital, reputation capital, monopolistic rents, investment opportunities, etc. (Lang & Stulz, 1994). It is expected that the MBR would be higher for insurers that are well managed and that have a strong competitive edge.

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A second measure of publicly traded P&L insurer performance is pretax return on revenue (ROR). ROR measures a company’s operating profitability and is computed as pretax operating income divided by net premiums earned. This return metric is calculated before capital gains/losses and income taxes and focuses on the profitability of normal business operations. In contrast to MBR, ROR is a short-run measure of performance. The third publicly traded P&L insurer performance measure used in this study is the operating ratio (OPR). This gauges an insurer’s overall operating profitability from underwriting and investment activities. This ratio does not reflect other income and expense(s), capital gains, or income taxes. Generally, a lower OPR reflects better performance from core operations. OPR, too, is viewed as a short-term measure. Our hypothesis addresses whether publicly traded P&L insurer performance measures are related to board size. The relation is more complex than a simple correlation as it is plausible that board size is interrelated with other corporate attributes and governance variables that affect insurer performance. For example, more diversified insurers are likely to have larger boards, because boards may grow in size when firms make acquisitions (Yermack, 1996). Also, evidence suggests that larger firms have larger boards, in general. Thus, we include a number of additional variables in our model(s) to control for possible alternative explanations for association between board size and P&L insurer performance. Next is an explanation of various firmspecific corporate governance factors used in this study as control variables.

Firm-Specific Control Variables Board Activity (ACTIV) Board activity, measured by frequency of actual board meetings, is often cited as a significant aspect of corporate governance. Board meeting time is an important resource in improving board effectiveness. Sound decisionmaking necessitates that a board functions in a cohesive manner. Board cohesiveness refers to the degree to which board members are attracted to one another and are motivated to remain on the board. Cohesion, however, is difficult to achieve because boards function episodically and intermittently, making them vulnerable to process losses (i.e., interaction difficulties that prevent groups from achieving their full potential) (Forbes & Milliken, 1999). To be effective, board members, particularly outside directors, must gain institutional knowledge. Directors often learn about business practices through their communication with other directors during board interaction.


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Information acquired from other directors is influential because it originates from a trusted source. Trust is difficult to build and sustain on boards of directors that meet only occasionally (Forbes & Milliken, 1999). More frequent board meetings mean that such information is more timely and salient because of its recency (Kahneman, Slovic, & Tversky, 1982). Frequent meetings, however, create a dilemma because directors confront competing demands for their time. Although many directors face time constraints, the time that directors devote to their tasks can differ considerably across boards, and these differences can significantly affect the degree to which boards are able to represent shareholders’ interests successfully (Forbes & Milliken, 1999). Arguments support the assertion that boards which meet more often are more likely to contribute positively to firm performance; however, empirical evidence on the issue is scarce. Vafeas (1999) investigates the relation between board meeting frequency (total actual meetings) and firm performance for a sample of 307 firms (excluding insurers, banks, and utilities). He documents an inverse relation between board meeting frequency and firm performance in the meeting year. However, years with an abnormally high meeting frequency are followed by improvement in operating performance. Also, boards appear to meet more often following poor performance suggesting that board meetings are reactive rather than proactive measures (Vafeas, 1999). Size (SIZE) Publicly traded P&L insurer size, board size, and firm performance may be correlated in complex ways. Any advantages that a large, diversified insurance firm may enjoy are offset by the increased costs of operating, monitoring, and governing a more complex organization (Schellhorn & Scordis, 2002). Improved governance mechanisms may provide more benefit to smaller insurers given that scale economies and efficiency gains have been shown to accrue primarily to smaller insurers (Cummins, Tennyson, & Weiss, 1999). Thus, insurer size is an important consideration. We proxy size with the market value of equity as of the fiscal year ends for 1999, 2000, and 2001. Leverage (LEV) Leverage (total liabilities-to-equity ratio) measures the relative ownership of the entity and is likely related to firm performance. A conservative or lower ratio enables an insurer to better withstand unexpected events and likely allows the entity to borrow additional funds at a lower rate. Greater leverage makes the firm more sensitive to short-term profits and losses and serves as a

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bonding or commitment device. Excessive leverage suggests that management will be limited in the ability to greatly expand its empire (Hart, 1995). Insider Ownership (INSOWN) Share ownership by directors and officers is also an important aspect of corporate governance. Jensen and Meckling (1976) argue that as managerial and director ownership in a firm increase, a firm’s performance improves. One reason is that managers’ and directors’ actions affect their own wealth (the convergence interest hypothesis). In contrast, the entrenchment hypothesis contends that higher levels of insider ownership lead to difficulty in controlling managerial actions (Short, Keasey, Wright, & Hull, 1999). Directors and managers with higher levels of ownership can undertake nonvalue-maximizing actions that extend their tenure or ensure their survival (John & Senbet, 1998). McConnell and Servaes (1990) find a significant curvilinear relation between MBR and the percentage of stock owned by insiders. MBR first increases, then decreases, as share ownership becomes concentrated in the hands of managers and directors. Morck, Shleifer, and Vishny (1988) document a similar non-linear relation. In contrast, Agrawal and Knoeber (1996) find an insignificant relation between insider ownership and firm performance involving a sample of 400 non-financial firms. Demsetz and Lehn (1985) find no relation between insider ownership and accounting rates of return. Board Independence (BDIND) Board independence, as measured by percentage of outside directors, is considered important for effective board monitoring. Agency theory asserts that outside directors (defined here as those who are not current or former employees or own o5% of firm stock) are more effective at monitoring managerial actions by limiting managerial discretion. Fama and Jensen (1983) argue that outside directors possess an incentive to act as monitors of management because they wish to protect their reputations. Inside directors, by virtue of their employment with the firm, are unlikely to aggressively monitor and evaluate the CEO. Other researchers have argued instead for the presence of an ‘‘insider effect.’’ Inside directors are more beholden to the CEO, but they also have more institutional knowledge that is crucial for effective decision-making (Daily, Johnson, & Dalton, 1999). Inside directors also play an important role in educating outside directors and in providing boards with more detailed information.


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Empirical evidence is mixed about whether the presence of outside directors enhances firm performance. Rosenstein and Wyatt (1990) find that announcements of appointments of outside directors are associated with increases in shareholder wealth. Mayers, Shivdasani, and Smith (1997) investigate the role of outside directors by examining changes in ownership structure (i.e., mutual to stock and vice-versa) in the life and P&L insurance industries. They document that outside directors perform an important monitoring role, particularly in mutuals. However, Bhagat and Black (2002) find no evidence that firms with more independent boards achieve higher levels of firm performance. Prior Insurer Performance (RPHt1 and RPHt2) Yermack (1996) notes that either smaller boards contribute to better firm performance or firms adjust board size in response to past performance. The latter would mean that the direction of causation in the board size-firm performance relation operates in the direction opposite that proposed by Lipton and Lorsch (1992). Hermalin and Weisbach (1988) and Yermack (1996) both document that poor firm performance is associated with higher levels of director appointments and departures. Moreover, Yermack (1996) finds a significant positive association between past profitability and MBR. Boards of directors are inclined to meet more often in the face of declining corporate performance. Vafeas (1999) documents an inverse relation between board meeting frequency and the prior year’s performance. Thus, our models include control variables for publicly traded P&L insurer performance for the prior two years. Our proxy for prior insurer performance is return on policyholders’ surplus (RPH).

Agency Control Variables The need for corporate governance stems from agency problems created by separation of ownership and control and the inability to write complete contracts for all possible future contingencies (Hart, 1995). Potential corporate governance issues pose a greater risk for publicly traded P&L insurers than most other business enterprises. High risk stems from two factors: a virtual absence of hostile takeovers considered as a form of management discipline (Booth et al., 2002) and a higher degree of leverage relative to other firms thus magnifying the impact of managerial actions on firm performance (Macey & O’Hara, 2003). To control for agency-related

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issues we include measures for distribution channel, market concentration, and reinsurance (or retention ratio). Distribution Channel (DISTR) A distribution channel is a network of organizations and institutions that, in combination, perform all the functions required to link procedures with end customers to accomplish the marketing task. For insurance products, the distribution channel exists to complete and/or facilitate transactions between the insurer and its customers (Dumm & Hoyt, 2003). Broker versus agent are the two primary distribution channels used by insurers. The essential legal difference between a broker and an agent is that a broker represents the insured, whereas an agent represents the insurer. Such a distinction is clouded because some insurers use both systems and because many states require that brokers be appointed as agents by insurers as a condition of doing business. A broker-oriented insurer opting to operate in a state that restricts broker distribution will encounter continuing inefficiencies. Such inefficiencies should manifest in greater expenses and reduced return on capital (in comparison with an agent-oriented insurer in the same state). An agent-oriented insurer also makes strategic decisions to exploit its chosen distribution system but does not encounter the same frictions as the broker insurer because every state recognizes agency distribution (Baranoff, Baranoff, & Sager, 2000). An approximate classification is based on A.M. Best Key Rating data. Following Baranoff et al. (2000), we use a dummy variable to indicate whether sample insurers have a broker- or agent-oriented distribution system. Market Power (CONC) Market power is a major feature of industry structure and may affect firm performance in two ways. First, firms in an industry with higher relative market power should more clearly recognize their mutual interdependence and such recognition can lead to collusion in pricing or restraint of price rivalry (Chidambaran, Pugel, & Saunders, 1997). Second, a positive relation between market power and profits may arise from heterogeneity in efficiency across firms. More efficient firms may gain larger market shares, resulting in higher concentration and these firms may also exhibit greater profit rates based on superior efficiency (Chidambaran et al., 1997). Rhoades (1985) provides strong arguments in favor of market share rather than concentration as a source of monopoly power. Industries with low concentration may in actuality have a market power problem if a large firm seeking to expand into a new market acquires one of the market leaders


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(Nissan, 2003). A high concentration level or ratio in an industry suggests that firms with superior management have lower costs, which leads to capturing larger shares of the market (Nissan, 2003). Other empirical studies also indicate that market share is a better predictor of market power than concentration ratio (Nissan, 2003; Cyree, Wansley, & Boehm, 2000). Following Nissan (2003), we use market share as a measure of market power. Specifically, we use each insurer’s mean market share of premiums written for its top three insurance product lines in 1998. Reinsurance (REIN) A reinsurance contract is an insurance policy issued by one insurer, the reinsurer, to another insurer, the ceding company. Reinsurance is an institutional response to the possibility that a large policy loss could result in bankruptcy for the insurer. Without reinsurance, an insurance firm would be unable to diversify risk and the insurance purchaser would be obliged to compensate the insurer for an increase in expected bankruptcy costs. The insured would have an incentive to purchase several smaller policies instead of one, more expensive, policy (Mayers & Smith, 1981). The insurance literature suggests that reinsurance use probability increases: (1) the smaller the insurer, (2) the larger the maximum claim under the policy, and (3) the higher the covariance of policy payoffs with the existing set of company policies (Mayers & Smith, 1981). A reinsurance control variable is included because there may be systematic differences in the use of reinsurance across distribution systems (Regan, 1997). Differences in reinsurance use across insurers are controlled by including the ratio of net-to-direct premiums written (retention ratio). This formulation has the additional advantage of discounting reinsurance transactions that take place between subsidiary firms within the groups (Regan & Tzeng, 1999).

SAMPLE SELECTION, METHODS, AND RESULTS Sample Selection We collect a sample of publicly traded P&L insurers by identifying all firms in the Research Insight file that have SIC Codes of 6330, 6331, and 6351. We select from this initial sample only those insurers that are listed in the 1999, 2000, and 2001 editions of Best’s Insurance Reports/PropertyCasualty, possess requisite financial data on Research Insight, and have corporate governance data available in 1999, 2000, and 2001 proxy

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statements. Information collected from proxy statements includes board size, board meeting frequency, insider common stock ownership, and percentage of outside directors. Various financial and corporate governance data are collected from SEC 10-K reports, Standard & Poor’s Corporate Register, Moody’s Finance Manual, and Best’s Key Rating Guide. Sampled firms must have complete financial and corporate governance data for the years 1999, 2000, and 2001. The three-year requirement allows us to compare the relation between corporate governance variables and insurer performance in pre- and the post-Financial Services Modernization Act environment. Since the Act places greater emphasis on corporate governance, a year-by-year analysis allows us to determine whether various governance mechanisms took on a more significant role in contributing toward firm performance after financial deregulation. Our final sample consists of 59 publicly traded P&L insurers. Table 1, Panel A, shows that 35 firms are listed on the NYSE, one on the AMEX, and 23 on the NASDAQ. Moreover, our findings apply only to publicly traded P&L insurers, as our sample does not contain any mutual P&L Table 1. Sample Statistics. Variable

BDSIZ MBR ROR OPR ACTIV SIZE ($millions) LEV INSOWN BDIND RPH CHNPW OWNDIS REIN CONC

Mean

Standard Deviation

1999

2000

2001

1999

2000

2001

10.40 1.06 .16 .83 5.68 6,216 4.05 .21 .64 .07 .01 31,130 .21 .04

10.36 1.13 .15 .86 5.58 8,462 4.38 .21 .64 .04 .02 33,748 .19 .04

10.51 1.15 .02 .97 5.86 8,183 4.18 .21 .64 .06 .18 36,442 .20 .05

3.07 .21 .32 .33 2.62 24,185 4.25 .21 .18 .13 .22 63,310 .21 .10

2.92 .22 .40 .36 2.24 32,788 5.06 .21 .18 .19 .42 78,086 .20 .09

2.95 .23 .37 .40 2.90 30,553 4.52 .21 .18 .23 .26 92,412 .20 .10

Notes: BDSIZ, number of directors; MBR, market-to-book ratio; ROR, return on revenues; OPR, operating ratio; ACTIV, board activity; SIZE, market value of equity ($millions); LEV, total liabilities-to-equity ratio; INSOWN, inside ownership; BDIND, board independence; RPH, return on policyholders’ surplus; CHNPW, change in new premiums written; OWNDIS, ownership dispersion; REIN, reinsurance ratio; and CONC, concentration ratio.


