CHAPTER 13. Investor Behavior and Capital Market Efficiency. Chapter Synopsis

Transcription

1 CHAPTER 13 Investor Behavior and Capital Market Eiciency Chapter Synopsis 13.1 Competition and Capital Markets When the market portolio is eicient, all stocks are on the security market line and have an alpha o zero. When a stock s alpha is not zero, investors can improve upon the perormance o the market portolio. As we saw in Chapter 11, the Sharpe ratio o a portolio will increase i we buy stocks whose expected return exceeds their required return that is, i we buy stocks with positive alphas. Similarly, we can improve the perormance o our portolio by selling stocks with negative alphas. Thus, as savvy investors attempt to trade to improve their portolios, they raise the price and lower the expected return o the positive-alpha stocks, and they depress the price and raise the expected return o the negative-alpha stocks, until the stocks are once again on the security market line and the market portolio is eicient. Notice that the actions o investors have two important consequences. First, while the CAPM conclusion that the market is always eicient may not literally be true, competition among savvy investors who try to beat the market and earn a positive alpha should keep the market portolio close to eicient much o the time. In that sense, we can view the CAPM as an approximate description o a competitive market. Second, trading strategies that take advantage o non-zero alpha stocks may exist, and by doing so actually can beat the market Inormation and Rational Expectations I news that alters a stock s expected return is publically announced, there are likely to be a large number o investors who receive this news and act on it. Similarly, anybody who hears the news will not want to sell at the old prices. The only way to remove this imbalance is or the price to rise so that the alpha is zero. Note that in this case it is quite possible or the new

2 148 Berk/DeMarzo Corporate Finance, Second Edition prices to come about without trade. That is, the competition between investors is so intense that prices move beore any investor can actually trade at the old prices, so no investor can proit rom the news. In order to proit by buying a positive-alpha stock, there must be someone willing to sell it. Under the CAPM assumption o homogenous expectations, which states that all investors have the same inormation, it would seem that all investors would be aware that the stock had a positive alpha and none would be willing to sell. In reality, investors have dierent inormation and spend varying amounts o eort researching stocks. Consequently, we might expect that sophisticated investors would learn that a stock has a positive alpha, and that they would be able to purchase shares rom more naïve investors. However, even dierences in the quality o investors inormation will not necessarily be enough to generate trade in this situation. An important conclusion o the CAPM is that investors should hold the market portolio (combined with risk-ree investments), and this investment advice does not depend on the quality o an investor s inormation or trading skill. Even naïve investors with no inormation can ollow this investment advice, and as the ollowing example shows, by doing so they can avoid being taken advantage o by more sophisticated investors. Because the average portolio o all investors is the market portolio, the average alpha o all investors is zero. I no investor earns a negative alpha, then no investor can earn a positive alpha, and the market portolio must be eicient. As a result, the CAPM does not depend on the assumption o homogeneous expectations. Rather it requires only that investors have rational expectations, which means that all investors correctly interpret and use their own inormation, as well as inormation that can be inerred rom market prices or the trades o others. For an investor to earn a positive alpha and beat the market, some investors must hold portolios with negative alphas. Because these investors could have earned a zero alpha by holding the market portolio, we reach the ollowing important conclusion: The market portolio can be ineicient (so it is possible to beat the market) only i a signiicant number o investors either: 1. Do not have rational expectations so that they misinterpret inormation and believe they are earning a positive alpha when they are actually earning a negative alpha, or 2. Care about aspects o their portolios other than expected return and volatility, and so are willing to hold ineicient portolios o securities The Behavior o Individual Investors One o the most important implications o our discussion o risk and return is the beneit o diversiication. By appropriately diversiying their portolios, investors can reduce risk without reducing their expected return. In that sense, diversiication is a ree lunch that all investors should take advantage o. Despite this beneit, evidence suggests that individual investors ail to diversiy their portolios adequately. Evidence rom the U.S. Survey o Consumer Finances shows that, or households that held stocks, the median number o stocks held by investors in 2001 was our, and 90% o investors held ewer than ten dierent stocks. There are a number o potential explanations or this behavior. One is that investors suer rom a amiliarity bias, so that they avor investments in companies they are amiliar with. Another is that investors have relative wealth concerns and care most about the perormance

