Investments

Investment Management Equations 1. Rate of re turn on an asset or portfolio Return = (End-of-period wealth - beginn ing -ofperiod weal t h )/( begi n n i n g-of~pe ri od wealth) 2. Actual margin in a stock purchase (nXmp) -[(I-im) X /,p X ,,] am = >I X mp 3. Market price at which a margin purchaser will re ceive a margin call _ (I - ;1>1) X pp

mp-

1 - mm

4. Actual margin in a short sale

[(spXn) X ( I +im)] -(mpX>l) X mp n

am =

5. Market price at which a short seller will receive a margin call .Ip X (1 + ;1>1) mp = 1+ mm 6. Expe cted return o n a portfolio ,\'

rp =

; =1

7. Covariance between two securities au = P'jUjU'j 8. Standard deviation of a portfolio Up

=

.v

~ ~ XiXi0';,

[

] 1/2

9. Standard deviation of a two-asset portfolio '1 ') 2 ~ I /~ U p = XjUI + X,1O'2 + 2XIX"PI2IT ,U 2j 10. The market model "j = Uj + {3;'/ + e, 11. Beta from the market model 'j

[

13,. =

Uj

12. Securitv variance from the market model

u; = l3~u7 + 0';,.

13. Security cov,~riance from th e market model U,j = f3if3 jUj 14. Variance of a portfolio (by market and unique risk) IT~ = f3~ u; + u;p 15. Mark et risk of a portfolio

.v

e, = ;L=1 x;f3; 16. Unique risk of a portfolio s

L XTu;,

j =1

17. Capital Market Line

r"

= 'j

Ii)] u p

( '.11 -

+ [- - - 0' .11

18. Variance of the market portfolio .\'

.\'

L L X,.\,Xj.\fU,j

a~, =

, =1 j =1

19. Security Market Line (covariance and beta versions)

r; =

'j

+ [( r.1I ~ r/)] Ui.1I fr .\1

r; =

'i + (1"11 -

Tj)f3,

20. Beta from the CAP:'.I = 17, .11

13

t

U ",\1

+ (b" hJ2 + [J' 2bjl) Coo( fj f ;) 24. Arb itrage Pricing Theory (two-factor model) 1-;=A o+A,II" +A 211'2 1- i = 'i+ (.O8 5.12 7.18 10.SS 11.24 14.71 10.54 8.80 9.85 7.72 6.16 5.47 6.35 8.37 7.81 5.60 3.51 2.90 3.90 5.60 5.21 3.79%

5.45%

5.96%

12.67%

3.22%

d~ation

3.26%

9.21%

8.69%

20.32%

".54%

"

14.64 18.65 1.71 -.07 -4020 -2.76 -1.24 42.56 6.26 16.86

30.09

-2.~1

-.27

9.67

10.70 16.2!l 6.78 19.89 9.39 13.19 - 5.76

UU) 6.18 19.:-\0 IW5

16.24 -7.77 !l1.67 -.93

27.20 1.40

37.20 23.84 -7.18 6.56 18.44 32.42 -4.91 21.41 22.51 6.27 32.16 18.47 5.23 16.81 31.49 -3.17 30.55 7.67 9.99 1.31 57,43 23.07

".81

6.77 9.0!! 1~.!l1

12.40 8.94 3.87 3.80 3.95 !I.77 1.33 ".41 4.42

".65 ' 6.11 3.06 2.90 2.75 2.67 2.54 ~.32

Source: Siodu. Bonds, Bills, a nd InjbJtion 1997 YrarlHJlJk (Chicago: Ibbotson Associates, 1997) . All righ ts reserved.

1.1.2

Risk, Return, and Diversification

Table 1.1 provides year-by-year annual returns for the four types of securities shown in Figure 1.1. The table also includes the annual percentage change in the Consumer Price Index (CPI) as an indicator of variations in the cost of living. Average annual returns are shown at the bottom of the table. Below these values are the standard deviations of annual returns, which serve as measures of the variability of the returns on the respective securities.i Table 1.2 provides average annual returns and standard deviations for securities from the United States.japan, Germany, and the United Kingdom during the period from 1970 to 1996. The historical record revealed in Figure 1.1, Table 1.1, and Table 1.2 illustrates a general principle: When sensible investment strategies are compared with one another, risk and return tend to go together. That is, securities that have higher average returns tend to have greater amounts of risk. It is important to note that historical variability is not necessarily an indication of prospective risk . The former deals with the record over some past period; the latter has to do with uncertainty about the future. The pattern of returns on Treasury 8

CHAPTER 1

TABLE

1.2

Summary Statistics for U.S•• Japan~e •.German. and U.K. SecuritIes, 1970-1996

I Short-term interest rates Government bonds Common stocks Inflation

I

Average Return *

Standard Deviation

U.S.

Japan

Germany

U.K.

U.S.

Japan

Germany

6.93%

5.95%

6.35%

10.69%

2.71%

2.39% 5.23 25.62 2.05

B4

9.88 13.47

13.32

5.52

4,48

8.05 10.59 3.611

11.96 18.45

16.14

3.21% 5.15 29.25

8.43

3.26

!U3

IU8

• Foreign returns are calculated ,n local currencies . Foreign stock returns include dividend income adjusted for the rax rare applicaOle to U.S. investors . Governmentbonas jnclude maturities greater than one year. Soun:e: U.S.linancial market data adapted £rom Slocb. Bond>, BillJ• • • d InJlnlitnt 1997 Y,a.wuk (Chicago: Ibbotson Associates . \997) . All righ15 reserved. Foreign financial market data provided by 8rinson Partners, Morgan SQnlc)' Capual Inte rnational. Interna tional Financial SlauraiCl, and DRI/McGr.lw·HiII.

bills provides one example. Although the values have varied from period to period, in any given period the amount to be earned is known in advance and is thus riskless. On the other hand, the annual return on a common stock is very difficult to predict accurately. For such an investment, variability in the past may provide a fairly good measure of the uncertainty surrounding the future return." To sec how difficult it is to predict common stock returns, cover the portion of Table 1.1 from 1941 on, and then try to guess the return in 1941. Having done this, uncover the value for 1941, and try to guess the return for 1942. Proceed in this manner a year at a time, keeping track of your overall predictive accuracy. Unless you are very clever or very lucky, you will conclude that the past pattern of stock returns provides little help in predicting the next year's return . It will later be seen that this apparent randomness in security returns is a characteristic of an efficient market: that is, a market in which security prices fully reflect information immediately. Is one of these four types of securities obviously the best? No. To oversimplify, the right security or combination of securities depends on the investor's situation and preferences for return relative to his or her distaste for risk. There may be "right" or "wrong" securities for a particular person or purpose. However, it would be surprising indeed to find a security that is clearly wrong for everyone and every purpose. Such situations are simply not present in an efficient market. Figure 1.2 illustrates the tradeoffs involved between risk and return . Note that the types of securities with higher historical returns also have had higher levels of risks, suggesting that no type of security dominates any other by having both higher return and lower risk. Also shown in the figure under "Blend" is the risk-return performance ofa portfolio that at the beginning of each year was reconfigured to have one-half of its funds invested in corporate bonds and the other half in common stocks. Careful examination reveals that the portfolio's average return equals one-half of the average return of corporate bonds and one-half the average returns of common stocks. However, the risk of the portfolio is less than half the risk of corporate bonds plus half the risk of common stocks. This outcome illustrates a fundamental principle of diversification: When securities are combined into a portfolio, the resulting portfolio will have a lower level of risk than a simple average of the risks of the securities. Intuitively, the reason is that when some securities are doing poorly, others are doing well. This pattern tends to reduce the extremes in the portfolio's returns, thereby lowering the portfolio's volatility.

1.1.3

Security Markets

Security markets exist in order to bring together buyers and sellers of securities, meaning that they are mechanisms created to facilitate the exchange of financial asIntroduction

9

U.K. 3.10% 12.82 33.02 5.73

25

~ e

20

0

' ;J

'" '> " ...

0

'0

15

'e" s

'0

hour hall Closed for rest of day

These trigger points are converted into points at the beginning of each quarter based on the average closing price of the DJIA during the last month of the previous quarter, and are rounded to the nearest 50 points. Thus, if inJune the average closing price of the DJIA was 8900, then the trigger points for the July-August-September quarter would be 900 (note 10% of 8900 is 890), 1800 (note that 20% of 8900 is 1780), and 2650 (note that 30% of 8900 is 2670). A 50-point move in the Dow Jones Industrial Average implies less than a 1% change in its value. As a result, Rule 80A is frequently triggered. Whether the rule actually reduces market volatility, as its originators intended, is open to considerable debate. The much larger intraday price decline implied by Rule 80B has occurred only once since the rule's inception. On October 27, 1997, the Dow plunged 554 .25 points (7.2%). Under Rule 80B's provisions at that time, a one-half hour shutdown was triggered, followed quickly thereafter by a one hour shutdown. Because the last trading halt took place at 3:30 P.M., the NYSE closed for the rest of the day. The next day the Dow rose 337 points. Critics claimed that the existence of the circuitbreakers actually destabilized the market. They argued that after the first trading halt, investors rushed to submit sell orders to beat the anticipated next shutdown, thereby 50

_ CHAPTER 3

accelerating the market's decline. Despite recent changes in Rule 80B, many market participants continue to call for elimination or substantial restructuring of the circuitbreakers. New York Stock Exchange Members

Members in the NYSE fall into one of four categories, depending on the type of trading activity in which they engage. These categories are commission brokers, floor brokers, floor traders, and specialists. Of the 1,366 members of the NYSE, roughly 700 are commission brokers, 400 are specialists, 225 are floor brokers, and 41 are floor traders. The trading activities of members in these categories are as follows: 1. Commission brokers. These members take orders that customers have placed with their respective brokerage firms and see to it that those orders are executed on the exchange. The brokerage firms that they work for are paid commissions by the customers for their services. 2. Floor brokers, also known as two-dollar brokers. These members assist commission brokers when there are too many orders flowing into the market for the commission brokers to handle alone. For their assistance, they receive part of the commission paid by the customer. (Sometimes floor brokers, as defined here, are lumped together with commission brokers and together are called floor brokers.) 3. Floor traders. These members trade solely for themselves and are prohibited by exchange rules from handling public orders. They hope to make money by taking advantage of perceived trading imbalances that result in temporary mispricings, thereby allowing them to "buy low and sell high." These members are also known as registered competitive market-makers, competitive traders, or registered traders. 4. Specialists. These members perform two roles. First, any limit order that the commission broker cannot execute immediately because the current market price is not at or better than the specified limit price will be left with the specialist for possible execution in the future. If this order is subsequently executed, the specialist is paid part of the customer's commission. The specialist keeps these orders in what is known as the limit order book (or specialist's book). Stop and stop limit orders are also left with the specialist, who then enters them in the same book. In this capacity the specialist is acting as a broker (that is, agent) for the customer's broker and can be thought of as a "broker's broker." Second, the specialist acts as a dealer, or market-maker, in certain stocks (in particular, for the same stocks in which he or she acts as a broker). This means that the specialist buys and sells certain stocks for his or her own account and is allowed to seek a profit in doing so. However, in acting as a dealer, the specialist is required by the NYSE to maintain a "fair and orderly market" in those stocks in which he or she is registered as a specialist. Thus the NYSE expects the specialist to buy or sell shares from his or her own account when there is a temporary imbalance between the number of buy and sell orders. (In doing so, specialists are allowed to short sell their assigned stocks, but they still must abide by the up-tick rule.) Even though the NYSE monitors the trading activities of the specialists, this requirement is so ill-defined that it is difficult, if not impossible, to enforce. As might be inferred from the preceding discussion, specialists are at the center of the trading activity on the NYSE. Each stock that is listed on the NYSE currently has one specialist assigned to it.? (In a few instances in the past, two or more specialists were assigned to the same stock.) There are almost 3,000 common stocks listed on the NYSE and only about 400 specialists. As those numbers suggest, each specialist is assigned more than one stock. All orders involving a given stock must be taken physically or electronically to a trading post, a spot on the floor of the NYSEwhere the specialist for that stock stands Security Markets

51

at all times during the hours the NYSE is open.f It is here that an order is either executed or left with the specialist. Placing a Market Order

The operation of the New York Stock Exchange is best described by an example. Mr. B asks his broker for the currcn t price of General Motors (GM) shares. The broker punches a few buttons on a PC·like quotation machine and finds that the current bid and asked prices on the NYSE are as favorable as the prices available on any other market, being equal to $61 and $61-~, respectively. In addition , the quotation machine indicates that these bid and asked prices are good for orders of at least 100 and 500 shares, respectively. This means that the NYSE specialist is willing to buy at least 100 shares of GM at a price of$61 (the bid price) and is willing to sell at least 500 shares of GM at $61-~ (the asked price)." After being given this information, Mr. B instructs his broker to "buy 300 at market," meaning that he wishes to place a market order with his broker for 300 shares of GM. At this point the broker transmits the order to his or her firm's New York headquarters, where the order is subsequently relayed to the brokerage firm's "booth" on the side of the exchange floor. Upon receiving the order, the firm's commission broker goes to the trading post for GM. The existence of a standing order to buy at $61 means that no lower price need be accepted, and the existence of a standing order to sell at $61-~ means that no higher price need be paid. All that is left for possible negotiation is the spread between the two prices. IfMr. B is lucky, another broker (for example, one with a market order to sell 300 shares for Ms. S) will "take" the order at a price "between the quotes," here at $61-~, resulting in "price improvement." (This happens often, as about one-third of the volume in l\'YSE-listed stocks is traded between the bid and asked quotes.) Information will be exchanged between the two brokers and the sale made. Figure 3.1 illustrates the procedure used to fill Mr. B's order. If the gap between the quoted bid and asked prices is wide enough, an auction may occur among various commission brokers, with sales made at one or more prices between the specialist's quoted values . This auction is known as a double (or two-way) auction, because both buyers and sellers are participating in the bidding process. What if no response came forth from the floor when Mr. B's order arrived? In such a case the specialist would "Lake the other side," selling 300 shares to Mr. B's broker at a price of$61-~ per share. The actual seller might be the specialist or another investor whose limit order is being executed by the specialist. Sometimes the specialist will "stop" the order, meaning that the order will not be immediately filled but that the specialist will guarantee that a price that is no worse than his or her quote will be obtained for the investor before the day is over. Often such orders are later filled at prices that are better than the quotes that were posted at the time the order was initially received. It is also possible that the specialist will take the other side at $61-k for strategic reasons even though the quote is $61-~. (Sometimes a specialist wants an order to be recorded at a specific price at a given time; for example, a trade at $61-k would make it subsequently easier to execute a short order under the up-tick rule than if the trade were executed at $61-~.) If the bid-ask spread on a stock is no larger than the standard unit in which prices are quoted (typically k of a point, or 6.25 cents, on the NYSE), market orders are generally executed directly by the specialist at the prevailing quote because there is little room for price improvement. In the previous example, if the specialist had quoted bid and asked prices of$61 and $61-k, then there would have been little incentive for Mr. B's commission broker to try to obtain a better price for the purchase order than $61-k, because any seller could have obtained a price of$61 from the specialist. That is, to entice someone other than the specialist to sell GM to Mr. B, his com52

CHAPTER 3

Mr.B

Ma.S Mr. B instructs his broker to buy 300 shares of GM

j

Ms. S instru cts her broker to sell 300 shares of GM

j

Mr.B',

Ma.S', ·

Broker

Brow

j

The buy order goes to the broker's NY office

The sell order goes to the broker's NY office

New York

NewYork

'. Office

S

j

The buy order is sent to the brokerage firm's booth on the NYSE

The sell order is sent to the brokerage firm's booth on the NYSE

The commission broker takes the buy order to "the crowd"

The commission broker takes the sell order to "the crowd"

'--

----mce

1+------./

The Floor of the New York Stock Exchange

Figure 3.1 Order Flow for a NYSE-Listed Security

mission broker would have to offer a better price than $61-the price the seller could obtain from the specialist. Given that the next highest price is $61-16, and that the specialist is willing to sell at that price, Mr. B's commission broker will typically deal with the specialist at the specialist's bid quote rather than deal with "the crowd." (In some instances, the specialist will provide price improvement in 16-point marketsperhaps for strategic reasons-by executing the trade at the opposite side quote, which is $61 in the example. 10) Placing a Limit Order

So far the discussion has been concerned with what would happen to a market order that was placed by Mr. B. What if Mr. B placed a limit order instead of a market order? Consider a buy limit order in which the specialist is quoting GM at $61 bid and $61-~ asked with order quantities of 100 and 500 shares, respectively (the concepts to be illustrated also apply, but in reverse, for a sell order). Three possible situations exist; the limit price associated with a limit buy can be : Security Markets

53

• At or above the asked price of $61-L or • Below the asked price of $61-~ but at or above the bid price of $61, or • Below the bid price of $61. The first case involves a "marketable limit order," meaning that the limit price is not a constraint given the existing bid and asked price quotations. Hence, it will he handled just like a market order because the specialist is willing to fill the order at a price that is at least as favorable as the limit price. For example, a limit buy of 300 shares at $62 would be filled immediately by the specialist at $61-t (or perhaps at an even better price by someone in "the crowd.") In the second case, in which the specialist is quoting prices of $61 and $61-t, assume that Mr. B has placed a limit order with his broker to buy 300 shares of GM at a limit price of $61-A (or $61). When this order is carried to the trading post, the commission broker could execute it for the limit price of $61-A if someone in the crowd (or even the specialist) were willing to take the other side of the transaction. After all, anyone with a sell order can transact with the specialist at the specialist's price of $61. To these people, the limit price of $61-k looks more attractive, because it represents a higher selling price to them. Thus they would prefer doing business with Mr. B's commission broker rather than with the specialist. However, if nobody is willing to trade with Mr. B's commission broker, then his order is recorded in the limit order book by the specialist within 30 seconds of receipt and the bid quote is increased from $61 to $61-k. (If the limit buy order had a limit price matching the specialist's bid of$61, then the quote would now be good for not 100 but 400 shares.) In the third case, assume that Mr. B has placed a limit order to buy 300 shares of GM with a limit price of $60 . When this order is carried to the trading post, the commission broker will not even attempt to fill it, because the limit price is below the specialist's current bid price. That is, because anyone with a sell order can deal with the specialist at a price of $61, there is no chance that anyone will want to sell to Mr. B for the lower limit price of$60. Thus the order will be given to the specialist to be entered in the limit order book for possible execution in the future. (As in the second case, any limit orders that cannot be immediately executed must be entered by the specialist in the book within 30 seconds of receipt.) Limit orders in the book are executed in order of price. For example, all purchase orders with limit prices of $60-~ will be executed before Mr. B's order is executed. If there are several limit orders in the book at the same price, they are executed in order of time of arrival (that is, first in first out). Furthermore, public limit orders take priority over the specialist's order if they are at the same price. It may not be possible to fill an entire order at a single price. For example, a broker with a market order to buy 500 shares might obtain 300 shares at $61-k and have to pay $61-i for the remaining 200. Similarly, a limit order to buy 500 shares at $61-k or better might result in the purchase of 300 shares at $61-k and the entry of a limit order in the specialist's book for the other 200 shares. Large and Small Orders

The NYSE has developed special procedures to handle both routine small orders and exceptionally large orders. In 1976 the NYSE developed an electronic system known as Designated Order Turnaround (or DOT) to handle small orders, defined at that time as market orders involving 199 or fewer shares and limit orders involving 100 or fewer shares. Subsequent developments led to DOT's being replaced by a procedure known as the Super Designated Order Turnaround system (or SuperDOT), which now accepts market orders involving 30,999 or fewer shares and limit orders involving 99,999 or fewer shares. In order to use SuperDOT, the member firm 54

CHAPTER 3

must be a participating subscriber. With this system, the New York office of the customer's brokerage firm can send the customer's order directly to the specialist, whereupon it will be exposed to the crowd and executed immediately (if possible), with a confirmation of the execution sent to the brokerage firm. Although SuperDOT usually sends relatively small market orders directly to the specialist for execution, it has been programmed to send certain other orders directly to the firm's floor brokers for execution." In deciding where to send the order, SuperDOT looks at such things as order size and type of order. For example, market orders and limit orders whose limit price is far from the current quotes of the specialist would be sent directly to the specialist. Each member firm sets the parameters that it wants SuperDOT to use in making such decisions. SuperDOT has greatly facilitated the execution of "basket" trades (a form of "program trading") , in which a member firm submits orders in a number of sec urities all at once. Before SuperDOT, brokers from member firms would carry trade tickets with preprinted amounts that were to be used if the firm suddenly launched a basket trade. These tickets had to be brought by hand to the appropriate trading posts for execution . With SuperDOT, all trades in a basket can be sent simultaneously to the various trading posts on the floor for immediate execution. Exceptionally large orders, which are known as blocks, are generally defined as orders involving at least 10,000 shares or $200,000, whichever is smaller. Typically, these orders are placed by institutional customers and may be handled in a variety of ways. One way of handling a block order is to take it directly to the specialist and negotiate a price for it. However, if the block is large enough, it is quite likely that the specialist will lower the bid price (for sell orders) or raise the asked price (for buy orders) by a substantial amount. This change will be made because specialists are prohibited by the exchange from soliciting offsetting orders from the public and, thus, do not know how easily they can obtain an offsetting order. Even with these disadvantages, this procedure is used on occasion, generally for relatively small blocks, and is referred to as a specialist block purchase or specialist block sale, depending on whether the institution is selling or buying shares. 12 Larger blocks can be handled by the use of an exchange distribution (for sell orders) or exchange acquisition (for buy orders). Here a brokerage firm attempts to execute the order by finding enough offsetting orders from its customers. The block seller or buyer pays all brokerage costs, and the trade price is within the current bid and asked prices as quoted by the specialist. A similar procedure, known as a special offering (for sell orders) or a special bid (for buy orders), involves letting all brokerage firms solicit offsetting orders from their customers. Another way of selling blocks is to conduct a secondary distribution, in which the shares are sold off the exchange after the close of trading in a manner similar to the sale of new issues of common stock. The exchange must give approval for such distributions and usually does so if it appears that the block could not be absorbed easily in normal trading on the exchange. Accordingly, secondary distributions generally involve the sale of exceptionally large blocks. Whereas all of these methods of handling block orders are used at one time or another, most block orders are handled in what is known as the upstairs dealer market. By using block houses, which are set up to deal with large orders, institutions have been able to get better prices for their orders. A block house, when informed that an institution wants to place a block order, will proceed to line up trading partners (including itself) to take the other side of the order. Once the trading partners have been identified, the block house will attempt to reach a mutually acceptable price with the original institution. If such a price is reached, the order wiIl be "crossed" on the floor of the exchange, meaning that the specialist wiIl be given the opportunity to fill any limit orders that are in the specialist's book at the block's selling price.P (If such a Security Markets

55

price is not reached, the institution can take the order to a different block house.) However, there is a limit on the number of shares (1,000 shares or 5% of the size of the block, whichever is greater) that can be taken by the specialist to fill these limit orders. For example, suppose that the PF Pension Fund informs a block house that it wishes to sell 20,000 shares of General Motors common stock. The block house then proceeds to find three institutional investors that want to buy, say, 5,000 shares apiece; the block house decides that it too will buy 5,000 shares of GM from PF. Noting that the buyers have said that they would be willing to pay $70 per share, the block house subsequently informs PF that it will buy the 20,000 shares for $69.75 each, less a commission of $8,000. If PF accepts the deal, the block house now becomes the owner of the shares but must first "cross" them on the NYSE because the block house is a member of the exchange. In this example assume that when the block is crossed at $69.75, the specialist buys 500 shares at this price for a limit order that is in his or her book. After the cross, the block house gives 5,000 shares to each of the institutional buyers in exchange for $350,000 (= 5,000 shares X $70 per share) and hopes that the remaining 4,500 shares that it now owns can be sold in the near future at a favorable price. Needless to say, the possibility of not being able to sell them at a favorable price is one of the risks involved in operating a block house.

3.2.2 Other Exchanges Table 3.2 shows the total trading volume of the securities listed on each of the active stock exchanges in the United States in 1996. Not surprisingly, the New York Stock Exchange dominates the list. Second in importance is the American Stock Exchange (AMEX), which lists shares of somewhat smaller companies of national interest (a few of which are also listed on the New York Stock Exchange) . All the others are termed regional exchanges, because historically each served as the sole location for trading

TABLE

3.2

'D"adfngVOlume of the Stock Exchanges

(a) 1996 Trading Volume

I

Annual NYSE Regiona1s

104,636 5.627 9,794

Nasdaq

138,112

AMEX

Third market

I

Shares (millionsl

7,486

"

Dally

Annual $4,063,655 91,530 380,345 3,301,777 290,727

Dally 412 '

Dollars (millionsl

22 39

M4 29

$15,999

360 1,497 12,999 1,145

[b] Five-Year Comparison

I Number of

1-

Year 1996 1995 1994 1993 1992

I

NYSE

Companies 2,907 2,67~.

2,570 ,2,361 2,088

Number of IssueS 3,285 3,126 3.060 2,904 2,658

Dally Shale , Volume (millions' 412 346 291 265 202

Nasdaq

Number of

Number of

Companies

Issues

5,556

6,384 5,955 5,761 5,393 4,764

5,122 4,902

.,611 4,113

Dally Share Volume (milnons, 544 401 295 263 191

Source: Adapted from Faa BooI. 1997) ,

S6

CHAPTER 3

securities primarily of interest to investors in its region. However, the major regional exchanges now depend to a substantial extent on transactions in securities that are also listed on a national exchange. Interestingly, the regional exchanges are now larger, in aggregate, than the AMEX. There are five major regional exchanges currently in existence-the Boston, Cincinnati, Chicago, Pacific , and Philadelphia exchanges-and they all use procedures similar to those of the New York Stock Exchange. The role of specialists and the extent of automation may differ slightly, but the approach is basically the same. Options exchanges and futures exchanges utilize some procedures that differ significantly from those employed by stock exchanges. Futures exchanges often have daily price limits instead of having specialists with directions to maintain "fair and orderly markets." The Chicago Board Options Exchange separates the two functions of the specialist: An order book official is charged with the maintenance of the book of limit orders, and one or more registered market-makers are assigned the role of dealer. These exchanges will be discussed in more detail in Chapters 19 and 20.

3.2.3 Over-the-Counter Market In the early days of the United States, banks acted as the primary dealers for stocks and bonds, and investors literally bought and sold securities "over the counter" at the banks. Transactions are more impersonal now, but the designation remains in use for transactions that are not executed on an organized exchange but, instead, involve the use of a dealer. Most bonds are sold over the counter, as are the securities of small (and some not so small) companies. Nasdaq

The over-the-counter (OTC) market for stocks is highly automated. In 1971 the National Association of Securities Dealers (NASD), which serves as a self-regulating agency for its members, put into operation the National Association of Securities Dealers Automated Quotations system (Nasdaq) . This nationwide communications network allows brokers to know instantly th e terms currently offered by all major dealers in securities covered by the system. Dealers who subscribe to Level III of Nasdaq are given terminals with which to enter bid and asked prices for any stock in which they "make a market." Such dealers must be prepared to execute trades for at least one "normal unit of trading" (depending on the security, this can be as large as 1,000 shares) at the prices quoted. As soon as a bid or an asked price is entered for a security, it is placed in a central computer file and may be seen by other subscribers (including other dealers) on their own terminals. When new quotations are entered, they replace the dealer's former prices. When there is competition among dealers, those who are not well informed either price themselves out of the market by having too wide a bid-ask spread, or go out of business after incurring heavy losses. 14 In the first situation, nobody does business with such a dealer, because there are better prices available with other dealers. The second situation occurs when the dealer accumulates a large inventory at too high a price or disposes of inventory at too Iowa price. Thus the dealer will be doing the opposite of the familiar advice of "buy low, sell high." It is argued that the interests of investors are best served by a market in which multiple dealers with unlimited access to all sources of information compete with one another, thereby leading to narrow bid-ask spreads around the "intrinsic" value of the security that provide investors with the "best" prices. However, organized exchanges counter with the argument that their system produces the "best" prices because all orders are sent to a central location for execution where they can be matched and bid on. Whereas trades in the over-the-counter market take place at the "best" Security Markets

57

quoted prices, the exchanges note that, although they have only one source of quoted prices (from the specialist), trades can (and often do) take place "inside" these prices. Thus, the exchanges argue that, unlike Nasdaq, they provide investors with the chance for "price improvement." Most brokerage firms subscrihe to Level II of Nasdaq for their trading rooms, obtaining terminals that can display the current quotations on any security in the system . All bid and asked quotations are displayed, with the dealer offering each quotation being identified, so that orders can be routed to the dealer with the best price. Imagine how difficult it would be to get the best price for a customer in the ahsence of such a terminal (as was the case before Nasdaq existed). A broker would have to contact dealers one by one to try to find the best price. After determining what appeared to be the best price, the broker would then proceed to contact that dealer again. However, by the time the dealer was contacted, the price might have gone up or down and the previously quoted price might no longer be the best one. Level I of Nasdaq is used by individual account executives to get a feel for the market. It shows the inside quotes, meaning the highest bid and the lowest asked price for each security, along with last-sale reports and market summary data. Sometimes the inside quotes are known as the NBBO, an abbreviation for "national best bid or offer." (Offer price is often used instead of asked price in reference to the price at which dealers are willing to sell, or "offer," a specific security.) Nasdaq classifies stocks with larger trading volumes (which also meet certain other requirements) as belonging to the National Market System (Nasdaq/NMS). Every transaction made by a dealer for such a stock is reported directly, providing upto-date detailed trading information to Nasdaq users. Furthermore, any stock included in Nasdaq/NMS is automatically eligible for margin purchases and short selling. Less active issues belong to the Small Cap Issues (Nasdaq Small Cap) section of Nasdaq; these issues generally are automatically "phased into" the National Market System when they meet the higher listing standards of NMS. For these issues, dealers report only the total transactions at the close of each day, and only certain ones are eligible for margin purchases and short sales. (The Federal Reserve Board determines which ones are eligible four times a year.) As its name indicates, Nasdaq is primarily a quotation system. The price paid by a customer buying shares is likely to be higher than the amount paid by the broker to procure the shares, with the difference being known as a markup when the broker's firm is acting as a principal (that is, the broker's firm is also a dealer who sells the shares out of inventory). Conversely, when selling shares, the customer receives a price less than that received by the broker, with the difference being known as a markdown when the broker's firm is acting as a principal. However, if the broker's firm is acting as an agent, meaning the broker is executing the order with a dealer who works for a different firm, then the customer will be charged a commission. The sizes of these markups, markdowns, and commissions are examined periodically by the Securities and Exchange Commission to see that they are "reasonable." To be included in Nasdaq, a security must have at least two registered market-makers (that is, dealers) and a minimum number of publicly held shares. Moreover, the issuing firm must meet stated capital and asset requirements. As shown in Table 3.2, at the end of 1996,6,384 issues were included in the system." Although this total is more than double the total for the NYSE, trading volume is less than that of the NYSE, especially when measured in dollars.

SOES During the market crash of October 19, 1987, many investors who placed orders involving Nasdaq stocks were unable to receive execution because their brokers were 58

CHAPTER 3

unable to get in touch by telephone with the appropriate dealers. As a result, NASD established the Small Order Execution System (SOES), an electronic order-routing system in which all Nasdaq dealers must participate. With SOES, brokers can electronically route a customer's order to the appropriate dealer for quick execution and confirmation . Large orders are typically not handled through SOES, as dealers are required only to accept orders as large as 1,000 shares. (Currently, the limit is 100 shares for 50 large Nasdaq/NMS stocks but 1,000, 500, and 200 shares for the remainder of the Nasdaq stocks, depending on trading volume, number of dealers, and best bid price.) Instead, most large orders involving Nasdaq stocks are handled by negotiation over the telephone with one of the dealers.

aTe Bulletin

Board and Pink Sheets Stocks

The Nasdaq system covers only a portion of the outstanding OTC stocks. Brokers with orders to buy or sell other OTC securities rely on quotations that are published daily either on Nasdaq's OTC Bulletin Board or in what are known as Pink Sheets (there are also less formal communication networks) in order to obtain "best execution" for their clients. The OTC Bulletin Board is essentially an electronic quotation forum run by Nasdaq, where brokers and dealers can find current price quotes, trading data, and a list of market-makers in several thousand securities. Although companies that are on the Bulletin Board typically cannot meet Nasdaq's listing standards (they still must meet some less-demanding standards), they must file quarterly financial statements with the SEC, banking, or insurance regulators (such filing was made mandatory only in late 1997). Pink Sheets are published daily by the National Quotation Bureau, an organization unaffiliated with Nasdaq. They also contain dealer quotations in thousands of unlisted stocks but, unlike the OTC Bulletin Board, they do not contain any trading data. Trading in both OTC Bulletin Board and Pink Sheet stocks takes place over the phone rather than electronically.

3.2.4 Third and Fourth Markets Until the 1970s the New York Stock Exchange required its member firms to trade all NYSE-listed stocks at the exchange and to charge fixed commissions. For large institutions, meeting this requirement was expensive. In particular, the existence of a required minimum commission rate created a serious problem, because it exceeded the marginal cost of arranging large trades. Brokerage firms that were not members of the exchange faced no restrictions on the commissions they could charge and thus could compete effectively for large trades in NYSE-listed stocks. Such transactions were said to take place in the third market. More generally, the term third market now refers to the trading of any exchange-listed security in the over-the-counter market. The existence of such a market is enhanced by the fact that its trading hours are not fixed (unlike exchanges) and sometimes it can continue to trade securities even when trading is halted on an exchange. As can be seen in Table 3.2 , on average , 29 million shares were traded in the third market during each day of 1996. Instinet and SelectNet

Many institutions have dispensed with brokers and exchanges altogether for transactions in exchange-listed stocks and other securities. Trades of this type, in which the buyer and seller deal directly with each other, are sometimes said to take place in the fourth market. In the United States some of these transactions are facilitated by an automated computer communications system called Instinet, which provides quotations and execution automatically. 16 A subscriber can enter a limit order in the Security Markets

59

computerized "book," where it can be seen by other subscribers who can, in turn, signal their desire to take it. Whenever two orders are matched, the system automatically records the transaction and sets up the paperwork for its completion. Subscribers can also use the system to find likely partners for a trade, then conduct negotiations by telephone. This facility grew in popularity because it allowed institu tio ns to trade securities inside the bid-ask quotes established by dealers. Interestingly, many dealers trade through either Instinct, or a dealer-only computer network called SelectNet, in order to cheaply manage their inventories while at the same time maintaining standard bid-ask quotes for their customers. In order to enhance the competitiveness of dealers' quoted prices, since 1997 orders posted on Instinet and SelectNet have also been made available to the public.

Crossing Systems

In recent years automated electronic facilities have been developed to permit institutional investors to trade portfolios of stocks, rather than individual securities, directly with each other. The two largest such systems are POSIT and the Crossing Network. They are discussed in this chapter's Institutional Issues: Crossing Systems. Some large investment managers maintain their own internal crossing systems . These managers invest billions of dollars for many institutional clients. On any given day, some clients will be withdrawing funds from such a manager and other clients will be contributing funds. The manager simply exchanges the contributing client's cash for shares from the withdrawing client, with the shares typically valued at closing market prices on the day of the "cross." A nominal commission is charged to handle the transactions.

3.2.5 Preferencing Preferencing is a practice that can be thought of as taking orders and sending them for execution along a predetermined route. More specifically, whenever a preferencing broker receives an order involving a particular stock, he or she has a standing arrangement with a dealer to send the order to him or her for execution.

Payment for Order Flow

Payment for order flow refers to the practice of preferencing in which a dealer pays cash to a broker in order to have that broker's order flow sent to the dealer for execution . If Ms. Beyer places an order to buy 100 shares of Widget with her broker, the broker will send the order to Acme Brokerage for execution, provided there is a preexisting arrangement with Acme to preference all orders involving Widget to Acme. How does this arrangement benefit Ms. Beyer's broker? The broker will receive a cash payment for the order of, generally, about $.01 or $.02 per share. This amount may seem small, but when aggregated over many orders it can accumulate to a sizable sum. Payment for order flow can be thought of as paid{orpreferencing. 17 Often when listed securities are involved, the order is executed on a regional exchange (Cincinnati, Boston, and Chicago are popular ones for preferencing). When Ms. Beyer's order to buy 100 shares of Widget is sent to Acme for execution, her broker will receive $1 from Acme because of their payment-for-order-flow arrangement. In return, Acme will check the NYSEquotes in order to determine the current ask and then will

60

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execute the order from its own inventory at that price on, for example, the Cincinnati Stock Exchange. Alternatively, if Widget is listed on Nasdaq instead of the NYSE, then Acme will execute the order at the inside quote (that is, the lowest ask). Given that the bid and asked prices are competitively set, one might wonder how Acme can afford to pay for order flow. The answer can be found in the Glosten-Milgrom adverse selection model, which will be presented shortly. For the moment, note that preferenced orders usually are small retail orders, and the dealer has little worry about transacting with informed traders who might possess valuable information about the particular stocks being bought or sold. By "cream skimming" these lowrisk orders, Acme can afford to pay for order flow, as the current bid-ask spread more than compensates it for the risk involved. Acme can settle for a lower net spread (that is, the spread after payment for order flow) than the spread being quoted on the NYSE (or Nasdaq) and still make money.

Internalization

Until 1976 NYSE member firms were prohibited by Rule 394 from either acting as dealers in the third market or executing orders involving NYSE-listed securities for their customers in the third market. In 1976 Rule 394 was replaced by Rule 390, which permits the execution of orders for NYSE-listed stocks in the third market but still prohibits member firms from acting as dealers in the third market. In 1979 the Securities and Exchange Commission issued Rule 19c-3, permitting member firms to act as dealers in securities that became listed on the NYSE after April 26, 1979. This rule has lead to the practice of internalization, in which broker-dealers who are NYSE members take their customers' orders in 19c-3 stocks and fill them internally instead of sending them to an exchange floor for execution. Internalization can also involve broker-dealers who are not NYSE members and who can execute their customers' orders in any NYSE-listed stock internally. Furthermore, Nasdaq stocks can be internalized when customers' orders are filled by a brokerage firm in its dual role as a dealer instead of sending the trades to other dealers. Thus, internalization can be thought of as preferencing orders tooneself since the orders never make it out of the customer's brokerage firm for execution.l'' Controversy still exists over Rules 394 and 19c-3. Some people argue that they should be abolished completely to spur competition between the NYSE and the overthe-eounter market. Others argue that having all orders funneled to the NYSE will lead to the most competitive marketplace possible.

Criticisms of Preferencing

Laws concerning best execution require the dealer who receives a preferenced order to at least match the best price that is currently being publicly quoted. Nevertheless, critics of preferencing contend that the customer may still be disadvantaged. If the order were taken to the exchange floor instead of being preferenced, the trade might be executed within the specialist's quotes. However, because the dealer executes a preferenced order at the current market quotes, no opportunity exists for the customer to benefit from price improvement. There is a potential social cost to preferencing as well. A preferenced order contributes nothing to the process of price discovery; that is, the incorporation of new and valuable information about a security into its price. It is the interplay of market participants that leads to price discovery. Brokers seeking the best prices for their orders determine the supply and demand functions, and ultimately the market-

Security Markets

61

INSTITUTIONAL ISSUES

Crossing Systems: Evolution of the Fourth Market Scientists define the evolution ofa species as its gradual adoption of features that facilitate its long-term survival. In this context it is fitting to refer to the evolution of the fourth market. From its rudimentary beginnings , the fourth market has evolved into a sophisticated trading mechanism in which millions of shares change hands daily. Furthermore, the fourth market is posing a threat to existing species, in this case the organized security exchanges. How this competition plays out will influence the nature of trading well into the twenty-first century. The fourth market, where large institutional investors deal directly with one another, began as a response to the high commission rates charged by brokerage firms . As discussed in the text, the original fourth market trading mechanism, run by Instinet, allows investors to trade with each other through an automated communications system at commissions that were originally only a small fraction of those charged by brokers. However, this trading process (which is still very much alive and well) has significant limitations. Investors submit buy or sell limit orders (see Chapter 2) on individual securities at irregular times. If an interested investor on the "other side" of the trade happens to acces s the system at the right time, the trade may be completed. Although the commission costs oftrading on the original fourth market are quite low (about $.03 to $.04 per share) . the odds of being able to complete large trades in numerous securities are small. What was needed was a system to allow institutional investors to trade entire portfolios instead of individual stocks. The fourth market evolved to accommodate this need through a mechanism generically known as a "crossing system." Several electronic crossing systems now conduct regular market sessions in which investors may submit large packages of securities for trade. More specifically, current crossing systems work as follows: 1. Periodic trading sessions are established and wide-

lyannounced.

2. Before these trading sessions, investors anonymously submit lists of stocks they wish to buy or sell and the associated quantities. 3. At scheduled times during the day, the lists of desired trades are compared automatically by computer. 4. Trade prices are based on current market prices as set on th e organized security exchanges or the OTC market. 5. Offsetting buys and sells are matched. When buy orders do not equal sell orders for a security, matches are allocated on the basis of the total dollar value of trades entered by each investor. Thus investors are encouraged to submit large trading volume requests. 6. Investors are notified ofthe completed trades, and the system handles the transfer of stocks. 7. Unmatched trades are returned to the investors for resubmission or execution elsewhere . Crossing systems offer investors several key advantages over traditional trading methods. First, they provide anonymity. Investors' identities or intentions are not revealed , making it extremely difficult for other investors or market-makers to strategize against them . Second. as discussed, investors can trade entire portfolios at one time instead of individual securities on a piecemeal basis. Third, and most important, crossing networks are low-cost portfolio trading mechanisms . The primary users of crossing networks are institutional investors with no urgent need to trade. Index funds (see chapter 23), for example, trade only to adjust their portfolios so as to track the performance of a specific market index most effectively. Whether they trade this morning or this afternoon usually has little bearing on their results. Therefore, transaction costs are their primary concern. Crossing systems charge only $.01 to $.02 per share (as opposed to the $.03 to $.12 charged to institutional investors by brokerage firms) . Furthermore, because trades are carried out at prevailing market prices, crossing systems

clearing price, for a particular security. (Price discovery is further discussed in Chapter 4). A preferencing broker, however, plays a purely passive role,letting others set the security's price. The situation is somewhat analogous to voting in an election. Each individual's vote, by itself, has little meaning. In aggregate, however, all the votes cast determine the election's outcome. A nonvoter passively accepts this outcome, without adding his or her opinion to the contest. 62

CHAPTER 3

permit investors to avoid both the costs associated with the bid-ask spread as well as the price impacts (discussed later in this chapter) of their trades. Crossing systems present some serious disadvantages as well. They do not offer liquidity in many stocks. Investors may not be able to complete trades in certain securities even after days of submitting those securities to the crossing networks. This problem is particularly acute for smaller-capitalization OTC stocks . In addition, the crossing systems require a certain amount of technological sophistication. Investors must submit trades computer to computer. Trading packages must be readied for entry at the appropriate times, and arrangements must be made for handling trades that cannot be completed through the crossing systems. Currently, the two largest crossing systems are POSIT (run by Investment Technology Group) and the Crossing Network (run by Instinet) . The two systems work under the same basic procedures described earlier, although there are differences. For example , the Crossing Network conducts one session daily, in the early evening on the basis of NYSE closing market prices . POSIT, on the other hand, conducts six daily crosses, three in the morning [with one of those devoted solely to trades in a type of foreign security known as American Depositary Receipts (see Chapter 25) 1 and three in the afternoon, based on prices prevailing in the market at the time of the crosses. When both began operations in 1987, their trading volumes were insignificant. In subsequent years, however, volumes have increased. In 1996, more than 10 million shares a da y on average changed hands through the crossing systems. (POSIT's trading volume was roughly twice that of the Crossing Network.) Although this figure translates into only about 2% of the New York Stock Exchange's daily volume, the potential for the crossing systems' long-term growth has created concern among members of the organized exchanges and OTC dealers. The success of POSIT and the Crossing Network

prompted several brokerage firms to attempt their own crossing operations. The NYSE has also entered the fray with two after-hours crossing systems. However, none of these organizations have been able to attract anywhere near the volume achieved by the original crossing systems. Trading systems tend to be natural monopolies. Traders loathe fragmented markets, which reduce their chances of finding the other side. Instead they prefer that trading be concentrated in a small number of markets, thereby enhancing liquidity. The NYSE dominates the continuous auction market. POSIT and the Crossing Network (and perhaps eventually only one of them) dominate the crossing system market. Many institutional investors have become sophisticated users of alternative trading mechanisms. For example, just after the NYSE's opening, an investor might send limit orders for a large set of stocks via the SuperDOT system (see this chapter) for immediate execution. The investor shortly thereafter withdraws uncompleted orders and submits them to POSIT for late morning and early afternoon crosses. Orders still unfilled are placed on the Crossing Network for that evening's session. Finally, the investor directs any orders still outstanding through traditional broker networks the next day. The trading mechanisms available to institutional investors continue to grow as their per unit trading costs continue to fall. Crossing syste ms have played an important role in these declining costs. Crossing systems are beginning to conduct global operations. Given that transaction costs on foreign markets are usually many times greater than they are in the United States, the room for crossing system growth in those markets appears enormous, Opportunities for growth also exist in the retail market, where investors typically pay much higher commission costs than do institutional investors. Brokers may eventually bundle their clients' trades and submit them through the crossing systems, thus saving commissions and allowing trades within the dealers' spreads rather than at the bid or asked prices. Inexorably, the evolution of the fourth market continues.

3.2.6 Foreign Markets The two largest stock markets in the world outside New York are located in London and Tokyo. Both of these markets have recently undergone major changes in their rules and operating procedures. Furthermore, both of them have active markets in foreign securities. In particular, at the end of 1996 the London Stock Exchange listed 533 foreign companies (in addition to 2,171 U.K. and Irish Security Markets

63

companies), and the Tokyo Stock Exchange listed 63 foreign stocks (in addition to 1,805Japanese stocks). Also of interest is the Toronto Stock Exchange, which by market value of securities listed is the fifth largest foreign stock market in the world (after Tokyo, London, Paris, and Frankfurt, according to the Tokyo Stock Exchange 1993 FactBook, p. 83). Its electronic trading system has been adopted by many foreign markets, either directly (by Paris) or indirectly (by Tokyo). At the end of 1996 the Toronto Stock Exchange listed 1,626 stocks, about 100 of which were foreign stocks. London

In October 1986 the "Big Bang" introduced several major reforms to the London Stock Exchange. Fixed brokerage commissions were eliminated, membership was opened up to corporations, and foreign firms were allowed to purchase existing member firms. Furthermore, an automated dealer quotation system similar to Nasdaq was introduced. This system, known as SEAQ (Stock Exchange Automated Quotations), involves competing market-makers whose quotes are displayed over a computer network. Small orders can be executed by using SAEF (SEAQAutomated Execution Facility), which functions like Nasdaq's SOES; large orders are handled over the telephone. Limit orders are not handled centrally but instead are handled by individual brokers or dealers who note when prices have moved sufficiently that they can be executed. The London Stock Exchange's reforms have proved highly successful. The exchange has attracted trading in many non-U .K. stocks, thereby enhancing its status as the dominant European stock market. Even the U.S. stock markets have felt the competition. In an attempt to recapture some of the lost trading in U.S. securities from the London Stock Exchange, the NASD received approval from the SEC for a computer system like Nasdaq, which involves trading of many of the stocks listed on either the NYSE, AMEX, or Nasdaq/NMS. This system, known as Nasdaq International, opens for trading six hours before the NYSE, which corresponds to the opening time of the London Stock Exchange, and closes a half-hour before the NYSE opens. Tokyo

Similar to the London Stock Exchange, the Tokyo Stock Exchange has recently experienced major reforms. CORES (Computer-assisted Order Routing and Execution System), a computer system for trading all but the 150 most active securities, was introduced in 1982 . Then in 1986 the exchange began to admit foreign firms as members, and in 1990 FORES (Floor Order Routing and Execution System) was introduced as a computer system to facilitate trading in the most active stocks. Interestingly, the system of trading both the most active and the relatively less active securities is quite different from any system found in either the United States or the United Kingdom. It is centered on members known as saitoriwho act, in a sense, as auctioneers in that they are neither dealers nor specialists. Instead they are intermediaries who accept orders from member firms and are not allowed to trade in any stocks for their own account. At the opening of the exchange (because the exchange is open from 9 A.M. to 11 A.M. and from 12:30 P.M. to 3 P.M., there are two openings each day) the saitori members follow a method called itayose, which operates like a call market in that the saitori seeks to set a single price so that the amount of trading is maximized (subject to certain constraints). Setting the price effectively involves constructing supply and demand schedules for the market and limit orders that have been received and noting where the two schedules intersect. (How this is done is described and illustrated in Chapter 4.) After the opening of the exchange, the saitori follows a method known 64

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as zaraba, wherein orders are processed continually as they are received; that is, market orders are offset against previously unfilled limit orders. New limit orders are filled, if possible, against previously unfilled limit orders. New limit orders that cannot be filled are entered in the limit order book for possible future execution. Unlike the limit order book on the NYSE, the limit order book in Tokyo is available for inspection by member firms. Furthermore, unlike the NYSE, the Tokyo Stock Exchange prohibits trading at prices outside a given range based on the previous day 's closing price. Hence there can be situations in which trading in a stock ceases until the next day (when the price range is readjusted) unless two parties decide to trade within the current range. Toronto

In 1977 the Toronto Stock Exchange began to use CATS (Computer-Assisted Trading System) on a trial basis with 30 stocks. Two years later CATS was expanded to cover about 700 stocks and was made permanent. All other listed stocks were traded in a specialist-driven system like the one in New York. However, the success of CATS led to more and more stocks being included so that, now, all listed stocks are traded on it. Furthermore, CATS now utilizes decimal pricing; stocks priced above $5 trade in $.05 increments and those priced below $5 trade in $.01 increments. With CATS, orders are entered electronically in brokers' offices and then routed to a computer file. This computer file displays limit orders against which other investors may trade. Market orders are matched against the limit order with the best price that is in the file (that is, a market order to buy is matched against the lowest priced limit order to sell, and a market order to sell is matched against the highest priced limit order to buy). If insufficient volume is available in the file at the best price, the remainder of the market order is then put in the file as a limit order at that price. However, brokers, responding to the wishes of the investor, can change this price at any time. At the daily opening CATS uses a different procedure. Like itayose in Tokyo, CATS sets an opening price so as to maximize the number of shares that are traded. Although both market and limit orders are accepted, there are constraints on the size of each market order, and these orders must be from the public (meaning that member firms are not allowed to submit opening market orders).

II1II

INFORMATION-MOTIVATED

AND LIQUIDITY-MOTIVATED TRADERS

Perhaps the single major concern of a dealer is the adverse consequences he or she experiences as a result of buying or selling from an informed trader. When a trader approaches a dealer, the dealer cannot tell whether the trader knows something about the stock that he or she does not know. That is, the dealer cannot tell whether the trader has an information advantage. However, the dealer understands that if the trader is informed, then it is likely that any information will soon be disseminated that is good news for the stock if the informed trader bought it and is bad news if the informed trader sold it. For example, assume that the bid and asked quotes for Widget are $20 and $21 and an informed trader (remember that at this point the dealer does not know whether the trader is informed) arrives and sells 1,000 shares to the dealer at $20. Typically, a negative piece of information about the company will be released shortly thereafter that will cause the dealer to lower his or her quotes to, say, $18 and $19 . Thus, the dealer hasjust bought 1,000 shares for $20 but now is offering and likely Security Markets

65

will sell them for $19, a potential loss of$I,OOO. (In this example it is also assumed that the dealer cannot quote an asked price of $20 because there are other dealers who would undercut him or her at that price.) Conversely, if an informed trader arrives and buys 1,000 shares at $21, typically there will be a positive piece of information an no u nced shortly thereafter that will cause the dealer to raise his or her quotes to, say,$22 and $23, resulting in an opportunity loss of $1 ,000. In both of these cases, the dealer has been "picked off' by informed traders, losing money in the process. So how does the dealer earn a profit? By transacting with uninformed traders, because their trades are not consistently followed by news of any particular type. After an uninformed trader buys 1,000 shares when the quotes are $20 and $21, it is equally possible that good or bad information (if any) about the stock will be released. The dealer, on average, will not be adversely affected by transacting with an uninformed trader. Consequently, the dealer will set a spread so that his or her expected losses from dealing with informed traders equals his or her expected gains from dealing with uninformed traders. In the language of financial economists, the dealer copes with this adverse selection problem by setting a spread so that the losses from trading with information-motivated traders are offset by the gains from trading with liquidity-motivated traders (so called because they either have excess cash to invest in stocks or else need cash and hence sell stocks to raise it) .19 The Glosten-Milgrom adverse selection model illustrates just how the spread is set. Imagine that the dealer believes there is a 40% probability that Widget stock is worth $10 and a 60% probability that it is worth $20. Hence, its expected value is $16 [= (.4 X $10) + (.6 X $20)] . Furthermore, 10% of all traders are informationmotivated in that they know what the stock is worth (they know whether it is worth $10 or $20), while the remaining 90% are not information-motivated. The dealer must set his or her asked price A at a level that will ensure that expected losses equal expected gains: .1 X .6 X ($20 - A) = .9 X .5 X (A - $16) or A = $16.47

The left-hand side of this equation shows that there is a 10% chance that an information-motivated trader will arrive and a 60% chance that he or she will buy. The loss on the trade with such an investor is $20 - A, so the expected loss with an asked price of$16.47 is $.21 [= .1 X .6 X ($20 - $16.47)]. On the right-hand side, there is a 90% chance that a liquidity-motivated trader will show up, and a 50% chance that he or she will buy. The gain on the trade with this investor is A - $16, so the expected gain with an ask price of $16.47 is $.21 [=.9 X.5 X ($16.47 - $16)]. Thus, the $.21 expected loss from selling to an information-motivated trader is exactly offset by the $.21 expected gain from selling to a liquidi ty-motivated trader when the asked price is set at $16.47. Similarly, the bid price B is set so that the expected losses from buying from the information-motivated investor equals the expected gains from buying from the liquidity-motivated trader: .1 X.4 X (B - $10) = .9 X .5 X ($16 - B) or B = $15.51

Thus, the spread is $16.47-$15.51, or $.96. If it is wider, the dealer will not get any business because of competition from other dealers (or will get business on just one side-either buying a lot of shares or selling a lot of shares). If it is narrower, then 66

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the dealer will likely be put out of business by too many losses from transacting with information-motivated traders." Although this model does not explicitly provide for the dealer's making a profit, that feature is easily accommodated by simply expanding the $.96 spread by an amount sufficient for the dealer to cover costs and earn a reasonable profit on his or her investment in inventory. However, competition among dealers will continue to limit the size of the spread and, hence, profits. One feature of this model is that the larger the proportion of informed traders, the larger the spread. For exam p le, in the above example if that proportion is 20% instead on 10%, then the asked and bid prices will be $16.92 and $15 .00, respectively, for a spread of $1.92 instead of $.96. Intuitively, this makes sense because there is now a greater likelihood that the dealer will be "picked off' by an informed trader.

111m

CENTRAL MARKET

The Securities Acts Amendments of 1975 mandated that the U.S. Securities and Exchange Commission move as rapidly as possible toward the implementation of a truly nationwide competitive central security market: The linking oj all markets for qualified securities through communication and data processingfacilities willfoster efficiency, enhance competition, increasethe information available to brokers, dealers, and investors, jacilitate the offsetting of investors' orders, and contribute to best execution ojsuch orderS. 21

Implementation of these objectives has proceeded in steps. In 1975 a consolidated tape began to report trades in stocks listed on the New York and American stock exchanges that took place on the two exchanges, on major regional exchanges, in the over-the-counter market using the Nasdaq system, and in the fourth market using the Instinet system. Since 1976 this information has been used to produce the composite stock price tables published in the daily press. The second step involved the setting of commissions charged to investors by brokerage firms that are members of the NYSE. Before 1975 the NYSE required its members to charge all investors the same commission for a given order. However, as a result of the Securities Acts Amendments of 1975, this system of fixed commissions was abolished and all brokerage firms were free to set their commissions at whatever level they desired. The next step involved quotations. To obtain the best possible terms for a client, a broker must know the prices currently available on all major markets. To facilitate this objective, the Securities and Exchange Comm ission instructed stock exchanges to make their quotations available for use in the Consolidated Quotations System (CQS). With the implementation of this system in 1978, bid and asked prices (along with the corresponding volume limits) were made more accessible to subscribers to quotation services. Increasingly a broker is able to rely on electronics to determine the best available terms for a trade, thus avoiding the need for extensive "shopping around ." In 1978 the Intermarket Trading System (ITS) was inaugurated. This electronic communications network links eight exchanges (NYSE,AMEX, the Boston, Cincinnati, Chicago, Pacific, and Philadelphia stock exchanges, and the Chicago Board Options Exchange) and certain over-the-counter security dealers, thereby enabling commission and floor brokers, specialists, and dealers at various locations to interact with one another. Intermarket Trading System display monitors provide the bid and asked prices quoted by market-makers (these quotes are obtained from CQS), and the system allows the commission and floor brokers, specialists, and dealers to Security Markets

67

route orders electronically to where the best price exists at that moment. However, the market-maker providing the best price may withdraw it on receipt of an order. Another drawback is that the customer's broker is not required to route the order to the market-maker providing the best price. At the end of 1996, according to the NYSE FactBook 1996 Data (p. 28), 4,001 exchange-listed stocks were included on the system, and daily trading volume averaged 12.7 million shares. In 1996 the SEC passed a series of in itiatives known as order handling rules. Among other things, these rules required that (1) the NASD establish a central limit order book for investors and (2) quotations posted on electronic communication networks (ECNs) be made available to all investors; previously, ECNs such as 1nstinet and SelectNet had made their quotations available to only certain investors such as institutions or dealers.

__

CLEARING PROCEDURES Most stocks are sold the "regular way," which requires delivery of certificates within three business days. On rare occasions a sale may be made as a "cash" transaction, requiring delivery the same day, or as a "seller's option," giving the seller the choice of any delivery day within a specified period (typically, no more than 60 days) . On other occasions extensions to the three-day time limit are granted. It would be extremely inefficient if every security transaction had to end with a physical transfer of stock certificates from the seller to the buyer. A brokerage firm might sell 500 shares of AT&T stock for one client, Mr. S, and later that day buy 500 shares for Ms. B, another client. Mr. S's 500 shares could be delivered to his buyer, and Ms. B's shares could be obtained by accepting delivery from her seller. However, it would be much easier to transfer Mr. S's shares to Ms. B and instruct Ms. B's seller to deliver 500 shares directly to Mr. S's buyer. This route would be especially helpful if the brokerage firm's clients, Mr. S and Ms. B, held their securities in street name. Then the 500 shares would not have to be moved and their ownership would not have to be changed on the books of AT&T. The process can be facilitated even more by a clearinghouse, the members of which are brokerage firms, banks, and other financial institutions. Records of transactions made by members during the day are sent there shortly afterward. At the end of the day, both sides of the trades are verified for consistency, then all transactions are netted out. Each member receives a list of the net amounts of securities to be delivered or received along with the net amount of money to be paid or collected. Every day each member settles with the clearinghouse instead of with various other firms. By holding securities in street name and using clearinghouses, brokers can reduce the cost of transfer operations. But even more can be done: Certificates can be immobilized almost completely. The Depository Trust Company (DTC) immobilizes certificates by maintaining computerized records of the securities "owned" by its member firms (brokers, banks, and so on). Members' stock certificates are credited to their accounts at the DTC, while the certificates are transferred to the DTC on the books of the issuing corporation and remain registered in its name unless a member subsequently withdraws them. Whenever possible, one member will "deliver" securities to another by initiating a simple bookkeeping entry in which one account is credited and the other is debited for the shares involved. Dividends paid on securities held by the DTC are simply credited to members' accounts on the basis of their holdings and may be subsequently withdrawn from the DTC in cash. 68

CHAPTER 3

__

INSURANCE

The Securities Investor Protection Act of 1970 established the Securities Investor Protection Corporation (SIPC), a quasigovernmental agency that insures the accounts of clients of all brokers and members of exchanges registered with the Securities and Exchange Commission (SEC) against loss due to a brokerage firm's failure. Each account is insured up to a stated amount ($500,000 per customer in 1998). The cost of the insurance is supposed to be borne by the covered brokers and members through premiums. Should this amount be insufficient, the SIPC can borrow up to $1 billion from the U.S. Treasury. A number of brokerage firms have gone further, arranging for additional coverage from private insurance companies.

IIIIm

COMMISSIONS

3.7.1 Fixed Commissions In the 1770s people interested in buying and selling stocks and bonds met under a buttonwood tree near present-day 68 Wall Street in New York City. In May 1792 a group of brokers pledged "not to buy or sell from this day for any person whatsoever, any kind of public stock at a less rate than one quarter percent commission on the specie value, and that we will give preference to each other in our negotiations.v" A visitor to the New York Stock Exchange today can see a copy of this "buttonwood agreement" publicly displayed. This is not surprising, since the exchange is a lineal descendant of the group that met under the buttonwood tree . Also, until 1968 the exchange required its member brokers to charge fixed minimum commissions for stocks, with no "rebates, returns, discounts or allowances in 'any shape or manner,' direct or indirect.t'P The terms had changed, but the principle established 180 years earlier remained in effect. In the United States most cartels designed to limit competition by fixing prices are illegal. This one, however, was exempted from prosecution under the antitrust laws. Before 1934 the exchange was, in essence, considered a private club for its members. This view of the exchange changed with passage of the Securities Exchange Act of 1934, which required most exchanges to be registered with the SEC . The commission, in turn, encouraged exchanges to "self-regulate" their activities, including the setting of minimum commissions.

3.7.2 Competitive Commissions As mentioned earlier in this chapter, the system affixed commissions was finally ter-

minated by the Securities Acts Amendments of 1975 (but only after repeated challenges by the NYSE). Since May 1,1975 (known in the trade as MayDay), brokers have been free to set commissions at any desired rate or to negotiate with customers concerning the fees charged for particular trades. The former procedure is more commonlyemployed in "retail" trades executed for small investors, whereas the latter is used more often when handling large trades involving institutional investors. Experience after May Day reveals that commissions for large trades have fallen substantially. So have those charged for small trades by firms offering only "barebones" brokerage services. On the other hand, broad-line firms that provided extensive services to small investors for no additional fee have continued to charge commissions similar to those specified in the earlier fixed schedules. In succeeding years, as costs have risen, charges for smaller transactions have increased, whereas those for large trades have not. During the 1960s and 1970s a number of procedures were used to subvert the fixed commission rates. In particular, the third and fourth markets expanded their Security Markets

69

,

INSTITUTIONAL ISSUES

Soft Dollars Suppose that you have decided to build a new home . your first step you hire a general contractor to oversee th e different construction phases. The general contractor, in turn, hires various subcontractors to lay the foundation, frame the house, install electrical wiring, and so on. You compensate the general contractor in large part on the basis of the charges billed by the subcontractors. Now assume that the general co n tracto r allowed the subcontractors to charge more than the true costs of their services. The difference between the billed COSL~ and the true costs was then rebated to the general contractor in the form of payments for goods and services only indirectly related to the general contractor's work on your home, such as accounting services or transportation vehicles. For example, the electrician buys the general contractor a new pickup truck after being requested to do so by the contractor. Presumably you would find such an arrangement objectionable. After all, fairness dictates that the general contractor's charges to you include only the actual cost of the subcontractors' labor and materials. The general contractor should pay for the pickup truck directly out of his or her own pocket. The efficiency and equity of such an arrangement seem unquestionable, except perhaps in the investment management business, where each year institutional investors pay hundreds of millions of "soft" dollars to brokerage firms in a situation analogous to our hypothetical home-building example. Soft dollars are brokerage commissions paid by institutional investors in excess of amounts required to compensate brokers for simply executing trades; they had their origin in the fixed commission rates A.~

imposed by the New York Stock Exchange before May I, 1975. Large institutional investors paid the same commission rates as sm all retail investors, despite the obvious economies of scal e present in carrying out large trades as opposed to small trades. Brokerage firms competed with one another, not by lowering com m issio n rates, but by rebating a portion of the commissions to large investors. These brokerage firms did so by offering a plethora of "free" services to the investors. These services typically involved various types of investment research , although on occasion they included such ethically questionable items as airline tickets and lodging for trips abroad. After the deregulation of commission rates in 1975, it was widely assumed that soft dollars would disappear. Investors would pay brokers only for executing their trades in the most cost-effective manner. Other services, such as investment research, would be purchased directly from the supplying firms. This decoupling of payments for trade execution from other services is known as "unbundling." Surprisingly, the soft dollar industry, despite some initial rough going after May Day, did not wither away. In fact, it flourished . IL~ prosperity was facilitated by two factors. First, Congress legislated in 1975 that commissions could continue to be used to pay for investment research, not just for trade execution. The conditions under which soft dollars could be used and the general types of investment research that can be purchased are specified (and occasionally modified) by the Securities and Exchange Commission (SEC) . Although the legislation had the effect of curbing some of the most egregious soft dollar abuses, it left soft dollar users with wide latitude.

operations while regional exchanges invented ways to serve as conduits to return a portion of the fixed commissions to institutional investors. No legal restriction gave the NYSE its monopoly power in the first instance. Instead, the situation has been attributed to the natural monopoly arising from economies of scale in bringing together many people (either physically or via modern communications technology) to trade with one another. The potential profits from such a monopoly are limited by the advantages it confers. The increasing institutionalization of security holdings and progress in communications and computer technology have diminished the advantages associated with a centralized physical exchange. Thus the removal of legal protection for this particular type of price fixing may have accelerated a trend already under way. Increased competition among brokerage firms has resulted in a wide range of alternatives for investors. After May Day, some firms "unbundled," meaning that they 70

CHAPTER 3

The second factor was the general trend of institutional investors toward hiring external investment managers to invest their assets. These managers, in a loose sense, act as the general contractor referred to earlier. The managers have discretion over the allocati on of their clients' commissions. They are permitted (and, in fact, have a strong incentive) to use soft dollars to pay for various forms of investment research. That research includes primarily fundamental company analyses, data on expected earnings, and economic forecasts. It also includes computer software and hardware, performance measurement, and educational services. By using soft dollars to pay for such research , the managers are effectively shifting the COSL~ to their clients, rather than paying for them themselves. Establishing the size of the soft dollar industry is difficult, but estimates of total soft dollar commissions in the range of $500 million to $1 billion annually appear reasonable. The soft dollar ind ustry is large and lucrative enough to support a number of brokerage firms devoted solely to supplying third-party research services to investors in exchange for soft dollars. These brokerage firms make arrangements with providers of investment research to funnel payments for services rendered to investment managers in exchange for having the managers ' execute trades through the brokerage firms. In the investment industry, prices for research services are often quoted on two levels: hard (straight cash payment) or soft (price in commission dollars) . The ratio of the two prices implies a conversion rate. Although this conversion rate is negotiable, a standard figure is 1.6 commission dollars paid to receive one dollar in services.

The stated rationale behind managers' use of soft dollars is that their clients benefit from the research services purchased. Presumably, in the absence of soft dollars managers would raise their fees to enable them to purchase the necessary research directly, yet maintain their current profit margins. However, managers are not required to provide their clients with a detailed accounting of their soft dollar use. Thus it is difficult for clien L~ to assess whether their commission dollars are being wisely allocated by their managers. One is hard-pressed to imagine how clien ts are better off under a system of unidentified, implicit fees than they would be if commission payments were completely unbundled. Why don't institutional clients insist that soft dollar use be prohibited or at least be full}' divulged? Inertia and ignorance appear to be two explanations. For another reason, many institutional investors have themselves become beneficiaries of soft dollars . They use soft dollars by directing their managers to purchase various services for their immediate benefit. (Soft dollars generated in this manner are sometimes called "d irected commissions.") For example, a corporate pension fund staff may use their managers' soft dollars to purchase performance measurement services that the corporate budget would not normally allow. Over the years, soft dollars have been criticized as inclficient and ripe for abuse. Calls for prohibition of soft dollars have occasionally been heard. The SEC has periodically rattled its regulatory saber and threatened to crack down on inappropriate practices. However, the status quo likely will prevail. The soft dollar industry is powerful and to date has been able to ward off any substantive changes.

priced their services separately from their pricing of order execution. Other firms "went discount," meaning that they dropped almost all ancillary services and cut commissions accordingly. Still others "bundled" new services into comprehensive packages. Some of these approaches have not stood the test of time, butjust as mail-order firms, discount houses, department stores, and expensive boutiques coexist in the retail clothing trade, many different combinations are viable in the brokerage industry.

__

TRANSACTION COSTS

3.8.1 Bid-Ask Spread Commission costs are only a portion of the total cost associated with buying or seIling a security. Consider a "round-trip" transaction, in which a stock is purchased and Security Markets

71

then sold during a period in which no new information is released that would cause investors to collectively reassess the value of the stock (more concretely, the bid and asked prices quoted by dealers do not change). The stock will be purchased typically at the dealers' asked price and sold at the bid price, which is lower. The bid-ask spread thus constitutes a portion of the round-trip transaction costs. How large is the spread between bid and asked prices for a typical stock? The spread generally amounts to less than 1% of the price per share for large actively traded stocks of this type-a reasonably small amount to pay for the ability to buy or sell in a hurry. However, not all securities enjoy this type of liquidity. Shares of smaller firms tend to sell at lower prices but at similar bid-ask spreads. As a result, the percentage transaction cost is considerably larger. Spreads are inversely related to the amount of trading activity in a stock. That is, stocks with more trading activity (that is, trading volume) tend to have lower spreads. 24 The inverse relationship between the amount of trading activity (or market value) and spread size can be explained once it is recognized that the spread is the dealer's compensation for providing investors with liquidity. The smaller the amount of trading, the less frequently the dealer will capture the spread (by buying at the bid and selling at the asked). Hence the dealer will need a wider spread in order to generate a level of compensation commensurate with more frequently traded securities.

3.8.2 Price Impact Brokerage commissions and hid-ask spreads represent transaction costs for small orders (typically 100 shares) . For larger orders the possibility of price impacts must also be considered. Owing to the law of supply and demand, the larger the size of the order, the more likely the investor 's purchase price will be higher (or sale price lower) . Furthermore, the more rapidly the order is to be completed and the more knowledgeable the individual or organization placing the order, the higher the purchase price (or lower the sale price) set by the dealer. Table 3.3 offers a profile of trading activity conducted by a sample of institutional investors over the 12-month period endingJune 30, 1996. The table presents information encompassing 1.3 million trades on both the NYSE and the Nasdaq/NMS markets. Stocks traded are divided into three groups based on their market capitalization, which equals the market value of the firm's outstanding equity (that is, its share price times the number of shares outstanding) . For example, large capitalization stocks are classified as those with market capitalizations greater than $10 billion. The table also segments the trades themselves into three groups based on the number of shares involved in the transactions. For example, large trades are classified as those involving over 50,000 shares. Table 3.3 indicates that the commissions charged on NYSE trades are relatively similar regardless of the stocks' market capitalizations. However, because average price per share tends to be inversely related to market capitalization, commissions, stated as a percentage of the dollar value of a trade, increase as market capitalization declines. Further, the smaller is the market capitalization of a traded stock, the greater is the price impact of the trade. Similarly, the larger is the trade in terms of shares traded, the greater is the price impact. Figure 3.2 provides estimates of the average cost of institutional trading. All three sources of costs are included: brokerage commissions, bid-ask spreads, and price impacts. The figure refers to the total cost of a "round trip" for a purchase followed by a sale. It illustrates the round-trip cost for stocks with varying market capitalizations and varying trade sizes, with the trade size expressed relative to the daily volume of trading carried out in that stock on a typical day. Transaction costs increase as both market capitalization declines and the proportion of a day's trading volume consumed by the trade rises. 72

CHAPTER 3

TABLE

3.3

Price Impact Analysis. 12 Months Ending June 30. 1996

la, New York Stock Exchange Trades

Large market capitalization

SIze More than $10 billion

Mid-market capitalization Small market capitalization

$1-$10 billion Less than $ I billion

Small trades

0-10,000 shares

Medium trades

10-50,000 shares More than 50,000 shares

Large ttades

Avg. Market

·Avg . No. of

Percent of

capltaliutlon

naded

Dally Volume 15

$.055 (.14%) $;l05 (.27%)

Avg. Commision $.045 $.046 $.044 $.040 $.044 $.046

7 32

$.17 (.35%)

NA

$34-1)

$.19 (.52%)

61 58

32

$.16 (.80%) $.06 (.23%) $.12.1) (.43%)

NA NA N.A. N.A.

$H $ 0.5 S 5.5 $ 4.6

]0

$.22 (.68%)

NA

$11.1

Percent ofTotaJ 28 51 21 63 26 11

Avg. PrIce

'mpad $.10 (.17%) $.09 (.25%) $.07 (.36%) $.04 (.10%)

(billionsl r,;, $34.4 $4.4 0.6 $15.2 $13 .6 $]8.7

s

Shales 24.000 24.000 17,000 2,000 23,000 133,000

32 54 4 14

Avg. PrlcelShare $75 $35 $19 $4] $39

~

$.'9

38.000 28,000

11 24

$48

17.000 3,000

48 13

$20 $28

22.000 128,000

23 33

$29 $32

(bl NasdaqlNMS Trades

Urge mykel capilalizatioo Mid·market capitalization

SmaI1 market Capitalization Sntall trades

-

Medium ndes Large trades

More than $10 billion $1-$10 billion Less than $1 billion 0-10,000 shares 1~,OOO shares More than 50,000 shares

Scwce: Plexus Group, 1997. All righu reserved.

......

\AI

$37

3.0

2.5

2.0

§ :;; 0

U

1.5

0.£:

1-;' "0 t: ::I 0

1.0

~

0.5

0.0 1%

5%

25%

10%

-+- $100 million

50%

100%

200%

500%

...... $500 million -- $1 billion . . $10 billion

Figure 3.2 Transaction Costs versus Percent of Daily Trading Volume (by market capitalization) Source: Plexus Group. 1997. All rights reserved .

__

REGULATION OF SECURITY MARKETS Directly or indirectly, security markets in the United States are regulated under both federal and state laws. Figure 3.3 denotes the four main laws that regulate U.S security markets. 1. The Securities Act of 1933 was the first major legislation at the federal level. Sometimes called the "truth in securities" law, it requires registration of new issues and disclosure of relevant information by the issuer. Furthermore, the act prohibits misrepresentation and fraud in security sales . 2. The Securities Exchange Act of 1934 extended the principles of the earlier act to cover secondary markets and required national exchanges, brokers, and dealers to be registered. It also made possible the establishment of self-regulatory organizations (SROs) to oversee the securities industry. Since 1934 both acts (and subsequent amendments to them, such as the Securities Acts Amendments of 1975 that were discussed earlier in the chapter) have been administered by the Securities and Exchange Commission (SEC), a quasijudicial agency of the U.S. government established by the 1934 Act. 25 3. The Investment Company Act of 1940 extended disclosure and registration requirements to investment companies, whose total assets at the end of 1997 amounted to more than $4 trillion. (Investment companies use their funds primarily to purchase securities issued by the U.S. government, state governments, and corporations; they are discussed in Chapter 21.)

74

CHAPTER 3

Figure 3.3 Pillars of Security Legislation

4. The Investment Advisers Act of 1940 required the registration of those individuals who provide others with advice about security transactions. Advisers were also required to disclose any potential conflicts of interest. As mentioned earlier, federal securities legislation relies heavily on the principle of self-regulation. The SEC has delegated its power to control trading practices for listed securities to the registered exchanges. However, the SEC has retained the power to alter or supplement any of the resulting rules or regulations. The SEC's power to control trading practices in over-the-counter securities has been similarly delegated to the National Association of Securities Dealers (NASD). a private association of brokers and dealers in aTC securities.P In practice, the SEC staff usually discusses proposed changes with both the NASD and the registered exchanges in advance. Consequently, the SEC formally alters or rejects few rules. An important piece oflegislation that makes security markets in the United States different from those in many other countries is the Banking Act of 1933, also known as the Glass-Steagall Act. This act prohibited commercial banks from participating in investment banking activities because it was felt that there was an inherent conflict of interest in allowing banks to engage in both commercial and investment banking. Consequently, banks have not played as prominent a role in security markets in the United States as they do elsewhere. Recently, however, their role has increased, as the federal government has taken action to spur competition among various types of financial institutions. Many banks now offer security brokerage services, retirement funds, and the like via subsidiaries of their holding companies. Furthermore, long-standing limitations on rates paid on deposits and checking accounts were removed. As a result, the line between commercial banking and investment banking is becoming more blurred every day. Initially, security regulation in the United States was the province of state governments. Beginning in 1911 , state blue sky lawswere passed to prevent "speculative Security Markets

75

schemes which have no more basis than so many feet of blue sky."27 Although such statutes vary substantially from state to state, most of them outlaw fraud in security sales and require the registration of certain securities as well as brokers and dealers (and, in some cases, investment advisers) . Some order has been created by the passage in many states of all or part of the Uniform Securities Acts proposed by the National Conference of Commissions on Uniform State Laws in 1956. Furthermore, the North American Securities Administrators Association (NASAA), an organzation of state securities regulators based in Washington, D.C., monitors federal regulation and attempts to coordinate state regulation. Securities that are traded across state lines, as well as the brokers, dealers, and exchanges involved in such trading, typically fall under the purview of federal legislation. However, a considerable domain still comes under the exclusive jurisdiction of the states. Generally, federal legislation only supplements state legislation; it does not supplant it. Some critics argue that the investor is overprotected as a result. Others suggest that the regulatory agencies (especially those that rely on "self-regulation" by powerful industry organizations) in fact protect the members of the regulated industry against competition, thereby damaging the interests of their customers instead of protecting them. Both positions undoubtedly contain some elements of truth.

am

SUMMARY 1. Security markets facilitate the trading of securities by providing a means of bringing buyers and sellers of financial assets together. 2. Common stocks are traded primarily on organized security exchanges or on the over-the-counter market. 3. Organized security exchanges provide central physical locations where trading is done under a set of rules and regulations. 4. The primary organized security exchange is the New York Stock Exchange. Various regional exchanges also operate. 5. Trading on organized security exchanges is conducted only by members who transact in a specified group of securities. 6. Exchange members fall into one of four categories, depending on the type of trading activity in which they engage. Those categories are commission broker, floor broker, floor trader, and specialist. 7. Specialists are charged with maintaining an orderly market in their assigned stocks. In this capacity they perform two roles. They act as brokers, maintaining limit order books for unexecuted trades, and they act as dealers, trading in their stocks for their own accounts. 8. In the OTC market, individuals act as dealers in a manner similar to specialists. However, unlike specialists, OTC dealers face competition from other dealers. 9. Most of the trading in the OTC market is done through a computerized system known as Nasdaq. 10. Trading in listed securities may take place outside the various exchanges on the third and fourth markets. 11. Foreign security markets each have their own particular operating procedures, rules, and customs. 12. Dealers typically make money trading with liquidity-motivated traders and lose money trading with adept information-motivated traders. A dealer must set a bid-ask spread that attracts sufficient revenue from the former group to offset losses to the latter. 76

CHAPTER 3

13. Since legislation in 1975 , the Securities and Exchange Commission has mandated procedures designed to create a truly nationwide central security market. 14. Clearinghouses facilitate the transfer of securities and cash between buyers and sellers. Most U.S. security transactions are now cleared electronically. 15. The SIPC is a quasigovernmental agency that insures the accounts of clients of all brokers and members of exchanges registered with the SEC against loss due to a brokerage firm's failure. 16. Since May Day (May 1, 1975), commissions have been negotiated between brokerage firms and their larger clients. In a competitive environment, commission rates typically vary inversely with the size of the order. 17. Transaction costs are a function of the stock's bid-ask spread, the price impact of the trade, and the commission. 18. The most prominent security market regulator is the SEC, a federal agency. Regulation of the U.S. security markets involves both federal and state laws. 19. The SEC has delegated to the various exchanges and the NASD the power to control trading practices through a system of self-regulation with federal government oversight. QUESTIONS

AND

PROBLEMS

1. Virtually all secondary trading of securities takes place in continuous markets as opposed to call markets. What aspects of continuous markets causes them to dominate call markets? 2. Circuitbreakers were first instituted after the market crash of October 1987. Some observers argue that the rapid increase in the stock market's value since 1987 has diminished whatever value the rules may originally have possessed. Why? 3. Discuss the advantages and disadvantages of the NYSE specialist system. 4. Differentiate between the role ofa specialist on the NYSE and the role ofa dealer on the OTC market. 5. Give several reasons why a corporation might desire to have its stock listed on the NYSE. 6. Describe the functions of commission brokers, floor brokers, and floor traders. 7. Pigeon Falls Fertilizer Company is listed on the NYSE. Gabby Hartnett, the specialist handling Pigeon Falls stock, is currently bidding 35~ and asking 35~. What would be the likely outcomes of the following trading orders? a. Through a broker, Eppa Rixey places a market order to buy 100 shares of Pigeon Falls stock. No other broker from the crowd takes the order. b. Through a broker, Eppa places a limit order to sell 100 shares of Pigeon Falls stock at 36. c. Through a broker, Eppa places a limit order to buy 100 shares of Pigeon Falls stock at 35~ . Another broker offers to sell 100 shares at 35~. 8. Bosco Snover is the NYSE specialist in Eola Enterprises' stock. Bosco's limit order book for Eola appears as follows: Limit-Sell

. Shares

PrIce

$30.250

200

$29.750

30.375 30.500

500

29.000

100

SOO

28.500

200

30.875 31.000

800 200

27.125 26.875

100 200

PrIce

Security Markets

LImit-Buy

Shares . 100

77

The last trade in the stock took place at $30. a. If a market order to sell 200 shares arrives , what will happen? b. If another market order to selllOO shares arrives just moments later, what will happen? c. Do you think that Bosco would prefer to accumulate shares or to reduce inventory, given the current orders in the limit order book? 9. Because specialists such as Chick Gandil are charged with maintaining a "fair and orderly" market, at times they will be required to sell when others are buying and to buy when others are selling. How can Chick earn a profit when required to act in such a manner? 10. Why can't all trade orders on the NYSE, no matter how large, be handled through the SuperDOT system? 11. Why is Nasdaq so important to the success of the OTC market? 12. If the NYSE moved to decimal pricing with prices moving in at $.05 increments, would there be greater opportunities for price improvement over the current pricing system? Explain. 13. Distinguish between two forms of preferencing: payment for order flow and internalization. 14. Using the model described in the text, calculate the appropriate bid-ask spread for a dealer making a market in a security under the conditions that 15% of all traders are information-motivated and there is a 30% chance that the stock is worth $30 per share and a 70% change that it is worth $50 per share. 15. How might a dealer attempt to discern whether a trader is information motivated? 16. What are some of the major steps that have been taken toward the ultimate emergence of a truly nationwide security market? 17. The NYSE has strongly opposed the creation of alternative market trading structures such as off-exchange crossing systems. The NYSE claims that these alternative structures undermine its ability to offer "best execution" to all investors. Discuss the merits of the NYSE's contention. 18. Distinguish between the third and fourth markets. 19. Why was May Day such an important event for the NYSE? 20. What is the purpose of SIPe insurance? Given the late 1980s experience of the ban king and savings and loan deposit insurance programs, under what conditions might SIPC insurance he expected to be effective? Under what conditions might it fail to accomplish its objectives? 21. After May Day, why did commission rates fall so sharply for large investors but decline so little (or even increase) for small investors? 22. Transaction costs can be thought of as being derived from three sources. Identify and describe those sources. 23. Why does the price impact of a trade seem to be directly related to the size of the trade? 24. What functions does a clearinghouse perform?

ENDNOTES

1 Enough

time is allowed to elapse between calls (for example, an hour or more) so that a substantial number of orders to buy and sell will accumulate by the time of the auction.

2

The applicant for membership must also pass a written examination, be sponsored by two current members of the exchange, and be approved by the board. Recently the NYSEbegan allowing members to lease their seats to individuals acceptable to the exchange. As of the end of 1996 there were 781 leased seats . In add ition to the 1,366 full memberships, at the

78

CHAPTER 3

end of 1996 there were 61 indi viduals who held special memberships. In return for an an nual fee, these members are granted access to the trading floor. 3

During 1996, trading volume on the NYSE averaged, on a daily basis, 412 .0 million shares, worth nearly $7 billion. The American Stock Exchange, the seco nd largest organized exchange , had daily values of less than one-tenth those amounts.

4

Fact Book 1997 Data (New York Stock Exchange, 1997), p. 37.

5

Note that the tick test for a down market is the same as the up-tick rule discussed in Chapter 2 with respect to short sales.

6

There is another circuitbreaker known as the Sidecar that halts certain trades on SuperDOT (discussed later in this chapter) for five minutes whenever the primary Standard & Poor's 500 futures contract (see Chapter 20) drops 12 points. Readers are encouraged to check the NYSE's Web page (www.nyse.com) for the current status of the various circuitbreakers, as they are subject to change.

7 The

assignment is made by the board of directors and also includes any preferred stock or warrants that the company has listed on the exchange . At the end of 1996 there were 2,907 companies listed on the NYSE, with 3,285 stock issues being traded, meaning that there were over 300 different issues of preferred stock and other classes of common stock being traded on the NYSE. There were also 116 warrants on these companies' stock that were traded. Bonds are also listed on the NYSE but are traded in an entirely different manner that does not involve the use ofspecialists. At the end of 1996 there were 563 companies that had 2,064 issues of bonds listed on the NYSE.

HThe

NYSE is currently open from 9:30 A.M. until 4 P.M. However, the NYSE often considers extending its hours of operation in order to overlap with the London and Tokyo stock markets. The NYSE does allow certain computerized trading to take place after close in Crossing Session I (4:15 P.M. to 5 P.M.) and Crossing Session II (4 P.M. to 5:15 P.M.). Trades in Crossing Session I are based on 4 P.M. closing prices, whereas each trade in Crossing Session II must involve a "basket" of at least 15 NYSE-listed stocks and an aggregate price of $15 million (prices are set for the baskets not for individual stocks).

9

These quotations may represent either orders for the specialist's own account or public orders. These quotations may not be the "best" ones, because under certain circumstances specialists are not required to display them on the screens of quotation machines. However, such "hidden orders" would appear in the limit order book and would be revealed on the exchange floor. A.", a matter ofNYSE policy, only the specialist is allowed to see the contents of the limit order book. However, in 1991 the NYSE began to allow the specialists to disclose some information about buying and selling interest to others on the floor.

10

Evidence of price improvement in minimum spread markets (as well as in markets with larger spreads) is provided in Lawrence Harris and Joel Hasbrouck, "Market vs. Limit Orders : The SuperDOT Evidence on Order Submission Strategy," Joumal ofFinancial and QuantitativeAnalysis31 , no. 2 (june 1996): 213-231, and Katharine D. Ross,James E. Shapiro, and Katherine A. Smith, "Price Improvement of SuperDOT Market Orders on the NYSE," NYSE Working Paper 96-02.

II

Odd lot market orders are executed immediately by the specialist at the quoted bid or asked price. Odd lot limit orders are held by the specialist and executed immediately after there has been another trade at the limit price. Typically, odd lot orders utilize the facilities of SuperDOT. There are special features of SuperDot that are used to execute opening orders; that is, orders that are received up to the time the NYSE opens in the morning.

12

One alternative for the institution that is thinking of placing the block order is to place many small orders sequentially. However, institutions generally do not want to do this because it means that their block order will not be executed with due speed. Furthermore, other traders may anticipate these additional transactions and develop strategies to take advantage of them.

13

The order must be crossed on an exchange where the stock is listed, provided that the block house is a member of that exchange.

Security Markets

79

14

In 1996 the Department ofJustice and the Securities and Exchange Commission reached settlements with NASD after concluding that NASD had engaged in anticompetitive behavior by, for example, colluding in the setting of spreads in large Nasdaq stocks. Interestingly, the investigation was triggered by an academic paper by William G. Christie and Paul H. Schultz, ·Why Do NASDAQ Market Makers Avoid Odd-Eighth Quotes?" Joumal of Finance49, no. 5 (December 1994): 1813-1840. For press articles describing the Settlement, see Anita Raghavan and Jeffrey Taylor, "Will NASD Accord Transform Nasdaq Market?" The Wall StreetJoumal, August 81996, pp. CI, C6; and Floyd Norris, "Tough Crackdown on NASDAQ Market Announced by US," New York Times, August 9, 1996, pp. AI, D16.

15

Of this total, 460 were foreign securities consisting of 142 American Depositary Receipts (ADRs) and 318 non-ADRs. (Many of the non-ADRs were Canadian securities.) ADRs are discussed in Chapter 25.

16 The

use of an intermediary such as a computer system, makes it difficult to categorize such trades. Some people would refer to the market where trades involving a "matchmaker" take place as the "3.5 market." The term fourth market would then be used only when referring to the market where no matchmaker is involved.

17

See James B Cloonan, "Payment for Order Flow Is No Deal for Investors," AAlIJoumall3, no. 3 (March 1991): 28-29.

IR There

is a another way that internalization can take place. Broker-dealers can also be specialists in NYSE-listed securities on either the NYSE itself or on a regional exchange. Hence, they can take their customers' orders and send them to their own specialists for execution. This practice is particularly common on certain regional exchanges where the specialists can make markets in many stocks (often several specialists will make a market in the same stock).

19

A similar classification of traders that has often been used by financial economists involves (I) informed speculative traders who possess both public and private information, (2) uninformed speculative traders who possess just public information, and (3) noise traders whose trades are not based on information. Hence the first two types can be viewed as information-motivated traders, and the third as liquidity-motivated traders. See Sanford J. Grossman and Joseph E. Stiglitz, "On the Impossibility of Informationally Efficient Markets," American Economic Review 70, no. 3 (June 1980): 393-408.