261

insurers. Hence, one avenue of future research is to test the relation between board size and mutual P&L insurer performance.

Descriptive Statistics As displayed in Table 1, the typical insurer board (BDSIZ) averaged 10.40 directors in 1999, 10.36 directors in 2000, and 10.51 directors in 2001. The median number of directors is 10 for all three years. Yermack (1996) documents that a sample of 452 large, non-financial U.S. firms averaged 12.25 directors over the 1984–1991 period. In fact, a number of studies have found that the average size corporate board remained between 12 and 14 from 1935 to 1985 (Chaganti et al., 1985). Moreover, commercial banks have considerably larger boards than publicly traded P&L insurers examined here. In 1999, the typical bank board of directors had 16.4 members (Booth et al., 2002). Hence, it is apparent that publicly traded P&L insurer boards in the years 1999–2001, on average, had fewer directors than large, non-insurer firms. Descriptive statistics for the dependent variables MBR, ROR, OPR; the independent variable of interest, board size (BDSIZ); and the independent control variables are also presented in Table 1. The mean MBR for sample firms shows a consistent increase from 1.06 in 1999 to 1.15 in 2001. The median MBR shows a similar increase. The mean ROR drops from .16 in 1999 to .02 in 2001. The median ROR declines from .10 in 1999 to .01 in 2001. The mean OPR exhibits a steady rise from .83 in 1999 to .97 in 2001. The median OPR shows a similar increase. The relative consistency in the ranges and the lack of outliers suggest stability in these measures. Board activity (ACTIV) is measured by the actual number of board meetings held during a year. In 1999, sample insurer boards met an average of 5.68 times. In 2000, the average number of board meetings dropped slightly to 5.58 with a rise in 2001 to 5.86. The median number of board meetings is 5 for the years 1999–2001. Moreover, both the standard deviation and range of board meetings grew in 2001. Vafeas (1999) reports that a sample of 307 non-financial firm boards met an average of 7.45 times per year during the 1990–1994 period. This suggests that publicly traded P&L insurer boards hold fewer meetings than non-financial firm boards. The mean market value of equity (SIZE) for sample insurers was $6.2 billion in 1999, $8.5 billion in 2000, and $8.2 billion in 2001. The median market values increased from $535 million in 1999 to $864 million in 2001. Mean and median financial leverage (LEV) increased from 4.05 in 1999 to

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4.18 in 2001 and from 2.83 in 1999 to 3.24 in 2001, respectively. The total liabilities-to-equity ratio (LEV) average appears fairly stable at just over 4 for all three years. It shows no pattern, however, and the ranges across years are large across the firms. Mean insider ownership (INSOWN) as measured by the percent of common stock owned by officers and directors averaged 21 percent for the years 1999–2001. Yermack (1996) and Vafeas (1999) report mean insider ownership of 9.1 and 7.1 percent(s) for their respective samples of nonfinancial U.S. firms. It appears that insider ownership is substantially higher for publicly traded P&L insurers than non-financial firms. Board independence (BDIND) is measured by the percent of outside directors on the board. The average publicly traded P&L insurer board was composed of 64 percent outside directors from 1999 to 2001. The percentage of outside directors ranged from 25 to 90 percent. Mayers et al. (1997) document that mutual insurers employ even more outside directors than stock insurers. Yermack (1996) and Vafeas (1999) document that nonfinancial services firm boards contain over 50 percent outside directors. The mean reinsurance (REIN) ratio declined slightly from .21 in 1999 to .20 in 2001. The median reinsurance ratio also showed a slight decline from .13 in 1999 to .12 in 2001. Mean market power concentration increased slightly from .04 in 1999 to .05 in 2001. The median was steady at .01 across the three study years 1999–2001. However, the large standard deviation and range suggest outliers for this measure. Distribution channel (DISTR) is an indicator variable for either a broker or an agency distribution system. As a dummy variable, it is not displayed in Table 1.

Univariate Analysis The pairwise correlations displayed in Table 2 suggest significant relations between a number of variables. For example, board independence (BDIND) is negatively related to board size (BDSIZ). Higher levels of inside ownership are associated with smaller boards of directors. This finding is consistent with Yermack (1996). And, as expected, larger boards (BDSIZ) are associated with larger insurers (SIZE). Insurers with greater inside ownership (INSOWN) also have fewer board meetings (ACTIV). Larger insurers (SIZE) tend to have more board meetings (ACTIV) than smaller insurers. This may be indicative of more time being necessary to achieve a sufficient level of monitoring in larger insurers.

Variable

BDSIZ 1999

BDSIZ

2000

Correlation Analysis.

ACTIV 2001

BDIND

INSOWN

1999

2000

2001

1999

2000

2001

.122 (.177)

.126 (.171)

.207* (.058)

.177* (.068) .207* (.058)

.183* (.062) .104 (.266)

.152* (.095) .112 (.199)

ACTIV

.122 .126 .207* (.177) (.171) (.058) BDIND .177* .183* .152* .207* .104 .112 (.062) (.062) (.095) (.058) (.266) (.199) INSOWN .177* .183* .152* .095 .297** .123* .417*** .441*** .426*** (.068) (.062) (.095) (.236) (.011) (.091) (o.01) (o.01) (o.01) OWNDIS .114 .087 .109 .095 .021 .074 .176* .191* .158 (.195) (.255) (.206) (.236) (.437) (.290) (.091) (.074) (.116) Note: See Table 1 for variable definitions. *** po.01; ** po.05; and * po.10.

1999

2000

2001

.177** .183* .152* (.068) (.062) (.095) .095 .297** .123* (.236) (.011) (.091) .417*** .441*** .426*** (o.01) (o.01) (o.01)

.214* (.052)

.152 (.126)

.161* (.091)


Table 2.

263

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CARL PACINI ET AL.

Inside ownership (INSOWN) is negatively related to board independence (BDIND). The interests of directors who have significant ownership positions may be more closely aligned with shareholders. The convergence interest hypothesis contends that as director ownership increases, their actions affect their own wealth. Higher levels of inside ownership (INSOWN) are more prevalent in smaller insurers for years 2000 and 2001. Greater inside ownership (INSOWN) is positively associated with insurers possessing higher retention ratios (REIN) for years 1999 and 2000. Inside ownership (INSOWN) is negatively related to insurers who have a higher market share (CONC) in their three largest insurance lines. Board independence levels are higher for insurers with less concentrated share ownership (OWNDIS). Smaller insurers tend to have more independent boards. Higher leverage ratios (LEV) are associated with less independent boards (INSOWN) and insurers with more independent boards (BDIND) tend to have lower reinsurance (REIN) ratios. In sum, sample correlations provide certain insights, but do not provide clear indications of the interrelations between board size and insurer performance. More conclusive evidence is provided through subsequent regression analyses, which control for potentially confounding relations.

Multivariate Analysis We use ordinary least squares (OLS) regression in non-rank and rank frameworks and two-stage least squares (2SLS) regression in a non-rank framework to examine the relation between board size and publicly traded P&L insurer performance. 2SLS regression is used to compensate for the joint endogeneity problem involved in empirical studies of corporate governance (Hermalin & Weisbach, 2003). Potential feedback effects and dual causality may require the application of simultaneous equations as used in a 2SLS framework (Studenmund, 1997). For example, insurer performance may be both a result of board size and itself a factor that potentially influences board size in the future (Hermalin & Weisbach, 2003). In the first-stage regression model, the dependent variable is board size. In the second stage, the dependent variable is insurer performance measured by MBR, ROR, and the OPR, respectively (Cummins, Phillips, & Tennyson, 2001). Ranks, in addition to actual data values, are used in the OLS model because ranks generalize the functional form of the model and minimize heteroscedasticity that can result from using a linear function to represent a non-linear relation (Cheng, Hopwood, & McKeown, 1992; Bamber &


265

Cheon, 1995). Moreover, we standardize the ranks by the number of observations plus 1 so that the lowest ranked variable has a value of 1/(N+1) and the highest ranked variable a value of N/(N+1) with N equaling the number of data values. These values range between 0 and 1. The standardization yields coefficients that are independent of the number of observations (Cheng et al., 1992). The same model is used for both the OLS and OLS rank regression with the only difference being that the variables in the OLS rank regression are transformed to standardized ranks. Each model is run three times, one for each performance measure, MBR, ROR and OPR as follows: PERFit ¼ b0 þ b1 BDSIZit þ b2 ACTIVit þ b3 SIZEit þ b4 INSOWNit þ b5 BDINDit þ b6 LEVit þ b7 REINit þ b8 CONCit þ b9 DISTRit þ b10 RPHit1 þ b11 RPHit2 þ eit

ð1Þ

where: PERFit

= the MBR, ROR, or OPR (or rank of the respective performance measure) for insurer i for year t; BDSIZit = the number (or rank) of directors for insurer i for year t; ACTIVit = the number (or rank) of board meetings for insurer i for year t; SIZEit = the market value of equity (or rank) of insurer i as of the end of year t; INSOWNit = the percentage of insurer i’s common stock owned by officers and directors (or rank) in year t; BDINDit = the percentage of outside directors (those who are not an employee and own o5% of insurer i’s stock) on insurer i’s board (or rank) in year t; LEVit = the total liabilities-to-equity ratio (or rank) of insurer i for year t; REINit = the ratio of net-to-direct premiums written (retention ratio) of insurer i (or rank) as of the end of year t; CONCit = insurer i’s mean market share (or rank) of total industry premiums written for its top three insurance product lines for year t; DISTRit = a dummy variable coded 1 when an insurer has a brokeroriented distribution channel, 0 otherwise; RPHit1 and = the return on policyholders’ surplus for insurer i (or rank) PHit2 for the two prior years; and eit = an error term.

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The next two models relate to the 2SLS analysis. The first model regresses board size (BDSIZ) on the potentially related independent variables. The predictions for board size generated from this model are used in the second stage as an independent variable. The first-stage rank regression model is BDSIZit ¼ b0 þ b1 ACTIVit þ b2 SIZEit þ b3 INSOWNit þ b4 BDINDit þ b5 LEVit þ b6 REINit þ b7 CONCit þ b8 DISTRit þ b9 RPHit1 þ b10 RPHit2 þ eit

ð2Þ

where: = the number of directors for insurer i for year t; = the number of board meetings for insurer i for year t; = the market value of equity of insurer i as of the end of year t; INSOWNit = the percentage of insurer i’s common stock owned by officers and directors in year t; BDINDit = the percentage of outside directors (those who are not an employee and own o5% of insurer i’s stock) on insurer i’s board in year t; LEVit = the total liabilities-to-equity ratio of insurer i for year t; REINit = the ratio of net-to-direct premiums written (retention ratio) as of the end of year t; CONCit = insurer i’s mean market share of total industry premiums written for its top three insurance product lines for year t; DISTRit = a dummy variable coded 1 when an insurer has a brokeroriented distribution channel, 0 otherwise; RPHit1 and = the return on policyholders’ surplus for insurer i for the RPHit2 two prior years; and eit = an error term. BDSIZit ACTIVit SIZEit

The second-stage model is run three times, one for each performance measure, MBR, ROR, and OPR as follows: PERFit ¼ b0 þ b1 BDSIZit þ b2 ACTIVit þ b3 SIZEit þ b4 INSOWNit þ b5 BDINDit þ b6 LEVit þ b7 REINit þ b8 CONCit þ b9 DISTRit þ b10 RPHit1 þ b11 RPHit2 þ eit

ð3Þ


267

The variables in Eq. (3) are defined as they are for the first-stage model except for two new variables shown below: PERFit = the MBR, ROR, or OPR for insurer i for year t and BDSIZit = predicted variable BDSIZ from Eq. (2) for insurer i for year t. Tables 3–5 display estimates of the relation between MBR, ROR, and OPR and board size, both in independently estimated OLS, OLS rank, and 2SLS frameworks between Eqs. (1) and (3). The equations are estimated for each of the years 1999, 2000, and 2001. The results for each year are presented to highlight any potential differences that may be attributable to the Financial Services Modernization Act taking effect in 2000. The approach used here is similar to that used by Vafeas (1999). Based on Tables 3–5, H0 is rejected for years 2000 and 2001 for all performance measures. In 1999, H0 is not rejected for all three measures for the three models. The models from Tables 3 and 4 show an inverse and significant relation between MBR1 and ROR, respectively and publicly traded P&L insurer board size for 2000 and 2001. That is, the MBR and ROR ratio increase as board size declines for the years 2000 and 2001. Table 5 reveals a positive and significant relation between board size and the OPR for the years 2000 and 2001. This is consistent with the results for MBR and the ROR ratio because the OPR declines as board size decreases. A smaller OPR means that an insurer is better able to generate profits from its underwriting and investment activities. Hence, board size is associated with better performance for publicly traded P&L insurers for 2000 and 2001 for all performance measures. In 1999, such a relation is reflected only for the ROR ratio for OLS and rank OLS estimation models. The association of smaller board size with better firm performance is consistent with an interpretation that, for the years 2000 and 2001, coordination, communication, and decision-making problems increasingly hindered board performance for large boards (Yermack, 1996). Decisions that involve complex and ambiguous tasks encompassing strategic change, such as deregulation by passage of the Financial Services Modernization Act, are apt to be more unfavorably influenced by large group dynamics (Olson, 1982). Such a finding is consistent with the contention that smaller publicly traded P&L insurer boards are more participatory, cohesive, and able to reach consensus. Moreover, results for 2000 and 2001 are consistent with the hypothesis of Lipton and Lorsch (1992) that smaller boards operate more efficiently and effectively.