3 Berk/DeMarzo Corporate Finance, Second Edition 149 o their portolio relative to that o their peers. This desire to keep up with the Joneses can lead investors to choose undiversiied portolios that match those o their colleagues or neighbors. In any case, this underdiversiication is one important piece o evidence that individual investors may choose suboptimal portolios. Another bias comes rom the inding that uninormed individuals tend to overestimate the precision o their knowledge. An implication o this overconidence hypothesis is that, assuming they have no true ability, investors who trade more will not earn higher returns. Instead, their perormance will be worse once we take into account the costs o trading (due to both commissions and bid-ask spreads). An implication o this overconidence hypothesis is that, assuming they have no true ability, investors who trade more will not earn higher returns. Instead, their perormance will be worse once we take into account the costs o trading (due to both commissions and bid-ask spreads). In order or the behavior o uninormed investors to have an impact on the market, there must be patterns to their behavior that lead them to depart rom the CAPM in systematic ways, thus imparting systematic uncertainty into prices. For investors trades to be correlated in this way, they must share a common motivation Systematic Trading Biases Investors tend to hold on to stocks that have lost value and sells stocks that have risen in value since the time o purchase. We call this tendency to hang on to losers and sell winners the disposition eect. Studies also show that individuals are more likely to buy stocks that have recently been in the news, engaged in advertising, experienced exceptionally high trading volume, or have had extreme (positive or negative) returns. In addition, investors appear to put too much weight on their own experience rather than considering all the historical evidence. As a result, people who grow up and live during a time o high stock returns are more likely to invest in stocks than people who grow up and live during a time o low stock returns. An alternative reason why investors make similar trading errors is that they are actively trying to ollow each other s behavior. This phenomenon, in which individuals imitate each other s actions, is reerred to as herd behavior. Traders might herd in their portolio choices because they might believe others have superior inormation that they can take advantage o by copying their trades; they may choose to herd in order to avoid the risk o underperorming their peers; and proessional und managers may ace reputational risk i they stray too ar rom the actions o their peers. Regardless o why individual investors choose not to protect themselves by holding the market portolio, the act that they don t has potential implications or the CAPM. I individual investors are engaging in strategies that earn negative alphas, it may be possible or a ew more sophisticated investors to take advantage o this behavior and earn positive alphas The Eiciency o the Market Portolio In order or sophisticated investors to proit rom investor mistakes, two conditions must hold. First, the mistakes must be suiciently pervasive and persistent to aect stock prices. Second, there must be limited competition to exploit these non-zero alpha opportunities. I competition is too intense, these opportunities will be quickly eliminated beore any trader can take advantage o them in a signiicant way.

4 150 Berk/DeMarzo Corporate Finance, Second Edition I enough other investors are not paying attention, perhaps one can proit rom public news announcements. However, investors should not expect this to be the case. Evidence shows that investors trying to proit rom such news announcements quickly incorporate the implications o the news into the market prices. Since the average investor earns an alpha o zero, beore including trading costs, beating the market should require special skills, such as better analysis o inormation or lower trading costs. Numerous studies report that the actual returns to investors o the average mutual und have a negative alpha. This suggests that mutual und managers do not have the special skills, such as better analysis o inormation, necessary to ind stocks that consistently beat the market and suggests that the market is largely eicient. Further, mutual unds generate trading costs and charge management ees, which urther erode investors returns. Some researchers urther categorize such tests as weak orm, semi-strong orm, and strong orm eiciency. Weak orm eiciency states that it should not be possible to proit by trading on inormation in past prices. Semi-strong orm eiciency states that it should not be possible to consistently proit by trading on any public inormation, such as news announcements or analysts recommendations. Finally, strong orm eiciency states that it should not be possible to consistently proit even by trading on private inormation Style-Based Anomalies and the Market Eiciency Debate Portolios o small stocks (those with a low market capitalizations = stock price x shares outstanding) have higher average returns. This empirical result is called the size eect. Portolios o stocks with high book-to-market ratios (the ratio o the book value o equity to the market value o equity) have higher average returns. Portolios o stocks that perormed well in the previous year have higher average returns in the ollowing year. Trading to take advantage o this relation is called a momentum strategy. Over the years since the discovery o the CAPM, it has become increasingly clear to researchers and practitioners alike that by orming portolios based on market capitalization, book-to-market ratios, and past returns, investors can construct trading strategies that have a positive alpha. Given these results, we are let to draw one o two conclusions. 1. Investors are systematically ignoring positive-npv investment opportunities. That is, the CAPM correctly computes required risk premiums, but investors are ignoring opportunities to earn extra returns without bearing any extra risk, either because they are unaware o them or because the costs to implement the strategies are larger than the NPV o undertaking them. 2. The positive-alpha trading strategies contain risk that investors are unwilling to bear but the CAPM does not capture. That is, a stock s beta with the market portolio does not adequately measure a stock s systematic risk, and so the CAPM does not correctly compute the risk premium. The only way a positive-npv opportunity can persist in a market is i some barrier to entry restricts competition. The existence o these trading strategies has been widely known or more than iteen years. Not only is the inormation required to orm the portolios readily available, but many mutual unds ollow momentum-based and market capitalization/bookto-market based strategies. Hence, the irst conclusion does not seem likely. That leaves the second possibility: The market portolio is not eicient, and thereore a stock s beta with the market is not an adequate measure o its systematic risk. Stated