20

There are a number of implicit assumptions associated with this model that have not been spelled out here. The interested reader is directed to Lawrence R. Glosten and Paul R. Milgrom, "Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders," Joumal ofFinancial Economics 14 no. I (March 1985): 71-100.

21

From Securities Acts Amendments of 1975, section IIA.

22

See WilfordJ. Eiteman, Charles A. Dice, and David K Eiteman, The Stock Market (New York: McGraw-Hill, 1969), p. 19.

23

Eitemen, Dice, and Eiteman, The Stock Market, P: 138.

24

Roger D. Huang and Hans R. Stoll, Major World Equity Markets: Current Structure and Prospects for Change, Monograph Series in Finance and Economics 1991-93, (New York: New York University Salomon Center, 1991), p. II.

25

The Commodity Futures Trading Commission (CITe) was established in 1974 by Congress to regulate futures markets, and the Municipal Securities Rulemaking Board (MSRB) was established in 1975 to regulate trading in municipal securities. A brief discussion of federal regulation in those two markets can be found in Chapters 20 and 13, respectively.

26

The Maloney Act of 1938 extended the SEC's jurisdiction to include the over-the-counter market and recognized the National Association of Security Dealers as a self-regulatory organization (SRO).

27

See Hall v. Geiger:Jones Co., 242 U.S. 539 (1917).

80

CHAPTER 3

/(EY

TERMS

security market financial market call markets continuous markets liquidity organized exchanges seat member firm listed security delist trading halt circuitbreakers minus tick zero-minus tick commission brokers floor brokers floor traders specialists limit order book dealer market-maker trading post bid price asked price double auction Super Designated Order Turnaround blocks specialist block purchase specialist block sale exchange distribution exchange acquisition special offering special bid secondary distribution upstairs dealer market block houses regional exchanges National Association of Securities Dealers

National Association of Securities Dealers Automated Quotations inside quotes NBBO offer price National Market System Small Cap Issues markup markdown Small Order Execution System (SOES) Pink Sheets third market fourth market Instinet preferencing paymen t for order flow internalization SEAQ SAEF Nasdaq International CORES FORES CATS consolidated tape composite stock price tables Consolidated Quotations System Intermarket Trading System clearinghouse Depository Trust Company Securities Investor Protection Corporation Securities and Exchange Commission (SEC) May Day soft dollars bid-ask spread price impacts market capitalization self-regulation

REFERENCES 1. A good reference source for U.S. stock markets is: Robert A. Schwartz, Equity Markets (New York: Harper & Row, 1988) .

2. Other valuable sources are the following fact books, which are updated annually, and Web sites : New York Stock Exchange, Fact Book: 1997 Data, 1998; (www.nyse.com). Security Markets

81

American Stock Exchange, American Stock Exchange 1997 Fact Book, 1998; (wwww.amex.com). National Association of Security Dealers, The Nasdaq Stock Market 1997 Fact Book & Company Directory, 1997; (www.nasd.corn) or (www.nasdaq.com) or (www.nasdr.com). London Stock Exchange, Stock Exchange Official Yearbook; (wwwlondonstockex.co.uk). Toronto Stock Exchange Press, 1997 Official Trading Statistics; (www.tse.com), Tokyo Stock Exchange, Tokyo Stock Exchange 1997 Fact Book; (www.tse.orJp/eindex.html). The Securities and Exchange Commission's Web site: (www.sec.gov). 3. For a description of foreign stock markets, see: Guiseppe Tullio and Giorgio P. Szego (eds.), "Equity Markets: An International Comparison: Part A," Journal of Banking and Finance 13, nos. 4/5 (September 1989): 479-782. Guiseppe Tullio and Giorgio P. Szego (eds.), "Equity Markets: An International Comparison: Part B," Journal of Banking and Finance 14, nos . 2/3 (August 1990) : 231-672. Roger D. Huang and Hans R. Stoll, Major World Equity Markets: Current Structure and Prospects for Change, Monograph Series in Finance and Economics 1991-1993 (New York: New York University Salomon Center, 1991). Roger D. Huang and Hans R. Stoll, "The Design of Trading Systems: Lessons from Abroad," Financial AnalystsJournal48, no . 5 (September/October 1992) : 49-54. Bruce N. Lehman and David M. Modest, "Trading and Liquidity on the Tokyo Stock Exchange: A Bird's Eye View,"Journal ofFinance 49, no. 3 Uuly 1994): 951-984. Alexandros Benos and Michel Crouhy, "Changes in the Structure and Dynamics of European Securities Markets," Financial AnalystsJournal 52 , no . 3 (May/June 1996): 37-50. 4. Other useful sources for information on market microstructure are: James L. Hamilton, "Off-Board Trading of NYSE-Listed Stocks: The Effects of Deregulation and the National Market System," Journal of Finance 42, no. 5 (December 1987): 1331-1345.

Ian Domowitz, "The Mechanics ofAutomated Execution Systems,"Journal ofFinancial1ntermediaiion I, no. 2 (june 1990): 167-194. Lawrence E. Harris, l.i'luidity, Trading Rules, and Electronic Trading Systems, Monograph Series in Finance and Economics 1990-1994, (New York: New York University Salomon Center, 1990). Peter A. Abken , "Globalization of Stock, Futures, and Options Markets," Federal Reserve Bank ofAtlanta Economic Review 76, no. 4 Uuly/ August 1991): 1-22. Joel Hasbrouck, George Sofianos, and Deborah Sosebee, "New York Stock Exchange Systems and Procedures," NYSE Working Paper 93-0 I, 1993. Maureen O'Hara, Market Microstructure Theory (Cambridge, Mt\.: Blackwell, 1995). 5. For a discussion of the effects of listing and delisting on a firm's stock, see : Gary C. Sanger andJohnJ. McConnell, "Stock Exchange Listings, Firm Value, and Security Market Efficiency: The Impact of NASDAQ," Journal ofFinancial and Quantitative Analysis 21, no. 1 (March 1986): 1-25. JohnJ. McConnell and Gary C. Sanger, "The Puzzle in Post-Listing Common Stock Returns," Journal ofFinance 42, no . 1 (March 1987) : 119-140. Gary C. Sanger andJames D. Peterson, "An Empirical Analysis of Common Stock Delistings," Journal ofFinancial and Quantitative Analysis 25, no. 2 (june 1990): 261-272. 6. Empirical studies that examine the costs of trading include: Harold Dernsetz, "The Cost of Transacting," QuarterlyJournal ofEconomics 82, no. 1 (February 1968): 33-53. Walter Bagehot, "The Only Game in Town," Financial Analysts Journal 27, no. 2 (March/April 1971): 12-14,22. Larry J. Cuneo and Wayne H. Wagner, "Reducing the Cost of Stock Trading," Financial AnalystsJournal31, no. 6 (November/December 1975): 35-44. Gilbert Beebower and William Priest, "The Tricks of the Trade," Journal of Portfolio Management6, no. 2 (Winter 1980): 36-42. 82

CHAPTER 3

Jack L. Treynor, "What Does It Take to Win the Trading Game?" Financial Analystsjourna137 , no . 1 (january/February 1981): 55-60. Thomas F. Loeb, "Trading Cost: The Critical Link between Investment Information and Results," Financial Analystsjournal 39, no . 3 (May/June 1983): 39-44. Wayne H. Mikkelson and M. Megan Partch, "Stock Price Effects and Costs of Secondary Distributions," journal oJFinancial Economics 14, no. 2 (june 1985) : 165-194. Robert W. Holthausen, Richard W. Leftwich, and David Mayers, "The Effect of Large Block Transactions on Security Prices," journal ofFinancial Economics 19, no. 2 (December 1987) : 237-267. Stephen A. Berkowitz, Dennis E. Logue, and Eugene E. Noser Jr., "The Total Cost of Transactions on the NYSE,"journal oJFinance43, no . 1 (March 1988) : 97-112. Andre F. Perold, "The Implementation Shortfall: Paper versus Reality," journal oj Portfolio Management 14, no. 3 (Spring 1988): 4--9. Lawrence R. Glosten and Lawrence E. Harris, "Estimating the Components of the Bid/Ask Spread ,"journaloJHnancialEconomics21 , no. 1 (May 1988): 123-142. Joel Hasbrouck, "Trades, Quotes, Inventories, and Information," journal oj Financial Economics 22, no. 2 (December 1988): 229-252. Hans R. Stoll, "Inferring the Components of the Bid-Ask Spread: Theory and Empirical Tests," journal oJFinanrr.44, no. 1 (March [989): [15-[34. Robert W. Holthausen , Richard W. Leftwich, and David Mayers, "Large-Block Transactions, the Speed of Response, and Temporary and Permanent Stock-Price Effects," journal oJFinancialEconomics 26, no . 1 Uu[y 1990) : 71-95. F. Douglas Foster and S. Viswanathan, "Variations in Trading Volume , Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models," journal of Finance 48, no . 1 (March [993): 187-211. Hans R. Stoll, "Equity Trading Costs In-the-Large ," journal oj PortJolio Management 19, no. 4 (Summer 1993) : 41-50. Joel Hasbrouck and George Sofianos, "The Trades of Market Makers : An Empirical Analysis ofNYSE Specialists," journal oJFinance48, no. 5 (December 1993) : 1565-1593. Ananth Madhavan and Seymour Smidt, "An Analysis of Changes in Specialist Inventories and Quotations" journal ojFinance 48, no. 5 (December [993): 1595-[ 628. Mitchell A. Petersen and David Fialkowski, "Posted versus Effective Spreads: Good Prices or Bad Quotes?" journal oJFinancial Economics 35, no . 3 (june 1994) : 269-292. Jack L. Treynor, "The Invisible Costs of Trading," journal of Portfolio Management 22, no. 1 (Fall 1995): 71-78. 7. For a comparison oftrading costs on Nasdaq and the NYSE, see: Roger D. Huang and Hans R. Stoll , "Competitive Trading of NYSE Listed Stocks: Measurement and Interpretation of Trading Costs," Financial Markets, Institutions & Instruments5, no. 2 (1996) . Roger D. Huang and Hans R. Stoll, "Dealer versus Auction Markets: A Paired Comparison of Execution Costs on NASDAQ and NYSE," journal oj Financial Economics 41, no. 3 (july [996): 313-357. Michele LaPlante and Chris]. Muscarella, "Do Institutions Receive Comparable Execution in the NYSE and Nasdaq Markets? A Transaction Study of Block Trades," journal of Financial Economics 45, no. 1 Uuly 1997): 97-134. 8. For a historical essay on the development of American capital markets, which includes a significant discussion of regulation, see: George David Smith and Richard Sylla, "The Transformation of Financial Capitalism: An Essay on the History of American Capital Markets," Financial Markets, Institutions & Instruments 2, no. 2 (1993). 9. For more on the adverse selection problem that dealers face in setting spreads, see: Lawrence R. Glosten and Paul R. Milgrom, "Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously 1nfonned Traders," journal ojFinancial Economics 14, no. 1 (March 1985): 71-100. Security Markets

83

Albert S. Kyle, "Continuous Auctions and Insider Trading," Econometrica 53, no. 6 (November 1985) : 1315-1335. Murugappa Krishnan, "An Equivalence between the Kyle (1985) and the Glosten-Milgrom (1985) Models, " Economic Letters 40, (1992) : 333-338. Steven V. Mann, "How Do Security Dealers Protect Themselves from Traders with Private Information: A Pedagogical Note," Financial Practice and Education 5, no. 1 (Spring/Summer 1995): 38-44. Michael]. Brennan and Avanidhar Subrahmanyam, "Investment Analysis and Price Formation in Securities Markets,".Ioumal ofFinancial Economics 38, no. 3 (july 1995): 361-381. 10. Articles on soft dollars include: Keith P. Ambachtsheer, "The Soft Dollar Question: What Is the Answer?" Financial Analysts.loumal49, no. 1 (january/February 1993): 8-10. Marshall E. Blume, "Soft Dollars and the Brokerage Industry," Financial Analysts Joumal 49, no. 2 (March/April 1993): 3~4. Miles Livingston and Edward S. O'Neal, "Mutual Fund Brokerage Commissions," Journal ofFinancial Research 19, no . 2 (Summer 1996) : 273-292.

84

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C HAP T E R

4

EFFICIENT MARKETS, INVESTMENT VALUE, AND MARKET PRICE Payments provided by securities ma y differ in size, timing, and riskiness. Thus a security analyst must estimate the size of such payments a lo ng with when , and under what conditions, these payments will be received. This estimate typically requires detailed analysis of the firm involved, the industry (or industries) in which the firm operates, and the economy (either regionally, nationally, or internationally) as a whole. Once such estimates have been made, th e overall investment value of the security must be determined. This determination generally requires conversion of uncertain future values to certain present values. The current prices of other securities can often be utilized in this process. If it is possible to obtain a similar set of payments in some other way, the market price of doing so provides a benchmark for the investment value of the security being analyzed, because an investor would neither want to pay more than this for the security nor want to sell it for less. In some cases, however, equivalent alternatives may not exist, or the mere act of buying or selling the security in question in the quantities being considered might affect the price substantially. Under these conditions the preferences of the investor may have to be utilized explicitly in the process of estimating the security's investment value. Later chapters discuss in detail the manner in which estimated future payments can be used to determine investment value. Methods for estimating the payments and finding equivalent alternatives will be discussed after the characteristics of the securities have been introduced. In this chapter some general principles of investment value and how it is related to market prices in an efficient market are presented, leaving valuation methodology for specific types of securities for later.

__

DEMAND AND SUPPLY SCHEDULES

Although there are over 1 billion shares of AT&T common stock outstanding, on a typical day only a few million shares will be traded. What determines the prices at which such trades take place? A simple (and correct) answer is: demand and supply. A more fundamental (and also correct) answer is: investors' estimates of AT&T's future earnings and dividends, for such estimates greatly influence demand and sup85

ply. Before dealing with such influences, it is useful to examine the role of demand and supply in the determination of security prices. As shown in the previous chapter, securities are traded by many people in many different ways. Although the forces that determine prices are similar in all markets, they are slightly more obvious in markets using periodic "calls." One such market corresponds to the itayose method of price determination that is used by the saitori at the twice-a-day openings of the Tokyo Stock Exchange, as discussed in Chapter 3.

4.1.1

Demand-to-Buy Schedule

At a designated time all brokers holding orders to buy or sell a given sto ck for customers gather at a specified location on the floor of the exchange. Some of the orders are market orders. For example, Mr. A may have instructed his broker to buy 100 shares of Minolta at the lowest possible price, whatever it may be. His personal demaud-to-buy schedule at that time is shown in Figure 4.1 (a): He wishes to buy 100 shares no matter what the price. Although this schedule captures the contractual nature of Mr. A's market order at a specific point in time, Mr. A undoubtedly has a good idea that his ultimate purchase price will be near the price for which orders were executed just before he placed his order. Thus his true demand schedule might be sloping downward from the upper left portion to the lower right portion of the graph. This schedule is shown by the dashed line in the figure. It indicates his desire to buy more shares if the price is lower. However, to simplify his own tasks as well as his broker's tasks , he has estimated that the price for which his order will be ultimately executed will be in the range at which he would choose to hold 100 shares. In the example shown here, this price is 945 yen per share. Other customers may place limit orders with their brokers. Thus Ms. B may have instructed her broker to buy 200 shares of Minolta at the lowest possible price if and only if that price is less than or equal to 940 yen per share. Her demand schedule is shown in Figure 4.1 (b) . Some customers may give tbeir broker two or more orders for the same security. Thus Mr. C may wish to buy 100 shares ofMinolta at a price of955 or less, plus an additional 100 shares if the price is at or below 945. To do this, Mr. C places a limit order for 100 shares at 955 and a second limit order for 100 shares at 945. Figure 4.1 (c) portrays his demand schedule. If one could look at all the brokers' books and aggregate all the orders to buy Minolta (both market and limit orders), it would be possible to determine how many shares would be bought at every possible price. Assuming that only Mr. A, Ms. B, and Mr. C have placed buy orders, the resulting aggregate demand-to-buy schedule will look like line DD in Figure 4.1 (d). Note that at lower prices more shares would be demanded.

4.1.2

Supply-to-Sell SchedUle

Brokers will also hold market orders to sell shares ofMinolta. For example, Ms. X may have placed a market order to sell 100 shares ofMinolta at the highest possible price. Figure 4.2(a) displays her supply-to-sell schedule. As with market orders to buy, customers generally place such orders on the supposition that the actual price will be in the range in which their true desire would be to sell the stated number of shares. Thus Ms. X's actual supply schedule might appear more like the dashed line in Figure 4.2(a), indicating her willingness to sell more shares at higher prices. Customers may also place limit orders to sell shares of Minolta. For example, Mr. Y may have placed a limit order to sell 100 shares at a price of 940 or higher, and 86

CHAPTER 4

(a) Mr,A's Market Order 10 Buy 100 Shares

(b) Mo" S'. Umit Order to Buy 200 Shares at 940 or Lower

Price

Price

955 -:

955

950 - ..

950 -

945 -

945,.--

940 -

c-

940f-------. I

I

I

I

100

I

100 200

Qu antity

(c) Mr, C'. Limit Order to Buy 100 Shares at 955 or Lower and 100 Shares at 945 or Lower

(d) Aggregate Demand-te-Buy Schedule

Price

Price

955-

955 1-

950 -

950

945-

Quantity

-

DL__

f-

945 I-

940 -

940 !I

100 200

I

I

I

I

Quantity

I

100 200

I

I

300 400

I

D

500 Quant ity

Figure 4.1 Ind ividual Investors ' Demand-to-Buy Schedules

Ms. Z may have placed a limit order to sell 100 shares at a price of 945 or higher. Panels (b) and (c) of Figure 4.2 illustrate these two supply-to-sell schedules. Similar to the buy orders, if one could look at all the brokers' books and aggregate all the orders to sell Minolta (both market and limit orders), it would be possible to determine how many shares would be sold at every possible price. Assuming that only Ms. X, Mr. Y, and Ms. Z have placed sell orders, the resulting aggregate supply-to-sell schedule will look like line 55 in Figure 4.2(d). Note that at higher prices more shares would be supplied.

4.1.3

Interaction of Schedules

The aggregate demand and supply schedules are shown on one graph in Figure 4.3. In general no one would have enough information to draw the actual schedules. However, this limitation in no way diminishes the schedules' usefulness as representations of the underlying forces that are interacting to determine the market clearing price of Minolta. What actually happens when all the brokers gather together with their order books in hand? A clerk of the exchange "calls out" a price-for example, 940 yen per Efficient Markets, Investment Value, and Market Price

87

(b) Mr.YO. Limit order to Sen 100 , Shares llt940 or Higher

(a)Ms. X'I Market Order to Sell . lOOShllres

Price

Price

,,

955 950 "

945

955 950

"

945 940

940 100

100

Quantity

(d) Aggregate Suppl)"to-Seil

(c) Ms. Z', Umit Order to Sell 100

Schedule

Shares at 945or Higher Price

Price

955

955

950

950

945

945

940

940 100

Quantity

Quantity

'

.

s

Quantity

Figure 4.2 Individual Investors' Supply-to-Sell Schedules

share. The brokers then try to complete transactions with one another at that price. Those with orders to buy at that price signify the number of shares they wish to buy. Those with orders to sell do likewise. Some deals will be tentatively made, but as Figure 4.3 shows, more shares will be demanded at 940 than will be supplied. In particular, 300 shares will be demanded, but only 200 shares will be supplied. When trading is completed (meaning that all possible tentative deals have been made), there will be a number of brokers calling "buy," but nobody will stand ready to sell to them . The price of 940 was too low. Seeing this outcome, the clerk will cry out a different price, for example, 950. As the previous trades are all canceled at this point, the brokers will consult their order books once again and signify the extent to which they are willing to buy or sell shares at this new price. In this case, as Figure 4.3 shows, when trading is completed, there will be a number of brokers calling "sell," but nobody will stand ready to buy from them. In particular, 300 shares will be supplied, but there will be a demand for only 200 shares. The price of 950 was too high. Undaunted, the clerk will try again. And again , if necessary. Only when there are relatively few unsatisfied brokers will the pri ce (and the associated tentative deals) be

88

CHAPTER 4

D

955

S

-

950 -- - - -- - - - - - -

-- - - -

o u

'I:

I:l-o

945 f-- - - -- - - - - - -

940 1-- - - -

s 100

, , ,

-- - - - ,

.

,

,

i

i

I

200

300

400

D

500

Quantity

Figure 4.3 Determ ining a Secuntys Price by the Interaction of the Aggregate Demand-to-Buy and Supply-ta-Sell Schedules

declared final. As Figure 4.3 shows, 945 is such a price. At 945, customers collectively wish to sell 300 shares. Furthermore, there is a collective demand for 300 shares at th is price. Thus quantity demanded equals quantity supplied. The price is 'Just right."

4.1.4

Elasticity of the Demand-ta-Buy Schedule

How elastic (that is, flat) will be the aggregate demand-to-buy schedule for a security? The answer depends in part on the extent to which the security is regarded as "unique." Securities are considered more unique when they have few close substitutes. Securities are considered less unique when they have more close substitutes. This relation means that the aggregate demand-to-buy schedule will be more elastic (that is, flatter) for less unique securities. Equivalently, the less unique a security is, the greater will be the increase in the quantity demanded for a given fall in price because these shares will produce a smaller increase in the typical portfolio's risk when substituted for other shares. At one extreme, other securities are viewed as perfect substitutes for the one being analyzed. In this case the security's demand-to-buy schedule will be horizontal, or perfectly elastic. At the other extreme, where there are no substitutes, the security has an almost vertical (or almost perfectly inelastic) demand schedule.

4.1.5

Shifts of the Demand-to-Buy and Supply-ta-Sell Schedules

If one investor becomes more optimistic about the prospects for a security while another investor becomes more pessimistic about the same security, they may very likely trade with one another with no effect on the aggregate demand-to-buy and supply-to-sell schedules. In this situation there will be no change in the market price Efficient Markets, Investment Value, and Market Price

89

The Arizona Stock Exchange: A Better Mousetrap So yo u think that supply and demand curves are merely esoteric figment.~ of ivory-tower thinking. Perhaps a valid concept, you sa}', but they cannot possibly be of any practical use in establishing security prices. Well, don't tell that to the owners of AZX Inc . (AZX) . Since early 1991 that organization (or its predecessor, Wunsch Auction Systems, Inc.) has been conducting regular security auctions a mo ng institutional investors for a broad list of common stocks. Market clearing prices in those auctions are determined by the explicit interaction of the investors' supply and demand preferences. Step back for a moment and recall how prices arc set on oq~anizcd security exchanges or the OTC market (see Chapter 3). Dealers (whether specialists or OTC dealers) "make markets" in particular securities ; that is, acting as intermediaries, the}' buy and sell from other investors for their own accounts. The dealers quote prices (bid and asked) to sellers and buyers on a continuous ba sis. They adjust prices as they sense supply and demand building and ebbing. It is the competitive efforts of these intermediaries that determine security prices. AZX has developed a market mechanism qu ite different from that of the conventional dealer markers. AZX calls this mechanism the Arizona Stock Exchange, although it bears no resemblance to any existing stock exchange. (The name derives from financial support provided to AZX by the State of Arizona.) The concept behind the Arizona Stock Exchange is simple. Auctions are scheduled on a regular basis. (Originally an auction was held once a day

at 5 P.M. EST, after the New York Stock Exchange closes. More recently, a second auction was added at 9:15 A.M . for Nasdaq National Market Sytsern issues , and an additional morning auction is being planned.) Before a scheduled auction, investors submit orders electronically to buy or sell specified quantities of a security at specified prices (essentially limit orders; see Chapter 2). At the time of the auction, the orders of all participating investors are aggregated by computer; that is, the computer calculates supply and demand curves for each security being auctioned. The intersection of these curves determines the market clearing price for a security. At that price the maximum number of shares of stock will be exchanged. (All buy orders above and all sell orders below the equilibrium price are matched; orders at the equilibrium price are matched on a time priority basis.) Investors are able to access the auction order information (in graphic or tabular form) up to the lime of the au ction through an open limit order book. As opposed to a specialist's use of a proprietary closed limit order book, the Arizona Stock Exchange permits investors to examine the current supply and demand for a stock. Having this information enables investors to raise their bid prices (or lower their asked prices) to adjust to the current market conditions. Manipulative behavior is di scouraged by the imposition of a penalty charge for withdrawn orders. The Arizona Stock Exchange possesses some intriguing advantages over traditional dealer markets:

for the security. However, if more investors become optimistic rather than pessimistic, the demand-to-buy schedule will shift to the right (for example, to D'D' in Figure 4.4) and the supply-to-sell schedule will shift to the left (for example, to S'S' in Figure 4.4) , causing an increase in price (to P'). Correspondingly, if more investors become pessimistic rather than optimistic, the demand-to-buy schedule will shift to the left and the supply-to-sell schedule will shift to the right, causing a decrease in price. A factor that complicates an analysis of this type is the tendency for some investors to regard sudden and substantial price changes in a security as indicators of changes in the future prospects of the issuer. In the absence of further information, an investor may interpret such a change as an indication that "someone knows something that I don't know." While exploring the situation, the investor may at least temporarily revise his or her own assessment of the issuer's prospects and, in doing so, may alter his or her demand-to-buy or supply-to-sell schedule. For this reason, few investors place limit orders at prices substantially different from the current price for

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.

';'

1. It is simple and fair. All investors have access to the same auction information, and all investors trade at the same price. 2. Investors have direct access to the market. This feature removes the inherent conflicts of interest present in dealer markets. 3. Investors' orders are a nonymo us. Orders and trade executions are handled by compute r. 4. It matches "natural" buyers and sellers (those with an explicit desire to transact), thereby perhaps establishing more robust and stable prices. 5. Transaction costs are low (about $.01 per share versus $. I 0 to $.20 per share or more in dealer markets) . This last point warrants elaboration. Traditional dealer markets are continuous; trading can occur at any time during the trading day. Continuous trading mechanisms are expensive and require dealers because the "other side" of a trade is not always immediately available. Dealers provide liquidity to investors who wish to transact immediately. With more frequent large trades having been made by institutional investors in the last decade, the ability of dealer markets to provide continuous liquidity has been severely tested. The market crash of October 1987 was an extreme, but not singular, example. Many (and perhaps most) institutional investors do not require immediate liquidity. They can wait several hours to trade, pa rticularly if by waiting they can significantly reduce transaction costs. In lieu of the con-

.. ..

-....., ; ~::l~ •

.' . ~ ' '; ~

~~4~' ~"., ...

.

..~'}~

Summary

Trading procedures employed in security markets vary from auction markets to dealer markets and from call markets to continuous markets. However, the similarities are more important than the differences. In the United States, for example, specialists at the New York Stock Exchange and dealers in the over-the-counter market provide some of the functions of the saitori at the Tokyo Stock Exchange, and trades can take place at any time. Nevertheless, the basic principles of security price determination still apply. In general, market price equates quantity demanded with quantity supplied.

Efficient Markets. Investment Value, and Market Price

.

tinuous intervention of the dealer, the Arizona Stock Exchange substitutes a periodic call to market (akin to the crossing systems discussed in Chapter 3) . Without the expensive overhead of the dealer, the Arizona Stock Exchange can afford to match buyers and sellers at a small fraction of the cost of the dealer market. What are the disadvantages of the Arizona Stock Exchange? Conceptually, there are none to investors who do not require immediate liquidity. However, if you throw a party and no one comes, the party is a failure no matter how elaborate the preparations. Likewise, to be successful, AZX must attract enough institutional investors to generate sufficient liquidity and to contribute to the "discovery" of market prices. Consequen tly, AZX must overcome investor inertia and ignorance. As does any fledgling trading mechanism, the Arizona Stock Exchange faces a difficult dilemma: Institutional investors want to see large trading volumes before they will participate, but those large volumes can occur only if institutional investors participate. To date , traders have not beaten a path to AZX 's door. Currently 20 to 25 institutional investors use the system on any given day, and daily trading volume runs around several hundred thousand shares. Although these figures pale in comparison to the activity on the New York Stock Exchange, participating investors and trading volumes have been growing over the last few years. Whether or not the Arizona Stock Exchange succeeds in its present form , the concept of an electronic call to market is likely to gain increasing attention in the years ahead.

fear that such orders would be executed only if the security's prospects changed significantly. Ifsuch a large price change actually occurred, it would imply the need for a careful reevaluation of the security before buying or selling shares.

4.1.6

~ ""'::~~'?' '''''::.::':;

91

,

Figure 4.4 Shifts in the Aggregate Demand-to-Buy and Supply-ta-Sell Schedules

II1II

MARKET EFFICIENCY The topic of market efficiency has been and is likely to continue to be a matter of intense debate in the investment community. In order to understand and participate in this debate, one must understand just what is meant by market efficiency. First of all, most financial economists would agree that it is desirable to see that capital is channeled to the place where it will do the most good. That is, a reasonable goal of government policy is to encourage the establishment of allocationally efficient markets, in which the firms with the most promising investment opportunities have access to the needed funds. However, in order for markets to be allocationally efficient, they need to be both internally and externally efficient. In an externally efficient market, information is quickly and widely disseminated, thereby allowing each security's price to adjust rapidly in an unbiased manner to new information so that it reflects investment value (a term that will be discussed shortly). In comparison, an internally efficient market is one in which brokers and dealers compete fairly so that the cost of transacting is low and the speed of transacting is high. External market efficiency has been the subject of much research since the 1960s, but internal market efficiency has only recently become a popular area of research.' Indeed, the Securities and Exchange Commission has adopted polices aimed at improving the internal efficiency of markets, primarily by setting rules and regulations that affect the design and operations of security markets. Nevertheless, from now on the term market efficiency will denote external market efficiency, because this is the subj ect that has generated the most interest among practitioners and academics.

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4.2.1

The Efficient Market Model

Imagine a world in which (1) all investors have costless access to currently available information about the future , (2) all investors are capable analysts, and (3) all investors pay close attention to market prices and adjust their holdings appropriately" In such a market a security's price will be a good estimate of its investment value, where investment value is the present value of the security's future prospects, as estimated by well-informed and skillful analysts who use the information that is currently at hand. (Investment value is often referred to as the security's "fair" or "intrinsic" value .) That is, an efficient market, defined as one in which every security's price equals its investment value at all times, will exist. In an efficient market a set of information is fully and immediately reflected in market prices . But what information? A popular distinction, offered by Eugene Fama, is the following: " Form or Efficiency Weak Semistrong Strong

Set Or Information Reflected

In Securtty PrIces Previous prices of securities

All publicly available infonnation All info rmation. both public and private

This distinction leads to an equivalent definition of an efficient market as follows: A market is efficient with respect to a particular set of information if it is impossible to make abnormal profits (other than by chance) by using this set ofinformation toformulate buying and selling decisions.

That is, in an efficient market investors should expect to make only normal profits by earning a normal rate of return on their investments. For example, a market would be described as being weak-form efficient ifit is impossible to make abnormal profits (other than by chance) by using past prices to formulate buying and selling decisions. Similarly, a market would be described as being semistrong-form efficient if it is impossible to make abnormal profits (other than by chance) by using publicly available information to formulate buying and selling decisions. Last, a market would be described as being strong-form efficient ifit is impossible to make abnormal profits (other than by chance) by using any information whatsoever to make buying and selling decisions. Typically. when people refer to efficient markets, they really mean semistrong-form efficient markets, because the United States has strict laws about the use of insider information (a form of private information) to formulate buying and selling decisions. Hence, it is interesting to investigate whether markets are semistrong-form efficient since that involves the set of publicly available information that analysts are restricted to using in preparing their recommendations. Why have the above statements included the qualifying phrase "other than by chance" in the definition of an efficient market? Simply because some people, for example, may invest on the basis of patterns in past prices and end up making extraordinarily high returns. However, in an efficient market this outcome would have had nothing to do with the investor's use of past price information. Instead, it would have been merely due to luck,just as someone who wins a lottery after using a method for picking a number does not necessarily have a successful method for picking winning lottery numbers. Figure 4.5 illustrates these three forms of efficiency. Note how in moving from weak to semistrong to strong-form efficiency, the set of information expands. Thus,

Efficient Markets, Investment Value, and Market Price

93

StTO~g Form: All Public and Private.Infonnation

Figure 4 .5 Information and the Levels of Market Efficiency

if markets are strong-form efficient, then they are also semistrong and weak-form efficient. Similarly, if markets are semistrong-form efficient, then they are also weakform efficient.

4.2.2

Famas Formulation of the Efficient Marl<et Model

Fama presented a general notation describing how investors generate price expectations for securities. That is:

(4.1) where: £ = expected value operator Pj.I+t Tj. ,+1

~,

= price of security jat time t + 1

= return on securityj during period t + I ::: the set ofinformation available to investors at lime t

so E(Pi, /+11 eJ>,) denotes the expected end-of-period price on security j, given the information available at the beginning of the period. Continuing, the term 1 + E( 1]. /+11 eJ>,) denotes the expected return over the forthcoming time period on securities having the same amount of risk as security j, given the information available at the beginning of the period. Last, Pi.' denotes the price of security j at the beginning of the period. Thus, Equation (4.1) states that the expected price for any security at the end of the period (t + 1) is based on the security's expected normal (or equilibrium) rate of return during that period. In turn, the expected rate of return is determined by (or is conditional on) the information set available at the start of the period, eJ>/. Investors are assumed to make full and accurate use of this available information set. That is, they do not ignore or misinterpret this information in setting their return projections for the coming period. What is contained in the available information set eJ>,? The answer depends on the particular form of market efficiency being considered. In the case of weak-form 94

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efficiency, the information set includes past price data. In the case of semistrongform efficiency, the information set includes all publicly available information relevant to establishing security values, incl ud ing the weak-form information set. This information would include published financial data about companies, government data about the state of the economy, earnings estimates disseminated by companies and securities analysts , and so on. Finally, in the case of strong-form efficiency, the information set includes all relevant valuation data, including information known only to corporate insiders, such as imminent corporate takeover plans and extraordinary positive or negative future earnings announcements. If markets are efficient, then investors cannot earn abnormal profits trading on the available information set cI>/ other than by chance. Again employing Farna's notation, the level of over- or undervaluation ofa security is defined as: Xj. t+l

= !JJ,I+I

-

E(Pj, 1+1 1J

(4.2)

where Xj, 1+1 indicates the extent to which the actual price for security j at the end of the period differs from the price expected by investors based on the information available at the beginning of the period. As a result, in an efficient market it must be true that: (4.3)

That is, there will be no expected under- or overvaluation of securities based on the available information set. That information is always impounded in security prices.

4.2.3

Security Price Changes As a Random Walk

What happens when new information arrives that changes the information set 1' such as an announcement that a company's earnings havejust experienced a significant and unexpected decline? In an efficient market, investors will incorporate any new information immediately and fully in security prices. New information is just that: new, meaning a surprise. (Anything that is not a surprise is predictable and should have been anticipated before the fact .) Because happy surprises are about as likely as unhappy ones, price changes in an efficient market are about as likely to be positive as negative. A security's price can be expected to move upward by an amount that provides a reasonable return on capital (when considered in conjunction with dividend payments), but anything above or below such an amount would, in an efficient market, be unpredictable. In a perfectly efficient market, price changes are random." This does not mean that prices are irrational. On the contrary, prices are quite rational. Because information arrives randomly, changes in prices that occur as a consequence of that information will appear to be random, sometimes being positive and sometimes being negative. However, these price changes are simply the consequence of investors' reassessing a security'S prospects and adjusting their buying and selling appropriately. Hence the price changes are random but rational. As mentioned earlier, in an efficient market a security's price will be a good estimate of its investment value, where investment value is the present value of the security's future prospects as estimated by well-informed and capable analysts. In a well-developed and free market, major disparities between price and investment value will be noted by alert analysts who will seek to take advantage of their discoveries. Securities priced below investment value (known as underpriced or undervalued securities) will be purchased, creating pressure for price increases due to the increased demand to buy. Securities priced above investment value (known as overpriced or overvalued securities) will be sold, creating pressure for price decreases due to the increased supply to sell. As investors seek to take advantage of opportunities Efficient Markets, Investment Value , and Market Price

95

created by temporary inefficiencies, they will cause the inefficiencies to be reduced, denying the less alert and the less informed a chance to obtain large abnormal profits. As a consequence of the efforts of such highly alert investors, at any time a security's price can be assumed to equal the security's investment value, implying that security mispricing will not exist.

4.2.4

Observations about Perfectly Efficient Markets

Some interesting observations can be made about perfectly efficient markets. 1. Investors should expect to make a fair return on their investment but no more. This statement means that looking for mispriced securities with either technical analysis (whereby analysts examine the past price behavior of securities) or fundamental analysis (whereby analysts examine earnings and dividend forecasts) will not prove to be fruitful. Investing money on the basis of either type of analysis will not generate abnormal returns (other than [or those few investors who turn out to be lucky) . 2. Markets will be efficient only if enough investors believe that they are not efficient. The reason for this seeming paradox is straightforward; it is the actions of investors who carefully analyze securities that make prices reflect investment values. However, if everyone believed that markets are perfectly efficient, then everyone would realize that nothing is to be gained by searching for undervalued securities, and hence nobody would bother to analyze securities. Consequently, security prices would not react instantaneously to the release of information but instead would respond more slowly. Thus, in a classic "Catch-22" situation, markets would become inefficient if investors believed that they are efficient, yet they are efficient because investors believe them to be inefficient. 3. Publicly known investment strategies cannot be expected to generate abnormal returns. If somebody has a strategy that generated abnormal returns in the past and subsequently divulges it to the public (for example, by publishing a book or article about it), then the usefulness of the strategy will be destroyed. The strategy, whatever it is based on, must provide some means to identify mispriced securities. The reason that it will not work after it is made public is that the investors who know the strategy will try to capitalize on it, and in doing so will force prices to equal investment values the moment the strategy indicates a security is mispriced. The action of investors following the strategy will eliminate its effectiveness at identifying mispriced securities. 4. Some investors will display impressive performance records. However, their performance is merely due to chance (despite their assertions to the contrary). Think of a simple model in which half of the time the stock market has an annual return greater than Treasury bills (an "up" market) and the other half of the time its return is less than T-bills (a "down" market). With many investors attempting to forecast whether the stock market will be up or down each year and acting accordingly, in an efficient market about half the investors will be right in any given year and half will be wrong. The next year, half of those who were righ t the first year will be right the second year too. Thus, 1/4 (= 1/2 X 1/2) of all the investors will have been right both years. About half of the surviving investors will be right in the third year, so in total 1/8 (= 1/2 X 1/2 X 1/2) of all the investors can show that they were right all three years. Thus, it can be seen that (1/2) T investors will be correct every year over a span of Tyears. Hence if T = 6, then 1/64 of the investors will have been correct all five years, but only because they were lucky, not because they were skillful. Consequently, anecdotal evidence about the success of certain investors is misleading. Indeed, any fees paid for advice from such investors would be wasted. 96

CHAPTER 4

5. Professional investors should fare no better in picking securities than ordinary investors. Prices always reflect investment value, and hence the search for mispriced securities is futile. Consequently, professional investors do not have an edge on ordinary investors when it comes to identifying mispriced securities and generating abnormally high returns. 6. Past performance is not an indicator of future performance. Investors who have done well in the past are no more likely to do better in the future than are investors who have done poorly in the past. Those who did well in the past were merely lucky, and those who did poorly merely had a streak of misfortune. Because past luck and misfortune do not have a tendency to repeat themselves, historical performance records are useless in predicting future performance records. (Of course, if the poor performance was due to incurring high operating expenses, then poor performers are likely to remain poor performers.)

4.2.5

Observations about Perfectly Efficient Markets with Transactions Costs

The efficient market model discussed earlier assumed that investors had free access to all information relevant to setting security prices. In reality, it is expensive to collect and process such information. Furthermore, investors cannot adjust their portfolios in response to new information without incurring transaction costs. How does the existence of these costs affect the efficient market model? Sanford Grossman and joseph Stiglitz considered this issue and arrived at two important conclusions.l 1. In a world where it costs money to analyze securities, analysts will be able to identify mispriced securities. However, their gain from doing so will be exactly offset by the increased costs (perhaps associated with the money needed to procure data and analytical software) that they incur. Hence, their gross returns will indicate that they have made abnormal returns, but their net returns will show that they have earned a fair return and nothing more. Of course, they can earn less than a fair return in such an environment if they fail to properly use the data. For example, by rapidly buying and selling securities, they may generate large transactions costs that would more than offset the value of their superior security analysis. 2. Investors will do just as well using a passive investment strategy where they simply buy the securities in a particular index and hold onto that investment. Such a strategy will minimize transaction costs and can be expected to do as well as any professionally managed portfolio that actively seeks out mispriced securities and incurs costs in doing so. Indeed, such a strategy can be expected to outperform any professionally managed portfolio that incurs unnecessary transaction costs (by, for example, trading too often) . Note that the gross returns of professionally managed portfolios will exceed those of passively managed portfolios having similar investment objectives but that the two kinds of portfolios can be expected to have similar net returns.

__

TESTING FOR MARKET EFFICIENCY

Now that the method for determining prices in a perfectly efficient market has been described, it is useful to take a moment to consider how to conduct tests to determine if markets actually are perfectly efficient, reasonably efficient, or not efficient at all. There are a multitude of methodologies, but three stand out. They involve conducting event studies, looking for patterns in security prices, and examining the investment performance of professional money managers. Efficient Markets. Investment Value. and Market Price

97

INSTITUTIONAL ISSUES

The Active versus Passive Debate The issue of market efficiency has clear and important ramifications for the investment management industry, At stake are billions of dollars in investment management fees, professional reputations, and, some would argue, even the effective functioning of our capital markets. Greater market efficiency implies a lower probability that an investor will be able to consistently identify mispriced securities. Consequently, the more efficient is a security market, the lower is the expected payoff to investors who buy and sell securities in search of abnormally high returns. In fact, when research and transaction costs are factored into the analysis, greater market efficiency increases the chances th at investors "actively" managing their portfolios will underperform a simple technique of holding a portfolio that resembles the composition of the entire market. Institutional investors have responded to evidence of significant efficiency in the U.S. stock and bond markets by increasingly pursing an investment approach referred to as passive management. Passive management involves a long-term , buyand-hold approach to investing. The investor selects an appropriate target and buys a portfolio designed to closely track the performance of that target. Once the portfolio is purchased, little additional trading occurs, beyond reinvesting income or minor rebalancings necessary to accurately track the target. Because the selected target is usually (although not necessarily) a hroad, d iversified market index (for example, the S&P 500 for domestic common stocks), passive management (see Chapter 23) is commonly referred to as "indexation," and the passive portfolios are called "index funds." Active management, on the other hand, involves a systematic effort to exceed the performance of a selected target. A wide array of active management in-

4.3.1

vestment approaches exists-far too many to summarize in this space. Nevertheless, all active management entails the search for mispriced securities or for mispriced groups of securities. Accurately identifying and adroitly purchasing or selling these mispriced securities provides the active investor with the potential to outperform the passive investor. Passive management is a relative newcomer to the investment industry. Before the mid-I 960s, it was axiomatic that investors should search for mispriced stocks . Some investment strategies had passive overtones, such as buying "solid, blue-chip" companies for the "long term." Nevertheless, even these strategies implied an attempt to outperform some nebulously specified market target. The concepts of broad diversification and passive management were, for pr actical purposes, nonexistent. Attitudes changed in the 1960s with the popularization of Markowitz's portfolio selection concepL~ (see Chapter 6), the introduction ofthe efficient market hypothesis (see this chapter), the emphasis on "the market portfolio" derived from the Capital Asset Pricing Model (see Chapter 9), and various academic studies proclaiming the futility of active management. Many investors, especially large institutional investors, began to question the wisdom of actively managing all of their assets. The first domestic common stock index fund was introduced in 1971. By the end of the decade, roughly $100 million was invested in index funds . Today, hundreds of billions of dollars are invested in domestic and international stock and bond index funds. Even individual investors have become enamored of index funds. Passively managed portfolios are some of the fastest growing products offered by many large mutual fund organizations. Proponents of active management argue that capital markets are inefficient enough to justify the

Event Studies

Event studies can be carried out to see just how fast security prices actually react to the release of information. Do they react rapidly or slowly? Are the returns after the announcement date abnormally high or low, or are they simply normal? Note that the answer to the second question requires a definition of a "normal return" for a given security. Typically "normal" is defined by the use of some equilibrium-based asset pricing model, two of which will be discussed in Chapters 9 and 11. An improperly specified asset pricing model can invalidate a test of market efficiency. Thus, event studies are really joint tests, as they simultaneously involve tests of the asset pricing

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search for mispriced securities. They may disagree on the degree of the markets' inefficiencies. Technical analysts (see Chapter 16), for example, tend to view markets as dominated by emotionally driven and predictable investors, thereby creating numerous profit opportunities for the creative and disciplined investor. Conversely, managers who use highly quantitative investment tools often view profit opportunities as smaller and less persistent. Nevertheless, all active managers possess a fundamental belief in the existence of consistently exploitable security mispricings. As evidence they frequently poin t to the stellar track records of certain successful managers and various studies identifying market inefficiencies (see Appendix A, Chapter 16, which discusses empirical regularities). Some active management proponents also introduce into the active-passive debate what amounts to a moralistic appeal. They contend that investors have virtually an obligation to seek out mispriced securities, because their actions help remove these mispricings and thereby lead to a more efficient allocation of capital. Moreover, some proponents derisively contend that passive management implies settling for mediocre, or average, performance. Proponents of passive management do not deny that exploitable profit opportunities exist or that some managers have established impressive performance results. Rather, they contend that the capital markets are efficient enough to prevent all but a few with inside information from consistently being able to earn abnormal profits. They claim that examples of past successes are more likely the result of luck rather than skill . If 1,000 people flip a coin ten times, the odds are that one ofthem will flip all heads. In the investment industry, this person is crowned a brilliant money manager.

Passive management proponents also argue that the expected returns from active management are actually less than those for passive management. The fees charged by active managers are typically much higher than those levied by passive managers. (The difference averages anywhere from .30% to 1.00% of the managers' assets under managernent.) Further, passively managed portfolios usually experience very small transaction costs, whereas, depending on the amount of trading involved, active management transaction costs can be quite high. Thus it is argued that passive managers will outperform active managers because of cost differences. Passive management thus entails settling for superior, as opposed to mediocre, results. The active-passive debate will never be totally resolved. The random "no ise" inherent in investment performance tends to drown out any systematic evidence of investment management skill on the part of active managers. Subjective issues therefore dominate the discussion, and as a result neither side can convince the other of the correctness of its Viewpoint. Despite the rapid growth in passively managed assets, most domestic and international stock and bond portfolios remain actively managed. Many large institutional investors, such as pension funds, have taken a middle ground on the matter, hiring both passive and active managers. In a crude way, this strategy may be a reasonable response to the unresolved active-passive debate. Assets cannot all be passively managed-who would be left to maintain security prices at "fair" value levels? On the other hand, it may not take many skillful active managers to ensure an adequate level of market efficiency. Further, the evidence is overwhelming that managers with above-average investment skills are in the minority of the group currently offering their services to investors.

model's validity and tests of market efficiency. A finding that prices react slowly to information might be due to markets' being inefficient, or it might be due to the use of an improper asset pricing model, or it might be due to both . As an example of an event study, consider what happens in a perfectly efficient market when information is released. When the information arrives in the marketplace, prices will react instantaneously and, in doing so, will immediately move to their new investment values. Figure 4.6(a) shows what happens in such a market when good news arrives; Figure 4.6(b) shows what happens when bad news arrives. Note that in both cases the horizontal axis is a time line and the vertical axis is the security's price, so the figure reflects the security's price over time. At time 0 (t = 0),

Efficient Markets, Investment Value, and Market Price

99

pA

~

'C

~------------------

P B f--------------------'

~

1=0

Time*

(a) Arrival of Good News

P B f--------------------,

~

pA

L-

__

'C

~

1=0

Time*

(b) Arrival of Bad News

Figure 4.6 The Effect of Information on a Firm's Stock Price in a Perfectly Efficient Market. *Information is assumed to arrive at time t = O.

information is released about the firm. Observe that, shortly before the news arrived, the security's price was at a price P ~ With the arrival of the information the price immediately moves to its new equilibrium level of P '\ where it stays until some additional piece of information arrives. (To be more precise, the vertical axis would represent the security's abnormal return, which in an efficient market would be zero until t = 0, when it would briefly be either significantly positive, in the case of good news, 100

CHAPTER 4

t=

0

1= I

Time*

(a) Slow Reaction of Stock Price to Information

pll - - - - - - - - - - -

~ .1:

P B f-------'

Q.,

1=0

1= I

Time*

(b) Overreaction of Stock Price to Information

Figure 4.7 Possible Effects of Information on a Firms Stock Price in an Inefficient Market. • Information is assumed to arrive at time I = O.

or significantly negative, in the case of bad news. Afterward, it would return to zero. For simplicity, prices are used instead of returns, because over a short time period surrounding t = 0 the results are essentially the same.) Figure 4.7 displays two situations that cannot occur with regularity in an efficient market when good news arrives. (A similar situation, although not illustrated here, cannot occur when bad news arrives.) In Figure 4.7(a) the security reacts slowly to Efficient Markets, Investment Value, and Market Price

101

the information, so it does not reach its equilibrium price pA until t = 1. This situation cannot occur regularly in an efficient market, because analysts will realize after t = 0 but before t = 1 that the security is not priced fairly and will rush to buy it. Consequently, they will force the security to reach its equilibrium price before t = 1. Indeed, they will force the security to reach its equilibrium price moments after the information is released at t = O. In Figure 4.7(b) the security's price overreacts to the information and then slowly settles down to its equilibrium value . Again , this situation cannot occur with regularity in an efficient market. Analysts will realize that the security is selling above its fair value and will proceed to sell it if they own it or to short sell it if they do not own it. As a consequence of their actions, they will prevent its price from rising above its equilibrium value, pA, after the information is released. Many event studies have been made about the reaction of security prices, particularly stock prices, to the release of information, such as news (usually referred to as "announcements") pertaining to earnings and dividends, share repurchase programs, stock splits and dividends, stock and bond sales, stock listings, bond rating changes, mergers and acquisitions, and divestitures. Indeed, this area of academic research has become a virtual growth industry.

4.3.2

looking for Patterns

A second method to test for market efficiency is to investigate whether there are any patterns in security price movements attributable to something other than what one would expect. Securities can be expected to provide a rate of return over a given time period in accord with an asset pricing model. Such a model asserts that a security's expected rate of return is equal to a riskfree rate of return plus a "risk premium" whose magnitude is based on the riskiness of the security. Hence , if the riskfree rate and risk premium are both unchanging over time, then securities with high average returns in the past can be expected to have high returns in the future. However, the risk premium, for example, may be changing over time, making it difficult to see if there are patterns in security prices. Indeed, any tests that are conducted to test for the existence of price patterns are once again join t tests of both market efficiency and the asset pricing model that is used to estimate the risk premiums on securities. In recent years, a large number of these patterns have been identified and labeled as "empirical regularities" or "market anomalies." For example, one of the most prominent market anomalies is the January effect. Security returns appear to be abnormally high in the month ofJanuary. Other months show no similar type returns. This pattern has a long and consistent track record, and no convincing explanations have been proposed. (The January effect and other market anomalies are discussed in Chapter 16.)

4.3.3

Examining Performance

The third approach is to examine the investment record of professional investors. Are more of them able to earn abnormally high rates of return than one would expect in a perfectly efficient market? Are more of them able to consistently earn abnormally high returns period after period than one would expect in an efficient market? Again, problems are encountered in conducting such tests because they require the determination of abnormal returns, which, in turn, requires the determination ofjust what are "normal returns." Because normal returns can be determined only by assuming that a particular asset pricing model is applicable, all such tests are joint tests of market efficiency and an asset pricing model. 102

CHAPTER 4

. . SUMMARY OF MARKET EFFICIENCY TEST RESULTS Many tests have been conducted over the years examining the degree to which security markets are efficient. Rather than laboriously review the results of those tests here, the most prominent studies are discussed in later chapters, where the specific investment activities associated with the studies are considered. However, a few comments about the general conclusions drawn from those studies are appropriate here.

4.4.1

Weak-Form Tests

Early tests of weak-form market efficiency failed to find any evidence that abnormal profits could be earned trading on information related to past prices. That is, knowing how security prices had moved in the past could not be translated into accurate predictions of future security prices. These tests generally concluded that technical analysis, which relies on forecasting security prices on the basis of past prices, was ineffective. More recent studies, however, have indicated that investors may overreact to certain types of information, driving security prices temporarily away from their investment values. As a result, it may be possible to earn abnormal profits buying securities that have been "oversold" and selling securities whose prices have been bid up excessively. It should be pointed out, however, that these observations are debatable and have not been universally accepted.

4.4.2

Semistrong-Form Tests

The results of tests of semistrong-form market efficiency have been mixed. Most event studies have failed to demonstrate sufficiently large inefficiencies to overcome transaction costs. However, various market "anomalies" have been discovered whereby securities with certain characteristics or during certain time periods appear to produce abnormally high returns. For example, as mentioned, common stocks in January have been shown to offer returns much higher than those earned in the other 11 months of the year.

4.4.3

Strong-Form Tests

One would expect that investors with access to private information would have an advantage over investors who trade only on publicly available information. In general, corporate insiders and stock exchange specialists, who have information not readily available to the investing public, have been shown to be able to earn abnormally high profits. Less clear is the ability of security analysts to produce such profits. At times, these analysts have direct access to private information, and in a sense they also "manufacture" their own private information through their research efforts. Some studies have indicated that certain analysts are able to discern mispriced securities, but whether this ability is due to skill or chance is an open issue.

4.4.4

Summary of Efficient Markets

Tests of market efficiency demonstrate that U.S. security markets are highly efficient, impounding relevant information about investment values into security prices quickly and accurately. Investors cannot easily expect to earn abnormal profits trading on publicly available information, particularly once the costs of research and transactions are considered. Nevertheless, numerous pockets of unexplained abnormal returns have been identified, guaranteeing that the debate over the degree of market efficiency will continue. Efficient Markets. Investment Value. and Market Price

103

. . SUMMARY 1. The forces of supply and demand interact to determine a security's market price. 2. An investor's demand-to-buy schedule indicates the quantity ofa security that the investor wishes to purchase at various prices. 3. An investor's supply-to-sell schedule indicates the quantity of a security that the investor wishes to sell at various prices. 4. The demand and supply schedules for individual investors can be aggregated to create aggregate demand and supply schedules for a security. 5. The intersection of the aggregate demand and supply schedules determines the market clearing price ofa security. At that price, the quantity traded is maximized. 6. The market price of a security can be thought of as representing a consensus opinion about the future prospects for the security. 7. An allocationally efficient market is one in which firms with the most promising investment opportunities have access to needed funds . 8. Markets must be both internally and externally efficient in order to be allocationally efficient. In an externally efficient market, information is quickly and widely disseminated, thereby allowing each security's price to adjust rapidly in an unbiased manner to new information so that it reflects investment value. In an internally efficient market, brokers and dealers compete fairly so that the cost of transacting is low and the speed of transacting is high. 9. A security's investment value is the present value of the security's future prospects, as estimated by well-informed and capable analysts, and can be thought of as the security's fair or intrinsic value . 10. In an efficient market a security's market price will fully reflect all available information relevant to the security's value at that time. 11. The concept of market efficiency can be expressed in three forms: weak, semistrong, and strong. 12. The three forms of market efficiency make different assumptions about the set of information reflected in security prices. 13. Tests of market efficiency are really joint tests about whether markets are efficient and whether security prices are set according to a specific asset pricing model. 14. Evidence suggests that U.S. financial markets are highly efficient. QUESTIONS

AND

PROBLEMS

0

1. What is the difference between call security markets and continuous security markets? 2. Using demand-to-buy or supply-to-sell schedules, explain and illustrate the effect of the following events on the equilibrium price and quantity traded of Fairchild Corporation's stock. a. Fairchild officials announce that next year's earnings are expected to be significantly higher than analysts had previously forecast. b. A wealthy shareholder initiates a large secondary offering of Fairchild stock. c. Another company, quite similar to Fairchild in all respects except for being privately held, decides to offer its outstanding shares for sale to the public. 3. Imp Begley is pondering this statement: "The pattern of security price behavior might appear the same whether markets were efficient or security prices bore no relationship whatsoever to investment value." Explain to Imp the meaning of the statement. 104

. (j--IAPTER 4

4. We all know that investors have widely diverse opinions about the future course of the economy and earnings forecasts for various industries and companies. How then is it possible for all these investors to arrive at an equilibrium price for any particular security? 5. Distinguish between the three forms of market efficiency. 6. Does the fact that a market exhibits weak-form efficiency necessarily imply that it is also strong-form efficient? How about the converse statement? Explain. 7. Consider the following types of information . If this information is immediately and fully reflected in security prices, what form of market efficiency is implied? a. A company's recent quarterly earnings announcement b. Historical bond yields c. Deliberations of a company's board of directors concerning a possible merger with another company d. Limit orders in a specialist's book e. A brokerage firm's published research report on a particular company f. Movements in the Dow Jones Industrial Average as plotted in The Wall StreetJournal 8. Would you expect that fundamental security analysis makes security markets more efficient? Why? 9. Would you expect that NYSEspecialists should be able to earn an abnormal profit in a semistrong efficient market? Why? 10. Is it true that in a perfectly efficient market no investor would consistently be able to earn a profi t? 11. Although security markets may not be perfectly efficient, what is the rationale for expecting them to be highly efficient? 12. When a corporation announces its earnings for a period, the volume of transactions in its stock may increase, but frequently that increase is not associated with significant moves in the price of its stock. How can this situation be explained? 13. What are the implications of the three forms of market efficiency for technical and fundamental analysis (discussed in Chapter I)? 14. In 1986 and 1987 several high-profile insider trading scandals were exposed. a. Is successful insider trading consistent with the three forms of market efficiency? Explain. b. Play the role of devil's advocate and present a case outlining the benefits to financial markets of insider trading. 15. The text states that tests for market efficiency involving an asset pricing model are really joint tests. What is meant by that statement? 16. In perfectly efficient markets with transaction costs, why should analysts be able to find mispriced securities? 17. When investment managers present their historical performance records to potential and existing customers, market regulators require the managers to qualify those records with the comment that "past performance is no guarantee of future performance." In a perfectly efficient market, why would such an admonition be particularly appropriate? CFA

EXAM

QUESTIONS

18. Discuss the role of a portfolio manager in a perfectly efficient market. 19. Fairfax asks for information concerning the benefits of active portfolio management. She is particularly interested in the question of whether active managers can be expected to consistently exploit inefficiencies in the capital markets to produce above-average returns without assuming higher risk. The semistrong form of the efficient market hypothesis (EMH) asserts that all publicly available information is rapidly and correctly reflected in securities Efficient Markets, Investment Value, and Market Price

lOS

prices. This assertion implies that investors cannot expect to derive above-average profits from purchases made after the information has become public because security prices already reflect the information 's full effects. a. (i) Identify and explain two examples of empirical evidence that tend to support the EMH implication stated above. (ii) Identify and explain two examples of empirical evidence that tend to refute the EMH implication stated above. b. Discuss two reasons why an investor might choose an active manager even if the markets were, in fact, semistrong-form efficient.

' E NDNOTES I

A burgeoning field of research in finance is known as market microstructure, which involves the study of internal market efficiency.

2

Actually, not all investors need to meet these three conditions in order for security prices to equal their investment values. Instead, what is needed is for marginal investors to meet these conditions, since their trades would correct the mispricing that would occur in their absence.

~ Eugene F. Fama, "Efficient Capital Markets: A Review of Theory and Empirical Work," Jour-

nal oj Finance 25, no. 5 (May 1970): 383-417. 4 Some

people assert that daily stock prices follow a random walk, meaning that stock price changes (say, from one day to the next) are independently and identically distributed. That is, the price change from day t to day t + 1 is not influenced by the price change from day / - I to day t, and the size of the price change from one day to the next can be viewed as being determined by the spin ofa roulette wheel (with the same roulette wheel being used every day) . Statistically, in a random walk p, P'-I + e, where e, is a random error term whose expected outcome is zero but whose actual outcome is like the spin of a roulette wheel. A more reasonable characterization is to describe daily stock prices as following a random walk with drift, where p, = P'-I + d + e, where d is a small positive number, since stock prices have shown a tendency over time to go up. However, since it can be reasonably argued that the random error term e, is not independent and identically distributed over time (that is, evidence suggests that the same roulette wheel is not used every period) , the most accuate characterization of stock prices is to say they follow a submnrtingale process. This simply means that a stock's expected price in period t + I, given the information that is available at time t, is greater than the stock's price at time t.

=

:;Sanford]. Grossman andJoseph E. Stiglitz, "On the Impossibility oflnformationally Efficient Markets," American EconomicReoieto 70, no . 3 Uune 1980).

' K E Y

TERMS

demand-to-buy schedule supply-to-sell schedule allocationally efficient market externally efficient market internally efficient market investment value

efficient market weak-form efficient semistrong-form efficient strong-form efficient random walk random walk with drift

REFERENCES 1. Discussion and examination of the demand curves for stocks are contained in : Andrei Shleifer, "Do Demand Curves Slope Down?" Journal oj Finance 41, no. 3 Uuly 1986) : 579-590. 106

CHAPTER 4

Lawrence Harris and Eitan Curel, "Price and Volume Effects Associated with Changes in the S&P 500: New Evidence for the Existence of Price Pressures," journal of Financ e 41, no .4 (September 1986): 815-829. Stephen W. Pruitt and K. C.John Wei, "Institution al Ownership and Changes in the S&P 500 ," journal of Finance 44, no . 2 (june 1989) : 509-513. 2. For articles presenting arguments that securities are "overpriced" owing to short sale restrictions, see: Edward M. Miller, "Risk, Uncertainty, and Divergence of Opin ion," journal ofFinance 32, no .4 (September 1977): 1151-1168. Douglas W. Diamond and Robert E. Verrecchia, "Constraints on Short-Selling and Asset Price Adjustment to Private Information," journal of Financial Economics 18, no. 2 (june 1987) : 277-311. 3. Allocational, external, and internal market efficiency are discussed in: Richard R. West, "Two Kinds of Market Efficiency," Financial Analysts journal 31, no. 6 (November/December 1975) : 30-34. 4. Many people believe that the following articles are the seminal pieces on efficient markets: Paul Samuelson, "Proof That Properly Anticipated Prices Fluctuate Randomly," Industrial Managemnu Reuieut 6 (1965): 41-49. Han)' V. Roberts, "Stock Market 'Patterns' and Financial Analysis: Methodological Suggestions,"./ournal of Finance 14, no. 1 (March 1959): 1-10. Eugene F. Fama, "Efficient Capital Markets: A Review of Theory and Empirical Work," journal ofFinance 25, no . 5 (May 1970) : 383-417. Eugene F. Fama, "Efficient Capital Markets: II," journal of Finance 46 , no . 5 (December 1991): 1575-1617. 5. For an extensive discussion of efficient markets and related evidence, see: Ceorge Foster, Financial Statement Analysis (Englewood Cliffs, NJ: Prentice Hall , 1986), Chapters 9 and 11. Stephen F. LeRoy, "Capital Market Efficiency: An Update," Federal Reserve Bank of San FranciscoEconomic Review no. 2 (Spring 1990) : 29-40. A more detailed version of this paper can be found in: Stephen F. LeRoy, "Efficient Capital Markets and Martingales," journal of Economic Literature 27, no. 4 (December 1989): 1583-1621. Peter Fortune, "Stock Market Efficiency: An Autopsy?" New England Economic Review (March/April 1991) : 17-40. Richard A. Brealey and Stewart C. Myers, Prin ciples of Corporate Finance (New York: McCraw-Hill, 1996), Chapter 13. Stephen A. Ross, Randolph W. Westerfield, and jeffrey F.Jaffe, Corporate Finance (Boston: Invin /McCraw Hill, 1996) , Chapter 13. 6. Interesting overviews of efficient market concepts are presented in: Robert Ferguson, "An Efficient Stock Market? Ridiculous!" journal ofPortfolio Management 9, no . 4 (Summer 1983) : 31-38. Bob L. Boldt and Harold L. Arbit, "Efficient Markets and the Professional Investor," Financial Analystsjournal 40, no. 4 (july /August 1984): 22-34. Fischer Black, "Noise," journal ofFinance 41, no . 3 Guly 1986): 529- 543. Keith C. Brown, W. V. Harlow, and Seha M. Tinic, "How Rational Investors Deal with Uncertainty (Or, Reports of the Death of Efficient Markets Theory Are Greatly Exaggerated)," journal ofApplied CorporateFinance 2, no. 3 (Fall 1989) : 45-58. Ray Ball, "T h e Theory of Stock Market Efficiency: Accomplishments and Limitations," journal ofApplied Corporate Finance 8, no. I (Spring 1995) : 4-17.

Efficient Markets. Investment Value. and Market Price

107

CHAPTER

5

THE VALUATION OF RISKLESS SECURITIES

A useful first step in understanding security valuation is to consider riskless securities, which are those fixed-income securities that are certain of making their promised payments in full and on time. Subsequent chapters will be devoted to valuing risky securities, for which the size and timing of payments to investors are uncertain. Whereas common stocks and corporate bonds are examples of risky securities, the obvious candidates for consideration as riskless securities are the securi ties that represen t the debt of the federal governmen t. Because the government can print money whenever it chooses, the promised payments on such securities are virtually certain to be made on schedule. However, there is a degree of uncertainty as to the purchasing power of the promised payments. Although government bonds may be riskless in terms of their nominal payments, they may be quite risky in terms of their real (or inflation-adjusted) payments. This chapter begins with a discussion of the relationship between nominal and real interest rates. Despite the concern with inflation risk, it will be assumed that there are fixedincome securities whose nominal and real payments are certain. Specifically, it will be assumed that the magnitude of inflation can be accurately predicted. Such an assumption makes it possible to focus on the impact of time on bond valuation. The influences of other attributes on bond valuation can be considered afterward.

II1II

NOMINAL VERSUS REAL INTEREST RATES Modern economies gain much of their efficiency through the use of money-a generally agreed-upon medium of exchange. Instead of trading present corn for a future Toyota, as in a barter economy, the citizen of a modern economy can trade his or her corn for money (that is, "sell it"), trade the money for future money (that is, "invest it"), and finally trade the future money for a Toyota (that is, "buy it") . The rate at which he or she can trade present money for future money is the nominal (or "monetary") interest rate-usually simply called the interest rate. In periods of changing prices, the nominal interest rate may prove a poor guide to the real return obtained by the investor. Although there is no completely satisfactory way to summarize the many price changes that take place in such periods, most governments attempt to do so by measuring the cost of a specified bundle of major 108

items. The "overall" price level computed for this representative combination of items is usually called a cost-of-living index or consumer price index. Whether the index is relevant for a given individual depends to a major extent on the similarity of his or her purchases to the bundle of goods and services used to construct the index. Moreover, such indices tend to overstate increases in the cost of living for people who do purchase the chosen bundle of items for two reasons. First, improvements in quality are seldom taken adequately into account. Perhaps more important, little or no adjustment is made in the composition of items in the bundle as relative prices change . The rational consumer can reduce the cost of attaining a given standard ofliving as prices change by substituting relatively less expensive items for those that have become relatively more expensive. Despite these drawbacks, cost-of-living indices provide at least rough estimates of changes in prices. And such indices can be used to determine an overall real rate of interest. For example, assume that during a year in which the nominal rate of interest is 7%, the cost-of-living index increases from 121 to 124. This means that the bundle of goods and services that cost $100 in some base year and $121 at the beginning of the year now cost $124 at year-end. The owner of such a bundle could have sold it for $121 at the start of the year, invested the proceeds at 7% to obtain $129.47 (= $121 X 1.07) at the end of the year, and then immediately purchased 1.0441 (= $129.47/$124) bundles. The real rate of interest was, thus, 4.41% (= 1.0441 - 1). Effectively then, the real interest rate represents the percentage increase in an investor's consumption level from one period to another. These calculations can be summarized in the following formula: Go(l

+

NIR) = 1

+

RIR

G\

(5.1 )

where:

Co' =:'level df the cost~f-livingindex at the beginning of the year C\ ~ level of the cOllt~f..Jivingindex at the end of the year NIR = the nomlnal interest rate RlR = the real-interest rate Alternatively, Equation (5.1) can be written as: 1 1

+

NIR

+ GGL

=

1

+ RIR

(5.2)

where GCL equals the rate of change in the cost of living index, or (G\ - Go)/ Co. In this case, CCL = .02479 = (124 - 121)/121, so prices increased by about 2.5%. For quick calculation, the real rate of interest can be estimated by simply subtracting the rate of change in the cost of living index from the nominal interest rate: RIR

== NIR - GGL

(5.3)

where == means "is approximately equal to." In thi s case the quick calculation results in an estimate of 4.5 % (= 7% - 2.5%), which is reasonably close to the true value of4.41 %. Equation (5.2) can be applied on either a historical or a forward-looking basis . The economist Irving Fisher argued in 1930 th at the nominal interest rate ought to be related to the expected real interest rate and the expected inflation rate through an equation that became known as the Fisher equation. That is: The Valuation of Riskless Securities

109

~ .'

.

INSTITUTIONAL ISSUES

Almost Riskfree Securities R iskfree securities playa central role in modern financial theory, providing the baseline against which to evaluate risky investment a ltern atives. It is perhaps surprising therefore that no risklree financial asset has historically been available to U.S. inve stors. Recent developments in the U.S. Treasury bond market, however, have made important strides toward bringing that deficiency to an end. A riskless security provides an investor with a guarante(~d (certain) return over the investor's time horizon . A~ the investor is ultimately interested in the purchasing power of his or her investments, the riskless security's return should be certain, not just on a nominal but on a real (or inflation-adjusted) basis. Although U.S. Treasury securities have zero risk of default, even they have not traditionally provided riskless real returns. Their principal and interest payments are not adjusted for infl ation over the securities' lives. As a result, unexpected inflation may produce re al returns quite different from those expected at the time the securities were purchased. However, assu m e for the moment that U.S. inflation remains low and fairly predictable so that we can effectively ignore inflation risk. Will Treasury securities provide investors with riskless returns? The answer is generally no. An investor's time horizon usually will not coincide with the life of a particular Treasury security. If the investor's time horizon is longer than the sec urity's life, then the investor must purchase another Treasury security when the first security matures. If interest rates have changed in the interim, the investor will earn a different return than he or she originally a nticipated. (This risk is known as reinvestment-rate risk; see Chapter 8.) If the Treasury security's life exceeds the investor's time horizon, then the investor will have to sell the security before it matures. If interest rates change before the sale, the price of the security will change, thereby causing the investor to earn a dif-

NIR

ferent return from the one originally anticipated. (This risk is known as interest-rate or price risk; see Chapter 8.) Even if the Treasury security's life matches the investor's time horizon, it generally will not provide a riskless return. With the exception of Treasury bills and STRIPS, all Treasury securities make periodic interest payments (see Chapter 13), which the investor must reinvest. If interest rates change over the security's life, then the investor's reinvestment rate will ch ange, causing the investor's return to differ from that originally anticipated at the time the security was purchased. Cle a rly, what inve stors need are Treasury securities th at make only one payment (which includes principal and all interest) when those securities mature . Investors could then select a security whose life matched their investment time horizons. These securities would be truly riskless, at least o n a nominal basis . A fixed-income security that makes only one payment at maturity is called a zero-coupon (or pure-discount) bond. Until the 1980s, however, zero-coupon Treasury bonds did not exist, except for Tr easury bills (which have a maximum maturity of one year). However, a coupon-bearing Treasury security can be viewed as a portfolio of zero-coupon bonds, with each interest payment, as well as the principal, considered a separate bond. In 1982, several brokerage firms came to a novel realization : A Treasury security's payments could be segregated and sold piecemeal through a process known as coupon stripping. For example, broke rage firm XYZ pu rchases a newly issued 20 -year Treasury bond and deposits the bond with a custodian bank. Assuming semiannual interest payments, XYZ creates 41 se p a ra te zero-coupon bonds (40 interest payments plus one principal repayment) . Naturally, XYZ can create larger zero-coupon bonds by buyin g and depositing more se curities of the same Treasury issue.

= [1 + E(RlR)]

X [1

+ E(CCL)]

- 1

where E( • ) indicates the expectation of the variable. If the real interest rate is fairly stable over time and relatively small in size, then the nominal interest rate should increase approximately one-for-one with changes in the expected inflation rate. Unfortunately, the precise magnitude of inflation is hard to forecast much in advance. Some people believe that with the U.S. Treasury Department's recent introduction of Treasury Inflation Indexed Securities it will be 110

CHAPTER 5

These zero-coupon bonds, in turn, are sold to investors (for a fee, of course) . As the Treasury makes its required payments on the bond, the custodian bank remits the payments to the zero-eoupon bondholders of the appropriate maturity and effectively retires that particular bond . The process continues until all interest and principal payments have been made and all of the zero-coupon bonds associated with this Treasury bond have been extinguished . Brokerage firms have issued zero-eoupon bonds based on Treasury securities under a number of exotic names , such as LIONs (Lehman Investment Opportunity Notes), TIGRs (Merrill Lynch's Treasury Investment Growth Receipts), and CATs (Salomon Brothers' Certificates of Accrual on Treasury Securities) . Not surprisingly, these securities have become known in the trade as "animals." Brokerage firms and investors benefit from coupon stripping. The brokerage firms found th at the sum of the parts was worth more than the whole, as the zero -coupon bonds could be sold to investors at a higher combined price than could the source Treasury security. Investors benefited from the creation of a liquid market in riskless securities. The U.S. Treasury only belatedly recognized the popularity of stripped Treasury securities. In 1985, the Treasury introduced a program called STRIPS (Separate Trading of Registered Interest and Principal Securities) . This program allows purchasers ofcertain interest-bearing Treasury securities to keep whatever cash payments they wan t and to sell the rest. The stripped bonds are "held" in the Federal Reserve System's computer (called the book entry system) , and payments on the bonds are made electronically. Any financial institution that is registered on the Federal Reserve System's computer may participate in the STRIPS program . Brokerage firms soon found that it was much less expensive to create zero-eoupon bonds through STRIPS than to use bank custody accounts.

They subsequently switched virtually all of their activity to that program. The in troduction of stripped Treasuries still did not solve the inflation risk problem faced by investors seeking a truly riskfree security. Finally, in 1997 the U.S. Treasury offered the first U.S. securities whose principal and interest payments were indexed to inflation , officially named Treasury Inflation Indexed Securities. With the introduction of these securities, the United States joined Australia, Canada, Israel, New Zealand, Sweden, and the United Kingdom in issuing debt that is indexed to the rate of inflation. To date, the Treasury has issued three maturities (5, 10, and 30 years). The principal amounts of these "indexed" bonds are adjusted semiannually on the basis of the cumulative change in the Consumer Price Index (CPI) since issuance of the bonds. A fixed rate of interest, determined at the time of the bonds' issuance, is paid on the adjusted principal, thereby producing inflation-adjusted interest payments as well. Coupon stripping is allowed so that investors can purchase zero-coupon inflation-protected U.S. bonds-apparently the real McCoy of riskfree securities. Only a nitpicker would note several flaws in this arrangement. The bonds ' issuer (the U.S. government) controls the definition and calculation of the CPI. In light of concerns over whether the CPI accurately measures inflation , there is some risk that the government might change the index in ways detrimental to inflation-indexed securityholders (although the Treasury could adjust the bond terms to compensate for such an adverse change). Further, for taxable investors, the adjustments to the bonds' principal values immediately become taxable income, reducing (perhaps significantly, depending on the investor's tax rate) the inflation protection provided by the bonds. Despite these complications, it appears that the Treasury has finally introduced a security that can truly claim the title of (almost) riskfree.

much easier to arrive at a consensus forecast of inflation in the United States by simply looking at their market prices. (These securities are discussed further in "Institutional Issues: Almost Riskfree Securities" and in Chapter 12.) Further consideration of real versus nominal interest rates and forecasting the rate of inflation is deferred until Chapter 12. Suffice it to say that it may be best to view the expected real interest rate as being determined by the interaction of numerous underlying economic forces, with the nominal interest rate approximately equal to the expected real interest rate plus the expected rate of change in prices. The Valuation of Riskless Securities

111

__

YIELD-TO-MATURITY There are many interest rates, not just one. Furthermore , there are many ways that interest rates can be calculated. One such method results in an interest rate that is known as the yield-to-maturity. Another results in an interest rate known as the spot rate, which will be discussed in the next section.

5.2.1

Calculating Yield-to-Maturity

In describing yields-to-maturity and spot rates, three hypothetical Treasury securities that are available to the public for investment will be considered. Treasury securities are widely believed to be free from default risk, meaning that investors have no doubts about being paid fully and on time. Thus the impact of differing degrees of default risk on yields-to-rnaturity and spot rates is removed. The three Treasury securities to be considered will be referred to as bonds A, B, and C. Bonds A and B are called pure-discount bonds because they make no interim interest (or "coupon") payments before maturity. Any investor who purchases this kind of bond pays a market-determined price and in return re ceives the principal (or "face") value of the bond at maturity. In this case, bond A matures in a year, at which time the investor will receive $1,000. Similarly, bond B matures in two years, at which time the investor will receive $1,000. Finally, bond C is not a pure-discount bond. Rather, it is a coupon bond that pays the investor $50 one year from now and matures two years from now, paying the investor $1,050 at that time. The prices at which these bonds are currently being sold in the market are: Bond A (the one-year pure-discount bond): $934.58 Bond B (the two-year pure-discount bond): $857.34 Bond C (the two-year coupon bond): $946.93 The yield-to-maturity on any fixed-income security is the single interest rate (with interest compounded at some specified interval) that, ifpaid by a bank on the amount invested, would enable the investor to obtain all the payments promised by the security in question. It is simple to determine the yield-to-maturity on a one-year purediscount security such as bond A. Because an investment of $934.58 will pay $1,000 one year later, the yield-to-maturity on this bond is the interest rate Ttl that a bank would have to pay on a deposit of $934.58 in order for the account to have a balance of$I,OOO after one year. Thus the yield-to-maturity on bond A is the rate Ttl that solves the following equation: (1

+ Ttl)

X $934.58

= $1 ,000

(5.4)

which is 7%. In the case of bond B, assuming annual compounding at a rate Tn, an account with $857.34 invested initially (the cost of B) would grow to (1 + Tn) X $857.34 in one year. If this total is left intact, the account will grow to (1 + Tn) X [( 1 + Tn) X $857.34] by the end of the second year. The yield-to-maturity is the rate Tn that makes this amount equal to $1,000. In other words, the yield-to-maturity on bond B is the rate Tn that solves the following equation: (1

+ Tn) X [(I + Tn) X $857.34]

= $1,000

(5.5)

which is 8%. 112

CHAPTER 5

For bond C, consider investing $946.93 in a bank account. At the end of one year, the account would grow in value to (1 + Te) X $946.93. Then the investor would remove $50, leaving a balance of [( 1 + Te) X $946.93] - $50. At the end of the seco nd year this balance would have grown to an amount equal to (1 + Tc) X {[(I + Tr.) X $946.93] - $50} . The yield-to-maturity on bond Cis the rate rc that makes this amount equal to $1,050:

(1

+ Tc) X {[(I + Te) X $946.93]

- $50}

= $1,050

(5.6)

which is 7.975%. Equivalently, yield-to-maturity is the discount rate that makes the present value of the promised future cash flows equal in sum to the current market price of the bond. I When viewed in this manner, yield-to-maturity is analogous to internal rate of return, a concept used for making capital budgeting decisions and often described in introductory fin ance textbooks. This equivalence can be seen for bond A by dividing both sides of Equation (5.4) by (1 + Ttl) , resulting in:

$934.58 =

$1,000

(5.7)

(1 + Ttl)

Similarly, for bond B both sides of Equation (5.5) can be divided by (1 sulting in:

$857.34

=(

$1,000 1

+ Tn

)2

+ Ter:

$1,050

$50 1

re-

(5.8)

whereas for bond C both sides of Equation (5.6) can be divided by (1

$946.93 - (

+ Tfj)2,

+ Te)

(1

+ Ter

or: $50 $946 .93 = (1

+ TC)

+

$1,050 (1 + Tc)2

(5.9)

Because Equations (5.7), (5.8), and (5.9) are equivalent to Equations (5.4), (5.5), and (5.6), respectively, the solutions must be the same as before, with Til = 7%, TB = 8%, and Te = 7.975%. For coupon-bearing bonds, the procedure for determining yield-to-maturity involves trial and error. In the case of bond C, a discount rate of 10% could be tried initially, resulting in a value for the right-hand side of Equation (5.9) of$913.22, a value that is too low. This result indicates that the number in the denominator is too high, so a lower discount rate is used next-say 6%. In this case, the value on the right-hand side is $981.67, which is too high and indicates that 6% is too low. The solution is somewhere between 6% and 10%, and the search could continue until the answer. 7.975%, is found . The Valuation of Riskless Securities

113

Fortunately, computers arc good at trial-and-error calculations. One can enter a very complex series of cash flows into a properly programmed computer and instantaneously find the yield-to-maturity. In fact, many hand-held calculators and spreadsheets come with built-ill programs to find yield-to-maturity; you simply enter the number of days to maturity, the annual coupon payments, and the current market price, then press the key that indicates yield-to-maturity.

11I:II

SPOTRATES A spot rate is measured at a given point in time as the yield-to-maturity on a purediscount security and can be thought of as the interest rate associated with a spot contract. Such a contract, when signed, involves the immediate loaning of money from one party to another. The loan, along with interest, is to be repaid in its entirety at a specific time in the future. The interest rate that is specified in the contract is the spot rate . Bonds A and B in the previous example were pure-discount securities, meaning that an investor who purchased either one would expect to receive only one cash payment from the issuer. Accordingly, in this example the one-year spot rate is 7% and the two-year spot rate is 8%. In general, the t-year spot rate s, is the solution to the following equation: P

,

=

M

(5.10)

I

(1 + s,)'

where P, is the current market price ofa pure-discount bond that matures in tyears and has a maturity value of MI' For example, the values of P, and M, for bond B would be $857.34 and $1,000, respectively, with t = 2. Spot rates can also be determined in another manner if only coupon-bearing Treasury bonds are available for longer maturities by using a procedure known as bootstrapping. The one-year spot rate (SI) generally is known, as there typically is a one-year pure-discount Treasury security available for making this calculation. However, it may be that no two-year pure-discount Treasury security exists. Instead, only a two-year coupon-bearing bond may be available for investment, having a current market price of P2 , a maturity value of M 2 , and a coupon payment one year from now equal to C 1 • In this situation, the two-year spot rate (S2) is the solution to the following equation: Po

CI

2=(I+sd

+

M2

(l+s2)2

(5.11 )

Once the two-year spot rate has been calculated, then it and the one-year spot rate can be used in a similar manner to determine the three-year spot rate by examining a three-year coupon-bearing bond. By applying this procedure iteratively in a similar fashion over and over again, one can calculate an entire set of spot rates from a set of coupon-bearing bonds. For example, assume that only bonds A and C exist. In this situation it is known that the one-year spot rate, SI' is 7%. Now Equation (5. I I) can be used to determine the two-year spot rate, S2' where P2 = $946.93, C I = $50, and M 2 = $1,050:

$946.93 = (I

$50 + .07)

+

$1,050

(1 +

S2?

The solution to this equation is S2 = .08 = 8% . Thus, the two-year spot rate is determined to be the same in this example, regardless of whether it is calculated directly by analyzing pure-discount bond B or indirectly by analyzing coupon-bearing 114

CHAPTER 5

bond G in conjunction with bond A. Although the rate will not always be the same in both calculations when actual bond prices are examined, typically the differences are insignificant.

__

DISCOUNT FACTORS

Once a set of spot rates has been determined, it is a straightforward matter to determine the corresponding set of discount factors. A discount factor d, is equivalent to the present value of $1 to be received t years in the future from a Treasury security and is equal to: 1 d=---

,

(1 + s,)'

(5.12)

The set of these factors is sometimes referred to as the market discount function, and it changes from day to day as spot rates change. In the example, d, = 1/(1 + .07)1 = .9346; and d2 = 1/(1 + .08)2 = .8573. Once the market discount function has been determined, it is fairly straightforward to find the present value of any Treasury security (or, for that matter, any default-free security) . Let G/ denote the cash payment to be made to the investor at year t by the security being evaluated. The multiplication of G/ by d, is termed discounting: converting the given future value into an equivalent present value. The latter is equivalent in the sense that P present dollars can be converted into G, dollars in year tvia available investment instruments, given the currently prevailing spot rates. An investment paying G, dollars in year twith certainty should sell for P = d.C, dollars today. If it sells for more, it is overpriced ; if it sells for less . it is underpriced . These statements rest solely on comparisons with equivalent opportunities in the marketplace. Valuation of default-free investments thus requires no assessment of individual preferences; instead, it requires only careful analysis of the available opportunities in the marketplace. The simplest and, in a sense, most fundamental characterization of the market structure for default-free bonds is given by the current set of discount factors, referred to earlier as the market discount function. With this set of factors, it is a simple matter to evaluate a default-free bond that provides more than one payment, for it is, in effect, a package of bonds, each of which provides a single payment. Each amount is simply multiplied by the appropriate discount factor, and the resultant present values are summed. For example, assume that the Treasury is preparing to offer for sale a two-year coupon-bearing security that will pay $70 in one year and $1,070 in two years. What is a fair price for such a security? It is the present value of$70 and $1,070. How can this value be determined? By multiplying the $70 and $1,070 by the one-year and two-year discount factors, respectively. Doing so results in ($70 X .9346) + ($1,070 X .8573), which equals $982.73. No matter how complex the pattern of payments, this procedure can be used to determine the value of any default-free bond of this type. The general formula for a bond's present value (PV) is: (5 .13) where the bond has promised cash payments G, for each year from year 1 through year n. At this point, it has been shown how spot rates and, in turn . discount factors can be calculated. However, no link between different spot rates (or different discount The Valuation

of Riskless Securities

115

factors) has been established. For example, it has yet to be shown how the one-year spot rate of 7% is related to the two-year spot rate of 8%. The concept of forward rates makes that link.

11III

FORWARD RATES In the example, the one-year spot rate was determined to be 7%. This means that the market has determined that the present value of$1 to be paid by the United States Treasury in one year is $1 /1.07, 01' $.9346. That is, the relevant discount rate for converting a cash flow one year from now to its present value is 7%. Because, as was also noted, the two-year spot rate was 8%, the present value of $1 to he paid by the Treasury in two years is $1/1.08 2 , or $.8573. An alternative view of $1 to be paid in two years is that it can be discounted in two steps. The first step determines its equivalent one-year value. That is, $1 to be received in two years is equivalent to $1/( 1 + ii. 2) to be received in one year. The second step determines the present value of this equivalent one-year amount by discounting it at the one-year spot rate of 7%. Thus its current value is: $1/( 1 + ii.2) (1 +.07) However, this value must be equal to $.8573, as it was mentioned earlier that, according to the two-year spot rate, $.8573 is the present value of $1 to be paid in two years. That is, $1/( 1 + ii. 2) (1 +.07)

= $.8573

(5.14)

which has a solution for ii.2 of 9.0 1%. Th e discount rate ii.2 is known as the forward rate from year one to year two. That is, it is the discount rate for determining the equivalent value one year from now of a dollar that is to be received two years from now. In the example, $1 to be received two years from now is equivalent in value to $1/1.0901 = $.9174 to be received one year from now (in turn, note that the present value of $.9174 is $.9174/1.07 = $.8573). Symbolically, the link between the one-year spot rate, two-year spot rate, and one-year forward rate is: (5.15) which can be rewritten as: (5.16) or: (5.17) Figure 5.1 illustrates this relation by referring to the example and then generalizing from it. More generally, for year t - 1 and year t spot rates, the link to the forward rate between years t - 1 and tis: (5.18)

116

CHAPTER 5

Now

1 Year

2 Years

1----1----1 An Example:

(1.07) (1 +11,2) = (1.08)2 11,2= [(1.08)2/0.07)] -1 =9.01%

'.-

Generalization:

0+ sJ) (1 + 11,2) = 0 + S2)2 = [(1 + S2)2/0 + sl)] - 1

Ii s

$2

Figure 5.1 Spot and Forward Rates

or: (5.19) There is another interpretation that can be given to forward rates . Consider a contract made now wherein money will be loaned a year from now and paid back two years from now. Such a contract is known as aforward contract. The interest rate specified on the one-year loan (note that the interest will be paid when the loan matures in two years) is known as the forward rate. It is important to distinguish this rate from the rate for one-year loans that wiII prevail for deals made a year from now (the spot rate at that time) . A forward rate applies to contracts made now but relating to a period "forward" in time. By the nature of the contract the terms are certain now, even though the actual transaction will occur later. If instead one were to wait until next year and sign a contract to borrow money in the spot market at that time, the terms might turn out to be better or worse than today's forward rate, because the future spot rate is not perfectly predictable. In the example, the marketplace has priced Treasury securities such that a representative investor making a two-year loan to the government would demand an interest rate equal to the two-year spot rate, 8%. Equivalently, the investor would be willing to simultaneously (1) make a one-year loan to the government at an interest rate equal to the one-year spot rate, 7%, and (2) sign a forward contract with the government to loan the government money one year from now, being repaid two years from now with the interest rate to be paid being the forward rate, 9.01 %. When viewed in this manner, forward contracts are implicit. However, forward contracts are sometimes made explicitly. For example, a contractor might obtain a commitment from a bank for a one-year construction loan a year hence at a fixed rate of interest. Financial futures markets (discussed in Chapter 20) provide standardized forward contracts of this type. For example, in September an investor could contract to pay approximately $970 in December to purchase a 90-day Treasury bill that would pay $1,000 in the following March. . The Valuation of Riskless Securities

, 17

11IIII

FORWARD RATES AND DISCOUNT FACTORS In Equation (5.12) it was shown that a discount factor for t years could be calculated by adding one to the t-year spot rate, raising this sum to the power t, and then taking the reciprocal of the result. For example, it was shown that the twa-year discount factor associated with the two-year spot rate of 8% was equal to 1/ (I + .08 )2 = .8573 . Equation (5.17) suggesL~ an equivalent method for calculating discount factors. In the case of the two-year factor, this method involves multiplying one plus the oneyear spot rate by one plus the forward rate and taking the reciprocal of the result: (5.20)

which in the example is:

d 2 = (1

+ .07)

X (1

+ .090 1)

= .8573.