268

Table 3.

OLS, OLS Rank, and 2SLS Regression Models of the Relation between Market-to-Book Ratio, Board Size, and Control Variables. 1999a

Variable Name

Intercept BDSIZ ACTIV

LEV INSOWN BDIND RPHt1

2001a

OLS

OLS-rank

2SLS

OLS

OLS-rank

2SLS

OLS

OLS-rank

2SLS

.419* (.064) .101 (.134) .086 (.110) .062*** (o.01) .008* (.096) .346*** (o.01) .187 (.118) .413** (.020)

.413* (.070) .097 (.214) .100 (.238) .734*** (o.01) .213** (.039) .238** (.05) .002 (.492) .022 (.432)

.430 (.141) .104 (.360) .079 (.131) .062*** (o.01) .008* (.096) .348** (.024) .181 (.184) .406** (.025)

.479** (.037) .251*** (o.01) .023 (.377) .071*** (o.01) .008** (.043) .347*** (o.01) .174 (.122) .357** (.040)

.587** (.015) .358*** (o.01) .093 (.233) .958*** (o.01) .190** (.032) .333*** (o.01) .226** (.026) .197** (.039)

1.51* (.061) 1.04* (.065) .062 (.285) .095*** (o.01) .016* (.054) .638** (.024) .646* (.081) .231 (.243)

.715 (.315) .853** (.049) .057 (.437) .189** (.011) .063* (.054) .128 (.426) 1.256* (.067) 1.150 (.102)

.587** (.032) .211** (.050) .088 (.295) .755*** (o.01) .301** (.013) .146 (.150) .119 (.179) .027 (.419)

7.61 (.206) 9.87* (.057) .057 (.466) .348* (.063) .066 (.178) 1.941 (.201) 4.75 (.120) .553 (.378)

CARL PACINI ET AL.

SIZE

2000a

REIN CONC DISTR W. R2 Adjusted R2 F-value

.144 (.303) .194* (.055) .054 (.422) .034 (.319)

.015 (.456) .107 (.219) .071 (.304) .011 (.452)

.137 (.317) .193* (.075) .056 (.423) .031 (.324)

.204 (.132) .043 (.360) .034 (.451) .057 (.186)

.104 (.171) .152* (.086) .207* (.056) .047 (.273)

.347 (.130) .205 (.188) .542 (.203) .061 (.269)

.746 (.249) .306 (.317) 1.775 (.116) .902*** (o.01)

.224** (.036) .068 (.298) .142 (.174) .038 (.344)

.519 (.415) .733 (.326) 2.053 (.327) .577 (.229)

.465 .340 3.72 (po.01)

.512 .398 4.49 (po.01)

.458 .331 3.62 (po.01)

.529 .419 4.80 (po.01)

.630 .544 7.28 (po.01)

.310 .148 1.92 (p=.061)

.249 .073 1.42 (p=.198)

.505 .389 4.36 (po.01)

.285 .114 1.77 (p=.071)

Notes: See Table 1 for variable definitions. Each OLS model in Tables 3–7 was tested for multicollinearity using partial correlation coefficients and variance inflation factors (VIF). No pair of independent variables had a partial correlation coefficient W.5 or o.5. Each independent variable had a VIFo3. Multicollinearity is a problem when a VIF exceeds 10 (Kennedy, 1992) or a partial correlation coefficient W.7 or o.7 (Mason & Lind, 1996). Standard errors of parameter estimates have been tested for heteroscedasticity. All tests results were at or below acceptable levels. *** po.01; ** po .05; and * po.10. a The statistics presented for each independent variable are parameter estimate and p-value, respectively (one-tail tests).


RPHt2

269

270

Table 4.

OLS, OLS Rank, and 2SLS Regression Models of the Relation between Return on Revenues, Board Size, and Control Variables. 1999a

Variable Name

Intercept BDSIZ

SIZE LEV INSOWN BDIND

2001a

OLS

OLS-rank

2SLS

OLS

OLS-rank

2SLS

OLS

OLS-rank

2SLS

.15 (.377) .227* (.081) .090 (.234) .040* (.092) .015* (.087) .058 (.406) .158 (.283)

.318 (.170) .247** (.041) .038 (.411) .401** (.021) .389*** (o.01) .086 (.308) .132 (.189)

.966 (.135) .578 (.183) .051 (.368) .01 (.427) .017 (.107) .350 (.177) .191 (.332)

.985** (.040) .595*** (o.01) .133 (.175) .026 (.199) .020** (.021) .186 (.248) .134 (.332)

.555** (.049) .230* (.058) .209* (.099) .304** (.046) .178* (.081) .129 (.229) .061 (.334)

1.46 (.249) 2.48** (.050) .182 (.227) .031 (.324) .037** (.044) 1.22** (.049) .966 (.174)

.201 (.330) .463*** (o.01) .058 (.303) .034* (.087) 012 (.169) .537*** (o.01) .233 (.184)

.236 (.245) .217** (.041) .126 (.242) .166 (.164) .283** (.028) .272** (.041) .052 (.358)

2.89 (.193) 3.20* (.069) .009 (.485) .026 (.372) .014 (.298) 1.45** (.037) 1.08 (.227)

CARL PACINI ET AL.

ACTIV

2000a

RPHt2 REIN CONC DISTR W. R2 Adjusted R2 F-value

.827*** (o.01) .082 (.434) .257 (.113) .246 (.305) .129 (.140)

.222* (.075) .054 (.368) .397*** (o.01) .052 (.376) .125 (.125)

.648* (.074) .141 (.412) .089 (.379) .032 (.480) .100 (.252)

.505 (.116) .663** (.043) .234 (.176) 1.094** (.034) .16 (.116)

.129 (.176) .241** (.041) .401*** (o.01) .252* (.060) .092 (.170)

.804 (.141) .340 (.310) .139 (.393) .229 (.437) .160 (.236)

.261 .088 1.51 (p=.16)

.300 .137 1.84 (p=.074)

.228 .065 1.14 (p=.28)

.398 .257 2.83 (po.01)

.422 .286 3.12 (po.01)

.303 .168 1.79 (p=.074)

1.045*** (o.01) .190 (.288) .314* (.060) .872** (.031) .099 (.200) .505 .389 4.36 (po.01)

.327** (.011) .126 (.176) .046 (.369) .154 (.178) .041 (.352)

.825 (.101) .642 (.233) .711 (.114) .562 (.375) .008 (.487)

.401 .261 2.86 (po.01)

.288 .164 1.73 (p=.078)

Note: See Table 1 for variable definitions. *** po.01; ** po.05; and * po.10. a The statistics presented for each independent variable are parameter estimate and p-value, respectively (one-tail tests).


RPHt1

271

272

Table 5.

OLS, OLS Rank, and 2SLS Regression Models of the Relation between Operating Ratio, Board Size, and Control Variables. 1999a

Variable Name OLS Intercept BDSIZ

SIZE LEV INSOWN BDIND

.528* (.074) .187 (.119) .051 (.391) .137 (.257) .294** (.031) .035 (.425) .062 (.353)

2SLS 1.601** (.042) .525 (.216) .023 (.442) .024 (.333) .013 (.176) .309 (.217) .192 (.338)

OLS

OLS-rank

.172 (.371) .535*** (o.01) .086 (.260) .029 (.163) .002 (.414) .167 (.254) .130 (.328)

.494* (.078) .219* (.075) .222* (.099) .272** (.073) .093 (.241) .146 (.199) .052 (.364)

2001a 2SLS 2.98 (.102) 3.16** (.026) .149 (.286) .037 (.308) .021 (.181) .601 (.216) 1.135 (.154)

OLS

OLS-rank

2SLS

.815** (.047) .464*** (o.01) .070 (.274) .030 (.127) .009 (.234) .583*** (o.01) .266 (.163)

.827*** (o.01) .204** (.048) .069 (.348) .018 (.457) .159 (.136) .293** (.029) .006 (.483)

4.11 (.124) 3.74* (.057) .020 (.468) .034 (.344) .012 (.338) 1.43* (.055) 1.136 (.230)

CARL PACINI ET AL.

ACTIV

.770* (.067) .300** (.041) .067 (.303) .027 (.197) .011 (.169) .011 (.483) .162 (.290)

OLS-rank

2000a

RPHt2 REIN CONC DISTR W. R2 Adjusted R2 F-value

.838*** (o.01) .093 (.429) .065 (.386) .46 (.185) .063 (.308) .224 .042 1.23 (p=.293)

.190 (.128) .044 (.402) .221 (.110) .155 (.196) .043 (.356)

.649* (.084) .140 (.426) .107 (.363) .176 (.385) .035 (.412)

.207 .035 1.10 (p=.387)

.199 .033 1.00 (p=.459)

.511 (.105) .671** (.033) .134 (.328) 1.054** (.031) .094 (.228) .346 .193 2.26 (p=.026)

.166 (.126) .266** (.033) .388*** (o.01) .175 (.150) .037 (.356) .366 .218 2.47 (p=.016)

1.27* (.058) .296 (.345) .880* (.056) .470 (.382) .096 (.346) .322 .185 2.23 (p=.029)

1.40*** (o.01) .078 (.413) .108 (.304) .92** (.029) .138 (.132) .547 .441 5.16 (po.01)

.382*** (o.01) .016 (.457) .003 (.491) .333** (.024) .014 (.448) .409 .271 2.96 (po.01)

Note: See Table 1 for variable definitions. *** po.01; ** po.05; and * po.10. a The statistics presented for each independent variable are parameter estimate and p-value, respectively (one-tail tests).

1.16** (.046) .56 (.274) .530 (.198) .608 (.372) .024 (.468) .311 .189 2.18 (p=.039)


RPHt1

273

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CARL PACINI ET AL.

Consideration of the impact of the control variables provides some insight. For example, MBR is greater for larger insurers across all three study years. ROR is also greater for larger firms for 1999 and 2000. Insurer size, however, does not demonstrate a relation with the OPR. MBR is greater for larger percentages of inside ownership for 1999 and 2000. OPR rises as inside ownership increases only in 2001. It seems that publicly traded P&L insurer profitability from underwriting and investment activity declined as inside ownership rose during 2001. Leverage (LEV) is inversely related to MBR and ROR. MBR increased as insurer leverage declined across all three study years. The same relation holds for ROR based on certain models. The OPR declines (reflecting better performance) as the reinsurance ratio (REIN) increases for the year 2000 only. Insurer market share (CONC) rises as the OPR declines (indicating better performance) as reflected in several models across 2000 and 2001. MBR and ROR are positively related to return on policyholders’ surplus (RPH) reported in several models.

Changes in Board Size and Past Insurer Performance Yermack (1996) suggests that smaller boards contribute to better performance or firms adjust board size in response to past performance. This proposition brings into focus the issue of the direction of the relation between board size and publicly traded P&L insurer performance. Tests of the relation between changes in board size and insurer performance can be considered apart from the endogeneity problem due to the relative stability of corporate governance mechanisms (Vafeas, 1999). Following Yermack (1996), we examine the relation, if any, between changes in board size and lagged insurer performance using the rank regression OLS model described by Eq. (4). Several industry-related lagged variables are added to this model to attempt to control for other factors that may be related to changes in board size other than prior performance. The model tested is as follows: CHBDSIZit ¼ b0 þ b1 PERFit1 þ b2 PERFit2 þ b3 CHSIZEit þ b4 LEVit1 þ b5 CHNPWit1 þ b5 OWNDISit þ eit ð4Þ where: CHBDSIZit = the standardized rank of the difference between the number of directors in year t and the average number of directors for insurer i over 1999–2001;


275

PERFit1

= the performance measure of standardized rank of MBR, ROR, or OPR for insurer i for the year t1; PERFit2 = the performance measure of standardized rank of MBR, ROR, or OPR for insurer i for the year t2; CHSIZEit = the standardized rank of the change in insurer i’s market value of equity from the prior year to year t; LEVit1 = the standardized rank of the total liabilities-to-equity ratio of insurer i for year t1; CHNPWit1= the standardized rank of the change in net premiums written for insurer i in year t1; OWNDISit = the standardized rank of the average number of common shares of insurer i owned by each shareholder in year t; and eit = an error term. Table 6 presents the rank regressions of changes in board size (dependent variable) on past publicly traded P&L insurer performance. The results suggest that P&L insurers increase board size two years after a decline in performance. Change in board size and MBR are negatively associated in 2000 (p=.041) and 2001 (p=.097). This finding is inconsistent with Yermack’s (1996) results for non-financial service firms. It appears that board size increased in a post-Financial Services Modernization Act environment possibly in response to declining publicly traded P&L insurer performance, but not prior to that time. Moreover, it seems that P&L insurers resorted to increasing board size to enhance monitoring. This finding, however, is specific to the proxy used for insurer performance, as change in board size is not significantly associated with ROR or OPR. Our OLS rank regression model controls for change in insurer size, leverage in the prior year, change in net premiums written in the prior year, and ownership dispersion. None of the control variables is significant in the same direction for at least two of the three years covered by the study. Change in net premiums written is significant for 2000 and 2001 for all insurer performance measures, but the parameter estimates have opposite signs.