5 Berk/DeMarzo Corporate Finance, Second Edition 151 another way, the proits (positive alphas) rom the trading strategy are really returns or bearing risk that investors are averse to and the CAPM does not capture Multiactor Models o Risk The expected return o any marketable security can be written as a unction o the expected return o the eicient portolio: eicient portolio i i i eicient portolio ER [ ] = r = r + β ( ER [ ] r ) However, identiying an eicient portolio is diicult to measure because expected returns and the standard deviations o a portolio cannot be measured with great accuracy. Fortunately, it is not actually necessary to identiy the eicient portolio itsel; all that is required is to identiy a collection o portolios rom which the eicient portolio can be constructed. The risk premium o any marketable security can then be written as the sum o the risk premium o each portolio multiplied by the sensitivity o the stock with that 1 2 portolio the actor betas, βs and β : S ER [ ] = r + β 1 ( ER [ ] r) + β 2 ( ER [ ] r ) S S 1 S 2 where beta is measured relative to portolios 1 and 2 which capture dierent risk actors. Thus, when more than one portolio is used to measure market risk, the model is known as a multiactor model, and the model can be extended to any number o portolios. The portolios themselves can be thought o as either the risk actors or a portolio o stocks correlated with an unobservable risk actor. This particular orm o the multiactor model was originally developed by Stephen Ross and is reerred to as the Arbitrage Pricing Theory (APT). The most common portolio to use in a multiactor model is the market portolio, which just needs to capture at least some components o systematic risk. Other popular portolios are the small-minus-big (SMB) portolio, the high-minus-low (HML) portolio, and the momentum portolio, which are generally constructed as ollows. SMB. Firms below the median market value o NYSE irms each month orm an equally weighted portolio, S, and irms above the median market value orm an equally weighted portolio, B. A trading strategy that each year buys portolio S and inances this position by short selling portolio B has historically produced positive risk-adjusted returns. HML. Each year irms with book-to-market ratios less than the 30th percentile o NYSE irms are used to orm an equally weighted portolio called the low portolio, L. Firms with book-to-market ratios greater than the 70th percentile o NYSE irms orm an equally weighted-portolio called the high portolio, H. A trading strategy that each year takes a long position in portolio H, which it inances with a short position in portolio L, has produced positive risk-adjusted returns. Momentum. Each year stocks are ranked by their return over the last year, and a portolio is constructed that goes long on the top 30% o stocks and short on the bottom 30%. This trading strategy requires holding this portolio or a year, and this process is repeated annually. The resulting portolio is known as the prior one-year momentum portolio (PR1YR). Berk (1995) provides the ollowing explanation or the size eect. When the market portolio is not eicient, some stocks will plot above the SML, and some will plot below this line. All else equal, a positive alpha implies that the stock also has a relatively higher expected return. A higher expected return implies a lower price the only way to oer a higher expected