More generally, the discount factor for year t that is shown in Equation (5.12) can be restated as follows:

dl

= (1 + 5/-1 )1-1

X

( 1 + it-I,t )

(5.21 )

Thus, given a set of spot rates, one can determine the market discount function in either of two ways, both of which will provide the same figures. First, the spot rates can be used in Equation (5.12) to arrive at a set of discount factors. Alternatively, the spot rates can be used to determine a set of forward rates, and then the spot rates and forward rates can be used in Equation (5.21) to arrive at a set of discount factors.

_

COMPOUNDING Thus far, the discussion has concentrated on annual interest rates by assuming that cash flows are compounded (or discounted) annually. This assumption is often appropriate, but for more precise calculations a shorter period may be more desirable. Moreover, some lenders explicitly compound funds more often than once each year. Compounding is the payment of "in te rest on interest." At the end of each compounding interval, interest is computed and added to principal. This sum becomes the principal on which interest is computed at the end of the next interval. The process continues until the end of the final compounding interval is reached. No problem is involved in adapting the previously stated formulas to compounding intervals other than a year. The simplest procedure is to count in units of the chosen interval. For example, yield-to-maturity can be calculated using any chosen compounding interval. If payment of P dollars now will result in the receipt of F dollars 10 years from now, the yield-to-maturity can be calculated using annual compounding by finding a value Tn that satisfies the equation: CHAPTER 5

P(1

+T ,yn

=

F

(5.22)

since Fwill be received ten annual periods from now. The result, Ta , will be expressed as an annual rate with annual compounding. Alternatively, yield-to-maturity can be calculated using semiannual compounding by finding a value T, that satisfies the equation :

p( 1 +

T,r

n

= F

(5.23)

since F will be received 20 semiannual periods from now. The result, Tn will be expressed as a semiannual rate with semiannual compounding. It can be doubled to give an annual rate with semiannual compounding. Alternatively, the annual rate with annual compounding can be computed for a given value of TJ by using the following equation: 1

+ Ttl

= (1

+ T,)2

(5.24)

For example, consider an investment costing $2,315.97 that will pay $5,000 ten years later. Applying Equations (5.22) and (5.23) to this security results in, respectively: $2,315.97 ( 1

+ T" ) 10

$2,315.97 ( 1

+ T, ) 20 = $5,000

= $5,000

and:

where the solutions are T" = 8 % and T, = 3.923%. Thus this security can be described as having an annual rate with annual compounding of 8%, a semiannual rate with semiannual compounding of 3.923%, and an annual rate with semiannual compounding of7.846% (= 2 X 3.923%).2 Semiannual compounding is commonly used to determine the yield-to-maturity for bonds, because coupon payments are usually made twice each year. Most preprogrammed calculators and spreadsheets use this approach .P

_

THE BANK DISCOUNT METHOD

One time-honored method to summarize interest rates is a procedure called the bank discount method. If someone "borrows" $100 from a bank, to be repaid a year later, the bank may subtract the interest payment of, for instance, $8, and give the borrower $92 . According to the bank discount method, this is an interest rate of 8%. However, this method understates the effective annual interest rate that the borrower pays. That is, the borrower receives only $92 , for which he or she must pay $8 in interest after one year. The true interest rate must be based on the money the borrower actually gets to use, which in this case is $92, making the true interest rate 8.70% (= $8/$92). It is simple to convert an interest rate quoted on the bank discount method to a true interest rate. (In this situation, the true interest rate is often called the bond equivalent yield.) If the bank discount rate is denoted BDR, the true rate is simply BDR/(l - BDR). Because BDR > 0, the bank discount rate understates the true cost of borrowing [that is, BDR < BDR/(l - BDR)] . The previous example provides an illustration: 8.70 % = .08/0 - .08 ). Note how the bank discount rate of 8% understates the true cost of borrowing by .70% in this example.

_

YIELD CURVES

At any point in time, Treasury securities will be priced approximately in accord with the existing set of spot rates and the associated discount factors. Although there have The Valuation of Riskless Securities

119

been times when all the spot rates are roughly equal in size, generally they have different values. Often the one-year spot rate is less than the twa-year spot rate, which in turn is less than the three-year spot rate, and so on (that is, s, increases as t increases). At other times, the one-year spot rate is greater than the twa-year spot rate, which in turn is greater than the three-year spot rate, and so on (that is, s/ decreases as t increases). It is wise for the securi ty analyst to know which case currently prevails, as this is a useful starting point in valuing fixed-income securities. Unfortunately, specifying the current situation is easier said than done . Only the bonds of the U.S. government are clearly free from default risk. However, government bonds differ in tax treatment, as well as in callability, liquidity, and other features. Despite these problems, a summary of the approximate relationshi p between yields-tomaturity on Treasury securities of various terms-to-maturity is presented in each issue of the Treasury Bulletin. This summary is given in the form of a graph illustrating the current yield curve. Figure 5.2 provides an example. A yield curve is a graph that shows the yields-to-maturity (on the vertical axis) for Treasury securities of various maturities (on the horizontal axis) as of a particular date. This graph provides an estimate of the current term structure of interest rates and will change daily as yields-to-maturity change. Figure 5.3 illustrates some of the commonly observed shapes that the yield curve has taken in the past." Although not shown in Figures 5.2 and 5.3, this relationship between yields and maturities is less than perfect. That is, not all Treasury securities lie exactly on the yield curve. Part of this variation is because of the previously mentioned differences in tax treatment, callability, liquidity, and the like. Part is because of the fact that the yield-to-maturity on a coupon-bearing security is not clearly linked to the set of spot rates currently in existence. Because the set of spot rates is a fundamental determinant of the price of any Treasury security, there is no reason to expect yields to lie exactly on the curve. Indeed, a more meaningful graph would be one on which spot rates instead of yields- to-maturity are measured on the vertical axis. With this caveat in mind, ponder these two interesting questions: Why are the spot rates of different magnitudes? And why do the differences in these rates change over time, in that long-term spot rates usually are greater than short-term spot rates but sometimes the opposite occurs? Attempts to answer such questions can be found in various term structure theories.

IIIIZ!I

TERM STRUCTURE THEORIES Four primary theories are used to explain the term structure of interest rates. In discussing them, the focus will be on the term structure of spot rates, because these rates (not yields-to-maturity) are critically important in determining the price of any Treasury security.

5.10.1

The Unbiased Expectations Theory

The unbiased expectations theory (or pure expectations theory, as it is sometimes called) holds that the forward rate represents the average opinion of what the expected future spot rate for the period in question will be. Thus, a set of spot rates that is rising can be explained by arguing that the marketplace (that is, the general opinion of investors) believes that spot rates will be rising in the future. Conversely, a set of decreasing spot rates is explained by arguing that the marketplace expects spot rates to fall in the future." 120

CHAPTER 5

7-.----------------------------------,

5--1-,---,----,----r-----r--,---,---..,---r-----r---.-----,----,--...---,---I 12/31 /97

99

01

03

05

07

09

II

13

15

17

19

21

23

25 12/31 /27

Year

Figure 5.2

Yield Curve of Treasury Securities. September 30, 1997 (based on closing bid quotations in percentages) Source: Tre"""ry Bulletin, December 1997, p. 5 1 Note: The curve is based only on the most actively traded issues. Market yields on coupon issues due in less than 3 months are excluded.

(b) Flat

(a) Upward Sloping

(c) Downward Sloping

"0

li

:>:1----------

Maturity

Maturity

Maturity

Figure 5.3

Typical Yield Curve Shapes Upward-Sloping Yield Curves

In order to understand this theory more fully, consider the earlier exam p le in which the one-year spot rate was 7% and the two-year spot rate was 8%. The basic question is this: Why are these two spot rates different? Equivalently, why is the yield curve upward-sloping? The Valuation of Riskless Securities

121

Consider an investor with $1 to invest for two years (for ease of exposition, it will be assumed that any amount of money can be invested at the prevailing spot rates). This investor could follow a "maturity strategy," investing the money now for the full two years at the two-year spot rate of 8%. With this strategy, at the end of two years the dollar will have grown in value to $1.1664 (= $1 X 1.08 X 1.08) . Alternatively, the investor could invest the dollar now for one year at the one-year spot rate of 7%, so that the investor knows that one year from now he or she will have $1.07 (= $1 X 1.07) to reinvest for one more year. Although the investor does not know what the one-year spot rate will be one year from now, the investor has an expectation about what it will be (this expected future spot rate will hereafter be denoted eSt. 2)' If the investor thinks that it will be 10%, then his or her $1 investment has an expected value two years from now of$1.177 (= $1 X 1.07 X 1.10) . In this case , the investor would choose a "rollover strategy," meaning that the investor would choose to invest in a one-year security at 7% rather than in the two-year security, because he or she would expect to have more money at the end of two years by doing so ($1.177 > $1.1664). However, an expected future spot rate of 10% cannot represent the general view in the marketplace. If it did, people would not be willing to invest money at the twoyear spot rate, as a higher return would be expected from investing money at the one-year rate and using the rollover strategy. Thus the two-year spot rate would quickly rise as the supply of funds for two-year loans at 8% would be less than the demand. Conversely, the supply of funds for one year at 7% would be more than the demand, causing the one-year rate to fall quickly. Thus, a one-year spot rate of7%, a two-year spot rate of8%, and an expected future spot rate of 10% cannot represent an equilibrium situation. What if the expected future spot rate is 6% instead of 10%? In this case, according to the rollover strategy the investor would expect $1 to be worth $1.1342 (= $1 X 1.07 X 1.06) at the end of two years . This is less than the value the dollar will have if the maturity strategy is followed ($1.1342 < $1.664), so the investor would choose the maturity strategy. Again, however, an expected future spot rate of 6% cannot represent the general view in the marketplace because if it did , people would not be willing to invest money at the one-year spot rate. Earlier, it was shown that the forward rate in this example was 9.01 %. What if the expected future spot rate was of this magnitude? At the end of two years the value of $1 with the rollover strategy would be $1.1664 (= $1 X 1.07 X 1.0901), the same as the value of$l with the maturity strategy. In this case, equilibrium would exist in the marketplace because the general view would be that the two strategies have the same expected return. Accordingly, investors with a two-year holding period would not have an incentive to choose one strategy over the other. Note that an investor with a one-year holding period could follow a maturity strategy by investing $1 in the one-year security and receiving $1.07 after one year. Alternatively, a "naive strategy" could be followed, where a two-year security could be purchased now and sold after one year. If that were done, the expected selling price would be $1.07 (= $1.1664/1.0901), for a return of7% (the security would have a maturity value of $1.1664 = $1 X 1.08 X 1.08, but since the spot rate is expected to be 9.01% in a year. its expected selling price isjust the discounted value of its maturity value). Because the maturity and naive strategies have the same expected return, investors with a one-year holding period would not have an incentive to choose one strategy over the other. Thus the unbiased expectations theory asserts that the expected future spot rate is equal in magnitude to the forward rate. In the example, the current one-year spot rate is 7%, and, according to this theory, the general opinion is that it will rise to a rate of 9.01 % in one year. This expected rise in the one-year spot rate is the reason 122

CHAPTER 5

behind the upward-sloping term structure where the two-year spot rate (8%) is greater than the one-year spot rate (7%).

Equilibrium

In equation form, the unbiased expectations theory states that in equilibrium the expected future spot rate is equal to the forward rate: (5.25 )

Thus Equation (5. I 7) can be restated with esJ, 2 substituted for [i, 2 as follows: (5.26)

which can be conveniently interpreted to mean that the expected return from a maturity strategy must equal the expected return on a rollover strategy, " The previous example dealt with an upward-sloping term structure; the longer the term, the higher the spot rate. It is a straightforward matter to deal with a downward-sloping term structure, where the longer the term, the lower the spot rate. Whereas the explanation for an upward-sloping term structure was that investors expect spot rates to rise in the future, the reason for the downward-sloping curve is that investors expect spot rates to fall in the future.

Changing Spot Rates and Inflation

Why do investors expect spot rates to change, either rising or falling, in the future? A possible answer can be found by noting that the spot rates that are observed in the marketplace are nominal rates. That is, they are a reflection of the underlying real rate and the expected inflation rate." If either (or both) of these rates is expected to change in the future, then the spot rate will be expected to change. For example, assume a constant real rate of 3%. Because the current one-year spot rate is 7%, a constant real rate of 3% means that the general opinion in the marketplace is that the expected rate of inflation over the next year is approximately 4% (the nominal rate is approximately equal to the sum of the real rate and the expected inflation rate; see Equation (5.3)). Now, according to the unbiased expectations theory, the expected future spot rate is 9.01 %, an increase of 2.01 % from the current one-year spot rate of 7%. On the assumption of a constant real rate, this increase can be attributed to investors, on average, expecting the inflation rate to rise by 2.01 %. That is, the expected inflation rate over the next 12 months is approximately 4%, and over the following 12 months it is expected to be higher, at approximately 6.01 %. To recapitulate, the two-year spot rate (8%) is greater than the one-year spot rate (7%) because investors expect the future one-year spot rate to be greater than the current one-year spot rate. They expect it to be greater because of an anticipated rise in the rate of inflation, from approximately 4% to approximately

6.01% . In general, when current economic conditions make short-term spot rates abnormally high (owing, say, to a relatively high current rate of inflation), according to the unbiased expectations theory, the term structure should be downward-sloping beThe Valuation of Riskless Securities

123

cause inflation would be expected to abate in the future. Conversely, when current conditions make short-term rates abnormally low (owing, say, to a relatively low current rate of inflation) , the term structure sho uld be upward-sloping because inflation would be expected to rise in the future. Examination of historical term structures suggests that this is what has actually happened; the structure has been upward-sloping in periods of lower interest rates and downward-sloping in periods of higher interest rates. However, examining historical term structures uncovers a problem . In particular, it is logical to expect that over time there will be roughly as many occurrences of investors expecting spot rates to rise as there are occurrences of investors expecting spot rates to fall. Therefore the unbiased expectations theory should imply that there will be as many instances of upward-sloping term structures as downward-sloping term structures. In reality, upward-sloping term structures occur much more frequently than downward-sloping term structures. The unbiased expectations theory would have to explain this phenomenon by suggesting that the majority of the time investors expect spot rates to rise. The liquidity preference theory (also known as the liquidity premium theory) provides a more plausible explanation for the observed prevalence of upward-sloping term structures.

5.10.2

The Liquidity Preference Theory

The liquidity preference theory starts with the notion that investors are primarily interested in purchasing short-term securities. That is, even though some investors may have longer holding periods, there is a tendency for them to prefer short-term securities. These investors realize that they may need their funds earlier than anticipated and recognize that they face less "price risk" (that is, "interest rate risk") if they invest in shorter-term securities.

Price Risk

For example, an investor with a two-year holding period would tend to prefer the rollover strategy because he or she would be certain of having a given amount of cash at the end of one year when it may be needed. An investor who followed a maturity strategy would have to sell the two-year security after one year if cash were needed. However, it is not known now what price that investor would get for the twoyear security in one year. Thus there is an extra element of risk associated with the maturity strategy that is absent from the rollover strategy." The upshot is that investors with a two-year holding period will not choose the maturity strategy if it has the same expected return as the rollover strategy because it is riskier. The only way investors will follow the maturity strategy and buy the twoyear securi ties is if the expected return is higher. That is, borrowers are going to have to pay the investors a risk premium in the form of a greater expected return in order to get them to purchase two-year securities. Will borrowers be inclined to pay such a premium when issuing two-year securities? Yes, they will, according to the liquidity preference theory. First, frequent refinancing may be costly in terms of registration, advertising, and paperwork. These costs can be lessened by issuing relatively long-term securities. Second, some borrowers will realize that relatively long-term bonds are a less risky source of funds than relatively short-term bonds because borrowers who use them will not have to be as concerned about the possibility of refinancing in the future at higher interest rates. Thus borrowers may be willing to pay more (via higher expected interest costs) for relatively long-term funds. 124

CHAPTER 5

In the example, the one-year spot rate was 7% and the two-year spot rate was 8%. According to the liquidity preference theory, the only way investors will agree to folIowa maturity strategy is if the expected return from doing so is higher than the expected return from following the rollover strategy. So the expected future spot rate must be something less than the forward rate of 9.01 %; perhaps it is 8.6%. At 8.6% the value of a $1 investment in two years is expected to be $1.1620 (= $1 X 1.07 X 1.086), if the rollover strategy is followed. Because the value of a $1 investment with the maturity strategy is $1.l664 (= $1 X 1.08 X 1.08) , it can be seen that the maturity strategy has a higher expected return for the two-year period that can be attributed to its greater degree of price risk.

Liquidity Premium

The difference between the forward rate and the expected future spot rate is known as the liquidity premium.f It is the "extra" return given investors in order to entice them to purchase the riskier longer-maturity two-year security. In the example, it is equal to .41% (= 9.01% - 8.6%). More generally, (5.27) where L I • 2 is the liquidity premium for the period starting one year from now and ending two years from now.!" How does the liquidity preference theory explain the slope of the term structure? In order to answer this question, note that with the rollover strategy the expected value of a dollar at the end of two years is $1 X (1 + SI) X (1 + es1,2)' Alternatively, wi th the maturity strategy, the expected value of a dollar at the end of two years is $1 X (1 + According to the liquidity preference theory, there is more risk with the maturity strategy, which in turn means that it must have a higher expected return. That is, the following inequality must hold:

s2t

(5 .28) or: (5.29) This inequality is the key to understanding how the liquidity preference theory explains the term structure. II

Downward-Sloping Yield Curves

Consider the downward-sloping case first, where SI > S2' The above inequality will hold in this situation only if the expected future spot rate (esl. 2) is substantially lower than the current one-year spot rate (Sl ).12 Thus a downward-sloping yield curve will be observed only when the marketplace believes that interest rates are going to decline substantially. As an example, assume that the one-year spot rate (SI) is 7% and the two-year spot rate (S2) is 6%. Because 7% is greater than 6%, this is a situation in which the term structure is downward-sloping. Now, according to the liquidity preference theory, Equation (5.29) indicates that, (1

+ .07)(1 + eSI.2)
differs from the beta of the stock according to the CAPM, {JiM because the market model beta is measured relative to a market index whereas the CAPM beta is measured relative to the market portfolio. In practice, however, the composition of the market portfolio is not precisely known , so a market index is used. Thus, although conceptually different, betas determined with the use of a market index are often treated as if they were determined with the use of the market portfolio. That is, {Jil is used as an estimate of {JiM' In the example, only three securities were in existence: the common stocks of Able , Baker, and Charlie. Subsequent analysis indicated that the CAPM market portfolio consisted of these stocks in the proportions of .12, .19, and .69, respectively. It is against this portfolio that the betas of the securities should be measured. However, in practice they are likely to be measured against a market index (for example, one that is based on just the stocks of Able and Charlie in proportions of .20 and .80, respectively) .

9.4.1

Marl<et Indices

One of the most widely known indices is the Standard & Poor's Stock Price Index (referred to earlier as the S&P 500), a value-weighted average price of 500 large stocks. Complete coverage of the stocks listed on the New York Stock Exchange is provided by the NYSE Composite Index, which is broader than the S&P 500 in that it considers more stocks. The American Stock Exchange computes a similar index (the Amex Composite) for the stocks it lists, and the National Association of Security Dealers provides an index of over-the-counter stocks traded on the Nasdaq system (the Nasdaq Composite) . The Russell 3000 and Wilshire 5000 stock indices are the most comprehensive indices of U.S. common stock prices published regularly in the United States. Because they consist of both listed and over-the-counter stocks, they are closer than the others to representing the overall performance of U.S. stocks.l" Without question the most widely quoted market index is the Dow Jones Industrial Average (DJIA). Although based on the performance of only 30 stocks and utilizing a less satisfactory averaging procedure than the other indices use, the DJIA provides at least a fair idea of what is happening to stock prices. 15 Table 9 .1 provides a listing of the 30 stocks whose prices are reflected in the DJIA. The Capital Asset Pricing Model

239

TAS LE 9. 1

Stocks In the Dow Jones Industrial Average

Alcoa Allied Signal American Express AT&T Boeing

IBM International Paper

Eastman Kodak Exxon General Electric General Motors

Johnson &Johnaon McDonald's Merck Minnesota Mining and Manufacturing (3M) J. P. Morgan Philip Morn. Procter & Gamble Sears, Roebuck Traveler'! Group Union Carbide United Technologies

Goodyear Tire Hewlett-Packard

Walt Dimey

Caterpillar Chevron Coca-Cola DuPont

Wal-MaJ1 Stores

Sow"., Web site (hltp:/ /dj ia IOO.dowjones .cum /frnmcscl.h lml).J une 3. 1997.

9.4.2

Marl<et and Non-Market Risk

In Chapter 7 it was shown that the total risk of a security, two components as follows:

uT, could be partitioned into (7.8)

where the components are:

f3t ooJ = market risk oo~ = unique risk

Because beta, or covariance, is the relevant measure of risk for a security according to the CAPM, it is only appropriate to explore the relationship between it and the total risk of the security. It turns out that the relationship is identical to that given in Equation (7.8) except that the market portfolio is involved instead of a market index :

(9.12) As in the market model, the total risk of security i, measured by its variance and denoted uT, is shown to consist of two parts. The first component is the portion related to moves of the market portfolio. It is equal to the product of the square of the beta of the stock and the variance of the market portfolio and also is often referred to as the market risk of the security. The second component is the portion not related to moves of the market portfolio. It is denoted U~i and can be considered non-market risk. Under the assumptions of the market model, it is also unique to the security in question and hence is also termed unique risk. Note that if f3il is treated as an estimate of f3iM then the decomposition of uT is the same in Equations (7.8) and (9.12).

9.4.3

An Example

From the earlier example, the betas ofAble, Baker, and Charlie were calculated to be .66, 1.11, and 1.02, respectively. Because the standard deviation of the market portfolio was equal to 15.2%, the market risk of the three firms is equal to (.66 2 X 15.22 ) = 100, (1.11 2 X 15.2 2) = 285, and (1.02 2 X 15.2 2) = 240, respectively.

240

CHAPTER 9

The non-market risk of any security can be calculated by solving Equation (9.12) forlT;j: (9.13) Thus, Equation (9.13) can be used to calculate the non-market risk of Able, Baker, and Charlie, respectively:

= 46

= 569 lT~3 = 289 - 240

= 49 Non-market risk is sometimes expressed as a standard deviation. This is calculated by taking the square root of IT;j and would be equal to = 6.8% for Able, = 23.9% for Baker, and = 7% for Charlie.

V569

9.4.4

V49

V46

Motivation for the Partitioning of Risk

At this point one may wonder: Why partition total risk into two parts? For the investor, it would seem that risk is risk-whatever its source. The answer lies in the domain of expected returns. Market risk is related to the risk of the market portfolio and to the beta of the security in question. Securities with larger betas will have larger amounts of market risk. In the world of the CAPM, securities with larger betas will have larger expected returns. These two relationships together imply that securities with larger market risks should have larger expected returns. Non-market risk is not related to beta. There is no reason why securities with larger amounts of non-market risks should have larger expected returns. Thus according to the CAPM, investors are rewarded for bearing market risk but not for bearing non-market risk.

II1II

SUMMARY

1. The capital asset pricing model (CAPM) is based on a specific set of assumptions about investor behavior and the existence of perfect security markets. 2. On the basis of these assumptions, it can be stated that all investors will hold the same efficient portfolio of risky assets. 3. Investors will differ only in the amounts of riskfree borrowing or lending they undertake. 4. The risky portfolio held by all investors is known as the market portfolio.

The Capital Asset Pricing Model

241

5. The market portfolio consists of all securities, each weighted in proportion to its market value relative to the market value of all securities. 6. The linear efficient set of the CAPM is known as the capital market line (CML). The CML represents the equilibrium relationship between the expected return and standard deviation of efficient portfolios. 7. Under the CAPM the relevant measure of risk for determining a security's expected return is its covariance with the market portfolio. 8. The linear relationship between market covariance and expected return is known as the security market line (SML). 9. The beta of a security is an alternative way of measuring the risk that a security adds to the market portfolio. Beta is a measure of the covariance between the security and the market portfolio relative to the market portfolio's variance. 10. The beta from the CAPM is similar in concept to the beta from the market model. However, the market model is not an equilibrium model of security prices as is the CAPM. Furthermore, the market model uses a market index, which is a subset of the CAPM's market portfolio. 11. Under the CAPM, the total risk of a security can be separated into market risk and non-market risk. Each security's non-market risk is unique to that security and hence is also termed its unique risk.

;OUESTJONS'AND

PROBLEMS'

"

,

1. Describe the key assumptions underlying the CAPM. 2. Many of the underlying assumptions of the CAPM are violated to some degree in the real world. Does that fact invalidate the model's conclusions? Explain. 3. What is the separation theorem? What implications does it have for the optimal portfolio of risky assets held by investors? 4. What constitutes the market portfolio? What problems does one confront in specifying the composition of the true market portfolio? How have researchers and practitioners circumvented these problems? 5. In the equilibrium world of the CAPM, is it possible for a security not to be part of the market portfolio? Explain. 6. Describe the price adjustment process that equilibrates the market's supply and demand for securities. What conditions will prevail under such an equilibrium? 7. Will an investor who owns the market portfolio have to buy and sell units of the component securities every time the relative prices of those securities change? Why? 8. Given an expected return of 12% for the market portfolio, a riskfree rate of 6%, and a market portfolio standard deviation of20%, draw the capital market line. 9. Explain the significance of the capital market line. 10. Assume that two securities constitute the market portfolio. Those securities have the following expected returns, standard deviations, and proportions:

Security

Expected Return

Standard Deviation

A

10%

20%

B

]5

28

Proportion .4 .6

On the basis of this information, and given a correlation of .30 between the two securities and a riskfree rate of 5%, specify the equation for the capital market line. 11. Distinguish between the capital market line and the security market line. 242

CHAPTER 9

12. The market portfolio is assumed to be composed of four securities. Their covariances with the market portfolio and their proportions are shown below: Covariance Security

with Market

A

242 360

B C

155

D

lUO

Proportion .2 .3 .2 .3

Given these data, calculate the market portfolio's standard deviation. 13. Explain the significance of the slope of the SML. How might the slope of the SML change over time? 14. Why should the expected return for a security be directly related to the security's covariance with the market portfolio? 15. The risk of a well-diversified portfolio to an investor is measured by the standard deviation of the portfolio's returns. Why shouldn't the risk of an individual security be calculated in the same manner? 16. The riskfree rate is 5% while the market portfolio's expected return is 12%. If the standard deviation of the market portfolio is 13%, what is the equilibrium expected return on a security that has a covariance with the market portfolio of 186? 17. A security with a high standard deviation of returns is not necessarily highly risky to an investor. Why might you suspect that securities with above-average standard deviations tend to have above-average betas? 18. Oil Smith, an investments student, argued, "A security with a positive standard deviation must have an expected return greater than the riskfree rate. Otherwise, why would anyone be willing to hold the security?" On the basis of the CAPM, is Oil's statement correct? Why? 19. The standard deviation of the market portfolio is 15%. Given the covariances with the market portfolio of the foBowing securities, calculate their betas. Security

Covariance 292

A B

180

C

225

20. Kitty Bransfield owns a portfolio composed of three securities. The betas of those securities and their proportions in Kitty'S portfolio are shown here. What is the beta of Kitty's portfolio? Security A

B C

Beta .90 1.30 1.05

Proportion .3 .1 .6

21. Assume that the expected return on the market portfolio is 15% and its standard deviation is 21%. The riskfree rate is 7%. What is the standard deviation of a well-diversified (no non-market-risk) portfolio with an expected return of 16.6%? 22. Given that the expected return on the market portfolio is 10%, the riskfree rate of return is 6%, the beta of stock A is .85, and the beta of stock B is 1.20: The Capital Asset Pricing ModeJ

243

a. Draw the SML. b. What is the equation for the SML? c. What are the equilibrium expected returns for stocks A and B? d. Plot the two risky securities on the SML. 23. You are given the following information on two securities, the market portfolio, and the riskfree rate: Correlation with Market Portfolio

Standard Deviation

15.5%

0.9

20.0%

9.2 12.0

0.8 1.0

12.0

5.0

0.0

0.0

Expected Return

Security 1 Security 2 Market portfolio

Riskfree rate

24.

25.

26. 27. 28.

9.0

a. Draw the SML. b. What are the betas of the two securities? c. Plot the two securities on the SML. The SML describes an equilibrium relationship between risk and expected return. Would you consider a security that plotted above the SML to be an attractive investment? Why? Assume that two securities, A and B, constitute the market portfolio. Their proportions and variances are .39, 160, and .61, 340, respectively. The covariance of the two securities is 190. Calculate the betas of the two securities. The CAPM permits the standard deviation of a security to be segmented into market and non-market risk. Distinguish between the two types of risk. Is an investor who owns any portfolio of risky assets other than the market portfolio exposed to some non-market risk? Explain. On the basis of the risk and return relationships of the CAPM, supply values for the seven missing numbers in the following table. Expected Return

Security

Beta

A

-_%

0.8

B

19.0

1.5

C

15.0

D E

7.0 16.6

Standard Deviation

Non-market Risk (11:;)

% 12

0

81

36 0

8 15

29. (Appendix Question) Describe how the SML is altered when the riskfree borrowing rate exceeds the riskfree lending rate. CFA

EXAM

QUESTIONS

30. The following information describes the expected return and risk relationship for the stocks of two of WAH's competitors. Expected Return

Standard Deviation

Stock X

12.0%

20%

1.3

Stock Y Market index

9.0 10.0

15 12

0.7 1.0

Rlskfree rate

5.0

Beta

Using only the data shown above: 244

CHAPTER 9

a. Draw and label a graph showing the security market line and position stocks X and Y relative to it. b. Compute the alphas both for stock X and for stock Y. Show your work. (Hint: Alpha is the difference between the stock's expected return and the equilibrium expected return given by the SML.) c. Assume that the riskfree rate increases to 7% with the other data remaining unchanged. Select the stock providing the higher expected risk-adjusted return and justify your selection. Show your calculations.

ApPENDIX A SOME EXTENDED VERSIONS OF THE

CAPM

.---,-- - - - - - - - - - - - - - - - - - - - - - - -

The original capital asset pricing model makes strong assumptions and gives strong implications. In the years since it was developed, more complex models have been proposed. These models generally involve relaxing some of the assumptions associated with the original CAPM and are often referred to as extended versions of the CAPM, or extended capital asset pricing models. Some of them are described in this appendix.

__

A.1.l

IMPOSING RESTRICTIONS ON RISI{FREE BORROWING

The Capital Market Line

The original CAPM assumes that investors can lend or borrow at the same riskfree rate of interest. In reality, such borrowing is likely to be either unavailable or restricted in amount. What impact might the relaxation of this riskfree borrowing assumption have on the CAPM? A useful way to answer the question makes the following assumptions: (1) Investors can lend money riskJessly-that is, they can purchase assets that provide a riskfree return of TJL> and (2) investors can borrow money without limit at a higher rate of interest, TJB' These riskfree rates are shown on the vertical axis of Figure 9.3; the umbrella area represents risk-return combinations available from investment solely in risky assets. 16 If there were no opportunities to borrow or lend at the riskfree rate, the efficient set would be the curve lVTL TB Y, and many combinations of risky securities would be efficient. However, the availability of riskfree lending at the rate TJL makes the risky portfolios between Wand TL inefficient, because combinations ofriskfree lending and the portfolio plotting at TL provide more return for the same risk. Similarly, the ability to borrow money at rate TJB makes another portfolio, denoted by T B , of special interest. Risky portfolios between T B and Yare now ineffiThe Capital Asset Pricing Model

245

B

Figure 9.3 Efficient Set When the Riskfree Rates Are Different

cient, because leveraged holdings of TlJ dominate them by providing more return for the same risk. Investors with attitudes toward risk that suggest neither borrowing nor lending should hold efficient combinations of risky securities plotting along curve TL TH • Accordingly, their holdings should be tailored to be consistent with differences in their degrees of aversion to risk. In this situation the CML is now two lines and a curve, corresponding to the line going from TIL to 1~, then the curve from T L to T lJ, and then the line from TlJ on out to the northeast in Figure 9.3.

A.l.2

The Security Marl<et Line

What becomes of the security market line when the riskfree borrowing rate exceeds the riskfree lending rate? The answer depends on whether the market portfolio is in fact one of the efficient combinations of risky securities along the boundary between 1/. and TlJ in Figure 9.3. 17 Ifit is not, little can be said other than that the CAPM does not hold. If it is, a great deal can be said. Figure 9.4 shows a case in which the market portfolio (shown by point M) is efficient. In panel (a) a line has been drawn that is tangent to the efficient set at point M. When this line is extended to the vertical axis, the resulting intercept is denoted T c ' In panel (b) only this tangency line is shown. A striking characteristic of Figure 9.4(b) is this: It is precisely the same picture that would be produced in a market in which investors could borrow and lend without limit at a hypothetical riskfree rate equal in value to T e- Whereas only point M along the line emanating from T. would be attainable, the expected returns of risky securities would be the same as they would be in a hypothetical market with borrowing and lending at T•. That is, all risky securities (and portfolios consisting of those securities) would plot along an SML going through point T., as shown in Figure 9.5. The vertical intercept of the SML indicates the expected return on a security or portfolio with a beta of zero. Accordingly, this extension of the CAPM is termed the zero-beta capital assetpricing model. This version of the CAPM im plies that the SML will be flatter than implied by the original version, because T z will be above TIL' As a practical matter, it means that T. must be inferred from the prices of risky securities, because it cannot simply be found in the quotations of curren t prices on, for example, 246

CHAPTER 9

(a) Drawing a Une TUgeDtto M

(b) Tugeocy Une at M

1.0

Figure 9.4

Figure 9 .5

Risk and Return When the Market Portfolio Is Efficient

The Zero-Beta SecurityMarket Line

Treasury bills. Many organizations that estimate the SML generally find that it conforms more to the zero-beta CAPM than to the original CAPM. Cases in which borrowing is either impossible or costs more as one borrows larger amounts lead to only minor modifications in the conclusions. As long as the market portfolio is efficient, all securities will plot along an SML, but the "zero-beta return" will exceed the riskfree rate at which funds can be invested.

__

INTRODUCING HETEROGENEOUS EXPECTATIONS

A number of researchers have examined the implications of assuming that different investors have different perceptions about expected returns, standard deviations, and covariances. More specifically, the assumption of homogeneous expectations has been replaced by these researchers with an assumption of heterogeneous expectations. In one such study, it was noted that each investor would face an efficient set that was unique to him or her." This means that the tangency portfolio (denoted by T in Chapter 8) is unique to each investor, because the optimal combination of risky assets for an investor depends on that investor's perceptions about expected returns, The Capital Asset Pricing ModeJ

247

standard deviations, and covariances. Furthermore, an investor will likely determine that his or her tangency portfolio does not involve an investment in some securities (that is, certain securities may have zero proportions in the tangency portfolio). Nevertheless, in equilibrium each security's price still has to be at a level where the amount of the security demanded equals the supply of the security. Now, however, the equilibrium expected return for each security will be a complex weighted average of all investors' perceptions of its expected return.

BIll

LlOUIDITY The original CAPM assumes that investors are concerned only with risk and return. However, other characteristics may also be important to investors. For example, liquidity may be important. Here, liquidity refers to the cost of selling or buying a security "in a hurry." A house is regarded as a relatively illiquid investment, because usually a "fair" price for it cannot be obtained quickly. In terms of securities, liquidity may be estimated by the size of the spread between the bid and asked prices, with smaller spreads suggesting greater liquidity. Furthermore, it is reasonable to assume that many investors would find more liquid securities to be more attractive, keeping everything else the same. However, investors undoubtedly differ in their attitudes toward liquidity. For some it is very important; for others, somewhat important; and for yet others, of little importance. Under these conditions, security prices would adjust until , overall. investors would be content to hold all of the outstanding securities. The expected return of a security would be based on two characteristics of the security: 1. The marginal contribution of the security to the risk of an efficient portfolio. This would be measured by the familiar beta (f3jM) of the security. 2. The marginal contribution of the security to the liquidity of an efficient portfolio. This would be measured by the liquidity (Lj ) of the security.

Now, other things being equal, investors dislike large values of f3 iM but like large values of L; This means that two securities with the same beta but different liquidities would not have the same level of expected return. To understand why they would have different levels of expected return, consider what would happen if they had the same level of expected return. In such a situation investors would buy the security with the greater liquidity and sell the one with the lesser liquidity. The price of the first security would be pushed up, and that of the second one down. Ultimately, in equilibrium the quantity demanded would equal the quantity supplied, and the security with the greater liquidity would have a relatively lower expected return. Similarly, two securities with the same liquidity but different betas would not have the same level of expected return. Instead, the security with the higher beta would have a higher expected return." Figure 9.6 shows the equilibrium relationship one might expect among ri o f3iM' and L j • For a given level of f3iM. securities that are more liquid have lower expected returns . And for a given level of L j , riskier securities have higher expected returns, as in the original CAPM. Last, there are securities with various levels of {JiM, and L, that provide the same level of rio The figure is three-dimensional. because now expected returns are related to two characteristics of securities. Accordingly, it is sometimes referred to as a Security Market Plane. 2o

248

CHAPTER 9

Lj

• • • • • • • • •. • • • • • • _ - - - - - - - - ...

Figure 9.6 Security Market Plane

If expected returns are based on beta, liquidity, and a third characteristic, then a four-dimensional CAPM would be necessary to describe the corresponding equilibrium." Although a diagram cannot be drawn for this type of extended CAPM, an equation can be written for it. Such an equation, by analogy to the three-dimensional plane, is termed a hyperplane. In equilibrium, all securities will plot on a security market hyperplane, where each axis measures the contribution of a security to a characteristic of efficient portfolios that matters (on average) to investors.

The relationship between the expected return of a security and its contribution to a particular characteristic of efficient portfolios depends on the attitudes of investors to the characteristic:

If, on the average, a characteristic (such as liquidity) is liked lJy investors, then those securities that contribute more to that characteristic will, other things being equal, offer lower expected returns. Conversely, if a characteristic (such as beta) is disliked lJy investors, then those securities that contribute more to that characteristic will offer higher expected returns.

In a capital market with many relevant characteristics, the task of tailoring a portfolio for a specific investor is more complicated, because only an investor with average attitudes and circumstances should hold the market portfolio. In general: If an investor likes a characteristic more (or dislikes it less) than the average investor, he or she should generally hold a portfolio with relatively more of that characteristic than is provided lJy holding the market portfolio. Conversely, if an investor likes a characteristic less (or dislikes it more) than the average investor, he or she should generally hold a portfolio with relatively less of that characteristic than is provided lJy holding the market portfolio.

For example, consider an investor who likes having a relatively liquid portfolio. Such an investor should hold a portfolio consisting of relatively liquid securities.

The Capital Asset Pricing Model

249

Conversely, an investor who has relatively little need for liquidity should hold a portfolio of relatively illiquid securities. The right combination of "tilt" away from market proportions will depend on the extent of the differences between the investor's attitudes and those of the average investor and on the added risk involved in such a strategy. A complex capital market requires all the tools of modern portfolio theory for managing the money of any investor who is significantly different from the "average investor." On the other hand, in such a world, investment management should be relatively passive: After the selection of an initial portfolio, there should be only minor and infrequent changes.

ApPENDIX A

B

DERIVATION OF THE SECURITY MARKET LINE

Figure 9.7 shows the location of the feasible set of the Markowitz model along with the riskfree rate and the associated efficient set that represents the capital market line. Within the feasible set of the Markowitz model lies every individual risky security. An arbitrarily chosen risky security, denoted i, has been selected for analysis and is shown on the figure.

CML

Figure 9.7 Deriving the Security Market Line

250

CHAPTER 9

Consider any portfolio, denoted p, that consists of the proportion Xj invested in security i and the proportion (1 - XJ invested in the market portfolio M. Such a portfolio will have an expected return equal to: (9.14)

and a standard deviation equal to: Up -_

[..,2

AiUi2

+ (1 -

2 ] 1/2 X,)2UM + 2X, ( 1 - Xi)UiM

(9.15)

All such portfolios will lie on a curved line connecting i and M such as the one shown in Figure 9.7. Of concern is the slope of this curved line. Because it is a curved line, its slope is not a constant. However, its slope can be determined with the use of calculus. First, using Equation (9.14), the derivative of r p with respect to X, is taken: (9.16)

Second, using Equation (9.15), the derivative of U" with respect to X, is taken: X,Ui - UM + XiUM + UiM - 2XjUiM 2

A_

uu"

dX, = [x'fU7

2

2

+ (1 - XJ2U~ + 2X (1 j

X,)U jM]'/2

(9.17)

Third, it can be noted that the slope of the curved line iM, drp/du,,, can be written as: drp du p

=

dr,,/ dX, du p/ dX;

(9.18)

This means that the slope of iM can be calculated by substituting Equations (9.16) and (9.17) into the numerator and denominator of Equation (9.18), respectively: dT" J_

uu P

[ -Ti

-

2 2 TM] [ XjUj

=

2

X,Uj -

+ ( 1 - Xi)2UM2 + 2X; ( 1 - X;)UiM] 1/2 2 2 UM + X;U M + UiM - 2X, UiM

(9.19)

Of interest is the slope of the curved line iM at the endpoint M. Because the proportion Xi is zero at this point, the slope of iM can be calculated by substituting zero for X, in Equation (9.19). After that substitution has been done, many terms drop out, leaving: dr p = du p

[rj -

rM][uM]

UiM - u~

(9.20)

At M the slope of the CML, (rM - T/)/UM, must equal the slope of the curved line iM. The reason is that the slope of the curved line iM increases when moving from the endpoint i, converging with the slope of the CML at the endpoint M. Accordingly, the slope of the curve iM at M, as shown on the right-hand side of Equation (9.20), is set equal to the slope of the CML: (9.21)

Solving Equation (9.21) for

rj results in the covariance version of the SML:

The Capital Asset Pricing Model

251

(9.6) The beta version of the SML is derived by substituting Equation (9.6). ~· E N D N O T E S •

','"

,.

..'.

•

"" , .

f3iM

for (IiMI(I~ in

'.

, •

. 9~

•

I

Some extended versions of the CAPM are discussed in Appendix A.

2

Milton Friedman, Essays in the TheMy of Positive Economics (Chicago: University of Chicago Press, 1953), p. 15.

:1 If the investor had initial wealth of $40,000, he or she would borrow $10,000 and then invest $50,000 (= $40,000 + $10,(00) in

1:

4

Note how the proportions in these three stocks sum to .5 for the panel (a) investor and 1.25 for the panel (b) investor. Because the respective proportions for the riskfree asset are .5 and - .25, the aggregate proportions for the stocks and riskfree asset sum to 1.0 for each investor. See Appendix B to Chapter 8.

5

Securities that have zero net amounts outstanding will not appear in the tangency portfolio. Options and futures, discussed in Chapters 19 and 20, are examples of such securities.

f>

Although the expected return of Charlie has been changed, all the variances and covariances as well as the expected returns for Able and Baker are assumed to have the same values that were given in Chapters 6, 7 and 8. The singular change in the expected return of Charlie alters not only the composition of the tangency portfolio but, more generally, the location and shape of the efficient set.

7

In this situation the market for each security is said to have cleared.

8

The aggregate market value for the common stock of a company is equal to the current market price of the stock multiplied by the number of shares outstanding.

9

The slope of a straight line can be determined if the location of two points on the line are known . It is determined by rise over run, meaning that it is determined by dividing the vertical distance between the two points by the horizontal distance between the two points. In the case of the CML, two points an: known, corresponding to the riskfree rate and the market portfolio, so its slope can be determined in this manner.

10

II

The equation of a straight line is of the form: y = a + bx, where a is the vertical intercept and b is the slope. Because the vertical intercept and slope of the CML are known, its equation can be written as shown here by making the appropriate substitutions for a and b. More precisely, (J'iM is the relevant measure of a security's risk because iJ(J'M/aXiM = (J'iM/(J'M' That is, a marginal change in the weight in security iwilI result in a marginal change in the variance of the market portfolio that is a linear function of the security'S covariance with the market portfolio. Accordingly, the relevant measure of the security's risk is its covariance, (J',M'

12

A more rigorous derivation of the SML is provided in Appendix B.

13

In this situation, Baker and Charlie have covariances with the market portfolio of 382 and 179, respectively, which means that their expected returns should be equal to 30.7% = 4 + (.07 X 382) and 16.5% = 4 + (.07 X 179) . However, these figures do not correspond to the respective ones (24.6% and 22.8%) appearing in the expected return vector, indicating that there are discrepancies for alI three securities. Although this example has used the covariance version of the SML, the analysis is similar for the beta version of SML that is shown in Equation (9.7).

14

Other indices of common stocks are commonly reported in the daily press. Many of these are components of the major indices mentioned here. For example, the Wall StreetJournal reporl5 on a daily basis not only the level of the S&P 500 but also the levels of four of its components: Industrials, Transportations, Utilities, and Financials. Standard & Poor's also reports the level of a 400 MidCap index based on the stock prices of middle-sized companies. See Chapters 24 and 25 for a more thorough discussion of stock market indices.

252

CHAPTER 9

15

Charles Dow created this index in 1884 by simply adding the prices of 11 companies and then dividing the sum by 11. In 1928 securities were added to bring the total number up to 30. Since then the composition of these 30 has been changed periodically. Owing to corporate actions such as stock dividends and splits as well as changes in the index's companies, the divisor is no longer simply equal to the number of stocks in the index.

16 A 17

more rigorous development of this figure is presented in Appendix A to Chapter 8.

Assume that (l) initial margin requirements for short sales do not exist; (2) investors can obtain the proceeds from short sales; and (3) neither riskfree borrowing nor lending is possible. In such a situation the feasible set would be bounded by a hyperbola that opens to the right. Furthermore, the efficient set would be the upper half of this boundary. Introducing riskfree borrowing and lending changes the shape and location of the efficient set to one that is similar to what appears in Figure 9.3. In such a situation the market portfolio would definitely plot on the efficient set between TL and TH • See Fischer Black, "Capital Market Equilibrium with Restricted Borrowing," Journal oj Business 45, no. 3 (july 1972): 444-455.

18 See

John Lintner, "The Aggregation ofInvestor's Diverse Judgements and Preferences in Purely Competitive Markets," Journal oj Financial and Quantitative Analysis 4, no . 4 (December 1969): 347-400.

19 The

ability of an investor to produce a stream of income by working shows that the investor possesses an asset known as human capital and that different investors have different amounts of human capital. As slavery is outlawed, this asset cannot be sold and hence is nonmarketable and completely illiquid . Nevertheless, because human capital is an asset, certain researchers have argued that it is relevant to each investor in identifying his or her optimal portfolio. Accordingly, the market portfolio should consist of all marketable and nonmarketable assets (such as human capital), and each security's beta should be measured relative to it. See David Mayers, "Nonmarketable Assets and Capital Market Equilibrium under Uncertainty," in Michael c.Jensen (ed.), Studies in the Theory oJ Capital Markets, (New York: Praeger, 1972), and "Nonmarketable Assets and the Determination of Capital Asset Prices in the Absence of a Riskless Asset," Journal ojBusiness 46, no. 2 (April 1973): 258-267.

20

The term security market plane is a trademark of Wells Fargo Bank. For more on the relationship between liquidity and stock returns, see YakovAmihud and Haim Mendelson, "Liquidity and Stock Returns," Financial AnalystsJournal 42, no. 3 (May/June 1986): 43-48; "Asset Pricing and the Bid-Ask Spread," Journal ojFinancial Economics 17, no. 2 (December 1986): 223-249; and "Liquidity, Asset Prices and Financial Policy," Financial Analysts Journal 47, no .6 (November/December 1991): 56-66.

21

Taxes might be such a third characteristic ifthe tax rate on income from capital gains is less than the tax rate on dividend income. In considering such taxes, one study found that the before-tax expected return of a security was a positive linear function of its beta and dividend yield . Securities with higher betas or dividend yields tended to have higher before-tax expected returns than securities with lower betas or dividend yields. The reason securities with higher dividend yields would have had higher before-tax expected returns was that they would be taxed more heavily. See M. J. Brennan, "Taxes, Market Valuation and Corporate Financial Policy," National TaxJournal23, no. 4 (December 1970): 417-427. The issue of whether dividends influence before-tax expected returns has been debated. It is discussed in Chapters 15 and 16 of Thomas E. Copeland and J. Fred Weston, Financial Theory and Corporate Policy (Reading, MA: Addison-Wesley, 1988) .

/(EY

TERMS

normative economics positive economics capital asset pricing model homogeneous expectations perfect markets separation theorem The Capital Asset Pricing Model

market portfolio capital market line security market line beta coefficient market risk non-market risk 253

f

~~R E FER ENe E S

"

1. Credit for the initial development of the CAPM is usually given to: William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal ofFinance 19, no. 3 (September 1964): 425-442. John Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets," Review of Economics and Statistics, 47, no. 1 (February 1965): 13-37; and "Security Prices, Risk, and Maximal Gains from Diversification," Journal ofFinance 20, no. 4 (December 1965): 587-615. Jan Mossin, "Equilibrium in a Capital Asset Market," Econometrica 34, no. 4 (October 1966): 768-783. 2. The Sharpe and Lintner papers were compared in: Eugene F. Fama, "Risk, Return, and Equilibrium: Some Clarifying Comments," Journal of Finance 23, no. 1 (March 1968): 29-40. 3. Some extended versions of the CAPM are described in: Gordon]. Alexander and Jack Clark Francis, Portfolio Analysis (Upper Saddle River, NJ: Prentice Hall, 1986), Chapter 8. Edwin]. Elton and Martin.J. Gruber, Modem Portfolio Theory and Investment Analysis (New York: Wiley, 1995), Chapter 14. 4. For a comparison of the market model and CAPM betas, see: Harry M. Markowitz, "The 'Two Beta' Trap," Journal ofPortfolio Management 11, no. 1 (Fall 1984): 12-20. 5. It has been argued that the CAPM is virtually impossible to test because (a) the only testable hypothesis of the ('APM is that the "true" market portfolio lies on the efficient set (when this happens securities' expected returns and betas have a positive linear relationship) and (b) the "true" market portfolio cannot be meaningfully measured. See: Richard Roll, "A Critique of the Asset Pricing Theory's Tests; Part 1. On Past and Potential Testability of the Theory," [oumal of Financial Economics 4, no. 2 (March 1977): 129-176. 6. Despite Roll's critique, several tests of the CAPM have been conducted. Some of them are summarized in: Gordon]. Alexander and Jack Clark Francis, Portfolio Analysis (Upper Saddle River, NJ: Prentice Hall, 1986), Chapter 10. Edwin]. Elton and Martin]. Gruber, Modem Portfolio Theory and Investment Analysis (New York: Wiley, 1995), Chapter 15. 7. Recently some people have concluded that the CAPM is no longer relevant on the basis of the following test results that show that the relationship between beta and average stock returns is flat: Eugene F. Fama and Kenneth R. French, "The Cross-Section of Expected Stock Returns," Journal ofFinance 47, no. 2 (June 1992): 427-465. Eugene F. Fama and Kenneth R. French, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of Financial Economics 33, no. 1 (February 1993): 3-56. James L. Davis, "The Cross-Section of Realized Stock Returns: The Pre-COMPUSTAT Evidence," Journal of Finance 49, no. 5 (December 1994): 1579-1593. Eugene F. Fama and Kenneth R. French, "The CAPM Is Wanted, Dead or Alive," Journal ofFinance 51, no. 5 (December 1996): 1947-1958. 8. However, these test results have been challenged by others, such as those listed below. For example, theJagannathan and Wang study shows that average returns and betas have a positive linear relationship when the market portfolio includes human capital (see endnote 19) and betas are allowed to vary over the business cycle: Louis K C. Chan and Josef Lakonishok, "Are the Reports of Beta's Death Premature?" Journal ofPortfolio Management 19, no. 4 (Summer 1993): 51-62.

254

CHAPTER 9

Fischer Black, "Beta and Return," Journal of Portfolio Management 20, no. 1 (Fall 1993): 8-18. S. P. Kothari, Jay Shanken, and Richard D. Sloan, "Another Look at the Cross-Section of Expected Stock Returns," Journal of Finance 50, no. 1 (March 1995): 185-224. RaviJagannathan and Ellen R. McGrattan, "The CAPM Debate," Federal Reserve Bank of Minneapolis Quarterly Review 19, no. 4 (Fall 1995): 2-17 Kevin Grundy and Burton Makiel, "Report of Beta's Death Have Been Greatly Exaggerated," Journal ofPortfolio Management 22, no. 3 (Spring 1996): 36-44. RaviJagannathan and Zhenyu Wang, "The Conditional CAPM and the Cross-Section of Expected Returns," Journal ofFinance 51 , no. 1 (March 1996): 3-53.

9. For an assertion that the use of modern portfolio theory does not depend upon successful testing of the CAPM, see: Harry M. Markowitz, "Nonnegative or Not Nonnegative: A Question about CAPMs,".Iournal ofFinance 38, no. 2 (May 1983): 283-295. 10. An interesting Web site that presents a wealth of information on the DowJones Averages can be found at: (http://averages.do\\jones.com/home.htmI).

The Capital Asset Pricing Model

255

CHAPTER

10

FACTOR MODELS

The objective of modern portfolio theory is to provide a means by which the investor can identify his or her optimal portfolio when there are an infinite number of possibilities. Using a framework involving expected returns and standard deviations shows that the investor needs to estimate the expected return and standard deviation for each security under consideration for inclusion in the portfolio along with all the covariances between securities. With these estimates the investor can derive the curved efficient set of Markowitz. Then for a given riskfree rate the investor can identify the tangency portfolio and determine the location of the linear efficient set. Finally, the investor can proceed to invest in this tangency portfolio and borrow or lend at the riskfree rate, with the amount of borrowing or lending depending on the investor's risk-return preferences.

II1II

FACTOR MODELS AND RETURN-GENERATING PROCESSES The task of identifying the curved Markowitz efficient set can be greatly simplified by introducing a return-generating process. A return-generating process is a statistical model that describes how the return on a security is produced. Chapter 7 presented a type of return-generating process known as the market model. The market model states that a security's return is a function of the return on a market index. However, there are many other types of return-generating processes for securities.

10.1.1

Factor Models

Factor models, or index models, assume that the return on a security is sensitive to the movements of various factors, or indices. The market model assumes that there is one factor-the return on a market index. However, in attempting to accurately estimate expected returns, variances, and covariances for securities, multiple-factor models are potentially more useful than the market model. They have this potential because it appears that security returns are sensitive to more than movements in a market index. That is, there probably is more than one pervasive factor in the economy that affects security returns. As a return-generating process, a factor model attempts to capture the major economic forces that systematically move the prices of all securities. Implicit in the 256

construction of a factor model is the assumption that the returns on two securities will be correlated-that is, will move together-only through common reactions to one or more of the factors specified in the model. Any aspect of a security's return unexplained by the factor model is assumed to be unique or specific to the security and therefore uncorreJated with the unique elements of returns on other securities. As a result, a factor model is a powerful tool for portfolio management. It can supply the information needed to calculate expected returns, variances, and covariances for every security-a necessary condition for determining the curved Markowitz efficient set. It can also be used to characterize a portfolio's sensitivity to movements in the factors.

10.1.2

Application

As a practical matter, all investors employ factor models whether they do so explic-

itly or implicitly. It is impossible to consider separately the interrelationship of every security with every other. Numerically, the problem of calculating covariances among securities rises exponentially as the number of securities analyzed increases.' Conceptually, the tangled web of security variances and covariances becomes mind-boggling as the number of securities increases beyond just a few securities, let alone hundreds or thousands. Even the vast data-processing capabilities of highspeed computers are strained when they are called upon to construct efficient sets from a large number of securities. Abstraction is therefore an essential step in identifying the curved Markowitz efficient set. Factor models supply the necessary level of abstraction. They provide investment managers with a framework to identify important factors in the economy and the marketplace and to assess the extent to which different securities and portfolios will respond to changes in those factors . Given the belief that one or more factors influence security returns, a primary goal of security analysis is to determine these factors and the sensitivities of security returns to movements in them. A formal statement of such a relationship is termed a factor model of security returns. The discussion begins with the simplest form of such a model, a one-factor model.

mil

ONE-FACTOR MODELS

Some investors argue that the return-generating process for securities involves a single factor. For example, they may contend that the returns on securities respond to the growth rate in the gross domestic product (GDP). Table 10.1 and Figure 10.1 illustrate one way of providing su bstance for such statemen ts .

TABLE

Year

1 2

3 4 5 6

Factor Models

10.1

Growth Rate in GOP

5.7% 6.4 7.9 7.0

5.1 2.9

Factor Model Data Rate of Inflation

Return on Widget Stock

1.1%

14.3% 19.2 23.4 15.6 9.2 13.0

4.4 4.4 4.6 6.• 3.1

257

Widget Tt

*

20.0

15.0 13.0% =T6 10.0

5.0

o

1.0

2.0

4.0

. / 3.0 2.9%

5.0

6.0

7.0

8.0 COPt

=COP fi

Figure 10.1 A One-Factor Model

10.2.1

An Example

On the horizontal axis of Figure 10.1 is the growth rate in GDP; the vertical axis measures the return on Widget's stock. Each point in the graph represents the combination of Widget's return and GDP growth rate for a particular year as reported in Table 10.1. A line has been statistically fitted to the data by using a technique known as simple linear regression analysis. (Simplerefers to the fact that there is one variableGDP in this example-on the right-hand side of the equation.j/ This line has a positive slope of 2, indicating that there exists a positive relationship between GDP growth rates and Widget's returns. Higher rates of GDP growth are associated with higher returns.:' In equation form, the relationship between GDP growth and Widget's return can be expressed as follows : r,

=

a

+ bGDP, + e,

(l0.1)

where: T, = the return on Widget in period t GOP, = the rate of growth in GOP in period t e, = the unique or specific return on Widget in period t b sensitivity of Widget to GOP growth' a = the zero factor for GOP

=

In Figure 10.1 the zero factor is 4% per period. This is the return that would be expected for Widget if GDP growth equaled zero. The sensitivity of Widget to predicted GDP growth is 2 and is the same as the slope of the line in Figure 10.1. This value indicates that, in general, higher growth in GDP is associated with higher returns for Widget. If GDP growth equaled 5%, Widget should generate a return of 14% [= 4% + (2 X 5%)]. IfGDP growth were 1% higher-that is, 6%-Widget's return should be 2% higher, or 16%.

258

CHAPTER 10

In this example, GDP growth in year 6 was 2.9%, and Widget actually returned 13%. Therefore Widget's unique return (given bye,) in this particular year was+3.2%. This was determined by subtracting an amount that represents Widget's expected return, given that GDP grew by 2.9%, from Widget's actual return of 13%. In this case, Widget was expected to return of9.8% [= 4 + (2 X 2.9%)], thereby resulting in a unique return of+3.2% (= 13% - 9.8%) . In effect, the one-factor model presented in Figure 10.1 and Equation (10.1) attributes Widget's return in any particular period to three elements: 1. An effect common in any period (the term a)

2. An effect that differs across periods depending on the factor, the growth rate ofGDP (the term bGDP,) 3. An effect specific to the particular period observed that is not attributable to the factor (the term e,)

10.2.2

Generalizing the Example

This example of a one-factor model can be generalized in equation form for any security i in period t: (10.2) where F, is the value of the factor in period t, and b, is the sensitivity of security ito this factor. If the value of the factor were zero, the return on the security would equal a, + eit. Note that eit is a random error term just like the random error term discussed in Chapter 7. This means that it is a random variable with an expected value of zero and a standard deviation Uri' It can be thought of as the outcome occurring from a spin of a roulette wheel in the same manner as described in Chapter 7. Expected Return

According to the one-factor model, the expected return on security ican be written as: Tj

= aj + b.F

(10.3)

where F denotes the expected value of the factor. This equation can be used to estimate the expected return on the security. For example, if the expected growth rate in GDP is 3%, then the expected return for Widget equals 10% [= 4% + (2 X 3%)]. Variance

With the one-factor model, it can also be shown that the variance of any security i is equal to : (10.4) where u~ is the variance of the factor Fand u;; is the variance of the random error term e.: Thus if the variance of the factor u~ equals 3 and the residual variance u~ equals 15.2, then according to this equation Widget's variance equals:

u; =

(22 X3) + 15.2

= 27.2 Covariance

With a one-factor model the covariance between any two securities i and j can be shown to equal: Factor Models

259

(10 .5) In the example of Widget, Equation (10.5) can be used to estimate the covariance between Widget and another hypothetical security, such as the stock of Whatever Company. Assuming that thc factor sensitivity of Whatever is 4.0, the covariance between Widget and Whatever equals: uij

= 2 X4 X3 = 24

Assumptions

Equations (10.4) and (10.5) are based on two critical assumptions. The first assumption is that the random error term and the factor are uncorrelated. This means that the outcome of the factor has 1I0 bearing on the outcome of the random error term . The second assumption is that the random error terms of any two securities are uncorrelated. This means that the outcome of the random error term of one security has no bearing on the outcome of the random error term of any other security. As a result, the returns of two securities will be correlated only through common responses to the factor. If either of these two assumptions is invalid, then the model is an approximation, and a different factor model (perhaps one with more factors) theoretically will be a more accurate representation of the return-generating process.

10.2.3

The Market Model

The market model can now be shown to be a specific example of a one-factor model in which the factor is the return on a market index. In Chapter 7, the market model appeared as: (7.3) Comparison of Equation (7.3) with the general form of the one-factor model in Equation (10.2) makes readily apparent the similarity between the two equations. The intercept Q;I from the market model equation corresponds to the zero factor term a; from Equation (l 0.2). Furthermore, the slope term {3i/ from the market model equates to the sensitivity term b, from the generalized one-factor model. Each equation has a random error term: ei/ in the factor model and £ ;1 in the market model.P Finally, the market index return plays the role of the single factor. However, as mentioned earlier, the concept of a one-factor model does not restrict the investor to using a market index as the factor. Many other single factors are plausible. Macroeconomic variables such as growth in the economy, interest rates, and the inflation rate offer a fertile ground in the search for pervasive factors.

10.2.4

Two Important Features of One-Factor Models

Two features of one-factor models are of particular interest: the tangency portfolio and diversification. The Tangency Portfolio

First, the assumption that the returns on all securities respond to a single common factor greatly simplifies the task of identifying the tangency portfolio. To determine the composition of the tangency portfolio, the investor needs to estimate all of the 260

CHAPTER 10

securities' expected returns, variances, and covariances. This task can be accomplished with a one-factor model by estimating ai' b.; and a "i for each of the N risky securi ties. Ii Also needed are the expected value of the factor F and its standard deviation rrF' With these estimates, Equations (10.3), (10.4), and (10.5) can subsequently be used to calculate expected returns, variances, and covariances for the securities. When these values are used, the curved efficient set of Markowitz can be derived. Finally, the tangency portfolio can be determined for a given riskfree rate. The common responsiveness of securities to the factor eliminates the need to estimate directly the covariances between the securities. Those covariances are captured by the securities' sensitivities to the factor and the factor's variance.

Diversification

The second interesting feature of one-factor models has to do with diversification. Earlier it was shown that diversification leads to an averaging of market risk and a reduction in unique risk. This feature is true of anyone-factor model except that instead of market and unique risk, the terms factor risk and nonfactor risk are used. In Equation (10.4) the first term on the right-hand side (bTrr}.) is known as the factor risk of the security, and the second term (rr~) is known as the nonfactor (or unique) risk of the sec uri ty. With a one-factor model, the variance of a portfolio is given by:

rr;

= b;rr}.

+ rr~

(10.6a)

where: N

bp =

2: Xibi

(1O.6b)

i=l

(l0.6c) Equation (1O.6a) shows that the total risk of any portfolio can be viewed as having two components similar to the two components of the total risk of an individual security shown in Equation (10.4). In particular, the first and second terms on the right-hand side of Equation (1O.6a) are the factor risk and nonfactor risk of the portfolio, respectively. As a portfolio becomes more diversified (meaning that it contains more securities), each proportion X; will become smaller. However, this change will not cause bp to either decrease or increase significantly unless a deliberate attempt is made to do so by continually adding securities with values of b, that are either relatively low or high, respectively. As Equation (10.6b) shows, the reason is that bp is simply a weighted average of the sensitivities of the securities b., with the values of X; serving as the weights. Thus diversification leads to an averaging offactor risk. However, as a portfolio becomes more diversified, there is reason to expect rr;, the non factor risk, to decrease. This change can be shown by examining Equation (1O.6c). On the assumption that the same amount is invested in each security, then this equation can be rewritten by substituting liN for X;:

rr;

=

2: (1-N )2rr~ N

;=1

=

Factor Models

(

_1 )

[rrel2 + rr 2e2 + ... + rr 2eN ]

N

N 261

The value inside the square brackets is the average nonfactor risk for the individual securities. But the portfolio's nonfactor risk is only one-Nth as large because the term 1/ N appears outside the brackets. As the portfolio becomes more diversified, the number of securities ill it, N, becomes larger. Consequently, 1/ N becomes smaller, and the nonfactor risk of the portfolio is, in turn, reduced. Simply stated, diversification reduces nonfuctor risk 7

l1li

MULTIPLE-FACTOR MODELS The health of the economy affects most firms. Thus changes in expectations concerning the future of the economy wilI generally have profound effects on the returns of most securities. However, the economy is not a simple, monolithic entity. Several common influences with pervasive effects might be identified. 1. 2. 3. 4. 5. 6.

The growth rate of gross domestic product The level of interest rates on short-term Treasury securities The yield spread between long-term and short-term Treasury securities The yield spread between long-term corporate and Treasury securities The inflation rate The level of oil prices

10.3.1

Two-Factor Models

Instead of a one-factor model, a multiple-factor model for security returns that considers these various influences may be more accurate. As an example of a multiplefactor model, consider a two-factor model which assumes that the return-generating process contains two factors . In equation form, the two-factor model for period tis: (10.7) where £../ and F21 are the two factors that are pervasive influences on security returns, and hi) and h i2 are the sensitivities of security i to those two factors . As with the onefactor model, eil is a random error term and ai is the expected return on security i if each factor has a value of zero. Figure 10.2 provides an ilIustration of Widget Company's stock, whose returns are affected by expectations concerning both the growth rate in GDP and the rate of inflation. As was the case in the one-factor example, each point in the figure corresponds to a particular year. (Only one point has been shown to avoid cluttering the figure.) This time, however, each point is a combination of Widget's return, the rate of inflation, and the growth in GDP in that year as given in Table 10.1. To this scatter of points is fit a two-dimensional plane by using the statistical technique of multiple-regression analysis. (Multiple refers to the fact that there is more than one variable on the right-hand side of the equation, in this case FI and F2 , explaining the variable on the left-hand side of the equation, in this case r,.) The plane for a given security is described by the following adaptation of Equation (10.7):

r, = a + hI GDP , + b2INF t The slope of the plane in the GDP growth-rate direction (the term hI) represents Widget's sensitivity to changes in GDP growth, assuming no change in inflation. The slope of the plane in the inflation rate direction (the term h2 ) is Widget's sensitivity to changes in the inflation rate, assuming no change in GDP growth. Note that the sen262

CHAPTER 10

Widget

Tt

-- '- COPt

3.1%

=

INF 6

2.9%

=

COP fi

Figure 10.2 A Two-Factor Model

sitivities b, and b2 in this example are positive and negative, respectively, having corresponding values of2.2 and -.7. 8 This slope indicates that as CDP growth rises Widget's return should increase, and as inflation rises Widget's return should decrease. The intercept term (the zero factor) in Figure 10.2 of 5.8% indicates Widget's expected return if both CDP growth and inflation are zero. Finally, in a given year, the distance from Widget's actual point to the plane indicates its unique return (Cit), the portion of Widget's return not attributed to either CDP growth or inflation. For example, given that CDP grew by 2.9% and inflation was 3.1%, Widget's expected return in year 6 equals 10% [= 5.8% + (2.2 X 2.9%) - (.7 X 3.1%)]. Hence its unique return for that year is equal to +3% (= 13% - 10%). Four parameters need to be estimated for each security with the two-factor model: aj, u«. bj 2 , and the standard deviation of the random error term, denoted uri' For each of the factors, two parameters need to be estimated. These parameters are the expected value of each factor (F 1and F2) and the variance of each factor (U~l and uh). Finally, the covariance between the factors COV(F1 , F2 ) needs to be estimated. Expected Return

With these estimates, the expected return for any security i can be determined by specifying the expected values for the two factors and using the following formula: Factor Models

263

Tj

=

aj

+ bi l PI + bj2 P 2

(10.8)

For example, the expected return for Widget equals 8.9% [= 5.8% + (2.2 X 3%) - (.7 X 5%)] provided that the expected increases in GDP and inflation are 3% and 5%, respectively. Variance

According to the two-factor model, the variance for any security i is:

u; = bTl uh

+ b;2U~ + 2bj] bi2COV(F;, F2) + u~

(10.9)

If, in the example, the variances of the first (U}I) and second (u~) factors are equal to 3 and 2.9, respectively, their covariance [ COV( Pi, F2)] equals .65, and the random error term has a variance U;j of 18.2, then the variance of Widget equals 32.1 [= (2.2 2 X 3) + (-.7 2 X 2.9) + (2 X 2.2 X -.7 X .65) + 18.2], because its two sensitivities are 2.2 and -.7, respectively. Covariance

Similarly, according to the two-factor model the covariance between any two securities i and j can be determined by:

uij = bilbj1u}1

+ bi2bj2U~ + (b ilbj2 + bj2bjl)COV(FI.F2)

(10.10)

Thus continuing with the example, the covariance between Widget and Whatever is estimated to equal 39.9 {= (2.2 X 6 X 3) + (-.7 X -5 X 2.9) + [(2 .2 X -5) + (-.7 X 6)] X .65} because the sensitivities of Whatever to the two factors are 6 and -5, respectively. The Tangency Portfolio As with the one-factor model , once the expected returns, variances, and covariances

have been determined using these equations, the investor can proceed to use an optimizer (a special kind of mathematical routine discussed in Chapter 7) to derive the curved efficient set of Markowitz. Then for a given riskfree rate, the tangency portfolio can be identified, after which the investor can determine his or her optimal portfolio. Diversification

Everything said earlier regarding one-factor models and the effects of diversification applies here as well. 1. Diversification leads to an averaging of factor risk. 2. Diversification can substantially reduce nonfactor risk. 3. For a well-diversified portfolio, nonfactor risk will be insignificant. As with a one-factor model, the sensitivity of a portfolio to a particular factor in a

multiple-factor model is a weighted average of the sensitivities of the securities where the weights are equal to the proportions invested in the securities. This relation can be seen by remembering that the return on a portfolio is a weighted average of the returns of its component securities: N Tp1

= ~

X;Tjz

(10.11)

j=1

264

CHAPTER 10

Substituting the right-hand side of Equation (l0.7) for Equation (10 .11) results in:

Tit

on the right-hand side of

N

rp/ =

L Xi(aj + bilF

II

+ bj2F2/ + Ci,)

;= 1

(10.12)

where: N

ap

= L x», i=l

N

bpI =

L X/b

i)

i=1 N

bp2 =

L X;b

i2

i=l

N

Cpt

=

L

x,'Ci/

i=l

Note that the portfolio sensitivities bl,1 and bl'2 are weighted averages of the respective individual sensitivities bi! and bi2 •

The Importance of Expectations

Security prices reflect investors' estimates of the present values of firms' future prospects. At any given time the price of Widget stock is likely to respond to the projcctcdvalues of such factors as the growth rate of GOP or the rate of inflation, as opposed to depending on the historical values of those factors. If investors ' projections of such fundamental economic conditions change, so too will the price of Widget. Because the return on a stock is influenced heavily by changes in its price, stock returns are expected to be more highly correlated with changes in expected future values of fundamental economic variables than with the actual changes that occur con tern poraneously. For example, a large increase in inflation that was fully anticipated might have no effect on the stock price of a company whose earnings are highly sensitive to inflation. However, if the consensus expectation was for a low inflation rate, then the subsequent large unanticipated increase would have a significant effect on the company's stock price, particularly if investors believed that the unexpected increase was a harbinger of larger than previously anticipated future inflation . For this reason, whenever possible it is desirable to select factors that measure changes in expectations rather than realizations, as the latter typically include both changes that were anticipated and those that were not. One way to accomplish this goal is to rely on variables that involve changes in market prices. Thus the difference in the returns on two portfolios-one consisting of stocks thought to be unaffected by inflation and the other consisting of stocks thought to be affected by inflationcan be used as a factor that measures revisions in inflation expectations. Factor Models

265

10.3.2

Sector-Factor Models

The prices of securities in the same industry or economic sector often move together in response to changes in prospects for that sector. Some investors acknowledge this relation by using a special kind of multiple-factor model referred to as a sectorfactor model. A sector-factor model is created by assigning to a sector each security under consideration. For a two-sector-factor model, there are two sectors, and each security must be assigned to one of them. For example, let sector factor 1 consist of all industrial companies and sector factor 2 consist of all nonindustrial companies (such as utility, transportation, and financial companies). Thus /

0

(11.5b)

The solution for this candidate shows that its expected return is (15% X .1) + (21% X .075) + (12% X - .175) = .975%. Because this is a positive number, an arbitrage portfolio has indeed been identified. The arbitrage portfolio just identified involves buying $1,200,000 of stock 1 and $900,000 of stock 2. How were these dollar figures arrived at? The solution comes from taking the current market value of the portfolio (~ = $12,000,000) and multiplying it by the weights for the arbitrage portfolio of Xl = .1 and X2 = .075. Where does the money come from to make these purchases? It comes from selling $2,100,000 of stock 3. (Note that X3 ~ = -.175 X $12,000,000 = -$2,100,000.) In summary, this arbitrage portfolio is attractive to any investor who desires a higher return and is not concerned with nonfactor risk. It requires no additional dollar investment, it has no factor risk, and it has a positive expected return. Arbitrage Pricing Theory

285

TABLE

I 1. I

How an Arbitrage POrtfolio Affects an Investon Position Old

Portfolio

+

Arbitrage Portfolio

=

New Portfolio

Weight

XI Xi X,

.100

.333 .333 .333

.433

.O7~

0408

-.175

.158

Property: Tp

16.000 %

,975%

bp

1.900 11.000

,000

1.900

Small

Approx. 11.000

up

11.1.3

16.975%

The Investors Position

At this juncture the investor can evaluate his or her position from either one of two equivalent viewpoints: (1) holding both the old portfolio and the arbitrage portfolio or (2) holding a new portfolio. Consider, for example, the weight in stock 1. The old portfolio weight was .333 and the arbitrage portfolio weight was .10 , with the sum of these two weights being equal to .433. Note that the dollar value of the holdings ofstock 1 in the new portfolio rises to $5,200,000 (=$4,000,000 + $1,200,000), so its weight is .433 (= $5,200,000/$12,000,000), equivalent to the sum of the old and arbitrage portfolio weights. Similarly, the portfolio's expected return is equal to the sum of the expected returns of the old and arbitrage portfolios, or 16.975% (= 16% + .975%). Equivalently, the new portfolio's expected return can be calculated using the new portfolio's weights and the expected returns of the stocks, or 16.975% [= (.433 X 15%) + (.408 X 21 %) + (.158 X 12%)]. The sensitivity of the new portfolio is 1.9 [= (.433 X .9 ) + (.408 X 3.0) + (.158 X 1.8)]. This is the same as the sum of the sensitivities of the old and arbitrage portfolios (= 1.9 + 0.0) . What about the risk of the new portfolio? Assume that the standard deviation of the old portfolio was 11%. The variance of the arbitrage portfolio will be small because its only source of risk is nonfactor risk. Similarly, the variance of the new portfolio will differ from that of the old only as a result of changes in its nonfactor risk. Thus it can be concluded that the risk of the new portfolio will be approximately II %.5 Table 11.1 summarizes these observations.

mil

PRICING EFFECTS What are the consequences of buying stocks 1 and 2 and selling stock 3? Because everyone will be doing so, the stocks' prices will be affected and, accordingly, their expected returns will adjust. Specifically, the prices of stocks 1 and 2 will rise because of increased buying pressure. In turn, this rise will cause their expected returns to fall. Conversely, the selling pressure put on stock 3 will cause its stock price to fall and its expected return to rise. This outcome can be seen by examining the equation for estimating a stock's expected return : -r = PI --1

Po

286

(11.6)

. CHAPTER 11

where ~) is the stock's current price and PI is the stock's expected end-of-period price. Buying a stock such as stock 1 or 2 will push up its current price ~) yet will have no impact on the stock's expected end-of-period price Pl ' As a result, its expected return l' will decline. Conversely, selling a stock such as stock 3 will push down its current price and result in a rise in its expected return . This buying-and-selling activity will continue until all arbitrage possibilities are significantly reduced or eliminated. That is, all possible portfolio adjustments that require no additional funds and that have zero factor exposures will all have zero expected returns. At this point there will exist an approximately linear relationship between expected returns and sensitivities of the following sort: (11.7)

where Ao and AI are constan ts. This equation is the asset pricing equation of the APT when returns are generated by one factor," Note that it is the equation of a straight line, meaning that in equilibrium there will be a linear relationship between expected returns and sensitivities. In the example, one possible equilibrium setting could have Ao = 8 and A] = 4.7 Consequently, the pricing equation is: 1'j = 8

+ 4b

(11.8)

j

This would result in the following equilibrium levels of expected returns for stocks 1,2, and 3:

+ (4 8 + (4 8 + (4

1'1 = 8

X .9) = 11.6%

1'2 =

X 3.0) = 20.0%

1'3 =

X 1.8)

=

15.2%

As a result, the expected returns for stocks 1 and 2 will have fallen from 15% and 21%, respectively, to 11.6% and 20% because of increased buying pressure. Conversely, increased selling pressure will have caused the expected return on stock 3 to rise from 12% to 15.2%. The bottom line is that the expected return on any security is, in equilibrium, a linear function of the security's sensitivity to the factor b/'

11.2.1

A Graphical J1Justration

Figure 11.1 illustrates the asset pricing equation of Equation (11.7). Any security that has a factor sensitivity and expected return such that it lies off the line will be mispriced according to the APT and will present investors with the opportunity of forming arbitrage portfolios. Security B is an example. An investor who buys security Band sells security Sin equal dollar amounts will have formed an arbitrage portfolio." How? First of all, by selling an amount of security S to pay for the long position in security B, the investor will not have committed any new funds. Second, because securities Band S have the same sensitivity to the factor, the selling of security Sand buying of security B will constitute a portfolio with no sensitivity to the factor. Finally, the arbitrage portfolio will have a positive expected return because the expected return of security B is greater than the expected return of security S.IO As a result of investors' buying security B, its price will rise and, in turn, its expected return will fall until it is located on the APT asset pricing line. II In the three-security example presented earlier, it can be shown that the securities do not initially all lie on a straight line. Instead, any line that is drawn will have at least one of them lying above or below the line. However, after stocks 1,2, and 3's expected returns have adjusted from 15%,21 %, and 12% to 11.6%, 20%, and 15.2%, Arbitrage Pricing Theory

287

APT Asset Pricing Line Al

Tn - - - - - - - - - - - - - - - - - - ., B

' - - - - - - - - - - ' - - - - - - - - - - - - b,

Figure 11.1 APTAsset Pricing Line

respectively, they will all lie on a line with a vertical intercept of 8% and a slope of 4. This result will be shown next.

11.2.2

Interpreting the APT Pricing Equation

How can the constants Ao and Al that appear in the APT pricing Equation (11.7) be interpreted? On the assumption that there is a riskfree asset in existence. such an asset will have a rate of return that is a constant. Therefore this asset will have no sensitivity to the factor. From Equation (11. 7) it can be seen that Tj = Ao for any asset with b, = O. In the case of the riskfree asset, it is also known that Tj = rf. implying that Ao = rf' Hence the value of Ao in Equation (11.7) must be rf• allowing this equation to be rewritten as: (11.9) The value of Al can be determined by considering a pure factor portfolio (or pure factor play) denoted p* that has unit sensitivity to the factor. meaning bp* = 1.0. (If there were other factors. such a portfolio would be constructed so as to have no sensitivity to them.) According to Equation (11.9). such a portfolio will have the following expected return: Tp• = rf

+ Al

( Il.lOa)

Note that this equation can be rewritten as: (1l.l0b)

lSS

CHAPTER 11

Thus A] is the expected excess return (meaning the expected return over and above the riskfree rate) on a portfolio that has unit sensitivity to the factor. Accordingly, it is known as a factor risk premium (or factor-expected return premium). Letting 0] = denote the expected return on a portfolio that has unit sensitivity to the factor, Equation (I1.10b) can be rewritten as:

r".

(IUOc) Inserting the left-hand side of Equation (I1.10c) for A] in Equation (11.9) results in a second version of the APT pricing equation: (ILll)

In the example, because Tf = 8% and Al = 0] - Tf = 4%, it follows that 01 = 12%. This means that the expected return on a portfolio that has unit sensitivity to the first factor is 12%. This outcome can also be seen by considering the formation of a pure factor portfolio from securities 1 and 3. Because the securities have sensitivities of .9 and 1.8, respectively, their weights in the pure factor portfolio will be 8/9 and 1/9, respectively. [Note that (.9 X 8/9) + (1.8 X 1/9) = 1] . Accordingly, the portfolio's expected return will be 12% [= (11.6% X 8/9) + (15.2% X 1/9)], as indicated earlier. In order to generalize the pricing equation of APT, one needs to examine the case in which security returns are generated by more than one factor. This examination is done by considering a two-factor model and then expanding the analysis to k factors where k > 2.

11II

TWO-FACTOR MODELS

In the case of two factors, denoted F] and F~ and representing, for example, industrial production and inflation, each security will have two sensitivities, bi] and b,'}.. Thus security returns are generated by the following factor model: (ILl2)

Consider a situation in which there are four securities that have the following expected returns and sensitivities. I Stock 1

Stoclt2 Stock 3 Sl<x:k 4

"

~,

b.,

.9

2.0

3.0

1.5 .7 3.2

15% 21 12

8

2.0

1.8

In addition, consider an investor who has $5,000,000 invested in each of the securities. (Thus the investor has initial wealth Wo of $20,000,000.) Are these securities priced in equilibrium?

11 .3. 1

Arbitrage Portfolios

To answer that question, one must explore the possibility of forming an arbitrage portfolio. First of all, an arbitrage portfolio must have weights that satisfy the following equations: Arbitrage Pricing Theory

289

XI + X z + X3 + X 4 = 0

(11.13)

.9X1 + 3X2 + 1.8X3 + 2X4 = 0

(11.14)

2X1 + 1.5X2 + .7X3 + 3.2X4 = 0

(11.15)

These conditions mean that the arbitrage portfolio must not involve an additional commitment of funds by the investor [Equation (11.13)] and must have zero sensitivity to each factor [Equations (11.14) and (11.15)]. Note that there are three equations that need to be satisfied and that each equation involves four unknowns . Because there are more unknowns than equations, there are an infinite number of solutions. One solution can be found by setting XI equal to .1 (an arbitrarily chosen amount) and then solving for the remaining weights. Doing so results in the following weights: X2 = .088, x:~ = - .108, and X4 = - .08. These weights represent a potential arbitrage portfolio. What remains to be done is to see if this portfolio has a positive expected return. Calculating the expected return of the portfolio reveals that it is equal to 1.41% [= (.1 X 15%) + (.088 X 21%) + (-.108 X 12%) + (-.08 X 8%)]. Hence an arbitrage portfolio has been identified. This arbitrage portfolio involves the purchase of stocks 1 and 2, funded by selling stocks 3 and 4. Consequently, the buying-and-selling pressures will drive the prices of stocks 1 and 2 up and of stocks 3 and 4 down. In turn, the expected returns of stocks 1 and 2 will fall and of stocks 3 and 4 will rise. Investors will continue to create such arbitrage portfolios until equilibrium is reached. Equilibrium will be attained when any portfolio that satisfies the conditions given by Equations (11.13), (11.14), and (11.15) has an expected return of zero. This expected return will occur when the following linear relationship between expected returns and sensitivities exists:

(11.16) As in Equation (11.7), this is a linear equation except that it now has three dimensions (ri' b,l , and bi2 ) instead of two (1'; and bj ) and hence corresponds to the equa-

tion of a plane instead of a line. In the example, one possible equilibrium setting is where Ao A2 = -2. Thus the pricing equation is:

=

8, Al

=

4, and

(11.17) As a result, the four stocks have the following equilibrium levels of expected returns: Tj

= 8 + (4 X .9) - (2 X 2) = 7.6%

Tj = 8 + (4 X 3) - (2 X 1.5) = 17.0%

r,' = 8 + (4 X 1.8) - (2 X .7) = 13.8% Tj

= 8 + (4

X 2) - (2 X 3.2) = 9.6%

The expected returns of stocks 1 and 2 have fallen from 15% and 21% while the expected returns of stocks 3 and 4 have risen from 12% and 8%, respectively. Given the buying-and-selling pressures generated by investing in arbitrage portfolios, these changes are in the predicted direction. One consequence of Equation (11.17) is that a stock with higher sensitivity to the first factor than another stock will have a higher expected return if the two stocks also have the same sensitivity to the second factor because A, > O. Conversely, because A2 < 0, a stock with higher sensitivity to the second factor will have a lower expected return than another stock with a lower sensitivity to the second factor, provided that the two stocks have the same sensitivity to the first factor. However, the effect of 290

CHAPTER 11

two stocks having different sensitivities to both factors can be confounding. For example, stock 4 has a lower expected return than stock 3 even though both of its sensitivities are larger. The reason is that the advan tage of having a higher sensitivity to the first factor (h4J = 2.0 > !>:II = 1.8) is not ofsufficient magnitude to offset the disadvantage of having a higher sensitivity to the second factor ( h42 = 3.2 > !>:I2 = .7).

11.3.2

Pricing Effects

Extending the one-factor APT pricing Equation (11.7) to this two-factor situation is relatively uncomplicated. As before, Ao is equal to the riskfree rate because the riskfree asset has no sensitivity to either factor, meaning that its values of hi! and hi 2 are both zero. Hence it follows that Ao = Tf' Thus Equation (11.16) can be rewritten more generally as: (11.18) In the example given in Equation (11.16), it can be seen that Tf = 8%. Next consider a well-diversified portfolio that has unit sensitivity to the first factor and zero sensitivity to the second factor. As mentioned earlier, such a portfolio is known as a pure factor portfolio (or pure factor play) because it has: (1) unit sensitivity to one factor, (2) no sensitivity to any other factor, and (3) zero nonfactor risk. Specifically, it has hi = 1 and b.l = O. It can be seen from Equation (11.18) that the expected return on this portfolio, denoted 8 J , will be equal to Tf + ,I" . As it follows that 8, - Tf = AI> Equation (11.18) can be rewritten as: (11.19) In the example given in Equation (11.16), it can be seen that 8 1 - Tj = 4. This means that 8 J = 12 because Tf = 8. In other words, a portfolio that has unit sensitivity to industrial production (the first factor) and zero sensitivity to inflation (the second factor) will have an expected return of 12%, or 4% more than the riskfree rate of 8%. Finally, consider a portfolio that has zero sensitivity to the first factor and unit sensitivity to the second factor, meaning that it has hi = 0 and b.l = 1. It can be seen from Equation (11.18) that the expected return on this portfolio, denoted 82 , will be equal to Tj + A2 . Accordingly, 82 - Tf = A2 , thereby allowing Equation (11.19) to be rewri tten as: (11.20) In the example given in Equation (11.16), it can be seen that 82 - Tf = -2. This means that 82 = 6 since Tf = 8. In other words, a portfolio that has zero sensitivity to industrial production (the first factor) and unit sensitivity to inflation (the second factor) will have an expected return of 6%, or 2% less than the riskfree rate of 8%.

mill

MULTIPLE-FACTOR MODELS

When returns were generated by a two-factor model instead of a one-factor model, APT pricing Equations (11.7) and (11.11) were simply expanded to accommodate the additional factor in Equations (11.16) and (11.20). What happens to these APT pricing equations when returns are generated by a multiple-factor model where the number offactors k is greater than 2? It turns out that the basic pricing equations are expanded once again in a relatively straightforward manner. Arbitrage Pricing Theory

291

bi2 ,

In the case of k factors (}j, };, ... , Fk ) each security will have k sensi tivities (b i l , bill) in the following k-factor model:

... ,

(11.21) In turn, securities will be priced hy the following equation, which is similar to Equations (11.7) and (11.16): (11.22) As before, this is a linear equation, except now it is in k mensions being Ti , bil , bi2 , ... , and bik •

+ 1 dimensions, with

the di-

Extending the APT pricing Equations (11.11) and (11.20) to this situation is relatively uncomplicated. As before, An is equal to the riskfree rate because the riskfree asset has no sensitivity to any [actor. Each value of 8} represents the expected return on a portfolio of stocks that has unit sensitivity to factor j and zero sensitivity to all the other factors. As a result, Equations (11.11) and (11.20) can be expanded as follows: (11.23) Hence a stock's expected return is equal to the riskfree rate plus k risk premiums based on the stock's sensitivities to the k factors.

l1li

A SYNTHESIS OF THE APT AND THE CAPM Unlike the APT, the CAPM does not assume that returns are generated by a factor model. However, this does not mean that the CAPM is inconsistent with a world in which returns are generated by a factor model. Indeed, it is possible to have a world in which returns are generated hy a factor model, where the remaining assumptions ofthe APT hold, and where all the assumptions of the CAPM hold. This situation will now be examined.