Past Board Size and Insurer Performance Finally, we test the proposition that past board size influences current value. We test a model that employs performance as the independent variable. Several industry-related control variables are added to control for other

276

Table 6.

OLS Rank Regression Models of the Relation between Changes in Board Size and Lagged Insurer Performance. 1999a

Variable

2001a

Coefficient

t-statistic

p-value

Coefficient

t-statistic

p-value

Panel A: Market-to-book ratio (rank regression) Intercept .778*** 4.69 o.01 .028 .12 .452 MBRt1 MBRt2 .059 .29 .386 CHSIZit .285** 2.05 .020 .123 .95 .171 LEVt1 CHNPWt1 .140 .70 .242 OWNDISt1 .059 .51 .305 R2 .117

.533*** .315** .300** .101 .149 .360*** .121 .127

3.43 1.89 1.74 .74 1.07 2.58 .96

o.01 .029 .041 .230 .142 o.01 .168

.846*** .213 .274* .120 .092 .137* .203** .103

5.76 1.17 1.30 .90 .75 1.63 1.90

o.01 .121 .097 .184 .227 .052 .029

Panel B: Return on revenues (rank regression) Intercept .840*** 6.67 o.01 .128 .54 .295 RORt1 RORt2 .147 .65 .258

.491*** .070 .036

2.51 .40 .21

o.01 .345 .417

.799*** .013 .006

4.71 .09 .04

o.01 .464 .484

CARL PACINI ET AL.

p-value

Coefficient

t-statistic

2000a

.313*** .159 .158 .050 .119

2.40 1.27 .81 .42

Panel C: Operating ratio (rank regression) Intercept .840*** 6.67 .128 .53 OPRt1 OPRt2 .147 .65 CHSIZit .314*** 2.40 LEVt1 .160 1.27 .158 .81 CHNPWt1 OWNDISt1 .050 .42 R2 .119

o.01 .102 .219 .338

.082 .119 .361*** .103 .085

.62 .88 2.38 .75

.268 .189 o.01 .226

.162 .082 .113* .155* .075

1.21 .65 1.38 1.43

.113 .258 .084 .076

o.01 .298 .258 o.01 .102 .219 .337

.569*** .120 .055 .080 .117 .336** .116 .091

4.19 .72 .34 .62 .90 2.27 .84

o.01 .236 .367 .268 .184 .012 .201

.797*** .066 .131 .137 .047 .114* .138 .084

5.76 .43 .77 .99 .36 1.53 1.19

o.01 .334 .221 .161 .359 .063 .117

Notes: See Table 1 for variable definitions. The three models above were also analyzed using OLS non-rank regression. The results obtained were quite similar to those produced by the rank regression analysis. *** po.01; ** po.05; and * po.10. a One-tail tests.


CHSIZit LEVt1 CHNPWt1 OWNDISt1 R2

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factors, other than changes in board size, which may be related to firm performance. The model is as follows: PERFit ¼ b0 þ b1 BDSIZit1 þ b2 BDSIZit2 þ b3 BDSIZit3 þ b4 CHSIZEit þ b5 LEVit þ b6 OWNDISit1 þ eit

ð5Þ

where: = the standardized rank of MBR, ROR, or OPR for insurer i for the year t; BDSIZit1 = the standardized rank of the number of directors for insurer i in the year prior to year t; BDSIZit2 = the standardized rank of the number of directors for insurer i two years prior to year t; BDSIZit3 = the standardized rank of the number of directors for insurer i three years prior to year t; CHSIZEit = the standardized rank of the change in insurer i’s market value of equity from the prior year to year t; LEVit = the standardized rank of the total liabilities-to-equity ratio of insurer i for year t; OWNDISit1 = the standardized rank of the average number of common shares of insurer i owned by each shareholder in year t; and eit = an error term. PERFit

The results in Table 7 show a significant positive (at least at the po.05 level) association between board size in year t1 and all three performance measures in 2001. A positive relation also exists between board size in year t1 and ROR in 2000. Significant results for one year or for one performance measure does not, however, establish a pattern. A marginally significant negative relation does exist between board size for year t2 and MBR and ROR for 2000 and 2001. That is, smaller board size two years prior is associated with better publicly traded P&L insurer performance for MBR and ROR. However, the opposite is true for the OPR. For board size three years prior, our results are inconsistent. We conclude that the evidence supports the contention that board size in years t1 and t2 appear to influence current publicly traded P&L insurer performance, but this result is sensitive to the proxy selected for insurer performance. The three control variables are marginally significant, at a minimum, for at least two out of three years. MBR and ROR improve as the market value of equity increases in 2000 and 2001. The OPR declines (performance improves) as the market value of equity increases in those two years.

OLS Rank Regression Models of the Relation between Insurer Performance and Lagged Board Size. 1999a

Variable

2001a

Coefficient

t-statistic

p-value

Coefficient

t-statistic

p-value

Panel A: Market-to-book ratio (rank regression) Intercept .652*** .371 o.01 .002 .01 .496 BDSIZt1 .213 .73 .233 BDSIZt2 BDSIZt3 .082 .31 .379 CHSIZE .170 1.14 .127 LEV .217** 1.66 .049 OWNDISit1 .063 .49 .312 R2e .084

.253*** .062 .450* .410*** .713*** .343*** .225** .561

2.60 .26 1.36 2.52 8.36 3.52 2.18

o.01 .398 .087 o.01 o.01 o.01 .015

.355*** .903*** .410* .487* .305*** .186* .710* .244

2.69 2.62 1.33 1.39 2.77 1.57 1.48

o.01 o.01 .092 .083 o.01 .058 .069

Panel B: Return on revenues (rank regression) Intercept .767*** 5.27 .311 1.12 BDSIZt1 .073 .16 BDSIZt2 BDSIZt3 .136 .34 CHSIZE .115 .86 LEV .286** 2.23 OWNDISit1 .239** 1.83 R2 .174

.453*** .674** .611* .131 .372*** .228** .208* .183

3.39 1.70 1.60 .48 2.77 1.77 1.58

o.01 .045 .055 .316 o.01 .038 .057

.701*** .723** .566* .376 .204* .335*** .240** .194

5.10 1.84 1.41 1.08 1.56 2.54 1.80

o.01 .033 .079 .143 .059 o.01 .036

o.01 .134 .436 .367 .197 .015 .036

279

p-value

Coefficient

t-statistic

2000a


Table 7.

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Table 7. (Continued ) 1999a

Variable

2000a

2001a

t-statistic

p-value

Coefficient

t-statistic

p-value

Coefficient

t-statistic

p-value

Panel C: Operating ratio (rank regression) Intercept .241* 1.63 .263 .93 BDSIZt1 BDSIZt2 .230 .50 BDSIZt3 .005 .01 CHSIZE .037 .27 LEV .210* 1.62 OWNDISit1 .298** 2.25 R2 .149

.055 .178 .309 .495 .393 .055 .014

.524*** .096 .422* .387** .302** .199** .191* .208

3.86 .31 1.33 1.94 2.22 1.68 1.42

o.01 .380 .092 .026 .015 .047 .081

.295** .787** .422* .375 .274*** .242** .249** .197

2.16 2.21 1.37 1.21 2.35 1.84 1.86

.018 .014 .085 .113 o.01 .036 .034

Coefficient

Notes: See Table 1 for variable definitions. The three models above were also analyzed using OLS non-rank regression. The results obtained were quite similar to those produced by the rank regression analysis. *** po.01; ** po.05; and * po.10. a One-tail tests.

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MBR and ROR both increase as leverage declines across all three study years. The OPR, however, increases (performance weakens) as leverage declines across the study period. Also, MBR and ROR increase in 2000 and 2001 as share ownership (average number of shares owned per shareholder) becomes more concentrated in year t1. The OPR increases (performance weakens) across all three study years as share ownership becomes more concentrated. In summary, even after controlling for other influential variables, publicly traded P&L insurer performance is associated with board size one and two years removed.

CONCLUSIONS AND LIMITATIONS Extant research indicates that boards of directors play an important monitoring role in the corporate governance process. One key determinant of board effectiveness is board size. Although existing research addresses the role of board size in non-financial service firm performance, publicly traded P&L insurers face a different set of agency costs and a more intense regulatory scheme than non-financial firms. Moreover, both of these factors were reinforced by implementation of the Financial Services Modernization Act in 2000. We provide some evidence of an inverse significant relation between publicly traded P&L insurer performance and board size in the postFinancial Services Modernization Act environment. Publicly traded P&L insurer performance was better for insurers with smaller boards in 2000 and 2001 for three different performance measures. In 1999, however, the relation between board size and insurer performance is sensitive to the proxy used for insurer performance. Board size was negatively related to publicly traded P&L insurer performance only for ROR in 1999. Our findings for 2000 and 2001 for publicly traded P&L insurers are consistent with those of Yermack (1996) for non-financial U.S. firms (for the years 1984–1991), Eisenberg et al. (1998) for small Finnish firms, and Conyon and Peck (1998) for non-financial firms across several European countries. These researchers, however, used only one proxy for firm performance. Our results provide support for the proposal of Lipton and Lorsch (1992) and an ongoing trend in non-financial firms to reduce board size to improve corporate governance. According to the 20th annual Board Index Survey of S&P 500 boards, average board size has decreased from 12 directors in 1998 to 10.7 in 2005. Reduced board size may be one means by which publicly traded P&L insurers may enhance corporate accountability in a post-Enron,

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post-Sarbanes-Oxley era. A large board could make it more difficult for a publicly traded P&L insurer to reach a conclusion on matters of strategy or management. We also find that publicly traded P&L insurers increased board size in 2000 and 2001 apparently in response to a decline in firm performance two years prior. This result is sensitive, however, to the proxy used for firm performance, as change in board size is associated with MBR in 2000 and 2001 but not with ROR or OPR. Moreover, our finding for MBR is inconsistent with Yermack (1996). He finds no evidence that boards of nonfinancial firms either expand or contract in response to performance. In sum, for one of three proxies for publicly traded P&L insurer performance, insurers may have increased board size in 2000 and 2001 as a means of enhanced monitoring in a post-Financial Services Modernization Act environment. We also document that smaller board size two years prior for publicly traded P&L insurers is associated with better firm performance for the years 2000 and 2001. This finding, however, is sensitive to the proxy selected for insurer performance. Our limited findings are consistent with Yermack’s (1996) results for non-financial firms. Our study’s focus is on board size. Board size, however, is only one of many corporate governance variables that may influence publicly traded P&L insurer performance. Further research into the relations, if any, among board activity, board independence, board committee structure, managerial ownership, board leadership structure, and publicly traded P&L insurer performance would provide a richer understanding of the role of corporate governance in P&L insurer performance in a post-Financial Services Modernization Act environment. Also, our findings may be generalized only to publicly traded not mutual P&L insurers. Corporate governance relations take on a different dimension in mutual P&L insurers due to restrictions on the transferability of ownership claims. A productive avenue of future research is the relation between board size and mutual P&L insurer performance. We encourage such research.

NOTE 1. When used as a dependent variable, MBR has been employed to explain a number of diverse corporate phenomena, such as the relation between managerial equity ownership and firm performance (McConnell & Servaes, 1990), stability in excellent corporate performance (Jose et al., 1996), the relation between agency


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control mechanisms and firm performance (Agrawal & Knoeber, 1996), board size and firm performance (Yermack, 1996), and board meeting frequency and firm performance (Vafeas, 1999). Market-to-book has also been used as an independent variable measuring the firm’s investment opportunity set or potential growth (Smith & Watts, 1992). A large MBR suggests that a firm’s value is composed of fewer hard assets and more growth opportunities. Although our study uses marketto-book as a dependent variable, it could be argued that a negative relation between insurer performance and board size implies that insurers with more growth opportunities have smaller boards of directors.

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THE ROLE OF HIGHER OIL PRICES: A CASE OF MAJOR DEVELOPED COUNTRIES T. J. O’Neill, J. Penm and R. D. Terrell ABSTRACT The primary aim of this chapter is to examine whether the recent increase in world oil prices has affected inflation expectations and stock market returns in major OECD countries. The key findings are as follows. First, we found no evidence to support the presence of a long term relationship between oil prices and inflation expectations – measured by the difference between yields of inflation indexed and non-inflation indexed government bonds – over the sample between early 2003 and late 2006. Second, higher oil prices are found to lead to expectations of higher inflation. This evidence is stronger over the period where oil prices had been higher and signs of capacity constraints in the economy were emerging. Third, the impact of higher oil prices on stock market returns differs among countries. While higher oil prices are found to adversely affect stock market returns in the United States, the United Kingdom and France, the effects are positive in Canada and Australia as these countries are significant exporters of energy resources.