6 152 Berk/DeMarzo Corporate Finance, Second Edition return is or investors to buy the stock s dividend stream at a lower price. A lower price means a lower market capitalization. Thus, when the market portolio is not eicient, you should expect to observe the size eect. All portolios except the market portolio are reerred to as sel-inancing portolios because the long position is inanced by taking a short position, and because they require no net investment. The collection o these our portolios is currently the most popular choice or the multiactor model and is sometimes reerred to as the Fama-French-Carhart (FFC) actor model, where: ER [ ] = r + β ( ER [ ] r) + β SMB ER [ ] + β HML ER [ ] + β PR1YR ER [ ] S S S SMB S HML S PR1YR The FFC actor speciication was identiied a little more than ten years ago. Although it is widely used in academic literature to measure risk, much debate persists about whether it really is a signiicant improvement over the CAPM Methods Used in Practice All o the techniques are imprecise, and there is no model o expected returns that gives an exact estimate o the cost o capital. John Graham and Campbell Harvey surveyed 392 CFOs and ound that 73.5% o the irms use the CAPM to calculate the cost o capital. They also ound that larger irms were more likely to use the CAPM. About one third reported using a multiactor model to calculate the cost o capital. Appendix: Building a Multiactor Model I an eicient portolio can be constructed out o a collection o well-diversiied portolios, the collection o portolios will correctly price assets. To keep things simple, assume that we have identiied two portolios that we can combine to orm an eicient portolio called actor portolios and denote their returns by RF1 and RF2. The eicient portolio consists o some (unknown) combination o these two actor portolios, represented by portolio weights x1 and x2: Re = x1 RF1 + x2 RF2 To see that we can use these actor portolios to measure risk, consider regressing the excess returns o some stock s on the excess returns o both actors: F ( ) ( ) F1 2 R r = α + β R r + β R r + ε s s s F1 s F2 s We write the excess return o stock s as the sum o a constant, αs, plus the variation in the stock that is related to each actor, and an error term εs that has an expectation o zero and is uncorrelated with either actor. The error term represents the risk o the stock that is unrelated to either actor. I we can use the two actor portolios to construct the eicient portolio, then the constant term αs is zero. To see why, consider a portolio in which we buy stock s, then sell a raction βs F1 o the irst actor portolio and βs F2 o the second actor portolio, and invest the proceeds rom these sales in the risk-ree investment. This portolio, which we call P, has return ( ) F1 F2 F1 F2 R = R β R β R + β + β r p s s F1 s F2 s s F ( ) β ( ) F1 2 = R β R r R r s s F1 s F2

7 Berk/DeMarzo Corporate Finance, Second Edition 153 The return o this portolio is R = r + α + ε. p s s That is, portolio P has a risk premium o αs and risk given by εs. Now, because εs is uncorrelated with each actor, it must be uncorrelated with the eicient portolio. But recall rom Chapter 11 that risk that is uncorrelated with the eicient portolio is irm-speciic risk that does not command a risk premium. Thereore, the expected return o portolio P is r, which means αs must be zero. Setting αs equal to zero and taking expectations o both sides o the equation we get the ollowing two-actor model o expected returns: F [ ] = + β 1 F ( [ ] ) + β 2 s s F s ( [ F ] ) ER r ER r ER r 1 2. Selected Concepts and Key Terms Alpha The dierence between a security s expected return and its CAPM required return rom the security market line. According to the CAPM, all stocks and securities should be on the security market line and have an alpha o zero. I some securities have a non-zero alpha, the market portolio is not eicient, and its perormance can be improved by buying securities with positive alphas and selling those with negative alphas. Arbitrage Pricing Theory (APT), Multiactor Model When more than one portolio is used to measure systematic risk, the model is known as a multiactor model. The portolios themselves can be thought o as either the risk actors or as portolios o stocks correlated with unobservable risk actors. The Arbitrage Pricing Theory is a orm o multiactor model originally developed by Stephen Ross. Disposition Eect The empirically documented tendency or investors to hold on to stocks that have lost value and sells stocks that have risen in value since the time o purchase. Fama-French-Carhart (FFC) Factor Speciication Because using the portolios, SMB, HML, and momentum, along with the market, were identiied by Eugene Fama, Kenneth French, and Mark Carhart, this speciication o the multiactor model is sometimes reerred to as the Fama-French-Carhart (FFC) actor model. Herd Behavior The tendency o individual investors to imitate each other s actions. Traders might herd in their portolio choices because they might believe others have superior inormation that they can take advantage o by copying their trades; they may choose to herd in order to avoid the risk o underperorming their peers; and proessional und managers may ace reputational risk i they stray too ar rom the actions o their peers.