11.5.1

One-Factor Models

Consider what will happen if returns are generated by a one-factor model and that factor is the market portfolio. In such a situation, 8] will correspond to the expected return on the market portfolio and b, will represent the beta of stock i measured relative to the market portfolio. Hence the CAPM will hold. What if returns are generated by a one-factor model and that factor is not the market portfolio? Now 15 1 will correspond to the expected return on a portfolio with unit sensitivity to the factor, and b, will represent the sensitivity of stock i measured relative to the factor.l" However, if the CAPM also holds, then security i's expected return will be a function of both its beta and its factor sensitivity:

+ (TM TJ + (81 -

Tj = TJ

TJ){3iM

(11.24)

Ti =

TJ)b i

(11.25 )

These relationships suggest that betas and sensitivities must somehow be related to each other.

Beta Coefficients and Factor Sensitivities It can be demonstrated that betas and factor sensitivities will be linearly related to each

other in the following manner: 292

CHAPTER 11

{3jM =

COV(FJ, TM)

+ COV(ei' TM) 2

UM

= ({3F

1M

+ {3.;M)b

j

b,

(11.26a) (11.26b)

where COV(F" TM) denotes the covariance between the factor and the market portfolio, COV( ej, TM) denotes the covariance between the residual return of the factor model for security i and the return on the market portfolio, u~ denotes the variance of the return on the market portfolio, and {3F1M and {3'i M are defined as being equal to COV(FI , TM)/U~ and COV( ei' TM)/U~, respectively.P Hence, {3F1M denotes the beta of the factor, and {3'i M denotes the beta of security z's residual returns; both of these betas are measured relative to the market portfolio. What if each security's residual return is uncorrelated with the market's return? In this situation, COV( ei' TM) = 0, which in turn means that {3.,M = O. Thus, Equation (11.26b) reduces to: (11. 27) Because the quantity {3/oj Mis a constant and does not change from one security to another, Equation (11.27) is equivalent to saying that {3iM will be equal to a constant times bjwhen Equations (11.24) and (11.25) both hold. Hence if the factor is industrial production, then Equation (11.27) states that each security's beta is equal to a constant times the security's sensitivity to industrial production, when the security's residual return is uncorrelated with the market's return. The constant wiII be a positive number if industrial production and the returns on the market portfolio are positively correlated because then {3F\M will be positive." Conversely, the constant will be negative if the correlation is negative because then {3FjM will be negative.

Factor Risk Premiums

Note what happens if the right-hand side of Equation (11.27) is substituted for {3iM on the right-hand side of Equation (11.24): (11.28) Comparing this equation with Equation (11.9) reveals that if the assumptions of both APT (with one factor) and the CAPM hold and each security's residual return is uncorrelated with the market's return , then the following relationship must hold: (11.29) By itself, APT says nothing about the size of the factor risk premium AI' However, if the CAPM also holds, it can provide some guidance. This guidance is given in Equation (11.29), which has been shown to hold if the assumptions of both APT and the CAPM are taken as given and each security's residual return is uncorrelated with the market's return. Imagine that the factor moves with the market portfolio, meaning that it is positively correlated with the market portfolio so that {3F1M is positive . IS Because (rM - ~) is positive, it follows that the right-hand side of Equation (11.29) is positive and hence Al is positive. Furthermore, because Al is positive, it can be seen in Equation (11.9) that the higher the value of b.; the higher will be the expected return of the security.16 To generalize, if a factor is positively correlated with the market portfolio but the residual return of each securi ty is uncorrelated with the market return, then each security's expected return will be a positive function of the security's sensitivity to that factor. Arbitrage Pricing Theory

293

- -.

~r " .~ ~.

:. .

....

-

"

. .

.

.' '". . .':'.. .~

-,-

I N $ TIT UTI 0 N A L I $ $ U E'.$: . ' .

.

.

'.. . . '

..

"

...'

'" .'

.. '.'

.

"

. ' ',' "

~ '.

.

Applying Arbitrage Pricing Theory Since its inception in the mid-1970s, arbitrage pricing theory (APT) has provided researchers and practitioners with an intuitive and flexible framework through which to address important investment management issues. As opposed to the capital asset pricing model (CAPM), with its specific assumptions concerning investor preferences as well as the critical role played by the market portfolio, APT operates under relatively weaker assumptions. Because of its emphasis on multiple sources of systematic risk, APT has attracted considerable interest as a tool for better explaining investment results and more effectively controlling portfolio risk, Despite its attractive features, APT has not been widely applied by the investment community. The reason lies largely with APT's most significant drawback: the lack of specificity regarding the multiple factors that systematically affect security returns as well as the long-term return associated with each of these factors. Rightly or wrongly, the CAPM unambiguously states that a security's covariance with the market portfolio is the only systematic source of its investment risk within a well-diversified portfolio, Arbitrage pricing theory, conversely, is conspicuously silent regarding the particular systematic factors affecting a security's risk and return. Investors must fend for themselves in determining those factors.

Few institutional investors actually use APT to manage assets. The most prominent organization that does use it is Roll & Ross Asset Management Corporation (R&R). Because Stephen Ross invented the APT, it is interesting to briel1y review how R&R translates this theory into practice. R&R begins with a statement of the systematic sources of risk (or factors) that it believes are currently relevant in the capital markets. Specifically, R&R has identified five factors that pervasively affect common stock returns: • The business cycle • In terest rates • Investor confidence • Short-term inl1ation • Long-term inflationary expectations R&R quantifies these factors by designating certain measurable macroeconomic variables as proxies. For example, the business-cycle factor is represented by real (inflation-adjusted) percentage changes in the index of industrial production, whereas short-term inflation is measured by monthly percentage changes in the consumer price index. At the heart of the R&R approach are several assumptions. First, each source of systematic risk has a certain current volatility and expected reward. Factor volatilities and expected rewards, and even the

The same kind of argument can be used to show that if the factor moves against the market portfolio, meaning that F1 is negatively correlated with TM' then A, will be negative. This statement means that the higher the value of b.; the lower will be the expected return on the security. Generalizing, if a factor is negatively correlated with the market portfolio, then a security's expected return will be a negative function of the security'S sensitivity to that factor.

A Market Index As the Factor What if returns are generated by a one-factor model and, instead of industrial production, the factor is the return on a market index such as the S&P 500? Consider a situation in which the following two conditions are met: (1) The returns on the index and market portfolio are perfectly correlated, and (2) the variances of the returns on the market portfolio and on the market index are identical. First of all, a stock's beta will be equal to its sensitivity, This equality can be seen by examining Equation (11.26b). Given the two conditions just described, COV(F1, TM) = PF/TrFM = (T~ so that COV(F1• TM)I(T~ = f3FIM = 1 and f3eiM = O. Hence Equation (11.26b) would reduce to f3iM = b.. Second, A, will equal TM - TJ under these two conditions, This relation can be seen

294

CHAPTER 11

~

....

~.

,~":" . ' ,: ." ~ ~ ...

: ,' .:

'

.

,

.

.

'

.:

'. "

'

., .

~

, (

by again noting that,8"jM = COV(FI , rM)/rr~ = 1, which in turn means that Equation (11.29) reduces to A, = rM - rf ' Because Equation (11.10c) states that S, - rf = AI, then 51 = rM' Hence the expected return on a portfolio that has unit sensitivity to the returns on the S&P 500 equals the expected return on the market portfol io. In summary, if a proxy for the market portfolio could be found such that the two conditions given previously were met, then the CAPM would hold where the role of the market portfolio could be replaced by the proxy. Unfortunately, because the market portfolio is unknown, it cannot be verified whether any proxy even roughly meets the two conditions.

Multiple-Factor Models

It is possible for the CAPM to hold even though returns are generated by a multiplefactor model such as a two-factor model. Again, Equations (11.24) and (11.25) can be extended to show that security i's expected return will be related to its beta and two sensitivities:

r; = rj =

Arbitrage Pricing Theory

+ (rM rf + (5\ rf

(11.30)

rf),8 iM rf)b i1

+ (52

.

.

viation. R&R does this by employing portfolio optimization techniques (see Chapter 7) that combine securities in a way that attempts to set portfolio standard deviation near that of the benchmark; reduce nonfactor risk to minimal levels; emphasize stocks with high market-to-book and market-to-earnings ratios as well as positive recent returns relative to other stocks; increase exposure to risk factors with attractive reward-to-risk; and minimize buying and selling of securities (to control transaction COSL~) . The process is repeated monthly to keep the portfolio properly aligned with the benchmark. The R&R approach is highly quantitative and, intrig-uingly, involves no judgmental forecasts of factor returns or risks. Rather, historical data on the factors and securities' factor sensitivities are mechanically manipulated to determine the desired portfolio composition . This approach may prove effective if the future mimics the past, hut it can produce disappointing results if past factor data display no stable relationship with future values. R&R captured considerable U.S. institutional investor interest when the firm was organized in 1986, although it never has gained a large U.S. clientele. The firm has expanded to take on foreign partners who now apply its techniques abroad. R&R provides an interesting example of converting theoretical investment concepts into practical investment products.

factors themselves, may change over time. Second, individual securities and portfolios possess different sensitivities to each factor. These sensitivities may also val)' through time. Third, a well-diversified portfolio's exposures to the factors will determine its expected return and total risk . Fourth, a portfolio should be constructed that offers the most attractive total expected reward-to-risk ratio, given the current expected rewards and volatilities exhibited by the factors. R&R has developed a security database (updared monthly) that covers roughly 15,000 individual common stocks in 17 countries. For each country's stock market, R&R applies the database to create a pure factor portfolio (discussed in this chapter) for each of the five factors. R&R uses the historical returns on these pure factor portfolios not only to estimate the sensitivity of every security in its database to ea ch of the factors but also to estimate factor sta ndard deviations, correlations, and risk premiums as well as to calculate nonfactor returns and risk for every security. Attention at this point turns to a client's benchmark. Typically, a U.S. institutional investor will select a market index such as the S&P 500 as its common stock benchmark. R&R's standard assignment is to devise a more efficient portfolio that exceeds the ben chmark's expected return by a prespecified (reasonable) amount, yet maintains a similar standard de-

11.5.2

'.

-

rf)b i2

(11.31) 295

-

In this situation, Equation (11.26a) can be extended to show that betas will be related to sensitivities in the following linear manner (when each security's residual return is uncorrelated with the market return): ( 11.32a) (11.32b) Here COV( F;, TM) and COV( ]'11 Apr 02n 7'/2 May 02n 6'/t Mly 02n 6'/. Jun 02" Jul021w J'I. Jul021 6 Jul02" 1;1/. Aug 02n 6". Aug 02n 5'1. 5el>02n 11'1. Nov02 61/. Fell OJn IO'/. Feb OJ 1~/. MayQ3 5)/. Aug 03n 111/. Aug 03

'II.

"I. "I.

U.I. TREAIURY ITRIPI

oct 99n 101: 1~ 101: 16 + 2 S.68 Nov 99n 1110:101110: 12 + 2 S.68 Mit. 10%) in order to arrive at the rate of return associated with purchasing the security. Then this rate of return would be annualized by mul tiplying it by 365 divided by the number of days until maturity. The resulting figure would be the equivalent yield , In the example, the equivalent yield would be 7.47% [=2.455% X (365/120) ]."

13.3.2

U.S. Treasury Notes

Treasury notes a re issued with maturities from one to ten ycars and generally make coupon payments semiannually. Some, issued before 1983, were in bearer form, with coupons attached; the owner simply submitted e ach coupon 011 its specified date to receive payment for the staled amount (hence the phrase, "clipping coupons") . Beginning in 1983, the Treasury ce ased the issuance of bearer notes (and bonds). All issues since then are in registered form ; the current owner is registered with the Treasury, which sends him or her each coupon payment when due and the principal value at maturity. When a registered note is sold, the new owner's name and address are substituted for those of the old owner on the Treasury's books. Treasury notes are issued in denominations of $1,000 or more. Coupon payments are set at an amount so th at the notes will initially sell close to par value. In most cases a single price auction is held man thly when two and five-year notes are sold, with both competitive and noncompetitive bids being submitted. As in a Treasury bill multiple price auction, all noncompetitive bids are accepted first, and then the competitive bids offering the highest prices (and thus the lowest yields ) are accep ted until the entire offering has been fully allocated. However, unlike the practice in the multiple price auction, in a single price auction all of the accepted noncompetitive and competitive bids pay the lowest price that was accepted. Every quarter the Treasury also sells three- and ten-year notes but uses a multiple price auction to alloc ate them. Treasury notes are traded in an active secondary market made by dealers in U .S. government securities. For example, as shown in Figure 13.4, the October 7, 1997 issue of The Wall StreetJournal carried the following quotation from the day before, October 6, 1997:

Mat. May 04n

350

BId

Asked

Chg.

Ask YIeld

107:00

107:02

+5

5.94

CHAPTER 13

The quotation indicated that a note (n), maturing in May 2004, carried a coupon rate of 7-t %. It could be sold to a dealer for 107-1ffi% of par value, which is equivalent to $1,070.00 per $1,000 of par value. Alternatively, it could be purchased from a dealer for 107-~% of par value, which is equivalent to $1,070.625 per $1,000 of par value. Thus the dealer's spread was equal to $.625 (=$1,070.00 - $1,070.625) . On October 6, 1997, the bid price was 5/32 more than it had been on the previous trading day, resulting in a reported change ("Chg.") of +5 (note that numbers are expressed in 32nds, reflecting an old tradition). The effective yield-to-maturity at the time, based on the asked price, was approximately 5.94% per year," In practice, the situation facing a potential buyer (or seller) is a little more complicated. The buyer is generally expected to pay the dealer not only the stated price ($1,070 .625) hut also any accrued interest. For example, if 122 days have elapsed since the last coupon payment and 61 days remain, then an amount equal to 2/3 [=122/(122 + 61)] of the semiannual coupon (2/3 X 1/2 X $72.50 = $24.167) is added to the stated purchase price to determine the total payment required (in this case , $24.167 + $1,070.625 = $1,094.792). Similarly, if an investor were to sell a note to the dealer, the dealer would pay the investor the stated bid price plus accrued interest (in this case, $1,070.00 + $24.167 = $1,094.167). This procedure is commonly followed with both government and corporate bonds." In 1997 the Treasury began to issue five- and ten-year inflation-indexed Treasury notes , followed by thirty-year bonds in 1998 (see Chapter 12 for a description of how they provide the investor with a known real return hut an uncertain nominal return; they are sold using a single price auction) . These securities make a coupon payment every six months that is determined by multiplyi ng one-half of the coupon rate times an inflation-adjusted amount of principal that is equal to $1,000 multiplied by the inflation rate from the date the note was first issued to the coupon date. (Technically, there is a three-month lag where, for example, the first coupon payment reflects the rate of inflation over the six-month period beginning three months before the note was issued.) Hence, if the coupon rate was 4% and the rate of inflation over the first six months was 3%, then the principal would be increased to $1,030 (= $1,000 X 1.03). Consequently, the coupon payment would be $20.60 (=$1,030 X .04/2). At the end of the life of the note, the investor would receive not only the final coupon payment but also the inflation-adjusted principal. Furthermore , the Treasury guarantees a minimum of $1,000 so that in a period of deflation (that is, falling prices) where the inflation-adjusted principal was less than $1,000, the investor would nevertheless receive $1,000. Given the record of the U.S. inflation over the last fifty years, however, it would seem quite unlikely that this guarantee would ever come into play.

13.3.3

U.S. Treasury Bonds

Treasury bonds have maturities greater than ten years at the time of issuance. Those issued before 1983 may be in either bearer or registered form ; subsequent issues are all in registered form . Denominations range from $1,000 upward. Unlike Treasury notes, some Treasury bond issues have call provisions that allow them to be "called" during a specified period (usually the period begins five to ten years before maturity and ends at the maturity date); at any scheduled coupon payment date during this period, the Treasury has the right to force the investor to sell the bonds back to the government at par value. Callable issues can be identified in Figure 13.4 by notingwhich issues have a range of years given as the maturity date (this "range of years" indicates the caIl period). For example, the 8-~ bonds of May 00-05 mature in 2005 but may be called beginning in 2000 (the "8-i" indicates that the bonds have a coupon rate of 8-i% , paid semiannually, just like the Treasury notes from earlier) . Fixed-Income Securities

351

For callable issues, the yield-to-maturity is calculated using the asked price. If this price is greater than par, then the yield-to-maturity is based on an assumption that the bond will be called at the earliest allowable date. Otherwise, Treasury bonds are comparable to Treasury notes, with dealers' bid and asked quotations being stated in the same form. Thirty-year bonds are sold semiannually using a multiple price auction.

13.3.4

U.S. Savings Bonds

Nonmarketable U.S. Savings Bonds are offered only to individuals and selected organizations. No more than a specified amount---eurrently $15,000 of issue price, which corresponds to a total face amount of$30,000 (the bonds are sold at half of their face amount)-may be purchased by any person in a single year. Two types are available. Series EE bonds are essentially pure-discount bonds, meaning that no interest is paid on them in the form of coupon payments before maturity. The term-to-maturity at the date of issuance has varied from time to time. For bonds issued in 1998, it was 17 years. However, they may continue to be held as long as an additional 13 years before they must be either redeemed or exchanged for an HH bond (ifheld, they will continue to earn interest during these additional years just as they did over the first 17 years). Series HH bonds mature in 20 years and pay interest semiannually but can be redeemed for their purchase price at any time. Both types are registered. Series EE bonds are available in small denominations (the smallest one has a face amount of$50) and may be purchased from commercial banks and many other financial institutions. Some employers even allow employees to obtain them through payroll savings plans. Series HH bonds are available only in exchange for eligible Series EE bonds (that is, a Series EE bond must be purchased first and then held for a minimum of six months before it can be exchanged) and can be obtained only from the Treasury or one of the 12 Federal Reserve banks. Series EE bonds utilize a floating market-based rate that is determined every six months (on May 1 and November 1) and is applicable for the next six months. This rate is set equal to 90% of the average market yield over the previous six months on five-year Treasury securities. The Treasury guarantees that these securities will be worth their face amount after 17 years. Thus, if an EE savings bond that was bought for $500 grows to be worth $900 after 17 years, the Treasury would step in and change its value to $1,000. This $1,000 could then be either redeemed for cash, swapped for a $1,000 HH savings bond, or kept in the EE bond, where interest would initially be based on the $1,000 value instead of the $900 (subsequent interest would be based on the ever-increasing value). Thus, should the savings bond be held for 17 years, the investor will be paid the higher of (1) the floating rates in existence since the bond was purchased or (2) 4.16% [= ($1,000/$500) 1/17 - 1], since $500 growing annually at 4.16% will be worth $1,000 after 17 years. Should the bond be held for less than five years, the investor forfeits the last three months' worth of interest. Unlike the taxation on interest of most other discount bonds, taxes are not paid on the interest as it accumulates monthly on the Series EE bonds. Only when these bonds are redeemed is the interest subject to federal income tax. In addition, no state or local income taxes are assessed." Thus a $15,000 investment that grows to $25,000 in 12 years will create a tax obligation only at the end of the twelfth year, provided it is redeemed at that time. Furthermore, should a Series EE bond be exchanged for a Series HH bond, this tax obligation on the interest earned on the Series EE bond can be deferred until the Series HH bond is redeemed. However, the HH bond interest is subject to federal income tax annually. Hence, the tax obligation on the $30,000 would be deferred if the EE bond were exchanged for an HH bond, but the $1,800 (=.06 X $30,000, assuming a 6% interest rate) annual HH interest would be taxable each year after the exchange. 352

CHAPTER 13

The terms on which Savings Bonds are offered have been revised from time to time . (The terms previously described apply only to newly issued savings bonds at the time of th is book's writing.) In some cases, improved terms have been offered to holders of outstanding bonds. Terms have sometimes been inferior to those available on less well-known or less accessible instruments with similar characteristics. At such times, the Treasury sel1s Savings Bonds by appealing more to patriotism than to the desire for high return.

13.3.5

Zero-Coupon Treasury Security Receipts

A noncal1able Treasury note or bond is, in effect, a portfolio of pure-discount bonds (or, equivalently, a portfolio of zero-coupon bonds). That is, each coupon payment, as wel1 as the principal, can be viewed as a bond unto itself; the investor who owns the bond can therefore be viewed as holding a number of individual pure-discount bonds. In 1982, several brokerage firms began separating these components, using a process known as coupon stripping. (Chapter 5's Institutional Issues: Almost Riskfree Securities also discusses zero-eoupon Treasury securities.) With this process, Treasury bonds of a given issue are purchased and placed in trust with a custodian (for example, a bank). Sets of receipts are then issued, one set for each coupon date. For example, an August 15,2005, receipt might entitle its holder to receive $1,000 on that date (and nothing on any other date) . The amount required to meet the payments on al1 the August 15, 2005, receipts would exactly equal the total amount received on that date from coupon payments on the Treasury securities held in the trust account. In addition to issuing sets of receipts corresponding to the particular Treasury bond issue's co n pan dates, another set of receipts would be issued that mature on the date the principal of the securities held in trust is due. Thus holders of these receipts share in the principal payment." Noting the favorable market reaction to the offering of these stripped securities, in 1985 the Treasury introduced a program for investors called Separate Trading of Registered Interest and Principal Securities (STRIPS). This program allows purchasers of certain coupon-bearing Treasury securities to keep whatever cash payments they want and to sel1 the rest. The prices at which such pure-discount securities sold on October 6, 1997 are shown in Figure 13.4. Figure 13.6 shows typical market prices for a set of stripped Treasury securities, where price is expressed as a percent of maturity value. As the figure shows, the longer the investor has to wait until maturity, the lower the price of the security. The Internal Revenue Service requires that taxes be paid annual1y on the accrued interest earned on such securities. That is, such securities are treated for tax purposes as original issue discount securities, also known as OlD debt instruments. They are securities that were issued at a discount from par because of their relatively smal1 (or nonexistent) coupon payments. III For example, a STRIP that matures in two years for $1,000 might be purchased currently for $900. Thus the investor would earn $100 in interest over two years, realizing it when the STRIP matures. However, the IRS would make the investor pay taxes on a portion of the $100 each year. The amount to be recognized must be calculated using the constant interest method, which reflects the actual economic accrual of interest. In this method the investor does not report $50 (= $100 /2) per year as interest income. Instead, first the annual yield needs to be calculated, which in this case is 5.4% [= ($1,000/$900) 1/2 - 1]. Accordingly the implied value of the STRIP at the end of the first year would be $948.60 (= $900 X 1.054). The amount of interest income to be reported would then be $48.60 (=$948.60 - $900). The amount of interest income to be reported in the second year, assuming that the STRIP is held to Fixed-Income Securities

353

100 90 U- 80 :l -;; > 70 c'I:

:l

60

'-

50

~

40

u u 'I:

30

~ ~ 0

g Cl.

20 10 0

10

5

15

20

Years to Maturity

Figure 13.6

Typical Market Prices for a Set of Stripped Treasury Securities

maturity, will be $51.40 (=$1,000 - $948 .60; note that $1,000 = $948.60 X 1.054). Consequently, the taxable investor has a cash outflow not only when purchasing the STRIP but also every year until it matures. Only at that time does the investor experience a cash inflow. As a result, such securities are attractive primarily for tax-exempt investors and for investors in low tax brackets. (For example, some people purchase them as investments that are held in the names of their children.)

l1li

FEDERAL AGENCY SECURITIES Although much of the federal government 's activity is financed directly, via taxes and debt issued by the Treasury, a substantial amount is financed in other ways, In some situations, various government departments provide explicit or implicit backing for the securities of quasigovernmental agencies. In other situations, the federal government has guaranteed both the principal and coupon payments on bonds issued by certain private organizations. In both cases, some of the arrangements are so convoluted that cynics suggest that the original legislative intent was to obscure the nature and extent of government backing. In any event, a wide range of bonds with different degrees of government backing has been created in this manner. Many of the bonds are considered second in safety only to the debt obligations of the U.S. government itself. Table 13.3 lists the issuers of these securities and the amounts outstanding at the end of 1996. A partial list of typical price quotations is shown in Figure 13.7; these quotations can be interpreted in a manner similar to that used for Treasury security quotations.

13.4.1

Bonds of Federal Agencies

Bonds issued by federal agencies provide funds to support such activities as housing (through either direct loans or the purchase of existing mortgages); export and im354

CHAPTER 13

TAB LEI 3, 3 Debt Outstanding of Federal and Federally Sponsored Agencies. End of 1996

Agency

Federal Agencies Defense Department: Family Housing and Homeowner's A..osistance Export-Import Bank Federal Hou.~ing Adniinistration Tennessee Valley Authority Total debt of federal agencies Federally Sponsored Agencies Federal Home Loan Banks Federal National Mortgage Association Federal Home Loan Mortgage Corporation Student Loan Marketing Association Farm Credit Banks Financing Corporation Farm Credit Financial Assistance Corporation Resolution Funding Corporation Other Total debt of federally sponsored agencies

Amount of Debt Imillions)

$

6 1.447 84 27,8!)3

$29~~90

$263,404 331,270 156,980 44,763 60.os3 8,170 1,261 29,996 546 $896,443

Source: FnUrml U'~\I'TtJf Bullrtin, September 1997, P' A30.

port activities (via loans, credit guarantees, and insurance); the postal service; and the activities of the Tennessee Valley Authority. Many issues are guaranteed by the full faith and credit of the U.S. government, but some (for example, those of the Tennessee Valley Authority) are not.

13.4.2

Bonds of Federally Sponsored Agencies

Federally sponsored agencies are privately owned agencies that issue securities and use the proceeds to support the granting of certain types of loans to farmers, students, homeowners, and others. A common procedure involves the creation of a series of governmental "banks" to buy securities issued by private organizations that grant the loans in the first instance. Some or all of the initial capital for these banks may be provided by the government, but subsequent amounts typically come from bonds issued by the banks. Although the debts of agencies of this type are usually not guaranteed by the federal government, governmental control is designed to ensure that each debt issue is backed by extremely safe assets (for example, mortgages insured by another quasigovernmental agency). Moreover, it is generally presumed that governmental assistance of one sort or another would be provided if there were any danger of default on such debt. As shown in Table 13.3, there are eight federally sponsored agencies. Federal Home Loan Banks make loans to thrift institutions, primarily savings and loan associations. The Federal National Mortgage Association (FNMA, also known as "Fannie Mae") purchases and sells real estate mortgages-not only those insured by the Federal Housing Administration or guaranteed by the Veterans Administration but also conventional mortgages. The Federal Home Loan Mortgage Corporation (known as "Freddie Mac") deals only in conventional mortgages. The Student Loan Marketing Association (known as "Sallie Mae") purchases federally guaranteed loans Fixed-Income Securities

355

GOVERNMENT AGENCY & SIMILAR ISSUES Monday. October 6, 1997 Over·the-Counter m'~atternoon Quotationsbased on large transactIons. usually II million or more. Colons In b l~and· asked Quotesrepresent 32nds; 101 :01 means 1011/32. All yields are calculated to maturity , and based on the asked Quote. ' - Callable Issue, maturity date shown. For Is, sues callable prior to maturity. yields Ire computed to the urllest csu dlte for Issues QUOted lbove per. or 100, Ind to the mlturlty dlte for Issues below par . Source: Beer. Stearns & Co. via Street SofTwlreTechnol· OIly Inc. Ral. Mal. lid Asked YId FNMA I...... Ral. Mal. Bid A.ked Yld. 6.80 HXI 103:06 103: 12 6.03 5.35 lM7' 100:00 100:01 0.00 6.40 J.OJ' 99:" 99:28 6.42 6.05 11-97 100:02 100:03 4.87 6.63 ~-OO' 100:02 100:01 6.08 9.55 11-97 100:12100: 1~ ~.6O 6.71 5-00 102:28 103:02 6.06 9.55 12·97 loo :2~ 100:25 ~ .82 US IHXI' 99:" 99:28 6.48 6.05 1·91 100:06 100:07 5.07 6.38 7-00' 100:00 100:06 6.~ 5.38 1·91' 99:28 99:29 5.66 6.20 7-00' 99: 12 99: 18 6.29 8.65 2·91 101 :01 101 :03 5.29 6.51 8-00" 100:00 100:06 6 .~7 5.01 2-98 99:29 99:31 5.06 6.25 1-00' 99:07 99: 13 6.37 5.51 2·91 100:03 100:05 5.05 5.45 10-03 96 :2~ 96:30 6.07 8.20 3-91 101 :02101 :~ 5.40 6.20 11-00' 91 :2~ 91:30 6.~1 5.30 3-91' 99:30 100:00 5.32 5.80 12-00 91:01 91:1~ 6.11 5.71 3-9tI 100:03 100:05 5.33 6.40 1~" 99: 18 99 :2~ 6.45 5.25 3-91 99:26 99:28 5.55 6.90 3~' 100:02 100:08 3.96 5.79 3-91 100:05 100:07 5.30 6.85 .c-o.c 103: 18 103:U 6.1~ 5.92 .91 100:06 100:08 5.39 7.60 .c-o.c' 100:00 100:06 0.00 9.15 ~·91 101 :22 101 :25 5.52 7.55 ~'101:03 101 :09 6.72 8.15 5·91 101 :12101 : 1~ 5.60 7.40 7~ 107: 10 107: 16 6.02 5.25 So9l' 99:23 99:25 5.62 7.70 8~'102:15102:21 6.1~ 5.40 s-9t1' 99:26 99:2' 5.57 7.85 9~' 102: 18 102:2~ 6.30 5.38 6-91 99:27 99:29 5.51 8.25 10-04' 103:26 I~:oo 6.11 6.101 6-91 100: 16100: 18 5.52 8.40 10-04'103:28 1~:02 6.U 6.29 7·91 100: I~ 100: 16 5.59 8.63 11~" 1~ :25 1~:31 6.05 5.10 7·91' 99:16 99:18 5.66 8.55 12~" 100: 1~ 100:20 U7 5.35 &-91' 99: 19 99:21 5.76 8.50 2005' 105:06 105: 12 5.97 00 9-91' 99:02 99 :~ 5.6. 7.88 2-05 109:22109:28 6.18 7.85 9-91 101:31 102:01 5.55 7.65 3-05 108:1"08 :2~ 6.16 05 9-91' 99:08 99: 10 5.61 8.00 4-05" 100:2. 101 :02 5.13 ~ ... 10-91' 99:02 99 :~ 5.79 6.35 6-05 100:20 100:26 6.21 5.n 11-91 100:02 lOO :~ 5.601 6.55 9-05 102 :~ 102: 10 6.18 5 .9~ 11·91' 100:00 100:02 5.87 6.85 9-05' 100: 2~ 100: 30 6.50 5.30 12·91' 99:08 99: 10 5.89 6.70 11005' 101 :00 101 :06 6.27 5.75 12·91' 100:00 100:02 5.70 5,9~ 12-05 97:31 91:05 6.23 7.05 12·91 101 :12 101 : 14 5.7~ UI 2006 97: II 97 :2~ 6.22 5.20 1·99 99:10 99: 12 5.70 6041 J.06 101:00 101:06 6.23 5.09 2·99 99 :~ 99:07 5.71 6.22 3·06 99:22 99:28 6 .2~ 5.32 2·99' 99:10 99:13 5.n 6.89 ~006 103:23 103:29 6.29 5.55 2·99' 99:20 99:23 5.76 6.75 ~ 103:10103:16 6.22 9.55 3·99 105:04 105:07 5.67 7.90 6006' 102 :08 102:1~ 6.38 6.00 3·99 100:10100: 13 5.12 7.07 7006 105:21106:02 6.16 8.70 1>-99 1~ :0I1~: 11 5.91 7.93 9006'102:31 103:05 6.11 6.60 1>-99 101 :10101:13 5.71 7.59 10006' 102:03 102:09 6.35 7.50 11006' 102 :08102 :1~ 6.U 8 .~5 7·99 1~ : 10 I~: 13 5.76 5.86 7·99 l00 :~ 100:07 5.12 6.88 11006" 101 :01101:07 6.53 6.00 &-99' l00 :~ 100:07 5.73 6.96 4-07 105 :1"05 :2~ 6.15 6.35 &-99 100:01 loo :~ 6.27 6.601 7007 102: 16102:22 6.26 8.55 &-99 1~:27 1~ :3O 5.76 6.52 7007 101 :31 102:05 6." 5.91 9-99" 100:00 100:03 5.86 6.54 9007 102:04 102: 10 6.22 6.07 10-99 100:16100: 19 5.75 7.13 9007' 100:27 101:01 6.73 8.35 11·99 1~ :26 1~:29 5.81 6.59 9-07 102: 16102:22 6.22 6.10 2-00 100:22 100:25 5.7~ 6.39 9007 100: 23 100:29 6.27 9.05 ~-oo 107: 18107:21 5.73 0.00 7·1~ 33:15 33:23 6.60 6.~1 see 101 : 15101 : 18 5.76 10.35 12·15 138:21138:29 6.63 8.90 1>-00 107:10107: 13 5.87 8.20 3·16 116:10116: 18 6.63 5.90 7-00 100:02 100:05 5.13 8.95 2·18 123:03 123:11 6.81 5.97 7-00 100: 11100:1~ 5.80 8.10 8·19 116:00 116:01 6.68 6.55 8000- 100:12100: 15 5.97 0.00 10-19 23:23 23:31 6.60 7.13 .26 107:~ 107:10 US 6.~I 9000- 100:09 lOll: 12 5.97 9.20 9-00 108: 11 101: 1~ 6.01 6.09 9-27 9~ :02 9~ : 10 6.52 6.38 10-00" l00 :~ 100:07 6.13 6.30 11000- 100:00 100:03 6.26 Fedaral Him. lIan lank 8.25 12-00 106: 18106:21 5.93 Rata Mal. lid A.ked Yld. 5.55 1001 91:22 91:26 5.95 US 11·97 100:01100:02 ~.6I 5.50 2-01 91:22 91:26 5.89 5.63 12-97'100:02 100: 03 5.03 5.97 2001' 99: 19 99:23 6.06 5.65 1·91' 100:03 lOO:~ 5.07 5.37 2001 91:01 91: 12 5.91 5.75 1·91' 100:04 100:05 5.08 5.65 2001" 91: 19 98:23 6.01 5.78 1·91 100:05 100:06 5.10

Rat. Mal lid A.ked 6.12 1001' 99:31100:03 5.58 2001' 91:20 91 :2~ 7.00 1-02' 100:06 100:10 7.01 12-00" 100:02 100:08 9.50 2~ 117:26 111:00 6.79 ~ 103:18103 :2~ 7.25 6-05' 100:02 100:08 6.95 2006' 100:00 100:06 7.00 700,. 100: 16100:22 7.00 8007" 100: 17100:23 7.18 1-11' 100:01100:09 8.00 1·12' 100:01100: 16 8.02 1·12' 100:08 100: 16 1.00 3-12' 100:06 100: 1~

I

Yld Rat. Mal lid Allied Yld 6.09 9.85 11·18 133:05 133:13 6.67 5.99 9.90 12·11 135: 15 135:23 6.71 5.95 9.60 12·18 132:05 132: 13 6.71 01 9.85 3-19 133:00 133:08 6.70 6.06 9.70 .,9 133 :11133:19 6.72 6.09 9.00 6-19 12~ :23 12~ :31 6.78 5.97 1.60 9·19 120: 19120:27 6.76 6.92 6.12 Inl.r·Am.r. Daval. lank 6.71 Ral. Mat. Bid A.ked Yld. 5.97 9.50 10-97 100: 03 100:05 1.40 5.~ 9.~5 9-91 103 : 13103:16 5.55 6.2~ 7.13 9·99 102:" 102:27 5.58 0.00 8.50 S-Ol 107:23 107:27 6.02 6.13 3-06 99:21 100:02 6.11 F_al Farm Credll lank 6.63 3-07 102:30 103 :~ 6.18 Rata Mal. lid A.ked Yld. 12.25 12-08 1~ :05 1~ : 13 6.58 11.90 10-97 100:07100:09 3.27 1.81 6-09 11I :16118:2~ 6.55 5.50 11·97 100: 00 100:01 5.00 8.40 9009 115: 15 115:23 6.48 5.60 11·97 100:00 100:01 4.81 1.50 3-11 116: ~ 116:12 6.601 5.61 11·97 100:00 100:01 5.10 7.13 J-23" 93:30 9~ :06 7.65 5.51 12·97 101 :12101:13 0.00 7.00 1>-25 102:27 103:03 6.75 5.62 12·97 100: 02 100:03 ~ .88 6.10 10-25 100: 16 l00 :2~ 6.7~ 5.40 12-97 100:01100:02 4.89 5.63 1·91 100:00 100:01 5.~1 ONMA MI... ISlut. 0'"7 5.53 2·91 99:31100:00 5.~7 Rat. Mal. lid A.ked Yld. 5.85 2·91 loo:~ 100:06 5.00 6.00 30Yr 96:03 96:05 6.66 5.90 ~·91 100:05 100:07 5 .~ 6.50 JOYr 91: 18 91:20 6.71 6.05 So91 100:09 100: 11 5 .~1 7.00 30Yr 100: 18 100:20 6.96 5.90 1>-91 100:07 100:09 5.~ 7.50 30Yr 102:07 102:09 7.15 5.75 7·91 l00:~ 100:06 5.~7 8.00 30Yr 103:" 103 :26 7.25 5.27 2-99" 99:00 99:03 5.99 8.50 30Yr 1~:28 1~ :3O 7.01 1.85 10-99 105:01105: 11 5.75 9.00 30Yr 106:25 106:27 6.71 6.21 6-01 101:03 101 :07 5.91 9.SO 30Yr 101: 17 108: 19 6.82 6.10 9-01 100: 11100: 15 5.97 10.00 30Yr 109:21 109:23 7 .~ 6.75 6-07 1~ :~ 1~: 10 6.15 10.50 JOYr 110:01 110:03 7.40 Sludanl Laan Mark.lIng 11.00 30Yr 111 :21111:23 7.28 Ral. Mal. lid A.ked Yid. T.nn ..... Vall.y AulhOrlly 5.63 12-97" 100:02 100:03 5.03 Rata Mat. lid A.ked Yld. 5.75 1·91" lOO :~ 100:05 5.11 5.13 3-91 99 :2~ 99:26 5.53 7.00 3·91 100:11100:20 5 .~ 5,95 9·91 100:08 100:10 5.61 6.25 1>-91 100:15100: 17 5.48 6.25 &-99' 100: 16100:19 5.19 5.82 9·91 100:00 100:02 5.73 1.38 10-99 1~:26 1~ :29 5.71 6.16 12·99' 99: 20 99:23 6.30 6.00 11-00 100:10 100:13 5.85 7.50 3-00 103:22 103:25 5.79 6.50 &-01 100:00 lOO:~ 6.~ 6.05 9-00 100:1~ 100:17 5.15 7.~ 10-01' 102:28 103:00 6.58 5." 2001" 99:03 99:07 6.1~ 6.88 1-02' 101 :20 101 : 2~ 6.39 6.38 12001" loo :~ 100:08 6.00 6.11 1-02' 101:2~ 101 :30 6.39 7.00 12-02 1~ :~ 1~ : 10 6.01 6.13 7-03' 99:19 99:25 6.17 7.30 1·12 108:01108:16 6.40 6.31 6-05 101:06101 :12 6.15 0.00 5·1~" ~ :25 35:01 6.~2 3.38 1007 97:20 97:26 3.66 0.00 10-22 17:29 18:05 6.95 7.63 9·22' 102:24 103:00 7.36 7.75 12·22' 103:28 1<W :~ 7.39 World lank londl 1.05 7·2~' 1~:06 1~ : I~ 5.39 Ral. Mal. lid A.ked Yld. 6.75 11·25 102 :~ 102:12 6.56 1.3110-99 105:16105:19 5.37 8.63 11·'" 110:02110:10 6.11 1.13 3001 107:22 107:26 5.57 1.25 9-~" 105:04 105: 12 5.28 6.31 5001 102:00 102 :~ 5.71 1.25 40~2' 111:10 111 :18 7.20 6.75 1-02 102: 1~ 102: II 6.05 7.2S 7·~" 102:02 102: 10 7.08 12.31 10-02 125:01125:07 6 .~2 6.88 12·~' 97 :2~ 91:00 7.02 5.25 9-03 97:09 97:15 5.76 7.15 I>-~' 106:23 106:31 7.32 6.38 7005 101: 22 101 :21 6.07 6.63 &-06 103: 12103:20 6.09 'arm Cr.elll "n. A••I. Corp. 8.25 9·16 116:01116:16 6.70 Rala M.l. lid Alked Yld. 1.63 10-16 12O:0612O :1~ 6.71 9.31 7-00 115:04115:10 6.11 9.25 7·17 127:15127:23 6.70 9.45 11-00" 103:27 1~ :01 5.67 7.63 1·23 113:02 113: 10 6.54 1.80 6-05 115:28 116:02 6.1~ 1.81 3-26 126:08 126:16 6.76 9.20 9-05' 107:27 108:01 6.20 Financing CorPOrallon R.tolullon Funding Corp. Ral. Mal. lid Allied Yld. Ra.. Mtl. lid A.kld Yld. 10.7010-17 139:12 139:20 6.99 8.13 10-19 116:12116:20 6.67 9.10 11·17 135:00 135:01 6.61 8.88 7·20 12~ :20 12~ :21 6.72 9.40 2·18 125:26126:02 6.91 9.38 10-20 129: 1~ 129:" 6.80 9.80 ~· 18 I~: 111~ :26 6.66 1.63 1·21 121 :09 121 : 17 «n 10.00 So18 136:09 136: 17 6.70 8.63 1-30 121 :08 121 : 16 6.95 10.35 8·11 139:29 1~0:05 6.73 8.18 ~·30 123:24 12~:OO 6.99

Figure 13.7 Price Quotations for Government Agency Issues IExcerptsj Source: Repr inted by permission of The WaU SITtttJourna~ DowJones & Company, ln c., October 7. 1997, p. C20. All

rights reserved worldwid e.

made to students by other lenders, such as commercial banks, and may make direct student loans under special circumstances. The Farm Credit Banks lend to farmers as well as farm associations and cooperatives, and the Farm Credit Financial Assistance Corporation was cr eated in 1987 to support the Farm Credit Bank System. The Fi356

CHAPTER 13

nancing Corporation was established in August 1987 to recapitalize the Federal Savings and Loan Insurance Corporation (FSLlC). Last, the Resolution Funding Corporation was created in 1989 to assist in the recovery of the thrift industry, mainly by assisting bankrupt or near-bankrupt savings and loans.

13.4.3

Participation Certificates

To support credit for home purchases, the government has authorized the issuance of participation certificates (or pass-throughs). In a process known as securitization, a group of assets (for example, mortgages) is placed in a pool, and certificates representing ownership of those assets are issued to pay for them. The holders of the certificates receive the interest and principal payments as they are made by homeowners, minus a small service charge. The most important certificates of this type are those issued by the Government National Mortgage Association (GNMA, or "Ginnie Mae") and are known as GNMA Modified Pass-Through Securities. These securities are guaranteed by GNMA and are backed by the full faith and credit of the U.S. government. GNMA pass-through securities are created by certain private organizations such as savings and loans and mortgage bankers that bundle a package of similar (in terms of maturity date and in terest rate) mortgages together. These mortgages must be individually guaranteed by either the Federal Housing Administration or the Veterans Administration (thus making them free from default risk) and have, in aggregate, a principal amount of at least $1 million. After these mortgages have been bundled together, an application is made to GNMA for a guarantee on the pass-through securities. Typically, each security represents $25,000 worth of principal. Once the guarantee is received, the securities are sold to the public through brokers. The interest rate paid on the securities is .5% less than the interest rate paid on the mortgages, with GNMA keeping.1 % and the creator .4%. Unlike most bonds, GNMA pass-through securities pay investors on a monthly basis an amoun t of money that represen ts both a pro rata return of principal and interest on the underlying mortgages. For example, the holder ofa $25,000 certificate from a $1 million pool would indirectly "own" 2-~% of every mortgage in the pool. Each month the homeowners make mortgage payments that consist of part principal and part interest. In turn, each month the investor receives 2-~% of the aggregate amount paid by the homeowners. Because the mortgages are free from default risk, there is no default risk on the pass-through securities. (If homeowner payments are late, GNMA will either use excess cash or borrow money from the Treasury to make sure that the investors are paid in a timely fashion.)

Prepayment Risk

There is one particular risk to investors, however, that arises because homeowners are allowed to prepay their mortgages. As a result of this prepayment provision, typical pass-through securities may actually have much shorter lives then their initially stated lives of thirty years. If interest rates have fallen since the time the pass-through security was created, homeowners may start to prepay their mortgages. If the investor bought an existing pass-through that was selling at a premium and homeowners prepay, then the investor will receive par value on the security shortly after having paid a premium for it. Therefore, the investor will incur a loss. In addition, the investor will be faced with the problem of reinvesting the proceeds of the prepayments because Fixed-Income Securities

357

similar risk securities will now yield a lower interest rate than had been paid by the pass-through security. Consider a pass-through security of $25,000, initially issued with a stated interest rate of 12%. Suppose that afterward interest rates unexpectedly fall so that new pass-throughs carry a Slated rate of 10%. At this time the older pass-through security has $20,000 of principal outstanding, but as a consequence of the fall in interest rates it is selling at a premium, perhaps for $22,000. Now suppose that interest rates unexpectedly fall again, this time to 8%. At this point many homeowners prepay their mortgages in order to refinance them at the current rate of 8%. As a result an investor who purchased the older pass-through security for $22 ,000 ends up shortly thereafter receiving $20,000, thereby quickly losing $2,000. 11 Further, the $20,000 can now be reinvested only in similar risk securities yielding 8% instead of 10%, resulting in an opportunity loss in income of$400 per year [=$20,000 X (.10 - .08)]. Innovations

The interest the investing public has shown in GNMA pass-through securities has caused a number of similar securities to be created. One, typically issued in denominations of$100,000 or more, is the "guaranteed mortgage certificate" sold by the Federal Home Loan Mortgage Corporation ("Freddie Mac"), a federally sponsored agency that was mentioned earlier. Some banks have offered similar pass-through mortgage certificates backed by private insurance companies. Some of them have repackaged the cash flows that are paid by the homeowners so that investors can receive something other than a pro rata share of them. A broad class of such securities named collateralized mortgage obligations are discussed next.

13.4.4

Collateralized Mortgage Obligations

Collateralized mortgage obligations (CMOs) are a means to allocate a mortgage pool 's principal and interest payments among investors in accordance with their preferences for prepayment risk. A CMO originator (or "sponsor") transforms a traditional mortgage pool into a set of securities, called CMO tranches (French for "slices"), that have different priority claims on the interest and principal paid by the mortgages underlying the CMO. Sponsors of CMOs may be government agencies, such as GNMA or FNMA, or they may be private entities, such as brokerage firms . Although there is no standard form of CMO, consider an example of a simple "sequential-pay" CMO structure that involves three tranches: A, B, and C. The tranches were formed from a pool of mortgages with a total principal value of $250 million. The mortgages in the pool all carry an interest rate of 8%. As shown in Table 13.4 , each tranche is initially allocated a specific proportion of the underlying mortgage pool's principal: $150 million for tranche A, $25 million for tranche B, and $75 million for tranche C. Interest payments, as with any bond, are paid as a percentage of the outstanding principal corresponding to each tranche. (The example assumes that interest and principal are paid annually. In practice, those payments occur monthly.) In this example, the three tranches earn the same interest rate on their principal. However, they differ in terms of how they are retired (that is, how principal payments are allocated among them). All principal payments (both scheduled and prepaid) made by the pool are funneled to the A tranche until its outstanding principal has been extinguished. The Band Ctranches receive only interest payments so long as the A tranche has not been fully paid off. Once it has, the B tranche receives all principal payments until it is retired; afterward, principal payments go to the C tranche. For example, in year 1, each tranche receives an 8% interest payment on its 358

CHAPTER 13

TABLE

Tranche

13.4

Three-'n'anme Sequential-Pay CMO

I

A

Year-End Balance

Principal

Interest

I

$150,000.000 132,742,627

$17,257,372

2 3

114,104.665 93,975,667

18.637.962 20,128,999

$12,000,000 10,619,410 9,128,373

4 5 6 7

72.236,348 48,757,884

21,739,319 23,478,464

7,518,053 5,778,908

23,401.142 0 0 0 0

25,356.741 23,401,142

!I,900.631 1,872.091 0 0 0

Year

0

8 9 10

0 0 0

0 1 2 3 4 5 6 7 8 9 10

Year-End Balance

75,000,000 75,000,000 75,000,000 f>6,43'J,758 34,497,567 0

Principal

$25.000,000 25,000,000

0 0 0 0 0

25.000,000 25,000,000 25.000,000 25,000,000 25,000,000 21.015,862 0 0 0

0 $3,984 ,138 21,015,862 0 0

Interest

$2,000,000 2,000,000 2,000,000 2.000,000 2,000,000 2,000,000 2,000,000 1,681,294 0

0

Mortgage Pool

Interest

Vear·End Balance

PrIncIpal

Interest

0

$6,000,000

$250,000.000 232,742,628

$17,257,372

$20,000,000

o

6.000,000 6,000,000

18,637,962 20,128,999

18,6]9.410 17,128,373 15,518,053 13,778,908

Prlncipal

$75,000,000 75,000,000 75,000,000 75,000,000 7,';,000,000

Year·End Balance

I

Tranche C

Year

Tranche B

0 0 0 0 0 $8,560.242 31,942,192 34,497,567

6.000,000 6,000,000

214,104,666 193,975,667 172,236,348 148,757,884

6.000,000 6,000,000

123,401,142 96,015,862

6,000.000 5,315,181

66,439,758 34,497,567

21.739 ,319 23,478,464 25.356.74] 27,385,281 29,576.103 31,942,192

2,759,805

0

34.497,567

1] .900.631 U,872,091 7,681,269 5,315,181 2.759,805

principal balance at the beginning of the year. Further, in year 1 the pool's mortgages make a combined principal payment of $17,257,372, which is assigned in full to tranche A. Its principal balance falls by the amount of the payment, leaving $132,742,627 in outstanding principal to begin the second year. In year 2, tranche A's interest payment is smaller because its beginning-of-the-year principal balance has been reduced by $17,257,372. The interest payments to tranches Band Cremain the same, however, because their principal balances have not yet been reduced. By the end of year 6 th e outstanding principal of tranche A has been completely extinguished and it receives no further interest or principal payments. Tranche B is now the recipient of all principal payments, with tranches Band C (the two remaining tranches) earning interest based on their outstanding principal. Because of its small size, the B tranche is quickly retired. Byyear 8, only the C tranche is still in existence. It now receives all of the pool's interest and principal payments. By the end of year 10 it too has been retired because all of the mortgages in the pool have paid off their principal balances. The primary purpose of dividing a mortgage pass-through pool's principal and income flows into various tranches is to create a set of securities with varying levels of interest rate and prepayment risk. Investors can match their risk preferences and Fixed-Income Securities

359

predictions with the appropriate securities. The CMO originator expects that investors will pay a premium for this flexibility, with the sum of the parts being worth more than the whole. Considerably more complex CMO structures than that involved in the simple sequential-pay CMO example are commonplace. Greater complexity allows an even greater fine-tuning of risk. Note that in the sequential-pay CMO example, investors seeking shorter-maturity mortgage-backed securities will generally hold the fasterpay tranches, whereas investors desiring longer-maturity mortgage-backed securities will hold the slower-pay tranches. Nevertheless, both types of investors are still exposed to considerable prepayment risk . If interest rates fall, prepayments will increase, shortening the maturities of all three tranches. Conversely, it interest rates rise, prepayments will decline, increasing the effective maturities of all three tranches. Solutions to this problem involve creating tranches whose interest and principal payments respond in various ways to movements in market interest rates and the prepayment tendencies of the pool's mortgages. Some CMO structures contain dozens of tranches. Instead of fixed interest rates, certain tranches may have interest rates that val)' directly with the movement of short-term interest rates. These securities are called "floaters." They are paired with "inverse floaters," whose interest payments move in the opposite direction of short-term interest rates. Other tranches, called planned amortization classes (PACs), make fixed principal and interest payments over a specified period, similar to a standard coupon bond. They are matched with support (or companion) bonds, which are exposed to high levels of prepayment risk. The seemingly endless list of CMO variations is limited only by the imaginations of CMO sponsors and the appetite of investors for different cash flow patterns and different levels of prepayment risk. Although the risk of principal prepayments can be allocated among various tranches, in the final analysis the prepayment risk of the mortgage pool cannot be reduced. Evaluating prepayment risk can prove extremely difficult, particularly in the more complex CMO structures. Various organizations have developed prepayment models designed to simulate the behavior of mortgage prepayments under specified interest rate scenarios. These models allow CMO investors to better evaluate the riskiness and, hence, the appropriate yields of the available CMO tranches.

II1II

STATE AND LOCAL GOVERNMENT SECURITIES The 1992 Census of Governments showed that there were 85,005 governmental units in the United States in addition to the federal government itself. 12 These nonfederal governmental units consist of: State govemm!'Jl~ .' Local government County Municipal Township and town School district Special district Total local governmental units

Total nonfederalgovemmentaJ unlll

50 3,043 19,279 16,656 14,422 31,555 84,955

8.!i,005

A great many of these units borrow money; their securities are called municipal bonds or simply "municipals" or "muni's." (Only the securities of the U.S. government are referred to as "governments.") Figure 13.8 provides estimates of the amounts of 360

CHAPTER 13

Other

f-

Consumer Credit Mortgages fMunicipal Securities I-

Corporate and Foreign Bonds IU.S. Government Securities '--_ _-'-_ I _---'I

$1,000

$0

I

I

I

I

I

.1..-_ _- ' -_ _- - - ' ' - -_ _- ' - - _ - - - - '

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

Figure 13.8 Estimated Amounts of Various Fixed-Income Securities Outstanding. Year-End 1996 (S billions) Source: Fcdeml Rsserue Bulle/in, September, 1997, p. A40.

various types of fixed-income securities outstanding at the end of 1996. With over $1 trillion in outstanding value, municipals clearly warrant attention.

13.5.1

Issuing Agencies

Figure 13.9 shows the dollar values of municipal bonds issued in 1996 by various agencies, and Figure 13.10 shows the purposes for the issuance of such debt. States generally issue debt to finance capital expenditures, primarily for highways, housing, and education;" The concept behind the issuance of such debt is that the revenue generated by the resulting facilities will be used to make the required debt payments. In some cases, the link is direct (for example, tolls may be used to pay for a bridge). In other cases it is somewhat indirect (for example, gasoline taxes may be used to pay for highway construction) or very indirect (for example, state sales taxes or income taxes may be used to pay for the construction of new government buildings). States cannot be sued without their consent. Thus bondholders may have no legal recourse in the event of default, and state-issued bonds that are dependent on

Municipality, County. or Township t-

Special District or Statutory Authority f-

States

I

$0

$20,000

I

$40,000

I

$60,000

I

I

I

$80,000 $100,000 $120,000

Figure 13.9 New Security Issues of State and Local Governments in 1996. Classified by Issues IS millions) Source: Federal Reserve Bulk/in , September, 1997. p. A.31 .

Fixed-Income Securities

361

,

INSTITUTIONAL ISSUES

Collateralized Bond Obligations Can lead really be turned into gold? More to the point, can a set of high-yield bonds be transformed into A.-\A-rated securities? The answer is yes, through some sophisticated financial alchemy that produces an investment instrument known as a collateralized bond obligation (CBO) . With the huge demand that has developed for high-yield bonds in the 1990s, CROs have become a popular means of investing in that type of debt. In fact, in 1997 it has been estimated that one in every five newly issued high-yield bonds was placed in a CBO . To understand CBOs requires some knowledge of two financial techniques: securitization and cash flow prioritization. Securitization is a two-stage process. First, assets that generate cash flows are brought together into a siugle pool. These assets are referred to as the collateral underlying the pool. Second, securities representing interests in the pool are sold to investors. A~ the collateral throws off cash flows (be they dividends, interest, royalties, principal payments, and so on), the securities entitle their owners to a pro rata share of those payments. Cash 110w prioritization involves defining a set of rules for how the cash flows generated by a pool's collateral are distributed to the pool's owners. In particular, the securities denoting ownership of the pool do not all receive the same pro rata participation in the pool's cash flows. Instead, the pool is divided into

tranches, and securities are issued for each tranche. The pool's cash flows are allocated to the securityholders of the tranches according to a specified formula . This formula may be very simple or quite complex. In either case, cash flow prioritization causes the expected pattern of payments to vary from one tranche to another. This variation potentially appeals to a wider set of investors, thereby enhancing the value of the entire pool. The concepts of securitization and cash flow prioritization should sound familiar. They are central to the creation of collateralized mortgage obligations (CMOs). Indeed, as their names imply, CBOs are very similar to CMOs. They differ, however, in terms of their underlying collateral. (Mortgages in the case of CMOs; high-yield bonds in the case orCBOs.) Just as important, they differ in terms of the types of cash flow risks that they are designed to address. Collateralized mortgage obligations are concerned with prepayment risk: the possibility that homeowners will prepay their mortgages at a time disadvantageous to the mortgage owner. Collateralized hand obligations, on the other hand, are created with default risk in mind. Producers of CBOs package together a number of below-investment-grade debt issues (or, in some cases, the government debt of various international emerging markets). Three tranches are typically established. These tranches have prioritized

Other Industrial Aid Social Welfare Utilities and Conservation Transportation Education

$0

$5,000

$10,000 $15,000 $20,000 $25,000 $30,000 $35,000

Figure 13.10 New Security Issues of State and Local Governments in 1996. Classified by Purpose 1$ millions) Source: Federal Reserue Bulletin, September, 1997, p. A31.

362

CHAPTER 13

claims on the principal and interest payments made by the pool's collateral. The senior tranche receives its principal and interest in full first, followed by the senior subordinated tranche, and lastly by the junior tranche. As a result, any default affects the junior tranches first. Because defaults tend to be relatively firm-specific, the senior claims in a well-diversified CBO pool are largely insulated from default risk. The junior securities, conversely, stand to gain or lose significantly depending on the pool's default experience. Therefore, they effectively convey equity ownership in the pool. In total, creating a CBO structure from a pool of collateral cannot alter the pool's default risk. It merely redistributes that risk. The senior tranche will have less default risk than the pool itself, whereas the junior tranche will have more default risk. A CBO pool is actually a managed portfolio of securities. A CBO sponsor purchases the pool's collateral, establishes tranches backed by the pool, and issues securities representing pro rata ownership of the tranches, Going forward, the CBO sponsor will buy and sell securities for the pool depending on the sponsor's view of the risk-reward opportunities available in the high-yield market. For this service, the CBO sponsor receives a fee in the range of .25% to .45% of the pool's value. Because of the prominent role played by the

CBO sponsor, CBO investors should evaluate the sponsor's abilities to assess credit risk, to create and maintain a well-diversified portfolio, and to take advantage of mispriced securities. Further, CBO investors should be prepared to analyze a pool's collateral and the design of the pool's tranches. What is the credit quality of the collateral? What is the collateral's average life? How liquid is the collateral? How might the collateral respond to different economic and interest rate environments? How are the senior tranches protected relative to the junior tranches? The major credit-rating agencies, such as Moody's and Standard & Poor's (see Chapter 14) can be of some assistance in this analysis. They provide ratings of the relative default risk of CBO tranche securities. Senior tranches in some pools have been rated as high as AAA, even though the collateral is almost entirely composed of below-investment-grade debt. Nevertheless, ratings by the credit-rating agencies do not speak to the fair market value of a CBO's securities. In that respect investors are left to fend for themselves. Despite the added complexity that CBOs bring to an existing financial instrument such as highyield bonds (or perhaps because of that added complexity), they represent an excellent example of how the financial markets respond to the needs of suppliers and users of funds by creating flexible new securities.

particular revenues from some capital project may involve considerable risk. However, bonds backed by the "full faith and credit" of a state government are generally considered quite safe despite the inability of the bondholders to sue. It is anticipated that state legislatures will do whatever is necessary to see that such bonds are paid off in a timely manner. Unlike state governments, local governments can be sued against their will, making it possible for bondholders to force officials to collect whatever amount is needed in order to meet required debt payments. In many cases, only revenues from specific projects may be used (for example, the tolls collected on a particular highway). In other cases, collections from a particular tax may be used, although possibly only up to some statutory limit. Some local governments (for example, Cleveland in 1978-1979) have defaulted on their debts, and others (for example, New York City in 1975 and Orange County, California, in 1996) have "restructured" their debt, giving current bondholders new certificates offering lower or deferred interest and longer maturities in exchange for currently outstanding certificates. Thus, the right of bondholders to sue does not always mean that they will be able to collect what they are owed in a timely fashion. Counties and municipalities are familiar to most people, but other forms of local government also exist. Examples include school districts as well as other districts and Fixed-Income Securities

363

authorities that have been created to finance and operate seaports or airports. AJI are created by state charter and may be granted monopoly powers as well as rights to collect certain types of taxes. However, limits are often placed on the amount of taxes collected, the tax rate charged, and the amount (or type) of debt issued. The primary source of funding for such agencies is the property tax. Because a given property may be liable for taxes levied by several agencies (such as a city, a county, a school district, a port authority, and a sewer district), the risk of an agency's bonds may depend on both the value of property subject to its taxes and the amount of other debt dependent on the same property.

13.5.2

Types of Municipal Bonds

In 1996, new municipal bonds with a par value of $177.2 billion were issued. Of this total, $60.4 billion were general obligation bonds (GOs) and $110.8 billion were revenue bonds.l" General obligation bonds are backed by the full faith and credit (and thus the full taxing power) of the issuing agency. Most are issued by agencies with unlimited taxing power, although in a minority of cases the issuer is subject to limits on the amount of taxes or on the tax rate (or both). Revenue bonds are backed by revenues from adesignated project, authority, or agency or by the proceeds from a specific tax. In many cases, such bonds are issued by agencies that hope to sell their services, pay the required expenses, and have enough left over to meet required payments on outstanding debt. Except for the possible granting of monopoly powers, the authorizing state and local government may provide no further assistance to the issuer. Such bonds are only as creditworthy as the enterprise associated with the issuer. Many revenue bonds are issued to finance capital expenditures for publicly owned utilities (for example, water, electricity, or gas). Others are issued to finance quasi-utility operations (for example, public transportation). Some are financed by special assessments levied on properties benefiting from the original expenditure (for example, those connected to a new sewer system). Industrial development bonds (IDBs) are used to finance the purchase or construction of industrial facilities that are to be leased to firms on a favorable basis. In effect, such bonds provide cheap financing to businesses choosing to locate in the geographical area of the issuer. Although most municipal financing involves the issuance of long-term securities, a number of different types of short-term securities have been issued in order to meet short-term demands for cash. Traditionally used types include tax anticipation notes (TANs), revenue anticipation notes (RANs), grant anticipation notes (GANs), and tax and revenue anticipation notes (TRANs). In each case, the name of the security refers to the source of repayment. Thus some can be classified as general obligation securities and others as revenue securities. More recently, municipalities have started to issue two other kinds of short-term securities. Tax-exempt commercial paper is similar to corporate commercial paper, having a fixed interest rate and a maturity typicaJly within 270 days. Variable-rate demand obligations have an interest rate that changes periodically (perhaps weekly) as some prespecified market interest rate changes. Furthermore, they can be redeemed at the desire of the investor within a prespecified number of days after the investor has given notice to the issuer (for example, seven days after notification of intent).

13.5.3

Tax Treatment

Through a reciprocal arrangement with the federal government, coupon payments on state and local government securities are exempt from federal taxation, and coupon payments on Treasury and agency (except FNMA) securities are exempt 364

CHAPTER 13

from state and local taxation. Similar tax treatment is accorded to the price appreciation on short-term and long-term issues that are original issue discount securities. (As mentioned earlier, OlD securities are securities that were issued for a below-par price.) However, a different tax treatment is generally given to coupon-bearing securities that were issued at par value but were subsequently bought at a discount in the marketplace. Such securities, known as market discount bonds, provide the investor with income not only from the coupons but also from the difference between the purchase price and the par value. Unlike the coupons, which are tax-exempt, this difference is treated as taxable interest income. Another interesting tax feature of municipals is that an investor who resides in the state of the issuer is generally exempt not only from paying federal taxes on the coupon payments but also from paying state taxes. Furthermore, an investor who resides in a city that has an income tax and who purchases municipals issued by the city usually is exempt from paying city taxes on the coupon payments. Thus a resident of New York City who purchases a municipal security issued by the city (or one of its political subdivisions) will not have to pay federal, state, or city income taxes on the coupon payments. However, if the New York City resident were to purchase a California municipal, then both New York State and New York City income taxes would have to be paid on the coupon payments. Although state and city income tax rates are much lower than those of the federal government, this feature nevertheless tends to make local issues more advantageous from an after-tax return viewpoint (an advantage that is offset to a certain degree by the resulting lack of diversification) . The avoidance of federal income tax on interest earned on a municipal bond makes such a security attractive to wealthy individual investors as well as corporate investors. As shown in Figure 13.11, the lack of federal taxation has resulted in municipal securities having yields that are considerably lower than those on taxable securities.P Consequently, the cost of financing to municipal issuers is lower, suggesting that a federal subsidy has been provided to the issuers. Over the years, this subsidy has been used to support activities deemed worthy of encouragement (even though the encouragement is somewhat hidden). For example, private universities may issue tax-exempt bonds to finance certain types of improvements, and private firms may do so to finance certain pollution-reducing activities. Such bonds are generally backed only by the resources of the issuer, with government involvement limited to the granting of favorable tax treatment. The Tax Reform Act of 1986 greatly restricted the granting of such tax treatment, leading to the emergence of taxable municipals, which are typically issued to finance projects that are not viewed as essential under the tax law.

13.5.4

The Market for Municipal Bonds

Municipals are usually issued as serial bonds; one prespecified group matures a year after issue, another two years after issue, another three years after, and so on. Alternatively, term bonds (that is, bonds that all mature on the same date) or a mixture of serial and term bonds may be issued. The overall package is generally offered by the issuer on a competitive basis to various underwriters. The winning bidder then reoffers the individual bonds to investors at a higher price. Unlike corporate bonds, municipal bonds do not need to be registered with the SEC before public issuance.l'' Indeed, the federal government leaves most regulation in this market to state and local authorities and the Municipal Securities Rulemaking Board. Municipal bonds may be callable at specified dates and prices. Occasionally, the issuing authority is obligated to make designated payments into a sinking fund, which Fixed·lncome Securities

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is used to buy similar bonds (or perhaps even its own bonds). As the issuing authority's bonds mature. the money for paying them off will come from having the sinking fund sell some of its holdings. A secondary market in municipal bonds is made by various dealers. Standard & Poor's Corporation publishes on a daily basis a listing of municipal bond quotations by various dealers in the Blue List. In addition, the Bond Buyer has an electronic system that provides dealer quotations. However, the relatively small amounts of particular issues and maturities outstanding limit the size of the market. Many individuals who invest in municipals simply buy new issues and hold them to maturity.

13.5.5

Municipal Bond Insurance

An investor concerned about possible default of a municipal bond can purchase an insurance policy to cover any losses that would be incurred if coupons or principal were not paid in full and on time. That is, an investor can contract with a company to have a specific portfolio of bonds insured. Alternatively, the issuer of the bonds can purchase such insurance from one of the firms that specialize in issuing this type of insurance. The cost of this insurance is generally more than offset by the lower interest rate that the issuer has to pay as a result of insuring its bonds. Regardless of whether the investor or the issuer purchases the insurance, the cost of the insurance will depend on the bonds included and their ratings. 366

CHAPTER 13

. . CORPORATE BONDS Corporate bonds are similar to other kinds of fixed-income securities in that they promise to make specified payments at specified times and provide legal remedies in the event of default. Restrictions are often placed on the activities of the issuing corporation in order to provide additional protection for bondholders (for example, there may be restrictions on the amount of additional bonds that can be issued in the future).

13.6.1

Tax Treatment

Corporate bonds that are original issue discount securities generally have the discount taxed as ordinary income by the federal government. The constant interest method is to be used to determine the portion of the discount that must be reported as taxable interest each year. (This method was described earlier when stripped Treasury bonds were discussed.) With this method a portion of the discount must be recognized as income each year that the security is held, thereby causing the investor to have to pay taxes on that amount. Corporate bonds carrying coupon payments have the coupon taxed as income each year. Furthermore, if the bond was originally sold at par but was later bought at a discount in the marketplace (as mentioned earlier, such bonds are known as market discount bonds), then the investor generally will have to pay ordinary income taxes on both the coupon payments and the discount. Using either the constant interest method or straight-line method , wherein the discount is sp read out evenly over the remaining life of the bond, the investor can recognize a portion of the discount as interest income each year that the bond is held and pay taxes on it. Alternatively, the investor can wait until the bond is sold and at that time recognize the market discount as taxable interest incorne.l" From the viewpoint of the issuing corporation, debt differs from equity in two crucial respects. First, principal and interest payments are obligatory. Failure to make any payment in full and on time can expose th e issuer to expensive, time-consuming, and potentially disruptive legal actions. Second, unlike dividend payments, interest payments are considered expenses to the corporation and hence can be deducted from earnings before calculating the corporation's income tax liability. As a result, each dollar paid in interest reduces earnings before taxes by a dollar, thereby reducing corporate taxes by $.35 for a firm in the 35% marginal tax bracket. This reduction leads to less than a dollar decline in earnings after taxes (in the 35 % tax bracket example, the decline in earnings is $.65).

13.6.2

The Indenture

An issue of bonds is generally covered by an indenture, in which the issuing corpo-

ration promises a specified trustee that it will comply with stated provisions. Chief among these is the timely payment of required coupons and principal on the issue. Other terms are often included to control the sale of pledged property, the issuance of other bonds, and the like. The trustee for a bond issue, usually a bank or a trust company, acts on behalf of the bondholders. Some actions may be required by the indenture; others, such as acting in response to a request from specific bondholders, may be done at the trustee's discretion. If the corporation defaults on an interest payment, then after a relatively short period of time (perhaps one to six months) the entire principal typically becomes due Fixed-Income Securities

367

and payable. This procedure is designed to enhance the bondholders' status in any forthcoming bankruptcy or related legal proceedings.

13.6.3

Types of Bonds

An exhaustive list of the names used to describe bonds would be intolerably long. Different names are often used for the same type of bond, and occasionally the same name will be used for two quite different bonds. A few major types do predominate, however, with relatively standard nomenclature. Mortgage Bonds

Mortgage bonds represent debt that is secured by the pledge of specific property. In the event of default, the bondholders are entitled to obtain the property in question and to sell it to satisfy their claims on the firm. In addition to the property itself, the holders of mortgage bonds have an unsecured claim on the corporation. Mortgage bondholders are usually protected by terms included in the bond indenture. The corporation may be constrained from pledging the property for other bonds (or such bonds, if issued, must be "[unior" or "second" mortgages, with a claim on the property only after the first mortgage is satisfied). Certain property acquired by the corporation after the bonds were issued may also be pledged to support the bonds. Collateral Trust Bonds

Collateral trust bonds are backed by other securities that are usually held by the trustee. A common situation of this sort arises when the securities of a subsidiary firm are pledged as collateral by the parent firm. Equipment Obligations

Known also as equipment trust certificates, equipment obligations are backed by specific pieces of equipment (for example, railroad cars and commercial aircraft). If necessary, the equipment can be readily sold and delivered to a new owner. The legal arrangements used to facilitate the issuance of such bonds can be very complex. The most popul ar procedure uses the "Philadelphia Plan," in which the trustee initially holds the equipment and issues obligations and then leases the equipment to a corporation . Money received from the lessee is subsequently used to make interest and principal payments to the holders of the obligations. Ultimately, if all payments are made on schedule, the leasing corporation takes title to the equipment. Debentures

Debentures are general obligations of the issuing corporation and thus represent unsecured credit. To protect the holders of such bonds, the indenture will usually limit the future issuance of secured debt as well as any additional unsecured debt. Subordinated Debentures

When more than one issue of debenture is outstanding, a hierarchy may be specified. For example, subordinated debentures are junior to unsubordinated debentures, meaning that in the event of bankruptcy, junior claims are to be considered only after senior claims have been fully satisfied. 368

CHAPTER 13

Asset-Backed Securities

Asset-backed securities are much like the participation securities that were described earlier. However, instead of mortgages being pooled and pieces of ownership in the pool being sold, debt obligations such as credit card revolving loans, automobile loans, student loans, and equipment loans are pooled to serve as col1ateral backing the securities. The basic concept, known as securitization, is the same, however. Originators of these loans pool them and sel1 securities that represen t part ownership of the pool. A servicing company collects the payments made by the debtors over a period of time, such as a month, and then pays each owner the appropriate percent of the aggregate amount received. As for investors in participation certificates associated with mortgages, two concerns for investors in asset-backed securities are default risk and prepayment risk. Other Types of BoneJ" Income bonds are more like preferred stock (described in a later section) than bonds. Payment of interest in fUI1 and on schedule is not absolutely required, and failure to do so need not send the corporation into bankruptcy. Interest on income bonds may not qualify as a tax-deductible expense for the issuing corporation. This type of bond has rarely been used, except in reorganizations of bankrupt railroads. Guaranteed bonds are issued by one corporation but backed in some way by another (for example, by a parent firm). Participating bonds require stated interest payments and provide additional amounts if earnings exceed some stated level. Voting bonds, unlike regular bonds, give the holders some voice in management. Serial bonds, with different portions of the issue maturing at different dates, are sometimes used by corporations for equipment financing (as mentioned earlier, they are also used by municipalities). Convertible bonds may, at the holder's option, be exchanged for other securities, often common stock. Such bonds, which have become very popular in recent years, are discussed in more detail in the appendix to Chapter 19. Putable bonds also give the holders an option, but this time it is to exchange their bonds for cash equal to the bond's face value. This option general1 y can be exercised over a brief period of time after a stated number of years has elapsed since the bond's issuance. 1M

13.6.4

Call Provisions

Management would like to have the right to payoff the corporation's bonds at par at any time before maturity. This ability would provide management with flexibility, because debt could be reduced or its maturity altered via refunding. Most important, expensive high-coupon debt that was issued during a time of high interest rates could be replaced with cheaper low-eoupon debt if rates decline. Not surprisingly, investors hold quite a different opinion on the matter. The issuer's ability to redeem an issue at par at any time virtual1yprecludes a substantive rise in price over par and robs the holder of potential gains from price appreciation associated with declining interest rates. Moreover, it introduces a new form of uncertainty. A bond with such a feature wil1 almost certainly sel1for less than one without it. Despite the cost of obtaining this sort of flexibility, many corporations include call provisions in their bond indentures that give the corporation the option to call some or al1 of the bonds from their holders at stated prices during specified periods before maturity. In a sense, the firm sells a bond and simultaneously buys an option from the holders. The net price of the bond is thus the difference between the value of the bond and the option. The indenture usual1y gives investors two kinds of cal1 protection. First of all, during the first few years after being issued, a bond may not be cal1able. Secondly, a Fixed-Income Securities

369

call premium may be specified in the call provision. Such a premium indicates that if the issue is called, the issuer must pay the bondholders a call price that is a stated amount above par. Often, the amount above par becomes smaller as time passes and the maturity date approaches. An entire issue may be called, or only specific bonds that are chosen randomly by the trustee. In either case, a notice of redemption will appear in advance in the financi al press.

13.6.5

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375

major trades of bonds are generally negotiated elsewhere by dealers and institutional investors, either directly or through brokers. Thus, reported prices on the NYSE may be poor guides to values associated with large transactions (the same can be said for quotes that are publicly supplied by bond dealers) but appear to be reasonable for small transactions. A second bond market, run by the Nasdaq Stock Market, is known as the Fixed Income Pricing System (FIPS). Unlike ABS, this market is devoted to trading highyield bonds, which are defined as bonds that are less than investment grade (bond grades are discussed in more detail in Chapter 15), meaning they are speculative and have a reasonable chance of default. All members of the National Association of Security Dealers (NASD) that hold themselves out to be dealers or brokers in highyield bonds are required to use FIPS. However, because FIPS lists only liquid highyield debt, brokers and dealers in less liquid issues are not required to use FIPS. Quotes are entered on FIPS by dealers and must be at least one-sided (that is, either a bid or asked quote must be given). Subsequent trades are made by contacting a dealer, typically by telephone, and depending on the bond, may have to be reported within five minutes of execution. Trade report summaries are disseminated by Nasdaq and other market data vendors on an hourly basis for the fifty most liquid issues and on a daily basis for all the others.

. .

FOREIGN BONDS The foreign bond market refers to bonds issued and denominated in the currency of a country other than the one in which the issuer is primarily located. For example, Inco has issued bonds that are denominated in U.S. dollars, mature in 2016, and carry a 7-~% coupon rate. Although some foreign bonds (such as Inco's) appear daily at the end of the "New York Exchange Bonds" quotations section in The Wall Streetjournal; as shown ill Figure 13.13, the amount of trading is often so small that all that is reported is the total volume. Foreign bonds that are issued in the United States and are denominated in U.S. dollars are referred to as Yankee bonds, and foreign (that is, non-Japanese) bonds that are issued in Japan are referred to as Samurai bonds. In issuing foreign bonds, the issuer must abide by the rules and regulations imposed by the government of the country in which the bonds are issued. Compliance may be relatively easy or difficult, depending on the country involved. One of the main advantages of purchasing foreign bonds is the opportunity to obtain international diversification of the default risk of a bond portfolio while not having to be concerned about foreign exchange fluctuations. For example, a U.S. investor might be able to buy a Toyota bond inJapan that is denominated in yen, but in doing so would have to worry about the yen-dollar exchange rate. The reason is that the coupon payments and ultimately the principal would be paid to the investor in yen, which would then have to be converted into dollars at a currently unknown exchange rate. However, the investor could avoid such worries by purchasing a Toyota bond that is denominated in U.S. dollars.

. .

EUROBONDS Owing in part to government restrictions on investment in foreign securities, some borrowers have found it advantageous to sell securities in other countries. The term Eurobond is loosely applied to bonds that are offered outside the country ofthe borrower and outside the country in whose currency the securities are denominated.P 376

CHAPTER 13

Thus a bond issued by a U.S. corporation that is denominated in Japanese yen (or U.S. dollars) and sold in Europe would be referred to as a Eurobond. As the Eurobond market is neither regulated nor taxed, it offers substantial advantages for many issuers and buyers of bonds. For example, a foreign subsidiary of a U.S. corporation may issue a Eurobond in "bearer" form. No tax will be withheld by the corporation , and the tax (if any) paid by the purchaser will depend on his or her country of residence. For tax reasons, interest rates on Eurobonds tend to be somewhat lower than those on domestic bonds denominated in the same currency.

mI

PREFERRED STOCI
y*, then the bond is underpriced , and if y < y*, then the bond is overpriced. If y = 1". then the bond is said to be fairly priced. 386

14.1.1

Promised Yield-to-Maturity

Letting Pdenote the current market price of a bond with a remaining life of n years, and promising cash flows to the investor of C1 in year 1, C2 in year 2, and so on, the yield-to-maturity (more specifically, the promised yield-to-maturity) of the bond is the value of y that solves the following equation:

With summation notation, this equation can be rewritten as: ~ P = £.J

C1

(14 .1 )

+ y)'

1=1 (1

For example, consider a bond that is currently seIling for $900 a n d has a remaining life of three years. For ease of exposition , assu m e that it makes a n n ua l coupon payments amounting to $60 per year and has a par value of $1,000 ; that is, C 1 = $60 , C 2 = $60, and C3 = $1,060 (=$1,000 + $60) . Using Equation (14 .1), the yield-to-maturity on this bond is the value of y that solves the following equation: $60

$60

$1,060

+ y)1 + (1 + y)2 + (1 + y)3

P = (1

which is Y = 10.02%. If subsequent analysis indicates that the yield-to-maturity should be 9.00 %, then this bond is underpriced because y = 10.02% > y* = 9.00%.

14.1.2

Intrinsic Value

Alternatively, the intrinsic value of a bond can be calculated using the following formula:

v=

C1

(1

+ y*)1

+

C2

(1

+ y*)2

+

C:i

(1

+ y*)3

+ '" +

C"

(1

+ y*)"

or, using summation notation, ~

V= £.J

1=1

C1

(1

(14.2)

+ y*)1

After V has been estimated, it should be compared with the bond's market price P in order to see if V > P, in which case the bond is underpriced, or if V < P, in which case the bond is overpriced. Alternatively, the net present value (NPV) of the bond can be calculated as the difference between the value of the bond and the purchase price:

NPV = V - P =

2:"

1=1 (1

C

1

+ y*)1

-

P

(14 .3)

The NPV of the bond in the previous example is the solution to the following equation: _ $60 NPV- (1 + .09)1

+

$60

(1

+ .09) 2

+

$1,060 (1 + .09)3 - $900

= $24.06 Bond Analys is

387

Because this bond has a positive NPV, it is underpriced. This will always be the case when a bond has a yield-to-maturity that is higher than the appropriate one. (Earlier it was shown that this bond's yield-to-maturity was 10.02%, which is more than 9.00%, the appropriate yiclrl-to-maturiry.) That is, in general, any bond with)' > .'\'* will always have a positive NPV and vice versa, so that under either method it would be underpriced." Alternatively, if the investor had determined that y* was equal to 11.00%, then the bond's NPV would have been -$22.19. This value would suggest that the bond was overpriced.just as would have been noted when the yield-to-maturity of 10.02% was compared with 11.00%. This outcome will always be the case: A bond with y < y* will always have a negative NPV and vice versa, so that under either method it would be found to be overpriced. If the investor had determined that y* had a value of approximately the same magnitude as the bond's yield-to-maturity of 10%, then the NPV of the bond would be approximately zero. In such a situation the bond would be viewed as being fairly priced. Note that in order for the capitalization of income method of valuation to be used, the values of Ct , P, and y* must be determined. It is generally quite easy to determine the values for C, and Phccause they are the bond's promised cash flows and current market price, respectively. However, determining the value of y* is difficult because it will depend on the investor's subjective evaluation of certain characteristics of the bond and current market conditions. Given that the key ingredient in bond analysis is determining the appropriate value of y*, the next section will discuss what attributes should be considered in making such a determination.

l1li

BOND ATTRIBUTES Six primary attributes of a bond are of significant importance in bond valuation : • • • • • •

Length of time until maturity Coupon rate Call and put provisions Tax status Marketability Likelihood of default

At any time the structure of market prices for bonds differing in those dimensions can be examined and described in terms of yields-to-maturity, This overall structure is sometimes referred to as the yield structure. Often attention is confined to differences along a single dimension, holding the other attributes constant. For example, the set of yields of bonds of different maturities constitutes the term structure (discussed in Chapter 5), and the set of yields of bonds of different default risk is referred to as the risk structure. Most bond analysts consider the yields-to-maturity for default-free bonds to form the term structure. "Risk differentials" are then added to obtain the relevant yieldsto-maturity for bonds of lower quality. Although subject to some criticism, this procedure makes it possible to think about a complicated set of relationships sequentially The differential between the yields of two bonds is usually called a yield spread. Most often it involves the bond that is under analysis and a comparable default-free bond (that is, a Treasury security of similar maturity and coupon rate) . Yield spreads are sometimes measured in basis points, where one basis point equals .01%. If the 388

CHAPTER 14

yield-to-maturity for one bond is 11.50% and that of another is 11.90%, the yield spread is 40 basis points.

14.2.1

Coupon Rate and Length of Time Until Maturity

The coupon rate and length of time to maturity are important attributes of a bond because they determine the size and timing of the cash flows that are promised to the bondholder by the issuer. If a bond's current market price is known, these attributes can be used to determine the bond's yield-to-maturity, which will subsequently be compared with what the investor thinks it should be. More specifically, if the market for Treasury securities is viewed as being efficient, then the yield-to-maturity on a Treasury security that is similar to the bond under evaluation can form a starting point in the analysis of the bond. Consider the previously mentioned bond that is selling for $900 and has promised cash flows over the next three years of $60, $60 , and $1,060. In this case, perhaps a Treasury security with a cash flow over the next three years of $50, $50, and $1,050 that is currently selling for $910.61 would form the starting point of the analysis. Because the yield-to-maturity on this security is 8.5%, the yield spread between the bond and the Treasury security is 10.02% - 8.50% = 1.52 %, or 152 basis points. Figure 14.1 illustrates the yield spread between an index of long-term Aaa-rated corporate bonds and U.S. Treasury bonds for a twa-year period ending September 1997. Note that the spread fluctuated slightly around 50 to 75 basis points during that time.

%

U.S. Treasury Bond Yields and Aaa Corporate Bond Yields

9-----------------------Aaa Corporales

8----------------=-----------

:~ 5- - - - - - - - - - - - - - - - - - - - - - - Yield Spread

Basis Points 150 - - - - - - - - - - - - - - - - - - - - - - - - 125 - - - - - - - - - - - - - - - - - - - - - - - 100 - - - - - - - - - - - - - - - - - - - - - - - - -

A .. 75 vvv

.....