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1. INTRODUCTION Inflation expectations play an important role in the determination of actual inflation and stock market valuations. Recent research has suggested that inflation expectations may have declined over the past decade (BIS, 2006). While the decline in inflation expectations could be attributed to several economic developments, including improved creditability in monetary policy setting and reduced wage pressure due to increased labour market flexibility and productivity growth, an issue of interest is the impact of recent significant increases in world oil prices on inflation expectations and stock market returns. World oil prices have increased significantly since 2003. For example, the price of commonly quoted West Texas Intermediate (WTI) crude oil rose from approximately US$28 a barrel in early 2003 to a high of approximately US$78 a barrel in mid-August 2006 before a partial reversal to approximately US$60 dollar a barrel in December 2006. The importance of oil to economic activity has been well documented in economic literature (for a survey, see Jones & Leiby, 1996; Barsky & Kilian, 2004). Energy, especially oil, expenditures account for a relatively large proportion of gross domestic product in most developed countries. As such, a significant increase in oil prices will lead to a substantial rise in production costs and hence upward pressures on wages and inflation. The resultant changes in investors’ inflation expectations will have important implications for their portfolio investment. There has been significant research interest in the role and impact that oil and other energy sources have on stock market returns. Papers such as Faff and Brailsford (1999), Jones and Kaul (1996), and Al-Mudhaf and Goodwin (1993) examined the influence of oil price movements in the determination of prices in the stock markets of the United States, Canada, the United Kingdom and Australia. While their findings indicate a negative response from many industries to higher oil prices, the issue is complicated by the ability of firms to pass on the cost increases to consumers or by the extent to which firms hedge against oil price risk. While the negativity of higher oil prices on inflation and stock market performance was evident in the previous oil price shocks, the effect of the recent oil price spike appears to be less clear. Notwithstanding the recent significant increase in world oil prices, inflationary pressures in major OECD countries have remained relatively modest. In the United States, for example, the inflation rate is estimated to have been approximately 3.2 per cent in 2006 and 3.4 per cent in 2005. This compares with annual inflation of

The Role of Higher Oil Prices: A Case of Major Developed Countries

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over 13 per cent in the late 1970s and early 1980s (during which oil price spiked to approximately US$80 dollar a barrel in 2006 dollar terms). Similarly, inflation in the euro area has been well below an annual rate of 3.0 per cent. Despite the significant increase in world oil prices, stock market valuations in major OECD countries have increased significantly. Between early 2003 and late 2006, for example, the Dow Jones industrial average in the United States increased by approximately 55 per cent, while rises of 87, 73 and 110 per cent were recorded in Canada, the United Kingdom and France respectively over the same period. Given these movements, an important question emerges as to whether oil prices remain a significant factor affecting inflation expectations and stock market returns. As mentioned earlier, there have been suggestions that inflation expectations may have declined in recent time due to labour market reforms and creditable monetary policy management. Under this economic environment, whether oil prices remain an important factor in investors’ decision making is a question that requires an investigation.

1.1. Managerial Implications for Financial Services and Standards In this chapter, the techniques of autoregression with exogenous variables are utilised to examine whether the recent increase in world oil prices has affected inflation expectations and stock market returns in major OECD countries. While the modelling techniques are applicable to other financial market analyses, several key findings in this chapter provide managers with important information for decision-making. First, no evidence is found to support the presence of a long term relationship between oil prices and inflation expectations – measured by the difference between yields of inflation indexed and non-inflation indexed government bonds. Second, higher oil prices are found to lead to expectations of higher inflation. This is especially the case when oil prices are higher and signs of capacity constraints in the economy are emerging. Third, the impact of higher oil prices on stock market returns, in aggregate, differs among countries. While higher oil prices adversely affect stock market returns in the United States, the United Kingdom and France, the effects are positive in Canada and Australia as these countries are significant exporters of energy resources. In recent years, there has been increased exposure of financial services companies and investment and superannuation funds to international stock

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and money markets. As such, the content of this chapter provides important information and a useful tool for decision-making. In this chapter, we examine the relationships between oil prices and inflation expectations and stock market returns for a number of OECD countries, including the United States, Canada, the United Kingdom, France and Australia. To examine the effect of oil price movements on inflation expectations, we employ daily observations on the difference between yields of inflation indexed and non-inflation indexed government bonds. Specifically, we test whether an increase in oil prices will lead to a widening between yields of these bonds. Because bond yields are market determined, they are expected to provide superior approximation of inflation expectations than the results obtained from surveys. To our knowledge, such a relationship has not been examined in previous studies. For stock market returns, we estimate the relationship between movements in oil prices and stock market indices. This estimation is also undertaken using daily observations. The remainder of this chapter is organised as follows. In Section 2, an examination of changes in inflation expectations and oil price movements is presented. The estimation results of the relationship between oil price movements and inflation expectations are discussed in Section 3. In Section 4, the sensitivity of stock market returns to oil prices is estimated. A summary is given in Section 5.

2. CHANGES IN INFLATION EXPECTATIONS World oil prices have exhibited considerable volatility over the past few years (Fig. 1). Reflecting strong growth in demand and concerns in marketplace about actual and potential supply disruptions, the price of WTI crude oil increased steadily between early 2003 and late 2004. After late 2004, the WTI price continued to rise with somewhat larger fluctuations, before a significant decline in late 2006. In Figs. 2–5, measures of inflation expectations in four OECD countries, namely the United States, the United Kingdom, Canada and France, are presented. These measures are obtained by calculating the difference between yields of inflation indexed and non-inflation indexed government bonds. These bond yields were obtained from central banks of the above named countries. For the United States and Canada, yields of the 10 year government bonds were adopted. For the United Kingdom, yields of the

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2006-01-18

2006-03-30

2006-06-12

2006-08-23

2006-03-30

2006-06-12

2006-08-23

2005-11-02

2005-08-19

2005-06-07

2005-03-23

2005-01-07

2004-10-22

2004-08-11

2004-05-28

2006-01-18

Fig. 1.

2004-03-17

2004-01-05

2003-10-15

2003-08-01

2003-05-21

90 80 70 60 50 40 30 20 10 0 2003-03-10

US$


West Texas Intermediate Oil Price.

3.5 3 %

2.5 2 1.5

Fig. 2.

2005-11-02

2005-08-19

2005-06-07

2005-03-23

2005-01-07

2004-10-22

2004-08-11

2004-05-28

2004-03-17

2004-01-05

2003-10-15

2003-08-01

2003-05-21

2003-03-10

1

US Inflation Expectations.

5 year government bonds were used. For France, we used the implied inflation rates released by Banque De France, which were calculated based on yields of inflation and non-inflation indexed government bonds. The sample period covers 10 March 2003 to 29 September 2006. Interestingly, inflation expectations in the four OECD countries exhibit similar movements over the sample period. Inflation expectations were relatively subdued, or in most cases declined, in the first half of 2003, before

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%

2.50 2.00 1.50

10/09/2005

10/12/2005

10/03/2006

10/06/2006

10/09/2006

10/12/2005

10/03/2006

10/06/2006

10/09/2006

10/06/2005

10/03/2005

10/12/2004

10/09/2004

10/09/2005

Fig. 3.

10/06/2004

10/03/2004

10/12/2003

10/09/2003

10/06/2003

10/03/2003

1.00

UK Inflation Expectations.

3.5 3 %

2.5 2 1.5

Fig. 4.

10/06/2005

10/03/2005

10/12/2004

10/09/2004

10/06/2004

10/03/2004

10/12/2003

10/09/2003

10/06/2003

10/03/2003

1

Canada Inflation Expectations.

a significant increase between mid-2003 and mid-2004. Between mid-2004 and late 2006, inflation expectations appear to have been fluctuating around a certain level in each country. For the United States, inflation expectations were centred on an annual rate of approximately 2.5 per cent. For the United Kingdom and Canada, the expectations were around annual inflation of 2.5–3.0 per cent. In France, inflation expectations were relatively low, fluctuating around an annual rate of 2.0 per cent.


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2.4 2.2

%

2 1.8 1.6 1.4 1.2

Fig. 5.

10/09/2006

10/06/2006

10/03/2006

10/12/2005

10/09/2005

10/06/2005

10/03/2005

10/12/2004

10/09/2004

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1

France Inflation Expectations.

Compared with the price of WTI crude, the measures of inflation expectations demonstrate a different movement in trend terms. While oil prices and inflation expectations both increased over the period mid-2003 to mid-2004, inflation expectations did not rise significantly after mid-2004. This is in contrast to oil price movements which exhibit a further upward trend after mid-2004.

3. OIL PRICES AND INFLATION EXPECTATIONS 3.1. Long Term Relationship The examination of data movements suggests that there is no long term relationship between inflation expectations and oil prices over the sample period investigated. To confirm this conclusion, we also utilise the test for co-integration developed by Engle and Granger (1987). In this test, we first test for the presence of unit roots in the inflation expectations series using the Dickey and Fuller (1979) test. The results indicate that the series are all integrated of order 1 (the so-called I(1) series). For crude oil, we took the benchmark price for each individual country and convert it into local currency terms. We used the price of WTI crude for the United States, the price of North Sea Brent crude for the United Kingdom and France and the price of Lloyd Blend crude for Canada. These

294


prices were sourced from the US Department of Energy and Datastream. All the oil price series were converted into local currency terms and in logarithms. The Dickey and Fuller test results indicate that all of the oil prices in local currency terms are characterised as I(1) series. Applying the Engle and Granger test, the results indicate that the series, inflation expectations and oil prices are not co-integrated over the sample. This suggests that, while oil prices are an important factor that can influence inflation, there is no long term relationship between oil prices and inflation expectations.

3.2. Short Term Influence To examine the short term effect of oil price movements on inflation expectations, we utilised a model of autoregression with exogenous variables (ARX). Because it is unlikely for inflation expectations to affect oil price movements, the ARX model is regarded as a suitable representation for such estimation. There are, of course, other factors that can also influence inflation expectations, such as the prospects for economic growth etc. However, the use of daily observations has limited the availability of data for economic variables. To approximate the effect of changing economic prospects on inflation expectations, we included the stock market index of each country in the associated ARX model. The ARX model is expressed as follows: dðF t Þ ¼ a þ

n X i¼1

dðF ti Þ þ

m X j¼0

d lnðPOtj Þ þ

l X

d lnðI tk Þ þ t

(1)

k¼0

where Ft, POt and It denote inflation expectations, oil price and the stock market index respectively at period t. The stock market indices (sourced from Datastream) are the index of Dow Jones industrial average for the United States, the TSX composite index for Canada, the FTSE 100 index for the United Kingdom and the CAC 40 index for France. We utilised the techniques developed by Penm, Penm, and Terrell (1994) to determine the specifications of the ARX models. For Canada, the initial results using the TSX composite index was unsatisfactory with coefficient signs inconsistent with a priori expectations. To improve the estimation, we replaced the TSX composite index by the Dow Jones index. Because the Canadian economy is closely linked to the US economy, it is likely that developments in the US economy, and hence


295

movements in the US stock market index, provide leading information for inflation expectations in Canada. The estimation results are presented as follows: United States dF t ¼ 0:0002 þ 0:1636 d lnðPOt Þ þ 0:3293 d lnðI t Þ

(2)

dF t ¼ 0:0004 þ 0:0359 d lnðPOt Þ þ 0:5293 d lnðI t Þ

(3)

United Kingdom dF t ¼ 0:0003 þ 0:0436 d lnðPOt1 Þ þ 0:2838 d lnðI t Þ

(4)

ð0:30Þ

ð4:07Þ

ð2:59Þ

Canada ð0:46Þ

ð0:39Þ

ð1:25Þ

ð1:45Þ

ð4:10Þ

ð3:49Þ

France dF t ¼ 0:0000 þ 0:0006 d lnðPOt Þ þ 0:0020 d lnðI t Þ ð0:16Þ

ð2:17Þ

(5)

ð3:29Þ

t-statistics in brackets. To ensure serial correction is not a problem in the estimations, we applied the order selection procedure developed by Penm and Terrell (1984) to each residual series. The results indicate that serial correction is not a problem. The specifications determined for the four OECD countries indicate that inflation expectations adjust rapidly based on oil price movements and changes in the economic prospects, as measured by the stock market index. For all countries, lagged inflation expectations were not selected in the specifications, indicating that lagged inflation expectations contain little information about current inflation expectations. Except for the United Kingdom, movements in oil prices are found to instantaneously affect inflation expectations. On the basis of the coefficient estimates, inflation expectations in the United States are most sensitive to changes in oil prices. This result is consistent with a priori expectations because the United States is the world’s largest oil consumer and its economy relies heavily on imports to meet its domestic oil and energy consumption. For all the countries investigated, inflation expectations are found to be relatively sensitive to changes in economic prospects measured by changes in the stock market index. The coefficient estimates of the oil price variables for Canada and the United Kingdom are not statistically significant at the 5 per cent level. One hypothesis to explain these results is that, in these two countries,

296

Table 1. Country


Impact on Inflation Expectations: Early 2006 to Late 2006. US

Canada

UK

France

0.3836 (5.00)

0.2498 (2.23)

0.0894 (2.17)

0.1219 (1.99)

Note: t-statistics in brackets.

inflation expectations will be significantly affected by oil prices only when oil prices rise to certain high levels. To test this hypothesis, we re-estimated the models using a latter period of the sample (between 17 January and 29 September 2006). Interestingly, all the coefficients of the oil price variables are statistically significant over this latter sample. The coefficient estimates of the associated oil price variables are presented in Table 1. It is noteworthy that the estimates presented in Table 1 are generally larger than those obtained for the whole sample period. This suggests that, in the latter sample, the sensitivity of inflation expectations to oil price movements increased, as oil prices rose to higher levels and the price increases had been sustained. There appear economic grounds to support this finding. Between 2003 and 2005, inflationary pressures were relatively subdued in many OECD countries. In 2006, however, there were increased market concerns about the inflationary impact of higher oil prices, as continued economic growth led to emerging signs of capacity constraints (IMF, 2006). As the economy approaches to its productive capacities, there will be a greater risk for higher oil prices to incur a significant increase in inflationary pressures.