8 154 Berk/DeMarzo Corporate Finance, Second Edition High-Minus-Low (HML) Portolio A portolio oten used in actor models that equals to the return on high book-to-market irms minus the return on low book-to-market irms. Each year irms with book-to-market ratios less than the 30th percentile o NYSE irms are used to orm an equally weighted portolio called the low portolio, L. Firms with book-to-market ratios greater than the 70th percentile o NYSE irms orm an equally weighted portolio called the high portolio, H. A trading strategy that each year takes a long position in portolio H, which it inances with a short position in portolio L, has produced positive risk-adjusted returns. Momentum Strategy Buying stocks that perormed well in the prior period, oten six months or a year, and holding them or the next period. Prior One-Year Momentum (PR1YR) Portolio A portolio oten used in actor models. To orm this portolio, each year stocks are ranked by their return over the last year and a portolio is constructed that goes long on the top 30% o stocks and short on the bottom 30%. This trading strategy requires holding the portolio or a year, and this process is repeated annually. Rational Expectations An economic theory that can be used to model how investors impound inormation in stock prices. In the context o the CAPM, it implies that although investors may have dierent inormation regarding expected returns, correlations, and volatilities, they correctly interpret the inormation contained in market prices and adjust their estimates o expected returns in a rational way. Semi-Strong Form Eiciency The theory that consistent proits should not be possible rom trading on any public inormation, such as news announcements or analysts recommendations. Size Eect The observation that small stocks have positive CAPM alphas, which was irst discovered in 1981 by Rol Banz in The Relationship between Return and Market Values o Common Stock, Journal o Financial Economics 9 (March 1981): Small-Minus-Big (SMB) Portolio A portolio oten used in actor models equal to the return on small irms minus the return on big irms. Firms below the median market value o NYSE irms each month orm an equally weighted portolio, S, and irms above the median market value orm an equally weighted portolio, B. A trading strategy that buys portolio S and inances this position by short selling portolio B is the SMB portolio has historically produced positive risk-adjusted returns. Strong Form Eiciency The theory that it should not be possible to consistently proit even by trading on private inormation.

9 Berk/DeMarzo Corporate Finance, Second Edition 155 Weak Form Eiciency The theory that it should not be possible to proit by trading on inormation in past prices by, or example, selling winners and hanging on to losers. Concept Check Questions and Answers I investors attempt to buy a stock with a positive alpha, what is likely to happen to its price and expected return? How will this aect its alpha? As savvy investors attempt to trade to improve their portolios, they raise the price and lower the expected return o the positive-alpha stocks, and they depress the price and raise the expected return o the negative-alpha stocks, until the stocks are once again on the security market line, the market portolio is eicient, and all stocks have zero alpha What is the consequence o investors exploiting non-zero alpha stocks or the eiciency o the market portolio? Competition among savvy investors who try to beat the market and earn a positive alpha should keep the market portolio close to eicient much o the time How can an uninormed or unskilled investor guarantee themselves a non-negative alpha? Naïve investors with no inormation can hold the market portolio (combined with risk-ree investments) to ensure a non-negative alpha Under what conditions will it be possible to earn a positive alpha and beat the market? For an investor to earn a positive alpha and beat the market, some investors must hold portolios with negative alphas Do investors hold well-diversiied portolios? There is much evidence that individual investors ail to diversiy their portolios adequately. Evidence rom the U.S. Survey o Consumer Finances shows that, or households that held stocks, the median number o stocks held by investors in 2001 was our, and 90% o investors held ewer than ten dierent stocks Why is the high trading volume observed in markets inconsistent with the CAPM equilibrium? Because the market portolio is a value-weighted portolio, it is also a passive portolio in the sense that an investor does not need to trade in response to daily price changes in order to maintain it. Thus, i all investors held the market, we would see relatively little trading volume in inancial markets What must be true about the behavior o small, uninormed investors or them to have an impact on market prices? In order or the behavior o uninormed investors to have an impact on the market, there must be patterns to their behavior that lead them to depart rom the CAPM in systematic ways, thus imparting systematic uncertainty into prices. For investors trades to be correlated in this way, they must share a common motivation What are several systematic behavioral biases that individual investors all prey to? Investors tend to hold on to stocks that have lost value and sells stocks that have risen in value since the time o purchase. We call this tendency to hang on to losers and sell winners the disposition eect. Studies also show that individuals are more likely to buy