~

50 - - - - - - - - - - - - - - - - - ' - - - - - - - - 25 - - - - - - - - - - - - - - - - - - - - - - - - -

o 1••• 111111'.111111111111111111 111.i.l, 111111111111•• 11i IIIII1 ,"ll1dllllllilrilllidii Ii I "Ilidiidlilliid

~~~ ~~~~M~~~~~~~~~~~M~~~~~~~

1995

1996

1997

Figure 14.1 Source: Moody ~ BondRecord, September 1997, p. 916.

Bond Analysis

389

14.2.2

Call and Put Provisions

There are times when, by historical standards, yields-to-maturity are relatively high . Bonds issued during such times may, at first glance, appear to be unusually attractive investments. However, deeper analysis indicates that this is not necessarily the case. Why? Because most corporate bonds have a call provision that enables the issuer to redeem the bonds before maturity, usually for a price somewhat above par." This price is known as the call price, and the difference between it and the par value of the bond is known as the call premium. An issuer will often find it financially advantageous to call the existing bonds if yields drop substantially after the bonds were initially sold because the issuer will be able to replace them with lower-yielding securities that are less costly." For example, consider a ten-year bond issued at par ($1,000) that has a coupon rate of 12% and is callable at $1,050 any time after it has been outstanding for five years ." If, after five years, yields on similar five-year bonds were 8%, the bond would probably be called. An in vestor who had planned on receiving annual coupon payments of $120 for ten years would instead actually receive $120 annual coupon payments for five years and the call price of $1,050 after five years. At this time the investor could take the $1,050 and reinvest it in the 8% bonds, thereby receiving $84 per year in coupon payments over the remaining five years (it is assumed here that the investor can purchase a fraction of a bond, so that the full $1 ,050 can be invested in the 8% bonds) and $1,050 at the end of the tenth year as a return of principal. With this pattern of cash flows, the bond 's actual yield-to-maturity (otherwise known as the realized return) over the ten years would be 10.96% instead of the 12% that would have been its actual yield ifit had not been called . This example suggests that the higher the coupon rate of a callable bond, the greater is the likely divergence between actual and promised yields. This relation is borne out by experience. Figure 14.2 plots the coupon rate, set at the time of issue, on the horizontal axis. Because most bonds are initially sold at (or very close to) par, the coupon rate is also a measure of the yield-to-maturity that an investor may have thought was obtainable by purchasing one of the newly issued bonds. The vertical axis in this figure plots the subsequent actual yields-to-maturity obtained up to the original maturity date by an investor, assuming that the payments received in the event of a call were reinvested in noncallable bonds with appropriate maturities. The curve is based on experience for a group of callable bonds issued by utility companies during a period of fluctuating interest rates. As can be seen, the coupon rate and actual yield are quite similar in magnitude until the coupon rate gets near 5%. At that point, higher coupon rates are no longer associated with higher actual yields because these coupon rates were relatively high during the time period examined. As a consequence, most of the bonds with coupon rates above 5% were ultimately called. The upshot is that a bond with a greater likelihood of being called should have a higher yield-to-maturity; that is, the higher the coupon rate or the lower the call premium, the higher the yield-to-maturity should be. Equivalently, callable bonds with higher coupon rates or lower call premiums will have lower intrinsic values, keeping everything else equal. A relatively new innovation in the issuance of bonds is the use of put provisions. Bonds with put provisions, known as putable bonds, allow the investor to return the bond to the issuer before maturi ty and receive the par value in return. Li ke call provisions, typically the put provision does not allow the bond to be "put" with the issuer until several years (for example, five) have elapsed after the issuance of the bond. Although call provisions are valuable to issuers and potentially detrimental to investors, resulting in callable bonds having a higher yield-to-maturity than non-callable bonds, 390

CHAPTER 14

6

5 lJ\i "0



Par value; Yield-to-maturity Par value; Yield-ta-maturity

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~

(1 (1

+ g)l] + k)'

(17.18)

The next step involves using a property of infinite series from mathematics. If g, then it can be shown that: ~ (1 1=1

(1

+ g)l + k)'

= 1

+g

k- g

(17.19)

Substituting Equation (17.19) into Equation (17.18) results in the valuation formula for the constant-growth model: V= D

O

(

1

+

g)

k-g

(17 .20)

Sometimes Equation (17.20) is rewritten as:

V=~

k-g

because D1 = Do(1

(17.21)

+ g).

An Example As an example of how this DDM can be used , assume that during the past year the

Copper Company paid dividends amounting to $1.80 per share. The forecast is that dividends on Copper stock will increase by 5% per year into the indefinite future. Thus dividends over the next year are expected to equal $1.89 [=$1.80 X (1 + .05)]. Using Equation (17.20) and assuming a required rate of return k of 11%, shows that the value of ashare of Copper stock is equal to $31.50 [=$1.80 X (1 + .05)/(.11 - .05) = $1.89/(.11 - .05 )] . With a current stock price of $40 per share, Equation (17.2) would suggest that the NPV per share is -$8.50 (=$31.50 - $40). Equivalently, because V = $31.50 < P = $40, the stock is overpriced by $8.50 per share and would be a candidate for sale if currently owned. 528

CHAPTER 17

17.3.2

Internal Rate of Return

Equation (17.20) can be reformulated to solve for the IRR on an investment in a constant-growth security. First, the current price of the security Pis substituted for V, and then k* is substituted for k. These changes result in:

g)

+1P=Do( k* - g

(17.22)

which can be rewritten as: k* = Do( 1

+ g) + g

(17.23a)

P D) P

=-+g

(17.23b)

An Example

Applying this formula to the stock of Copper indicates that k* = 9.72% 1=[$1.80 X (1 + .05)/$40] + .05 = ($1.89/$40) + .051. Because the required rate of return on Copper exceeds the IRRfrom an investment in Copper (11% > 9.72%), this method also indicates that Copper is overpriced.

17.3.3

Relationship to the Zero-Growth Model

The zero-growth model can be shown to be a special case of the constant-growth model. In particular, if the growth rate gis assumed to be equal to zero, then dividends will be a fixed dollar amount forever, which is the same as saying that there will be zero growth. Letting g = 0 in Equations (17.20) and (17.23a) results in two equations that are identical to Equations (17 .13) and (17.15a), respectively. Even though the assumption of constant dividend growth may seem less restrictive than the assumption of zero dividend growth, it may still be viewed as unrealistic in many cases. However, as will be shown next, the constant-growth model is important because it is embedded in the multiple-growth model.

11III

THE MULTIPLE-GROWTH MODEL

A more general DDM for valuing common stocks is the multiple-growth model. With this model, the focus is on a time in the future (denoted by T), after which dividends are expected to grow at a constant rate g. Although the investor is still concerned with forecasting dividends, these dividends do not need to have any specific pattern until time T, after which they will be assumed to have the specific pattern of constant growth. The dividends up to T (D) , ~, Dg , ... , DT) will be forecast individually by the investor. (The investor also forecasts when this time Twill occur.) Thereafter dividends a re assumed to grow by a constant rate g that the investor must also forecast, meaning that:

DT+\

= DT(l + g)

DT+'l = DT+I(l DT+3

= DT+2(1

+ g) + g)

= DT(l

= DT(l

+ g)2 + g?

and so on. Figure 17.1 presents a time line of dividends and growth rates associated with the multiple-growth model. The Valuation of Common Stocks

529

-I

0

+

+

~

+

+

+

D~

-(1 + k)2

:~

T-1

'1'

'1'+1

+

+

+

+..........

+ ...

+

>

00

+

v Figure 17.1 Time Line for Multiple-Growth Model

17.4.1

Net Present Value

Valuing a share of common stock with the multiple-growth model requires that the present value of the forecast stream of dividends be determined. This process can be facilitated by dividing the expected dividend stream into two parts, finding the present value of each part, and then adding these two present values together. The first part consists of finding the present value of all the forecast dividends that will be paid up to and including time T. Denoting this present value by Vr- , it is equal to:

Do

7'

Vr- =

~

(1

+ k)/

(17.24)

The second part consists of finding the presen t value of all the forecast dividends that will be paid after time Tand involves the application of the constant-growth model. The application begins by imagining that the investor is not at time zero but is at time Tand has not changed his or her forecast of dividends for the stock. As a result, the next period's dividend Dn l and all those thereafter are expected to grow at the rate g. Because the investor would be viewing the stock as having a constant growth rate, its value at time T, VI" can be determined with the constant-growth model of Equation (17 .21) : Vr = DT+1(_1 )

k-g

(17.25)

One way to view Vr is that it represents a lump sum that isjust as desirable as the stream of dividends after T. That is, an investor would find alum p sum of cash equal to Vr , to be received at time T, to be equally desirable as the stream of dividends DT+l' D T +2, DT +3 , and so on. Now given that the investor is at time zero. not at time T, the present value at t = 0 of the lump sum VT must be determined. This present value is found simply by discounting VT for T periods at the rate k, resulting in the following formula for finding the present value at time zero for all dividends after T, denoted VT +: (17.26)

(k - g)(l 530

+ k)T CHAPTER 17

Having found the present value of all dividends up to and including time T with Equation (17.24), and the present value of all dividends after time Twith Equation (17.26), the investor can determine the value of the stock by summing up these two amounts: V= VT -

-f -

+ VT+ D,

1=1

(1

+ k)'

+

DT+I

(k - g)(1

+ k)T

(17 .27)

Figure 17.1 illustrates the valuation procedure for the multiple-growth DDM that is given in Equation (17.27) . An Example

As an example of how this DDM can be used, assume that during the past year the Magnesium Company paid dividends amounting to $.75 per share. Over the next year, Magnesium is expected to pay dividends of $2 per share. Thus gl = (D 1 - Do)/Do = ($2 - $.75)/$.75 = 167%. The year after that, dividends are expected to amount to $3 per share, indicating that g2 = (D 2 - D1)/D 1 = ($3 - $2)/$2 = 50%. At this time, the forecast is that dividends will grow by 10% per year indefinitely, indicating that T = 2 and g = 10%. Consequently, DT+J = D:i = $3(1 + .10) = $3.30. Given a required rate of return on Magnesium shares of 15%, the values of Vr- and Vr+ can be calculated as follows:

v = T-

$2

(l

+ .15 )1

+

$3

(1

+ .15)2

= $4.01 V T+

$3.30 = ----"-----~ (.15 - .10)(1

+ .15)2

= $49.91

Summing Vr- and Vr+ results in a value for Vof $4.01 + $49.91 = $53.92. With a current stock price of$55 per share, Magnesium appears to be fairly priced. That is, Magnesium is not significantly mispriced because Vand Pare nearly of equal size.

17.4.2

Internal Rate of Return

The zero-growth and constant-growth models have equations for V that can be reformulated in order to solve for the IRR on an investment in a stock. Unfortunately, a convenient expression similar to Equations (17.15a), (17 .15b), (17.23a) , and (17.23b) is not available for the multiple-growth model. Note that the expression foriRR is derived by substituting P for V. and k* for k in Equation (17.27) : P=

f

1=1

(1

, D

+ k*)'

+

DT+I

(k* - g)(1

+ k*)T

(17.28)

This equation cannot be rewritten with k* isolated on the left-hand side, so a closedform expression for IRR does not exist for the multiple-growth model. However, all is not lost. It is still possible to calculate the IRR for an investment in a stock conforming to the multiple-growth model by using an "educated" trialand-error method. The basis for this method is in the observation that the righthand side of Equation (17.28) is simply equal to the present value of the dividend The Valuation of Common Stocks

531

stream, where I!.* is used as the discount rate. Hence the larger the value of I!.*, the smaller the value of the right-hand side of Equation (17.28). The trial-and-error method proceeds by initially using an estimate for 11.*. If the resulting value on the right-hand side of Equation (17.28) is larger than P, then a larger estimate of 11.* is tried. Conversely, if the resulting value is smaller than P, then a smaller estimate of 11.* is tried. Continuing this search process, the investor can home in on the value of 11.* that makes the right-hand side equal Pon the left-hand side. Fortunately, it is a relatively simple matter to program a computer to conduct the search for 11.* in Equation (17.28). Most spreadsheets include a function that does so automatically. An Example

Applying Equation (17.28) to the Magnesium Company results in: $2 $55

=

(1

$3

+ I!.*)I + (1 + 11.*)2 + (I!.*

$3.30 - .10)(1

+ k*?

(17.29)

Initially a rate of 14% is used in attempting to solve this equation for 11.*. Inserting 14% for I!.* in the right-hand side of Equation (17.29) results in a value of$67.54. Earlier 15% was used in determining Vand resulted in a value of $53.92. This means that 11.* must have a value between 14% and 15%, since $55 is between $67.54 and $53.92. If 14.5% is tried next, the resulting value is $59 .97, suggesting that a higher rate should be tried. If 14.8% and 14.9% are subsequently tried , the respective resulting values are $56.18 and $55.03. Because $55.03 is the closest to P, the IRR associated with an investment in Magnesium is 14.9%. Given a required return of 15% and an IRR of approximately that amount, the stock of Magnesium appears to be fairly priced.

17.4.3

Relationship to the Constant-Growth Model

The constant-growth model can be shown to be a special case of the multiple-growth model. In particular, if the time when constant growth is assumed to begin is set equal to zero, then:

L T

Vr-

=

I= I

(1

D,

+ 11.) = 0 I

and DH 1 D1 r+= V (k-g)(l +11.)'1'= k-g

because T = 0 and (1 + 11.)0 = 1. Given that the multiple-growth model states that V = Vr- + Vr+ , one can see that setting T = 0 results in V = Dd(k - g), a formula that is equivalent to the formula for the constant-growth model.

17.4.4

Two-Stage and Three-Stage Models

Two dividend discount models that investors sometimes use are the two-stage model and the three-stage model." The two-stage model assumes that a constant growth rate gl exists only until some time T, when a different growth rate g2 is assumed to begin and continue thereafter. The three-stage model assumes that a constant growth rate g. exists only until some time T I , when a second growth ra te is assumed to begin and last until a later time T2 , at which time a third growth rate is assumed to begin and last thereafter. Letting Vr+ denote the present value of all divid ends after the last growth rate has begun and VT - denote the present value of all the preceding dividends, indicates that these models are just special cases of the multiple-growth model. 532

CHAPTER 17

In the application of the capitalization of income method of valuation to common stocks, it might seem appropriate to assume that a particular stock will be sold at some point in the future. In this case the expected cash flows would consist of the dividends up to that point as well as the stock's expected seIIing price. Because dividends after the selling date would be ignored, the use of a dividend discount model may seem to be improper. However, as will be shown next, it is not.

11III

VALUATION BASED ON A FINITE HOLDING PERIOD

The capitalization of income method of valuation involves discounting all dividends that are expected throughout the future. Because the simplified models of zero growth, constant growth, and multiple growth are based on this method, they too involve a future stream of dividends. Upon reflection one may think that such models are relevant only for an investor who plans to hold a stock forever, because only such an investor would expect to receive this stream of future dividends. But what about an investor who plans to sell the stock in a year? 10 In such a situation, the cash flows that the investor expects to receive from purchasing a share of the stock are equal to the dividend expected to be paid one year from now (for ease of exposition, it is assumed that common stocks pay dividends annually) and the expected selling price of the stock. Thus it would seem appropriate to determine the intrinsic value of the stock to the investor by discounting these two cash flows at the required rate of return as follows: D] +p]

V= (1 +k) DI (l+k)

+

PI

(l+k)

(17 .30)

where D I and PI are the expected dividend and seIIing price at t = I, respectively. In order to use Equation (17 .30), one must estimate the expected price of the stock at t = 1. The simplest approach assumes that the seIIing price will be based on the dividends that are expected to be paid after the selling date. Thus the expected selling price at t = 1 is:

00

=

~

D, (1 + k)H

Substituting Equation (17.31) for results in:

PI

(17.31)

in the right-hand side of Equation (17.30)

D,

00

=~_-'-------: 1=1

(1

+ k)'

which is exactly the same as Equation (17.7). Thus valuing a share of common stock by discounting its dividends up to some point in the future and its expected selling price at that time is equivalent to valuing stock by discounting all future dividends. The Valuation of Common Stocks

533

Simply stated, the two arc equivalent because the expected selling price is itself based on dividends to be paid after the selling date. Thus Equation (17 .7), as well as the zero-growth, constant-growth , and multiple-growth models that are based on it, is appropriate for determining the intrinsic value of a share of common stock regardless of the length of the investor's planned holding period. An Example As an example, reconsider the common stock of the Copper Company. Over the

past year Copper paid dividends of $1.80 per share and the investor forecasted that the dividends would grow hy 5% per year forever. This means that dividends over the next two years (D, and D2 ) arc forecast to be $1.89 [=$1.80 X (1 + .05)] for the first year and $1.985 [= $1.89 X (1 + .05)] for the second. If the investor plans to sell the stock after one year, the selling price can be estimated by noting that, at t = 1, the forecast of dividends for the forthcoming year will be D2 , or $1.985. Thus the anticipated selling price at t = 1, denoted PI' will be equal to $33.08 [= $1.985/(.11 - .05)]. Accordingly, the intrinsic value of Copper to such an investor would equal the present value of the expected cash flows, which are D, = $1.89 and PI = $33.08. Using Equation (17.30) and assuming a required rate of 11%, this value is equal to $31.50 [= ($1.89 + $33.08)/(1 + .11)]. Note that this is the same amount that was calculated earlier when all the dividends from now to infinity were discounted using the constant-growth model: V = D,/(k - g) = $1.89/(.11 - .05) = $31.50.

11III

MODELS BASED ON PRICE-EARNINGS RATIOS Despite the inherent sensibility of DDMs, many security analysts use a much simpler procedure to value common stocks. First, a stock's earnings per share over the forthcoming year E 1 are estimated, and then the an alyst (or someone else) specifies a "normal" price-earnings ratio for the stock. The product of these two numbers gives the estimated future price PI ' Together with estimated dividends D I to be paid during the period and the current price P, the estimated return on the stock over the period can be determined: Expected return =

(p, - p) + D} P

(17.32)

where PI = (PI/E,) X E,. Some security analysts expand this procedure, estimating earnings per share and price-earnings ratios for optimistic, most likely, and pessimistic scenarios to produce a rudimentary probability distribution of a security's return. Other analysts determine whether a stock is underpriced or overpriced by comparing the stock's actual price-earnings ratio with its "normal" price-earnings ratio, as will be shown next.'! In order to make this comparison, one must rearrange Equation (17 .7) and introduce some new variables. First, note that earnings per share E1 are related to dividends per share D1 by the firm's payout ratio P"

D1 =PIEI

(17.33)

Furthermore, if an analyst has forecast earnings per share and payout ratios, then he or she has implicitly forecast dividends.

534

CHAPTER i7

Equation (17.33) can be used to restate the various DDMs where the focus is on estimating what the stock's price-earnings ratio should be instead of on estimating the intrinsic value of the stock. In the restatement, PIE/ is substituted for D, in the righthand side of Equation (17.7), resulting in a general formula for determining a stock's intrinsic value that involves discounting earnings:

=

pJE(

(l+k)1

= ~ /=1

+ P'l.E'l. (1+k)2

+

P3 E3 + ... (1+k)3

PIE/ (1

(17.34)

+ k)/

Earlier it was noted that dividends in adjacent time periods could be viewed as being "linked" to each other by a dividend growth rate g/. Similarly, earnings per share in any year t can be "linked" to earnings per share in the previous year t - 1 by a growth rate in earnings per share, gel> (17.35) This equation implies that E 1 =Eo(l +grl)

E'l. = E,(l + g'2) = Eo(l + g,I)(l + g,2) E i = E2(1

+ g,3)

= Eo(l

+ g,,)(l + g,.2)(1 + g,.3)

and so on, where Eo is the actual level of earnings per share over the past year, E 1 is the expected level of earnings per share over the forthcoming year, E2 is the expected level of earnings per share for the year after E1 , and E3 is the expected level of earnings per share for the year after E 2 • These equations relating expected future earnings per share to Eo can be substituted into Equation (17 .34), resulting in: V=

Pl[Eo(l + gel)]

(l+k)1

P2[Eo(1 + g,I)(l + g,2)] + .:....::..::.--.:..;'---:----:::.:..:..:....:'-;;-----:::---=--::. (1+k)2

+ P3[Eo(1 + gel)(l + g,2)(1 + ge3)] + ... (1 + k?

(17.36)

Because Vis the intrinsic value of a share of stock, it represents what the stock would be selling for ifit were fairly priced. It follows that VIEo represents what the price-earnings ratio would be if the stock were fairly priced and is sometimes referred to as the stock's "normal" price-earnings ratio. Both sides of Equation (17.36) can be divided by Eo and the results simplified in the formula for determining the "normal" priceearnings ratio:

(17.37)

The Valuation of Common Stocks

535

This approach shows that, other things being equal, a stock's "normal" price-earnings ratio will be higher: The greater the expected payout ratios (PI' fJ2, fJ?, ...), The greater the expected growth rates in earnings per share (gel, gc2' gr:~' ...) The smaller the required rate of return (k) The qualifying phrase "other things being equal" should not be overlooked. For example, a firm cannot increase the value of its shares by simply making greater payouts. This will increase PI' /)2' /):\, , but it will decrease the expected growth rates If the firm's investment policy is not altered, the in earnings per share grl' gr2' gr3' effects of the reduced growth in its earnings per share will just offset the effects of the increased payouts, leaving its share value unchanged. Earlier it was noted that a sto ck was viewed as underpriced if V > Pand as overpriced if V < P. Because dividing both sides of an inequality by a positive constant will not change the direction of the inequality, such a division can be done here to the two inequalities involving Vand P, where the positive constant is Eo. The result is that a stock can be viewed as being underpriced if VIE o > PIEo and overpriced if VIEo < PIEo. Thus a stock will be underpriced if its "normal" price-earnings ratio is greater than its actual price-earnings ratio, and overpriced ifits "normal" price-earnings ratio is less than its actual price-earnings ratio. Unfortunately, Equation (17.37) is intractable; it cannot be used to estimate the normal price-earnings ratio for any stock. However, simplifying assumptions can be made that result in tractable formulas for estimating normal price-earnings ratios. These assumptions, along with the formulas, parallel those made previously regarding dividends.

17.6.1

The Zero-Growth Model

The zero-growth model assumed that dividends per share remained at a fixed dollar amount forever. This situation is most likely to occur if earnings per share remain at a fixed dollar amount forever, with the firm maintaining a 100% payout ratio. Why 100%? Because the assumption that a lesser amount was being paid out would mean that the firm was retaining part of its earnings. These retained earnings would be put to some use and would thus be expected to increase future earnings and hence dividends per share. Accordingly, the zero-growth model can be interpreted as assuming P, = 1 for all time periods and Eo = E. = E2 = E 3 , and so on. Consequently, Do = Eo = D. = E 1 = D 2 = E 2 , and so on. Thus, the valuation Equation (17.13) can be restated as:

Eo

V=k

(17.38)

Dividing Equation (17.38) by Eo results in the formula for the normal price-earnings ratio for a stock having zero growth :

536

V

1

Eo

k

(17.39)

CHAPTER 17

An Example

Earlier it was assumed that the Zinc Company was a zero-growth firm paying dividends of $8 per share, selling for $65 a share, and having a required rate of return of 10%. Because Zinc is a zero-growth company, it will be assumed that it has a 100% payout ratio which, in turn, means that Eo = $8. At this point Equation (17.38) can be used to calculate a normal price-earnings ratio for Zinc of 1/.10 = 10. Because Zinc has an actual price-earnings ratio of $65/$8 = 8.1 , and because V/E o = 10 > P/Eo = 8.1, it can be seen that Zinc stock is underpriced.

17.6.2

The Constant-Growth Model

Previously, it was noted that dividends in adjacent time periods could be viewed as being connected to each other by a dividend growth rate g,. Similarly, it was noted that earnings per share can be connected by an earnings growth rate g". The constantgrowth model assumes that the growth rate in dividends per share will be the same throughout the future. An equivalent assumption is that earnings per share will grow at a constant rate g, throughout the future, with the payout ratio remaining at a constant level p. These assumptions mean that:

E,

= 1'.'0(1 + g,) = Eo(l + g,)1

£2

= E1(1 + g,) = Eo(l + g,)(l + g,) = Eo(l + g.)2

E~

= E2(1 + g,) = Eo(l + g,)(l + g,)(1 + g,) = Eo(1 + g.)3

and so on. In general, earnings in year t can be connected to

Eo as follows: (17.40)

Substituting Equation (17.40) into the numerator of Equation (17.34) and recognizing that p, = p results in:

V= ~ pEo(l + gJ' (1

1=1

00

=pEo

[

~

+ k)'

(1 + g,)I] (I +k)'

(17.41)

The same mathematical property of infinite series given in Equation (17.19) can be applied to Equation (17.41), resulting in:

v = pEo(

+ g,. ) k - g,

1

(17.42)

It can be noted that the earnings-based constant-growth model has a numerator that is identical to the numerator of the dividend-based constant-growth model, because pEo = Do . Furthermore, the denominators of the two models are identical. Both assertions require that the growth rates in earnings and dividends be the same (that is, g. = g). This equality can be seen by recalling that constant earnings growth means:

The Valuation of Common Stocks

537

Now when both sides of this equation are multiplied by the constant payout ratio, the result is:

Because pE, = D, and pE,- t = D'_I' this equation reduces to:

which indicates that dividends in any period t - I will grow by the earnings growth rate g,. Because the dividend-based constant-growth model assumed that dividends in any period t - I would grow by the dividend growth rate g, the two growth rates must be equal for the two models to be equivalent. Equation (17.42) can be restated by dividing each side by Eo, resulting in the following formula for determining the normal price-earnings ratio for a stock with constant growth:

(Ik - g.)

-v-_p -+Eo

g,

(17.43)

An Example

Earlier it was assumed that the Copper Company had paid dividends of $1.80 per share over the past year, with a forecast that dividends would grow by 5% per year forever. Furthermore, it was assumed that the required rate of return on Copper was 11%, and the current stock price was $40 per share. Now assuming that Eu was $2 .70, one can see that the payout ratio was equal to 66-~% (=$1.80/$2.70). So the normal price-earnings ratio for Copper, according to Equation (17.43), is equal to 11.7 [=.6667 X (1 + .05)/(.11 - .05)]. Because this is less than Copper's actual price-earnings ratio of 14.8 (= $40/$2.70), it follows that the stock of Copper Company is overpriced.

17.6.3

The MUltiple-Growth Model

Earlier it was noted that the most general DDM is the multiple-growth model, wherein dividends are allowed to grow at varying rates until some point in time T, after which they are assumed to grow at a constant rate. In this situation the present value of all the dividends is found by adding the present value of all dividends up to and including T, denoted by V7"-' and the present value of all dividends after T, denoted by V7"+ :

v = V r- + Vr+

- L

D,

T

-

1=1

(1

+ k)'

DT +1 + --~----= (k - g)(1 + k)7"

(17.27)

In general, earnings per share in any period t can be expressed as being equal to Eo times the product of all the earnings growth rates from time zero to time t: (17.44)

538

CHAPTER 17

Because dividends per share in any period Iare equal to the payou t ratio for that period times the earnings per share, it follows from Equation (17.44) that: DI = PIEI

(17.45 ) Replacing the numerator in Equation (17.27) with the right-hand side of Equation (17.45) and then dividing both sides by Eo gives the following formula for determining a stock's normal price-earnings ratio with the multiple-growth model: V

-= l~l

+ gel) + P2(1 + gel)(1 + ge2) + ... (I + k)1 (I + k)2 PT(I + &\)(1 + g'2) ... (I + geT) + . (I + kf

PI(I

p(1

+ g Do + 10 ) , Given that the amount ofinvestment has been determined by the number of positive NPV projects available to the firm, the reason for this inequality is that the firm has decided to pay its stockholders a lower dividend than was paid in Figure 18.1 (a). In paying this smaller dividend, the firm will be left with excess cash . It is assumed that the firm will use this cash to repurchase some of its outstanding shares in the marketplace (and that the transaction costs associated with such repurchases are negligible). The reason for this assumption is the desire to keep the situation comparable to the two earlier ones. Allowing the firm to keep the excess cash would be tantamount to letting the firm invest the cash, an investment decision that was not made in the two earlier cases and therefore does not have a positive NPV (remember that 10 consists of all positive NPV projects). Allowing the firm to keep the excess cash would also mean that the firm has made a decision to lower its debt-equity ratio because retention of the excess cash would increase the amount of equity for the firm , thereby decreasing the amount of debt outstanding relative to the amount of equity. The Plum Company could set dividends at $1,000 instead of $2,000 or $3,000. In this case, the firm would have a cash outflow for dividends and investment amounting to $4,000 (=$1,000 + $3,000). With earnings of$5,000, there would then be $1,000 (=$5,000 - $4,000) of cash left for the firm to use to repurchase its own stock. The Dividend Decision

The firm has a decision to make regarding the size of its current dividends. The amount of current earnings Eo and the amount of new investment 10 have been determined. What is left to be decided is the amount of dividends, Do . They can be set equal to earnings less investment [as in Figure 18.1 (a)], or greater than that amount [as in Figure 18.1 (b)], or less than that amount [as in Figure 18.1 (c)] . The question that remains to be answered is this: Will one of these three levels of dividends make Earnings

561

the current stockholders better off than the other two? That is, which level of dividends-$l,OOO, $2,000, or $3 ,OOO-will make the current stockholders better off? The simplest way to answer that question is to consider a stockholder who presently holds 1% of the common stock of the firm and is determined to maintain this percentage ownership in the future." If the firm follows a dividend policy as shown in Figure 18.1 (a), the stockholder's current dividends will equal .01Do or, equivalently, .01(Eo - 10 ) , Similarly, the stockholder's future dividends will be equal to .0 1D, or, equivalently, .01 (E, - I,). Because the stockholder wants to be certain of receiving this amount regardless of the level of current dividends, he or she will take whatever actions are necessary to maintain a 1% ownership position in the firm. When the situation is analyzed in this manner, there is only one variable that can affect the stockholder's current wealth-the amount of the current dividend. If the firm follows a dividend policy as shown in Figure 18.1 (b), the stockholder must invest additional funds in the firm's common stock in order to avoid a diminished proportional ownership position in the firm. Why ? Because in this situation the firm must raise funds by selling additional shares in order to pay for the larger cash dividends. Because Eo < Do + l a, the total amount of funds that the firm needs to raise is the amount F;) such that: Eo+Fo=Do+~)

(18.1)

or: (18.2) The amount of the additional investment that the stockholder needs to make in order to maintain a 1% position in the firm is .0 1F;" which from Equation (18.2) is equal to .01 (Do + ~) - Eo). Because the stockholder receives 1% of the dividends, the net amount the stockholder receives at time zero is equal to .01Do - .01F;), or: (18 .3) Interestingly, the net amount the stockholder rec eives, .01Eo - .0 1Io• is the same as in the first situation. The amount of the extra cash dividend received is exactly offset by the amount the stockholder needs to spend to maintain his or her ownership position in the firm. If the firm follows a dividend policy as shown in Figure 18.1 (c), then the firm will repurchase shares. Accordingly, the stockholder must sell some shares back to the firm in order to avoid having an increased ownership position in the firm. Because Eo > Do + la, the total amount of funds that the firm will spend on repurchasing its own shares is the amount ~ such that: (18.4) or: ( 18.5) The amount of stock that the stockholder needs to sell back to the firm to maintain a 1% position in the firm is .01Ro, which from Equation (18 .5) is equal to .01(Eo - Do - 10 ) , Because the stockholder receives 1% of the dividends, the net amount the stockholder receives at time zero is equal to .0 1Do + .Ol~, or:

.01Do + .01(Eo - Do - 10 )

= .0 1t.o-

.01Io

(18.6)

Again this net amount, .01Eo - .0110 • is the same as in the first situation. That is, in the third situation, the smaller amount of the cash dividend received by the stockholder is exactly made up for by the amount of cash received from the repurchase of shares by the firm. 562

CHAPTER 18

Thus no matter what the firm's dividend policy, a stockholder choosing to maintain a constant proportional ownership will be able to spend the same amount of money on consumption at time zero. This amount will be equal to the proportion times the quantity Eo - 10 , Furthermore, this will also be true in the future. That is, in any year t the stockholder will be able to spend on consumption an amount that is equal to the proportion times the quantity E/ - 1/.

18.1 .2

Earnings Determine Market Value

In determining the value of 1% of the current shares outstanding, remember that the firm is about to declare and pay current dividends. Regardless of the magnitude of these dividends, the stockholder will be able to spend on consumption only an amount equal to .01 (Eo - 10 ) , Furthermore, the stockholder will be able to spend on consumption an amount equal to .01 (E/ in any future year t: Discounting these expected amounts by a (constant) rate k reveals that the value Vof 1% of the current shares outstanding will be:

IJ

.01(Eo - 10 ) .0 1 V =

(l+k)O

+

.Ql(E I

-

II)

(l+k)l

+

.01(E2 -12 )

(l+k?

+ ...

Multiplying both sides of this equation by 100 results in the following expression for the total market value of all shares outstanding: _ (Eo - 10 )

V - (1

+ k)O +

(E 1

(1

-

II) +

+ k)\

(E2

(1

-

12)

+ k)2

+ .. . (18.7)

Equation (18.7) shows that the aggregate market value of equity is equal to the present value of expected earnings net of investment. Note that the size of the dividends does not enter into the formula. This fact indicates that the market value of the stock is independent of the dividend decision made by the firm, meaning that the dividend decision is irrelevant to stock valuation. Instead, the market value of the firm is related to the earnings prospects of the firm, along with the required amounts of new investment needed to produce those earnings."

Dividend Discount Models

In Chapter 17 it was shown that the value of a share of common stock was equal to the present value of all dividends expected in the future. Hence it is tempting to believe that, contrary to the assertion above, the market value of a firm's stock is dependent on the dividend decision. However, it turns out that there is nothing inconsistent between valuation based on dividend discount models and the irrelevancy of the dividend decision. The dividend irrelevancy argument suggests that if the firm decides to increase its current dividend, then new shares will need to be sold. In turn , future dividends will be smaller because the aggregate amount of dividends will have to be divided among an increased number of shares outstanding. Ultimately. the current stockholders will be neither better off nor worse off, because the increased current dividend will be exactly offset by the decreased future dividends. Conversely, if the firm decides to decrease its current dividend, then shares will be repurchased and future dividends will be increased because there will be fewer shares outstanding. Ultimately, the decreased current dividend will be exactly offset by the increased future dividends, again leaving current stockholders neither better off nor worse off. Earnings

563

An Example

These situations can be illustrated with the example of the Plum Company. Because Plum currently has reported earnings of $5,000 and investments totaling $3,000, if dividends amounting to $2,000 were paid, then the stockholder owning 1% of the firm would receive cash amounting to $20 (=.01 X $2,000). Alternatively, if dividends amounting to $3,000 were paid, then Plum would have to raise $1,000 from the sale of new common stock. The stockholder would receive $30 (=.01 X $3,000) in dividends but would have to pay $10 (=.01 X $1,000) to purchase 1% of the new stock, thereby maintaining his or her 1% ownership position. Consequently, the net cash flow to the stockholder would be $20 (=$30 - $10), the same amount as in the previous situation. Last, if dividends amounting to $1,000 were paid, then Plum would have cash amounting to $1,000 to use to repurchase common stock. The stockholder, desirous of maintaining a 1% position, would thus sell shares amounting to $10 (= .01 X $1,000). As a result, the stockholder would have a cash inflow totaling $20 (=$10 + $10), again the same amount as in the two previous situations. Under all three situations, the 1% stockholder would receive the same cash flow at the present time (=$20) and would have the same claim on the future earnings of Plum [= .01(£, - IJ]. That is, in all three cases, the stockholder would still own 1% of Plum and would therefore receive the same amount of dividends in the future. Accordingly, the 1% stockholder (and all the others) would be neither better off nor worse off if Plum pays a dividend amounting to $1,000, $2,000, or $3,000. In summary, the dividend decision is a nonevent; whatever the level of dividends, current stockholders will be neither better off nor worse off. This result is sometimes referred to as the dividend irrelevancy theorem.

lID

DETERMINANTS OF DIVIDENDS Few firms attempt to maintain a constant ratio of dividends to current earnings; doing so would result in a fluctuating dollar amount of dividends. The dividends would fluctuate because earnings on a year-to-year basis are likely to be quite variable. Instead, firms attempt to maintain a desired ratio of dividends to earnings over some relatively long period, meaning that there is a target payout ratio of dividends to long-run or sustainable earnings. As a result, dividends are usually kept at a constant dollar amount and are increased only when management is confident that it will be relatively easy to keep paying this increased amount in the future.P Nonetheless, larger earnings are likely to be accompanied by some sort of increase in dividends, as Table 18.1 shows.

18.2.1

Changes in Earnings and Dividends

The first two lines of Table 18.1 indicate that 59.3% of the time the earnings of the firms examined rose, and the remaining 40.7% of the time earnings fell. The majority of the times when current earnings rose, firms increased their current dividends. However, whenever current earnings fell, firms would increase their current dividends as frequently as they would decrease their current dividends (note that, roughly speaking, 42.8% == 39.5%). The next two lines of the table suggest that firms are more likely to increase current dividends if they have had two consecutive years of rising earnings than if they have had falling and then rising earnings (74.8% > 54.1%) . The last two lines of the table suggest that firms are more likely to decrease current dividends if they have had two consecutive years of falling earnings than if they have had rising and then 564

CHAPTER 18

TABLE

18.1

I?arnlngs and DMdend Changes of 392 Firms, 1946-1964

Earnings Changes Current Year

+ + + -

I

Percent of Cases

I

Previous Year 59.3% 40.7

+

33.4

+

25.9 24.7 16.0

-

Percent of Cases in Which Firms Increased DIvidends

Did Not Change Dividends

Decreased Dividends

65.8% 42.8 74.8

13.9% 17.9

20.3% 39.5 13.8

11.4 17.2 16.9 19.4

54.1 49.7 31.8

Source: Euge ne ~~ Farua and Harvey Babiak, "Divide nd Policy: An Empirical Analysis," Jemmal a/1M IIU. ~ 2 4 (Dece mber J9liH): 11:14 .

28.7 33.4 48.8 A.~an

StntiJtiud ASJocitlli01l 63,

falling earnings (48.8 % > 33.4%). Overall, the table shows that firms in general are more likely to increase dividends than to decrease them .

18.2.2

The Lintner Model

A formal representation of the kind of behavior implied by a constant long-run target payout ratio begins by assuming that the goal of the firm is to payout p* (for example, p* = 60%) of long-run earnings. If this target ratio were maintained every year, total dividends paid in year t would be: (18.8) where OJ denotes the target amount for dividends to be paid in year t, and E, is the amount of earnings in year t. The difference between target dividends in year t and the previous year's actual dividends is determined by subtracting D'-l from both sides of Equation (18.8), resulting in: (18.9) Although firms would like to change their dividends from D' -l to OJ, few (if any) firms would actually change their dividends by this amount. Instead, the actual change in dividends will be a proportion of the desired change: D, - D'_I

= a(Di -

D,_I)

(18 .10)

where a is a "speed of adj ustme n t" coefficien t, a number between 0 and 1. For example, if a firm hasjust earned $5 million (E, = $5 million) and has a target payout ratio of60%, then it would like to pay dividends amounting to $3 million (=.6 X $5 million) . If it paid dividends of$2 million last year, this amount represents an increase of$l million (=$3 million - $2 million). However, if a = 50%, then the firm will actually increase the dividends by $500,000 (=.5 X $1 million). Thus actual dividends will be equal to $2 .5 million (=$2 million + $500,000), an amount equal to last year's dividends plus the change in dividends from last year to this year. This model can be summarized by substituting p*E, for Di in Equation (18.10) and then solving the resulting expression for D,: (18.11) Equation (18.11) indicates that the amount of current dividends is based on the amount of current earnings and the amount of the last year's dividends." In the previous example, a = 50%, p* = 60%, E, = $5 million, and D,_1 = $2 million. Thus Earnings

565

actual dividends D1 would be equal to $2.5 million [= (.5 X .6 X $5 million) + (1 - .5) X $2 million)] . Subtracting D'_I from both sides of Equation (18.11) shows that the change in dividends is equal to :

D1 - D,_\ = ap* E, - aD'_1

(18 .12)

When written ill this form, the model suggests that the size of the change in dividends will be positively related to the current amount of earnings (because ap* is a positive number) and negatively related to the amount of the previous period's dividends (because -aJ),_1 is a negative number). Thus the larger current earnings are, the larger the change in dividends; but the larger the previous period's dividends, the smaller the change in dividends.

18.2.3

Test Results

Statistical analysis has been used to test how well this model describes the way a sample of firms set the amount of their dividends. Table 18.2 summarizes some of the values obtained in one such study. The average firm had a target payout ratio of 59.1 % and adjusted dividends 26.9% of the way toward its target each year. However, most firms' dividends varied substantially from the pattern implied by their targets and adjustment factors. Somewhat less than half (42%) of the annual variance in the typical firm's dividends could be explained in this manner. This result means that the model, although explaining a portion of the changes in dividends that occurred, leaves a substantial portion unexplained. A refinement of the model presented in Equation (18 .12) uses an alternative definition of earnings. Specifically, the term £1 in Equation (18 .8) can be defined as the permanent earnings of the firm in year t instead of total earnings. Here total earnings can be thought of as having two components: permanent earnings, which are likely to be repeated, and transitory earnings, which are not likely to be repeated. Accordingly, the refinement is based on the idea that management ignores the transitory component of earnings in arriving at its target amount of dividends . Hence, the target amount is based on the permanent earnings of the firm , not on the total earnings, and the change in dividends shown in Equation (18.12) is related to the past

TABLE 18.2 Target Payout Ratios and Speed of Dlvldend Adjustment Factors of 298 Firms, 1946-1968 Speed of Adjustment Coefficient

Value .104 .182 .25 1

.339 .470 Average .269

Percent of Flrmswtth Smaller value 10% 30 50 70 90

Percent of Variance Explained

Target Payout Ratio

Value

Percent of Firms with Smaller Value

.40 1

10%

.525 .584 .660 .779 Average .591

30 50 70 90

Value 11% 32 42 54 72 Average 42

Percent of Finns with Smaller Value 10% 30 50 70 90

Source: Eugene F. Fama, "The Empirical Relationship between the Dividend and Investment Decisions of Firms," Ammam Economic Revin.64 , 00 , 3 (june 1974): 310.

566

CHAPTER 18

level of dividends and permanent earnings. A test of this model found that it described changes in dividends better than the previously described model that was based on total earnings."

11II

THE INFORMATION CONTENT OF DIVIDENDS

It is reasonable to believe that management has more information about the future earnings of the firm than does the public (which includes its own stockholders) . This situation of asymmetric information suggests that managers will seek to convey the information to the public if they have an incentive to do so. If they do have such an incentive, one way of conveying information is to announce a change in the amount of the firm's dividends. When used in this manner, dividend announcements are said to be a signaling device."

18.3.1

Signaling

A relatively simple view of dividend changes is that an announced increase in dividends is a signal that management has increased its assessment of the firm's future earnings. The announced increase in dividends is therefore good news and will, in turn, cause investors to raise their expectations regarding the firm's future earnings. Conversely, an announced decrease in dividends is a signal that management has decreased its assessmen t of the firm's fu ture earnings. The announced decrease in dividends is therefore bad news and will, in turn, cause investors to lower their expectations regarding the firm's future earnings. An implication is that an announced increase in dividends will cause the firm's stock price to rise, and an announced decrease will cause it to fall. This simple model of dividend changes can be thought of as a special case of the model given in Equation (18 .12) , where the speed of adjustment, a, is zero. With this model, the expected change in dividends, D, - D,-J, is zero, suggesting that a simple increase in dividends will be viewed as good news. Conversely, a simple decrease in dividends will be viewed as bad news. One way of testing to see if dividend changes do indeed convey information to the public is to see how stock prices react to announcements of changes in dividends. However, care must be exercised in conducting such a study because the firm's announcement of dividends is often made at the same time that the firm announces its earnings. When such announcements are made at the same time, any price change in the firm's common stock may be attributable to either (or both) announcements. One study attempted to avoid this problem of contamination by looking only at cases in which the announcement of earnings was at least II trading days apart from the announcement of dividends. Figure 18.2 illustrates the average abnormal return associated with a firm's dividend announcement for firms that announced their dividends II or more days after they announced their earnings. (Similar results were obtained when the authors of the study exam ined cases in which dividend announcements preceded earnings announcements.) In cases in which firms announced an increase in their dividends, there was a significant positive reaction in their stock prices. Conversely, for firms that announced a decrease in their dividends, there was a significant negative reaction in their sto ck prices. These findings strongly support the information content of dividends hypothesis, which asserts that dividend announcements contain inside information about the firm's future prospects. It should be noted that there is nothing inconsistent with dividends being used as a signal and with the dividend irrelevancy argument of Miller and Modigliani that Earnings

567

(b) Dividend Increase

(a) Dividend Decrease

0.15

1.04

-0.37

0.91

ii

~

-0.90 ....e -1.43 ::l U c:r:: -1.96 C;;

E 0 c

E

.,

3

c:r::

C;;

E 0

-2.49

e

- P, Throwaway put, have slack worth P,

Exercile can, get stockworth 'P,

CHAPTER 19

. . THE BLACK-SCHOLES MODEL FOR CALL OPTIONS Consider what would happen with the binomial option pricing model if the number of periods before the expiration date were allowed to increase. For example, with Widget's option for which the expiration date was a year in the future, there could be a price tree with periods for each one of the approximately 250 trading days in a year. Hence there would be 251 possible year-end prices for Widget stock. Needless to say, the fair value of any call associated with such a tree would require a computer to perform calculations such as those shown earlier for Widget. If the number of periods were even larger, with each one representing a specific hour of each trading day, then there would be about 1,750 (=7 X250) hourly periods (and 1,751 possible yearend prices). Note that the number of periods in a year gets larger as the length of each period gets shorter. In the limit there will be an infinite number of infinitely small periods (and, consequently, an infinite number of possible year-end prices). In this situation the BOPM given in Equation (19.7) reduces to the Black-Scholes model, so named in honor of its originators. 12

19.6.1

The Formula

In a world not bothered by taxes and transaction costs, the fair value of a call option can bc estimated by using the valuation formula developed by Black and Scholes. It has becn widely used by those who deal with options to search for situations in which the market price of an option differs substantially from its fair value. A call option that is found to be selling for substantially less than its Black-Scholes value is a candidate for purchase, whereas one that is found to be selling for substantially more is a candidate for writing. The Black-Scholes formula for estimating the fair value of a call option v,. is: (19.10) where:

In(p,/E) + (R + .50"2)T d, =

O"VT In( P,/ E)

d2 = = d, -

(19.11)

+ (R - .50"2) T

O"VT O"VT.

(19.12a) (19.12b)

and where:

p, ;::: .cun'ent,market price of theundei'lyiug stoek: " E = exercise price of the option R = continuously compounded riskfree rate of return expressed on an annual basis T = time remaining before expiration, expressed as a fraction of a year (T = risk of the underlying common stock, measured by the standard deviation of the continuously compounded annual rate of return on the stock and commonly referred to as voladUty Note that E/e R T is the present value of the exercise price where a continuous discount rate is used. The quantity In(p,/E) is the natural logarithm of P,/E. Finally, Options

623

TABLE

d -2.95 -2.90 -2.85 -2.80 -2.75 -2.70 -2.65

-2.60 -2.55 -2.50 - 2.45 -2.40 -2.35 -2.30 -2.25 -2.20 -2.15 -2.10 - 2.05

-2.00 -1.95 -1.90 -1.85 -1.80 -1.75 -1.70 -1.65 -1.60 -1.55 -1.50 -1.45 -1.40 -1.35 -1.50 -1.25 -1.20 -1.15 -1.10 -1.05 Source: Sioc/u.

19.2 Nld)

.0016 .0019 .0022 .0026 .0030 ~ OO35

.0040 .0047 .0054 .0062 .0071 .0082 .0094 .0107 .0122 .0139 .0 158

.01'19 .0202 .0228 .0256 .0287 .0322 .0359 .0401 .0446 .0495 .0548 .0606 .0668 .0735 .0808 .0885 .0968 .1057 .1151 .1251 .1357 .1469

Values of Nld' for Selected Values of d d

NidI

d

NidI

-1.00 - .95 -.00 -.85 -.80 -.75 -.70 - .65 -.60 -.55 . -.50

.1587 .1711 .1841 .1977 .2119 .2266

1.00

.8413 .8531

-.45 -.40 - .35

- .30 -.25 -.20 - .15 -.10 -.05 .00 .05 .10 .15 .20 .25 .30 .35 .4t) .45 .50 .55 .60

.65 .70 .75 .80 .85 .90 .95

.2420 .2578 .2743 .2912 .5085 .3264 .344.6 .3632 .3821 .4013 .4207 .4404

1.05 1.10 1.15 1.20 1.25 1.50 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85

.4602 .4801

1.90

.5000

2.00

.5199 .5398 .5596 .5793 .5987 .6179 .6368 .6554 .6736 .6915 .7088 .7257 .7422 .7580 .7734 .7M] .8023 .8159 .8289

2.05 2.10 2.15 2.20 2.25 2.30 2.35

&mds. lJillJ. find [nflu'ion /997 Yfflrboo.t (Chicilgo: Ibbotson Associate s,

1.95

2.49 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95

.8643

.8749 .8849 .8944 .9032 .9115 .9192 .9265 .9332 .9394 .9452 .9505 .9554 .9599 .9641 .9678 .9713 .9744 .9773 .9798 .9821 .9842 .9861 .9878 .9893 .9906 .99 18 .9929 .9938 .9946 .99 53 .9960

.9965 .9970 .9974 .9978 .9981 .9984

IlJlJ7) . A1I righu reserv ed .

N(d!) and N(~) denote the probabilities that outcomes of less than d, and d2 , respectively, will occur in a normal distribution that has a mean of 0 and a standard deviation of 1. Table 19.2 provides values of N( d1 ) for various levels of d!. 13 Only this table and a pocket calculator are needed to use the Black-Scholes formula for valuing a call option. With this formula the interest rate R and the stock volatility a are assumed to 624

CHAPTER 19

be constant over the life of the option. (More recently formulas have been developed where those assumptions are relaxed.) For example, consider a call option that expires in three months and has an exercise price of$40 (thus T = .25 and E = $40). Furthermore, the current price and volatility of the underlying common stock are $36 and 50% , respectively, whereas the riskfree rate is 5% (thus P,; = $36, R = .05, and (T = .50). Solving Equations (19.11) and (19 .12b) provides the following values for d, and d2 : d) =

In(36/40)

+ [.05 + .5(.50?].25

= -.25

.50 V25 d2

= - .25 - .50 V25 = - .50

Now Table 19.2 can be used to find the corresponding values of N(d)) and N(d l )

N( d.J

= N(-.25) = .4013

N(d.l ) = N(-.50)

=

.3085

Finally, Equation (19.10) can be used to estimate the fair value of this call option:

Y,.

=

(.4013 X $36) -

= $14.45

(e.!5~~25

X .3085 )

- $12.19 = $2.26

If this call option is currently selling for $5, the investor should consider writing some of them because they are overpriced (according to the Black-Scholes model), suggesting that their price will fall in the near future. Thus the writer would receive a premium of $5 and would expect to be able to enter a closing buy order later for a lower price, making a profit on the difference. Conversely, if the call option were selling for $1, the investor should consider buying some of them because they are underpriced and can be expected to rise in value in the future.

19.6.2

Comparison with the Binomial Option Pricing Model

At this juncture the BOPM formula [given in Equation (19.7) where VI) is now denoted Y,.] can be compared with the Black-Scholes option pricing formula [given in Equation (19 .10)]: (19.7) (19.10) Comparison of the two equations shows the quantity N(d)) in Equation (19.10) corresponds to h in Equation (19 .7). Remember that h is the hedge ratio, so the quantity N(d]) in the Black-Scholes formula can be interpreted in a similar manner. That is, it corresponds to the number of shares that an investor would need to purchase in executing an investment strategy that was designed to have the same payoffs as a call option. Similarly, the quantity EN( d.l ) / eRT corresponds to B, the amount of money that the investor borrows as the other part of the strategy. Consequently, the quantity EN( d2 ) corresponds to the face amount of the loan, because it is the amount that must be paid back to the lender at time T, the expiration date. Hence eRT is the discount (or present value) factor, indicating that the interest rate on the loan is R Options

625

per period and that the loan is for Tperiods. Thus the seemingly complex Black-Scholes formula can be seen to have an intuitive interpretation. It simply involves calculating the cost of a buy-stock-and-borrow-money investment strategy that has the same payoffs at T as a can option. In the example, N(dl ) was equal to .4013 and EN(~)leIlT was equal to $12.19. Hence an investment strategy that involves buying .4013 shares and borrowing $12.19 at time 0 will have payoffs exactly equal to those associated with buying the call.!" Because this strategy costs $2.26, it follows that in equilibrium the market price ofthe call must also be $2.26.

19.6.3

Static Analysis

Close scrutiny of the Black-Scholes formula reveals some interesting features of European can option pricing. In particular, the fair value of a call option is dependent on five inputs: the market price of the common stock p" the exercise price of the option E, the length of time until the expiration date T, the riskfree rate R, and the volatility of the common stock a . What happens to the fair value of a call option when one of these inputs is changed while the other four remain the same? 1. The higher the price of the underlying stock p" the higher the value of the call option. 2. The higher the exercise price E, the lower the value of the call option. 3. The longer the time to the expiration date T, the higher the value of the can option. 4. The higher the riskfree rate R. the higher the value of the call option. 5. The greater the volatility a of the common stock, the higher the value of the call option.

Of these five factors, the first. three (p" E, and T) are readily determined. The fourth factor, the riskfree rate R, is often estimated by using the yield-to-maturity on a Treasury bill having a maturity date close to the expiration date of the option . The fifth factor, the volatility of the underlying stock a, is not readily observed; consequently various methods for estimating it have been proposed. Two of these methods are presented next.

19.6.4

Estimating a Stocks Volatility from Historical Prices

One method for estimating the volatility of the underlying common stock associated with a call option involves analyzing historical prices of the stock. Initially a set of n + 1 market prices on the underlying stock must be obtained from either financial publications or a computer database. These prices are then used to calculate a set of n continuously compounded returns as follows: T 1

= In

_ P,,_, ) ( P',-l

(19.13)

where P', and P',-I denote the market price of the underlying stock at times t and t - I, respectively. Here, In denotes taking the natural logarithm of the quantity p',j P',-l, which thus results in a continuously compounded return. For example, the set of market prices for the stock might consist of the closing price at the end of each of 53 weeks. If the price at the end of one week was $105 and the price at the end of the next week was $107, then the continuously compounded return for that week T, will be equal to 1.886% [= In (107/105)]. Similar calculations will result in a set of 52 weekly returns. 626

CHAPTER 19

Once a set of n returns on the stock has been calculated, the next step involves using them to estimate the stock's average return:

r:

1 = -

n

n

L

(19.14)

T/

1=1

The average return is then used in estimating the per period variance: that is, the square of the per period standard deviation: S

2 -_ - -1 - k.J ~ (r t n - 1

-

r,m )2

(19.15)

1=1

This is called the per period variance because its size is dependent on the length of time over which each return is measured. In the example, weekly returns were calculated and would lead to the estimation of a weekly variance. Alternatively, daily returns could have been used, leading to a daily variance that would be of smaller magnitude than the weekly variance. However, what is needed is not a weekly or a daily variance but an annual variance. This is obtained by multiplying the per period variance by the number of periods in a year. Thus an estimated weekly variance would be multiplied by 52 in order to estimate the annual variance (I2 (that is, (I2 = 52s 2 ) . lf' Alternative methods of estimating a stock's volatility exist. One such method involves subjectively estimating the probabilities of possible future stock prices. Another method involves combining the historical and subjective estimates of volatility. For any estimate of future uncertainty, historical data are likely to prove more helpful than definitive. And because recent data may prove more helpful than older data, some analysts study daily price changes over the most recent 6 to 12 months, sometimes giving more weight to more recent data than to earlier ones. Others take into account the price histories of related stocks and the possibility that a stock whose price has recently decreased may be more volatile in the future than it was in the past. Still others make explicit subjective estimates of the future, taking into account changes in uncertainty concerning the economy in general as well as un certainty in specific industries and in stocks . In some cases an analyst's estimate of a stock's volatility over the next three months may differ from that for the following three months, leading to the use of different values of (I for call options on the same stock that have different expiration dates.

19.6.5

The Market Consensus of a Stocks Volatility

Another way to estimate a stock's volatility is based on the assumption that a currently outstanding call option is fairly priced in the marketplace. Because this means that P; = 'V-, the current market price of the cal1 Pc can be entered on the left-hand side of Equation (19.10) in place of the fair value of the call v... Next al1 the other factors except for (I are entered on the right-hand side, and a value for (I, the only unknown variable, is found that satisfies the equation. The solution for (I can be interpreted as representing a consensus opinion in the marketplace on the size of the stock's volatility, and it is sometimes known as the stock's implied volatility. In For example, assume that the riskfree rate is 6% and that a six-month call option with an exercise price of $40 sells for $4 when the price of the underlying stock is $36. Different estimates of (I can be "plugged into" the right-hand side of Equation (19.10) until a value of $4 for this side of the equation is obtained. In this example an estimated value of.40 (that is, 40%) for (I will result in a number for the right-hand side of Equation (19.10) that is equal to $4, the current market price of the cal1 option that is on the left-hand side. The procedure can be modified by applying it to several cal1 or put options on the same stock. For example, (I can be estimated for each of several call options Options

627

on the same stock that have different exercise prices but the same expiration date . Then the resulting estimates for a can be averaged and, in turn, used to determine the fair value of another call option on the same stock having yet another exercise price but a similar expiration date. In the example, (T can he estimated not only for a six-month option having an exercise price of $40, but also for six-month options having exercise prices of $35 and $45. Then the three estimates of (J' can be averaged to produce a "best estimate" of (T that is used to value a six-month $50 option on the same stock. Alternatively, the procedure can be modified by averaging the estimates for (T associated with each of several expiration dates. In the example, (T can be estimated not only for a six-month option having an exercise price of $40 but also for a threemonth and a nine-month option that each have an exercise price of $40. The three estimates of (T can be averaged to produce a best estimate of (T that will subsequently be used to determine the fair value of a one-month $40 option on the same stock. There are other ways of using a set of estimates of (T that correspond to different call options on the same stock. Perhaps (T will be estimated for a set of calls having different expiration dates and different exercise prices, and then averaged. Perhaps (T will be estimated from historical returns using Equation (19.15), with the resulting figure averaged with one or more estimates of the stock's implied volatility. Although the evidence is still unclear, it appears that methods based on calculating implied volatility are better than methods based on historical returns. 17 It should be remembered, however, that all of these methods assume that volatility remains constant over the life of the option-an assumption that can be challenged.

19.6.6

More on Hedge Ratios

The slope of the Black-Scholes value curve at any point represents the expected change in the value of the option for each dollar change in the price of the underlying common stock. This amount corresponds to the hedge ratio of the call option and is equal to N(d 1) in Equation (19.10). As can be seen in Figure 19.6 (assuming that the market price of the call is equal to its Black-Scholes value), the slope (that

I Out of the Money

I

T

Intrinsic Value = P,- E I In the Money

L . . '- - - - , - - - - - '

At the Money Stock Price

Figure 19.6 Option Terminology for Calls

628

CHAPTER 19

is, the hedge ratio) of the curve is always positive. Note that if the stock has a relatively low market price, the slope will be near zero. For higher stock prices the slope increases and ultimately approaches a value of 1 for relatively high prices. Because the hedge ratio is less than 1, a $1 increase in the stock price will typically result in an increase in a call option's value of less than $1. However, the percentage ch ange in the value of the call option will generally be much greater than the percentage change in the price of the stock. It is this rel ationship that leads people to say that options offer high leverage. The reason for referring to the slope of the Black-Scholes value curve as the hedge ratio is that a "hedge" portfolio, meaning a nearly riskfree portfolio, can be formed by simultaneously writing one call option and purchasing a number of shares equal to the hedge ratio, N(d1 ) . For example, assume that the hedge ratio is .5, indicating that the hedge portfolio consists of writing one call and buying .5 shares of stock. Now if the stock price rises by $1, the value of the call option will rise by approximately $.50. The hedge portfolio would lose approximately $.50 on the written call option but gain $.50 from the rise in the stock's price. Conversely, a $1 decrease in the stock 's price would result in a $.50 gain on the written call option but a loss of $.50 on the half-share of stock. Overall, it can be seen that the hedge portfolio will neither gain nor lose value when the price of the underlying common stock changes by a relatively small amount.!" Even if the Black-Scholes model is valid and all the inputs have been correctly specified, risk is not permanently eliminated in the hedge portfolio when the portfolio is first formed (or, for that matter, at any time). There will still be risk because the hedge ratio will change as the stock price changes and as the life of the option decreases with the passage of time. In order to eliminate risk from the hedge portfolio, the investor will have to alter its composition continuously. Altering it less often will reduce but not completely eliminate risk.

19.6.7

Limitations on Use of the Black-Scholes Model

At first the Black-Scholes model might seem to have limited use, because almost all options in the United States are American options that can be exercised at any time up to their expiration date, whereas the Black-Scholes model applies only to European options. Furthermore, strictly speaking, the model is applicable only to options on stocks that will not pay any dividends over the life of the option. However, most of the common stocks on which options are written do in fact pay dividends. The first drawback of the Black-Scholes model-that it is applicable only to European options-s-can be dispensed with rather easily when the option is a call and the underlying stock does not pay dividends. The reason is that it is unwise for an investor holding an American call option on a non-dividend-paying stock to exercise it before maturity." Because there is no reason for exercising such an option before maturity, the opportunity to do so is worthless. Consequently there will be no difference in the valu es of an American and a European call option. In turn, the BlackScholes model can be used to estimate the fair value of American call options on non-dividend-paying stocks. The reason can be seen in Figure 19.6, but first some terminology must be introduced. A call option is said to be at the money if the underlying stock has a market price roughly equal to the call's exercise price. If the stock's market price is below the exercise price, the call is said to be out of the money, and if the market price is above the exercise price, the call is said to be in the money. Occasionally, finer gradations are invoked, and one hears of "near the money," "deep in the money," or "far out of the money." Options

629

As mentioned earlier, the value of an option if it were exercised immediately is known as its intrinsic value. This value is equal to zero if the option is out of the money. However, it is equal to the difference between the stock price and the exercise price if the option is in the money. The excess of the option's price over its intrinsic value is the option's time value (or time premium). As shown in Figure 19.3 (a), for call options at expiration the time value is zero. However, before then the time value is positive. Note that a call option's premium is simply the sum of its intrinsic and time values. An investor considering exercising a call option on a non-dividend-paying stock before its expiration date will always find it cheaper to sell the call option and purchase the stock in the marketplace. Exercising the call would result in the investor's losing the time value of the option (hence the expression that call options are "worth more alive than dead"). For example, consider a stock that has a current price of $110. If this stock has a call option with an exercise price of $100 that is selling for $14, then the intrinsic and time values of this option are $10 (=$110 - $100) and $4 (=$14 - $10), respectively. An investor who owns one of these calls could exercise it by spending an additional $100. However, it would be cheaper for the investor to get the share of stock by selling the call option and buying the share of stock in the marketplace, because the additional cost would be only $96 (=$110 - $14). The second drawback of the Black-Scholes model-that it is applicable only to non-dividend-paying stocks-cannot be easily dismissed, because many call options are written on stocks that will pay dividends over the life of the option. Some procedures have been suggested for amending this formula to value call options on such stocks.f" As will be seen shortly, European options on dividend-paying stocks can generally be valued using the Black-Scholes formula by making one simple alteration, but American options are more problematic.

19.6.8

Adjustments for Dividends

Thus far the issue of dividend payments on the underlying stock during the life of an option has been avoided. Other things being equal, the greater the amount of the dividends to be paid during the life of a call option, the lower the value of the call option because the greater the dividend that a firm declares, the lower its stock price will be. Options are not "dividend-protected," so this lower stock price will result in a lower value for the call option (and a higher value for put options). The simplest case is valuing European call options on dividend-paying stocks when the future dividends can be accurately forecast, both in size and date. An accurate forecast is often possible, because most options have an expiration date that is within nine months. In such cases, all that is done in valuing European call options is to take the current stock price, subtract from it the discounted value of the dividends (using the ex-dividend date and the riskfree rate for discounting), and insert the resulting adjusted price in the Black-Scholes call option formula along with the other inputs. The reason is quite straightforward. The current stock price can be viewed as consisting of two components: the present value of the known dividends that will be paid over the life of the option and the present value of all the dividends thereafter (see the discussion of dividend discount models in Chapter 17). Because the option is exercisable only at expiration, it is applicable to only the second component, whose current value is just the adjusted price. Thus, if the stock previously discussed that is currently priced at $36 will pay a dividend in six months of $1, its adjusted price is $35.025 given a riskfree rate of 5% [$35.025 = $36 - ($1/ e·05 X .5 )]. Consequently any European calls that expire in more than six months but before 630

CHAPTER 19

the next ex-dividend date can be valued by using the Black-Scholes call option formula and a current price of $35.025. When it comes to American call options, things are much more complicated because it may pay to exercise such an option just before an ex-dividend date. Earlier it was mentioned that, in the absence of dividends, an American call option would be worth at least as much "alive" (not exercised) as "dead" (exercised). When dividends are involved, however, the situation may be different. This difference is shown in Figure 19.7. The call option's value if exercised immediately, referred to as the option's intrinsic value, lies along the lower boundary OEZ If the option is allowed to live, its value will lie along the higher Black-Scholes curve, as shown in the figure. Imagine that the stock is currently priced at p. 1 and is about to go ex-dividend for the last time before the option's expiration. Afterward it can be expected to sell for a lower price PJ2 • The Black-Scholes formula can be used to estimate the option's value if it

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631

remains alive just after the ex-dividend date. In Figure 19.7, this alive value is P~ . If instead the option is exercisedjust before the ex-dividend date while the stock price is still P,l' the investor will obtain the dead value (that is, the intrinsic value) of p1. Because the investor is interested in maximizing the value of the option, exercising earlier or not involves comparing P~ and p1. If p1 is greater than P~ [as is the case in panel (a)], the option should be exercised now,just before the ex-dividend date; if p1 is less than P~ [as is the case in panel (b)], the option should not be exercised. Hence for an American call option on a dividend-paying stock, the possibility of early exercise must be taken into consideration." Fortunately, the BOPM is capable of handling such a situ ation.

l1li

THE VALUATION OF PUT OPTIONS Similar to a call option, a put option is said to be at the money if the underlying stock has a market price roughly equal to the put's exercise price. However, the terms out of the money and in the money have, in one sense, opposite meanings for puts and calls. In particular, a put option is out of the money if the underlying stock has a market price above the exercise price and is in the money if the market price is below the exercise price. Figure 19.8 provides an illustration of how these terms apply to a put option. An option's intrinsic value equals zero if the option is out of the money and equals the difference between the exercise price and the stock price if the stock is in the money. Thus, in another sense, the terms out of the money and in the money have similar meanings for puts and calls. As mentioned earlier, the excess of the price of a call or a put over this intrinsic value is the option's time value (or time premium) . As shown for calls and puts in panels (a) and (b) of Figure 19.3, respectively, the time value is 0 at expiration. However, Figures 19.6 and 19.8 show that the time value is generally positive before expiration. Note that an option's premium is simply the sum of its intrinsic value and its time value.

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Figure 19.8 Option Terminology for Puts

632

CHAPTER 19

19.7.1

Put-Call Parity

Consider a put and a call on the same underlying stock that have the same exercise price and expiration date. Earlier it was shown in Equation (19 .9) that thei r market prices should he related , with the nature of the relationship known as put-call parity. However, thi s relationship is valid only for European options on non-dividendpaying stocks. Equation (19.9) can be rearrauged in the following manner so that it can be used to estimate the value of Europeau put options: (19 .16) Thus the value of a put can be estimated by using either the BOPM or the Black-Scholes formula to estimate the value ofa matching call option, then adding an amount equal to the present value of the exercise price to this estimate, and finally subtracting from this sum an amount that is equal to the current market price of the underlying common stock. For example, consider a put option that expires in three months and has an exerci se price of $40, while the current market price and the volatility of the underlying common stock are $36 and 50%, respectively. It was shown earlier that, if the riskfree rate is 5%, the Black-Scholes estimate of the value for a matching call option is $2.26. Because the 5% riskfree rate is a continuously comrounded rate, the present value of the exercise price equals $39.50 [= $40/( e·0 5 X.2!i) • At this point, because it has been determined that ~ = $2.26, tiel/T = $39.50, and P; = $36, Equation (19.16) call be used to estimate the value of the put option as being equal to $5.76 (=$2.26 + $39 .50 - $36) . Alternatively, the Black-Scholes formula for estimating the value ofa call given in Equation (19.10) can be substituted for P; in Equation (19.16). After the substitution the resulting equation ca n be used directly to estimate the value of a put. That is: (19.17) where d, and d2 are given in Equations (19.11) and (19.12a) , respectively. In the previous example, d, = - .25 and d2 = - .50; thus N( -d l ) N(.25) = .5987 and N( -d.2 ) = N(.50) = .69 15. With the application of Equation (19.17), the value of this put can be estimated directly: ) If, = ( e $40 - ($36 X .5987) 0!iX.25 X .69 15 = $27.31 - $21.55 = $5 .76 which is the same estimated value as indicated earlier when Equation (19. I 6) was used.

19.7.2

Static Analysis

Close scrutiny of the put-call parity equation reveals some interesting features ofEuropean put option pricing. In particular, the value of a put option is dependent on the values of the same five inputs used for call valuation: the market price of the common stock P, the exercise price of the option E, the length of time until the expiration date T, the riskfree rate R, and the volatility of the common stock a . What happens to the value of a put option when one of these inputs is changed while the other four remain the same? 1. The higher the price of the underlying stock put option.

Options

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the lower the value of the

633

2. The higher the exercise price E, the higher the value of the put option. 3. In general , but not always, the longer the time to the expiration date T, the higher the value or the put option . 4. The higher the riskfree rate R, the lower the value of the put option . 5. The greater the volatility (J of the common stock, the higher the value of the put option. The relationships for the underlying stock price P; exercise price E, and riskfree rate R are in the opposite direction from those shown earlier for cal1 options; the relationships for the time to the expiration date T and volatility (J are in the same direction. Exceptions can occur with T when the put is deep in the money. In such a situation a longer time to expiration could actually decrease the value of the put.

19.7.3

Early Exercise and Dividends

Equations (19.16) and (19.17) apply to a European put on a stock that wil1 not pay dividends before the option 's expiration. As with call options, it is straightforward to handle European put'; if there are dividends that will be paid on the underlying common stock during the option's life, provided they can be accurately forecast. All that needs to be done is to follow the same procedure as described earlier for calls: Reduce the current stock price by the present value of the dividends that are to be paid during the option's life, and then use this adjusted price in the Black-Scholes put option formula along with the other inputs. However, complications arise when it is recognized that most put options are American, meaning that they can be exercised before expiration, and that often dividends on the underlying common stock will be paid before the expiration date. Consider first the ability to exercise a put option at any time up to its expiration date. Earlier it was shown that if there were no dividends on the underlying stock, then a call option was worth more alive than dead, meaning that call options should not be exercised before expiration. Such an argument does not hold for put options . Specifically, if a put option is in the money, meaning that the market price of the stock is less than the exercise price, then the investor may want to exercise the put option. In doing so , the investor will receive an additional amount of cash equal to E - P; In turn, this cash can be invested at the riskfree rate to earn money over the remaining life of the option . Because these earnings may be greater than any additional profits received by the investor if the put option were held, it may be advantageous to exercise the put early and thereby receive the earnings. An example can be used to illustrate the point. Consider a put option on Widget that has a year left until its expiration date. The exercise price on the put is $100, and the annual riskfree rate is 10%. Imagine that the stock price of Widget is now at $5 per share, having recently plunged in value. If an investor owned such a deep-inthe-money option, it would be in his or her best interest to exercise it immediately. The logic is as follows. The intrinsic value of the put is currently $95 (=$100 - $5), indicating that if the put is exercised immediately, the buyer will receive $95. That is, the buyer will spend $5 to buy a share of Widget and then turn the share and the put over to the writer in return for the exercise price of $100. The net cash inflow to the put buyer of $95 could be invested in the riskfree asset so that in one year it would be worth $104.50 (= $95 X 1.10). Alternatively, if the put is held, what is the best that the buyer can hope to earn at year-end? If the stock price of Widget drops to $0, the buyer will receive $100 at expiration from the put writer. Clearly the buyer would be better off exercising the put now instead of holding onto it. Hence early exercise is merited in such a situation. 634

CHAPTER 19

What will happen to the market price of the put in such a situation? In equilibrium it will be equal to the put's intrinsic value E - P, (in this instance, $95) . Hence the put's time premium would be zero because nobody would pay more than the intrinsic value for the put, knowing that a better return could be obtained by investing in the riskfree asset. In addition, nobody would be willing to sell a put for less than its intrinsic value because doing so would open up the opportunity for immediately earning riskfree profits by purchasing the put and exercising it right away. Hence the only price that the put could sell for would be its intrinsic value. Consider next the impact of dividends on put valuation. Previously it was shown that the owner of a call may find it optimal to exercise just beJorean ex-dividend date, because doing so allowed the investor to receive the forthcoming dividends on the stock. With respect to a put, the owner may find it optimal to exercise just after the ex-dividend date, because the corresponding drop in the stock price will cause the value of the put to rise. 22 In summary, the uncertainty of when to exercise makes American puts difficult to value regardless of whether the underlying stock pays dividends. Fortunately, as it is for calls, the BOPM is capable of handling such situations.

__

INDEX OPTIONS

Not all options are written on individual issues of common stock. In recent years many new options have been created that have as an underlying asset something other than the stock of a particular company. One of them-index options-is discussed here. The appendix discusses others, and the next chapter discusses what are known as futures options.

19.8.1

Cash Settlement

A call option on General Motors stock is a relatively simple instrument. Upon exercise, the call buyer literally calls away 100 shares of GM stock. The call writer is expected to physically deliver the shares. In practice, both the buyer and the writer may find it advantageous to close their positions in order to avoid the costs associated with the physical transfer of shares. In this event the buyer may expect a gain (and the seller a loss) approximately equal to the difference between the current market price of the security and the option's exercise price, with a net gain equal to this amount less the premium that was paid to purchase the call. It would be entirely feasible to use only a "cash settlement" procedure upon expiration for any option contract. The writer would be required to pay the buyer an amount equal to the difference between the current price of the security and the call option's exercise price (provided that the current price is larger than the exercise price). Similarly for puts, the writer could be expected to pay the buyer an amount equal to the difference between the option's exercise price and the current market price (provided that the exercise price is larger than the current price). Although listed options on individual securities retain the obligation to "deliver," the realization that cash settlement can serve as a substitute has allowed the creation of index options.

19.8.2

The Contract

An index option is based on the level of an index of stock prices and thus allows investors to take positions in the market that the index represents . Some indices are designed to reflect movements in the stock market, broadly construed. Other "specialized" indices are intended to capture changes in the fortunes of particular industries or sectors. Figure 19.9 shows two of the major indices on which options

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635

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636

CHAPTER 19

were offered in 1997, along with their quotations. Some indices are highly specialized, consisting of only a few stocks. Others are broadly representative of major portions of the stock market. Roughly one-half are European and the other half are American . In general, the options expire within a few months, but a few expire in up to two years. Contracts for index options are not stated in terms of numbers of shares. Instead, the size of a contract is determined by multiplying the level of the index by a multiplierspecified by the exchange on which the option is traded. The premium (price) of an index option times the applicable multiplier indicates the total amount paid. Consider, for example, the Dow Jones Industrial Average (DJX) index call option that is traded on the Chicago Board Options Exchange with an exercise price of 80 and expiring in December 1997. Note that it had an indicated premium of 4 ~ on October 7,1997. Because the multiplier for these contracts is 100, an investor would have to pay $450 (=4.5 X 100) for this contract (plus a commission) . After purchasing this contract, the investor could later sell it or exercise it for its cash settlement value. Perhaps in November 1997 the Dow will be at 8500. In this case the investor could exercise the call, receiving its intrinsic value of $500 [= (85 - 80) X 100] for doing so . Alternatively, the investor could simply sell the call on the exchange. In doing so, the investor would almost certainly receive an amount greater than $500 because the call would sell for an amount equal to the sum of its intrinsic and time values (see Figure 19.6).

19.8.3

Flex Options

In an effort to counteract the growing off-exchange over-the-counter market for customized call and put options, the CBOE now lists "flexible option contracts," called "flex options" for short. These contracts are on individual stocks or indices, and they allow an investor (typically an institution) to specify the exercise price and expiration date. In addition , the investor can specify whether the option is American (exercisable at any time) or European (exercisable only at expiration). Once the investor has placed the order, it is executed on the CBOE, where someone else takes the other side of the contract. Because the OCC is in the middle between the buyer and the writer, there is little risk of default on the contract. This is an advantage to these customized options, because options created off-exchange (say between investors A and B) are only as good as the creditworthiness of the parties themselves. (The possibility that the writer of one of these off-exchange options may default on his or her obligations is referred to as counterparty risk. 2:J )

. . PORTFOLIO INSURANCE In the mid-1980s one of the more popular uses of options was a strategy called portfolio insurance, which is a way of synthetically creating a put on a given portfolio. Consider an investor who holds a highly diversified portfolio. This investor would like to be able to benefit from any upward movements that may subsequently occur in the stock market but would also like to be protected from any downward movernents.i" There are, in principle, at least two ways this goal might be accornplished.P

19.9.1

Purchase a Protective Put

Assume that the investor's portfolio is currently worth $100,000 and that a put option is available on a stock market index that closely resembles the investor's portfolio. The investor's portfolio will have a value indicated by the line OBC in Figure 19.1O(a) if Options

637

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nothing is done. The kinked line ADEin Figure 19.10(b) shows the value to a buyer of the index put at the expiration date, where the put has an exercise price of $100,000. What would happen to an investor who (1) held the portfolio and (2) purchased this put? Figure 19.10(c) shows the answer. The value of the portfolio (ABC) is simply the sum of the values OBCand ADEshown in Figures 19.1O(a) and (b). In this case the purchase of a put provides protection against declines in portfolio value. In this role it is termed a protective put (or "married put") . In practice, stock indices may not closely correspond with an investor's portfolio. Thus the purchase of a put on a stock index may provide only imperfect insurance. In a graph such as that shown in Figure 19.1O(c), the resulting curve would be somewhat fuzzy owing to the possible divergence of values of the portfolio and the index. For example, the portfolio may decline in value by $25,000, whereas the index might decline by only $10,000. In this case the portfolio would be insured for only 40% (=$10,000/$25,000) of its decline in value. What if an appropriate put were not available? Can something still be done to insure the portfolio's value against market declines? Yes, if the allocation of funds between the portfolio and a riskless security can be altered frequently enough (and at reasonable cost) . This type of portfolio insurance involves the creation of a synthetic put, and its application involves the use of a dynamic strategy for asset allocation, which will be discussed next. 638

CHAPTER 19

19.9.2

Create a Synthetic Put

Insuring a portfolio by creating a synthetic put can most easily be described with an example."! Assume that the investor ha s $100,000 and is considering the purchase of a portfolio of common stocks. It is believed that the market value of this portfolio will either increase to $125,000 or decrease to $80,000 in six mon ths . If it does increase to $125,000, then it will end up being worth either $156,250 or $100,000 after another six months. Alternatively, if it decreases to $80,000, then it will subsequently end up being worth either $100,000 or $64,000. Each one of these possible states of nature is indicated by a letter in Figure 19.11 (a), with the current state being denoted as stat e A. Figure 19.11(a) also shows two sets of terminal portfolio values (that is, portfolio values after 12 months) on the assumption that the common stock portfolio is purchased. The first set gives the values of the portfolio if it is uninsured . The second shows the desired portfolio values-that is, the values of an insured portfolio. In this example the investor wants to be certain that the ending portfolio is worth at least $100,000, while also being able to earn the returns associated with state D, should that state occur." What should the investor do initially in order to he certain of this outcome? Clearly, the investor cannot simply purchase the portfolio ofstocks because the portfolio would be worth only $64,000 ifstate Goccurs. However, the investor could purchase portfolio insurance-that is create a synthetic put-by investing in both the stock portfolio and riskfree bonds. (a)Ponfolio Value.

B

A

'125,000 - {

Uninsured Portfolio

Insu red Portfolio

$156,250

$156,250

SIOO,OOO

$100,000

F

$100,000

$100 ,000

Q.

$64,000

$100,000

:

$100,000

c

$80,000

-{

6 Months

Now

12 Months

(b) Asset AlI~on

B

A

Stocks : $66,138 Bonds: $40 ,312 Total : $106.450

[

Stocks: $125,000 Bonds: _ _ 0_ Total: $125,000

Stocks: 0 Bonds: S95,238 Total: $95,238 6 Months C

Now

Figure 19.11 Creation of a Synthetic Put Options

639

The way this is done is to imagine that six months have passed and that slate B has occurred. In this situation, how might one be certain to have $156,250 if the final state is D and $100,000 if the state is E? The answer is simple; if state B occurs, make sure that the portfolio at that point is worth $125,000. Thus an initial investment strategy is required that will provide $125,000 if the six-month state turns out to be state B. It is also possible that after the first six months state C will occur. In this situation, how might one be certain to have $100,000 regardless of the final state? If riskfree bonds return 5% (compounded discretely) per six months, the investor should purchase $95,238 (=$100,000/1.05) of these bonds ifstate C occurs. Consequently, an initial investment strategy is required that will provide $95,238 if the six-month state turns out to be state C. Figure 19.11(b) shows the investments and the amounts required in situations Band C. It remains only to determine an appropriate initial set of investments (at point A). An amount of $1 invested in the common stock portfolio at A will grow to $1.25 after six months if the state at that time is B. More generally, 5 invested in the common stock portfolio at A will grow to 1.255 if the six-man th state is B. Similarly, b invested in bonds at A will grow to 1.05h after six months. Thus, a set of initial investments 5 and b that will provide $125,000 if state B occurs must solve the following equation: 1.255

+

1.05b = $125,000

(19.18)

If the six-month state is C, then 5 invested in the common stock portfolio will be worth .85, while b invested in bonds will be worth 1.05b. Thus the set of initial investments 5 and b that will provide $95,238 if state C occurs must solve the following equation: .85

+

1.05b = $95,238

(19.19)

Actual solutions for 5 and b can now be found because there are two equations and two unknowns. The solution, shown in Figure 19.11(b), is that the investor should initially put $66,138 in common stocks and $40,312 in bonds (that is, 5 = $66,138 and b = $40,312), for a total initial investment of $106,450 (=$66,138 + $40,312). Making this initial investment is equivalent to investing $100,000 in the common stock portfolio and buying a protective put option (or an insurance policy) for $6,450. Indeed, this analysis could be used to determine the appropriate price for such an option. Equivalently, the actions of the investor have resulted in the creation of a synthetic put for which the stocks being held are the underlying asset. By design, this initial investment will provide precisely the desired ending values but only if the "mix" is altered as values change. The goal is achieved by using a dynamic strategy in which investments are bought and sold at intermediate points, depending on the returns of the underlying assets. In the example, if state B occurs, the stocks will be worth $82,672 (=$66,138 X 1.25), and the bonds will be worth $42,328 (=$40,312 X 1.05), for an aggregate value of $125,000. In this situation the $42,328 of bonds would be sold and the proceeds used to make an additional investment in the common stock portfolio so that the investor is entirely invested in common stocks for the last six months. However, if state C occurs, the stocks will be worth $52,910 (=$66,138 X .8) , and the bonds will be worth $42,328 (=$40,312 X 1.05), for an aggregate value of $95,238. In this situation the $52,910 of stocks would be sold and the proceeds used to make an additional investment in the riskfree bonds for the last six months. Thus more money is invested in common stocks if the initial portfolio rises in value , with the money obtained by seIling bonds. However, if the initial portfolio falls in value , 640

CHAPTER 19

more money is invested in bonds, with the money obtained by selling stocks . In this example the percentage invested in stocks is initially 62.13% (=$66,138/$106,450) and subsequently goes to either 100% (ifstocks go up) or 0% (ifstocks go down) with the reverse happening to the initial 37.87% investment in bonds. More realistic applications involve many time intervals within the one-year period, with smaller stock price movements in each interval. Consequently, there would be more changes in the mix of stocks and bonds after each interval, but the changes would be of smaller magnitude. Nevertheless, the essential nature of the strategy would be the same: When stock prices rise, sell some bonds and buy more stocks, When stock prices fall, sell some stocks and buy more bonds.

Often, computers are used to monitor stock price movements of investors who have obtained portfolio insurance in this manner. When these movements are of sufficient magnitude , the computer is used to place the requisite buy and sell orders electronically. Because much of this monitoring and ordering is programmed into a computer, portfolio insurance is often referred to as a form of program trading." If there are only two states of nature in each interval, and reallocation is possible after every interval, and there are no transaction costs, then the values associated with any desired "insured portfolio" can be replicated exactly with a dynamic strategy. In practice, however, the results are likely to be only approximately equal. First there are transaction costs associated with buying and selling securities for the dynamic strategy.~\J Second, if an interval is defined as a length of time over which only two alternative states may occur, then the amount of time to an interval may be so short that reallocation is impossible after each interval. In practice, arbitrary rules are applied to avoid frequent revisions and the associated high level of transaction costs while being reasonably certain of providing the portfolio with the desired level of insurance. 311 Unfortunately these arbitrary rules did not work very well on Black Monday (October 19, 1987) . During these two days stock prices moved downward so fast that reallocation could not be performed in a timely fashion , resulting in a situation in which portfolio insurance did not provide the protection that had been anticipated. As a result, dynamic strategies have been used much less frequently and to some extent have been replaced by index putS. 3 1

mil

SUMMARY

1. An option is a contract between two investors that grants one investor the right (but not the obligation) to sell to or buy from the other investor a specific asset at a specific price within a specific time period. 2. A call option for a stock gives the buyer the right to buy a specific number of shares of a specific company from the option writer at a specific price at any time up to and including a specific date . 3. A put option for a stock gives the buyer the right to sell a specific number of shares of a specific company to the option writer at a specific price at any time up to and including a specific date. 4. Option trading is facilitated by standardized contracts traded on organized exchanges. These exchanges employ the services of a dearing corporation, which maintains records of all trades and acts as a buyer from all option writers and a wri ter to all option buyers.

Opt ions

641

5. Option writers are required to deposit margin to ensure performance of their obligations. The amount and form of the margin will depend on the particular option strategy involved. 6. The intrinsic value of a call option equals the difference between the stock's price and the option's exercise price, if this difference is positive. Otherwise the option's intrinsic value is zero. 7. The intrinsic value of a pilI option equals the difference between its exercise price and the stock's price, if this difference is positive. Otherwise, the option's intrinsic value is zero. 8. Calls and puts will not sell for less than their intrinsic values. However, they may sell for more than their intrinsic values owing to their time values. 9. The binomial option pricing model can be used to determine the fair value of an option based on the assumption that the underlying asset will attain one of two possible known prices at the end of each ofa finite number of periods, given its price at the start of each period. 10. An option's hedge ratio indicates the change in the option's value resulting from a one dollar change in the value of the underlying asset. 11. The Black-Scholes option valuation model shows that the fair value of an option is determined by five factors : the market price of the stock, the exercise price, the life of the option, the riskfree rate, and the volatility of the common stock. It assumes that the riskfree rate and common stock vo la tility are constant over the option's life. 12. Put-call parity states that buying both a put option on a stock and a share of the stock will produce the same payoff as buying both a call option on the stock and a riskfree bond (assuming that both options have the same exercise price and expiration date). 13. In addition to put and call options on individual common stocks, options on other assets are traded, such as options on stock indices, debt instru me n ts, and foreign currency. 14. Synthetic options can be created by holding the underlying asset and a riskfree asset in relative amounts that vary with the market price of the underlying asset.

OUESTIONS

AND

PROBLEMS

1. Why have organized options exchanges been so important to the growth in options trading? 2. How do organized options exchanges permit option buyers and writers to open and close positions without having to contact one another directly? 3. Consider the following stocks selling for the prices listed below: Stock · A

Current Price S 26

·B

73

C

215

Specify the likely exercise prices that will be set for newly created options on these stocks. 4. From the latest two consecutive issues of The Wall Streetjournal; find the price of the General Motors call option with the nearest expiration date and the exercise price closest to the current price of GM stock. What is the premium on the call option? What has been the percen rage change in the option's price from the previous day? From another part oftheJouma~ calculate the percentage change in 642

CHAPTER 19

the price of GM stock from the previous day. Compare this number with the option's percentage price change. 5. Draw a profit-loss graph for the following option strategies: a. Buya put, $2 premium, $70 exercise price b. Write a call, $3 premium, $40 exercise price c. Buy a stock for $80 and buy a put on the same stock, $1 premium, $70 exercise price 6. Elizabeth Stroud had only a few hours left to decide whether to exercise a call option on Carson Company stock. The call option has an exercise price of $54. Elizabeth originally purchased the call six months ago for $400 (or $4 per share). a. For what range of stock prices should Elizabeth exercise the call on the last day of the call's life? b. For what range of stock prices would Elizabeth realize a net loss (including the premium paid for the call)? c. If Elizabeth had purchased a put instead of a call, how would your answers to parts (a) and (b) change? 7. On November 18, three call options on Eden Prairie Associates stock, all expiring in December, sold for the following prices:

8. 9.

10.

11.

Exercise Price

Option Price

$50 60 70

$7-~

3 l-~

Firpo Marberry is considering a "butterfly spread" that involves the following positions: Buy 1 call at $50 exercise price. Sell (write) 2 calls at $60 exercise price. Buy 1 call at $70 exercise price. a. What would be the values at expiration of Firpo's spread if Eden Prairie Associates' stock price is below S50? Between $50 and $60? Between $60 and $70? Above $70? b. What dollar investment would be required of Firpo to establish the spread? What is the time value of an option? Why does an option's time value decline as the option approaches expiration? Shorewood Systems stock currently sells for $50 per share. One year from today the stock will be worth either $58.09 or $43.04. The continuously compounded riskfree rate is 5.13% for one year. On the basis of the binomial option pricing model, what is the fair value for a call option on Shorewood stock with one year to expiration and a $50 exercise price? Hopkins Pharmaceuticals stock is currently priced at $40 per share. Six months from now its price will be'either $44.21 or $36.19. If the price rises to $44.21, then six months later the price will be either $48 .86 or $40. If, however, the price initially falls to $36.19. then six months later the price wiII be ei ther $40 or $32.75. The riskfree rate (continuously compounded) is 3.05% over each six-month period. Use the binomial option pricing model to determine the fair value of a one-year call option on Hopkins stock. Given the information below, calculate the three-month call option price that is consistent with the Black-Scholes model:

p, = 47,

E

= 45,

R

= .05,

(T

= .40

12. If the premium on a call option has recently declined, does this decline indicate that the option is a better buy than it was previously? Why? Options

643

13. List the variables needed to estimate the value of a call option . Describe how a change in the value or these variables affects the value of a call option. 14. Calculate the hedge ratio ofa call option for a stock with a current price of $40, an exercise price of $45 , a standard deviation of 34%, and a time to expiration of six months, given a riskfree return of 7% per annum . 15. Using the Black-Scholes model , calculate the implicit volatility ofa stock with a three-month call option cu rren tly selling for $8.54 and: I~

= $83,

E = $80,

R

= .05

16. Blondy Ryan owns 20,000 shares of Merrimac Monitoring Equipment stock. This stock makes up the bulk of Blondy's wealth . Concerned about the stock's nearterm prospects, Blondy wishes to fully hedge the risk of the stock. Given a hedge ratio of .37 and a prem ium of $2 .50 for the near Merrimac put option, how many put options should Blondy buy? 17. A six-month call option with an exercise price of $40 is selling for $5. The current price of the stock is $41.25. The hedge ratio of the option is .65. a. What percentage change in the option's price is likely to accompany a 1% change in the stock's price? b. If the beta of the sto ck is 1.l0, what is the beta of the option? (Hint: Recall what the beta of a stock implies about the relationship between the stock's price and that of the rnarket.) 18. The fair value of a three-month call option on Portage Industries stock is $1.50. The exercise price of the call option is $30. The riskfree rate is 5%, and the stock price of Portage is currently $28 per share. What is the fair value of a three-month put option on Portage stock with the same exercise price as the call option? 19. Given the following information, calculate the three-month put option price that is consistent with the Black-Scholes model :

p. = $32,

E = $45,

R

= .06,

(J'

= .35

20. Explain why call options on non-dividend-paying stocks are "worth more alive than dead." 21. In February Gid Gardner sold a September 55 call on Dane Corporation stock for $4.375 per share and simultaneously bought a September 55 put on the same stock for $6 per share. At the time, Treasury bills coming due in September were priced to yield 12.6%, and Dane stock sold for $53 per share. a. What value would put-call parity suggest was appropriate for the Dane put? b. Dane was expected to make three dividend payments between February and September. Could that account for the discrepancy between your answer to part (a) and the actual price of the put? Why o r why not? c. If Dane stock were to fall to a ver), low value before September, might it pay for Gid to exercise the put? Why? 22. Why does a stock index option sell at a lower price than the cost of a portfolio of options on the constituent stocks (assuming that the index call option and the portfolio of call options control the same dollar value of stocks)? 23. Distinguish between portfolio insurance implemented through a protective put and through dynamic asset allocation . 24. (Appendix Question) What is the primary advantage to an investor ofa warrant compared with a call option? 25. (Appendix Question) Wheeling Corp. has a 10% subordinated convertible debenture outstanding, maturing in eight years. The bond's face value is $1,000. It currently sells for 99 of par. The bond is convertible into 15 shares of common stock. The company's common stock currently sells for $50 per share. Nonconvertible bonds of similar risk have a yield of 12%. 644

CHAPTER J 9

a. What is the bond's conversion value? b. What is the bond's conversion premium? c. What is the bond's investment value?

ApPENDIX SECURITIES WITH QPTIONLIKE FEATURES

Many securities have features that are similar to stock options, particularly call options. In some cases the option like features are explicit. Examples include options on stock market indices (discussed earlier in the chapter), debt instruments, and foreign currencies." These options let investors take positions based on their forecasts of movements of the stock market, interest rates, and foreign exchange rates. In other cases more subtle optionlike features are involved. This appendix discusses some of these securities.

_

WARRANTS

A stock purchase warrant (or, more simply, a warrant) is a call option issued by the firm whose stock serves as the underlying security. At the time of issue, a warrant usually has a longer time to expiration (for example, five or more years) than a typical call option or even a LEAP option. Some perpetual warrants, with no expiration date, have also been issued. In general, warrants may be exercised before expiration-that is, they are like American call options-but some require an initial waiting period. The exercise price may be fixed, or it may change during the life of the warran t, usually increasing in steps. The initial exercise price is typically set to exceed the market price of the underlying security at the time the warrant is issued, often by a substantial amount. At the time of issue, one warrant typically entitles the holder to purchase one share of stock for the appropriate exercise price. However, most warrants are protected against stock splits and stock dividends. This means that any warrant with such protection will enable the investor to buy more or less than one share at an altered exercise price if a stock dividend or stock split is declared. For example, a two-for-one stock split would allow the warrant holder to purchase two shares at one-half the original exercise price, whereas a one-far-two reverse stock split would allow the warrant holder to purchase one-half share at twice the original exercise price. Warrants may be distributed to stockholders in lieu of a stock or cash dividend or sold directly as a new security issue. Alternatively, warrants may be issued in order to "sweeten" an offering of some other kind of security. For example, a bond may be Options

645

sold by the firm with warrants attached to it. In some cases, the warrants are nondetachable, except upon exercise; if an investor wants to sell one of the bonds, the warrants must be either exercised or sold with the bond. In other cases the warrants are detachable, meaning that after the initial sale of the bonds an investor may sell either the bonds or the warrants (or both) . Terms associated with a warrant are contained in a warrant agreement, which serves the same function as an indenture for a bond issue. In this agreement the scope of the warrant holder's protection is defined (for example, the treatment of warrants in the event of a merger). It may also specify certain restrictions on corporate behavior. Some warrants that are issued with bonds have an additional attribute. Although they may be detached and exercised by paying cash to the corporation, an alternative method of payment is provided. This alternative allows bonds from the initial issue to be used in lieu of cash to pay the exercise price, with the bonds being valued at par for this purpose. One difference between warrants and call options is the limitation on the amount of warrants that are outstanding. A specific number of warrants of a particular type will be issued. The total generally cannot be increased and typically will be reduced as the warrants are exercised. In contrast, a call option can be created whenever two people wish to create one. Thus the number outstanding is not fixed. Exercise of a call option on its stock has no more effect on a corporation than a transaction in its stock on the secondary market. However, the exercise of a warrant does have an effect. In particular, it leaves the corporation with more cash, fewer warrants outstanding, and more stock outstanding. Warrants are traded on major stock exchanges and on the over-the-counter market. Quotations for those with active markets are provided in the financial press in the sections devoted primarily to stocks.

__

RIGHTS A right is similar to a warrant in that it also is like a call option issued by the firm whose stock serves as the underlying security. Rights, also known as subscription warrants, are issued to give existing stockholders their preemptive right to subscribe to a new issue of common stock before the general public is given an opportunity. Each sh are of stock receives one right. A stated number of rights plus cash equal to a specified subscription price are required in order to obtain one new share. The sale of the new stock is ensured by setting the subscription price below the stock's market price at the time the rights are issued. New subscribers do not get a bargain, however; they must pay old stockholders for the required number of rights, which become valuable as a result. Rights generally have short lives (from two to ten weeks when issued) and may be freely traded before exercise. Up to a specified date, old shares ofthe stock trade cum rights, meaning that the buyer of the stock is entitled to receive the rights when issued. Afterward the stock trades ex rights at a correspondingly lower price. Rights for popular issues of stock are sometimes traded on exchanges; others are available in the over-the-counter market. Often trading begins before actual availability, with the rights sold for delivery on a when-issued basis. A right is, in effect, a warrant, although one with a rather short time before expiration. It also differs with regard to exercise price, which is typically set above the stock's market price at issuance for a warrant and below it for a right. Because of their short lives, rights need not be protected against stock splits and stock dividends. Otherwise they have all the attributes of a warrant and can be valued in a similar manner/" 646

CHAPTER 19

. . BOND CALL PROVISIONS Many firms issue bonds with call provisions that allow the firm to repurchase the bonds before maturity, usu ally at a price above par value . This amounts to the simultaneous sale of a straight bond and purchase of a call option that is paid by the corporation in the form of a relatively lower selling price for the bond. The writer of the option is the bond purchaser. Bond call provisions usually can be exercised only after some specified date (for example, five years after issue). Moreover, the exercise price, known as the call premium, may be different. for different. exercise dates (typically shrinking in size the longer the bond is outstanding). The implicit call option associated with such a bond is thus both longer-lived and more complex than those traded on the listed option markets.t"

II1II

CONVERTIBLE SECURITIES

A particularly popular financial instrument is a security that can be converted into a different security of the same firm under certain conditions. The typical case involves a bond or a preferred stock convertible into shares of the firm's common stock, with a stated number of shares received for each bond or share of preferred stock. Usually no cash is involved: the old security is simply traded in, and the appropriate number of new securi ties is issued in return. Convertible preferred stocks are issued from time to time, but tax effects make them, like other preferred stock, attractive primarily to corporate investors. For other investors, issues of convertible bonds are more attractive. If a $1 ,000 par value bond can be converted into 20 shares of common stock, the conversion ratio is 20. Alternatively, the conversion price may be said to be $50 (= $1,000/20), because $50 of the bond's par value must be given up to obtain one common share. Neither the conversion ratio nor the conversion price is affected by changes in a bond's market value. Conversion ratios and conversion prices are typically set so that conversion will not prove attractive unless the stock price increases substantially from its value at the time the convertible security was first issued. This is similar to the general practice used in setting exercise prices for warrants. A convertible bond's conversion value, obtained by multiplying the conversion ratio by the stock's current market price , is the value that would be obtained by conversion; it is the bond's current "value as stock." The conversionpremium is the amount by which the bond's current market price exceeds its conversion value, expressed as a percent of the latter. A related amount is the convertible's investment value. This value is an estimate based on the convertible's maturity date, coupon rate, and credit rating of the amount for which the bond might sell ifit were not convertible. Equivalently, it is the convertible's "value as a straight bond." Consider a $1,000 par value bond convertible into 20 shares of stock. If the market price of the stock is $60 per share, then the conversion value of the bond is $1,200 (=$60 X 20). If the current market price of the convertible bond is $1,300, then its conversion premium is $100 (=$1,300 - $1,200). Its investment value might be estimated to be, say, $950, meaning that the bond would sell for this much if it did not provide the investor with the option of convertibility. Convertible securities of great complexity can be found in the marketplace. Some may be converted only after an initial waiting period. Some may be converted at any time up to the bond's maturity date ; others, only for a stated, shorter period. Some have different conversion ratios for different years. A few can be converted Options

647

into packages of two or more different securities; others require the additional payment of cash upon conversion. Convertible bonds are usually protected against stock splits and stock dividends via adjustment in the conversion ratio. For example, a bond with an initial conversion ratio of20 could be adjusted to have a ratio of22 following a 10% stock dividend. Protection against cash dividends is not generally provided, but some indentures require that the holders of convertible bonds be notified prior to payment of cash dividends so that they may convert before the resultant fall in the stock's market price. Convertible securities often contain a call provision, which may be used by the corporation to force conversion when the stock's market price is sufficiently high to make the value of the stock obtained on conversion exceed the call price of the bond. For example, if the conversion value of the bond is $1,200 (the bond is convertible into 20 shares of stock that are currently selling for $60 per share) and the call price is $1,100, the firm can force conversion by calling the bond. The reason this provision forces conversion is that a bondholder faces two choices when the call is received--either convert and receive 20 shares collectively worth $1,200 or receive cash of $l,100-and should choose the shares because they have a higher value . A convertible bond is, for practical purposes, a bond with nondetachable warrants plus the restriction that only the bond is usable (at par) to pay the exercise price. If the bond were not callable, the value of this package would equal the value of a straight noncallable bond (that is, the estimated investment value) plus that of the warrants. However, most convertible bonds are callable and thus involve a double option: The holder has an option to convert the bond to stock, and the issuing corporation has a n option to buy the bond back from the investors. ENDNOTES

Before 1973, options were traded over the counter through the efforts of dealers and brokers in a relatively illiquid market. These dealers and brokers brought buyers and writers together, arranged terms, helped with the paperwork, and charged fees for their efforts, 2 However, there is protection lor any cash dividend that is formally designated a "return of capital." Furthermore, options that are traded over the counter typically are protected from any type of cash dividend. In both cases the protection is in the form of a reduction in the exercise price. 3 For some active stocks, options may be introduced that have only one or two months to expiration . 4 If the stock sells for less than $25, then the interval may be $2.50 (for example, at $15 and $17.50 for a stock selling at $16). If the stock sells for more than $200, the interval will be $10 (or perhaps even $20). Exchange officials have discretion in setting the terms of the options. 5 For more on commissions, see John C. Hull, Options, Futures and Other Derivatives, (Upper Saddle River, NJ, Prentice Hall, 1997), pp. 147-148. 6 A call or put buyer is not allowed to use margin. Instead, the option buyer is required to pay 100% of the option's purchase price. In contrast, the stock buyer can use margin , where part of the cost of purchasing the stock is borrowed. For the specifics on margin requirements, see the option textbooks cited at the end of the chapter. 7 Because the premium is paid by the buyer to the writer at the time the option is created, its value should be compounded to the expiration date using an appropriate rate of interest when calculating profits and losses . S Strips and straps are option strategies similar to a straddle . The forme r involves combining two PUL~ with one call, and the latter involves combining two calls with one put. Another kind of strategy is known as a spread, where one call is bought while another is written on the same underlying security. Specifically, a price spread involves two calls having the same expiration date but different exercise prices . A time spread involves two calls having the same exercise price but different expiration dates. I

648

CHAPTER 19

9

If there are dividends, they should be expressed as a compounded value at the expiration date associated with the options (as they would have been previously received) and added to the line , thereby shifting it upward.

general, $1 will grow to $lil T at the end of Tperiods if it is continuously compounded at a rate of R per period . Here e represents the base of the natural logarithm, which is equal to approximately 2.71828. For a more detailed discussion, see the Appendix to Chapter 5. 1\ Equations (19 .5) and (19.6) can be derived by solving the set of Equations (19 .3a) and (l9.3b) using symbols instead of numbers. 12 Fischer Black and Myron Scholes, "The Pricing of Options and Corporate Liabilities," journal cfPolitiral Economy 81 , no. 3 (May/June 1973) : 637--654. Also see Fischer Black, "How We Came Up with the Option Formula," joumal ofPortjolio Management 15, no . 2 (Winter 1989): 4-8, and "How to Use the Holes in Black-Scholes,"joumal of Applied Corporate Finance 1, no. 4 (Winter 1989): 67-73. For an intuitive explanation ofthe Black-Scholes formula, see Dwight Grant, Gautaru Vora, and David Weeks, "Teaching Option Valuation: From Simple Discrete Distributions to Black/Scholes via Monte Carlo Simulation," Financial Practice and Education 5, no. 2 (Fall/Winter 1995): 149-155. Scholes and Robert Merton were the co-recipients of the 1997 Nobel Prize in Economic Science, largely for their contributions in this area. Undoubtedly, Black would have shared the Prize with them had he not suffered an untimely death. 1:1Table 19.2 is an abbreviated version of a standard cumulative normal distribution table. More detailed versions can be found in most statistics textbooks. H The investment strategy is more complicated than it might appear because the number of shares that are to be held will change over time as the stock price changes and the expiration date gets closer. Similarly, the amount of the loan will change over time . Hence it is a dynamic stmtegy. 15 If daily data are used, it is best to multiply the daily variance by 250 instead of 365 because there are about 250 trading days in a year. See Mark Kritzman, "About Estimating Volatility: Part I," Financial Analystsjoumal47, no . 4 (July/August 1991) : 22-25; and "About Estimating Volatility: Part II," Financial Analystsjoumal47, no. 5 (September/October 1991): 10-11. For a method of estimating (J' that uses high, low, opening, and closing prices as well as trading volume , see Mark B. Garman and Michael]. Klass, "On the Estimation of Security Price Volatilities from Historical Data," joumal of Business 53, no. 1 (January 1980) : 67-78. 16 Alternatively, Equation (19 .10) could be solved for the interest rate R; doing so gives an estimate of the implied interest rate. See Menachem Brenner and Dan Galai, "Implied In terest Rates," [oumnl ofBusiness 59, no . 3 (July 1986) : 493-507 . 17 For a further discussion of these methods, see any of the options textbooks cited at the end of the chapter, or see Menachem Brenner and Marti Subrahrnanyam, "A Simple Formula to Compute the Implied Standard Deviation," Financial Analystsjoumal44, no. 5 (September/October 1988) : 80-83; and Charles]. Corrado and Thomas W. Miller Jr., "A Note on a Simple Accurate Formula to Compute Implied Standard Deviations, " joumal ofBanking and Finance 20, no . 3 (April 1996): 595-603. 18 This explanation of a hedge ratio follows from the BOPM-based interpretation of the BlackScholes formula that was given earlier. That is, if a call's payoffs can be duplicated by buying stock and borrowing at the riskfree rate, it follows that buying stock and writing a call will duplicate investing in the riskfree asset. 19 See Robert C. Merton, "Theory of Rational Option Pricing," Belljoumal of Economics and Management Science A, no. 1 (Spring 1973) : 141-183. 20 These procedures are reviewed in the options textbooks cited at the end of the chapter. 21 See Thomas]. Finucane, "An Empirical Analysis of Common Stock Call Exercise: A Note," joumal ofBanking and Finance 21, no. 4 (April 1997): 563-571. 22 See Robert Geske and Kuldeep Shastri, "T he Early Exercise of American Puts," joumal of Banking and Finance 9, no. 2 (June 1985) : 207-219. 23 For a discussion of how the possibility of default by the writer affects the prices of options, see HerbJohnson and Rene Stulz, "The Pricing of Options with Default Risk,"joumal ofFinance42, no. 2 (June 1987): 267-280. 10 In