4. STOCK MARKET IMPACTS Higher oil prices have the potential to affect stock market returns. In this study, we focus on the aggregate effect, rather than the sensitivity of equity returns on different industries. Higher oil, or more broadly energy, prices will lead to an increase in production costs, which will place downward pressures on industry equity returns. In energy exporting countries, however, higher energy prices will boost returns from the oil and gas, coal and diversified resources industries. Depending on the relative importance of these industries, higher oil prices may result in a rise in stock market valuations for energy exporting countries. To examine the sensitivity of stock market returns to oil price movements, we adopted the same techniques as used in the above analysis. An ARX


297

model including three variables – stock market index, oil price in local currency terms and inflation expectations – was utilised. In most cases, however, the variables of present and lagged inflation expectations were not selected in the specifications. We also include Australia in this estimation, as it is a significant energy exporter. We used the All Ordinaries index for Australia’s stock market valuation and the price of Tapis crude in Australian dollar terms. In the cases of Canada and Australia, we also included the Dow Jones index in the models because the influence of this index to the respective stock markets. The estimation results are presented as follows: United States us d lnðI us t Þ ¼ 0:0006 0:0502 d lnðPOt Þ 0:0559 d lnðI t1 Þ ð2:22Þ

ð4:75Þ

ð1:67Þ

(6)

Canada d lnðI ct Þ ¼ 0:0004 þ 0:0797 d lnðPOt Þ þ 0:5643 d lnðI us t Þ ð1:89Þ

ð9:68Þ

þ 0:1042 d ð4:10Þ

ð22:15Þ

lnðI us t1 Þ

0:0117 dF t1

ð7Þ

ð1:66Þ

United Kingdom uk d lnðI uk t Þ ¼ 0:0007 0:0253 d lnðPOt Þ 0:1510 d lnðI t1 Þ

(8)

d lnðI ft Þ ¼ 0:0009 0:0381 d lnðPOt1 Þ 0:0820 d lnðI ft1 Þ

(9)

ð2:65Þ

ð2:05Þ

ð4:55Þ

France ð2:61Þ

ð2:38Þ

ð2:43Þ

Australia d lnðI at Þ ¼ 0:0007 þ 0:0451 d lnðPOt Þ þ 0:0366 d lnðPOt1 Þ ð2:28Þ

ð2:71Þ

0:1695 d ð5:09Þ

lnðI at1 Þ

ð2:19Þ

0:2703 d lnðI at2 Þ ð8:56Þ

us þ 0:4488 d lnðI us t1 Þ þ 0:1213 d lnðI t2 Þ ð10:23Þ

ð10Þ

ð2:63Þ

t-statistics in brackets. The estimation results confirm our hypothesis that the impact of higher oil prices on stock market returns, in aggregate, differs between countries. For significant energy consuming countries, such as the United States, the

298


United Kingdom and France, the aggregate impact is found to be negative. In contrast, higher oil prices provide support for aggregate stock market returns in Canada and Australia, both of which are significant exporters of energy resources. As expected, movements in the Dow Jones index are found to have significant influences on stock market returns in Canada and Australia. In the United States and the United Kingdom, the impacts of higher oil prices on stock market returns are instantaneously, while the effect in France is lagged. On the basis of the coefficient estimates, the adverse impact of higher oil prices is most significant in the United States, followed by France and the United Kingdom.

5. SUMMARY Over the past few years, world oil prices have increased significantly. But inflationary pressures remain modest in the major world economies and stock market valuations continue to rise. An important question associated with these movements is whether oil prices remain an important factor in determining inflation expectations and stock market returns. In this chapter, we examine the impacts on inflation expectations and stock market returns of recent increases in world oil prices. For a number of OECD countries, we found no evidence to support a long term relationship between oil prices and inflation expectations. However, an increase in oil prices, in local currency terms, is found to lead to expectations of higher inflation. This evidence is stronger over the latter sample period where oil prices had been significantly higher and capacity constraints were emerging in the economy. For stock market returns, we found the impact of higher oil prices is different between countries. While higher oil prices adversely affect aggregate stock market returns in major oil consuming countries, such as the United States, the United Kingdom and France, the effects are positive for the exporters of energy resources, including Canada and Australia. An interesting extension will be to investigate the sectoral or industrial effects of higher oil prices on stock markets. Such an analysis is, however, outside the scope of the current study. In recent years, many superannuation and investment funds have chosen to target the stock market index as performance benchmarking or have increased their exposure to the so-called ‘index funds’. As such, an analysis of the impact of higher oil prices on aggregate stock market returns has its own importance.


299

REFERENCES Al-Mudhaf, A., & Goodwin, T. H. (1993). Oil shocks and oil stocks: Evidence from the 1970s’. Applied Economics, 25, 181–190. Barsky, R., & Kilian, L. (2004). Oil and the macroeconomy since 1970s. Journal of Economic Perspectives, 18(4), 115–134. BIS. (2006). The evolving inflation process: An overview, Bank of International Settlements (BIS), monetary and economic department. Working Paper no. 196. February, Basel, Switzerland. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431. Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction representation, estimation and testing. Econometrica, 55, 251–276. Faff, R., & Brailsford, T. (1999). Oil price risk and the Australian stock market. Journal of Energy and Development, 4(1999), 69–87. IMF – International Monetary Funds. (2006). World economic outlook. International Monetary Funds (September). Jones, C., & Kaul, G. (1996). Oil and the stock markets. Journal of Finance, 51, 463–491. Jones, D., & Leiby, P. (1996). The macroeconomic impacts of oil price shocks: A review of literature and issues. Energy Division, Oak Ridge National Laboratory, US Department of Energy. Penm, J. H. W., Penm, J. H., & Terrell, R. D. (1994). The recursive fitting of subset ARX models. Journal of Time Series Analysis, 14(6), 602–619. Penm, J. H. W., & Terrell, R. D. (1984). Multivariate subset autoregressive modelling with zero constraints for detecting overall causality. Journal of Econometrics, 24, 311–328.

THE FUTURES HEDGING EFFECTIVENESS WITH LIQUIDITY RISK UNDER ALTERNATIVE SETTLEMENT SPECIFICATIONS Donald Lien and Mei Zhang ABSTRACT A futures contract may rely upon physical delivery or cash settlement to liquidate open positions at the maturity date. Contract settlement specification has direct impacts on the behavior of the futures price, leading to different effects of liquidity risk on futures hedging. This chapter compares such effects under alternative settlement specifications with a simple analytical model of daily price change. Numerical simulation results demonstrate that capital constraint reduces hedging effectiveness and tends to produce a lower optimal hedge ratio. As the futures contract proceeds toward the maturity date, hedgers will take larger hedge position in order to achieve better hedging effectiveness. Finally, optimal hedge ratios are higher (resp. lower) under cash settlement for the bivariate normal (resp. lognormal) assumptions, whereas hedging effectiveness is almost always greater under cash settlement.


301

302

DONALD LIEN AND MEI ZHANG

1. INTRODUCTION In the context of futures hedging, liquidity risk, or more precisely funding liquidity risk (Jorion, 2001), is referred to cash flow uncertainty a hedger faces due to daily resettlement practice before liquidation. While the hedger expects the gains and losses from futures and spot positions to offset each other, the offset occurs at the liquidation date. Although changes in the values of spot positions do not entail daily cash inflows and outflows, changes in the values of futures positions do as a result of daily marking to market. Prior to the liquidation date, the daily loss from futures trading is a cash outflow for the hedger and may constitute a large cost. The effect of liquidity risk on financial risk management is vividly demonstrated in the case of MG Refining and Marketing, Inc. (MGRM). Specifically, MGRM hedged their forward fixed-price sales on energy futures. When oil prices plummeted in 1993, MGRM could not meet the margin calls and was forced to foreclose the futures positions. Culp and Miller (1994, 1995) defended the hedge programs and faulted the supervisionary board members for abandoning the program. Mello and Parsons (1995) and Pirrong (1997), however, argued the hedge program is conceptually flawed. Regardless, the Committee on Payments and Settlement Systems (1998) identified liquidity risk as one of the risks derivatives users must take into account. What happens to the optimal hedge ratio if hedgers face a capital constraint in covering losses on the futures positions? The impacts of capital constraints on firms’ hedging strategies have been the focus of various studies. Brown and Khokher (2001) and Lien and Li (2003) demonstrated that mark to market risk leads to a smaller optimal hedge ratio for hedgers concerned with maximum daily loss. Lien (2003) provides a theoretical analysis of the optimal hedging policy under liquidity constraint because of the mark to market concerns. Wong (2004) showed that a liquidityconstrained firm optimally opts for a long nearby futures position and a short distant futures position, thereby rendering the optimality of using futures spreads for hedging purposes. Moreover, the firm’s production decision is adversely affected by the presence of the liquidity constraint. Wong and Xu (2006) examined the impact of liquidity risk on the behavior of competitive firms under price uncertainty, and offered a rational for the hedging role of options when liquidity risk prevails. In addition, Mello and Parsons (2000) found that futures hedging may enhance the value of a firm with borrowing constraints providing additional liquidity. Arias, Brorsen, and Harri (2000) incorporated a proportional

The Futures Hedging Effectiveness with Liquidity Risk

303

liquidity cost into the hedging decision. Liu and Longstaff (2004) suggested that the margin account may cause underinvestment in the arbitrages. A futures contract may rely upon physical delivery or cash settlement to liquidate open positions at the maturity date. Contract settlement specification has direct impacts on the behavior of the futures price. Lien and Yang (2005) and Lien and Tse (2006) provides surveys of futures price behavior under alternative settlement specifications. As a result, the effects of liquidity risk on optimal hedge ratio and hedging effectiveness differ with alternative settlement specifications. Garbade and Silber (1983a) provided detailed analyses on cash settled futures contracts and evaluated the hedging performance. Adopting the framework of Garbade and Silber (1983b) and Kamara and Siegel (1987), Lien (1989) compared the hedging effectiveness of a cash settled futures contract to that of a physical delivery futures contract. It was found that the cash settlement would provide better hedging performance. This analytical conclusion was supported by the empirical work (see, e.g., Ditsch & Leuthold, 1996; Kimle & Hayenga, 1994; Lien & Tse, 2002). How will the consideration of liquidity risk and capital constraints impact the hedging performance under alternative settlement specifications? Lien and Yang (2005) suggested analytically that future price becomes less volatile and the correlation between spot and futures prices increases when the futures contract switches from physical delivery to cash settlement. There is no theoretical prediction for the effect of a change in the settlement mechanism on the statistical properties of futures returns (i.e., changes in futures prices). However, empirical results from Lien and Tse (2002) indicated that the futures return becomes less volatile and the correlation between spot and futures returns increases when cash settlement replaces physical delivery in feeder cattle contract. An increase in correlation improves hedging effectiveness. A smaller volatility in futures return suggests that the capital allowance is less likely to be met. Therefore, liquidity constraint is less likely to be binding and hedging effectiveness is enhanced. In other words, if the empirical results apply to the general case, cash settlement would help reduce the need for a larger capital allowance for a futures contract to be an effective hedging instrument. To address this issue, this chapter provides a simple analytical model to examine the effects of liquidity risk and capital constraints on futures hedging, and compare the resultant hedging effectiveness and optimal hedge ratios in various constraints scenarios under alternative settlement specifications. The chapter proceeds as follows. We begin with a basic mathematical framework that allows for two deliverable grades underlying both cash and

304


physical delivery settlement systems. First, futures prices under both settlement specifications are derived assuming the changes in daily spot prices are identically and independently normally distributed. We then provide a similar analysis to derive futures prices with an alternative bivariate lognormal distribution assumption. Admittedly, the lognormal assumption is more readily accepted in the literature. The fact that the Black–Scholes option pricing formula is based upon a geometric Brownian motion helps promote the acceptance of this assumption. On the other hand, Kamara and Siegel (1987) adopted the normality assumption to analyze optimal hedging in wheat futures market. Poitras (1998) adopted the arithmetic Brownian motion to price spread options. In addition, theoretical framework frequently applies the normality assumption due to its analytical simplicity, e.g., Kyle (1985). From the analytical results, we generate simulated data and then apply these data to evaluate the two-period hedging decisions under different levels of capital constraints. Optimal hedge ratio and hedging effectiveness under alternative settlement specifications are calculated and compared. Two scenarios are examined. In the first scenario, a perfect timing match prevails between the future spot transaction date and the maturity date of the futures contract. For the second scenario, there is a timing imperfection such that the future spot trading occurs before the futures contract expires. We discuss some notable observations. Finally, the last section provides concluding remarks.