10 156 Berk/DeMarzo Corporate Finance, Second Edition stocks that have recently been in the news, engaged in advertising, experienced exceptionally high trading volume, or have had extreme (positive or negative) returns. In addition, investors appear to put too much weight on their own experience rather than considering all the historical evidence. As a result, people who grow up and live during a time o high stock returns are more likely to invest in stocks than people who grow up and live during a time o low stock returns What implication might these behavioral biases have or the CAPM? Regardless o why individual investors choose not to protect themselves by holding the market portolio, the act that they don t has potential implications or the CAPM. I individual investors are engaging in strategies that earn negative alphas, it may be possible or a ew more sophisticated investors to take advantage o this behavior and earn positive alphas Should uninormed investors expect to make money by trading based on news announcements? I enough other investors are not paying attention, perhaps one can proit rom public news announcements. However, investors should not expect this to be the case. Evidence shows that investors trying to proit rom such news announcements quickly incorporate the implications o the news into the market prices I und managers are talented, why do the returns o their unds to investors not have positive alphas? Numerous studies report that the actual returns to investors o the average mutual und have a negative alpha. This suggests that mutual und managers do not have the special skills, such as better analysis o inormation, necessary to ind stocks that consistently beat the market and suggests that the market is largely eicient. Further, mutual unds generate trading costs and charge management ees, which urther erode investors returns What does the existence o a positive-alpha trading strategy imply? There are two dierent implications. 1) The positive-alpha trading strategies contain risk that investors are unwilling to bear but the CAPM does not capture. That is, a stock s beta with the market portolio does not adequately measure a stock s systematic risk, and so the CAPM does not correctly compute the risk premium. 2) Investors are systematically ignoring positive-npv investment opportunities. That is, the CAPM correctly computes required risk premiums, but investors are ignoring opportunities to earn extra returns without bearing any extra risk, either because they are unaware o them or because the costs to implement the strategies are larger than the NPV o undertaking them I investors have a signiicant amount o non-tradeable (but risky) wealth, why might the market portolio not be eicient? I investors have a signiicant amount o non-tradeable wealth, this wealth will be an important part o their portolios, but will not be part o the market portolio o tradeable securities. In such a world, the market portolio o tradeable securities will likely not be eicient What is the advantage o a multiactor model over a single actor model? Multiactor models have a distinct advantage over single-actor models in that it is much easier to identiy a collection o portolios that captures systematic risk than just a single portolio.

11 Berk/DeMarzo Corporate Finance, Second Edition How can you use the Fama-French-Carhart actor speciication to estimate the cost o capital? The Fama-French-Carhart actor speciication identiies the collection o our portolios that are most commonly used in a multiactor model. These portolios include the market portolio, small-minus-big portolio, high-minus-low portolio, and prior one-year momentum portolio Which is the most popular method used by corporations to calculate the cost o capital? John Graham and Campbell Harvey surveyed 392 CFOs and ound that 73.5% o the irms use the CAPM to calculate the cost o capital and that larger irms were more likely to use the CAPM What other techniques do corporations use to calculate the cost o capital? John Graham and Campbell Harvey surveyed 392 CFOs and ound that about one third reported using a multiactor model to calculate the cost o capital. Two other methods that some irms in the survey reported using are historical average returns (40%) and the dividend discount model (16%). Examples with Step-by-Step Solutions Solving Problems Quantitative problems using the concepts in this chapter may require determining i stocks are over- or undervalued according to the CAPM and interpreting stock alphas. They may also involve inding the cost o capital using a actor model, such as the Fama-French-Carhart model. Below are examples o each. Examples 1. Suppose that a irm with a stock price o $80 just announced that it expects to pay a $100 per share liquidating dividend in 1 year, although the exact amount o the dividend depends on the perormance o the company this year. Assume that the CAPM is a good description o stock price returns and that the stock s beta is 1.5, the market s expected return is 12%, and the risk-ree rate is 5%. [A] Is the stock priced correctly now? [B] What is the alpha o the stock? [C] What would you expect to happen to the stock price in the market ater the announcement? Step 1. Determine the stock s expected return. ER [ ] = r + β ( R r ) = (.12.05) = = 15.5% i Step 2. Determine the value o the stock. $100 P 0 = = $ Thus, the stock is undervalued by $86.58 $80 = $6.58.