Options

649

24

In an efficient market, investors with "average" attitudes toward risk should not purchase portfolio insurance. Those who are especially averse to "downside risk" (relative to "upside potential") may find it lise t"1I I to buy insurance. The key is the investor's attitude toward risk and return. See Hayne E. Leland, "Who Should Buy Portfolio Insurance?" journal of Finance 35, no . 2 (May 1980) : 581-5!H. people would argue that the use of Stop orders or geuing an insurance company to sell the investor a policy represent two other ways.

25 Some

26

For an exposition, see Mark Rubinstein and Hayne E. Leland, "Replicating Options with Positions in Stock and Cash," Financial Analysts joumn! 37, no . 4 Uuly/August 1981): 63-72 ; Mark Rubinstein, "Alternative Paths to Portfolio Insurance," Financial Analysts./ournal4l, no.4 (july/August 1985) : 42-52; Robert Ferguson, "How to Beat the S&P SOO (Without Losing Sleep)," Financial AnIlZ";.lts'/ournal 42, no. 2 (March /April 1986) : 37-46; and Thomas J. O'Brien, "The Mechanics of Portfolio Insurance," [ournal ofPortfolio Management 14, no. 3 (Spring 1988): 40-47 .

27

In th is example, portfolio insurance is sought for a one-year horizon with a floor of 0% (meaning that the investor docs not want to lose any of the initial investment over the next 12 months). Other horizons and floors, such as a two-year horizon with a floor of -5 % (meaning that the investor does not want to lose more than 5% of the initial investment over the next 24 months), are possible. Note the parallel to thc discussion of the BOPM, which provides a theoretical basis for the development of portfolio insurance .

2MThe

29

next chapter discu sses another form of program trading that is known as index arbitrage,

There is another dynamic strategy for insuring the portfolio that is often preferred because it has smalle r transaction costs. It involves index futures, which are a type of financial contract that is discussed in the next chapter. For a survey of dynamic trading strategies, see Robert R. Trippi and Richard B. Harriff, "Dynamic Asset Allocation Rules: Survey and Synthesis," [ournnl ofPortfolio Manaeement 17, no. 4 (Summer 1991) : 19-26.

so For a discussion of transaction COSL~, seejohn E. Gilsterjr., and William Lee, "The Effects of Transactions Costs and Different Borrowing and Lending Rates on the Option Pric ing Model : A Note," journal of Finance 39, no. 4 (September 1984): 1215-1222; Hayne E. Leland, "Option Pricing and Replication with Transactions COSL~," [ourna! ofFinance 40, no . 5 (December 1985) : 1283-130J ; Fischer Black and Robert jones, "Simplifying Portfolio Insurance," journal of Portfolio Management 14, no. I (Fall 1987) : 48-51 ; and Phelirn P. Boyle and Ton Yorst, "Option Replication in Discrete Time with Transactions Costs,"journal ofFinanre47, no. 1 (March 1992): 271-293. ~ l See Mark Rubinstein, "Portfolio Insurance and the Market Crash," Financial Arudystsjour-

na144 , no . I (january/February 1988) : 38-47. For a discussion of various types of dynamic strategies, see Andre F. Perold and William F. Sharpe, "Dynamic Strategies for Asset Allocation," Financial A nalys tsjournal 44 , no. 1 (Ianuary/February 1988) : 16--27; and Philip H. Dybvig, "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," Review of Finan cial Studies 1, no. I (Spring 1988): 67-88. :12 See

the textbooks cited at the end of the chapter for more on these types of options. For mo re on foreign exchange options, see Ian Giddy, "The Foreign Exchange Option A~ a Hedging Tool," Midland Corporate Fmancejournal i, no. 3 (Fall 1983): 32-42; Niso Abauf, "Foreign Exchange Options: The Leading Hedge," Midland Corporate Finance joumal S, n o. 2 (Summer 1987): 51-58; and Mark Kritzrnan, "About Option Replication," Financial AnalystsJournal48, no . I (lanuarv/February 1992): 21-23.

:1:1

Rights are also discussed in Chapter 16. Valuation of rights is relatively simple if it is assumed that there is no chance that they will end up being out of th e money on the expiration date and the time value of money is ignored (meaning that the riskfree rate is assumed to be zero).

:14

Bond call and put provisions are discussed in Chapters 13 and 14.

650

CHAPTER 19

I(EY

TERMS

option call option exercise price expiration date premium closing sale closing purchase put option floor traders floor brokers market-makers order book officials intrinsic value naked call writing naked put writing

straddle covered call writing European options American options hedge ratio put-call parity implied volatility at the money out of the money in the money time value counterparty risk portfolio insurance syn thetic put program trading

REFERENCES

l. Investment strategies involving options are discussed in many papers. Here are three of

the most notable ones: Robert C. Merton, Myron S. Scholes, and Mathew L. Gladstein, "The Returns and Risk of Alternative Call Option Portfolio Investment Strategies," [ournal ofBusiness 51, no. I (April 1978): 183-242. Robert C. Merton, Myron S. Scholes, and Mathew L. Glad stein, "The Returns and Risk of Alternative Put-Option Portfolio Investment Strategies," Journal ofBusiness 55, no . 1 (January 1982): I-55. Aimee Gerbcrg Ronn and Ehud I. Ronn, "The Box Spread Arbitrage Conditions: Theory, Tests, and Investment Strategies," Review of Financial Studies 2, no. 1 (1989): 91-107. 2. A description and comparison of the specialist and market-maker systems for trading options are presented by: Robert Neal, "A Comparison of Transaction Costs between Competitive Market-Maker and Specialist Structures," journal of Business 65, no. 2 (July 1992) : 3 I7-334. 3. The binomial option pricing model was initially developed in: William F. Sharpe, Inuestments (Englewood Cliffs, !'!J: Prentice Hall, 1978), Chapter 14. 4. A short while later the following two papers expanded upon Sharpe's model: John C. Cox, Stephen A. Ross, and Mark Rubinstein. "Option Pricing: A Simplified Approach ...[ournal ofFinancial Economics 7, no. 3 (September 1979) : 229-263. Richard.J. Rendleman Jr., and Brit J. Barner, "Two-State Option Pricing," [ournni of Finnnce 34, no. 5 (December 1979) : 1093-1110. 5. For more on the theory of binomial models, see: Daniel B. Nelson and Krishna Ramaswamy, "Simple Binomial Processes As Diffusion Approximations in Financial Models," Review ofFinancial Studies 3, no. 3 (1990) : 393-430. 6. Two seminal papers on option pricing are: Robert C. Merton, "Theory of Rational Option Pricing," BellJournal ofEconomics and Management Science 4, no. 1 (Spring 1973) ; 141-183. Fischer Black and Myron Scholes, "The Pricing of Options and Corporate Liabilities," Journal of Political Er.onomy 81. no . 3 (May/June 1973): 637-654. 7. The Black-Scholes option pricing model assumes that the riskfree rate is constant over the life of the option. Four interesting papers that relax this assumption are: Ramon Rabinovitch, "Pricing Stock and Bond Options When the Default-Free Rate Is Stochastic," Journal ofFinancial and Q}tantitative Analysis 24, no. 4 (December 1989) : 447-457.

Options

651

Stuart M. Turnbull and Frank Milne, "A Simple Approach to Interest-Rate Option Pricing," Reoieui ofFinnncial Studies A, no. 1 (1991): 87-121. Jason Z. Wei, "Valuing American Equity Options with a Stochastic Interest Rate: A Note," Journal oJFinancialJ~n",rinel'ring2,no. 2 (June 1993): 195-206. T. S. Ho, Richard C. Stapleton. and Marti G. Subrahmanyam, "The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-johnson Technique," Journal ojFinance 52, no. 2 (June 1997): 827-840. 8. The Black-Scholes model also assumes that the volatility of the underlying asset is constant over the life of the option. For papers that relax this assumption, see: Andrew A. Christie, "The Stochastic Behavior of Common Stock Variances: Value, Leverage, and Interest Rate Effects,"Joumal oJFinancial Economics 10, no. 4 (December 1982): 407-432. John Hull and Alan White, "The Pricing of Options on Assets with Stochastic Volatilities," Journal oJFinance42, no. 2 (June 1987): 281-300. HerbJohnson and David Shan no, "Option Pricing When the Variance Is Changing," Journal ojFinancial and Quantitative Analysis 22, no. 2 (June 1987): 143-151. Louis O. Scott, "Option Pricing When the Variance Changes Randomly: Theory, Estimation, and an Application," Journal ojFinancial and Quantitative Analysis 22, no. 4 (December 1987): 419-438. James B. Wiggins, "Option Values under Stochastic Volatility: Theory and Empirical Estimates,"Journal cfFinancial Economics 19, no. 2 (December 1987): 351-372. Marc Chesney and Louis Scott, "Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model," Journal oj Financial and Quantitative Analysis 24, no. 3 (September 1989): 267-284. Thomas]. Finucane, "Black-Scholes Approximations of Call Option Prices with Stochastic Volatilities: A Note," [ournal oJFinancial and Quantitative Analysis 24, no. 4 (December 1989): 527-532. Steven L. Heston, "A Closed-Form Solution for Options in Stochastic Volatility with Applications to Bond and Currency Options," Review ojFinancial Studies 6, no. 2 (1993): 327-343. Stephen Figlewski, "Forecasting Volatility," Financial Markets, Institutions & Instruments 6, no. 1 (1997): 1-88. 9. For an interesting paper on static analysis of calls, see: Don M. Chance, "Translating the Greek: The Real Meaning of Call Option Derivatives," Financial AnalystsJournal50, no. 4 (July/August 1994): 43-49. 10. Portfolio insurance has received much attention. In addition to the citations given in the chapter, see: M.]. Brennan and R. Solanki, "Optimal Portfolio Insurance," Journal oj Financial and Quantitative Analysis 16, no. 3 (September 1981): 279-300. Ethan S. Etzioni, "Rebalance Disciplines for Portfolio Insurance," Journal ojPortfolio Management 13, no. 1 (Fall 1986): 59-62. Richard]. Rendelman Jr. and Richard McEnally, "Assessing the Costs of Portfolio Insurance," Financial AnalystsJournal43, no. 3 (May/June 1987): 27-37. C. B. Garcia and F.]. Gould, "An Empirical Study of Portfolio Insurance," Financial AnalystsJournal43, no. 4 (July/August 1987): 44-54. Robert Ferguson, "A Comparison of the Mean-Variance and Long-Term Return Characteristics of Th ree Investmen t Strategies," Financial AnalystsJournal 43, no. 4 (July/August 1987): 55-66. Fischer Black and RobertJones, "Simplifying Portfolio Insurance,"Journal ojPortfolio Management 14, no. 1 (Fall 1987): 48-51. Yu Zhu and Robert C. Kavee, "Performance of Portfolio Insurance Strategies," Journal oj Portfolio Management 14, no. 3 (Spring 1988): 48-54. Fischer Black and RobertJones, "Simplifying Portfolio Insurance for Corporate Pension Plans," Journal oj Portfolio Management 14, no. 4 (Summer 1988): 33-37.

652

CHAPTER 19

Thomas]. O'Brien, How Option RepliCaling PortfolioInsurance Works: Expanded Details, Monogrdph Series in Finance and Economics No . 1988-4 (New York University Salomon Center, Leonard N. Stern School of Business, 1988) . Erol Hakanoglu, Robert Koppraseh, and Emmanuel Roman, "Constant Proportion Portfolio Insuran ce for Fixed-Income Investment," Joumal of Portfolio Management IS, no. 4 (Summer 1989) : 58-66. MichaelJ. Brennan and Eduardo Schwartz, "Portfolio Insurance and Financial Market Equilibrium," Joumal of Business 62 , no. 4 (October 1989) : 455-472. SanfordJ. Grossman and Jean-Luc Vila, "Po rtfo lio Insurance in Complete Markets: A Note,".Ioumal of Business 62, no. 4 (October 1989): 473-476. Robert R. Trippi and Richard B. Harriff, "Dynamic Asset Allocation Rules : Survey and Synthesis," [oumal of Portfolio Management 17, no. 4 (Summer 1991): 19-26. CharlesJ.Jacklin , Allan W. Kleidon, and Paul Pfleiderer, "U nderestimation of Portfolio Insurance and the Crash of October 1987," Review ofFinancial Studies 5, no. 1 (1992): 35-63. 11. A great deal ha s been written on warrants and convertibles. For an introduction to this

literature, see : Richard A. Brealey and Stewart C. Myers, Principles of Corporate Finance (New York : McGraw-Hill, 1996), Chapter 22 . Stephen A. Ross, Randolph W. Westerfield, and Jeffrey Jaffe, Corporate Finance (Boston : Irwin McGraw Hill, 1996), Chapter 22. 12. Man y textbooks are devoted exclusively to options or have options as one of their primary subjects. Most cover everything discussed in this chapter but in more detail and with a more complete list of citations. Here are a few: RobertA.Jarrow and Andrew Rudd, Option Pricing (Homewood, IL: Richard D. Irwin, 1983) . John C. Cox and Mark Rubinstein, Options Markets (Englewood Cliffs, N.J: Prentice Hall, 1985). Richard M. Bookstaber, Option Pricing and Investment Strategies (Chicago: Probus Publishing, 1987). Peter Ritchken, Options: Theory, Strategy, and Applications (Glenview, IL: Scott, Foresman, 1987) . Robert W. Kolb, Options: An Introduction (Miami : Kolb Publishing, 1991). Alan L. Tucker, Financial Futures, Options, and Swaps (St. Paul, MN: West Publishing, 1991). David A. Dubofsky, Options and Financial Futures (New York: McGraw-Hill, 1992). Han s R. Stoll and Robert E. Whaley, Futures and Options (Cincinnati: South-Western Publishing, 1993). Don M. Chance, An Introduction to Derivatives (Fort Worth: Dryden Press, 1995). Fred D. Arditti, Derivatives (Boston: Harvard Business School Press, 1996) . Robert jarrow and Stuart Turnbull , Derivative Securities (Cincinnati: South-Western Publishing, 1996). John C. Hull, Options, Futures, and Other Derivative Securities (Upper Saddle River, N.J: Prentice Hall, 1997). 13. The various exchanges where options are traded all have Web sites containing useful information about their products (the New York Stock Exchange withdrew from the option trading business in 1997): American Stock Exchange: (www.amex.com). Chicago Board Options Exchange: (www.cboe.com). Pacific Exchange: (www.pacificex.com). Philadelphia Stock Exchange: (www.phlx.com).

Options

653

CHAPTER

Z

0

FUTURES

Consider a contract that involves the delivery of some specific asset by a seller to a buyer at an agreed-upon future date. Such a contract also specifies the purchase price, but the asset is not to be paid for until the delivery date. However, the buyer and the seller will both be requested to make a security deposit at the time the contract is signed. The purpose of this deposit is to protect each person from experiencing an}' losses should the other person renege on the contract. Hence the size of the deposit is checked daily to see that it provides sufficient protection. Ifit is insufficient, it will have to be increased. If it is more than sufficient, the excess can be withdrawn. These contracts are often referred to as futures (short for futures contract), and in the United States they involve assets such as agricultural goods (for example, wheat), natural resources (for example, copper), foreign currencies (for example, Swiss francs), fixed-income securities (for example, Treasury bonds), and market indices (for example, the Standard & Poor's 500).1 As with options, standardization of the terms in these contracts makes it relatively easy for anyone to create and subsequently trade the contracts.

Ell

HEDGERS AND SPECULATORS There are two types of people who deal in futures (and options): speculators and hedgers. Speculators buy and sell futures for the sole purpose of making a profit by closing out their positions at a price that is better than the initial price (or so they hope) . Such people neither produce nor use the asset in the ordinary course of business. In contrast, hedgers buy and sell futures to offset an otherwise risky position in the spot market. In the ordinary course of business, they either produce or use the asset.

20.1.1

Example of Hedging

For example, consider wheat futures. A farmer might note today that the market price for a wheat futures contract with delivery around harvest time is $4 per bushel, a price that is high enough to ensure a profitable year. The farmer could sell wheat futures today. Alternatively the farmer could wait until harvest and at that time sell the wheat on the spot market (which involves the immediate exchange of an asset 654

for cash). However, waiting until harvest entails risk because the spot price (the purchase price of an asset) of wheat could fall by then, perhaps to $3 per bushel. Such a fall would bring financial ruin to the farmer. In contrast, selling wheat futures today will allow the farmer to "lock in" a $4 per bushel selling price. Doing so would remove an element of risk from the farmer's primary business of growing wheat. Thus a farmer who sells futures is known as a hedger or, more specifically, a short hedger. Perhaps the buyer of the farmer's futures contract is a baker who uses wheat in making bread. Currently the baker has enough wheat in inventory to last until harvest season. In anticipation of the need to replenish the inventory at that time, the baker could buy a wheat futures contract today at $4 pe r bushel. Alternatively, the baker could simply wait until the inventory runs low and then buy wheat in the spot market. However, there is a chance that the spot price will be $5 per bushel at that time. If it were, the baker would have to raise the selling price of bread and perhaps lose sales in doing so . Alternatively, by purchasing wheat futures, the baker can "lock in" a $4 per bushel purchase price, thereby removing an element of risk from the bread business. Thus a baker who buys futures is also known as a hedger or, more specifically, a long hedger.

20.1.2

Example of Speculating

The farmer and the baker can be compared to a speculator-a person who buys and sells wheat futures, based on the forecast price of wheat, in the pursuit of relatively short-term profits. As mentioned earlier, such a person neither produces nor uses the asset in the ordinary course of business. A speculator who thinks that the price of wheat is going to rise substantially will buy wheat futures. Later this person will enter a reversing trade by selling wheat futures. If the forecast was accurate, a profit will have been made on an increase in the wheat futures price. For example, consider a speculator expecting at least a $1 per bushel rise in the spot price of wh eat. Whereas this person could buy wheat, store it, and hope to sell it later at the anticipated higher price, it would be easier and more profitable to buy a wheat futures con tract today at $4 per bushel. Later, if the spot price of wheat did rise by $1, the speculator would enter a reversing trade by selling the wheat futures contract for perhaps $5 per bushel. (A $1 rise in the spot price of wheat will cause the futures price to rise by about $1.) Thus the speculator will make a profit of$1 per bushel, or $5,000 in total , because these contracts are for 5,000 bushels. As will be shown later, the speculator might need to make a security deposit of$I,OOO at the time the wheat futures contract is bought. This deposit is returned when the reversing trade is made, so the speculator's rate of return is quite high (500%) relative to the percentage rise in the price of wheat (25%) . Alternatively, if a speculator forecasts a substantial price decline, then initially wheat futures would be sold. Later the person would enter a reversing trade by purchasing wheat futures . If the forecast was accurate, a profit will have been made on the decrease in the wheat futures price.

_

THE FUTURES CONTRACT

Futures contracts are standardized in terms of delivery as well as the type of asset that is permissible for delivery. For example, the Chicago Board of Trade specifies the following requirements for itsJuly wheat contract: Futures

655

1. The seller agrees to deliver 5,000 bushels of either no. 2 soft red wheat, no. 2 hard red winter wheat, no. 2 dark northern spring wheat, or no. 1 northern spring wheat at the agreed-upon price. Alternatively, a number of other grades can be delivered at specified premiums or discounts from the agreed-upon price. In any case, the seller is allowed to decide which grade shall be delivered. 2. The grain will be delivered by registered warehouse receipts issued by approved warehouses in Chicago or Toledo, Ohio. (Toledo deliveries are discounted $.02 per bushel.) 3. Delivery will take place during the month ofjuly, with th e seller allowed to decide the actual date. 4. Upon delivery of the warehouse receipt from the seller to the buyer, the latter will pay the former the agreed-upon price in cash .

After an organized exchange has set all the terms ofa futures contract except for its price, the exchange will authorize trading in the contract." Buyers and sellers (or their representatives) meet at a specific place on the floor of the exchange and try to agree on a price at which to trade. If they succeed, one or more contracts will be created, with all the standard terms plus an additional one-the price involved. Prices are normally stated on a per uni t basis. Thus if a buyer and a seller agree to a price of $4 per bushel for a contract of 5,000 bushels of wheat, the amount of money involved is $20,000. Figure 20.1 shows a set of daily quotations giving the prices at which some popular futures contracts were traded and the total volume of sales for each type of contract. Such listings of active futures markets are published regularly in the financial press, with each item for delivery (such as corn) having a heading that indicates the number of units per contract (5,000 bushels) and the terms on which prices are stated (cents per bushel). Below the heading for the asset are certain details for each type of contract. Moving from left to right in Figure 20.1, the first column shows the delivery dates for the contracts. For example, there are six different futures contracts for corn, each one involving the same item but having different delivery dates . Next comes open, denoting the price at which the first transaction was made on that day; high and law, representing the highest and lowest prices during the day; and settle (short for settlement price), a price that is a representative price (for example, the average of the high and low prices) during the "closing period" designated by the exchange in question (for example, the last two minutes of trading). After change from the previous day's settlement price come the highest and lowest prices recorded during the lifetime of the contract. The last column on the right shows the open interest (the number of outstanding contracts) on the previous day. For each futures contract, summary figures are given below the figures for the last delivery date. (In the case of corn, these summary figures are below the December 1998 delivery date figures.) They indicate the total volume (that is, the number of contracts) traded on that day and on the previous trading day as well as the total open interest in such contracts on that day and the change in total open interest from the previous day.

mil

FUTURES MARKETS The futures contracts shown in Figure 20.1 are traded on various organized exchanges. The Chicago Board of Trade (CBT) was the earliest one, founded in 1848, and currently is the largest futures exchange in the world. Other futures exchanges are listed in the lower right-hand corner of Figure 20.1. 656

CHAPTER 20

INTEREST RATE

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~ 351.00 15i·.oo m~oo ~:l~ : :: ~;:: t~ &~ :::: :::: ~:~ :~:: : :: :::

rc

JUOI

J1~,.,

+ 2JO 441.00 447.00 312.00 + 2.411 429.50 31".00

~f 'flol39,ooO; 'YOI iii i9.~:-:;" l~t~I2~~ .;f"~

CRUDE OIL, LlllltS.", INYM) NO't' 21.96 n.J4. 21.71 21.1' + DK 21.96 n.)O 21.n n,1J + JI9I 21.11 n.15 2l.6~ 21.97 + Fib 21.60 21.90 21.50 21.16 + Mar 21.411 2U' 21.304 21.51 + Apr 21.n 21.47 21.n 21.40 + M.y 21.(1 21.)0 21.01 21.23 + Junt 20,9'1 21.13 20.19 21.06 ... July 20.11 2O.fl 20.11 '20.91 + Aug 2O.n 20.19 2O.n 20.19 + Sept 2O.J,4 20.61 20.12 20.61 + Oct 20.50 20.60 20.50 20.55 + NO't' 20.«1 20.411 20.411 20.44 + Dec 20.20 20.)5 20.20 20.13 + J I99 20,27 + FHI 20,17 +

I• • bills.; I 0.22 21.15 0.1' n.95 0.16 n.65 0.13 n ,3O 0.11 n ,ns 0.10 21.1~ 0.09 21.S9 0.01 21.)5 0.01 nos 0.01 21.00 0.C16 20.12 0.05 20.75 0.04 20.63 O.OJ 20.7' (UD 20.17 G.lD 20.31

2.119 4.62.. 1,39'

per MI . 16,90 96.U9 16." 19.11' 11.0. 4.5.397 11.15 n,SCI 11.30 ,,,,290 11.31 11.21. 11.39 12,m 11.11 19.631 11.60 10.150 1'.80 1l.236 11.N 1-"" 11.11 .. It9 19.n tn. 11.os 23A01 n."50 " . . "'11

'1.1,

TREASURY 10NDS (CITHI.,,*, ph. nllllb .. l.' LIfCltlmt Open Open High L.ow Settlt ChenQle High Low Interett Dec 111·15 111-2. 115·22 115-29 - 4911"11 I~ 61M'" Mr9I 117-(11 117-1. 115-13 115-19 - 50111-(17 10HI 51,151 June . . 1Is-D1 - 50111·15 104-03 6.,310 SePI .. .. .. .. .." 110'·29 - SO 115-00 103-22 1,956 Dec ""-20 H4-20 n"·19 114-19 - 501160-\0 10.1-13 ".669 Eshol 758,(100; '101 TIWm .n6; open Inl 151,1", +1.203. TREASURY IIONDS IMCE)·ISCI.CIOCI: pli. !2ttdt.' I'"' Dec 111·21 111·2" 1I5·n 116-00 - 1511 .. 11 105-10 1".9t2 ElhcK 6,200: 'flolTu, • •939. ooenIn' 15,001, +21" . TREASURY NOTES ICIITHIOO,OOOi IJh. nndl.f Ion. Dec IlHJ9 111-1. 1IG-CJ9 ll G-13 - 21111-2'9 104·10 -400.001 Mr9I 111-03111-03 110-00 110- P'I - $50). Going long strategy 1 means that the investor is to do exactly what was indicated earlier-purchase the stocks in the S&P 500 and hold them until the December delivery date. Going short strategy 2 means to do exactly the opposite of what was indicated earlier. Specifically, the investor is to short (that is, sell) a December S&P 500 futures contract and sell Treasury bills that mature in December. (It is assumed that the investor has these in his or her current portfolio.) The net cash outflow of going long strategy 1 and short strategy 2 is zero; $1.000 is spent buying the stocks in going long strategy 1, which is obtained by selling $1 ,000 worth of December Treasury bills when the investor goes short strategy 2. The margin necessary for being short the futures contract is met by having purchased the underlying stocks . Thus no additional cash needs to be committed in order to engage in index arbitrage; all that is necessary is for the investor to own Treasury bills that mature in December. Next, consider the investor's position on the delivery date in December. First of all, the investor "bought" the individual stocks in the S&P 500 at $1.000 and "sold" them at $1,100 by being short the S&P 500 futures contract. Thus the investor has made $100 from being long the individual stocks and short the futures on the index. Second, the investor will have received dividends totaling $30 (=.03 X $1,000) from owning the stocks from June to December. Third. the investor will have given up $50 (= .05 X $1,000) in in terest that would have been earned on the December Treasury bills. This interest is forgone because the investor sold $1,000 of these Treasury bills inJune in order to get the requisite cash to buy the individual stocks. Overall, the investor has increased the dollar return that would have been made on the Treasury bills by $80 (=$100 + $30 - $50). Furthermore. this increase is certain, meaning that it will be received regardless of what happens to the level of the S&P 500. Thus by going long strategy 1 and short strategy 2 the investor will not have increased the risk of his or her portfolio but will have increased the dollar return .

Futures

679

Earlier it was mentioned that an investor going long strategy 1 would rec eive cash of P" + $30 in December, whereas an investor going long strategy 2 would receive cash of P" - $50 . It can now be seen that going long strategy 1 and short strategy 2 will provide a net dollar return of$80 [that is, (P" + $30) - (P" - $50)] .just as was shown in the previous paragraph. However, if enough investors do this , the opportunity for making the $80 profit will disappear. The reason is that (1) going long will push the prices of the individual stocks up, thereby raising the current level of the S&P 500 from 1000, and (2) going short the S&P 500 futures will push the price of the futures down from 1100. These two adjustments will continue until it is no longer profitable to go long strategy 1 and short strategy 2. What if the price of the S&P 500 December futures contract is $900 instead of $1 ,100? The net cash inflow from being long strategy 1 is still equal to P" + $30 . However, the net cash inflow from being long strategy 2 will be different. In particular, purchasing Treasury bills and the futures contract will provide the investor with P,I + $150 [that is, (P" - $900) + (1.05 X $1,000)] on the delivery date. Because these two inflows are not equal, again there is an opportunity for index arbitrage. However, it would involve the investor's going short strategy 1 and long strategy 2. Why? Because strategy I now has a lower payoff than strategy 2 (note that P" + $30 < P" + $150) . By doing this, the investor will, without risk, earn $120 [that is, (P" + $150) - (P" + $30)]. Furthermore, being short the individual stocks and long the futures will push the curren t level of the S&P 500 down from 1000 and the price of the futures up from 900. In equilibrium, because these two strategies cost the same to implement, prices will adjust so that their net cash inflows are equal. Letting y denote the dividend yield on the stocks in the index, Prthe current price of the futures contract on the index, and P, the curren t spot price of the index (that is, P, denotes the curren t level of the index), the net cash inflow from strategy 1 is:

P"

+ yP,

Letting R denote the interest rate on Treasury bills, the net cash inflow from strategy 2 is:

Setting these two inflows equal to each other results in: (20.11 ) Simplifying this equation results in: (20.12) or: (20.13) Equation (20.12) indicates that the difference between the price of the futures contract and the current level of the index should depend only on (1) the current level of the index P, and (2) the difference between the interest rate on Treasury bills and the dividend yield on the index R - y. A~ the delivery date nears, the difference between the interest rate and the dividend yield diminishes, converging to zero on the delivery date. Thus as the delivery date approaches, the futures price PJ should converge to the current spot price P j

680

•

CHAPTER 20

Equation (20 .13) shows that index futures are priced according to the cost of carry model given earlier in Equation (20.4). where the costs of ownership Care zero. Here the interest forgone by ownership I is equal to RPJ' whereas the benefit of ownership B is the dividend yield yP Hence the cost of carry is: J

•

Carry = RP, - yP,

(20.14)

which will be positive as long as the riskfree interest rate R is greater than the dividend yield on the index y-a situation that exists nearly all the time. In the example the interest rate was 5%, the dividend yield was 3%, and the curren t level of the S&P 500 was 1000. This means that the difference between the S&P 500 December futures contract and the current level of the S&P 500 should be 20 [= (.05 - .03) X 1000]. Equivalently, the equilibrium price of the futures contract when the S&P 500 is 1000 would be 1020 because the cost of carry is 20. Note that when three of the six months have passed, the interest rate and the dividend yield will be 2.5% (=5%/2) and 1.5% (=3%/2), respectively. Thus the difference should be about 10 [= (.025 - 015) X 1000], assuming that the S&P 500 is still at 1000 at that time. In practice, the situation is not this simple for a number of reasons. Positions in futures, stocks, and Treasury bills involve transaction costs .2 1 Consequently, arbitrage will not take place unless the difference diverges far enough from the amount shown in Equation (20.12) to warrant incurring such costs. The futures price, and hence the difference, can be expected to move within a band around the "theoretical value," with the width of the band determined by the costs of those who can engage in transactions most efficiently. To add to the complexity, both the dividend yield and the relevant interest rate on Treasury bills are subject to some uncertainty. Neither the amounts of dividends to be declared nor their timing can be specified completely in advance. Furthermore, because futures positions must be marked to market daily, the amount of cash required for strategy 2 may have to be varied by means of additional borrowing (if short this strategy) or lending (iflong this strategy). Also, on occasion market prices may be reported with a substantial time lag, making the current level and the futures price of the index appear to be out of line when they actually are not. (An extreme example of this situation occurred on Black Monday, October 19, 1987.) Thus an investor may enter into the transactions necessary for index arbitrage when actual prices are in equilibrium, thereby incurring useless transaction costs. Nevertheless, index arbitrage is still actively pursued, most notably by brokerage firms, as shown in Figure 20.6. Stock index futures are also used extensively by other professional money managers. As a result, prices of such contracts are likely to track their underlying indices very closely, taking into account both dividends and current interest rates. It is unlikely that a private investor will be able to exploi t "rnispricing" of such a contract by engaging in index a rbitrage. Nevertheless, sto ck index futures can provide inexpensive ways to take positions in the stock market or to hedge portions of the risk associated with other positions. Furthermore, their use can lower transaction costs by reducing the size of the bid-ask spread in individual securities, thereby benefiting investors who may never take direct positions in futures contracts.

__

FUTURES VERSUS OPTIONS

People occasionally make the mistake of confusing a futures contract with an options coruract.f With an options contract there is the possibility that both parties involved will have nothing to do at the end of the life of the contract. In particular, if Futures

681

PROGRAM TRADING NEW YORK - Program Iradlng In the week ended Ocl. 3, accounl.d lor 19.1%, or an average 105.8million dally sheres. 01 New York Stock Exchange volume. Brokerage Ilrms execuled an additional 51.7 million dally shernol program Iradlng away Irom lhe Big Board, mostly on lorelgn markets. Program Iradlng Is Ihe slmullaneous pur· cnasecr sele 01alleasl15 dlnerenl slocks wllh alolal value 01 S1 million or more . 01 Ihe program lolal on IIle Big Board, 13.9% Involved slock lnoex arbllrage. down Irom 15.6% lhe prior week. In Ihls stralegy. Iraders darl belween slocks and slock·lndex OPtions and lulures 10caplure tleellng price dlnerences. Some 76.6% 01 program Iradlng was execuled by Ilrms lor Ihelr customers, while 19.9% was done lor Ihelr own accounts . or prlnclpallradlng. Anolher 3.5% wu deslgnaled as customer lacllllallon, In which IIrms use principal posllions 10laclllla le cuslomer Irades. The reporl InclUdes a special profile ollradlng whenever the Oow Jones Induslrlal Average moves more than SO points In a single direction during anyone hour period. There were six such periods In lhe put week. Unless otherwise SIlIlCllled, all tlrms listed here execuled both buy and sell orders. The IIrsl period occurred on Monday when the DJIA moved up more Ihan SO POlnls. The lollowlng IIrms rePOrled making program Irades during 10:15 a.m, 10 11: 15 a.m.: BNP securl· lies (moslly buying). Nalwesl (moslly buying), Lawrence Heltanl. Bridge Trading (buying) and RBC Dominion (buyIng). The second period occurred on Tuesday when lhe DJIA moved down more Ihan SO points. The lollowlng IIrms rePOrled making program Ira des during 10 a.m, 10 11 a .m.: BNP securities. Donaldson Lulkln, Nalwesl, Merrill Lynch. and Susquehanna Brokerage Services. The Ihlrd period occurred on Wednesday when lhe OJ I A moved UP more than SO points. The lollowlng IIrms rePOrled making program trades during 9:30s.m. 10 10: 30 a.rn.: Merrill Lynch (moslly seiling), Inleracllve Brokers, BNP Securllies. Natwest , and Salomon Brofhers . The lourth period also occurred on Wednesday . The lollowIng IIrms reporled making program Irades during 2:30 p.m. to 4 e.m. when lhe DJIA moved UPmore Ihan SO POlnls: BNP Securities. Morgan Slanley, Nalwesl, W&Dsecurities (moslly buying), and Salomon Brolhers. The luI two periods occurred on Friday. The lollowlng IIrms rlPOrled making program Iredes during 9:30 a.m. 1o 10:30 e.m. when the DJIA moved uP more Ihan SOPOlnls: BNP securilles, Inleracllve Brokers (bUYing). Salomon Brothers, Merrill Lynch. and Susquehanna Brokerage Services . The lollowlng IIrms reporled making program trades durIng2 p.m.103 :30p .m . when lhe DJIA moved down more IhanSO POlnls: BNP securllies. Goldman Sachs (mostly seiling), Nomura Securilles. Natwesl, and Flrsl Boslon. 01 the live most acuve Ilrms , Nalwesl and Inleracllve Brokers executed all 01 lhelr program adlvlty lor cuslomers as agenl. BNP Securities, Morgen Slanley, and Salomon Brothers executed mosl 01 Ihelr program Iradlng lor cuslomers as agenl. NY5E PROGRAM TRADING Volume (In millions 01shares) lor Ihe week ending Odober 3. 1997 Index Derlvallve- other Top 15 Firms Arbltn,e Reilled' 5lrll..les Tolel BNP Securilles 146.5 146.5 NalWesl 16.2 0.5 SO.7 67.4 Morgan Slanley 1.9 0.7 40.8 43.4 Salomon Bros . 32.7 32.7 Inleracllve Brokers 29.1 29.1 FlrslBoslon 5.4 15.2 2D.6 Merrill Lynch 3.6 16.9 20.5 Susquehanna Bkrg svcs 10.6 8.0 18.6 W&DSecurities 16.8 16.8 Lehman Brolhers 1.9 3.0 7.7 12.6 Nomura Securities 6.5 5.2 11.7 Smith Bernev 11 .0 11.0 Goldman Sachs 8.B B.8 Soclele Generale 7.9 7.9 RBC Dominion 7.3 0.2 7.5 OVERALL TOTAL 73.B 7.9 ~7 .3 529.0 'Olher derlvallve-relaled slralegles besides Index arbitrage Source: New York Slock Exchange

Figure 20.6 Index Arbitrage as a Form of Program Trading Source: Repr int ed by permission of The Willi Stree! [ournnl; DowJones & Co mpany, Inc. , O ctober 10. 1997. p. C17.

the option is out of the money on the expiration date, then the options contract will be worthless and can be thrown away. However, with a futures contract, both parties involved must do something at the end of the life of the contract. The parties are obligated to complete the transaction, either by a reversing trade or by actual delivery. Figure 20.7 contrasts the payoffs for the buyer and the seller of a call option with the payoff for the buyer and the seller of a futures contract. Specifically, payoffs for 682

CHAPTER 20

(a) CaDOpdon :

(b) Futures Cootraa

Seller

c

:~

s

Exercise Price

Q.,

:~s

Contract

•

prT•••• ••• "'-Buyer

Q.,

'01--------'>.+----"---.., ::l

,Ol----~'-----~-­

..,

::l

~

~

./

Price of Asset in Deliver}' Month

Figure 20.7 Terminal Values of Positions in Calls and Futures

buyers and sellers are shown at the last possible moment-the expiration date for the option and the delivery date for the futures contract. As shown in Figure 20.7(a), no matter what the price of the underlying stock, an option buyer cannot lose and an option seller cannot gain on the expiration date. Option buyers compensate sellers for putting sellers in this position by paying them a premium when the contract is signed. The situation is quite different with a futures contract. As shown in Figure 20.7(b), the buyer may gain or lose, depending on the price of the asset in the delivery month . Whatever the buyer gains or loses, an exactly offsetting loss or gain will be registered by the seller. The higher the contract price (that is, the price of the futures contract when the buyer purchased it from the seller), the greater the likelihood that the buyer will lose and the seller will gain. The lower the contract price, the greater the likelihood that the seller will lose and the buyer will gain.

IZ!III

SYNTHETIC FUTURES

For some assets, futures contracts are unavailable, but both put and call options are available. In such cases, an investor can create a synthetic futures contract. The clearest example involves European options on common stocks. As shown in the previous chapter, the purchase of a European call option and the sale of a European put option at the same exercise price and with the same expiration date will provide a value at expiration that will be related, dollar for dollar, to the stock price at that time. This relation is shown in Figure 20.8. Panel (a) shows the payoff associated with the purchase of a call at an exercise price E, whereas panel (b) shows the payoff associated with the sale of a put at the same exercise price. The results obtained by taking both positions are shown by the solid line in panel (c). Depending on the prices (that is, premiums) of the call and the put, this strategy may initially either require a net outflow of cash or provide a net inflow. For comparability with the purchase of a futures contract, this cash flow may be offset with borrowing or lending as required to bring the net investment to zero. The dashed line in panel (c) shows a case in which the call option costs more than is provided by the sale of the put option. The difference is borrowed, requiring the loan repayment shown in the figure. The dashed line thus indicates the net end-of-period payoffs for a strategy requiring no initial outlay. Because these payoffs are equivalent to Futures

683

INSTITUTIONAL ISSUES

Transportable Alpha Years aj:{o trustees of the multi-billion General Mills pension fund adopted a disciplined approach to allocating assets among various broad categories was accomplished by establishing specific long-run allocation targets: 60% to common stocks and 40% to fixed-income securities. The trustees believe that this Iloliey asset allocation provides an optimal balance of expected return and risk, given their collective tolerance for possible adverse outcomes. The trustees expect the fund's staff, which handles the fund's day-to-day investment operations, to stick closely to this policy asset allocation. In turn, the staff follows a procedure of reducing exposure to any asset category that has appreciated in relative value and increasing exposure to any asset category that has depreciated in relative value. To manage the pension fund's assets, the staff had retained what the trustees considered to be a superior g-roup of domestic common stock managers. Over a ten-year period , those managers, in aggrej:{ate, had outperformed the S&P 500 by 1.5% annually (after all fees and expenses)-an exceptional amount by the standards of the investment management business . The trustees and staff expected such superior performance to continue in the future. More recently the trustees found themselves facing a dilemma: The trustees would have liked to have assigned more than 60 % of the fund's assets to the co m mo n stock managers. However, the trustees were also committed to the d iscipline of their asset allocation process. Could the trustees have their proverbial cake and eat it too? The answer was yes, through a concept called transportable alpha. Consider three strategies through which General Mills could have maintained its policy asset allocation yet taken advantage of its common stock managers' skills. Each strategy involves a llo ca ting more than 60% of the pension fund's assets to the common stock managers, while simultaneously reducing the pension fund's common stock exposure and increasing its fixed-income exposure in order to comply with the fund's asset allocation targets.

1. Long-short strategy. The managers, in aggregate , purchase long positions in stocks as they typically would with their assigned assets. However, they also short sell stocks (see Chapter 2) equal in value to the pension fund's overweighting of domestic equity assets . The cash generated by these short sales is used to buy fixed-income securities that are held as margin but nevertheless provide returns through interest income and price changes. The particular long-short transactions result from the managers' investment research, which identifies under- and overpriced securities. 2. Futures strategy. The managers purchase long stock positions with their assigned assets. At the same time the pension fund 's staff sells futures contracts on a stock market index and buys futures contracts on Treasury bonds in sufficient amounts to compensate for the over- and underweighting of common stocks and fixed-income securities, respectively. 3. Swap strategy. The managers purchase long stock positions with their assigned assets . Through a financial in te rmed iary (such as a bank or a broker) the pension fund "swaps " (exchanges) with a nother institutional investor the return on a common stock index in order to receive the return on a fixed-income index. These swaps (see Chapter 23) are based on dollar amounts equal to the overand underweightings of the common stocks and fixed-income securities, respectively. In general, these strategies can be characterized as allowing the pension fund to earn (I) the total return generated by a 40% alloc ation to fixed-income securities, (2) the total return produced by a 60% allocation to common stocks (that is, the normal plus abnormal returns of the common stock managers), and (3) the abnormal returns earned by the common stock managers associated with the allocation in exc e ss of 60% to common stocks. The common stock managers' abnormal returns (known as alphas) are effectively "transported" to the fixed-income asset category.

the payoffs from a futures contract with a contract price equal to F, a synthetic futures contract has been created. In practice, the equivalence is not perfect. Most listed options are American, not European, raising the possibility that the buyer ofthe put will exercise it before rna684

CHAPTER 20

In the final analysis, General Mills chose to implement the second strategy. The pension fund's staff believed that listed futures contracts provided the cheapest and administratively least cumbersome means of carrying out its alpha transport program. Nevertheless, the ability to customize the other strategies to specific situations may make those strategies attractive at times to certain institutional investors. These strategies highlight fundamental changes in the financial markets that began in the 1980s and have rapidly gathered momentum in the 1990s. Through the development of derivative financial instruments (options, futures, and swaps) and the technological advancements in communications and computing power, financial markets have become highly integrated and fungible. Investors are increasingly able to exploit perceived profit opportunities and simultaneously maintain desired risk positions. Pacific Investment Management Company (P[MCO) provides another example of the transportable alpha concept. P[MCO is one of the largest fixed-income managers in the world, with assets under management exceeding $120 billion . Over the years, the firm has produced an enviable track record, earning positive risk-adjusted returns under a variety of fixed-income investment assignments. Since 1986, P[MCD has transported its fixed-income management skills to the U.S. stock market through a product called StocksPlus. PIMCO's process is simple. The firm purchases S&P 500 futures contracts equal to a specified notional principal: (Notional principal is the market exposure of the futures contracts; that is, the number of contracts purchased times the contracts' price times the contract multiplier.) At the same time P[MCD sets aside cash reserves equal to the notional principal. The cash reserves serve as collateral for the futures contracts. A~ the text discusses, futures prices are set by investors on the assumption that they can hold a combination of futures contracts and the riskfree asset. P[MCD uses its investment skills to create a short-term fixed-income portfolio with the cash reserves that has

substantially outperformed 9O-day Treasury bills with little incremental risk . As a result, the firm's combination of S&P 500 futures contracts and short-term fixed-income investments has consistently exceeded the returns on the S&P 500. P[MCD uses a variety of cash management strategies to add value relative to a portfolio of90-day Treasury bills. The firm takes advantage of the most consistently upward-sloping portion of the yield curve-that is, maturities between zero days and one year. Because the StocksPlus strategy needs liquidity from only a small portion of its fixed-income portfolio to meet margin requirements, P[MCD extends roughly one-half of its portfolio to maturities past 90 days . Further, the firm accepts some credit risk by purchasing nongovernment securities such as commercial paper. P[MCD also takes advan tage of certain securities that offer little credit risk but relatively high yields. At times these securities have included shortterm tranches of collateralized mortgage obligations, floating-rate notes, and foreign government shortterm securities (with currency risk fully hedged). Transportable alpha involves investors' capturing inefficiencies in certain markets while maintaining desired exposure to markets beyond those in which the superior performance is earned. Transportable alpha is not a free lunch. Investors must pay commissions on their trades in stocks, options, futures, and swaps either directly or through bid-ask spreads. Real-world frictions such as collateral requirements and even custodial accounting difficulties still complicate the smooth implementation of the alpha transport strategies. Further, investors must take active management risk in order to earn their alphas. For example, General Mills's common stock managers, in aggregate, may underperform the stock market, or PIMCD's shortterm portfolio may underperform 90-day Treasury bills. However. institutional investors applying the transportable alpha concept believe that their active management investment strategies possess sufficiently positive expected returns that more than compensate for the additional risk assumed.

turity. Moreover, the synthetic future is not marked to market on a daily basis. Despite these differences, the existence of well-functioning markets for call and put options will enable investors to synthetically create arrangements that have payoffs that are similar to those of futures on the underlying asset. Futures

685

(a)

Buy. Call .-

End-o fPeriod Value

a I-------..L--------I~

Stoc k Price at End of Pe riod

\

(b) SeU a Put

....

End-o fPer iod Valu e

I~

(c:) Multiple P~ldons End-ofPeriod Value

.'

Buy a Call . Sell a . ' ' '-.... Pill. and Borrow ~ Money •• Loan Repayment

l

BII }" a

Ca ll and Sell a Pill '--....

F

Figure 20.8

Creating a Synthetic Futures Contract

686

CHAPTER 20

IZIIII

SUMMARY

1. A futures contract involves the delivery of a specific type of asset at a specific location at a given future date. 2. People who buy and sell futures can be classified as either hedgers or speculators. Hedgers transact in futures primarily to reduce risk because these people either produce or use the asset in their ordinary course of business. Speculators transact in futures in pursuit of relatively short-term profits. 3. Futures are bought and sold on organized exchanges. Futures are standardized in terms of the type of asset, time of delivery, and place of delivery. 4. Each futures exchange has an associated clearinghouse that becomes the "seller's buyer" and the "buyer's seller" as soon as the trade is concluded. 5. A futures investor is required to deposit initial margin in order to guarantee fulfillment of his or her obligations. 6. A futures investor's account is marked to market daily, with the equity in the investor's account adjusted to reflect the change in the futures contract's settlement price. 7. A futures investor must maintain his or her account's equity equal to or greater than a certain percentage of the amount deposited as initial margin. If this requirement is not met, the investor will be requested to deposit variation margin in the account. 8. The basis for futures is the difference between the current spot price of the asset and the corresponding futures price. 9. There are three possible relationships between the current futures price and the expected spot price: the expectations hypothesis (futures price equal to expected spot price), normal backwardation (futures price less than expected spot price), and normal contango (futures price greater than expected spot price). 10. The current futures price should equal the current spot price plus the cost of carry. The cost of carry equals (I) the amount of interest that the owner forgoes by holding onto the asset less (2) the benefits of owning the asset plus (3) the costs of owning the asset. 11. If the price of a fu tures con tract becomes too far removed from the curren t spot price of the asset plus the cost of carry, arbitrageurs will enter into transactions that generate riskless profits from the perceived price discrepancy. Their actions will cause prices to adjust until the opportunity to make such profits disappears. QUESTIONS

AND

P ROBLEMS

1. Distinguish between a speculator and a hedger. Give an example of a short hedger and a long hedger. 2. Using the latest Wall StreetJournal, for the near futures contracts in corn, orange juice, and gasoline, calculate the percentage change in the settlement price from the previous day. Find the open interest in these contracts. Into how many units of the commodities do these open interest figures translate? 3. How do organized futures exchanges ensure that the obligations incurred as various parties enter into futures contracts are ultimately satisfied? 4. What is the purpose of initial and maintenance margins? How does marking to market affect the amount of funds held in the futures investor's margin account? 5. Chicken Wolf sells tenJune 5000-bushel corn futures at $2 per bushel. Chicken deposits $5,000 in performance margin. If the price of corn rises to $2 .20 per bushel, how much equity is in Chicken's margin account? What if corn falls to $1.80 per bushel?

Futures

687

6. Zack Wheat hasjust bought four September 5000-bushel corn futures contracts at $1.75 per bushel. The initial margin requirement is 3%. The maintenance margin requiremen tis 80% of the initial margin requirement. a. How many dollars in initial margin must Zack put up? b. If the September price of corn rises to $1.85, how much equity is in Zack's commodity account? c. If the September price or corn falls to $1.70, how much equity is in Zack's commodity account? Will Zack receive a margin call? 7. How does a futures contract differ from a forward contract? 8. Do exchange-imposed price limits protect futures traders from losses that would result in the absence of such limits? Explain. 9. Corky Withrow is long a stock market futures contract and short a diversified portfolio of stocks. Would Corky prefer the basis to widen or to narrow? Why? 10. A publication used by farmers such as Mordecai Brown provides diagrams of the typical annual patterns of cash prices for a number of seasonal commodities. Should Mordecai expect that the price ofa futures contract will follow the same pattern? Why? 11. In the market for a particular agricultural or natural resource commodity, what kind of market forces might lead to normal backwardation or normal contango? 12. Consider a futures contract on mangoes that calls for the delivery of 2,000 pounds of the fruit three months from now. The spot price of mangoes is $2 per pound. The three-month riskfree rate is 2%. It costs $.10 per pound to store mangoes for three months. What should be the price of this futures contract? 13. Byrd Lynn owns a famous Renoir painting that has a current market value of $5,000,000. It costs Byrd $200,000 annually to insure the painting, payable at the start of the year. Byrd is able to loan the painting to a local art gallery for $300,000 per year, paid at the end of the year. Byrd is considering selling the painting under a futures contract arrangement that calls for delivery one year from today. If the one-year riskfree rate is 5%, what is the fair value of the futures con tract? 14. Tuck Turner is planning a trip in six months to Germany, where Tuck plans to purchase a BMW for 80,000 German marks (DM). Using a recent Wall Streetjournat, calculate how much the purchase would cost in U.S. dollars at the current exchange rate. Given the recent settlement price of a six-month DM futures contract, how much would Tuck have to pay to hedge the cost of the BMW purchase? 15. Assume that the exchange rate between British pounds and U.S. dollars is currently $1.80 per pound. If the six-month riskfree rate is 3% in the United States and 3.5% in Great Britain, what should the six-month futures price of U.S. dollars in British pounds be? Why is the futures exchange rate greater or less than the current spot exchange rate? 16. The one-year futures price of the Utopian currency darmas is $2.03 per darma. The interest forgone by selling darmas in the futures market instead of the spot market is $.0591. The benefit of owning darrnas instead of selling them is $.0788. If the U.S. one-year riskfree rate is 3%, according to interest-rate parity, what should be the Utopian one-year riskfree rate? 17. What should be the price of a three-month 90-day Treasury bill futures contract if the spot price of a six-month Treasury bill is currently $98 and the three-month riskfree rate is 1%? 18. Estel Crabtree believes that the spread between long-term and short-term interest rates is going to narrow in the next few months but does not know in which direction interest rates in general will move. What financial futures position would permit Estel to profit from this forecast if it is correct? 19. Sleeper Sullivan bought ten S&P 500 December futures contracts at 310. If the S&P 500 index rises to 318, what is Sleeper's dollar profit?

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20. Why does hedging a common sto ck portfolio using stock index futures work

21.

22.

23.

24. 25. 26. 27.

best if the portfolio being hedged is very similar to the underlying stock index of the futures contract? Assume that the S&P 500 currently has a value of 200 (in "index" terms). The dividend yield on the underlying stocks in the index is expected to be 4% over the next six months. New-issue six-month Treasury bills now sell for a six-month yield of6%. a. What is the theoretical value of a six-month fu tures con tract on the S&P 500 ? b. What potential problems are inherent in this calculation? In December 19X1 Granny Hamner bought aJanuary 19X2 gold futures contract on the New York Commodity Exchange for $487.50 per ounce. Simultaneously, Granny sold an October 19X3 contract for $614.80. At the time, yields on Treasury notes with 1.75 years to maturity were 10.50%. Will this transaction be profitable for Granny? What factors are relevant to making this calculation? In each of the following situations, discuss how Hippo Vaughn might use stock index futures to protect a well-diversified stock portfolio: a. Hippo expects to receive a sizable bonus check next month and would like to invest in stocks, believing that current stock market prices are extremely attractive (but realizing they may not remain so for long). b. Hippo expects the stock market to decline dramatically very soon and realizes that selling a stock portfolio quickly would result in significant transaction costs. c. Hippo has a large, unrealized gain and for tax purposes would like to defer the gain until the next tax year, which is several weeks away. Does the fair value of a stock index futures contract depend on investors' expectations about the future value of the underlying stock index? Why? Swats Swacina, a futures investor who has lost considerable sums in fu tures investments, said, "Even though I don't directly borrow to invest in futures, the performance of my investments acts as if I were highly leveraged." Is Swats correct?Why? (Appendix Question) Distinguish between futures contracts and options on futures contracts. (Appendix Question) Pinky Swander buys a call option on a March 5000-bushel soybean futures contract. The call costs $.50 per bushel and has an exercise price of$5.25 per bushel. If Pinky exercises the option in February at a price of$5.55 per bushel, what is Pinky 's return on investment in the option?

CFA

EXAM

QUESTIONS

28. Robert Chen, CFA, is reviewing the characteristics of derivative securities and their use in portfolios. a. Chen is considering the addition of either a short position in stock index futures or a long position in stock index (put) options to an existing well-diversified portfolio of equi ty securi ties. Contrast the way in which each of these two alternatives would affect the risk and return of the resulting combined portfolios. b. Four factors affect the value of a futures contract on a stock index. Three of these factors are the current price of the stock index, the time remaining until the contract maturity (delivery) date, and the dividends on the stock index. Identify the fourth factor and explain how and why changes in this factor affect the value of the futures contract. c. Six factors affect the value of call options on stocks. Three of these factors are the current price of the stock, the time remaining until the option expires, and the dividend on the stock. Identify the other three factors and exFutures

689

plain how and why changes in each of these three factors affect the value of call options. 29. The foundation 's grant-making and investment policy issues have been finalized . Receipt of the expected $45 million Franklin cash gift will not occur lor 90 days , yet the committee believes current stock and bond prices are unusually attractive and wishes to take advantage of this perceived opportunity. a. Briefly describe two strategies that utilize derivative financial instruments and could be implemented to take advantage of the committee's market expectations. b. Evaluate whether it is appropriate for the foundation to undertake a derivatives-based hedge to bridg-e the expected 90-day time gap, considering both positive and negative factors.

ApPENDIX FUTURES OPTIONS

The previous chapter described options, and this chapter has described futures. Interestingly, there are contracts currently in existence that are known as futures options (or options on futures). As might be expected, these C011lraCL~ are, in a sense, combinations of futures and options contracts. In particular, a futures option is an option in which the underlying asset is a specific futures contract, with the expiration date on the option normally being shortly before the delivery date on the futures contracl.2~ Figure 20.9 provides a set of quotations on some of the more frequently traded ones. As the figure shows, there are both put and call options on futures. Thus an investor can be either a buyer or a writer of either a put or a call option on a futures contract."

IIEIIIII

CAll OPTIONS ON FUTURES CONTRACTS Ifa call option on a futures contract is exercised, then the writer must deliver the appropriate futures contract to the buyer; that is, the writer must assume a short position in the futures contract while the buyer assumes the long position. For example, consider the buyer of a call option on May corn futures where the exercise price is 300 (that is, $3) per bushel. Because the futures contract is for 5,000 bushels, the total exercise price is $15,000 (= 5,000 X $3). If the buyer purchased this option at the settle price on October 8, 1997, which is given in Figure 20.9, then the buyer would have paid the writer a premium of 181 (that is, $.18375) per bushel, or $918.75 (=5,000 X $.18375) in total. . 690

CHAPTER 20

FUTURES OPTIONS PRICES Wednesday. Oclober 8.1997.

AGRICUL11JRAL CORN ICBTl 5.000bu.; conll per bu. SirIke Calls-Settle PuIs-Settle Price Dec Mar May Dec Mar May 260 25'/. 34'12 4~ 2'h 3'12 4'12 270 lAi 27 33V. 4'4 6V. 7 2BO llV. 2lV, 27 B¥o 10 10 290 7 16'12 21'/. 14'12 15 14'4 300 H" 12'/. IB"" 21'/] 21 20'/. 310 2'12 9'/] 15 292,(, 27'4 ., . , Esl yol 30.000 Tu 17.B55 calls IB.43O puts Op Inl Tues 121,814 call. 203.566 puts SOYBEANS (CBn 5.000bu.; cenll per bu. SIrlke Calls-Settle Puts-settle Price NOY Jan Mar Noy Jan Mar 625 "'1', 52'12 62 2"" 7V. 11 6SO 24V. 35 46'12 61'. 1~lh 20 675 10'12 12'1. 34 IB 27 32 700 4V, 14'/. 24'12 J6-\'a 43 47 ns 1'4 8'1. IB 59 63 65 750 1', 5'/] 12 83 .. .. .. .. Esl YOI 30.000 Tu 2~.480 calls 25.31B puts Op Inl Tues 15B.720 calls 131 .323puts

OIL CRUDE OIL (NYM) 1.000 bbll .; 1 per bbl. SIrIke Calls·Settle PUI.-Settle Price Nov Dec Jan Noy Dec Jan 2100 1.31 1.59 1.65 .13 .46 .69 2150 .94 1.27 1.37 .26 .64 .90 1200 .63 .9'1 1.11 .e .86 1.14 nso .29 .77 .91 .71 I .I~ 2300 .24 .59 .73 1.06 1.46 2350 .14 .... .59 1.46 .. .. .. .. Esl yol .... M3 Tu 2O.m calls 13.099 oul. oe Inl Tues 282.491 calls 191.174 puts

METALS COPPERICMX) 25.000 Ibl.; cenll per lb. SIrlke Calls-settle Puts-Settle Price Noy Dec Jan Noy Dec Jan 90 4.60 6.05 6.75 .M 1.80 2.25 92 3.25 O~ ~ .SS 1.50 2.50 3.05 94 2.15 3.75 4.SO 2.40 3,50 3.95 96 1.35 2.70 3.60 3.60 4.45 5.00 98 .80 2.10 2.80 5.05 5 .8~ 6.25 100 .~ I.SO 2.20 6.65 7.25 7.60 Esl vol JOO Tu 320calls 29ouls OP Inl Tues 7.715calls 2.B02 pull GOLDICMX) 100Irof ounc..; 1 _ Irof ounce SIrlke Calls·Settle PuIs· settle Price Noy Dec Feb Noy Dec Feb J2S 10.50 11.90 14.SO .20 1.60 2.90 JJO 5.70 B.oo 10.20 .40 2.70 00 335 1.80 UO 8.20 I.SO 4.SO 6.20 340 .SO 3.00 5.30 5.10 7.70 10.10 W .20 1.70 3.60 9.90 11.40 11 .40 JSO .10 1.00 2.60 100 15.70 16.30 Esl vol ~.OOO Tu J.S53 call. 942 puis OP Inl Tues 307.8-46 calls 1240693 puts

INTEREST RATE T·BONDS (CBn 1100,000; IIOlnliand "'!huf 1M SIrIke Calls-settle Puis-settle Price Nov Dec Mar NOY Dec Mar 113 3-01 0-07 114 2-09 2-32 3·26 0-15 0-38 I-53 115 1-26 0-32 116 0-53 I·IB 2·23 0-59 1-24 2-49

m

~?~

J:~ 2~~

EUROPOLLARICME) 1 million; pll. of 100~ SIrIke Calls-Settle PuIs-Settle Price OCI Noy Dec Oct Noy Dec 937~ 0.... 0.... 0.00 0.00 0.00 9400 0.20 0.20 0.21 0.01 0.01 0.02 942~ 0.00 0.Q2 0.03 0.07 0.08 0.09 9450 0.00 0.00 0.00 0.31 947~ , , . . 0.00 0.56 9~00 .. 0.00 0.81 E.I. vot, 2....657; Tu vot. 62.195 calls ; 37.324 pull oe, Int. Tues 1.229.8'25 call.; 1.223.· 667puts

INDEX OJ INDUSTRIAL AVG (CBOn 1100Ilmullremium SIrIke Call.-Settle Pull·settle Price Noy Dec Mar Noy Dec Mar 80 32.00 29.00 59.00 16.15 23.15 81 25.70 32.75 "" 19.7027.00 82 20.10 27.25 24.15 31.SO 83 15.25 12.50 .. .. 8-4 11.25 18.40 .. .. 85 8.00 14.60 33.00 .. .. .. .. E., yol 2.000Tu 1.JJ8 calls 1.6J.S puts OP Inl Tue. 2.869calls 3.531I1Ul. S&P 500STOCK INDEX (CME) 1500Ilmel premium SIrIke Calls·settle Pul.-Settle Price ocr Noy Dec Ocl Noy Dec 970 19.0532.70 41.10 6.70 20.~ 28.90 975 15.60 29.60 38.15 8.25 12.30 30.90 980 12 .~ 26.65 3~.35 10.10 24.3033.00 9~ 9.65 23.95 32.65 12.30 26.~ 35.25 990 7.30 21.35 30.10 14.95 28.~ 37.65 9'15 5.25 18.90 27.65 17.90 31.~ , . . Esl yol 13.758 Tu 6.723call. 7.456 puts oe Inl Tues 5-4.658 call. 125.559 PUts

CURRENCY JAPANESE YEN (CMEI 12.500.000 fen ; cenll per 100fon SIrlke Calls·Settle PuIs-Settle price Noy Dec Jan NOY Dec Jan 8250 1.5-4 1.95 0.74 1.16 8JOO 1.25 1.68 0.95 1.3B B3SO 1.00 U2 1.20 1.62 8-400 0.79 1.21 1.49 1.90 8-450 0.62 1.02 1.81 2.21 ~oo 0.49 0.B5 .. " 2.IB 2.53 ' .. , Esl yol 6.643 Tu 4.568 calls 2.347 puts oe Inl Tues 39.866 calls 35.692 puIs DEUTSCHEMARK ICME) 125.000 markl; conll per mark Slrlke Calls·settle Puis-Settle Price Noy Dec Jan Noy ~c Jan 56SO 1.24 1.43 0.31 0.51 ' .. , 5700 0.90 I. 13 0.47 0.70 57SO 0.63 0.8B 0.70 0.95 S800 0.43 0.68 1.24 5850 0.2B 0.51 5900 O.IB 0.37 .. . . .. .. 1.93 Esl yol 2.432Tu 98-4 calls l.323puts Op Inl Tues 30.041 calls 29.017 puts

0-34 1·]6 Esl. vor, :MO.ooo; Tu vot, 71.Bn calls ; 52.430 puts OP. lnt, Tues 659.n6 call.; 416.052 Puts

Figure 20.9 Quotations for Futures Options (Excerpts) Source: Reprinted by permission of The 'laU Streetjournal; DowJ ones & Company. Inc., October 9. 1997. p. C17.

Futures

691

Now if the buyer subsequently decides to exercise this option, then the writer of this option must deliver a May corn futures contract to the buyer. Furthermore, this futures contract will be fully marked to market at the time it is delivered. In the example, assume that the option is exercised in February when May corn futures are selling for $4 per bushel. In February the call writer must provide the call buyer with a May corn futures contract that has a delivery price of $3 which has been marked to market. This can be accomplished in two steps. First, the writer must purchase a May corn futures contract and deliver it to the call buyer. Because the cost of the futures will be $4 per bushel (the current market price of May corn futures), this purchase is costless to the call writer. Second, the futures contract that has been delivered must be marked to market, which is done by having the call writer pay the call buyer an amount of cash equal to $1 (=$4 - $3) per bushel, or $5,000 (=5,000 X $1) in aggregate. Thus the call writer has lost $4,081.25 (=$5,000 - $918.75) while the caB buyer has made an equivalent amount. Whereas this example has shown what happens when the call is exercised, it should be noted that most futures options are not exercised. Instead, just as with most options and futures, buyers and writers of futures options typically make reversing trades before the expiration date .

__

PUT OPTIONS ON FUTURES CONTRACTS If a put option on a futures contract is exercised, then the writer must accept delivery of the appropriate futures contract from the buyer; that is, the writer must assume a long position in the futures contract while the buyer assumes the short position. For example, consider the buyer of a put option on May corn where the exercise price is 300, meaning $3 per bushel or $15 ,000 in total because the futures contract is for 5,000 bushels. If the buyer purchased this put at the settlement price on October 8, 1997 that is given in Figure 20.9, then the buyer would have paid the writer a premium of 20-~ per bushel, or $1,037.50 (= 5,000 X $.2075) in total. Now if the buyer subsequen tly decides to exercise this option, then the writer of this option must accept delivery of a May corn futures contract from the buyer. Furthermore, this futures contract. must be fully marked to market at the time it is delivered. In the example, assume that the option is exercised in April when May corn futures are selling for $2 per bushel. In April the put buyer will become the seller of a May corn futures contract where the purchase price is $2 per bu shel. That is, when this contract is marked to market, the put writer must pay the put buyer an amount of cash equal to $1 (=$3 - $2) per bushel, or $5,000 (=5,000 X $1) in aggregate. Thus the put writer has lost $3,962.50 (=$5,000 - $1,037.50), whereas the put buyer has made an equivalent amount. Again, it should be kept in mind that most put options on futures are not exercised. Instead, these option buyers and writers typically enter reversing trades at some time before the expiration date. In summary, the positions of futures options buyers and writers in the futures contracts upon exercise by the buyer are as follows:

Call

Put

Buyer Long Short

seller Short

Long

As mentioned earlier, neither a writer nor a buyer needs to maintain his or her position . Both are free to enter into offsetting trades at any time, even after the buyer 692

CHAPTER 20

has exercised the option (but then the offsetting trade would be made in the futures market) .

IIIEIIII

COMPARISON WITH FUTURES

At this point it is worthwhile to think about the distinctions between futures and futures options. In doing so, consider an investor who is contemplating buying a futures contract. If this contract is purchased, the investor can potentially make or lose a great deal of money. In particular, if the price of the asset rises substantially, then so will the price of the futures, and the investor will have made a sizable profit. In contrast, if the price of the asset drops substantially, then the investor will have lost a sizable amount of money. In comparison, if the investor had bought a futures call option on the asset, then the investor would also make a sizable profit if the price of the asset rose substantially. Unlike with futures, however, if the price of the asset dropped, then the investor need not worry about incurring a sizable loss. Instead, only the premium (the price paid to buy the futures option) would be lost. Nevertheless, purchasing a futures call option is not a better (or worse) strategy than purchasing a futures contract. Why? Because the protection on the downside that an investor gets from buying a futures call option is paid for in the form of the premium. This premium would not be present if the investor had bought a futures contract instead. Consider next an investor who is contemplating selling a futures contract. In doing so, the investor can potentially make a great deal of money if the price of the asset declines substantially. However, if the price of the asset rises substantially, then the investor will have lost a sizable amount of money. In comparison, the investor could buy a futures put option on the asset. In this case, the investor would make a sizable profit if the price of the asset declined substantially. However, if the price of the asset rose, then the investor need not worry about incurring a sizable loss. Instead, only the premium would be lost. Again, this does not mean that purchasing a futures put option is better (or worse) strategy than selling a futures contract.

_

COMPARISON WITH OPTIONS

Having established that futures options can exist if futures already exist, one may wonder why futures options exist if options already exist. The commonly given reason why futures options exist in such a situation is that it is easier to make or take delivery of a futures contract on the asset as required by the futures options contract than to make or take delivery in the asset itself as required by the options contract. In addition, there is sometimes more timely price information on the deliverable asset for the futures option contract (namely, price information on the futures contract) than on the deliverable asset for the options contract (namely, price information in the spot market). For these reasons (although they are not compelling for certain contracts), futures, futures options, and options can exist simultaneously with the same underlying asset. ENDNOTES

I

The term commodity futures is often used to refer to futures on agricultural goods and natural resources. The term financial futures is typically used in reference to futures on financial instruments such as Treasury bonds, foreign currencies, and stock market indices.

Futures

693

~

:1

4

For a relatively complete description of the terms for many exchange-traded futures contracts, see the Cumllll)(li/~V Trading Manual (Chicago Board of Trade, 1989); and Malcolm J Robertson , Directory ol World Fut ures and Options (Upper Saddle River, NJ: Prentice Hall, 1990) . These two books also contain descriptions of' various futures exchanges, Since Black Monday and 'n.. rrihle Tuesday (October 19 and 20, 1987), a number of people have advocated an increase in the size of the initial margin deposit for certain futures contracts (particularly stock index futures, which will be discussed later). The levels of initial and maintenance margins arc set by each exchange, with brokers being allowed to set them higher. Typically, higher amounts of margin are required on futures contracts that have greater price volatility because the clearinghouse faces larger potential losses on such contracts. Actually, only brokerage firms belong to a clearinghouse, and it is theiraccounL~ that are settled by the clearinghouse at the end of every day. Each brokerage firm acts in turn as a clearinghouse for its own clients. For more information on clearing procedures, see Chapter 6 of the Commodity Trnding Mmnutl.

:; Interestingly, it has been observed that typically the volatility of the futures price changes increases as the contract approaches its delivery date. This phenomenon is known as the "Samuelson hypothesis"; see Paul A. Samuelson, "Proof That Properly Anticipated Prices Fluctuate Randomly," Industrial MaTl(lgt!1l1nll Reuietu 6, no . 2 (Spring 196!»): 41-49. Also see Hendrik Bessembinder, Jay F. Coughenour, Paul ]. Seguin, and Margaret Monroe Smoller, "Is There a Term Structure of Futures Volatilities? Reevaluating the Samuelson Hypothesis," journal ofDerivalivl's4 , no. 2 (Winter 1996) : 45-58. [; Merrill Lynch, Pierce, Fenner & Smith, Inc., StJeculalingon Inflation: !'i!IUTI'S Trading in Interest Rail'S, Foreign Currencies arul F'71'!'i01!S Metals, July 1979. 7

For more on the relationship between spot and futures prices as reflected in the basis, see the Commodity Trading Manuul, Chapter 8. Sometimes basis is defined as the futures price less the current spot price-the reverse of what is shown in Equation (20.1).

H

The futures contracts consisted of agricultural goods and natural resources. See Zvi Bodie and Victor Rosansky, "Risk and Return in Commodity Futures," Financial Analyslsjournal 36, no, 3 (May/June 1980) : 27-:\!l. Similar conclusions were reached when the period from 1978 to 1981 was examined. See Cheng F. Lee, Raymond M. Leuthold, and Jean E. Cordier, "The Stock Market and the Commodity Futures Market: Diversification and Arbitrage Potential," Financial Analysls.!ml1'TwI41, no . 4 Uuly/August 198!»):53-60.

\1

These first two points do not mean that the current spot price will not change as time passes. For futures involving a seasonal commodity (such as wheat), the spot price will sometimes be greater than and sometimes he less than the futures price during the life of the contract. Furthermore, sometimes a futures contract involving a more distant delivery date will sell for more than one with a nearer delivery date, whereas at other times it will sell for less.

IIlJ . M. Keynes, Treatise on Money, vo!. 2 (London: Macmillan, 1930), 142-144. II

There are other hypotheses regarding the relationship between futures prices and expected spot prices. See, for example, Paul H. Coomer; "Speculation and Hedging," Stanford University, Food Research Institute Studies, Supplement, J 967.

I~ This section and the next one borrow from Kenneth R. French, "Pricing Financial Futures

Contracts: An Introduction," .!ournal of Applied Corporate Finance I, no. 4 (Winter 1989): 59-66. It ignores the apparently minor effect that daily marking to market has on the futures price that is stated in futures contracts (see P: 65 and footnotes fi and 6 in French's paper). I~ The prices of foreign currency forward and futures contracts appear to be quite similar.

See Bradford Cornell and Marc Reinganum, "Forward and Futures Prices: Evidence from the Foreign Exchange Market," journal oJFinance 36. no. 5 (December 1981): 1035-1045. Their findings are challenged by Michael A. PolakofTand Paul C. Grier, "A Comparison of Foreign Exchange Forward and Futures Prices," [oumal oj Banking and Finance 15, no. 6 (December 1991): 1057-1079, but they are supported by Carolyn W. Chang andJack S. K. Chang, "Forward and Futures Prices: Evidence from the Foreign Exchange Markets," [our-

694

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nal of Finance 45, no. 4 (September 1990): 1333-1336. See Kenneth R. French, "A Comparison of Futures and Forward Prices," Joumal ofFinancial Economics 12, no. 3 (November 1983): 311-342 for a discussion of the difficulties encountered when testing to see whether the prices of forward and futures contracts are similar. 14

Actually the typical speculator will plan to realize this profi t by entering a reversing trade instead of buying }'en on the spot market and then making delivery, Similarly, the previously mentioned hedging importer will typically plan to enter a reversing trade .

l!i

See Chapter 5 for a discussion of term structure and forward rates.

16 Delivery

on Treasury bond futures can take place on any business day in the delivery month even though the trading ceases when there are seven business days left in the month .

17 For

this and certain other interest-rate futures contracts there is flexibility injust what the seller has to deliver, known as the qualit)l option. The short position in the contract will usually decide on the cheapest-to-deliuer Trezsurv bond and will deliver it to the long position. Sometimes there is also some flexibility regarding when during a business day that an intention to deliver must be announced, known as the wild rrntl option.

IH Similarly,

interest-rate futures are often used by financial institutions to hedge interest-rate risk to which they may be exposed; that is, when a large movement in interest rates would cause a large loss, these institutions will seek protection by either buying or selling interestrate futures.

HI The

3% dividend yield is actually the accumulated December value ofthe dividends divided by the purchase price of the stocks. Hence the dividends might be received in three months and amount to 2.93% uf the purchase price of the index. Putting them in a riskfree asset that returns 2.47% for the last three months results in a yield of 3'Yr'" or $3, in December.

~f1 Index arbitrage is one of two major forms of program trading. The other form, known as

portfolio insurance, was discussed in the previous chapter. For a discussion and example of how futures can be used to procure portfolio insurance, see Stephen R. King and Eli M. Remolona, "The Pricing and Hedging of Market Index Deposits," Federal Reserve Bank of Netu York Qllar/rrly Rruino 12, no . 2 (Summer 1987): 9-20; or ThomasJ. O'Brien, How Option Replicating Portfolio Insurance Works: Expanded Details, Monograph Series in Finance and Economics, 1988-4 (New York University Salomon Center, Leonard N. Stern School of Business, 198H). 21

People involved in index arbitrage need to be able to quickly make a large number of transactions in individual stocks. In order to do this, they often have their computers send in their orders through the SuperDOT system (discussed in Chapter 3) . For a discussion of some of the complications involved in successfully executing index arbitrage strategies, see David M. Modest, "On the Pricing of Stock Index Futures," Joumal ofPortfolio Management 10, no. 4 (Summer 1984): 51-57.

22

Adding to the confusion is the existence of a contract known as a futures option, which is an option that has a futures contract instead of a stock as its underlying asset. Futures options are discussed in more detail in the appendix.

2~ The near-simultaneous quarterly expiration of (1) options on individual stocks and market

indices, (2) futures on market indices, and (3) options on market index futures has been referred to as the triple witching hour. When it occurs, the stock market is allegedly roiled, particularly in the latter part of the day. See Hans R. Stoll and Robert E. Whaley, "Program Trading and Expiration Day Effects," Financial Analy.st.sJoumal 43, no. 2 (March z April l Sd"): 16-28; Arnold Kling, "How the Stock Market Can Learn to Live with Index Futures and Options," Financial Analsstsjournal 43, no. 5 (September/October 1987): 33-39; and G.J. Santoni, "Has Programmed Trading Made Stock Prices More Volatile?" Federal Reseroe Bank of St. Louis Review 69, no. 5 (May 1987): 18-29. 24

For more on futures options, see Chapter 12 of the Crnnmodity Trading Manual For a computer program that can be used to determine the "true" value of these complex contracts, see Chapter 8 of Stuart M. Turnbull, option Valuation (Holt, Rinehart and Winston of Canada, 1987).

Futures

695

KEY

TERMS futures specula tors hedgers spot market spot price short hedger long hedger reversing trade settle open interest futures commission merchant locals performance margin marking to market variation margin

Commodity Futures Trading Commission basis basis risk expectations hypothesis normal backwardation normal contango cost of carry interest-rate parity arbitrageurs index arbitrage synthetic futures contract futures options triple witching hour

REFE R E N C E S 1. Many books either are devoted exclusively to futures or have futures as one of their pri-

mary subjects. Most cover everything discussed in this chapter in more detail and with a more complete list of citations. Here are a few: Stephen Figlewski, Hedging with Financial Futuresfor Institutional Investors (Cambridge, MA: Ballinger, 1986) . Edward W. Schwarz,Joanne M. Hill, and Thomas Schneeweis, Financial Futures (Homewood, IL: Richard D. Irwin, 1986). Commodity Trading Manual (Chicago: Chicago Board of Trade, 1989). Darrell Duflie, Futures Markets (Englewood Cliffs, NJ: Prentice Hall, 1989). Daniel R. Siegel and Diane F. Siegel, Futures Markets (Hinsdale, IL: Dryden Press, 1990). Alan L. Tucker, Financial Futures, Options, & Swaps (St. Paul, MN: West, 1991) . David A. Dubofsky, options and Financial Futures (New York: McGraw-Hili, 1992) . Hans R. Stoll and Robert E. Whaley, Futures and options (Cincinnati: South-Western Publishing, 1993) . Robert T. Daigler, Financial Futures and Markets: Concepts and Strategies (New York: HarperCollins, 1994). Robert W. Kolb, Understanding Futures Markets (Miami, FL: Kolb, 1994) . Don M. Chance, An Introduction to Derivatives (Fort Worth: Dryden Press, 1995). Fred D. Arditti, Derivatives (Boston: Harvard Business School Press, 1996). RobertJarrow and Stuart Turnbull, Derivative Securities (Cincinnati: South-Western Publishing, 1996). John C. Hull, options, Futures, and Other Derivative Securities (Upper Saddle River, NJ: Prentice Hall, 1997) .

2. For a discussion of the market structure of futures exchanges, see: SanfordJ. Grossman and Merton H. Miller, "Liquidity and Market Structure," Journal of Finance 43, no. 3 (july 1988): 617-633.

Michael J. Fishman and Francis A. Longstaff, "Dual Trading in Futures Markets," Journal ofFinance 47, no. 2 (june 1992): 643-671.

3. For a more complete discussion of margin and marking to market, see: Robert W. Kolb, Gerald D. Gay, and William C. Hunter, "Liquidity Requirements for Financial Futures Investments," Financial AnalystsJournal 41, no. 3 (May/June 1985): 60-68.

696

CHAPTER 20

Don M. Ch ance The Effect ofMargins on the Volatility ojStock and Derivative Markets: A Review ofthe Euulenre Monograph Series in Finance and Economics 1990-2 (New York University Salomon Center, Leonard N. Stern School of Business, 1990) . Ann Kremer, "Clarifying Marking to Market,"Journal ojFinancial Education 20 (November 1991): 17-25. 4. The

concepL~ of spreads

and basis are discussed in:

Martin L. Leibowitz The Analysis o] Value and Volatility in Financial Futures Monograph Series in Finance and Economics 1981-3 (New York University Salomon Center, Leonard N. Stern School of Business, 1981). 5. Foreign currency markets are discussed in: J. Orlin Grabbe International Financial Markets (Upper Saddle River, NJ: Prentice Hall, 1996), Part 2. 6. Interest-rate futures were shown to be useful in immunizing bond portfolios by: Robert W. Kolb and Gerald D. Gay, "Immunizing Bond Portfolios with Interest Rate Futures," Financial Management II, no . 2 (Summer 1982) : 81-89. Jess B. Yawitz and William J. Marshall, "The Use of Futures in Immunized Portfolios," [uurnnl of Portfolio Management 11, no. 2 (Spring 1985): 51-58. 7. Using futures to hedge bond portfolios is discussed in : Richard Bookstaber and David P.Jacob, "The Composite Hedge: Controlling the Credit Risk of High-Yield Bonds," Financial A naly stsJourn al 42, no. 2 (Marchi April 1986): 25-35. Robin Grieves, "Hedging Corporate Bond Portfolios," journal oj Portfolio Management 12, no. 4 (Summer 1986): 23-25. 8. Stock index futures and the ir relationship to the market crash in October 1987 have been heavily researched . Some of the papers are: Paula A. Tosini, "Stock Index Futures and Stock Market Activity in October 1987," Firumcial Anuiystsjourual Aa, no. I (january/February 1988) : 28-37. F. .J. Gould, "Stock Index Futures: The Arb itrage Cycle and Portfolio Insurance," Financial AnalystsJournal44, no . 1 (january/February 1988) : 48-62. Lawrence Harris, "The October 1987 S&P 500 Stock-Futures Basis," Journal ojFinrmce44, no . I (March 1989): 77-99 . Marshall E. Blume, A. Craig MacKinlay, and Bruce Terker, "Order Imbalances and Stock Price Movements on October 19 and 20, 1987:' Journal of Finance 44 , no . 4 (September 1989) : 827-848. Lawrence Harris, "S&P 500 Cash Stock Price Volatilities:' Journal ojFinance 44, no. 5 (Decernber l sxs) : 1155-1175. Hans R. Stoll and Robert E. Whaley, "T he Dynamics ofStock Index and Stock Index Futures Returns,"Jollmal ojFinanc ial and Quantitative Analysis 25, no. 4 (December 1990): 441-468. Kolak Chan, K. C. Chan, and G. Andrew Karolyi, "Intraday Volatility in the Stock Index and Stock Index Futures Markets," Review ojFinancial Studies 4, no. 4 (1991): 657-684 . Avanidhar Subrahrnanyarn, "A Theory of Trading in Stock Index Futures," Review oj Financial Studies 4, no . I (1991) : 17-51. Kolak Chan, "A Further Analysis of the Lead-Lag Relationship between the Cash Market and Stock Index Futures Market," Review ofFinancial Studies 5, no. I (1992) : 123-152. 9. Papers on index arbitrage and program trading include: A. Cra ig MacKinlay and Krishna Ramaswamy, "Ind ex-Futures Arbitrage and the Behavior of Stock Index Futures Prices:' Review ojFinancial Studies I, no. 2 (Summer 1988): 137-158. Michael J. Brennan and Eduardo S. Schwartz, "Arbitrage in Stock Index Futures:' Journal oj Business 63 , no . I, part 2 (january 1990) : S7-S31. Hans R. Stoll and Robert E. Whaley, "Program Trading and Individual Stock Returns: Ingredients of the Triple-Witching Brew:'Journal ojBusiness63, no. I, part 2 (january 1990) : SI65-SI92.

Futures

697

Gary L. Gastineau, "A Short History of Program Trading," Financial Analyslsjuurrwl47, no.:; (September/October 1991): 4-7. 10. Forward and futures prices were shown to be equal when interest rates are constant over time in: .John C. Cox.jonathan E.. Ingersoll, and Stephen A. Ross, "The Relation between Forward Prices and Futures P,ices,".IuurnalufFinancial Eammnics'[; no. 4 (December 1981): ~2()-~4(j. I I. The performance of connuodity funds, which are investment companies that speculate in futures, has not been attractive, according to: Edwin ] , Elton, Martin.J. Gruber, andjoel C. Reruzler, "Professionally Managed, Publicly Traded Commodity Funds," [ournal ofBusiness 60, no. 2 (April 1987): 175-199. 12. Construction and performance of the Goldman Sachs Commodity Index is described in: Scott L. Lummer and l.aucnce B. Siegel, "GSCI Collateralized Futures: A Hedging and Diversification Tool for Institutional Portfolios," [ournnl o] Inuesting 2, no . 2 (Summer 1993): 75-82. 13. The relationships among futures, options, and futures options are discussed in: Clifford W. Smith .Jr., Charles W. Smithson, and D. Sykes Wilford, "Managing Financial Risk," jou17!alo/A/1Jlied Corporate Finance I, no. 4 (Winter 1989) : 27-48. Charles W. Smithson. Clifford W. Smith.Jr., and D. Sykes Wilford M(ll/aging Financial Risk: A Guide 10 Derioatiue Products, Financial Engineering, and Value Maximization (Homewood, IL: Irwin Professional Publishing, 199:i). 14. The seminal paper on the pricing of futures options is: Fischer Black, "The Pricing of Commodity Contracts," .IouTTwloJ Financial Economics 3, nos. 1/2 (january/March 1976): 167-179. 15. For a thought-provoking book that covers futures markets, among other subjects, see: Merton H. Miller FintmcialInnmnuions and Mrnket Volmilily (Cambridge, MA:Blackwell, 1991). 16. The various exchanges where futures are traded all have Weh sites containing useful information about their products: Chicago Board of Trade: <www.cboLcom>. Chicago Mercantile Exchange: <www.cme.com>. Coffee, Sugar & Cocoa Exchange : <www.csce.com>. Kansas City Board of Trade: <www.kcbLcom>. MidAmerica Commodity Exchange: <www.midam.com>. Minneapolis Grain Exchange: <www.mgex.com>. New York Cotton Exchange/New York Futures Exchange: <www.nyce.com>. New York Mercantile Exchange/Commodity Exchange: <www.nymex.com>. 17. The Commodity Futures Trading Commission, the federal regulator of trading in futures contracts that was established in 1974, has a Web site at: <www.cftc.gov>.

698

CHAPTER 20

CHAPTER

Z

1

INVESTMENT COMPANIES

I nvestment companies are a type of financial intermediary. They obtain money from investors and lise it to purchase financial assets such as stocks and bonds. In return, the investors receive certain rights regarding the financial assets that the investment company has bought and any earnings that the company may generate. In the simplest and most common situation, the investment company has only one type of investor-stockholders. These stockholders own the investment company directly and thus own indirectly the financial assets that the company itself owns . For an individual there are two advantages to investing in such companies instead of investing directly in the financial assets that these companies own. Specifically. the advantages arise from (I) economies of scale and (2) professional management. Consider an individual with moderate financial resources who wishes to invest in the stock market. In terms of economies of scale, the individual could buy stocks in odd 10L~ and thus have a diversified portfolio. However, the brokerage commissions on odd lot transactions are relatively high. Alternatively, the individual could purchase round lots but would be able to afford only a few different securities. Unfortunately the individual would then be giving up the benefits of owning a well-diversified portfolio. In order to receive the benefits of both diversification and substantially reduced brokerage commissions, the individual could invest in the shares of an investment company. Economies of scale make it possible for an investment company to provide diversification at a lower cost per dollar of investment than would be incurred by a small individual investor. In terms of professional management, the individual investing directly in the stock market would have to go through all the details of investing, including making all buying and selling decisions as well as keeping records of all transactions for tax purposes. In doing so, the individual would have to be continually on the lookout for mispriced securities in an attempt to find undervalued ones for purchase, while seiling any that were found to be overvalued. Simultaneously. the individual would have to keep track of the overall risk level of the portfolio so that it did not deviate from some desired level. However, by purchasing shares of an investment company, the individual can turn over all of these details to a professional money manager. Many of these managers hope to identify areas of mispricing in the market, exploit them, and share the resultant abnormal gains with investors by charging them for a portion of the gains. However, it appears that most managers cannot find mispriced situations frequently enough to recoup more than the additional costs they 699

have incurred, costs that take the form of increased operating expenses and transaction costs owing to the continual buying and selling of securities. Nevertheless, other potential advantages to he gained from investing in an investment company may still outweigh any disadvantages , particularly for smaller investors. Investment companies differ in many ways,and classification is difficult. Common practice will be followed here, where the term investment compan.}' will be restricted to those financial intermediaries that do not obtain money from "depositors." Thus the traditional operations of savings and loan companies and banks, for example, will be excluded. However, the process of deregulation is rapidly breaking down barriers that previously prevented financial intermediaries from competing with traditional investment companies. The future will likely find many different types of organizations offering investment company services.

ID:I

NET ASSET VALUE An important concept in understanding how investment companies operate is net asset value. Given that an investment company has assets consisting of various securities, it is often (but not always) easy to determine the market value of all the assets held by the investment company at the end of each business day. For example, an investment company that holds various common stocks traded on the New York Stock Exchange, the American Stock Exchange, and Nasdaq could easily find out what the closing prices of those stocks were at the end of the day and then simply multiply these prices by the number of shares that it owns. After adding up these figures, the investment company would subtract any liabilities that it had outstanding. Dividing the resulting difference by the number of outstanding shares of the investment company produces its net asset value , Equivalently, an investment company's net asset value at the end of day t, NAV" can be determined by using the following equation: MVA, - LIAB, NSO,

NA V. = -----'---------'/

(21.1)

where MVA" LJAB" and NSO, denote the market value of the investment company's assets, the dollar amount of the investment company's liabilities, and the number of sh ares the investment company has outstanding, re spectively, as of the end of day t. As an example, consider an investment company with 4,000,000 shares outstanding whose assets consisted of common stocks with an aggregate market value of $102,000,000 and whose liabilities amounted to $2,000,000 as of November IS. This company would report a net asset value on that date of $25 [= ($102,000,000 $2,000,000)/4,000,000] per share. This amount will change every day, because the values of MVA/J LJAB" or NSO, (or of some combination of the three) will typically change daily. Investors should note that calculating NA V, can be difficult if so me of the assets do not trade frequently or involve foreign securities that trade in vastly different time zones. In such situations, estimates of their fair market value are often used. Continuing with the previous example, what if, in on November 16 there were still 4,000,000 shares outstanding, the liabilities were still $2,000,000, but the common stocks had not been traded on any market since November IS? In this situation MVA, is often calculated by using the last bid prices for the stocks on November 16, which in this example is assumed to result in a value for MVA, of $106,000,000. 1 Hence the net asset value on November 16 is $26 [= ($106,000,000 - $2,000,000)/4,000,000] per share. 700

CHAPTER 21

Ell

MAJOR TYPES OF INVESTMENT COMPANIES

The Investment Company Act of 1940 classifies investment companies as followsr' 1. Unit investment trusts 2. Managed investment companies a. Closed-end investment companies b. Open-end investment companies These types of investment companies are discussed next.

21.2.1

Unit Investment Trusts

A unit investment trust is an investment company that owns a fixed set of securities for the life of the company.' That is, the investment company rarely alters the composition of its portfolio over the life of the company. Formation

To form a unit investment trust, a sponsor (often a brokerage firm) purchases a specific set of securities and deposits them with a trustee (such as a bank). Then a number of shares known as redeemable trust certificates are sold to the public. These certificates provide their owners with proportional interests in the securities that were previously deposited with the trustee. All income received by the trustee on these securities is subsequently paid out to the certificate holders, as are any repayments of principal. Changes in the original set of securi ties (that is, selling some of them and buying different ones) are made only under exceptional circumstances. Because there is no active management of a unit investment trust, the annual fees charged by the sponsor are correspondingly low (perhaps equal to .15% of the net asset value per year). Most unit investment trusts hold fixed-income securities and expire after the last one has matured (or, possibly, sold). Life spans range from six months for unit investment trusts of money market instruments to over 20 years for trusts of bond market instruments. Unit investment trusts usually specialize in certain types of securities. Some trusts include only federal government bonds, others only corporate bonds, others only municipal bonds, and so on. Not surprisingly, the sponsor of a unit investment trust will seek compensation for the effort and risk involved in setting up the trust by setting a selling price for the shares that exceeds the cost of the underlying assets. For example, a brokerage firm might purchase $10,000,000 worth of bonds, place them in a unit investment trust, and issue 10,000 shares. Each share might be offered to the public for $1,035. When all the shares have been sold, the sponsor will have received $10,350,000 (=$1,035 X 10,000). This is enough to cover the $10 ,000,000 cost of the bonds, leaving $350,000 for selling expenses and profit. Markups (or load charges) of this sort range from less than 1% for short-term trusts to 3.5% for long-term trusts. Secondary Market

Typically an investor who purchases shares of a unit investment trust is not required to hold the shares for the entire life of the trust. Instead the shares usually can be sold back to the trust at net asset value, calculated on the basis of bid prices for the assets in the portfolio; that is, the market value of the securities in the portfolio is determined, using dealers' bid quotations. Because unit investment trusts have no liabilities, this amount is divided by the number of shares outstanding to obtain the net asset value per share. Having determined the per share price, the trustee may sell one or more securities to raise the required cash for the repurchase. Investment Companies

701

Alternatively, it is possible that a secondary market is maintained by the sponsor of the trust. In this situa tio n investors can sell their shares back to the sponsor. Afterward, other investors (including those who did not participate in the initial sale) ca n purchase these sha res. Typically the sponsor's selling price in the secondary market is equal to the net asset value of the securities in the portfolio (based on dealers ' asked prices) plus a markup charge equal to that in effect at the time the trust was created.

21.2.2

Managed Companies

Whereas a unit investment trust has no board of directors and no portfolio manager, managed investment companies have both . Because they are organized as corporations or trusts (a few are limited partnerships), a managed investment company will have a board of directors or trustees that is elected by its shareholders. In turn, the board will commonly hire a firm-the management company-to manage the company's assets for an annual fee that is typically based on the total market value of the asse ts. These management companies may be independent firms, investment advise rs, firms associated with brokers, or insuran ce companies. Often the management company is the business entity (for example, a subsidiary of a brokerage firm) that started and promoted the investment company. A management company may have contracts to manage a number of investment companies, each of which is a separate organization with its own board of directors or trustees . Annual management fees (also known as advisory fees) usually range from .50 % to I % of the average market value of the investment com parry's total assets, with the percentage sliding downward as the dollar value of the assets increases. Some funds provide "incentive compensation," where the better the fund's investment performance, the higher the fee paid to the management company. In addition to the fee paid hy an investment company to its management company, there are administrative expenses that cover record keeping and services to shareholders. (Sometimes these are embedded in the management fee.) Such annual expenses usually range from .20% to .40% of the average market value of total assets. Last, there are other operating expenses that the investment company incurs annually for such things as state and local taxes, legal and auditing expenses, and directors' fees. These annual expenses usually range from .10 % to .30 % of the average market value of total assets. The combination of management fees, administrative expenses, and other operating expenses results in total annual operating expenses typically ranging from .80 % to I. 70% of the average total assets." This figure is referred to as a fund's operating expense ratio. During 1996 the average bond and equity fund had an operating expense ratio of 1.12% and 1.51%, respectively." Closed-End Investment Companies

Unlike unit investmen t trusts, closed-end investment companies (or closed-end funds) do not stand ready to purchase their own shares whenever one of their owners decides to sell them . Instead their shares are traded either on an organized exchange or in the over-the-counter market. Thus an investor who wants to buy or sell shares of a closed-end fund would simply place an order with a broker,just as if the investor wanted to buy or sell shares of IBM. Most closed-end funds have unlimited lives. Dividends and interest received by a closed-end fund from the securities in its portfolio are paid out to its shareholders, as are any net realized capital gains. However, most funds allow (and encourage) the reinvestment of su ch payments. The fund keeps the money and sends the investor 702

CHAPTER 21

additional shares based on the lower of net asset value or market price per share at that time. For example, consider a closed-end fund whose shares are selling for $20 that has just declared a dividend of $1 per share. If its net asset value were $15 per share, a holder of 30 shares wou Id have a choice of receiving ei ther $30 (= 30 X $1) or two shares (=$30/$15). However, if the shares were selling for $10, then the choice would be between $30 and three shares. Being a corporation, a closed-end fund can issue new shares not only through reinvestment plans but also with public stock offerings. However, this is done infrequently, and the fund's capitalization is "closed" most of the time. Furthermore, the fund's capitalization will have little or no interest-bearing debt in it because of certain restrictions imposed by the Investment Company Act of 1940. In general, a closed-end fund's shares are initially offered to the public at a price that is nearly 10% above its net asset value because of investment banking fees charged to the fund. This practice suggests that the shares are overpriced because most funds' shares sell for a price below their net asset value in the aftermarket. Evidence indicates that there are no unusual movements in the price of a typical fund on the offering day but that in the 100 days thereafter its price declines relative to the market to the point at which it sells for roughly 10% below its net asset value. This movement is in sharp contrast to the price behavior of non-fund initial public offerings, where the stocks, on average, experience a substantial price jump on the offering day of about 14% and no notable price movements in roughly the following 100 days.'; Left unanswered is why an investor would want to be involved in the initial public offering of a closed-end fund." Most closed-end funds can repurchase their own shares in the open market, although they seldom do. Whenever a fund's market price falls substantially below its net asset value, a repurchase will increase the fund's net asset value per share. For example, if the net asset value were $20 per share at a time when the fund's shares could be purchased in the open market (say, on the New York Stock Exchange) for $16 per share, the managers of the fund could sell $20 worth of securities from the fund's portfolio, buy back one of the fund's outstanding shares, and have $4 left over. If the $4 were used to buy securities for the fund, the net asset value per share would increase, with the size of the increase depending on the number of remaining shares, the number of shares repurchased, and their repurchase price. Quotations

The market prices of the shares of closed-end funds are published daily in the financial press, provided that the funds are listed on an exchange or traded actively in the over-the-counter market. However, their net asset values are published only weekly, on the basis of closing market prices for securities in their portfolios as of the previous Friday. Figure 21.1 provides an example. The first column indicates where a fund's shares are traded (N = NYSE, A = AMEX, 0 = Nasdaq, C = Chicago Stock Exchange, T = Toronto Stock Exchange). Both the net asset value and the last price at which the fund's shares traded on the day in question are shown next, followed by the percentage of net asset value that the difference between the two figures represents. Ifthis percentage is positive (meaning that the stock price is greater than the net asset value), then the fund's shares are said to be selling at a premium. Conversely, if this difference is negative (meaning that the stock price is less than the net asset value). then the fund's shares are said to be selling at a discount. For example, Figure 21.1 indicates that the India Growth Fund was selling at a 13.0% discount while the Indonesia Fund was selling for an 90.7% premium. (These two investment companies are known as "country funds," as they specialize in Indian and Indonesian Investment Companies

703

iZweelt

Fund Name (Symbol)

Stoek Exch

NAY

Markel Prlca

Prem

100ac

Mllket Return

Friday, March 20, 1998 General Equity Funda Ada"", Express(ADX) IoN l1.97 27 - 15.5 4l.9 AllianceAII-Mkl (AMO) 84.5 N l6.72 l6111 - OJ Ayalon Caplla1 (MIST) N/A N/A N/A N/A 0 Baker Fentress (BKF) lO .9 "N 2l.77 20lfI - !J.2 1h Bergstrom Cap (BEM) 40.0 A 175.82 155 - 11.6 Blue Chip Value (BLU) 5J.1 "N 11.12 111/, +1.2 Central Seca (CET) A n.oo lO'" - 1.6 20.8 Corp Renaissance (CREN)-c 0 9J2 7uh. - 17.5 9.8 Engex (EOX) A 12.91 10'" - 21.6 - 4.7 EQuus II (EQS) - IIJ 68.9 "A n .58 28 N/A 40J Gabelll Equity(GAB) N N/A lI uh. General Amencan (GAM) "N l2.56 281/. - 11.7 47.6 librty AIIStr EQ (USA)-g "N 14.74 14"" - 4.6 H.2 librty AIISlr Gr (ASG) 45.9 "N 14.29 !Juh. - JJ MFS Spec ial Val (MFV) N 15.98 19"" + 19J 120.1 N/A N/A Morgan FunSharas (MFUN)-c 0 N/A N/A 46.0 Morgan Gr Sm Cap (MGC) "N 12.89 1I'!l. - 10J NAIC Growth(GRF)-c H.6 C 12.15 16"'u + l4J Royce Micro-Cap (OTCM) 60 11.75 100/11 - 6.9 SO.4 52.8 Royce Valua(RVT) "N 18.12 17'" - l4 Royce,5.75'04Cy-w N N/A N/A N/A N/A Royce,5.75 '04Cy- w N/A N/A N N/A N/A Salomon SBF (SBF) l5,8 N 20.56 181/1 - 10.0 Source Capital (SOR) N 5l.87 55D/11 + l .8 19,5 Trl-Contlnenlal (TV)-a "N . lUI 290/1. - 17.6 l4.2 Zweig (ZF)-g "N B.54 iJuhl + 2.0 J5.2 Speciellzed Equity Funda cas Realty (RIF) l .5 "A 10.86 11'" + 5.9 cas Total Rln (RFI) 2.0 12.8 "N 16.97 16'11 DelawareGr Diy (ODF) N 18JO 18'11 + J.1 26.2 Delawara Grp GI (DGF) N 17.56 17uh. + 1.4 26.6 Ouff&Ph Ulllinc (ONP) N 10.51 IDill - 0.1 25.1 Emer MktsInlra (EMG) 4.4 "N 15.18 12'/. - 19.1 Emer MktaTel (ETF) 10.7 "N 11.70 14'!l. - 17.7 6l.0 First Financial (FF) N 18.92 21"hl + 15J GabelllGIMedia (GGT) N N/A 10'/. N/A 62.6 HaQ Heallh Iny (HQH) 9.5 20.60 17 17 .5 "N HaC Life Sci Iny (HQl) 17.01 14'11 - 17.0 !JJ "N INVESCO GI HUh (GHS) "N 2l.Dl 18'hi - 12J J5.1 J Han Bank (BTO) "N B.7l Bill - 2.6 79.9 J Han Pal Olobl(PGD) 15.1 "N 15.59 !J'hl - !J .O J Han Pal Sel (OIV) "N 17.21 15'h, - 9.6 20.0 Nations Bal Tgt (NBM) N 10.47 9'1. - 5.7 26.9 Petroleum&Res (PEO) 21.5 "N 42.94 J81/11 - 11.4 SlhEaalrn Thrm (STBF) 60 29.02 JO + l.4 85.0 Thermo Opprtunty (TMF) A IUD 10'/1 - 18.9 - 7.6 Preferred Stock Funde J Han Pat Prel (PPF) 14.57 14'/1 + 1.2 20.0 "N J Han Pat Prm (PDF) 5.8 14.7 "N IUS 101ft J Han Pat Prm II (PDT)-a "N n .55 121/, - 9.6 17.7 Preferred Inc Op (PFO) N/A N/A "N N/A NlA Prelerred IncMgt (PFM) N/A IoN N/A N/A NlA PreferredIncome (PFD) IoN N/A N/A NlA N/A PutnamDIvd Inc (PDI)-e N 11.74 10ll/li - 9.0 15.7 Convertible Sec'e. Funde Bancroft Cony(BCV) 2.2 45.5 29.27 28'11 "A Castle Cony (CVF) A 29.06 26 -10.1 17.8 '/. Ellsworth Cony (ECF) 8.4 l8.0 "A 1l.55 IIIII GabelllCony Sec (OCV) N 11.89 10ll/l. - 8.0 26.1 lincoln Cony (LNV)-c 8.1 18.1 "N 19.59 18 PutnamCony()pp (PCV) N 27.99 27'11 i .i 26.5 Putnam HI Inc c- (PCF)-a N 10.04 10'11 + 8J 17.5 TCWConySees (CVT)-g "N 10.14 101il + l .6 26J VKAC cv Sec (ACS) N 25.74 22'Iu - 12.l 25.9 World Equity Funds ASA Umlted (ASA)-ev N 18.89 20'11 + 6.5 - 19,6 Anchor Gold&Curr (GCT) C 4.67 41/11 - 2.J -27.0 Argenllna (AF) N 15.92 Hlfu - 17.9 2.4 Aala Pacific (APB) N s.n 80/1. - 5.5 - 18J

-

-

-

-

52",..k FundN.ma (Symbol)

Slack Exch

Global Small Cap (GSG) A GrowthFd Spain (GSP) "N Herzfeld Carlbb (CUBA) 0 India Fund (lFN) N India Growth (lGF)-d N Indonesia (IF) "N Irish Iny (IRL) N lIaly (ITA) N Jakarta Growth (JGF) N Japan Equity (JEQ) "N Japan OTC Equity (JOF) N Jardine FIChina (JFC) "N Jardine FIIndia (JFI)-gc "N Korea (KF) N Korea Equity (KEF) N Koraan Iny (KIF) N l.alIn AmSmCoIrc>Mies (llF)"N lalin Amer Disc (LDF) N latin Amer Eq (LAQ) "N latin Amer Iny (LA M) "N Malaysia (MF) N Mexico (MXF)-c N MexicoEQly&lnc (MXE)-c N Morgan 51 Africa (AFF) N Morgan 51 Asia (APF) N Morgan St Em (MSF) N MorganSt India (tlF) N Morgan St Ruasla (RNE) N New South Afrlce (NSA) "N Pakiatan Iny (PKF) N Portugal (POF) "N ROC Taiwan (ROC) N Royce Global Trust (FUND) 60 Schroder Aalan (SHF)-cs N Scud Spain &Por (IBF) N Scudder New Asia (SAF) N Scudder New Eur (NEF) N Singapore (SGF)-c "N Soulhern Africa (8OA) N Spain (SNF) N Swlaa HelYetla (SWZ) "N Taiwan (TWN)-c N Taiwan Equity (TYW)-c "N Templelon Chine(TCH)-c N Templelon Dragon (TDF) N TempletonEm App (TEA)-c N Templelon Em Mkt (EMF) N Templeton Russia (TRF)-c N TempletonVlelnm (TVF) N Thai (ITF) N Thai Capital (TC) "N Third Canadian (THD)-cy T Turkish Iny (TKF) N UnitedCorps Ltd (UNC)-cy T United Kingdom (UKM) IoN Z-Seyen (ZSEV) 0

NAY

19.1l 22.78 6.64 8.45 10.71 l .08 24.60 lUI 2.24 6.18 4,52

11.77 8.18 7.64 l .20 3.95 11.21 !J .04 16.86 18.0l 6.12 22.71 11.64 16.62 8.84 101 9.11 27.21 17.49 5.22 25.56 10.20 6.64 8.78 19.02 12.}} 22.98 7.97 18.18 2UI l7,65 21.07 15J6 10Jl U.59 1J.16 16.69 28.66 U8 6.15 4.18 24.49 7.55 75.75 17J5 8J8

Mllltet Prlca

Pr.m

Marltet

IDisc

Return

15'11 -17.9 20'/1 - 8.4 71/, + 9.2 7'h. - 14.9 9lfu - !J.O 5'" + 90.7 B I/. - 5.5 J4111 -15.5 l'II + no 71f1. + 22,4 5'h. + 17.5 9uh. - 16.6 6"1u - 15.2 8'/11 + 7.2 l'h + 9.4 41/. + 7,6 91/. - 17.5 12 - 8.0 !Juh, - 18.1 14111 - 18.9 8lf1 + l2.8 171/. - 21.8 9uh. - 16.8 !J I/II - 20.1 71/. - 12J 12'/. - 10.9 7'11 - !J.6 24lftl - 11.1 14'/, - 15,7 4'h. - 15.0 1l'1u - 16.1 8"h. - !J ,6 5111 - 17.2 N/A N/A 17'11 - 7.l 10'11 - 11.8 19 - 17.l 70/1. - l5 15'h, - 17.1 18'!l1 - 12.9 n'II -16.7 18'11 - 14,0 !J - 15.4 8lftl - 17.1 11'" - 15.4 12'It. - 6,4 181fu + 8.2 l6 + 25.6 8\'1 - 10.7 8'11 + 40 5lf1 + 28.6 20 -18J 61/1 -11.2 60 - 20.8 15'11 -11.4 8'11 +1.4

27.0 80.6 lO .9 10.2 2l.2 19.7 61.5 67.4 56.1 19.1 12.0 ISJ 15.9 19.5 41.7 41.4 10.0 26.9 1.5 0.8 50.0 15.1 27.7 5J 19.2 5.9 26.7 15.5 11.7 ISJ 69.1 0.2 27.0 N/A 84.6 12.1 44,9 14.6 10.4 88.2 55 .4 9.1 8J lO.l 12.2 7.1 2.4 16.8 24.0 43.5 J9.4 7.9 0.2 51.1 28.8 5.6 12Mo.

Fund Nome(Symbol)

Sioek Exch

NAY

M8fltet

Prom

YIeld

Price

iDiot

2IZIII1

U.S. Gov'l. Bond Funds ACM GoY! Inc(ACG) N 10.78 l1'1u + ACM GoY! Oppty (AOF) N 8.65 81ft ACM Govt Sees (GSF) N 10.67 101ft ACM Goul Spec (SI) N 7.22 61/1 Am« Goul lncome (AGF)-c N 5.87 51/1 AmerOoul Port (AAF)-c N 6.97 60/1. BuII&Bear USOY! Sec (BBO)-a"A 14.73 Hill Dean Wilter Goul (GVT) IoN 9.44 8'11 Excelsior Income (EIS)·c 6N IUO 17 Kemper IntOovl (KOT) 7.84 7'11 "N

---

---

4.9 6.1 5.1 8.2 4.2 4.1 8.4 8.6 9.6 4.l

7.9 7.7 8.8 8.9 6.l 6J 6.1 6.9 6.9 8.4

Figure 21.1 Listing of Closed-End Funds (Excerpts) Source: Reprinted by permissi on of Barrtlll J, DowJon es & Company, ln c., March 23. 1998. p. MW91. All righLs reserved worldwide .

704

CHAPTER 21

stocks, respectively.) Most closed-end funds that invest in stocks (other than a few country funds) sell at a discount.f Finally, the last column in the figure shows the rate of return over the past 12 months for funds investing primarily in stocks and the past 12-month yield for funds investing primarily in fixed-income securities. Open-End Investment Companies

An investment company that stands ready at all times to purchase its own shares at or near their net asset value is termed an open-end investment company (or openend fund). Most of these companies, commonly known as mutual funds, also continuously offer new shares to the public for a price at or near their net asset values. Hence their capitalization is "open," with the number of shares outstanding changing on a daily basis. There are two methods used by mutual funds to sell their shares to the public: direct marketing and the use of a sales force. With direct marketing the mutual fund sells shares directly to investors without the use of a sales organization. In such a situation the open-end companies, known as no-load funds, sell their shares at a price equal to their net asset value. The other method of selling shares involves the use of a sales force that is paid a commission based on the number of shares it sells. This sales force often involves brokers, financial planners, and employees of insurance companies and banks. The open-end companies that use this method are known as load funds, because the commission involves adding a percentage load charge to the net asset value. The percen tage load charge by law cannot exceed 8.5% of the amount invested. For example, a se lling organization receiving $1,000 to be invested in a fund might retain as much as $85, leaving $915 to purchase the fund's shares at the current net asset value per share. Although this is usually described as a load charge of 8.5%, it is actually equal to 9 .3% (= $85/$915) of the amount ultimately invested . Load charges of this magnitude are levied by some funds for small purchases, but typically they are reduced for larger purchases. Furthermore, some funds have loads of less than 3.5% for purchases of all sizes and are hence dubbed low-load funds." When mutual fund shareholders want to sell their shares, they usually receive an amount equal to the fund's net asset value times the number of shares sold. However, a few funds charge a redemption fee, which usually is no more than I % of the fund's net asset value and typically is not levied if the investor has owned the shares for more than a specified time, such as one year. Hence its basic purpose is to discourage investors from selling their shares right after buying them. By discouraging such in-and-out trading the fund avoids the transaction costs associated with having to sell securities frequen tly in order to satisfy some investors' desires to sell their mutual fund shares rapidly. III In addition, mutual funds may charge current shareholders a distrihution fee annually. This 12b-1 fee (named for an SEC ruling involving a section of the Investment Company Act of 1940) is legally not allowed to exceed I % of the average market value of the total assets. It pays for advertising, promoting, and selling the fund to prospective purchasers as well as for providing certain services to existing investors. I I Sometimes the fee is coupled with a load charge that is paid when shares are initially purchased. One alleged benefit of the 12b-1 fee to the current owners of the fund is that the subsequent increased size of the portfolio will bring with it certain economies of scal e. Some mutual funds have different classes of stock. In such a situation an investor can choose the class that he or she wants to purchase. For example, class A stock might involve a 5% load charge but no annual12b-1 fee, whereas class B stock might Investment Companies

705

not have a load charge. Instead this class might have a 12b-1 fee of .5% per year plus a contingent deferred sales charge (paid when the investor sells shares) that starts at 5% if the investor sells his or her shares within a year of purchase and declines thereafter by 1% a year for each year that the stock is held, reaching zero after the fifth year. In addition, the class B shares might be set up so that they convert to class A shares after five years (when the contingent deferred sales charge has declined to zero). This feature allows investors who in itially bought class B shares to avoid 12b-l fees after five years. There might also be class C stock for which the investor pays an annual 12b-l fee of I % for as long as the shares are held. In summary, there are many different methods that mutual funds use to get the cash needed to pay for sales commissions and other selling costs. Some methods (such as the class C stock) are more attractive to investors who plan to hold their investment only for the short term. Others (such as the class B stock) are more attractive to investors who plan to hold their investment for the long term. As will be discussed later, the investment performance of no-load funds as a whole does not differ in any notable way from that of load funds. This fact is not surprising. The load charge (roughly 30% to 50% of which goes to the individual who sold the shares, with the selling organization keeping the rest) represents the cost of advertising, education, and persuasion. Mail-order firms often sell items for less than stores charge. Sales representatives who work in stores and those who sell mutual funds provide a service and require compensation. Buyers who consider such services worth less than their cost can and should avoid paying for them . Ouotations

Figure 2\.2 shows a portion of the quotations for mutual funds provided in The Wall Streetjournal for each business day except Friday. Funds that are listed under a name in boldface type have a common management company that is associated with that name. For example, note all the funds listed under AARP Invst. (AARP Invst stands for AARP Investment Program from Scudder, an investment program sponsored by the American Association of Retired People that involves mutual funds run by the management company of Scudder, Stevens & Clark.) After the abbreviated name of the mutual fund comes its net asset value, based on closing prices for the fund's securities on the day in question . The third column displays the change in net asset value from the close of the previous trading day, and the fourth column indicates the fund's rate of return for the year so far. On Friday of each week, The Wall StreetJoumal presents much more detailed information on mutual funds. Besides presenting net asset value, its change from the previous day, and the year-to-date return for each fund, the following additional information is presented: 1. Investment objective 2. Four-week return 3. Total return for the last year, three years, and five years, along with an indication of the fund's pentile rank relative to other funds with the same investment objective (top 20% = A, next 20% = B, middle 20% = C, next 20% = D, bottom 20% = E) for each of these time periods 4. Front-end load charge 5. Operating expense ratio

Figure 21.3 shows the weekly quotations that appear for a special type of mutual fund known as a money market fund. These funds invest in short-term, fixed-income securities, such as Treasury bills, commercial paper, and bank certificates of deposit. A special type of money market fund that invests primarily in short-term municipal 706

CHAPTER 21

LIPPER INDEXES Friday. Oclober 3. 1997 Prelim. Percenlage chg. since Eqully Indexes Prev. Wk ago Dec. 31 Close C.pllal Apprecl.tlon . 1937.65 + 0.57 + 2.05 + 24.48 . 6332.15 + 0.61 + 2.14 + 29.•3 Growlh Fund Sm.1I Cap Fund .. 674.73 + 0.66 + 2.22 + 23.50 .. 6064.80 + 0.51 + 1.94 + 27.52 Growlh & Income Eoulty Income Fd . 3217.23 + 0.38 + 1.77 + 25.96 Science .nd Tech Fd . 600.10 + 0.84 + 1.37 + 29.21 inlernallonal Fund .. 665.79 + 0.88 + 2.0'2 + 17.81 Gold Fund . 119.10 + 0.45 + 6.78 - 18.05 Bal.nced Fund .. 3669.49 + 0.33 + 1.46 + 19.74 Emerging M.rkels . 1006 + 0.15 + 1.16 + 12.81 Bond Index .. Corp A·Rated Debt...... 730.61 + 0.01 + 0.49 + 7.05 275.48 + 0.0'2 + 0.45 + 6.35 US Governmenl GNMA 299.09 - 0.04 + 0.25 + 6.62 756.• 1 + 0.19 + 0.88 + 11.85 High Currenl yield...... Intmdllnv Gr.de ........ 201.01 + 0.04 + 0.•4 + 6.54 185.22 + 0.03 + 0.22 + •.91 Short Inv Gr.de General Municipal ...... 527.59 + O.oJ + 0.33 + 6.38 High Yield Municipal .. 255.94 + 0.01 + 0.31 + 6.71 1u.n + 0.Q2 + 0.11 + 3.35 Short Municipal.......... 200.68 + 0.32 + 0.59 + 3.94 GlObal Income Inlernallonal Income.. . 126.50 + 0.58 + 0.68 + 2.22 OVERSEAS FUND INDEXES·a Friday. October 3. 1997 N/A + 0.97 + 14.65 LOFT GL Eoty Idx ..... 591.93 N/A - 0.11 - 2.58 LOFT GL Bond Idx ..... 203.99 Indexes .re based on the larges t funds wllhln the serne Investment cntecnve and do not Include muiliple share classes of similar funds . The Yardsllcks table, appearing wllh Frld.y's listings, Includes all funds wllh the same oblecllve. Source : Lipper Analvllc.1 Services, Inc. The Lipper Funds Inc.•re not affilialed wllh Lipper An.lvllc.1 Services. R.nges for Inveslmenl companies. wllh dallv price d.,. supplied bV Ihe N.llonal ASSocl.llon of Securilies De.lers and eerrorrnence .nd cosl c.lculatlons by Lipper Analvtlc.1 Services Inc. The NASD requires. mutual fund to h.ve at least 1.000 sh.reholders or nel assets of 525 million before being IIsled . NAV-Net Assel V.lue. Delalled expl.n.lorv noles .ppe.r elsewhere on Ihls p.ge. Nel YTD N.ma NAV Chg %rel AAL Mulual A :

~g~o'!Jh p r6~1:;:g:~t2~:~

HIYBdA 10.49+0.02 NS Inll p 12.17+0.0'2+11.0 MldC.p P 17.03+0.09 +25 .4 MunlBd p 11.47 ... + 7.0 SmCap p 14.19+0.12 +26 .7 A'i~~.ftJNt-o.ol + 14.3 CGrowthp 26.05 + O. 19 NS Inll p 12.09 +0.02 NS MldCap 16.93 +0.08 NS SmCap p 14.11+0.12 NS AARP In'lSI: BaIS&B 21.68 +0.08 +21.5 Bdlnc 15.29+0.02 NS CaGr 58.83 +0.37 +39.8 DlvGr 17.62+0.08 NS NS Dlvl nc 16.08 +0.03 GlnlM 15.17-0.01+ 5.9 GlblGr 19.67 +0.18+20.7 Gthlnc 59.27+0.38+32.8 HQ Bd 16.21 +0.01 + 6.0 InllSkl 17.62+0.18 NS SmCoSlk 20.27+0.06 NS ... + 6.4 TxF Bd 18.« NS USSlkl 18.31 +0.08 AHA Funds: Balan 16.17 +0.05+22.6 D1vrEo 23.17 +0.12 +33.5 Futl 9.99 ... + 7.1 Lim 10.22+0.01 + 5.0 AIM Funds A: Agrsv p 53.71 +0.26 +25.3 Balp 26.99+0.12+25.7 BIChp p 32.66 +0.14 +32.1 C.pDev p 15.28+0.10 +31.6 CharI p 14.27 +0.09 +30.1

~y~~'& ~UUg:~~tm

GIGr p 18.26+0.16+22.1 Gllnc p 11.00+0.04 + 6.7 GIUIII p 18.53-0.01 +18 .3 Grlh p 18.97 +0.13 +28.3 HYld p 10.26+0.01 +11.1 Inco p 8.58+0.02+ 9.6 .. . + 6.6 InlGov p 9.39 InllEQ p 18.48 +0.19 + 16.5 L1mM p 10.07 + 0.01 + 4.6 Munl p 8.29 +0.01 + 5.4 Sumll 16.18+0.13+33.2

t~~~f l~:fe

::: t

~:~

Valu p 37.56 +0.38 +28.9 Welng p 24.23+0.18+30.9

Nel YTD Name NAV Chg %rel MuPAB t 10.36 + 7.2 + 7.0 NIIMuB t 10.93 NEurB t 19.14+0.26+22.1 NAGvB I 8.40 ... + 15.5 PrGrlhB 122.61+0.22 +39.0 QusarB I 28.15+0.06+25.2 ReElnvB I 1•.29+0 .16+23.3 ST Mlb I 7.67 . .. + 3.9 SIrBalB I 16.77 +0.11 + 13.4 TeehB I 60.61 +0.60+26 .5 WldPrlvBI 13.9.+0.15 +25.6 Alliance Cap C:

~g~I~~C'~M~ +0.06 t l~:~

GovlC I 7.53 .. . + 5.3 Grine I 3.66+0.01 +28.9 GwthC 138.05 +0.24 +26.8 InBldC I 13.01 +0.03+ 19.0 InsMuC I 10.49 .. . + 6.4 InliC I 18.\9 +0.22+11.9 LldMtGC 19.• 1 + 4.4 MrlgC t 8.62 + 6.0 MuCA C I 11,02-0.01 + 7.1 MuF LC I 10.16 + 7.1 MuNJC 110.18 + 6.9 MuNYC I 10.10 + 7.8 MuOHC I 10.19 + 8.2 + 7.0 NIiMuC 1\0.93 NAGvC I 8.40 + 15.5 PrGrthC I 22.64+0.22 +39 .0 QuasarC I 28.16+0.05 + 25.2 ReElnvC I lU9 +0.16 +23 .3 TechC 160.60+0.59+26.4 Amanalncomel'. 12-0.01 +22.7 AmUIIFd 27.01 ... + 10.8 Amer AAdvanl Funds: Bal 16.6\ +0.03 + 18.7 BalPlan 16.46+0.03+18 .4 Bdlnst 10.12 ... NA Grine 22.80 +0.07 +27.4 GrlnPlan 22.54+0.08 +27 .1 InllEo 18.26 +0.13 + 18.9 L1dTr 9.65 .. . + 5.0

A~f:n~:3~~W+0.15 + 18.5 EoGro EQlnc GIGold IneGro NatRes Real SIrAgg SIrConv SIr Mod UIII Value

21.39+0 .15+35 .3 7.80+0.01 +26.6 9.63 +0.05 -14 .5 26.58+0.15+33.5 13.86+0.13+17.7 16.85 +0.10+26.4 6.53+0.04 + 19.8 5.62+0.02+ 12.9 6.14 + 0.03 + 16.7 13.25 -0.01 + 18.2 8.37 +0.01 +28.6

Net YTD Name NAV Chg 'Yorel L1dMat 10.42 .. . NA MunlBd 10.13+0.01 NA RegEo 29.92 +0.08 NA AmerlSlar Funds: CapGro 14.51 +0.08 +28.5 coretnc 10.16 .. . + 6.0 DlvGr 11.73 +0.05 NS L1mDUt'lnc 10.00+0 .01 + 5.0 NS L1mDurTn 10.07 +0.01 L1mDurus 10.10 NS TnTEBd 10.05 + 4.7 Amway 9.50 + 0.03 + 24.7 Analyllc Funds: MstrFlxl 1M3 .. . + 8.0