2. THE BASIC FRAMEWORK Suppose that there are two deliverable grades underlying both cash and physical delivery settlement systems. Let pt and st denote the prices of the two grades at time t. We assume the spot prices follow the following stochastic process: " # " # " #" # " # pt a10 pt1 e1t a11 a12 ¼ þ þ (1) st a20 a21 a22 st1 e2t where (e1t, e2t) is a white noise. Let ft and Ft denote the prices of physical delivery settled and cash settled futures contracts (with the same maturity date T) at time t, respectively. The physical delivery futures contract allows both grades to be deliverable against a short position. Thus, the futures price is expected to be the minimum of the spot prices of the two grades at the


305

maturity date. On the other hand, the cash settlement futures contract relies upon a cash index. We assume the index is a simple weighted average of the two spot prices. When both futures markets are unbiased, f t ¼ E½minðpT ; sT ÞjI t and F t ¼ E½bpT þ ð1 bÞsT jI t , where b is the weight allocated to the first grade in the cash index and It the information available at time t. We now adopt simplifying assumptions: ai0=0, aii=1,P and aij=0 when i6¼j; i,P j=1, 2. From these assumptions, at t=0, pT ¼ p0 þ Tt¼1 e1t and sT ¼ s0 þ Tt¼1 e2t . Therefore, " !# T T X X e1t ; s0 þ e2t f 0 ¼ E min p0 þ (2) t¼1

t¼1

F 0 ¼ bp0 þ ð1 bÞs0

(3)

Similarly, at t=1, " f 1 ¼ E min p1 þ

T X

e1t ; s1 þ

t¼2

T X

!# e2t

(4)

t¼2


(5)


(6)

And at t=2

We now have the change in the daily price of the cash settled futures contract as follows: F 1 F 0 ¼ bð p1 p0 Þ þ ð1 bÞðs1 s0 Þ ¼ be11 þ ð1 bÞe21

(7)

On the other hand, there is no explicit expression for the change in the daily price of the physical delivery settled futures contract. The joint distribution of (e1t, e2t) must be specified for further analysis. Let (X,Y)u be a bivariate normal vector with mean (mx, my)u and variance– covariance matrix: " s2 s # xy X x Var (8) ¼ 2 s s xy Y y

306


Kamara and Siegel (1987) shows that E½minðX ; Y Þ ¼ mx Fðmz =sz Þ þ my Fðmz =sz Þ sz fðmz =sz Þ

(9)

s2z

are the mean and variance of the random variable where mz and Z=XY, respectively; f( ) and F( ) are the probability density and distribution functions of the standard normal random variable, respectively. In our framework, we assume (e1t, e2t)u is identically and independently normally distributed random vector such that E(eit)=0 and Varðeit Þ ¼ s2i , i=1, 2, and Covðe1t ; e2t Þ ¼ s12 . Under this assumption, the change in the daily price of the cash settled futures contract, F 1 F 0 , is normally 2 2 2 2 distributed with zero PT mean and variance b s1 þ ð1 bÞ s2 þ 2bð1 bÞs12 . In addition, pP 0þ t¼1 e1t is normally distributed with mean p0 and variance Ts21 and s0 þ Tt¼1 e2t is normally distributed with mean s0 and variance Ts22 . The covariance between the two random variables is Ts12 . As a result, s 0 p0 p0 s0 p0 s 0 1=2 f 0 ¼ p0 F F sf þ s T (10) 0 T 1=2 s T 1=2 s T 1=2 s where s2 ¼ s21 þ s22 2s12 . Similarly, ! ! ! s1 p1 p1 s 1 p1 s 1 1=2 f 1 ¼ p1 F þ s1 F ðT 1Þ sf ðT 1Þ1=2 s ðT 1Þ1=2 s ðT 1Þ1=2 s (11)

f 2 ¼ p2 F

!

s2 p2 ðT 2Þ1=2 s

þ s2 F

p2 s 2 ðT 2Þ1=2 s

! 1=2

ðT 2Þ

sf

!

p2 s 2 ðT 2Þ1=2 s

(12) Moreover, p1=p0+e11, s1=s0+e21, and s1p1=(s0p0)+(e21e11). The change in the daily price of physical delivery settled futures contract is therefore ! s0 p0 þ e21 e11 s 0 p0 f 1 f 0 ¼ ½ p0 þ e11 F p0 F T 1=2 s ðT 1Þ1=2 s ! p s0 þ e11 e21 p0 s 0 þ ½s0 þ e21 F 0 F s 0 T 1=2 s ðT 1Þ1=2 s ! p0 s 0 p0 s0 þ e11 e21 1=2 1=2 þ T sf ðT 1Þ sf ð13Þ T 1=2 s ðT 1Þ1=2 s


307

It can be shown that E ( f1)=f0. The variance and the exact distribution function of f1f0, however, are difficult to characterize analytically. To proceed further, we rely upon numerical simulations to investigate liquidity risk which is related to the tails of the distribution.

3. BIVARIATE LOGNORMAL DISTRIBUTIONS In the futures market literature, bivariate lognormal distribution is deemed to be a more plausible description of spot and futures prices than the normal distribution. Consider the following price generation process: " # " # " #" # " # log pt1 log pt a10 e1t a11 a12 ¼ þ þ (14) log st log st1 a20 a21 a22 e2t Given the assumptions that ai0=0, aii=1, and aij=0 when i6¼j; i, j=1, 2, we obtain 2 2 Ts1 Ts2 F 0 ¼ E½bpT þ ð1 bÞsT jI 0 ¼ bp0 exp þ ð1 bÞs0 exp (15) 2 2 Similarly, ðT 1Þs21 F 1 ¼ E½bpT þ ð1 bÞsT jI 1 ¼ bp0 exp e11 þ 2 ðT 1Þs22 þ ð1 bÞs0 exp e21 þ 2 From the above two equations, 2 Ts1 s2 exp e11 1 1 F 1 F 0 ¼ bp0 exp 2 2 2 Ts2 s2 þ ð1 bÞs0 exp exp e21 2 1 2 2

ð16Þ

ð17Þ

The futures price under the physical delivery specification involves the order statistics of bivariate lognormal distributions. Let (log X, log Y)u be a bivariate normal vector with mean (mx, my)u and variance–covariance matrix # ! " 2 sx sxy log X Var (18) ¼ sxy s2y log Y

308


Lien (1986) shows that # " mx þ my s2x þ sxy s2x E½minðX ; Y Þ ¼ exp mx þ F 2 ðs2x þ s2y 2sxy Þ1=2 # ! " s2y my þ mx s2y þ sxy þ exp my þ F 2 ðs2x þ s2y 2sxy Þ1=2

ð19Þ

As a consequence, we have # 2 " Ts1 logðs0 =p0 Þ Ts21 þ Ts12 f 0 ¼ p0 exp F 2 ðs21 þ s22 2s12 Þ1=2 T 1=2 # 2 " Ts2 logðp0 =s0 Þ Ts22 þ Ts12 þ s0 exp F 2 ðs21 þ s22 2s12 Þ1=2 T 1=2

ðT 1Þs21 f 1 ¼ p0 exp e11 þ 2 " # logðs0 =p0 Þ Ts21 þ Ts12 e11 e21 s21 þ s12 F ðs21 þ s22 2s12 Þ1=2 ðT 1Þ1=2 ðs21 þ s22 2s12 Þ1=2 ðT 1Þ1=2 ðT 1Þs22 þ s0 exp e21 þ 2 " # logðp0 =s0 Þ Ts22 þ Ts12 e21 e11 s22 þ s12 F ðs21 þ s22 2s12 Þ1=2 ðT 1Þ1=2 ðs21 þ s22 2s12 Þ1=2 ðT 1Þ1=2

ð20Þ

ð21Þ

From which we can determine the price change f1f0. Adopting a similar analysis, we obtain analytical expressions for F2 and f2 as follows. ðT 2Þs21 F 2 ¼ E½bpT þ ð1 bÞsT jI 2 ¼ bp0 exp e11 þ e12 þ 2 2 ðT 2Þs2 þ ð1 bÞs0 exp e21 þ e22 þ 2

ð22Þ


ðT 2Þs21 f 2 ¼ p0 exp e11 þ e12 þ 2 " # logðs0 =p0 Þ Ts21 þ Ts12 e11 þ e12 e21 e22 2s21 þ 2s12 F ðs21 þ s22 2s12 Þ1=2 ðT 2Þ1=2 ðs21 þ s22 2s12 Þ1=2 ðT 2Þ1=2 ðT 2Þs22 þ s0 exp e21 þ e22 þ 2 " # 2 logðp0 =s0 Þ Ts2 þ Ts12 e21 þ e22 e11 e12 2s22 þ 2s12 F ðs21 þ s22 2s12 Þ1=2 ðT 2Þ1=2 ðs21 þ s22 2s12 Þ1=2 ðT 2Þ1=2

309

ð23Þ

4. HEDGING UNDER LIQUIDITY RISK To evaluate the effect of liquidity risk, we need to consider a framework with at least two periods (i.e., three dates). The current date is t=0. A firm anticipates to sell the commodity of the first grade at date t=2. To reduce the price risk, the firm establishes a short position in the corresponding futures market. Meanwhile, the firm commits a fixed amount of capital to the hedge program. If the losses on the futures position at the end of date t=1 exceed the committed amount, the futures position will be liquidated. Otherwise it will be held until date t=2. Let h denote the hedge ratio. Consider a physical delivery settled futures contract. If the futures position is held until t=2, the firm’s revenue at t=2 is p ¼ p2 þ ðf 0 f 2 Þh. However, if the firm chooses to liquidate the futures position earlier at t=1, the firm’s revenue at t=2 becomes p ¼ p2 þ ðf 0 f 1 Þh. We assume the hedger attempts to minimize the risk associated with his total revenue. The optimal hedge ratio is therefore the one that minimizes the variance of the firm’s revenue at the end of date t=2. Hedging effectiveness is measured by the difference between the variance of p2 and the variance of the firm’s revenue at the end of date t=2 corresponding to the optimal hedge ratio, as a percentage of the variance of p2. If we have a cash settled futures contract instead, then the revenue becomes p ¼ p2 þ ðF 0 F 2 Þh when there is no early liquidation and p ¼ p2 þ ðF 0 F 1 Þh, otherwise.

5. NUMERICAL RESULTS Tables 1(A) and (B) display the numerical results for bivariate normal distributions under cash settlement and physical delivery, respectively.

310


Table 1. Liquidity Risk under Cash Settlement and Physical Delivery: Bivariate Normal Distribution. A: Liquidity Risk under Cash Settlement Correlation

0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

Var (F2)

Capital Allowance

Optimal Hedge Ratio

Var (p)

Hedging Effectiveness (%)

1.7865 1.7865 1.7865 1.6371 1.6371 1.6371 1.4875 1.4875 1.4875

No constraint 2.1 1.4 No constraint 2.1 1.4 No constraint 2.1 1.4

0.9998 0.9979 0.9917 1.0007 0.9979 0.9955 1.0018 0.9983 0.9976

0.1951 0.2064 0.2461 0.3415 0.3487 0.3823 0.4881 0.4927 0.5167

90.2 89.6 87.6 82.8 82.4 80.7 75.4 75.1 73.9

B: Liquidity Risk under Physical Delivery Correlation

Var (f2)

Capital Allowance

Optimal Hedge Ratio

Var (p)


0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

1.8288 1.8288 1.8288 1.7162 1.7162 1.7162 1.6041 1.6041 1.6041


0.9738 0.9720 0.9675 0.9509 0.9509 0.9475 0.9248 0.9245 0.9245

0.2466 0.2548 0.2949 0.4292 0.4326 0.4625 0.6092 0.6110 0.6326

87.6 87.1 85.1 78.4 78.2 76.7 69.3 69.2 68.1

Fig. 1 compares the results reported in Tables 1(A) and (B). Numerical results for bivariate lognormal distributions are presented in Tables 2(A), (B), and Fig. 2. The tables present optimal hedge ratios, variances of p and the hedging effectiveness under various correlations between e1t and e2t, with different capital allowances. In these simulations, we set T=3, i.e., the futures contracts mature one day after the hedging period ends. In addition, s21 ¼ s22 ¼ 1 and b=0.5. We consider three possible values for the correlation s12=0.5, 0.65, or 0.8. From these parameter configurations, we generate 3,000 data points of spot and futures prices. We apply hedging decisions to these data points to derive optimal hedge ratios and hedging effectiveness under liquidity risk. The choices of capital allowance are determined by the standard deviations of futures prices at t=2.

100.00% 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%

1 0.98 0.96 0.94 0.92

Fig. 1.

ρ=0.5,allowance=1.4


ρ=0.5 no constraint





Optimal Hedge Ratio (Cash Settlement) Hedging Effectiveness (Cash Settlement)


0.9 0.88

Hedging Effectiveness

311

1.02


Optimal Hedge Ratio


Optimal Hedge Ratio (Physical Delivery) Hedging Effectiveness (Physical Delivery

Hedging Effectiveness and Optimal Hedge Ratio – Bivariate Normal Distribution (T=3).

For bivariate normal distributions, the average of standard deviations for f2 and F2 over all three cases of correlation is 1.3. We set capital allowance at 1.1 times and 1.6 times of the average standard deviation, which equals to 1.4 and 2.1, respectively. For bivariate lognormal distributions, the average standard deviation of f2 and F2 over all three cases of correlation is 72, and we set capital allowance at 0.9 times and 1.1 times of the average standard deviation, which equals to 65 and 80, respectively. We then set T=2, i.e., the futures contracts mature after two periods. In this case, futures price and spot price converge at date t=2. We have f 2 ¼ minðp2 ; s2 Þ and F 2 ¼ ðp2 þ s2 Þ=2. Keeping all other parameters unchanged, we apply hedging decisions to the 3,000 data points again to gauge the impact of liquidity risk. Tables 3(A) and (B) display the numerical results when T=2, for bivariate normal distributions under cash settlement and physical delivery, respectively. Fig. 3 compares the results. Numerical results for bivariate lognormal distributions when T=2 are presented in Tables 4(A), (B), and Fig. 4. Again, the choices of capital allowance are determined by the standard deviations of futures prices at t=2. We use average standard deviation of f2 and F2 over all three cases of correlation, which gives us capital allowance levels of 1.4 and 2.1 for bivariate normal distributions, and capital allowance levels of 42 and 52 for bivariate lognormal distributions.