12 158 Berk/DeMarzo Corporate Finance, Second Edition Step 3. To determine the stock s alpha, ind the stock s expected return. $100 $100 P0 = $86.58 = 1 + r = = 1.25 r = 25% 1 + r $80 Thus, the alpha is 25% 15.5% = 9.5%. Step 4. Predict what would happen in an eicient market. Since the stock has a positive alpha, investors should now increase the market price to $ Thus, when the stock begins trading ater the announcement, you should not expect to be able to buy the stock or a price below $ Assume that the CAPM is a good description o stock price returns. You observe the ollowing inormation or three stocks: Beta Expected Return Ford % General Electric % Yahoo! % Based on the stocks alphas, which should you buy i the market s expected return is 12% and the risk-ree rate is 5%? Step 1. Calculate the CAPM expected returns on each stock. ER [ ] = r + β ( R r) = (.12.05) = = 14.8% Ford i ER [ ] = r + β ( R r) = (.12.05) = = 12.0% GE i ER [ ] = r + β ( R r) = (.12.05) = = 24.6% Yahoo! i Step 2. Calculate the alpha o each stock. ( βi ) α = ER [ ] r = ER [ ] r + ( ER [ ] r) i i i i α α Ford GE = 18% 14.8% = 3.2% = 12% 12% = 0% α Yahoo! = 22% 24.6% = 2.6% So you should buy Ford because it has a positive alpha. 3. Based on the Fama-French-Carhart actor model, which o the ollowing stocks has the most systematic risk? I the risk-ree rate is 5%, what are the irms equity costs o capital? Factor Stock A Stock B MKT SMB HML PR1YR

13 Berk/DeMarzo Corporate Finance, Second Edition 159 Mean Monthly Return MKT r 0.64% SMB 0.17% HML 0.53% PR1YR 0.76% Step 1. The stock with the most systematic risk has the highest risk premium, so the risk premiums or stocks A and B must be calculated. First, the monthly risk premiums: RPA= 1.26(0.64) (0.17) (0.53) (0.76) = 0.281% RPB= 0.45(0.64) (0.17) (0.53) (0.76) = 0.200% Then the annual risk premiums, RPA = ( ) 12 1 = 3.4% RPB = ( ) 12 1 = 2.4% So, stock A has the highest risk premium and thus the most systematic risk. Step 2. Calculate the equity cost o capital or each irm. The expected return can be calculated based on the FFC actor model: SMB HML PR1YR ER [ ] = r + β ( ER [ ] r) + β ER [ ] + β ER [ ] + β ER [ ] S S S SMB S HML S PR1YR ER [ ] = = 8.4% A ER [ ] = = 7.4% B Questions and Problems 1. What are the three types o portolios discussed in this chapter that have had positive CAPM alphas. 2. Explain the Berk (1995) explanation or the size eect. 3. Describe the actors in the Fama-French-Carhart actor model. 4. How is the small-minus-big (SMB) actor in the Fama-French-Carhart actor model estimated? 5. How is the high-minus-low (HML) actor in the Fama-French-Carhart actor model estimated? Solutions to Questions and Problems 1. The three types o portolios that have positive CAPM alphas are small irms (irms with a low stock market capitalization), irms with high book value o equity-to-market value o equity ratios, and irms with positive momentum (i.e. high returns in the prior period). 2. When the market portolio is not eicient, you should expect to observe the size eect. When the market portolio is not eicient, some stocks will plot above the SML, and some will plot below this line. All else equal, a positive alpha implies that the stock also has a relatively higher expected return. A higher expected return implies a lower price the only way to oer a higher expected return is or investors to buy the stock s dividend stream at a lower price. A lower price means a lower market capitalization. Thus, when a inancial economist orms a

14 160 Berk/DeMarzo Corporate Finance, Second Edition portolio o stocks with low market capitalizations, that collection contains stocks that will likely have higher expected returns and, i the market portolio is not eicient, positive alphas. 3. The actors in the Fama-French-Carhart actor model are as ollows. The market. This is similar to the CAPM market portolio. SMB (the small-minus-big portolio). This actor equals the return on small capitalization irms minus the return on large capitalization irms. HML (the high-minus-low portolio). This actor equals to the return on high book-tomarket irms minus the return on low book-to-market irms. Momentum. This actor measures the return on a stock over a prior period, such as one year. 4. Firms below the median market value o NYSE irms each month orm an equally weighted portolio, S, and irms above the median market value orm an equally weighted portolio, B. 5. Each year irms with book-to-market ratios less than the 30th percentile o NYSE irms are used to orm an equally weighted portolio called the low portolio, L. Firms with book-tomarket ratios greater than the 70th percentile o NYSE irms orm an equally weighted portolio called the high portolio, H.