~~~~avlu~+O·~t'U

AnchrCa 30.46 + 0.29 + 15.8 AnchrlnBd 7.54+ 0.06 - 9.4 ApeIMCapGr7.56+0.13+ 7.1 Aon Funds: AstAlio 17.20+0.10+32.5 GovSec 10.41 +0.01 + 7.0 InllEo 12.21 +0.06 + 14.6 REIT 14.27+0.13+ 18.6 S&P5OO 14.92 +0.07 + 31.7 Aquila Funds: AZ TF 10.76 + 6.1 + 5.2 CO TF 10.55 HI TF 11.60 + 5.4 KY TF 10.70 + 5.6 Nrgnsl TF 10.36 + 6.1 + 5.4 OR TF 10.70 TxFUT 10.12 + 6.2 Aquinas: Balance 13.45 +0.03 + 18.8 EoGrth 17.34 +0.10+28.9 Eolnc 16.67+0.02+27.4 Fxlne 10.10+0.01 + 6.4 Arch Funds: Bal 13.46 +0.07 + 18.1 Bdldx 10.14+0.01 NS EQldxA p 12.06+0.06 NS sernc 11.67+0.10 NS smCap 16.17+0.07+28.6 GovCorp 10.32+ 0.01 + 5.8 orernc 21.71 +0.17+29.1 InllEolnv 13.26+0.07 + 13.7 IntmCorBd 10,10+0.01 NS MoTF 11.86 ... + 5.8 '" + 7.2 NatlMuBd 10.28 ShlntmMu 10.11 + 3.8 US Gov 10.62 + 4.8 ARMADA FUNDS: CorEql 10.07 +0.07 NA Enhlncl p 10.07 .. . + 5,0 EoGrol p 21.86+0.16+36.1 EoGroR p 21.90 +0.16 +35.9

~~I~'crp 11~·.~ + O,?~ t 2~J

GNMA I p 10,37 .. . + 7.3 IntEql 10.11 +0.07 NA InlmGvl p 10.21+ 0.01 + 6.2 MldCapl p 18.51+0.05 + 35.9 + 5.2 OH TE I p 11.07 + 4.9 PA Mul p 10.40 TotAdvl p 10.23+0.01 + 7.4 Ariel MUlual Funds: Apprec p 34.03 - 0.01 + 30.5 Bondlnsl 10.34-0.01 + 6.8 Growth p 41.86-0.07+31.0 Amslng 12.03+0.08 + 18.9 Arrow Funds: Eoullv 19.19+0.14 +28.7 Fxdlncm 10.00 + 5.5 Munl 10.45 + 4.6 Artisan Inil 15.01 + 0.16 + 12.7 Artls.nSmCp17.43 +0.18 +27.8

Altl'~ ~~ouf.~5

+ 5.9 ARSI 3.11 +2.6 ARS I·A 3.09 + 1.8 AdIUSI 5.63 + 5.9 Ad USII 5.70+0.01 + 6.1 Alias Funds: BalancA p 14,20+0.04 + 19.6 CalnsA p 10.55 + 4.9 CaMunlA p 11.36 + 5.6 GlbGroA 14.42+0.20 + 31.6 GvlSCA p 10.21 ... + 6.6 GrolncA p 22.09+0.15+24 .3 GrolncB p 22.03+0.15 + 24.0 NaMunlA p 11.47 ... + 6.0 StrGroA p 18.94+0.05+35.2 SIr IncA p 5.26 + 0.01 + 8.4 AVESTA Trusl: Balanced 29.03+ 0.11 +22.7 CoreEo 21.02+0.10+31.9 EQGro 38.34 +0.24 +37.2 Eolncm 36.53+0.14+29.5 Income 19.76+0.01 + 6.5 ShTmGv 12.23 +0 .0\ + 4.9 SmCap 23.02+0.14 +31.2 BB&T : BalA p 13.76+0.04+ 17.8 BaiT 13.73+0.04+18.0 Grol ncA p 20.28 + 0.09 + 30.0 GrolncB p 20.22+0.08 + 29.2 GrolneT 20.32 +0.09 +30.3 InlGavT 9.91 .. . + 6.0

Name

NAV

Nel YTD Chg %rel

8:8? t

Fn~~t~kt ~:fH 1N InllEo 11.36+0.07+ 12.5 inllFx 8.47 +0.05 - 1.9 LgGrw 18.52+0.11 + 30.6 LgVal 16.04+0.10+30.7 + 8.8 L TBnd 8.52 MIOBkd 8.04 + 6.8 Mu nl 8.72 + 6.4 SmGrw 20.16 + 0.14 + 23.1 SmVal 15.75+0.10+35.2 CGM Funds: AmerTF 9.62-0.05 NE ceoov 41.69+0.25+43.4 Focus 11.06+0.04 NA Fxdlnc 12.06-0.02+ 8.7 Mull 37.75+0.15+21.4 Reallv 18.20+0.20+28.1

~l~~~~r: 11~:JJ t 8:Y~ t HJ

CRMSmCapV 18.06+0.24+28.8 California Trusl: CalincTF 13.03 + 6.8 CailnsTF 10.81 + 5.1 CalUS 10.6\ + 5.6 S&P5oo 21.36 + 0.\0 + 31.7 S&PMldCap19.83 + 0.10 + 32.6 Calmos 16.86+0.05+21.0 Calvert Group: CapAccm p 27.75 + 0.10 + 24.5 Inca p 17.31 ... + 8.0 IntlEQA p 22.14+0.12 + 16.0 InllEoC p 21.46+ 0.11 + 15.2 MuBdCAI10.55+0.01 + U Munlnl 10.68 ... + 4.8 Social p 35.39 +0.16 + 19.5 SoeBd p 16.75+0.01 + 7.4 socea P 28.23 +0.22 +25 .9 secor p 35.02 +0.15 + 18.5 StrGwthAp 17.•0+0.03- 7.7 StrGwthC p 1),0. + 0.02 - 8.1 TxF Lt 10.71 +0.01 + 3.2

t~~IJ!11l:~~t8:glt

U

capValEq5e1 13.78 + 0.11 + 18.2 CapVaIToISelll .f6+ 0.05 + 12.4 Cappiello·Rushmore : EmgGr 17.16+0.03+28.4 Grwth 23.03 + 0.25 + 35.1 11.15+0.04+11.0 UIII Capslone Group: Gvllnc p 24.78 ... + 3.5 Grlh p 17.57 +0.07 +27.9 NJap.n p 5.56-0.03- 9.6 NZland p 12.56- 0.08 - 4.6 The Cardinal Group:

~~Y~n~~~It:~t8:~~t~~:~

Fund 16.93+0.06+31.2 Govl Oblo 8.21 ... + 6.7 CarllCa 13.63 +0.01 + 7.9 Centura Funds: EoGrC 19.08 + 0.04 + 27.0 EolncmC 13,05-0.01 +24.6 FedSecC 10.13 + 5.2 + 5.8 NC TxFr 10.31 CnlShs 43.81 +0.42+40.7 ChaconlalnGr p 12.53 +0.04 + 20.0 Chesapeake Funds: Class A 21.56 +0.14 + 36.4 Growth 24.56 +0.11 +37.7 Insll 21.7\ +0.14+36.7 Suplnsll 21.77+0.15+36.9 Cheslnl 300.15 + 1.42 + 24.4 Chicago Trusl : Balncd p 11.24 + 0.05 + 18.1 Bond 10.10 +0.01 + 6.9 Grolne 20.43+0.14+24 .3 Talon p 18.20 -0.24 NE ChubbGrln 27.92+ 0.23 + 36.2 ChubbTR 21.80+0.12+27.7 CIlISelecl : Fa1l0200 p 11.52 +0.03 NA Foll0300p 12.03+ 0.04 NA Fol104llO p 12.50 + 0.07 NA FolioSOO p 12.68 +0.07 NA Cllizens Trusl: CltEmGro 16.55+ 0.12 + 23.6 Ciline 10.85+0.01 + 8.0 Clllndx 20.25+0.14+34.9 CIIGbl \5 .47+0.11 +25.8 Clipper 84.28+0.48+24.7 Colonial Funds CI A: CA TEx 7.62-0.01 + 6.7 + 6.8 CT TEx 7.70 FedSec 10.70 + 7.0 + 6.2 FL TEx 7.63 Col Fund 11.69+ 0.08 + 27.5

glo~1v H:Htg:Mtl~:~

HIYld 7.28+0.01 +12 .2 HYMu p 10.31-0.01 + 6.9 Income p6.53+0.02+ 7.4 I nllGr 10.87 + 0.07 + 11.1 InllHz 16.39+0.10+18.1 MA TEx 8.04 ... + 6.7 MI TEx 7.17 +0.01 + 6.7 + 6.9 MN TEx 7.39 + 6.3 NY TEx 7.22

Figure 21.2 Listing of Mutual Funds (Excerpts) Source: Reprinted by pennission of TM Wall StreetJouma~ DowJones & Company. Inc.• October 6, 1997, p. C21. All rights reserved worldwide.

Investment Companies

707

The following quotallons. coltecteo by 'he Nationa l Asscctalion of Securities Dealers Inc.• represent the average of annua lized yields and dollar·welghted portlollo maturit ies ending Wednesday. october 8. 1997. Yields don't Include capital ga ins or losses. Avg. 7Dav Fund

Mat. Yield Auets

Money Markel: AARP HQ 52 4.66 45 4.67 AAdMlleP 44 4.60 AAdvGovP AAdvMMPlat 45 4.83 AIMMMC 18 4.66 18 4.59 AIMMMA ARK Gvln II 40 5.19 ARK MMln II 50 5.30 50 5.40 ARKMM A 50 5.09 ARKMM B ARKUSG A 40 5.29 ARKUST A 85 4.94 ARKUST C 85 4.84 AVESTA Tr 50 5.13 74 5.01 AccUSGov 69 4.93 ActAsGv AclAsMny 80 5.21 43 4.68 Advantus a 49 5.32 AetnaAdvs 49 5.32 Aetna Sel 47 4.93 AlexBwn 53 4.64 AlxBTr 20 4.71 AlperMM AlilaGenMu 65 2.93 35 4,58 AltiaGov Altlaprlme 53 4.73 37 4.68 Alii TrResv AiliaCpRs 58 4.n 41 4.60 AllaGvR 62 4.71 AiliMny AmAAdGvl 44 5.32 AmAAdMMI 45 5.53 51 4.86 AmCRes 47 5.01 AmPerCsh 1 4.81 AmPerTrs Amcore Gv 53 4.73 AmAAdMMP 45 5.23 AmAAdGvM 4-4 4.98 AmAAdMMM 45 5.09 AmSlarPr I 2lI 4.83 ArnerSlarPrT 28 5.08 AmStarUST I 45 4.73 AmSta rUST T 45 4.98 AmSPuthPrC 55 4.91 AmSouthPrP 55 5.01 AmSOUthUSC 57 4.58 AmSouthUSP 57 4.68 58 5.43 AonMMktY 50 4.90 ArchFd Armada Gvl 48 5.14 ArmadaGvR 48 5.04 Armada MMI 45 5.24 Armada MMR 45 5.14 Armada Trs yl 52 4.75 13 4.77 Ar rowGovl AMF MM Pt 3 5.17 Atlas USTrs 53 4.77 41 5.09 Autcsh 39 4.96 AutGvt 42 4.94 AuGvSvc 41 4.92 AutCshCIi 47 4.58 AutTreasC BB&T UST Tr 46 4069 BNYHam TrHm 2 4.93 BNYHmltTrPr 2 4.68 BNY Hmlln 49 5.37 BNY HmllnPr 49 5.10

4n 47 75 470 277 264 94 90 331 158 1173 244 88 126 51 690 10129 55 151 271 2956 661 173 152 127 33017 714 6295 4078 1101 33 1353 297 313 340 146 160 29 105 58 42 74 118 118 508 10 273 846 152 940 200 1996 412 274 140 48 60 1459 2294 619 635 290 255 82 126 809 593

Avg. 7Dav Mat. Yield Ami' Fund GoldenOK·PC 58 5.27 105 GovTxMgSS 0 5.07 541 41 5.42 301 16 GovOb IS 41 5.17 1023 GovOb SS GovTxMplS 43 5.32 682 GradisonGvtRv 56 4.84 1653 49 4.97 236 GrtHa llGv GrlHa liPr 46 5.01 3273 Gr illln 49 4.86 233 26 4.74 115 GrdCMA 29 5.06 360 GrdCsFd 47 5.06 178 HSBC csn n 49 4.95 HSBC Gvt 23 HSBC USTrea 60 4.95 64 61 5.19 Harbor HarrlsCashA 66 5.25 597 HarrlsCashC 66 5.54 933 HTlnsgtGv p 61 5.05 255 71 Harr lsGovtC 61 5.37 HtgCshA 43 4.87 2094 HIMrkUSF ld 39 5.02 209 HIMrkTrsFld 67 4.95 255 HIMrkTrsRtl p 67 4.70 632 HIMrkDvF ld 37 5.12 1052 HIMrkDvRII p 37 4.87 8n 50 HiMrkUSRII p 39 4.78 HllrdGovl 52 5.01 617 HmestdDlv 6l 4.86 54 Tax Exempt : AARPHTe 54 2.89 103 10 2.82 67 AAdvMunP 41 3.11 50 AIMTx ARKTaxFr A 80 3.44 110 ActAsCal 40 2.70 537 49 3.06 1805 ActAstTx 44 3.38 230 ALMunl 49 3.12 740 AlxB TF 77 2.76 142 AIiMuNJ 47 2.78 406 AIiMunCal AIiMuCT 64 2.83 115 42 3.00 \06 AIliMuFL AllianMuVA 27 3.00 96 44 2.81 471 AIiMuNY AliiaMun 52 2.88 1118 AmAAdMuM 10 3.22 25 AmCBnCA Mu 56 3. 17 170 AmCBn CATF 56 3.17 421 AmCBn FL 56 3.24 81 AmCBn NatTF 51 3.78 114 AmSoulhTEC 46 2.97 23 AmSouthTE P 46 3.07 57 11 ArchFd 25 2.73 ArmadaPA rxr 43 3.30 66 67 Armada TE R 41 3.26 Armada TE l 41 3.36 370 49 55 2.94 AllasCA 40 2.78 107 BT InvNY

Figure 21.3 Listing of Money Market Mutual Funds (Excerpts) Source: Repr irucd by permission or TIlL Wall Street journal; DowJ on es & Company. Inc.• October 9. 1997. p. C12. All rights reserved worldwide.

debt is also shown in the lower right-hand part of the figure . Next to the name of such a fund are shown the average maturity of its holdings, the annual yield based on what was earned over the last seven days, and the aggregate market value of its assets. Not shown, but an important factor in selecting a money market fund, is the degree of safety (that is, default risk) associated with the assets held by each fund . An Example

In order to highlight the differences in purchasing shares of closed-end funds, noload funds, and load funds, consider the following example. An investor has $1,000 to use in purchasing shares of a fund and is considering the following funds, all of which have the same net asset value (NAV) of$10 per share. Closed-end fund E is selling for a market price that equals its NAV, whereas closed-end fund D is seIling at a 20% discount, or $8 (= $10 X .80). The broker 708

CHAPTER 21

charges a commission equal to 2% of the market price for each share purchased. Mutual fund N is a no-load fund, whereas mutual fund L charges an % load. How many shares does the investor end up with in each case?

8-4

Closed-end fund E: Closed-end fund D: Mutual fund N: Mutual Fund L:

cost per share = $10 + $.20 commission = $10.20 number of shares = $1,000/$10.20 = 98.04 cost per share = $8 + $.16 commission = $8 .16 numberofshares = $1,000/$8.16 = 122.55 cost per share = $10 number of shares = $1,000/$10 = 100 cost per share = $10 + $.93 load = $10.93 (note: 8.5% X $10.93 = $.93) number of shares = $1,000/$10.93 = 91.50

Thus the largest number of shares would be received when buying the shares of discounted closed-end fund D; the fewest shares would be received when buying the shares of load fund L

IEIIII

INVESTMENT POLICIES

Different investment companies have different investment objectives (also termed investment styles). Some companies are designed as substitutes for their shareholders' entire portfolio; others expect their shareholders to own other securities. Some restrict their domain or selection methods severely; others give their managers wide latitude. Many engage in highly active management, with substantial portfolio changes designed to exploit perceived superior investment predictions. Others are more passive, concentrating instead on tailoring a portfolio to serve the interests of a particular clientele. Although categorization is difficult, broad classes of investment objectives are often defined. As mentioned earlier, money market funds hold short-term (typically less than one year) fixed-income instruments, such as bank certificates of deposit, commercial paper, and Treasury bills. The fund manager will extract an annual fee for this service, usually between .25% and 1% of the average value of total assets. There are usually no load charges, and investors may add or remove money from their accounts at almost any time. Dividends are usually declared daily. Arrangements with a cooperating bank often make it possible to write a check on an account, where the bank obtains the amount involved by redeeming "shares" in the fund when the check clears. Bond funds invest in fixed-income securities. Some go further, specifying that only particular types will be purchased. There are corporate bond funds, U.S. government bond funds, GNMA (or Ginnie Mae) funds, convertible bond funds, and so on. Some a re organized as open-end investment companies, others as closed-end investment companies. As indicated earlier, the predominant type of unit investment trust in the United States is the bond unit investment trust. Some purchase only government issues, others purchase only corporate issues, and still others specialize to an even greater extent. Municipal bond unit investment trusts often make it easier for those in high tax brackets to obtain diversification and liquidity while taking advantage of the exemption of such securities from personal income taxation. Bond unit investment trusts typically hold securities with different coupon payment schedules and pay roughly equal-size dividends every month. Investment Companies

709

Many open-end companies consider themselves managers for the bulk of the investment assets of their clients. Those that hold both equity and fixed-income securities particularly tit this description. CDA/Wiesenberger Investment Companies Service refers to such companies as balanced funds, provided that at least 25% of their portfolios are invested in bonds. These funds seek to "minimize investment risks without unduly sacrificing possibilities for long-term growth and current incorue.t'" Somewhat similar to balanced funds are flexible income funds. These funds seek to "provide liberal current income. ,,1:1 Whereas balanced funds typically hold relatively constant mixes of bonds, preferred stock, convertible bonds, and common stocks, flexible income funds often alter the proportions periodically in attempts to "time the market." Similar to these flexible funds are asset allocationfunds, which also attempt to time the market hut, in doing so, focus on total return instead of current income. A diversified common stock fund invests most of its assets in common stocks, although some short-term money market instruments may be held to accommodate irregular cash flows or to engage in market timing. In 1997 CDA/Wiesenberger classified the majority of diversified common stock funds as having one of three types of objectives: (I) capital gain, (2) g-rowth, or (3) growth and income.!" Two factors appear to be involved in this classification: the relative importance of dividend income versus capital gains and the overall level of risk taken. The classifications are arranged in decreasing order of emphasis the funds place on capital appreciation but in increasing order of emphasis the funds place on current income and relative price stability. Because high-dividend portfolios are generally less risky th an portfolios with low dividends, relatively few major conflicts arise, although two rather different criteria are involved. There is also another class, equity income funds, that CDA/Wiesenberger describes as seeking to generate a stream of current income by investing in stocks with sizable dividend yields. Borderline cases remain in which the differen ce between a capital gain fund and a growth fund is a matter of degree, which, in some cases, can be small. Similarly, the differences between a growth fund and a growth-incomc fund can be small. Classification is difficult because the official statement of investment objectives in a fund's prospectus is often fuzzy. A few specialized investmen t companies concentrate on the securities of firms in a particular industry or sector; these are known as sectorfunds. For example, there are chemical funds, aerospace funds, technology funds, and gold funds. Others deal in securities of a particular type; examples include funds that hold restricted (that is, "letter") stock, funds that invest in over-the-counter stocks, and funds that invest in the stocks of small companies. Still others provide a convenient means for holding the securities of firm s in a particular country, such as the previously mentioned India and Indonesia funds. There are also investment companies that, by design, invest more widely internationally, purchasing stocks and bonds from a variety of countries. (From a U.S . viewpoint, international funds are those investing in non-U.S. securities. whereas global funds invest in both U.S. and non-U.S. securities.) 15 Although municipal bond unit investment trusts have been available for many years, open-end municipal bond funds were first offered in 1976. Some municipal bond funds hold long-term issues from many states. Others specialize in the long-term issues of governmental units in one state ("single-state" funds) in order to provide an investment vehicle for residents of that state who wish to avoid paying state taxes (as well as federal taxes) on the income. Still others buy short-term municipal securities (as noted in Figure 21.3), with some specializing in the short-term issues of governmental units in one state. An index fund attempts to provide results similar or identical to those computed for a specified market index. For example, the Vanguard Index 500 Trust, a noload open-end investment company, provides a vehicle for small investors who wish 710

CHAPTER 21

TABLE

21.1

Mutual Fund Classifications as of Year-end 1996 Number of Funds

Total Net Assets (billions)

Equity

2,626

$1,751

Bond and income

2.679

886

Taxable money market

n6r.

762

Tax-exempt.money market

323

140

6,2H~

$3,539

Classification (a) Classification bya&Se1Jl

Total (b) Classification by investment objectives

$275

Aggressive growth Growth

482

Growth and Income

Global-equity

589 5 177 107

Income-equity

116

Precious metals International

63

Flexible portfolio Balanced

99

Income-mixed

88

Income-bond

.

U.S. government income Ginnie Mae Global bond Corporate bond

101 80 51 37 36 78

High-yli:1d bund

136

National municipal bond-s-lcng-term State municipal bond-s-long-term Taxable money market Tax-exempt money market Total Source: Adapted from /997 MIltlwl Fu"d Fart BoaH (W;t~hin~lO with permission or the IIlWSlll1t"lll Compauy lustitun-.

~

117

762 140 $3,539 n.

DC: lnvesrment Corupauy lnxriuuc. 1997). pp. lj{)....fil. 64 . H~5 . U... ed

to obtain results matching those of the Standard & Poor's 500 stock index, less operating expenses. Similarly, a number of banks have established commingled index funds, and corporations and other organizations have set up index funds for their own employee retirement trust funds . Table 21.1 provides an indication of the number of mutual funds pursuing various kinds of investment objectives, along with the amount of assets under their control. In total there were nearly 6,300 mutual funds in existence at year-end 1996. At that time these funds had nearly $3 .6 trillion invested in a variety of financial assets. Both the number of funds and the dollars invested in them have continued to rise rapidly as investors, ranging from individuals to large institutions, have come to appreciate the advantages of investing through mutual funds.

IIZII

MUTUAL FUND TAXATION

The U.S. Internal Revenue Code allows an investment company to avoid corporate income taxation, provided it meets certain standards and pays at least 90% of its net Investment Companies

711

income to its stockholders. Instead, its stockholders must pay taxes on the income that they receive. Most investment companies choose to distribute their net income by making two kinds of cash payments to their shareholders-one for income (from dividends and interest that the fund has received) and one for net realized capital gains. These two payments are then taxed at the shareholder level as ordinary income and capital gains, respectively. This practice creates a porential problem for investors near the end of the year that can best be seen with an example. Imagine on December 15 an investor pays $10,000 in a no-load fund whose shares are selling for $20, thus receiving 500 shares. On December 16 the fund declares and pays a dividend of $2 per share, thereby lowering its net asset value by $2 per share to $18. When the new year arrives, the investor will have to report $1,000 of taxable income, because he or she received a dividend check for $1,000 (=$2 X 500), even if the shares are still selling for $18 at the end of the year. Thus, the investor has not seen his or her investment increase in value but will still owe income taxes on the investment. Consequently, most financial advisers suggest that investors avoid investing in a taxable mutual fund near year-end. (Investors who buy mutual funds with their tax-exempt accounts such as IRAs would escape such taxation at this time, as mentioned in Chapter 12.)

Ell

MUTUAL FUND PERFORMANCE Mutual funds are required to compute and publicize their net asset values daily. Because their income and their capital gain distributions are also publicized, they are ideal candidates for studies of the performance of professionally managed portfolios. Thus it is hardly surprising that mutual funds have frequently been the subject of extensive study.

21.5.1

Calculating Returns

In studies of performance, the rate of return on a mutual fund for period t is calculated by adding the change in net asset value to the amount of income and the capital gains distributions made during the period, denoted by I, and G respectively, and " dividing this total by the net asset value at the beginning of the period: T1

=

(NAV, - NAV,_I) NA V,-I

+ I, + G,

(21.2)

For example, a mutual fund that had a net asset value of $10 at the beginning of month t, made income and capital gain distributions of, respectively, $.05 and $.04 per share during the month, and then ended the month with a net asset value of $10.03 would have a monthly return of: T I

=

($10.03 - $10.00) + $.05 $10.00

+ $.04

= 1.20%.

Returns calculated in this manner can be used to evaluate the performance of the portfolio manager of a mutual fund because this method reflects the results of the manager's investment decisions. However, it does not necessarily indicate the return earned by the shareholders in the fund because a load charge may have been involved. In the example, perhaps the investor paid $10.50 at the beginning of the month for one share of this fund, with $.50 being a front-end load. If this were the case, the investor's return for this month is calculated using Equation (21.2), where NA V,-l is $10.50, not $10.00: 712

CHAPTER 21

r=

($10.03 - $10.50)

f

+ $.05 + $.04

$10.50

= -3.62% Thus the return for the investor who bought one share at the beginning of the month and paid a $.50 per share load charge at that time would be -3.62%. However, the portfolio manager was only given $10.00 per share to invest, because the load charge was paid to certain people who were responsible for getting the investor to buy the share. Accordingly, the portfolio manager should be evaluated on the basis of the return provided on the $10.00, which in this example was 1.20%. Recently, data on professionally managed pension funds and bank commingled funds have become available. The performance of the managers of such funds appears to be similar to that of mutual fund managers: They do reasonably well tailoring portfolios to meet clients' objectives, but few seem to be able to consistently "beat the market." Although the following sections deal only with U.S. mutual funds, many of the results apply to other investment companies, both in the United States and in other countries. A more detailed discussion of certain risk-adjusted measures of performance and their application to mutual funds is deferred to Chapter 24.

21 .5.2

Average Return

Some organizations have established two kinds of indices based on the net asset values of mutual funds that have similar investment objectives. One kind of index includes nearly all of the U.S.-based mutual funds, whereas the second kind uses a much smaller sample. As shown in Figure 21.4, both types of indices are presented every week (and, more extensively, every quarter) in Barron S, where mutual fund indices that have been prepared by Lipper Analytical Services are published. Many studies have compared the performance of investment companies that have invested primarily in common stocks with the perfo rmance of a benchmark portfolio that generally consisted of a combination of (1) a market index, such as Standard & Poor's 500 stock index; (2) a riskfree asset, such as Treasury bills; and sometimes other indices, such as (3) an index to account for the difference in performance between large and small capitalization stocks and (4) an index to account for the difference in performance between high and low book-to-market price stocks . Each particular combination was chosen so that the benchmark portfolio had a risk level that was equal to that of the investment company. Thus an investment company that had a beta of .80 would be compared with a benchmark portfolio that had 80% invested in the market index and 20% in the riskfree asset (provided these were the only indices used to construct the benchmark portfolio). Hi Alternatively. sometimes styk analysis is used to arrive at the appropriate benchmark. With this approach, a fund's returns are matched with those of a set of indices, such as the Standard & Poor's/BARRA Value and Growth indices, the Wilshire 4500 index (for small-cap stocks), and various others in order to arrive at a combination of the indices that seem to best describe the investment style of the fund (for more on style analysis , see Institutional Issues: Custom Benchmark Portfolios in Chapter 24) . One way of determining whether a mutual fund has had superior performance is to subtract the average return on the benchmark portfolio from the average return of the mutual fund. This abnormal return, known as the fund's ex post alpha, is denoted O:p:

(21.3) where arp is the average return on portfolio p and arbp is the average return on the benchmark portfolio associated with portfolio p. Note that if O:p > 0, then the Investment Companies

713

;~> .'.

INS TIT UTI 0 N A LIS SUE S

. ,.

".

Variable Annuities Variable annuities have become one of the hottest products to hit the institutional investment market in the 1990s. Despite the rather incongruous name, assets invested in variable annuities have grown to over $500 billion. What is a variable annuity? To start, perhaps a better question is, "What is an annuity?" In the world of' financial services, an annuity is a tax-advantaged form ofinvesunent made through an insurance company. The insurer makes certain promises about how and in what amounts the proceeds of the investment will be returned to the investor (or the investor's beneficiaries). There are two types of annuities: fixed and variable. A familiarity with fixed annuities is helpful in understanding variable annuities. With a fixed annuity, you as the investor enter into a contract with an insurance company, agreeing to pay a stated amount known as the premium, which represent~ the cost of the annuity. This premium is usually paid in a lump sum. In exchange for the premium, the insurance company sets an interest rate that it will credit your investment with over a specilied guarfmlrr {wriodof time. You choose the length of the guarantee period, with rates usually higher for longer periods. At the end of the guarantee period, the insurance company will establish new rates and you must again choose a guarantee period. The commitment involved in a fixed annuity is a two-waystreet. In the early years of your contract, withdrawing more than a small proportion (usually up to 10%) of your investment annually invokes a surrender {WI/ally. Over several years , the size of the penalty declines to zero. Further, if at the end of a rate guarantee period, the newly offered rate is materially lower (as defined by the annuity contract) than the previous rate, you can withdraw from the contract penalty-free and move the balance to another annuity provider. Fixed annuities are similar in many respects to bank certificate of deposits (CDs) . There are several distinctions however. Most important, your investment is allowed to accumulate interest on a tax-deferred basis. Only when you withdraw from the annuity must you pay tax on the earned in terest. In the case of a CD, you pay taxes annually on your earnings. In exchange for this tax advantage, however, you cannot withdraw funds from your annuity until age 59.5 (un-

714

less you transfer to another annuity) without being assessed a 10% penalty by the IRS. Fixed annuities are also different from CDs in that you have the option to "annuitize" the distribution of your accumulated investment. There are many different annuity variations. Payments are typically monthly or quarterly. You can receive payments for a specified period of time, or you can have the payments continue over your entire life, ending only when you die . You can even have your payments go to your beneficiary after you die . The size of yonI' annuity payments will depend on the selected payout option. Variable annuities are really not much more complicated than fixed annuities. Essentially the word variable refers to the rate of return earned on the premiums that you invest with the insurance company. Instead of offering a fixed interest rate guaranteed over a specified period of time, the annuity provider offers you a set of investment options in to which your premiums can be invested, such as a portfolio of growth stocks. You make the decision as to where to place your investment and if, and when, to switch those choices. The value of your accumulated earnings will respond commensurately (up or down) with the returns on your investment selection . Variable annuities are different from fixed annuities in two other key ways. First, you can add more funds to a variable annuity at any time before starting to receive annuitized distributions . In the case of fixed-rate annuities, adding additional funds requires purchasing a new contract at possibly a different interest rate. Second, the insurance company promises your beneficiaries a "death benefit" equal to the greater of your paid premiums (less any withdrawals) or the value of your investments at the time of yotll' death. Thus, variable annuities offer an insured "floor" on the value of your investments. (Because of the guaranteed interest rate, fixed-rate annuities have no need for such a provision.) The remainder of the variable annuity contract is essentially no different from the fixed annuity contract. Your earnings compound on a tax-deferred basis. Withdrawals are subject to surrender penalties depending on the terms of your contract. IRS penalties are charged on withdrawals before age 59.5. And

CHAPTER 21

when you move from the accumulation phase to the distribution phase, you can annuitize your distributions in a similar variety of ways. Variable annuities have been around since the early 1950s. The explosion in variable annuity popularity has come in recen t years as the federal government has vastly reduced the ability of investors to shelter investment income from taxes. Especially for people without access to employer-sponsored 40 I (k) retirement plans or who make contributions to either lRAs or Keogh Plans that are by law capped (see Chapter 12), variable annuities offer the only means to easily make large tax-deferred investments. Traditionally, insurance companies offered their variable annuity customers only investment options managed by the insurance companies themselves. Today, many insurance companies have made arrangements with mutual fund providers to offer versions or the mutual funds to variable annuity investors, with the insurers handling the death benefits. Although variable annuity investments must be kept in legally separate po rtfolios (known as "separate accounts"), mutual fund providers in many cases create "clone" versions of their popular funds specifically for variable annuity clients. More recently, an increasing number of mutual fund companies have turned the tables on the insurance companies by offering their own variable annuity products and making arrangements with insurance companies to provide the death benefits, Should you invest in mutual funds on a taxable basis or in variable annuities on a tax-deferred basis? The answer is not as clear-cut as many proponents of variable annuities might contend. Certainly if you are under age 59 .5 and may need access to your funds soon, you should factor in the IRS 10% withdrawal penalty and any insurance company surrender charges into your calculations. Suppose though that you are investing for the long haul. The tax-deferred benefits of variable annuities appear attractive compared with the alternative of facing annual taxation of distributed income and realized capital gains that investors in taxable mutual funds must pay. However, these tax benefits may be overwhelmed by two adverse aspects ofvariable annuities. The first is their cost. Variable annuity in-

Investment Companies

vestors not only must pay standard management and administrative expense fees similar to those paid by mutual fund shareholders, but they must also pay a fee to cover the death benefit. That fee typically runs in the range of I% to 1.5% per year. Only you can decide whether the option to redeem your investment at its original value is worth this expense. (It is true that variable annuities do not involve explicit sales commissions, but an informed mutual fund investor generally should not purchase a load fund.) Further, when assets are ultimately withdrawn from a variable annuity, the investor must pay taxes at ordinary income tax rates. The mutual fund investor, on the other hand, has annually been paying taxes primarily on realized capital gains at capital gains tax rates which are currently much lower than ordinal)' income tax rates (see Chapter 12) . Depending on how quickly capital gains in the taxable mutual funds are realized and the amount of dividend and interest income earned , it is possible that the combination of no death benefit expenses and lower taxes paid at capital gains tax rates may be better than deferring ordinal)' income taxes until distribution. In general, the longer your investment horizon, the more the taxdeferred aspects of variable annuities arc able to overcome their higher costs relative to taxable mutual funds. If you are an investor who likes to move among funds (lor example, between stock and bond funds) within a family of funds, variable annuities do offer a significant advantage over taxable mutual funds in rising markets. Within a variable annuity's fund family. switches occur without triggering a taxable event. With taxable mutual funds, a switch among funds will require payment of capital gains taxes on any appreciation in fund share values, regardless of whether the funds belong to a family of"funds. Finally, in terms of estate planning, variable annuities are at a disadvantage compared with taxable mutual funds. The death proceeds from a variable annuity bypass probate, easing administration of your estate. However, those proceeds are taxable to your beneficiaries as ordinary income. Conversely, the cost basis of taxable mutual funds will be stepped up to their market value at the time of your death-potentially a huge tax benefit.

715

LIPPER M UTUAL FU ND PEH FOHM A NCE AVERAGES Weekly Summary Report: Thursday. March 19, 1998 Cumulative Performances With Dividends Reinvested Net No. Asset Funds General Equity Funds: 107,074.8 258 Capital Appreciation 609,120.4 979 Growth Funds 302 Mid Cap Funds 89,436.1 140,082.7 577 Small Cap Funds 3,270.7 45 Micro Cap Funds 549,876.0 721 Growth and Income 123,675.8 88 S&P 500 Obiecllve 219 Equity Income 142,015.0 1,764.551.5 3,189 Gen. EqUity Funds Avg. Other Equity Funds: 43 Health/Biotechnology 14.906.0 6.289.6 59 Natural Resources 24 .520.S 72 SCience & Techno!. 16 Telecommunication Funds 3.847.7 105 Utility Funds 22.690.2 45 Financial Services 20.648.2 12,893.5 87 Real Estate Fund 63 Specialty/M isc. 3.130.1 44 Gold Oriented Funds 2,785.2 216 Global Funds 102.907.6 20.911.9 35 Global Small Cap Funds 162.712.1 SIS International Funds 4,324.6 50 Inn Small Cap Funds 14,621.4 92 European Region Fds 4,836.6 50 Pacific Region Funds 1,694.4 35 Japanese Funds 4,496.1 82 Pacific Ex Japan Funds 22 China Region Funds 1.002.8 19.178.4 153 Emerging Markets Funds 3,903.7 43 Latin American Funds 113.4 S Canadian Funds 343,488.2 1,342 World Equity Funds Avg. 2,216,965.5 5,021 All Equity Funds Avg. Other Funds: 62,767.8 218 Flexible Portfolio 24,039.7 92 Global Flex Port. 144,88S.4 391 Balanced Funds 1.206.3 IS Balanced Target 7.S86.7 57 Cony. Securities 26,767.5 74 Income Funds 22,74S.6 266 World Income Funds 416,625.8 1.814 Fixed Income Funds 2,923,590.3 7,948 Long-Term Average N/A Long- Tarm Median N/A Funds with a % Change

03/1219803/19/98

1213119703/19/98

02119/9803/19/98

12118/9703119/98

03120/9703/19/98

+ + + + + + + + +

10.76% 11.77% 10.94% 9.15% 8.94% 10,80% 12.54% 9.38% 10.73%

+ + + + + + + + +

1.47% 1.51% 1.46% 1.54% 1.26% 1.S2% 1.83% 1.40% 1.S1%

+ + + + + + + + +

5.26% 5.37% 5.73% 4.90% 5.15% 5.46% 6.04% 5.33% 5.34%

+ + + + + + + + +

14.37% 14.59% 15.68% 13.77% 12.88% 12.87% 14.34% 11.30% 13.88%

+ + + + + + + + +

33.41% 36.60% 36.51% 37.73% 45.86% 35.19% 40.77% 33.76% 36.21%

+ + + + + + + + + + + + + + + + + + + +

11.43% 0.13% 15.25% 20.47% 8.29% 10.54% 2.40% 6.52% 1.65% 11.69% 11.04% 12.50% 15.69% 17.45% 2.32% 1.32% 4.98% 2.84% 3.S3% 0.60% 1.93% 9.S0% 10.0S%

+ + + + + + + + + + + + + + + + + +

0.69% O.OS% 1.30% 3.60% 2.54% 2.76% 0.16% 0.61% 2.98% 1.73% 1.72% 1.96% 2.49% 2.63% 1.47% 0.98% 3.58% 3.91% 1.28% 2.06% 2.34% 1.76% I.SS%

+ + + + + + + + + + + + + + + + + + + +

4.25% 2.S4% 3.07% 11.17% 6.84% 7.61% 0.90% 3.37% 1.88% 5.98% 6.01% 6.29% 8.60% 9.16% 0.43% 4.11% 00% 6.17% 5.98% 7.90% 3.19% S.62% 5.28%

+ + + + + + + + + + + + + + + + + + + + + +

14.71% 3.03% 21.15% 23.20% 11.14% 12.23% 0.46% 8.S1% 1.67% 13.02% 13.45% 12.S1% 15.32% 17.54% 1.03% 1.02% 3.70% 1.12% S.95% 5.12% 8.72% 10.16% 12 .S3%

+ + + + + + + + + + + + +

+ + +

32.04% 0.S2% 3S.13% SS .88% 35.79% 49.43% 14.64% 32.62% 42.71% 25.08% 18.S4% 19.99% 13.S9% 35.76% 22.23% 7.19% 31.12% 18.99% 8.28% 8.34% 7.89% 9.S3% 28.3S%

+ + + + + + + + + + +

7.81% 7.68% 7.19% 5.24% 6.70% 4.93% 2.43% 1.84% 7.61% 8.23% 7,686

+ + + + + + + + + + +

1.02% 1.14% 0.91% 0.42% 0.89% 0.73% 0.24% 0.07% 1.10% 1.17% 7,381

+ + + + + + + + + + +

3.69% 3.87% 3.36% 1.45% 3.77% 2.60% 0.84% 0.25% 3.79% 07% 7,644

+ + + + + + + + + + +

9.35% 8.69% 8.61% 6.35% 8.71% 6.04% 2.62% 2.05% 9.38% 10.37% 7,650

+ + + + + + + + + + +

25.37% 18.83% 24.98% 18.40% 23.07% 20.24% 8.09% 10.32% 22.87% 24.48% 6,898

+ + + + + + + +

4.42% 6.0S% 5.27% 5.98% S.10%

+ + + + + + + +

12.83% 13.09% 14.32% 14.07% 12.19%

+ + + + +

34.63% 37.79% 37.82% 39.24% 29.07%

3.20% 16.05% 18.48%

+ +

9.81% 40.86% S1.20%

Securities Market Indexes Value

4700 567.38 1,260.82 1,089.74 8,803.0S Value

1.667.90 5,997.90 4,936.32

U.S. Equities: Russell 2000 Index xd NYSE Composite xd S&P Industrials S&P 500 xd Dow Jones Ind. Avg. xd International Equilles: Nikkei 22S Average xd FT 50E 100 Index DAX Index

+ + + + + + + +

8.S3% 10.99% 12.43% 12.29% 11.31% 9.31% 16.79% 16.16%

+ + + + + + + +

1.40% 1.70% 1.41% 1.8S% 1.66% 0.63% 3.S0% 2.00%

0.38% 4.89% 7.72%

Fund Management Companies Value:

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CHAPTER 22

(a) Head and Shoulders

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Details of construction of point and figure charts vary, hut the idea is to plot closing prices that form a trend in a single column, moving to the next column only when the trend is reversed. For example, closing prices might be rounded to the nearest dollar and the chart begun by plotting a beginning rounded price on a certain day. As long as the (rounded) price does not change, nothing is done. When a different price is recorded, it is plotted on the chart. A price higher than the initial price is indicated with an X, with any gaps between the prices also marked with an X A price below the initial price is marked with an 0 in a similar fashion. Then when a price that is different from the last one is recorded, it is plotted in the same column only ifit is in the same direction. (In general, Xs denote advancing prices and Os denote declining prices.) For example, if the first different price is above the beginning price, it is plotted above the beginning one. Then, if a price is recorded that is above the second one, it is plotted in the same column, but if it is below the second one, it is plotted in a new column to the right of the first column. Continuing, as long as new prices are in the same direction, they are plotted in the same column. Whenever there is a reversal, a new column is started. Figure 22.4(d) presents a point and figure chart for the same hypothetical stock used in the other panels. Point and figure enthusiasts look for all sorts of patterns in their charts. As with all chartist techniques, the idea is to recognize a pattern early enough to profit from one's ability to foresee the course of prices-a neat trick, if one can do it.