312


Table 2. Liquidity Risk under Cash Settlement and Physical Delivery: Bivariate Lognormal Distribution. A: Liquidity Risk under Cash Settlement Correlation

0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

Var (F2)

Capital Allowance

Optimal Hedge Ratio

Var (p)

Effectiveness (%)

10961.0530 10961.0530 10961.0530 8640.0208 8640.0208 8640.0208 6872.6666 6872.6666 6872.6666

No constraint 80 65 No constraint 80 65 No constraint 80 65

0.5960 0.5596 0.5575 0.6598 0.6448 0.5790 0.7321 0.6745 0.6024

810.6586 2699.1532 2805.5998 942.6521 2080.5947 2878.9301 1020.5867 2191.8533 3007.5341

82.8 42.7 40.4 80.0 55.8 38.8 78.3 53.4 36.1


0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

Var (f2)

Capital Allowance

Optimal Hedge Ratio

Var (p)

Effectiveness (%)

4059.0431 4059.0431 4059.0431 2501.2899 2501.2899 2501.2899 1410.2178 1410.2178 1410.2178


0.8623 0.9999 0.9865 0.9795 1.1471 1.1323 1.1906 1.2681 1.2816

1686.1559 2392.6757 2479.7298 2305.1924 2903.0483 2972.5030 2706.1428 3288.2120 3319.0666

64.2 49.2 47.3 51.0 38.3 36.8 42.5 30.1 29.5

Some notable observations are summarized as follows: 1. Hedging is less effective with capital constraints. For example, in Table 1(B), when correlation is 0.8 and there is no capital constraint, the optimal hedge ratio is 0.9738 with hedging effectiveness of 87.6%. With a capital constraint of 1.4, the optimal hedge ratio is reduced to 0.9675 resulting in a lower hedging effectiveness of 85.1%. Similarly in Table 2(A), with the correlation being 0.65, the optimal hedge ratio is 0.6598 leading to the hedging effectiveness of 80.0% if there is no capital constraint. With a capital constraint of 65, the optimal hedge ratio is reduced to 0.5790 resulting in a lower hedging effectiveness of 38.8%. Also, in Table 4(A), with the correlation being 0.5, the optimal

90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%

Fig. 2.

ρ=0.5,allowance=65

ρ=0.5,allowance=80


ρ=0.65,allowance=65


ρ=0.65no constraint

ρ=0.8,allowance=65

ρ=0.8,allowance=80

Optimal Hedge Ratio (Cash Settlement) Hedin Effectiveness (Cash Settlement)


313

1.4 1.2 1 0.8 0.6 0.4 0.2 0 ρ=0.8 no constraint

Optimal Hedge Ratio


Optimal Hedge Ratio (Physical Delivery) Hedging Effectiveness (Phsical Delivery)

Hedging Effectiveness and Optimal Hedge Ratio – Bivariate Lognormal Distribution (T=3).

hedge ratio is 1.2070 with hedging effectiveness of 78.3% if there is no capital constraint. With a capital constraint of 42, the optimal hedge ratio is reduced to 1.1128 resulting in a lower hedging effectiveness of 53.0%. 2. The larger the capital allowance, the less are its impacts on optimal hedge ratio and hedging effectiveness. For example, in Table 1(B) with a correlation of 0.8, when capital allowance increases from 1.4 to 2.1, the optimal hedge ratio increases from 0.9675 to 0.9720 and hedging effectiveness improves from 85.1% to 87.1%. Similarly, in Table 2(B) with a correlation of 0.8, when capital allowance increases from 65 to 80, the optimal hedge ratio increase from 0.9865 to 0.9999 with hedging effectiveness being improved from 47.3% to 49.2%. Also, in Table 3(A) with a correlation of 0.65, when capital allowance increases from 1.4 to 2.1, the optimal hedge ratio increases from 0.9955 to 0.9979 and hedging effectiveness improves from 80.7% to 82.4%. 3. When subjected to the same capital allowance, hedging effectiveness under cash settlement is better than that under physical delivery. As shown by Figs. 1–4, the lines depicting hedging effectiveness under cash settlement are almost always on top of the corresponding lines under physical delivery. For specific examples, Table 1(B) shows that with a correlation of 0.5 and a capital allowance of 1.4, the hedging effectiveness under physical delivery is 68.1%, while Table 1(A) shows that under the

314


Table 3. Liquidity Risk under Cash Settlement and Physical Delivery: Bivariate Normal Distribution (T=2). A: Liquidity Risk under Cash Settlement Correlation

0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

Var (F2)

Capital Allowance

Optimal Hedge Ratio

Var (p)


1.7865 1.7865 1.7865 1.6371 1.6371 1.6371 1.4875 1.4875 1.4875


0.9998 0.9979 0.9917 1.0007 0.9979 0.9955 1.0018 0.9983 0.9976

0.1951 0.2064 0.2461 0.3415 0.3487 0.3823 0.4881 0.4927 0.5167

90.2 89.6 87.6 82.8 82.4 80.7 75.4 75.1 73.9


Var (f2)

Capital Allowance

Optimal Hedge Ratio

Var (p)


0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

1.8562 1.8562 1.8562 1.7683 1.7683 1.7683 1.6793 1.6793 1.6793


0.9592 0.9569 0.9541 0.9238 0.9242 0.9209 0.8851 0.8857 0.8880

0.2731 0.2803 0.3224 0.4720 0.4746 0.5048 0.6656 0.6669 0.6876

86.2 85.9 83.7 76.2 76.1 74.5 66.4 66.3 65.3

same parameter configuration, hedging effectiveness under cash settlement is 73.9%. Similarly, Table 2(A) shows that with a correlation of 0.65 and a capital allowance of 80, the hedging effectiveness under cash settlement is 55.8%, higher than 38.3% under physical delivery as shown in Table 2(B). Also, in Table 4(A) with correlation of 0.65 and a capital allowance of 52, the hedging effectiveness under cash settlement is 56.1%, higher than 35.6% under physical delivery as shown in Table 4(B). 4. Subjected to the same capital allowance, the lower the correlation between e1t and e2t, the worse the hedging effectiveness. For example, in Table 1(B), with a correlation of 0.8 and a capital allowance of 1.4, the hedging effectiveness is 85.1%, which is reduced to 68.1% under same

100.00% 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%

Fig. 3.











315

1.02 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 ρ=0.8 no constraint

Optimal Hedge Ratio


Optimal Hedge Ratio (Physical Delivery) Hedging Effectiveness (Physical Delivery)

Hedging Effectiveness and Optimal Hedge Ratio – Bivariate Normal Distribution (T=2).

capital allowance but a lower correlation of 0.5. Similarly, in Table 2(B), with a capital allowance of 65, the hedging effectiveness is improved from 29.5% to 47.3% when the correlation coefficient increases from 0.5 to 0.8. Also, in Table 3(A) with a correlation of 0.8 and a capital allowance of 2.1, the hedging effectiveness is 89.6% , which is reduced to 75.1% under same capital allowance but a lower correlation of 0.5. 5. Under the bivariate normal assumptions, with same parameter configuration, optimal hedge ratios are lower under physical delivery than under cash settlement, while under the bivariate lognormal assumptions the opposite is true. For example, in Tables 1(A) and (B), with a correlation of 0.8 and a capital allowance of 1.4, optimal hedge ratio is 0.9675 under physical delivery and 0.9917 under cash settlement. The same pattern appears in Tables 3(A) and (B), and illustrated by Figs. 1 and 3. In contrast, in Tables 2(A) and (B), with a correlation of 0.8 and a capital allowance of 65, optimal hedge ratios are 0.9865 and 0.5575 under physical delivery and cash settlement, respectively. We find similar results in Tables 4(A) and (B). Figs. 2 and 4 highlight the comparison. 6. For bivariate normal distributions, the variance of the futures price at date t=2, is lower under cash settlement than that under physical delivery; that is, Varðf 2 ÞoVarðF 2 Þ. On the other hand, in the case of

316


Table 4. Liquidity Risk under Cash Settlement and Physical Delivery: Bivariate Lognormal Distribution (T=2). A: Liquidity Risk under Cash Settlement Correlation

0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

Var (F2)

Capital Allowance

Optimal Hedge Ratio

Var (p)

Effectiveness (%)

4032.3460 4032.3460 4032.3460 3178.4860 3178.4860 3178.4860 2528.3127 2528.3127 2528.3127


0.9826 1.0201 0.9291 1.0878 1.0641 0.9566 1.2070 1.1126 1.1128

810.6586 1882.1951 2725.4557 942.6521 2065.6261 2874.0114 1020.5867 2162.4077 2212.3536

82.8 60.0 46.1 80.0 56.1 38.9 78.3 54.1 53.0


0.8 0.8 0.8 0.65 0.65 0.65 0.5 0.5 0.5

Var (f2)

Capital Allowance

Optimal Hedge Ratio

Var (p)

Effectiveness (%)

1862.6362 1862.6362 1862.6362 1544.0501 1544.0501 1544.0501 923.6451 923.6451 923.6451


1.2513 1.4315 1.4184 1.1986 1.5343 1.5087 1.4118 1.5369 1.5276

1788.0027 2532.9420 2578.2754 2486.9487 3028.6505 3095.6988 2864.2470 3468.9826 3479.2289

62.0 46.2 45.2 47.2 35.6 34.2 39.1 26.3 26.1

bivariate lognormal distributions, the variance of the futures price at date t=2 is lower under physical delivery than that under cash settlement, i.e., Varðf 2 Þ4VarðF 2 Þ. As shown by Tables 1(A) and (B), with a correlation of 0.8, the variances of the futures price at date t=2 are 1.7865 and 1.8288 under cash settlement and physical delivery, respectively. If the correlation coefficient is 0.5, the variances become 1.4875 and 1.6041 respectively. The same pattern is observed in Tables 3(A) and (B). In contrast, as shown by Tables 2(A) and (B), with a correlation of 0.65, the variances of the futures price at date t=2 are 8640.0 and 2501.3 under cash settlement and physical delivery, respectively. When the correlation is 0.5, the variances are 6872.7 and 1410.2 respectively. Similar results prevail in Tables 4(A) and (B).


Optimal Hedge Ratio

1.8

90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%

1.6 1.4 1.2 1 0.8 0.6 0.4


Fig. 4.

ρ=0.5,allowance=42

ρ=0.5,allowance=52




ρ=0.8,allowance=42

ρ=0.8,allowance=52


0


0.2


317

Optimal Hedge Ratio (Physical Delivery) Hedging Effectiveness (Physical Delivery)

Hedging Effectiveness and Optimal Hedge Ratio – Bivariate Lognormal Distribution (T=2).

7. As shown in Tables 1(A), 1(B), and 2(A) optimal hedge ratios with capital constraints are lower than those with no constraints. We have similar results in Tables 3(A), 3(B), and 4(A). Considerations of liquidity risk prevent the hedger from choosing a conventional hedge strategy that minimizes the price risk. Instead, a smaller position is adopted to balance price risk and liquidity risk (Lien & Li, 2003). On the other hand, we noticed that under physical delivery in lognormal case as reported in Table 2(B) and Table 4(B), optimal hedge ratios are larger when there are capital constraints. In these cases, hedging effectiveness is relatively low even when there is no capital constraint. For example, hedging effectiveness is 64.2% with a correlation of 0.8 in Table 2(B) whereas the corresponding values are above 80% with the same correlation in Tables 1(A), 1(B), and 2(A). Note that the variance of the futures price at date t=2 is lower with physical delivery than with cash settlement under bivariate lognormal assumptions. A hedge program is more likely to survive in this case. The hedger thus chooses a larger futures position to improve hedging effectiveness. 8. When T=2, under bivariate lognormal assumptions the variances of f2 and F2 are smaller compared to their corresponding values in T=3. For example, in Tables 4(A) and (B), when T=2 with correlation of 0.8, the

318


variances of f2 and F2 are 1862.6 and 4032.3, respectively, lower than their corresponding values when T=3, which are 4059.0 and 10961, respectively as shown in Tables 2(A) and (B). Moreover, when T=2, under bivariate lognormal assumptions the optimal hedge ratios are larger than their corresponding values in T=3. For example, in Table 4(B) with correlation of 0.65 and no capital constraint, the optimal hedge ratio is 1.1986, higher than its corresponding value when T=3, which is 0.9795 as shown in Table 2(B). In other words, as the futures contract proceeds toward the maturity date, hedgers tend to take larger hedge positions in order to achieve better hedging effectiveness.

6. CONCLUSION This chapter compares the effects of liquidity risk on futures hedging under alternative settlement specifications. We construct a simple analytical model of daily price change to generate the futures price under physical delivery and cash settlement. The prices are assumed to be either jointly normally distributed or jointly lognormally distributed. Numerical simulations are performed to compare and contrast the effects of liquidity risk on hedging effectiveness and optimal hedge ratios. The results demonstrate that capital constraint reduces hedging effectiveness, and the hedging effectiveness is further reduced as capital allowance becomes smaller. Subjected to same level of capital allowance, hedging is almost always more effective under cash settlement than under physical delivery. Optimal hedge ratios are higher under cash settlement for the bivariate normal assumptions, while for the bivariate lognormal assumptions the optimal hedge ratios are higher under physical delivery. Capital constraint also leads to lower optimal hedge ratios under joint normality assumptions. The same conclusion almost always holds for joint lognormality assumptions if the futures contract is cash settled. On the other hand, under joint lognormality assumptions, optimal hedge ratios for a physical delivery contract are larger when there are capital constraints as the hedger takes a larger futures position to improve the hedging effectiveness when the hedging program is more likely to survive. Finally, as the futures contracts proceed towards maturity date, hedgers will take larger hedge position in order to achieve better hedging effectiveness.


319

ACKNOWLEDGEMENT The authors are grateful to the editor, Andrew Chen, for helpful comments and suggestions.

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