IE!II

MOVING AVERAGES

Many other procedures are used by technicians. Some construct moving averages to try to detect "intermediate" and "long-term" trends. With this procedure, a set number of the most recent closing prices on a security are averaged each day. (For example, daily closing prices over the previous 200 days may be used.) This means that each day, the oldest price is replaced with the most recent price in the set of closing prices that will be averaged. Frequently a line chart of these moving averages is plotted, along with a line chart of daily closing prices. Each day the charts are updated and then examined for trends to see if there is a buy or a sell signal present somewhere. Financial Analysis

783

Alternatively, a long-term moving average may be compared with a short-term moving average (the distinction between the two averages is that the long-term average uses a substantially larger set of closing prices in its calculations than the shortterm average). When the short-term average crosses the long-term average, a "signal" is said to have been given. The action recommended will depend on such things as whether the averages have been rising or falling, as well as the direction from which the short-term average crossed the long-term average (it may have been below and now is above, or it may have been above and now is below). A moving average trading rule was used to generate the returns shown in part (a) of Table 22 .2.

__

RELATIVE STRENGTH MEASURES Another procedure used by technicians involves measuring what they call relative strength. For example, a stock's price may be divided by a price index of its industry each day to indicate the stock's movement relative to its industry. Similarly, an industry index may be divided by a market index to indicate the industry'S movement relative to the market, or a stock's price may be divided by a market index to indicate a stock's movement relative to the market. The idea is to examine changes in these relative strength measures with the hope of finding a pattern that can be used to accurately predict the future. The momentum trading rules used in preparing Table 22.1 were based on the notion of relative strength in its simplest form. Stock returns over ajust-ended holding period were calculated, and then portfolios of winners and losers were formed. When semiannual or annual returns were used, the momentum trading rules seemed to have merit. Some procedures of technical analy sts focus on relationships among different indexes. For example, the Dow Theory requires that a pattern in the Dow Jones Industrial Average be "confirmed" by a certain movement in the Dow Jones Transportation Average before action be taken." Another example involves computing the difference between the number of issues advancing and the number declining each day. A chart of the differences cumulated over time, known as the advance-decline line, may then be compared with a market index such as the DowJones Industrial Average.

II:1II

CONTRARY OPINION Many technical procedures are based on the idea of contrary opinion. The idea is to determine the consensus opinion and then do the opposite. Two examples that were discussed earlier involved (1) buying stocks that had recently dropped in price and selling stocks th at had recently risen in price and (2) buying stocks with low PIE ratios and selling stocks with high PIE ratios. For a third example, one might see whether the "odd-letters" (those with trade orders involving less than 100 shares) are buying and then sell any holdings of these stocks. If "the little investor is usually wrong," this procedure will usually be right. However, the basic premise about the little investor has yet to be factually established. The widespread availability of personal computers and on-line services with data on stock prices and trading volumes has made it possible for individual investors to engage in technical analysis in the privacy of their own homes. Producers of software have been quick to provide programs to perform such analysis, complete with multicolored graphs. Nevertheless, the number of investors using fundamental analysis is much larger than the number using technical analysis . 784

CHAPTER 22

ENDNOTES

Sumner N. Levine (ed.) , Financial Analyst's Handbook 1 (Homewood, IL: Dow Jones-Irwin, 1975) .

I

~ William C. Norby, "Overview of Financial Analysis," in Levine, Financial Analyst's Hand-

bookI, p. 3. :1 To

obtain more information about becoming a CFA, contact the Institute of Chartered Financial Analysts . Their mailing address is P.O . Box 3668, Charlottesville, VA 22903, and their telephone number is (804) 980-3668. Information can also by obtained by contacting the AIMR Web site at (www.aimr.org).

4

Some would acid a third reason for conducting financial analysis: monitoring the firm's management in order to prevent managers from consuming an excessive amount of perquisites and making inappropriate decisions to the detriment of the finn's shareholders. See Michael C. Jensen and William H. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure," Jaumal of Financial Economics 3, no . 4 (October 1976) : 305-360.

r>

For a discussion regarding portfolio selection by an investor who has earned income (for example, from wages or from running a business), see Edward M. Miller, "Portfolio Selection in a Fluctuating Economy," Financial A nalystsJoumal34, no . 3 (Mayljune 1978) : 77-83.

Ii

If the added benefits exceeded the added costs, then it would be profitable to perform more financial analysis, because the incremental benefits from doing so would cover the associated costs. If, on the other hand, the added costs exceeded the added benefits, then it would be profitable to cut back on the amount of financial analysis, because costs would be reduced by an amount greater than benefits.

7

For an interesting argument on why the existence of trading costs results in some investors' performing financial analysis in an efficient market, see Sanford]. Grossman, "On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information," [ournal ofFinance31, no . 2 (May 1976): 573-585; Sanford]. Grossman and Joseph E. Stiglitz, "On the Impossibility of Informationally Efficient Markets," American Economic Review 70, no . 3 (june 1980) : 393-408; and Bradford Cornell and Richard Roll, "Strategies for Pairwise Compet itions in Markets and Organizations," Bell journal of Economics 12, no . 1 (Spring 1981): 201-213.

H

Felix Rosenfeld (ed.), The Evaluation of Ordinary Shares, is a summary of the proceedings of the Eig-hth Congress of the European Federation of Financial Analysts Societies (Paris: Dunod, 1975), p . 297.

9

Rosenfeld, The Evaluation of Ordinary Shares, pp. 297-298. For an argument that technical analysis can be of value in an efficient market, see David P. Brown and Robert H.Jennings, "On Technical Analysis," Reoieioof Financial Analysis 2, no. 4 (1989) : 527-551. Also see Jack L. Treynor and Robert Ferguson, "In Defense of Technical Analysis," [ournal of Finance 40, no.3 Ouly 1985) : 757-773; and Lawrence Blume, David Easley, and Maureen O'Hara, "Market Statistics and Technical Analysis: The Role of Volume," Joumal of Finance 49, no . 1 (March 1994) : 153-181.

III

See, for example, Eugene F. Farna, "Efficient Capital Markets: A Review of Theory and Empirical Work," [ournal ofFinance 25, no . 2 (May 1970) : 383-417.

See, for example, Eugene F. Farna , "Efficient Capital Markets: II," [oumal of Finance 46, no. 5 (December 1991) : 1575-1617. I~ Other studies present evidence that is consistent with these results. See Barr Rosenberg, Kenneth Reid, and Ronald Lanstein, "Persuasive Evidence of Market Inefficiency," [ournal of Portfolio Management II , no. 3 (Spring 1985): 9-16; John S. Howe, "Evidence on Stock Market Overreaction," Finan cial AnalystsJaurnal42. no. 4 Uul}'/August 1986): 74-77; and Andrew W. Lo and A. Craig MacKin lay, "When Are Contrarian Profits Due to Stock Market Overreaction?" Review ofFinancial Studies 3, no. 2 (1990): 175-205.

II

13

One explanation for these results that has been offered is that investors underreact to quarterly earnings announcements. See Chapter 18, particularly section 18.7, and Victor L.

Financial Analysis

785

Bernard.jacob K. Thomas, and jeffery S. Abarbanell, "How Sophisticated Is the Market in Interpreting Earnings News?" journal oj Applied Corporate Finan ce fi, no. 2 (Summer 1993) : 54-63. Another related observation involving one-year form ation periods concerns the Dow dividend strategy. This strategy requires buying the ten highest-dividend-yielding stocks in the Dow Jones Industrial Average (DJIA) and holding them for one year, at which point the portfolio is revised accordingly for another year. From 1973 through 1992 this strategy outperformed the QJlA by 5. I5'YrJ per year, on average. Interestingly, it turns out that the stocks purchased in any yea r had a return that was 5.99 % less than the QIIA the previous year, on average. Thus the strategy actually involves buying last year's "losers" among the Dow Jones 30. See Dale L. Damian, David A. Louton, and Irene M. Seahawk, "The Dow Dividend Strategy: How It Works and Why," AA//journall6, no . 4 (May 1994): 7-10. 14 A

puzzling observation associated with part (f) was that 5% of the 7.2% abnormal return for the loser portfolio was earned during the Januaries that occurred during the test period. Conversely, -.8% of the -2.4% abnormal return for the winners was earned during Januaries. Hence the January anomaly (discussed in Appendix A to Chapter 16) appears to somehow be intertwined with the long-term contrarian strategy.

Other studies have examined contrarian strategies and hare been unable to confirm the usefulness of such strategies. In two of these studies it was argued that the benchmark portfolio returns were incorrectly determined. This means that the abnormal returns were not calculated correctly because by definition they are equal to the difference between the returns on the portfolio and its benchmark. In a third study, the alleged cause of the overreaction-security analysts' underpredicting earnings on losers and overpredicting earnings on winners-was contested. A fourth study suggested that the size effect (discussed in Appendix A to Chapter 16) was largely responsible for the results because losers tend to be smaller than winners. Last, a Iili.hstudy argued that incorrect prices were used when the COSL~ of buying and selling sto cks were determined in arriving at the results reflected in parts (e) and (f) of Table 22. I. However, these studies have , in turn, been contested in a sixth study. Specifically, after their objections had been taken into consideration it was found that losers outperform winners by 5% LO 10% per year, with the difference being the largest when only small firms were classified into winners and losers. The six studies are, respectively, K. C. Chan, "On the Contrarian Investment Strategy," journal oj Business () I, no. 2 (April 19S8): 147-163; Ray Ball and S. P. Kothari, "Nonstationary Expected Returns: Implications for Tests of Market Efficiency and Serial Correlations in Returns," [ournal oj Financial Economics 25, no. 1 (November 1989): 51-74; April Klein, "A Direct Test ofthe Cognitive Bias Theory of Share Price Reversals,"jourrwl of Accounting arul Economics 13, no. 2 (July 1990): 155-166; Paul Zarowin, "Size, Seasonality, and Stock Market Overreaction," journal oj Financial and Quantitative Analysis 25, no . I (March 1990) : 113-125;Jennifer Conrad and Gautam Kaul, "Lo ngTerm Overreaction or Biases in Computed Returns?" [ournal oj Finan ce 48, no. 1 (March (993): 39-63; and Navin Chopra.josef Lakonishok, andJay R. Ritter, "Measuring Abnormal Performance: Do Stocks Overreact?" [ournal oj Financial Economics 31, no. 2 (April 1992) : 235-268. Adding to the puzzle is the behavior of Canadian stocks. For one-year test periods the results were similar to those in the United States in that a momentum strategy seemed to work (as in part (d) of Table 22.1). For three-year and five-year test periods, neither a momentum nor a contrarian strategy worked [unlike parL~ (e) and (f) of Table 22.1]. See Lawrence Kryzanowski and Hao Zhang, "The Contrarian Investment Strategy Does Not Work in Canadian Markets," [ournal oj Financial and Quantitative Analysis 27, no. 3 (September 1992) : 383-395. 16 Apparently significant returns can be earned from the weekly strategy if transaction costs are small (such as for large institutional investors) . However, larger transaction costs result in negative net returns. See Bruce N. Lehmann, "Fad s, Martingales, and Market Efficiency," QuarterlyjoumaloJEconomics105, no . 1 (February 1990) : 1-28. For an argument that Lehmann underestimated the size of transaction costs, see Jennifer Conrad, Mustafa N. Gultekin, and Gautam Kaul, "Profitability of Short-Term Contrarian Portfolio Strategies," unpublished paper, University of Michigan, 1991.

10

786

CHAPTER 22

Lehmann, "Fads , Martingales, and Market Efficiency," p. 26. analysis is sometimes used to ensure consistency between various industries and the economy in aggregate. This type of analysis is based on the notion that the output of certain industries (for example, the steel industry) is the input for certain other industries (for example, the household appliance industry) . 19 In 1997, the Financial Accounting Standards Board proposed rule no. 128, which would affect how earnings per share are reported. The rule would replace primary earnings per share, which factors in some dilution for certain common-stock equivalents, with an entirely undiluted measure of earnings per share called basic earnings per share. Fully diluted earnings per sharewould remain calculated in almost the same manner as before but would now be called diluted earnings per share. Financial analysts will have two distinct measures of earnings per share: one with no dilution and one with full dilution. For many companies, the change will be insignificant. For some companies, however, the change will highlight the large impact that dilutive securities, such as warrants and employee stock options, potentially can have on earnings per share. ~Il For more on free cash flow and how it can be used to value a firm and its equity, see Aswath Damodaran, Corporate Finance: Theory and Practice (New York: Wiley, 1997), pp. 170-] 71, 634-646. ~I Analysts typically calculate an average value for balance sheet items used in financial ratios. This approach facilitates comparisons of point-in-time levels on the balance sheet with pe riod flows on the income statement. In the Dayton Hudson example, the financial ratios were computed using an average of beginning-of-year and year-end values for balance sheet items. ~~ In recent years analysts have increasingly come to view earnings before interest, taxes, depreciation, and amortization (EBITDA) relative to the total market value of the firm (its equity and debt) as a more effective measure of operating performance than pre-tax ROA. EBITDA is essentially a measure of the company's pre-tax cash flow. ~:j Similar observations have been made in regard to other studies of the recommendations made by major brokerage houses. See John C. Groth, Wilbur G. Lewellen, Gary G. Schlarbaum, and Ronald C. Lease, "An Analysis of Brokerage House Securities Recommendations," Financial Analystsjournal35, no. I (january/February 1979): 32-40;James H. Bjerring, Josef Lakonishok, and Theo Vermaelen, "Stock Prices and Financial Analysis' Recommendations," journal ojFinance 38, no. I (March 1983) : 187-204; and Philip Heitner, "Isn 't It Time to Measure Analysts ' Track Records?" Financial Analystsjournal 47, no. 3 (May/June 1991) : 5-6. For a comment on the first study, see the Letter to the Editor in the May/June] 980 issue by Clinton M. Bidwell, with a responding Letter to the Editor in the July/August 1980 issue by Wilbur G. Lewellen. Also see endnote 1 in Chapter 23. ~4 Two other studies of "Heard on the Street" recommendations reached similar conclusions to those shown here. See Peter Lloyd-Davies and Michael Canes, "Stock Price s and the Publication of Second-Hand Information," journal oj Business, 51, no. I GanualY 1978): 43-56; and Pu Liu, Stanley D. Smith, and Azmat A Syed, "Stock Price Reactions to The Wall Street [ournate Securi ties Recommendations," journal ojFinancial and Quantitative Analysis 25, no. 3 (September 1990) : 399-410. Interestingly, a former author of the "Heard on the Street" column, R. Foster Winans, was convicted of fraud and theft in ]985 for leaking the contents of his column to four brokers and subsequently sharing in the associated trading profits. 25 Value Line has a service called Value Line Investmen t Surve y for Windows to which investors can subscribe that involves software and periodic updates of their ran kings as well as other data. Besides its stock recommendations, Value Lin e also provides a measure of the risk of individual securities that is known as Safety Rank. This risk measure was found to be more highly correlated with subsequent returns than either beta or standard deviation, suggesting that it is a more useful measure of risk. See Russell]. Fuller and G. Wenchi Wong, "Traditional versus Theoretical Risk Measures," Financial Analystsjournal44, no. 2 (March/April ]988) : 52-57, 67, and the Value Line Web site (www.valueline.com). 17

IH Input-output

26

One study of Value Line recommendations found that most rank changes occur shortly after earnings announcements are made. Subsequent investigation revealed that Value

Financial Analysis

787

Line's superior performance was attributable to the "post-earnings-announcement drift" (this phenomenon was discussed in Chapter 18). Hence the two anomalies appear to be related . See John Affleck-Graves and Richard R. Mendenhall , "The Relation between the Value Line Enigma and Post-Earnings-Announcement Drift," journal ojFinan cial Economics 31, no. 1 (February 1992): 75-96. 27 Jennifer

Francis and Leon ard Soffer, "The Relative Informativeness of Analysts' Stock Recommendations and Earnings Forecast Revisions," [oumal oj Accounting Research. 35, no . 2 (Autumn 1997): 193-211 . Chapter IRcontains a discussion of analysts ' forecasts of earnings.

28

See Appendix A in Chapter 16 for a discussion of the size effect.

29

The presence of the size effect can be seen by noting that the average return for small firms of 13.5% is much larger than the average return for medium a nd large firms of 10.7% and 9.8%, respectively. It should be noted, however, that the existence of the neglected-firm effect has been contested; see Craig G. Beard and Richard W. Sias, "Is There a NeglectedFirm Effect?" Financial Analystsjournal 53, no. 5 (September/October 1997): 19-23.

~ll This reporting requirernen t should not be confused with SEC Rule 13d, which requires in-

vestors to disclose their holdings in a company once they are equal to 5% or more of the company's stock. Unlike form 4 investors, Rule 13d investors are not viewed as insiders by the SEC, and they do not have to report every transaction they subsequently make. ~I The Value Line Investment Suroey (published by Value Line, Inc ., New York, NY) reports an

"index of insider decisions" for' each stock covered in its weekly service. In essence, th is is a cumulative index of the net number of purchasers (including those who exercise options) and sellers. The Wffkly Insider Repor! (published by Vickers Stock Research Corp., Brookside, NJ) reports a ratio of total insider buying to total insider selling. For an article about what constitutes insider trading, see Gary L. Tidwell, "Here's a Tip-Know the Rules of Insider Trading," Sloan Management Reuietu 28, no . 4 (Summer 1987): 93-98 . ~2 If the insider bought the stock by exercising an option that was given to him or her as part

of his or her compensation, then the six-month period is measured from the day the option was granted . :1:1

An alternative method is to examine stock returns on days of illegal insider trading. Looking at 183 SEC cases from 19RO to 1989, one study found that stock prices had an average abnormal return of 3.0% on each day that illegal insider buying took place and -3.5% on each day that illegal insider selling took place. See Lisa K. Meulbroek, "An Empirical Analysis of Illegal Insider Trading," journal ofFinance A'l, no. 5 (December 1992) : 1661-1699.

:14 Jeffrey

F.Jaffe, "Special Information and Insider Trading," Journal oj Business 47, no . 3 (July 1974): 410-428. Also see Joseph E. Finnerty, "Insiders and Market Efficiency," journal oj Finance31 , no . 4 (September 1976) : 1141-1148; and Aaron B. Feigen, "Information Opportunities from Insider Trading Laws," MlIjournalll, no . 8 (September 1989) : 12-15.

~5 See Herbert S. Kerr, "The Battle of Insider Trading and Market Efficiency," Journal oj Part-

Jolio Management 6, no . 4 (Summer 1980): 47-58; Wayne Y. Lee and Michael E. Solt , "Insider Trading: A Poor Guide to Market Timing," Journal oj Portfolio Management 12, no. 4 (Summer 1986) : 65-71; H. Nejat Seyhun, "Inside rs' Profits, Costs of Trading, and Market Efficiency," journal oj Financial Economics 16, no . 2 (June 1986): 189-212; Michael S. RozefT and Mir A. Zaman, "Market Efficiency and Insider Trading: New Evidence," journal oj Busine5S61, no. 1 (January 1988): 25-44; andJi-Chai Lin andJohn S. Howe, "Insider Trading in the OTC Market," journal oj Finanr.e45, no. 4 (September 1990): 1273-1284.

Such information can become quickly outdated, but a comprehensive list of useful investment-related Web sites is found in Jean Henrich, "The Individual Investor's Guide to Investment Web Sites," MIIJournal19, no. 8 (September 1997): 15-23. Also see the following three articles in the Fall/Winter 1996 issue (vol. 6, no . 2) of Financial Practiceand Education: "An Introduction to Finance on the Internet" by Russ Ray; "A Guide to Locating Financial Information on the Internet" byJames B. Pettijohn; and ''The Ways in Which the Financial Engineer Can Use the Internet" by Anthony F. Herbst. 37 For details on many kinds of patterns, see Alan R. Shaw, "Technical Analysis," in Levine, Financial Analyst's Handbook I, pp . 944-988; Chapter 8 in Jerome B. Cohen , Edward D. Zinbarg, 36

788

CHAPTER 22

and Arthur Zeikel, Investment Analysis and Portfolio Management (Homewood, IL: Richard D. Irwin, 1987); and Richard L. Evans, "Chart Basics Using Bars, Point & Figure and Candlesticks," AAlIJourna~ 15, no. 4 (April 1993): 24-28. :IX For more on the Dow Theory, see Richard L. Evans, "Dow's Theory and the Averages: Relevant. . . or Relics?" AAlIJournall5, no . I (january 1993) : 27-29.

KEY

TERMS

financial analyst security analyst portfolio managers fundamen tal analysis technical analysis top-down forecasting bottom-up forecasting

probabilistic forecasting econometric model endogenous variables exogenous variables neglected-finn effect insiders chartists

REFERENCES 1. For a discussion of contrarian investment strategies, see , in addition to the references in Table 22.1 and endnotes 12 and 15, the following: David Drernen, Contrarian Investment Strategies (New York: Random House, 1979). Paul Zarowin, "Short-Run Market Overreaction: Size and Seasonality Effects," Journal of Portfolio Management 15, no . 3 (Spring 1989) : 26-29. Paul Zarowin, "Does the Stock Market Overreact to Corporate Earnings Information?" Journal of Finance 44, no. 5 (December 1989): 1385-1399. Jennifer Conrad, Mustafa N. Gultekin, and Gautam Kaul, "Profitability of Short-Term Contrarian PortJolio Strategies," unpublished paper, University of Michigan, 1991. Victor L. Bernard,jacob K. Thomas, andJefTery S. Abarbanell, "How Sophisticated Is the Market in Interpreting Earnings News?"Journal ofApplied CorporateFinan ce 6, no . 2 (Summer 1993) : 54-63. josef Lakonishok, Andrei Shleifer, and Robert W. Vishny, "Contrarian Investment, Extrapolation , and Risk," Journal of Finance 49, no. 5 (December 1994): 1541-1578. Ray Ball, S. P. Kothari, and Charles E. Wasley, "Can We Implement Research on Stock Trading Rules?" Journal ofPortfolio Management 21, no. 2 (Win ter 1995): 54-63. Ray Ball, S. P. Kothari, andjay Shanken , "Problems in Measuring Portfolio Performance: An Application to Contrarian Investment Strategies," Journal of Financial Economics 38, no. I (May 1995): 79-107. Tim Loughran andjay Ritter, "Long-Term Market Overreaction: The Effect of Low-Priced Stocks,"Journal of Finance 51, no. 5 (December 1996): 1959-1970. S. P. Kothari and jerold Warner, "Measuring Long-Horizon Security Price Performance," Journal of Financial Economics 43, no . 3 (March 1997) : 301-339. 2. Closely related to the issue of contrarian investment strategies is the issue of how stock price levels in one period are related to stock price levels in a subsequent period. This issue, like the usefulness of contrarian strategies, has been open to debate. Two of the earliest papers and two recent ones that contradict them are: Eugene F. Fama and Kenneth R. French, "Permanent and Temporary Components of Stock Prices," Journal ofPolitical Economq 96 . no. 2 (April 1988): 246-273. James M. Poterba and Lawrence H. Summers, "Mean Reversion in Stock Prices: Evidence and Implications,"Joumal ofFinancial Economics 22, no. 1 (October 1988): 27-59.

Financial Analysis

789

Myungjig Kim, Charles R. Nelson , and Richard Startz, "Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence," Review oj Economic Studies !l8, no. 3 (May 1991): 515-528. Grant McQueen, "Long-Horizon Mean-Reverting Stock Prices Revisited ," [oumal oj Financial and Qurl1ltitalill/' A//(/I)'.\i.\ 27, no. I (March 1992): 1-18.

3. Momentum strategies are discussed in: Narasimhan jegadeesh unrl Sheridan Titman, "Returns to Buying Winners and Selling Losers: Implications Ior Stock Market Efficiency," Journal of Finance 48, no. 1 (March 1993): 65-91. 4. Moving average and trading rangc breakout strategies are discussed in: William Brock.josef Lakonishok, and Blake LeBaron, "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal oj Frnance 47, no . 5 (December 1992) : 1731-1764.

5. The reaction of stock prices to the publication of analysts' recommendations is discussed in the sources given in Table 22.8 and in: Peter Lloyd-Davies and Michael Canes, "Stock Prices and the Publication of Second-Hand Information," Journal of BUIin 1'.1.\ 51, no . I (january 1978) : 43-56. john C. Groth , Wilbur G. Lewellen, Gal)' G. Schlarbaum , and Ronald C. Lease, "An Analysis of Brokerage House Securities Recommendations," Financial Analssts journal Sb, no. I (January/February 1979): 32-40. Clark Holloway, "A Note on Testing an Aggressive Investment Strategy Using Value Line Ranks," Journal oj Finance 36, no. 3 (june 1981) : 711-719 . Thomas E. Copeland a n d David Mayers, "The Value Line Enigma (1965-1978) : A Case Study of Performance Evaluation Issues," Journal oj Financial Economics 10, no . 3 (Novern bel' 1982) : 289-32 I. James H. Bjerriug, joset' Lakonishok, and Theo Vermaelcu , "Stock Prices and Fin ancial Analysts' Recommendations," Journal oj Finance 38, no. I (March 1983): 187-204. Gur Huberman and Shmuel Kandel, "Value Line Rank and Firm Size,"Joumal oj Business 60, no. 4 (October 1987): 577-589. Gur Huberman and Shmuel Kandel, "Market Efficiency and Value Line's Record," Journal oj Business 63, no . 2 (April 1990) : 187-216. Pu Liu, Stanley D. Smith, and AzmatA Syed, "Stock Price Reactions to The Wall StreetJournars Securities Recomrnendatious,' Journal ojFinancial and QuantitatiVI' Analysis 25, no. 3 (September 1990): 399-410. Philip Heimer, "Isn't It Time to Measure Analysts' Track Records?" Fiuan cial Analsstsjourna147 , no. 3 (May/june 1991): 5-6. Donna R. Philbrick and William E. Ricks, "Using Value Line and IBES Analyst Forecasts in Accounting Research," [ournnl ojAccounting Research 29, no. 2 (Autumn 1991): 397-417. john Affleck-Craves and Richard R. Mendenhall, "The Relation between the Value Line Enigma and Post-Earnings-Announcement Drift," Journal ojFinancial Economics 31, no . I (February 1992): 75-96. john Markese, "The Role of Earnings Forecasts in Stock Price Behavior," AAllJournal14, no. 4 (April 1992): 30-32. Rajiv Sant and Mir A. Zaman , "Market Reaction to Business Week 'Inside Wall Street' Column : A Self-Fulfilling Prophecy," Journal oj Banking and Finance 20, no. 4 (May 1996) : 617-643. jennifer Francis and Leonard Soffer, "The Relative Informativeness of Analysts' Stock Recommendations and Earnings Forecast Revisions," Journal oj Accounting Research 35, no. 2 (Autumn 1997): 193-211.

790

CHAPTER 22

6. The "Heard on the Street" column also sometimes discusses takeover rumors. For an analysis of the effects these rumors have on stock prices. see: J ohn Pound and Richard Zeckhauser, "Cle arly Heard on the Street: The Effect of Takeover Rumors on Stock Prices," Journal of Business 63, no. 3 (July 1990): 291-308. 7. For a discussion of the neglected firm effect, see: Avner Arbel and Paul Strebel , "Pay Attention to Neglected Firms!"JollrnI11 ofPonfolio Management 9. no . 2 (Winter 1983) : 37-42. Avner Arbel, Steven Carvel, and Paul Strebel. "Giraffes, Institutions, and Neglected Firms," Financinl Analystsjournnl S'), no. 3 (May/June 1983): 57-63. Craig G. Beard an d Richard W. Sias, "Is There a Neglected-Firm Effect?" Financial Analysts.JouTnnlfl3, no. fI (September/October 1997) : 19-23. 8. Insider trading has been examined in a number of studies. Some of the major ones are: Jeffrey F, Jaffe, "Special Information and Insider Trading." Journal of Business 47. no. 3 (July 1974): 410-428. Joseph E. Finnerty. "Insiders and Market Efficiency." Journal of Finance 31 , no. 4 (September 197n) : 1141-1148. Herbert S. Kerr. "T he Battle of Insider Trading and Market Efficiency." Journal of Portfolio Managnrumt 6, no. 4 (Summer 1980): 47-58. Wayne Y. Lee and Michael Solt, "Insider Trading: A Poor Guide to Market Timing." Journal of Portfolio Management 12. no. 4 (Summer 1986) : 65-71. H. Nejat Seyhun, "Insiders' Profits, Costs of Trading, and Market Efficien cy,"Journal of F'inancial Economics 16. no. 2 (June 1986): 189-212.

H. Nejat Seyhun, "The Information Content of Aggregate Insider Trading," Journal of Busine.u61, no. 1 (January 1988): 1-24.

Michael S. Rozcff and Mir A. Zaman, "Ma rket Efliciency and Insider Trading: New Evidence,"Jourllnl of/Jusiness61 , no. I (January 1988): 2f1-44.

Ji-Chai Lin andJohn S. Howe. "Insider Trading in the OTe Market." [ournal ofFinance 45, no .4 (September 1990): 1273-1284. Lisa K. Meulbroek, "An Empirical Analysis of Illegal Insider Trading." Journal of Finance 47. no . fI (December 1992): 1661-1699. Mustafa Chowdhury.john S. Howe. andJi-Chai Lin, "The Relation between Aggregate Insider Transactions and Stock Market Returns....Joumal cf Financial and Quantitative Analysis 28, no. 3 (September 1993) : 431-437. 9. Leading books on technical analysis. financial statement analysis, and fundamental analysis are. respectively: Robert D. Edwards and John Magee, Technical Analssis ofStock Trends (Boston:John Magee. 1966) . George Foster. Financial Statement Analysis (Englewood Cliffs. Nj: Prentice Hall. 1986). Sidney Cottle, Roger Murray. and Frank Block. Graham and Dodd's Security Analysis (New York: McGraw-Hill. 1988). 10. The new FASB reporting rules for earnings per sh are are discussed in : Ross Jennings. Marc]. Le Clere , and Robert B. Thompson II. "Evidence on the Usefulness of Alternative Earnings per Share Measures." Financial Analysts [ournnl fl3. no. 6 (November/ Dece mber 1997) : 24-33. 11. Information sources for investing are described in: Maria Crawford Scott and John Bajkowski, "Sources of Information for the Simplified Approach to Valuation," AAJIJ01lrna116. no. 3 (April 1994): 29-32.

John Markese, "Picking Common Stocks: What Seems to Work. At Least Sometimes." AAIIJourna1l6. no. 5 (June 1994): 24-27.

Financial Analysis

791

CHAPTER

Z

3

INVESTMENT MANAGEMENT

'nvestment management, also known as portfolio management, is the process by which money is managed. It may (1) be active or passive, (2) use explicit or implicit procedures, and (3) be relatively controlled or uncontrolled. The trend is toward highly controlled operations consistent with the notion that capital markets are relatively efficient. However, approaches vary, and many different ones can be found. This chapter will discuss investment management, and in doing so it will present various types of investment styles.

Em

TRADITIONAL INVESTMENT MANAGEMENT ORGANIZATIONS Few people or organizations like to be called "traditional." However, some investment management organizations follow procedures that have changed little from those that were popular decades ago and thus deserve the title. Figure 23.1 shows the major characteristics of a traditional investment management organization. Projections concerning the economy and the financial markets are made by economists, technicians, fundamentalists, or other market experts within or outside the organization. The projected economic environment is communicated by means of briefings and written reports-usually in a rather implicit and qualitative manner-to the organization's security analysts. Each analyst is responsible for a group of securities, often those in one or more industries (in some organizations, analysts are called industry specialists). A group of analysts may report to a senior analyst responsible for a sector of the economy or market. The analysts, often drawing heavily on reports of others (for example, "street analysts" in brokerage houses), make predictions about the securities for which they are responsible. In a sense, such predictions are conditional on the assumed economic and market environments, although the relationship is typically quite loose. Analysts' predictions seldom specify an expected rate of return or the time over which predicted performance will take place. Instead, an analyst's feelings about a security may be summarized by assigning it one of five codes, such as where a 1 represents a buy and a 5 represents a sell, as indicated in Figure 23.1. 1 In many organizations, a simple buy-hold-sell designation is given. 792

Portfolio Managen

Security Analysts

Economist APproved

List / Investment Committee

Model Portfolio Market Experts

I

I

Occasional Briefings, Reports Etc.

I

I

Security Codings I: Buy 2: OK to Buy 3: Hold 4: OK to Sell 5: Sell

Figure 23.1 A Traditional Investment Management Organization

These security codings and various written reports constitute the information formally transmitted to an investment committee, which typically includes the senior management of the organization. In addition, analysts occasionally brief the investment committee on their feelings about various securities. The investment committee's primary formal output is often an approved (or authorized) list, which consists of the securities deemed worthy of accumulation in a given portfolio. The rules of the organization typically specify that any security on the list may be bought, whereas those not on the list should be either held or sold, barring special circumstances. The presence or absence of a security on the approved list constitutes the major information transmitted explicitly from the investment committee to a portfolio manager. In some organizations, senior management supervises a "model portfolio" (for example, a bank's major commingled equity fund) , the composition of which indicates to portfolio managers the relative intensity of senior management's feelings regarding different securities. In many ways, this description is a caricature of an investment organization--even one run along traditional lines. Nevertheless, most of these attributes can be observed in practice in one form or another. In recent years, specialty investment firms have gained considerable popularity. As opposed to traditional investment firms that invest in a broad spectrum of securities, these organizations concentrate their investment efforts on a particular asset class, such as stocks or bonds. They often specialize even further, focusing on a narrow segment of a particular asset class, such as the stocks of small start-up companies. Although these specialty investment firms may follow many of the security analysis procedures of the traditional investment organizations, they usually employ few Investment Management

793

security analysts. Often the portfolio managers serve jointly as analysts. Furthermore, their decision-making processes are typically more streamlined, often avoiding investment committee structures entirely, thereby permitting portfolio managers considerable discretion to research securities and construct portfolios. Whether this less hierarchical approach to investing actually produces superior results is open to question.

_

INVESTMENT MANAGEMENT FUNCTIONS In Chapter 1 a five-step procedure was outlined for making investment decisions. These steps can all be viewed as functions of investment management, and they must be undertaken for each client whose money is being managed. They are as follows : 1. Set investment policy. Identify the client's investment objectives, particularly as regards his or her attitude toward the tradeoff between expected return and risk. 2. Perform security analysis. Scrutinize individual securities or groups of securities . in order to identify mispriced situations. 3. Construct a portfolio. Identify specific securities in which to invest, along with the proportion of investable wealth to be put into each security. 4. Revise the portfolio. Determine which securities in the current portfolio are to be sold and which securities a re to be purchased to replace them. 5. Evaluate the performance of the portfolio. Determine the actual performance of a portfolio in terms of risk and return, and compare the performance with that of an appropriate "benchmark" portfolio.

The remainder of this chapter deals with how an investment management organization could perform the first four functions ; the next chapter deals with the fifth function.

lID

SETTING INVESTMENT POLICY An investment manager who is in charge of a client's entire portfolio must be concerned with the client's risk-return preferences. Investors who use more than one manager can select one to help in this important phase, or they may employ the services of a consultant or financial planner. In any event, one of the key characteristics that differentiates clients from one another concerns their investment objectives. These objectives are reflected in the client's attitude toward risk and expected return. As discussed in Chapter 6, specifying indifference curves is one method of describing these objectives. However, determining a client's indifference curves is not a simple task. In practice, it can be done in an indirect and approximate fashion by estimating the client's level of risk tolerance, defined as the largest amount of risk that the client is willing to accept for a given increase in expected return.

23.3.1

Estimating Risk Tolerance

The starting point in making such an estimation is to provide the client with a set of risks and expected returns for different combinations of two hypothetical portfolios. For example, imagine that the client is told that the expected return on a stock portfolio is 12%, while the return on a riskfree portfolio consisting of Treasury bills is 7.5% (that is, "is = 12% and rf = 7.5%). Similarly, the client is told that the standard 794

CHAPTER 23

TABLE

23.1

Combinations of Stock and Rlskfree lTeasury 8111 Portfolios

Proportion In

Stock

I

Expected Return

Standard Deviation

Implied level of Risk Tolerance

Bills

(00%

0%

7.50%

0.0%

0

10

90

7.95

J.5

10

20

80

8.40

3.0

20

30

70

8.85

4.5

30

40

flO

9.30

6.0

40 50

..

50

9.75

7.!>

60

40

10.20

9.0

60

70

30

10.65

10.5

70

80

20

11.10

12.0

80

50

,

90

10

11.55 .

13.5

90

100

0

12.00

15.0

100

110

-10

12.45

16.5

110

120

-20

12.90

18.0

120

130 140

: ,...36

1!U5

19.5

130

-40

13.80

21.0

140

-50

14.25

22.5

150

150

..

deviation of the stock portfolio is 15%, while the standard deviation of the riskfree portfolio is, by definition, 0.0 % (that is, Us = 15% and uJ = 0.0%).2 In addition, the client is told that all combinations of these two portfolios lie on a straight line that connects them . (The reason is that the covariance between these two portfolios is 0.0, meaning that u.'ij = 0.0.) Some combinations of these two portfolios are shown in Table 23.1. Note that the investor is being presented with the efficient set that arises when there is a set of stocks and a riskfree borrowing and lending rate. As shown in Chaptcr 8, this efficient set is linear, meaning that it is a straight line that emanates at the riskfree rate and goes through a tangency portfolio that consists of a certain combination of securities. (In this case those securities are common stocks.) Hence negative percentages in Treasury bills (shown at the bottom of Table 23.1) represent riskfree borrowing in order to purchase greater amounts of stocks. At this point, the client is asked to identify the combination that appears to be most desirable, in terms of expected return and standard deviation. Note that asking the investor to identify the most desirable combination is equivalent to asking the investor to locate where one of his or her indifference curves is tangent to the linear efficient set; this point will represent the most desirable portfolio." After the client has selected the best mix of stocks and Treasury bills, what can be said about his or her risk tolerance? One would , of course, like to identify all the indifference curves that represent a client's attitude toward risk and expected return. However, in practice a more modest goal is usually adopted: to obtain a reasonable represen tation of the shape of such curves in the region of risk and expected return within which the client's optimal choices will most likely fall. The points in Figure 23.2 plot the alternative mixes presented to the client that were given in Table 23.1. Curve fCS shows the risk-return charac te ristics of all possible mixes, and point C identifies the attributes of the mix chosen by the client. Note Investment Management

795

s

Variance of Return

Figure 23.2 Inferring Client Risk Tolerance.

that in this figure expected return is measured on the vertical axis and variance on the horizontal axis. Although the combinations available to the client plot on a straight line when standard deviation is measured on the horizontal axis, the combinations plot on a concave curve when variance is used (as in this figure) . If all the possible mixes have been presented to the client and point C has been chosen, it can be inferred that the slope of the client's indifference curve going through C is precisely equal to that of curve fCS at this point. As mentioned earlier, this inference follows from the observation that the portfolio on the efficient set that a client identifies as being the "best" corresponds to the one where the client's indifference curves are just tangent to the efficien t set.

23.3.2

Constant Risl< Tolerance

In principle, the choice of a mix provides information about the slope of an indifference curve at only one point. To go beyond this inference, the analyst must make an assumption about the general shape of the client's indifference curves. An assumption commonly made is that the client has constant risk tolerance over a range of alternative portfolios in the neighborhood of the point originally chosen. Figure 23.3 shows the nature of this assumption. As indicated in panel (a), indifference curves in a diagram with variance on the horizontal axis are linear when it is assumed that the client has constant risk tolerance. This means that the equation for an indifference curve of such an investor is equivalent to the equation for a straight line, where the variable on the horizontal axis is variance (a~) and the variable on the vertical axis is expected return (1',,). Given that the equation of a straight line takes the form of Y = a + bX, where a is the vertical intercept and b is the slope, the equation for an indifference curve can be written as:

or: (23.1 ) where Uj is the vertical intercept for indifference curve i and the slope of the indifference curve is l/T. 4Any two indifference curves for a client differ from one another 796

CHAPTER 23

(a)

Inrerm.of VarillllCe

Variance of Return

15

E

3

c:i ]10 v

[

x

\.LJ

51-----~

5

IO

Standard Deviation of Return

Figure 23.3 Constant Risk Tolerance

only by the value of the vertical intercept because the indifference curves are parallel, meaning that they have the same slope, liT. Figure 23.3(b) plots the same indifference curves in a more familiar mannerwith standard deviation on the horizontal axis. Note that the curves have the conventional shape; they indicate that the investor requires more return to compensate for an additional unit of standard deviation as the risk of the portfolio increases. That is, the curves are convex when standard deviation is measured on the horizon tal axis. In the estimation of the client's level of risk tolerance T, as was mentioned, the slope of the indifference curve, l iT, would be set equal to the slope of the efficient set at the location of the portfolio that was selected, denoted portfolio C. Doing so results in the following formula for estimating T: Investment Management

797

T=

rf)a~]

2( (1' r. (1'S -

(23.2)

rf)2

where r c denotes the expected return of the portfolio that the client selected, rs and rf denote the expected return of the stock portfolio and riskfree rate, respectively, and a~ denotes the variance of the stock portfolio. (A detailed presentation of how this formula was derived is presented in the appendix.) In the example, the client was given a choice between S, f, and various combinations of Sand fwhere rs = 12%, rf = 7.5%, and a~ = 152 = 225 . Now, by using Equation (23.2), the level of risk tolerance T inferred from the choice of portfolio C can be determined to equal: T

-

= ~I(rc 7.5) 225 (12 - 7.5)2

=

22.22

rc-

1

(23.3)

166.67

Assuming the choice of a portfolio consisting of a 50% investment in stocks and a 50% investment in riskfree Treasury bills, the client in this example has chosen a portfolio Cwith an expected return of9.75%. Accordingly, Equation (23 .3) can be used to determine the value of T for this client, resulting in an estimated level of T equal to 50 = (22.22 X 9.75) - 166.67. This means that the client will accept up to an additional 50 units of variance, in order to receive an extra 1% in expected return. Thus, the client's indifference curves are estimated to have the form of: _ r /' = u,

1"

+ 50 a p

(23.4)

Table 23.1 shows the inferred level of risk tolerance if a differen t portfolio had been chosen by the client [these levels were determined by substituting the appropriate values for r (; into the right-hand side of Equation (23.3) and then solving for T]. First, note that the level of risk tolerance is the same as the percentage invested in the stock portfolio associated with C. That is, Equation (23.3) can be rewritten as T = 100X:~, where x:~ is the proportion invested in the stock portfolio associated with C. It can be shown that this will always be the case when rs - rr = 4.5% and as = 15%. Other estimates would give different expressions for T, but the relationship between x:~ and T would still be linear. Second, note that the level of risk tolerance is lower if the selected portfolio is more conservative (that is, when the selected level of expected return and standard deviation is lower) . Thus more conservative risk-averse clients will have lower levels of risk tolerance (and thus steeper indifference curves) than less conservative riskaverse clients. Having estimated the client's indifference curves, recall from Chapter 6 that the objective of investment management is to identify the portfolio that lies on the indifference curve farthest to the northwest because such a portfolio will offer the investor the level of expected return and risk that is preferable to what is offered by all the other portfolios. Identifying this portfolio is the same as identifying the portfolio that lies on the indifference curve that has the highest vertical intercept, Uj' This equivalence can be seen graphically in both panels of Figure 23.3, where the indifference curves have been extended to the vertical axis.

23.3.3

Certainty Equivalent Return

The term Uj can be though t of as the certainty equivalent return for any portfolio that lies on indifference curve i.5 Thus portfolio C in Figure 23.2 is as desirable for this particular client as a hypothetical portfolio with an expected return of Uj and no 798

CHAPTER 23

risk-that is, one providing a return of u, with certainty. When viewed in this manner, the job of the portfolio manager is to identify the portfolio with the highest certainty equivalent return. Equation (23.1) can be rewritten so that the certain ty equivalent return u, appears on the left-hand side. Doing so results in:

_

U;

= r I'

I

-

.,

T (Tj,

(23.5)

This equation shows that the certainty equivalent return can be thought of as a riskadjusted expected return because a risk penalty that depends on both the portfolio's variance and the client's risk tolerance must be subtracted from the portfolio's expected return in determining Uj' In the example, the investor selected the portfolio with I'l = 9.75 % and a~ = 56.25{ = 7 .5~). Thus the certainty equivalent return for this portfolio is 8.625% [= 9.75 - (56.25/50)]. Equivalently, the risk jHmalty for the portfolio that was selected was 1.125% (=56.25/50). If the certainty equivalent return for any other portfolio shown in Table 23.1 is calculated, it will have a lower value {[ for example, the 80/20 portfolio has a certainty equivalent return of 8.22% [= 11.1 - {I44/50)]}. Thus the goal of investment management can be thought of as identifying the portfolio that has the maximum value of 1'" - (a;'/T), because it will provide the client with the maximum certainty equivalent return . l

. . SECURITY ANALYSIS AND PORTFOLIO CONSTRUCTION

23.4. t

Passive and Active Management

Within the investment industry, a distinction is often made between passive management-holding securities for relatively long periods with small and infrequent changes-and active management. Passive managers generally act as if the security markets are relatively effici ent. Put somewhat differently, their d ecisions are consistent with the acceptance of consensus estimates of risk and return. The portfolios they hold may be surrogates for the market portfolio that are known as index funds. or they may be portfolios that are tailored to suit clients with preferences and circumstances that differ from those of the average investor," In either case, passive portfolio managers do not try to outperform their designated benchmarks. For example, a passive manager might only have to choose the appropriate mixture of Treasury bills and an index fund that is a surrogate for the market portfolio. The best mixture would depend on the shape and location of the client's indifference curves. Figure 23.4 provides an illustration. Point fplots the riskfree return offered by Treasury bills, and point M plots the risk and expected return of the surrogate market portfolio, using consensus forecasts. Mixtures of the two investments plot along line fM. The client's attitude toward risk and return is shown by the set ofindifference curves, and the optimal mixture offand M lies at the point 0', where an indifference curve is tangent to line fM. In this example, the best mixture uses both Treasury bills and the surrogate market portfolio. In other situations, the surrogate market portfolio might be "levered up" by borrowing (that is, money might be borrowed and added to the client's own investable funds, with the total being used to purchase the surrogate market portfolio) . When management is passive, the optimal mixture is altered only when: • the client's preferences change; or • the riskfree rate changes; or • the consensus forecast about the risk and return of the benchmark portfolio changes. Investment Management

799

Standard Deviat ion of Return

Figure 23.4

Passive Investment Management The manager must continue to monitor the last two variables and keep in touch with the client concerning the first one. No additional activity is required. Active managers believe that from time to time there are mispriced securities or groups of securities. They do not act as if they believe that security markets are efficient. Put somewhat differently, they use deviant predictions; that is, their forecasts of risks and expected returns differ from consensus opinions. Whereas some managers may be more bullish than average about a security, others may be more bearish. The former will hold "more-than-normal" proportions of the security; the latter will hold "less-than-normal" proportions. It is useful to think of a portfolio as having two components: (1) a benchmark portfolio and (2) deviations designed to take advantage of security mispricing. For example, a portfolio can be broken down as follows:

Name Security

Proportion in Actual Portfolio

Proportion In Benchmark Portfolio

III

121

131

0'

Active

Position

Sl

.30

.45

141 -.15

52

.20

.25

-.05

S3

.50

.30

+.20

1.00

1.00

.00

The second column shows the actual proportions in the activel y managed portfolio. . The third column indicates the percentages in a benchmark portfolio. The active positions can be represented by the differences between the proportions in the actual and benchmark portfolios. Such differences arise because active managers disagree with the consensus forecast about expected returns or risks. When expressed as differences of this sort, the actual portfolio can be viewed as an investment in the benchmark portfolio with a series of bets being placed on certain securities (such as S3) 800

CHAPTER 23

and against certain other securities (such as Sl and S2). Note that the bets are "balanced" in that the amount of the negative bets exactly counters the amount of the positive bets.

23.4.2

Security Selection, Asset Allocation, and Market Timing

Security Selection

In principle, the investment manager should make forecasts of expected returns, standard deviations, and covariances for all available securities. These forecasts will allow an efficient set to be generated, upon which the indifference curves of the client can be plotted. The investment manager should then invest in those securities that form the optimal portfolio (that is, the portfolio indicated by the point at which an indifference curve is tangent to the efficient set) for the client in question. Such a one-stage security selection process is illustrated in Figure 23.5(a). In practice, this is rarely (if ever) done. Excessive costs would be incurred to obtain detailed forecasts of the expected returns, standard deviations, and covariances for all the individual securities under consideration. Instead, the decision on which securities to purchase is made in two or more stages. Figure 23.5(b) illustrates a two-stage procedure in which the investment manager has decided to consider investing in common stocks and corporate bonds for a client. In this case, the expected returns, standard deviations, and covariances are forecast for all common stocks under consideration. Then, on the basis of just these common stocks, the efficient set is formed and the optimal stock portfolio identified. Next the same analysis is performed for all corporate bonds under consideration, resulting in the identification of the optimal bond portfolio. The security selection process used in each of these two asset classes can be described as being myopic. That is, covariances between the individual common stocks and corporate bonds have not been considered in the identification of the two optimal portfolios. Although this example has only two asset classes-stocks and bonds-the number of asset classes can be relatively large. Other asset classes that are often used consist of money market securities ("cash"), foreign stocks, foreign bonds, venture capital, and real estate.

Asset Allocation

The second stage of the process divides the client's funds among two (or more) asset class portfolios and is known as asset allocation." In this stage, forecasts of the expected return and standard deviation are needed for both the optimal stock portfolio and the optimal bond portfolio, along with the covariance between the two portfolios. This information will allow the expected return and standard deviation to be determined for all combinations of these two portfolios. Finally, after the efficient set has been generated, the indifference curves of the client can be used to determine which portfolio should be chosen' Some people refer to two types of asset allocation. Strategic asset allocation refers to how a portfolio's funds would be divided, given the portfolio manager's long-term forecasts of expected returns, variances, and covariances, whereas tactical asset allocation refers to how these funds are to be divided at any particular moment, given the investor's short-term forecasts . Hence the former reflects what the portfolio manager would do for the long term, and the latter reflects what he or she would do under current market conditions. Investment Management

801

(a) Security Selection

s<curilicsl~ O \,er;11I PClrt ln ho

(b) Security Selection and Asset AlloCation

=0 }

Securities

$e clIri lY A''C I..f:la!lO.c

Silldc. Po rtfu lic

A\.\.t"'

Overa ll

AJI.o!

Ouarter

4 5

14.14

-9.09 11.29

21.96 3.71

23.08 1.81

10.65 - .22

8.65 -2.44 -1.84 -5.24

S&P 500

-5.86% -2.94 13.77 14.82 11.91 11.5!l -.78

7

1.90 2.00 2.22

8 9

2.11 2.16

.27 -3.08

10

2.34 2.44

-6.72 8.58

2.40 1.89 1.94 1.72

1.15 7.87

5.98

8.73 1.63 10.82

5.9'l -3.10

3.98 -4.82

7.24 -2.78

1.75

13.61

11.86

14.36

6

11 12 13 14 15 16

Excess Return

Return

.02 - 2.52 -1.85

-9.06 6.14 -1.25

-8 .83%

-6.00 10.92 12.94 10.01 9.55 -3.00 -2.09 -4.68 -4.19 6.29 - .77 8.93 5.30 - 4.50 12.61

fbI Calculations· First Fund Excess Returns $ Y

S&P 500 Excess Returns $ X

Y'

X'

III

121

131

(41

151

1

-11.74%

-8.83%

137.83

2

-9.09 11.29 23.08 1.81 8.6!) -2.44 -1.84 -5.24 -9.06 6.14 -1.25 5.98

-6.00 10.92 12.94 10.01

82.63 127.46 532.69

77.93 36.05 119.26

103.66 54.54 123.29

167.53 100.11

298.66

9.5!l

74.82 5.95 !t39 27.46 82.()14

91.28 8.97

82.61 7.32 3.85

:~.98

-4.82

5.30 -4.50

11.86 27.31

=ty

Quarter

3 4 :;

6 7 8 9 10

11 12 13 14 15 16 Sum (S)

-:tOO -2.09 -4.68

3.28

4.35 21.94 17.54 39.53

YXX

18.12

79.82

24.52 37.96 38.62 .96 53.40

12.61 -42.49 -

15.84 23.23 J4O.66 1,332.34

28.07 20.25 158.93 972.16

21.09 21.69 149.56 1,039.85

=~X

=Iyt

=:oIXI

;;IXY

-4.19 6.29

-.77 8.93

37.70 1.!l6 35.76

.60

Thus, after a portfolio's ex post beta has been estimated and this value entered on the right-hand side of Equation (24 .15), a benchmark return for the portfolio can be determined. For example, a portfolio with a beta of.8 during the 16-quarter time interval would have a benchmark return of 4.35% [= 2.23 + (2.65 X .8)]. Figure 24.5 presents a graph of the ex post SML given by Equation (24.15). 838

CHAPTER 24

TABLE

24. 1 f con tin ue d J

The Ex PostCharaeterlstl~ Une for the First Fund

I. Bela:

(TX };X1') - (!YX };x) _ (Hl X 1,039.85) - (27.31 X 42,49) _ (TXIX~)-(!X)2 (16X972.1fi)-(42.49)1 -1.13 2. Alph a:

[L Y/T] - [Beta X (LX/T)]

= [42.49/16]

- [1.13 X (42.49/16)]

= -1.29

3. Standard Deviation of Random ErrOT Tenn: {[~ y' - (Alpha X ~Y) - (Beta X (IXY)l/[T - 2]}'/l!

= {[l,332.34

- (-1.29 X 27.31) - (1.13 X 1 ~0!\9.85)1/{16 - 2]}'/'l

= 3.75

,

4. Standard Error of Beta:

Standard Deviation of Random Error Term / {L X~ - [( L X)2/

TW n

= 3.75/ {972. 16 -

[(42 .49)2/16]}'!2

= .13

5. Standard Error of Alpha: Standard Deviation of Random Error Term/{ T - ( 1:X)1/l: X

2W12

= 3.75/{16 - [(42.49)2/H72.J6j)In = 1.00 6. Correlation Coefficient: (T X~XY)-(~YX~X)

{[( T X ~ y 2 )

-

_ (~yn X [(7' X };X 1) - (kX) 1J}'i~ (16 X 1,039.85) - (27.31 X 42.49) {[(16 X 1,332.34) - (27.31f) X [(16 X 972.1fi) -

(42.49fJ}"~

_ - .92

7. Coefficient of Determination. (Correlation Coefficient)' = (.92)2

= '.85

8. Coefficient of Nondet ermination :

I - Coeffi cient of det ermination

=I

- .85

= .15

• All summations are to be carried out over I. where 1go es from 1 to T lin this example. 1 = I .... . 16).

As shown in Chapter 21, one measure ofa portfolio's risk-adjusted performance is the difference between its average return (aTp) and the return on its corresponding benchmark portfolio, denoted aTbp' This difference is generally referred to as the portfolio's ex post alpha (or differential return), and is denoted Ctp: (21.3) A positive value of Ctp for a portfolio would indicate that the portfolio had an average return greater than the benchmark return, suggesting that its performance was superior. On the other hand, a negative value of Ctp would indicate that the portfolio had an average return less than the benchmark return, suggesting that its performance was inferior. Bysubstituting the right-hand side of Equation (24.14) for aT"" in Equation (21.3), one can see that a portfolio's ex post alpha based on the ex post SML is equal to:" (24.16) Portfolio Performance Evaluation

839

ExPosl SML

5.22%

l

ClFF =

1/

M

4.88%

I

I

I

I

I

___ ...J _",.... ",1", IFF

3.93%

",

I

-1.29% '" ",'

., "'"

"" "

I I I I I I

2.23%

I I

I I I I

I I

l.1l1l 1.13

Figure 24.5 Performance Evaluation Using the Ex Post SML.

After the values for Ci." and f3" for a portfolio have been determined, the ex post characteristic line for the portfolio can be written as:

Til - Tf =

Ci./I

+ f3,,( TM

- Tf)

(24 .17)

The characteristic line is similar to the market model (introduced in Chapter 7) except that the portfolio's returns and the market index's returns are expressed in excess of the riskfree return . Graphically, the characteristic line formulation is the equation of a straight line where (TM - Tf) is measured on the horizontal axis and (T" - TJ) is measured on the vertical axis. Furthermore, the line has a vertical intercept of Ci." and a slope of f3 I,. As an example, consider the performance of the hypothetical portfolio "First Fund," indicated in panel (a) of Table 24.1, for the given 16-quarter time interval. During this interval, the First Fund had an average quarterly return of 3.93%. Equation (24 .11), shows that First Fund had a beta of 1.13. Having an average beta over the 16 quarters that is greater than the market portfolio's beta of I indicates that First Fund was relatively aggressive (if its average beta had been less than I, it would have been relatively defensive). Given these values for its beta and average return, the location of First Fund in Figure 24.5 is represented by the point having coordinates (1.13,3.93), denoted FF. The exact vertical distance from FF to the ex post SML can be calculated by using Equation (24.16): Ci. p

= aT" - [aT! + (aTM + aTJ)f3,,] = 3.93% - [2 .23%

+ (4.88%

- 2.23%)1.13]

= -1.29% Because FF lies below the ex post SML, its ex post alpha is negative, and its performance would be viewed as inferior." Using Equation (24.17), the ex post characteristic line for First Fund would be: 840

CHAPTER 24

•

20%

15%

-15%

Figure 24.6 Ex Post Characteristic Line for First Fund.

r" -

rf

= -1.29 %

+ 1.13( rM - Yj)

Figure 24.6 provides an illustration of this line." Th e method for determining a portfolio's ex post alpha, beta, and characteristic line suggests the use of a five-step procedure: 1. Determine the periodic rates of return for the portfolio and market index over the time interval, as well as the corresponding riskfree rates. 2. Determine the average market return and riskfree rate by using the formulas in Equations (24.12) and (24.13). 3. Determine the portfolio's expost beta by using the formula in Equation (24.11). 4. Determine the portfolio's ex post alpha by using the formula given in Equation (24.16). 5. Insert these values for alpha and beta in Equation (24.17) in order to determine the portfolio's ex post characteristic line. However, there is a simpler method for determining a portfolio's ex post alpha, beta, and characteristic line that also provides a number of other pieces of information relating to the portfolio's performance. This method involves the use of simple linear regression, and corresponds to the method presented in Chapters 7 and 16 for estimating the market model for an individual security. With this method, the excess return on portfolio p in a given period t is viewed as having three components. The first component is the portfolio's alpha; the second component is a risk premium equal to the excess return on the market times the portfolio's beta; and the third component is a random error term." These three components can be seen on the right-hand side of the following equation: rpl -

rfi

= a p + f3p( rMI -

rfi)

+ BpI

(24.18)

Because a p and f3 p are assumed to be constant during the time interval, Equation (24.18) can be viewed as a regression equation. Accordingly, there are certain standard formulas for estimating aI" f3 p, and a number of other statistical parameters associated with the regression equation. Portfolio Performance Evaluation

841

Panel (b) of Table 24. t presents these formulas, with First Fund being used as an example. As can be seen, the formulas indicate that First Fund's ex post alpha and beta were equal to -1.29 and 1.13, respectively, over the 16-quarter time interval. These values are the same as those arising when Equations (24.11) and (24.16) were used earlier. Indeed, they will always result in the same values. Figure 24.6 presents a scatter diagram of the excess returns on First Fund and the S&P 500 . Based on Equation (24.18), the regression equation for First Fund is: Tn.: - 7j = -1.29%

+ 1.13(T,\/ -

Tf)

+ en.

(24 .19)

where -1.29 and 1.13 are the estimated ex post alpha and beta for First Fund over the 16-quarter time interval. As mentioned earlier, also shown in the figure is the ex post characteristic line for First Fund, a line that is derived by the use of simple linear regression: (24.20) The vertical distance between each point in the scatter diagram and the regression line represenrs an estimate of the size of the random error term for the corresponding quarter. The exact distance can be found by rewriting Equation (24.19) as: (24 .21) For example, in the l l th quarter the excess return on First Fund and the S&P 500 were 6.14% and 6.29%, respectively. The value of en. for that quarter can be calculated by using Equation (24.21) as foIlows:

ew

=

(6.14%) - [-1.29%

+ 1.13(6.29%)]

= .32%

The value of en" can be calculated similarly for the other 15 quarters of the time interval. The standard deviation of the resulting set of 16 numbers is an estimate of the standard deviation of the random error term (also known as the residual standard deviation) and is shown in panel (b) of Table 24.1 to be equal to 3.75%. This number can be viewed as an est imate of the ex post unique (or unsystematic or non-market) risk of First Fund. The regression line for First Fund that is shown in Figure 24.6 is the line of best fit for the scatter diagram and corresponds to First Fund's ex post characteristic line. What is meant by "best fit"? Given that a straight line is defined by irs intercept and slope, it means that there are no other values for alpha and beta that fit the scatter diagram any better than th is one. In terms ofsimple linear regression, this means that there is no line that could be drawn such that the resulting standard deviation of the random error term would be smaller than the one of best fi t, A portfolio's "true" ex post beta cannot be observed; all that can be done is to estimate irs value. Thus, even if a portfolio's true beta remained the same forever, irs estimated value, obtained in the manner illustrated in Table 24.1 and Figure 24.6, would still change from time to time because of errors (known as sampling errors) in estimating it. For example, if a different set of 16 quarters were examined, with the first quarter being replaced by a more recent quarter, the resulting estimated beta for First Fund would almost certainly be different from 1.13. The standard error of beta shown in Table 24.1 attempts to indicate the extent of such estimation errors. Given a number of necessary assumptions (for example, the "true" beta did not change during the 16-quarter estimation period), the chances are roughly two out of three that the true beta is within one standard error, plus or minus, of the estimated beta. Thus First Fund's true beta is likely to be between the values of 1.00 (= 1.13 - .13) and 1.26 (= 1.13 + .13). Similarly, the value under 842

CHAPTER 24

standard error of alpha provides an indication of the magnitude of the possible sampling error that has been made in estimating the portfolio's alpha. The value under correlation coefficient provides an indication of how closely the excess returns on First Fund were associated with the excess returns on the S&P 500. Because its range is between -1 and +1, the value for First Fund of .92 indicates a strong positive relationship between First Fund and the S&P 500. That is, larger excess returns for First Fund seem to have been closely associated with larger excess returns for the S&P 500. The coefficient of determination is equal to the squared value of the correlation coefficient; it represents the proportion of variation in the excess return on First Fund that is related to the variation in the excess return on the S&P 500. That is, it shows how much of the movement in First Fund's excess returns can be explained by movements in the excess returns on the S&P 500. The a value of .85 shows that 85% of the movement in the excess return on First Fund over the 16 quarters can be attributed to movement in the excess return on the S&P 500. Because the coefficient of nondetermination is 1 minus the coefficient of determination, it represents the proportion of movement in the excess return on First Fund that does not result from movement in the excess return on the S&P 500 . Thus 15% of the movement in First Fund cannot be attributed to movement in the S&P 500. Although Table 24.1 shows the formulas for calculating all these values , it should be pointed out that there are many different software packages that can quickly carry out these calculations. The only substantive effort involves gathering all the return data shown in panel (a) of Table 24.1 and then entering it into a computer spreadsheet.

24.4.2

The Reward-to-Volatility Ratio

Closely related to the ex post alpha measure of portfolio performance is a measure known as the reward-to-volatility ratio," This measure, denoted RVOL,,, also uses the ex post security market line to form a benchmark for performance evaluation, but in a somewhat different manner. The calculation of the reward-to-volatility ratio for a portfolio involves dividing its average excess return by its market risk as follows : RVOL p =

ar. - aTJ I' {3p

(24.22)

Here the beta of the portfolio can be determined using the formula in Equation (24.11). In the example of First Fund, it was noted earlier that its average return for the If-quarter time interval was 3.93%. Furthermore, it was noted that the average Treasury bill rate was 2.23%. Thus the average excess return for First Fund was 1.70% (=3.93% - 2.23%) and, given a beta of 1.13, its reward-to-volatility ratio was 1.50% (= 1.70%/1.13). The reward-to-volatility ratio corresponds to the slope of a line originating at the average riskfree rate and going through the point ({3p, aTp) . This correspondence can be seen by noting that the slope of a line is easily determined if two poin ts on the line are known; it is simply the vertical distance between the two points ("rise") divided by the horizontal distance between the two points ("run"). In this case, the vertical distance is aTp - aTJ and the horizontal distance is {3p - 0, so the slope is (aTp - aTJ)/{3p and thus corresponds to the formula for RVOLp given in Equation (24.22). Note that the value being measured on the horizontal axis is {3p and the value being measured on the vertical axis is aTp, suggesting that the line can be drawn on the same diagram as the ex post SML. In the First Fund example, remember that the ex post SML for the I6-quarter time interval was shown by the solid line in Figure 24.5 . Also appearing in this figure Portfolio Performance Evaluation

843

was the point denoted Fr; corresponding to ([31" arl,) = (1.13, 3.93%) for First Fund. The dashed line in this figure originates from the point (0, arf) = (0,2.23%), goes through FE', and has a slope of 1.50% [= (3.93% - 2.23%)/1.13] that corresponds to the value noted earlier for RVOLI,. The benchmark for comparison with this measure of performance is the slope of the ex post SML. Because this line goes through the points (0, arf) and (1, aTM), its slope is simply (arM - flIj)/( I - 0) = (arM - a1j) If RVOLI, is greater than this value, the portfolio lies above the exJJOst SML, indicating that it has outperformed the market. Alternatively, if RVOLI, is less than this value, the portfolio lies below the ex post SML, indicating that it has not performed as well as the market. In the case of First Fund, the benchmark is 2.65% [= (aTM - aTf) = (4.88% - 2.23%)]. Because RVOL" for First Fund is less than the benchmark (1.50% < 2.65%), according to this measure of portfolio performance, First Fund did not perform as well as the market. In the comparison of the two measures of performance that are based on the ex post SML, Ci l, and RVOLI" it should be noted that they will always give the same assessment ofa portfolio's performance relative to the market portfolio. That is, if one measure indicates that the portfolio outperformed the market, so will the other. Similarly, if one measure indicates that the portfolio did not perform as well as the market, the other measure will show the same thing. This correspondence can be seen by noting that any portfolio with a positive expost alpha (an indication of superior performance) lies above the ex post SML and thus must have a slope grl'aterthan the slope of the ex post SML (also a n indication of superior performan ce) . Similarly, any portfolio with a negative ex post alpha (an indication of inferior performance) lies beloiu the ex post SML and thus must have a slope less than the slope of the ex post SML (also an indication of inferior performance) . However, it should also be noted that it is possible for the two measures to rank portfolios differently on the basis of performance simply because the calculations are different. For example, if Second Fund had a beta of 1.5 and an average return of 4.86%, its ex post alpha would be -1.34% 1=4.86% - [2.23 + (4.88 - 2.23) X 1.5]1. Thus its performance appears to be worse than that of First Fund because it has a smaller ex post alpha (-1.34% < -1.29%). However, its reward-to-volatility ratio of 1.75% [= (4.86% - 2.23%)/1.5] is larger than the reward-to-volatility of 1.50% for First Fund, suggesting that its performance was better than First Fund's,

24.4.3

The Sharpe Ratio

Both measures of risk-adjusted performance described so far, ex post alpha (that is, differential return) and the reward-to-volatility ratio, use benchmarks that are based on the ex post security market line (SML). Accordingly, they measure returns relative to the market risk of the portfolio. In contrast, the Sharpe ratio (or reward-to-vanabilit)1 ratio) is a measure of risk-adjusted performance th at uses a benchmark based on the ex post capital market line (CML).IO It measures returns relative to the total risk of the portfolio, where total risk is the standard deviation of portfolio returns. In order to use the Sharpe ratio (S~,), one must determine the location of the ex post CML. This line goes through two points on a graph that measures average return on the vertical axis and standard deviation on the horizontal axis. The first point is the vertical intercept of the line and corresponds to the average riskfree rate during the 16-quarter time interval. The second point corresponds to the location of the market portfolio, meaning that its coordinates are the average return and standard deviation of return for the market portfolio during the evaluation interval, or

844

CHAPTER 24

(U M, arM)' Because the ex post CML goes through these two points, its slope can readily be calculated as the vertical distance between the two points divided by the horizontal distance between the two points, or (arM - arj)/(UM - 0) = (arM - arj)/uM' The return given by the ex post CML for a portfolio with total risk u can be used as I' a benchmark return, ar~p' for that portfolio. That is, given a vertical intercept of arJ, the equation of this line is: _ ar"p - arj

+

arM -

arJ

UM

(24.23)

Up

In the example shown in Table 24. I. the average return and standard deviation for the S&P 500, calculated using Equations (24.9) and (24.10), were 4.88% and 7.39%, respectively. The average return on Treasury bills was 2.23%, so the ex postCML during these 16 quarters was: ar"I' =

+

2.23%

4.88% - 2.23% 7 (ff .39/'0

up

(24.24)

+ .36u p

= 2.23%

Figure 24.7 presents a graph of this line. Once the location of the ex post CML has been determined, the average return and standard deviation of the portfolio being evaluated can be calculated next by using Equations (24.9) and (24.10). When these values are known, the portfolio can be located on the same graph as the ex post CML. In the case of First Fund, its average return and standard deviation were 3.93% and 9.08%, respectively. Thus in Figure 24.7 its location corresponds to the point having coordinates (9.08%,3.93%), which is denoted FF.

4.88% I I -

-

-

~ I -I. - - - ....""""t ' I ~ ~ FF ~-i~

-

2.23%

7.39%

9.08%

up

Figure 24.7 Performance Evaluation Using the Ex Post CML.

Portfolio Performance Evaluation

845

The calculation of the Sharpe ratio SRi} is analogous to the calculation of the reward-to-volatility ratio RVOL" described earlier. Specifically, RVOL,} involves dividing the portfolio's average excess return by its beta, whereas SRI' involves dividing the portfolio's average excess return by its standard deviation: (24.25 ) Note that SRI' corresponds to the slope of a line originating at the average riskfree rate and going through a point having coordinates of (U'I> aT,}). This correspondence can be seen by noting that the slope of this line is simply the vertical distance between the two points divided by the horizontal distance between the two points, or (aTp - aTj)/( up - 0) = (aT" - aTj)/Up, which corresponds to the formula for SRI' given in Equation (24.25). In the First Fund example, recall that the ex post CML was shown by the solid line in Figure 24.7. Also appearing in this figure was the point denoted FF, corresponding to (u'I> aT,,) = (9.08%, 3.93%) for First Fund. The dashed line in this figlife originates from the point (0, flTA = (0,2.23%) and goes through FF. The slope of this line is simply .19 [= (3.93 - 2.23)/9.08] . Because the ex post CML represents various combinations of riskfree lending or borrowing with investing in the market portfolio, it can be used to provide a benchmark for the Sharpe ratio in a manner similar to the SML-based benchmark for the reward-to-volatility ratio. As noted earlier, the slope of the ex post CML is (aTM - aTj)/UM' If SRi' is greater than this value, the portfolio lies above the ex post CML, indicating that it has outperformed the market. Alternatively, if SRi} is less than this value, the portfolio lies below the ex post CML, indicating that it has not performed as well as the market. In the case of First Fund, the benchmark is .36 [= (4.88 - 2.23)/7.39]. Because SR" is less than the benchmark (.19 < .36), First Fund did not perform as well as the market according to this risk-adjusted measure of portfolio performance.

24.4.4

M2

The measure M-squared uses standard deviation as the relevant measure of risk. II Thus, like the Sharpe ratio, it is based on the ex post CML. This measure simply takes a portfolio's average return and determines what it would have been if the portfolio had had the same degree of total risk as the market portfolio (in the case of a common stock portfolio usually represented by the S&P 500). Consider a line that goes through the average riskfree rate and the average return on the portfolio, where standard deviation is being used as the measure of risk, such as the line going through the average riskfree rate of2.23% and First Fund (FF) in Figure 24.7. The following equation describes such a line: ar,

= aTj

+(

aTp - aTj) Up

U;

(24.26)

because the line has a vertical in tercept of aTj and a slope of (aTp - aTj)/up' This equation indicates the average return, ar., that would have been earned by investing in portfolio p and either investing or borrowing at the riskfree rate to such a degree that the resulting standard deviation was U;. The risk-adjusted return Mj is the average return that would have been earned if the amount of riskfree investing or lending had resulted in the standard deviation of the portfolio being equal to that of the market portfolio. Hence, setting a , equal to UM in Equation (24.26) results in the value of M,~ for portfolio p: 846

CHAPTER 24

(24.27) Accordingly, M,; measures the return an investor would have earned if the portfolio had been altered by use of the riskfree rate through borrowing or lending in order to match the market portfolio's risk level as measured by standard deviation. For example, First Fund had on a quarterly basis an average return of 3.93% and a standard deviation of9.08%. Because the average riskfree rate was 2.23 %, the equation describing the dashed line in Figure 24.7 can be determined by using Equation (24 .26) to be: 2 ar·= 2 .3+ ( I = 2.23

+.

3.93 - 2.23) (T 9.08 I

19(Tj

(24.28)

The standard deviation of the market portfolio (estimated by using the S&P 500) was 7.39%, so it follows that M,~ for the First Fund was 3.61 %. That is, by investing 7.39/9.08 = 81.4% in First Fund and 18.6% in the riskfree rate, the investor would have had a portfolio that had the same standard deviation as the market portfolio. In this example, M2 effectively "de-levers" First Fund's return to bring its risk level down to that of the market portfolio and then proportionately reduces First Fund's return by the degree of de-leveraging. If the market portfolio's standard deviation had been greater than that of First Fund, then M2 would have leveraged First Fund's return by borrowing at the riskfree rate to increase its standard deviation to that of the market portfolio. This action would have proportionately increased First Fund's return by the degree of leveraging. M,~ can be compared directly with the average return on the market portfolio arM in order to see if the portfolio outperformed or underperformed the market portfolio on a risk-adjusted basis. In the case of First Fund, the market portfolio had an average return of 4.88 %, suggesting underperformance on the fund's part since M1..,.. = 3.61 % < 4.88% = arM' When the two measures of risk-adjusted performance that are based on the ex post CML, SRp and M~, are compared, they will always give the same assessment of a portfolio's performance relative to the market portfolio.l'' Hence, it is impossible for one measure to indicate that a portfolio performed better than the market and the other to indicate that it performed worse. This correspondence can be seen by noting that if a portfolio plots below the ex post CML, then (1) the slope of the line going through the portfolio (SRp) will be less than the slope of the ex post CML, and (2) M,~ will lie on the line going through the portfolio at a point that is directly below the location of the market portfolio on the ex post CML. The converse is also true if the portfolio plots above the ex post CML. Furthermore, the two measures will rank a set of portfolios exactly the same, because comparing slopes oflines that all go through the average riskfree rate will rank portfolios exactly the same as comparing the average returns on all of these lines at a given level of standard deviation. Equivalently, Equations (24.25) and (24.27) can be combined to show that: (24.29)

Ml

Thus, the value of for any portfolio is simply equal to a positive constant plus the portfolio's reward-to-variability ratio multiplied by a positive constant. Because these Portfolio Performance Evaluation

847

.

. INSTITUTIONAL ISSUES

.

Custom Benchmark Portfolios Investment management has become increasingly specialized. Many managers have chosen not only to concentrate on specific asset classes (for example, stocks or bonds), but within those asset classes they have further focused their efforts on certain types of securities. This specialization has been particularly prevalent among managers owning U.S. common stocks. For example , some managers specialize in small, emerging growth company stocks. Others select only from certain industries, such as health care. These specializations have come to be known as "investment styles." Investment styles have significant ramifications for the evaluation of investment manager performance. Investment management can be viewed as a fishing contest. Each angler has his or her own fishing hole (investment style). No one fishing hole is asSUllied to be any better than another, although from year to year the sizes and quantity of fish fluctuate independently in each hole. The anglers attempt to catch the largest fish from their fishing holes. How should institutional investor clients evaluate the proliciency of these anglers on the basis of their catches? II would make little sense to directly compare the anglers' respective catches. If Angler A's fishing hole was extremely well stocked this year and Angler B's was not, Angler n would be at a tremendous disadvantage. More appropriately, clients would like to compare what each angler caught against the opportunities available in their respective fishing holes. In other words, the clients should want to take into account

the impact of managers' investment styles on their performance. Investment styles tend to dominate the performance of investment managers within a particular asset class . For example, suppose that the domestic common stock market was split along two dimensions similar to those discussed in Chapter 16: market capitalization (share price times shares outstanding) and growth prospects. In 1997, for example, the best-performing group was small value stocks, which returned 32%. Conversely, small growth stocks returned 13%, a difference of 19 percentage points. Differences between investment styles of similar magnitudes can be found in other years . These differences are typically large enough so that no investment manager can hope to consistently overcome the performance effect of his or her investment style. Therefore to evaluate a manager's investment skill, how the manager has performed relative to his or her investment style should be considered explicitly. One means of dealing with this issue is to develop a comparison portfolio that specifically represent~ the manager's investment style. This comparison portfolio is referred to as a custom benchmark portfolio. The custom benchmark contains the types of securities from which the manager typically selects. Further, these securities are weighted in the custom benchmark in a manner similar to weights typically assigned by the manager. Moreover, the custom benchmark displays portfolio characteristics (for example, priceearnings ratios, earnings growth rates, and market

two constants are the same for all portfolios, the ranking for same as the ranking for SRp.

24.4.5

M; will be exactly the

Comparing the RiSk-Adjusted Measures of Performance

The measures of performance that are based on the ex post SML, cx p and RVOLp, can be compared with the measure of performance that is based on the ex post CML, SRp Because the ex post CML-based measure evaluates portfolios exactly the same as SRp, there is no need to compare cxp and RVOLp with it. It should be noted that in certain situations, RVOLp and SRp can give different assessments ofa portfolio's performance relative to the market portfolio. (The comparson also applies to cx p and SRp.) In particular, if RVOLp indicates that the portfolio outperformed the market, it is possible for SRp to indicate that the portfolio did not perform as well as the market. The reason is that the portfolio may have a rela-

M;

848

CHAPTER 24

capitalizations) consistent with the manager's actual portfolio. Consider a manager whose investment style entails investing in large-capitalization, high-dividendyield stocks. In building portfolios, the manager follows certain rules, some explicitly, others implicitly. For example, the manager does not buy stocks with less than $5 billion in market capitalization. All stocks in the manager's portfolio must display at least a 3% dividend yield. The manager assigns each stock an equal weight in the portfolio. Further, to avoid overconcentrations, no industry may constitute more than 10% of the portfolio's market value. A cust om benchmark can be designed to reflect these characteristics of the manager's investment style. The custom benchmark might be composed of 300 stocks, as opposed to the manager's portfolio, which might contain only 30 stocks. The manager, in effect, has searched through his or her fishing hole and selected the 30 stocks that he or she thinks will perform the best. An evaluation of the manager's performance will be based over time on how these 30 stocks perform relative to the 300 stocks. This performance evaluation process takes advantage ofa powerful paired-eomparison test. Given a group of stocks, can the manager consistently identily the best-performing issues? The question is simple and the results easy to interpret. No special risk-adjusted performance measures are required. If the custom benchmark has been properly constructed, it

exhibits a risk level consistent with that exhibited on average by the manager. The primary drawback of custom benchmarks is the effort required to design them. Each manager's investment style has unique aspects, and not all of them are as explicit as those of the large-eapitalization, high-yield manager discussed above . Typically, identifying those unique aspects involves examining past portfolios and engaging in lengthy discussions with the manager. Recently a number of analysts have adopted a method in which a benchmark made up of combinations of standard indices is constructed on the basis of statistical analysis of a manager's past returns. The use of this procedure, known as style analysis, can in many cases provide some of the advantages of more elaborate custom benchmark portfolios at a fraction of the cost, time, and effort. (For details on this approach, see the references listed at the end of the chapter.) Custom benchmarks, whether derived via detailed analyses or using style analysis, can provide effective performance evaluations. Moreover, they have uses outside of performance evaluation. For example, as discussed in Chapter 23's Institutional Issues: Manager Structuring, clients who hire more than one investment manager can use custom benchmarks to examine how various investmen t styles fit together into an aggregate portfolio. This type of analysis permits a client to better understand and control the investment risks present in the client's total portfolio.

tively large amount of unique risk . Such risk would not be a factor in determining the value of RVOL p for the portfolio, because only market risk is in the denominator. However, such risk would be included in the denominator of SRp for the portfolio because this measure is based on total risk (that is, both market and unique risk). Thus a portfolio with a low amount of market risk could have a high amount of total risk, resulting in a relatively high RVOL p (due to the low amount of market risk) and a low SRp (due to the high amount of total risk). Accordingly, RVOLp could indicate that the portfolio outperformed the market at the same time that SRp indicated that it did not perform as well as the market. 13 As an example, consider Third Fund, which had an average return of 4.5%, a beta of .8, and a standard deviation of 18%. Accordingly, RVOL TF = 2.71% [= (4.5% 2.23%)/.8], indicating that Third Fund outperformed the market portfolio because the benchmark is 2.65% [= (4.88% - 2.23%)/1.0]. However, SRTF = .12 [= (4.5% 2.23%)/18%], indicating that Third Fund did not perform as well as the market portfolio because the benchmark is .36 [= (4.88% - 2.23%)/7.39%]. The reason for the difference can be seen by noting Third Fund's low beta relative to the market Portfolio Performance Evaluation

849

(.8 < 1.0) but high standard deviation relative to the market (18% > 7.39%). This outcome suggests that Third FUlId had a relatively high level of unique risk . It also follows that it is possible for RVOL" and SR" to rank two or more portfolios differently on the basis of their performance because these two measures of riskadjusted performance use different types of risk. Recall that earlier it was shown that First Fund had an average return of 3.93 %, a beta of 1.13 , and a standard deviation of 9.08 %. Thus, RVOL n,' = 1.50% [= (3 .93% - 2.23 %)/1.13], which is less than RVOLTF = 2.65%, thereby indicating that First Fund ranked lower than Third Fund. However, SRi'Jo' = .13 [= (3.93% - 2.23%)/9.08%], which is greater than SR'I1,' = .12, thereby indicating that First Fund ranked higher than Third Fund. Did Third Fund do better or worse than the market on a risk-adjusted basis? And did Third Fund perform better or worse than First Fund? The answer to those two questions lies in identifying the appropriate measure of risk for the client. If the client has many other assets, then beta is the relevant measure of risk, a nd performance should be based on RVOL . To such a client, Third Fund should be viewed as a superior performer relative to" both the market and First Fund. However, if the client has few other assets, then standard deviation is the relevant measure of risk, and performance should be based on SR,), To such a client, Third Fund should be viewed as an inferior performer relative to both the market and First Fund.

_

MARKET TIMING A market timer structures a portfolio to have a relatively high beta when he or she expects the market to rise and a relatively low beta when a market drop is anticipated . Why? Because, as noted earlier, the expected return on a portfolio is a linear function of its beta: (24.30) This means that the market timer will want to have a high-beta portfolio when he or she expects the market to have a higher return than the riskfree rate because such a portfolio will have a higher expected return than a low-beta portfolio. Conversely, the market timer will want to have a low-beta portfolio when he or she expects the market to have a lower return than the riskfree rate because it will have a higher expected return than a high-beta portfolio. Simply put, the market timer will want to: 1. Hold a high-beta portfolio when r M > rf' and 2. Hold a low-beta portfolio when r M < rf'

If the timer is accurate in his or her forecasts of the expected return on the market, then his or her portfolio will outperform a benchmark portfolio that has a constant beta equal to the average beta of the timer's portfolio. For example, if the market timer set the portfolio beta at 0.0 when r M < rf and at 2.0 when rM > rf' the return on the portfolio would be higher than the return on a portfolio having a beta constantly equal to 1.0, provided that the timer is accurate in forecasting r M ' Unfortunately, if the market timer's forecast are inaccurate and consequently alters the portfolio's beta in ways unrelated to subsequent market moves , then the timer's portfolio will not perform as well as a constant-beta portfolio. For example, if the timer sometimes sets the portfolio's beta equal to 0 when the market is forecast to fall but actually rises and at other times sets the beta equal to 2 when the market is forecast to rise but actually falls, then the portfolio will have an average return that is less than what a portfolio with a constant beta of 1 would have earned. To "time the market," one must change either the average beta of the risky securities held in the portfolio or the relative amounts invested in the riskfree asset and 850

CHAPTER 24

risky securities. For example, the beta of a portfolio could be increased by selling bonds or low-beta stocks and using the proceeds to purchase high-beta stocks. Alternatively, Treasury bills in the portfolio could be sold (or the amount of borrowing increased), with the resulting proceeds being invested in stocks or stock index futures . Because of the relative ease of buying and selling derivative instruments such as stock index futures, most investment organizations specializing in market timing prefer the latter approach. In Figure 24.8, the excess returns of two hypothetical portfolios are measured on the vertical axis and those of a market index are on the horizontal axis. Straight lines, fit via standard regression methods, reveal positive ex post alpha values in each case. However, the scatter diagrams tell a different story. The scatter diagram for the portfolio shown in panel (a) seems to indicate that the relationship between the portfolio's excess returns and the market's excess returns was linear, because the points cluster close to the regression line. This result suggests that the portfolio consisted of securities in a manner such that the beta of the portfolio was roughly the same at all times. Because the ex post alpha was positive, it appears that the investment manager successfully identified and invested in some underpriced securities. The scatter diagram for the portfolio shown in panel (b) seems to indicate that the relationship between this portfolio's excess returns and the market's excess returns was not linear because the points in the middle lie below the regression line and those at the ends lie above the regression line. This diagram suggests that the portfolio consisted of high-beta securities during periods when the market return was high and low-beta securities during periods when the market return was low. Upon examination, it appears that the portfolio has a positive ex post alpha because of successful market timing by the investment manager.

24.5.1

Quadratic Regression

Measuring the ability of an investment manager to successfully time the market requires that something more complex than a straight line be "fit" to scatter diagrams such as those shown in Figure 24.8. One procedure fits a curve to the data; statistical methods are used to estimate the parameters a, b, and c in the following quadratic regression equation:

(a) Superior Stock Selection

(b) Superior Market Timing

• •• ••• • ••

Figure 24.8 Superior Fund Performance. Portfolio Performance Evaluation

851

(a)

(b) &Posl

F.JfP~

Characterilltic Uoet

Characteristic Curve

•

.-....

• •• • ••

Figure 24.9 Ex Post Characteristic CUNe and Line.

(24.31 ) where E:/>I is the random error term. The ex post characteristic curoeshown in Figure 24.9(a) is simply the following quadratic function, where the values of a, b, and c for the portfolio have been estimated by standard regression methods: Tpt -

TjI

= a + b( TMt -

TjI)

+ c[ (TMt

-

TjI)2]

(24.32)

If the estimated value of c is positive [as it is for the portfolio depicted in Figure 24.9 (a) ], the slope of the curve will increase as one moves to the right. This change in slope would indicate th at the portfolio manager successfully timed the market. Note that this equation corresponds to the equation for the ex post characteristic line if c is approximately equal to zero. In such a situation, a and b would correspond to the portfolio's ex post alpha and beta, respectively."

24.5.2

Dummy Variable Regression

An alternative procedure fits two ex post characteristic lines to the scatter diagram, as

shown in Figure 24.9(b). Periods when risky securities outperform riskfree securities (that is, when TMt > Tfl) can be termed up markets. Periods when risky securities do not perform as well as riskfree securities (that is, when TM' < TjI) can be termed down markets. A successful market timer would select a high up-market beta and a low down-market beta. Graphically, the slope of the ex postcharacteristic line for positive excess market returns (up markets) is greater than the slope of the ex post characteristic line for negative excess market returns (down markets). Such a relationship can be estimated by using standard regression methods to determine the parameters a, b,and cin the following dummy variableregression equation: Tpt -

TJt

= a

+ b( TMt -

Tfl)

+ c[ D t( TMt -

TIt)]

+ E: pt

(24 .33)

Here, E: pt is the random error term, and D, is a "dummy variable" that is assigned a value of zero for any past time period t when TMt > Tft and a value of -} for any past 852

CHAPTER 24

time period t when TM, < Tit. To see how this procedure works, consider the effective equations for different values of TMt - Tit • .Value

0'

filii -

Equation

f ll

>0 coO