Learning Objectives

Learning Objectives1. Compute a stock’s alpha.2. Explain how investors’ attempts to “beat the market”

should keep the market portfolio efficient.3. Describe the effect of homogeneous expectations on a

security’s alpha.4. Explain why holding the market portfolio does not

depend on the quality of an investor’s information or trading skills.

5. Understand what the CAPM requires about investors’ expectations.

Learning Objectives (cont’d)

6. Evaluate under what conditions the market portfolio would be inefficient.

7. Explain diversification bias and familiarity bias.

8. Discuss why uninformed investors trade too much.

9. Assess how uninformed investors’ behavior deviates from the CAPM in systematic ways.

10. Explain the disposition effect.


11. Review why investors, on average, earn negative alphas when they invest in managed mutual funds.

12. Assess the strategy of an investor “holding the market.”

13. Discuss the size effect.14. Describe the momentum trading strategy.15. Explain how the choice of the market proxy may lead

to non-zero alphas.


16. Discuss how systematic behavioral biases may affect the efficiency of the market portfolio.

17. Assess how a preference for stocks with a positively skewed return distribution would impact the market portfolio’s efficiency.

18. Describe the Arbitrage Pricing Theory.19. Discuss the expected return on a self-financing

portfolio.20. Discuss the Fama-French-Carhart model.

13.1 Competition and Capital Markets

• Identifying a Stock’s Alpha– To improve the performance of their portfolios,

investors will compare the expected return of a security with its required return from the security market line.

( [ ] )s f s Mkt fr r E R r

13.1 Competition and Capital Markets (cont'd)

• Identifying a Stock’s Alpha– The difference between a stock’s expected return

and its required return according to the security market line is called the stock’s alpha.

– When the market portfolio is efficient, all stocks are on the security market line and have an alpha of zero.

[ ] s s sE R r

Figure 13.1 An Inefficient Market Portfolio

13.1 Competition and Capital Markets (cont'd)

• Profiting from Non-Zero Alpha Stocks

– Investors can improve the performance of their portfolios by buying stocks with positive alphas and by selling stocks with negative alphas.

Figure 13.2 Deviations from the Security Market Line

13.2 Information and Rational Expectations

• Informed Versus Uninformed Investors– In the CAPM framework, investors should

hold the market portfolio combined with risk-free investments

– This investment strategy does not depend on the quality of an investor’s information or trading skill.

Example 13.1

13.2 Information and Rational Expectations (cont’d)

• Rational Expectations– All investors correctly interpret and use their own

information, as well as information that can be inferred from market prices or the trades of others.


• Regardless of how much information an investor has access to, he can guarantee himself an alpha of zero by holding the market portfolio.


• Because the average portfolio of all investors is the market portfolio, the average alpha of all investors is zero.

• If no investor earns a negative alpha, then no investor can earn a positive alpha, and the market portfolio must be efficient.


• The market portfolio can be inefficient only if a significant number of investors either:

– Misinterpret information and believe they are earning a positive alpha when they are actually earning a negative alpha, or

– Care about aspects of their portfolios other than expected return and volatility, and so are willing to hold inefficient portfolios of securities.

13.3 The Behavior of Individual Investors

• Underdiversification and Portfolio Biases– There is much evidence that individual investors

fail to diversify their portfolios adequately.– Familiarity Bias• Investors favor investments in companies they are

familiar with

– Relative Wealth Concerns• Investors care more about the performance of their

portfolios relative to their peers.

13.3 The Behavior of Individual Investors (cont’d)

• Excessive Trading and Overconfidence– According to the CAPM, investors should hold risk-

free assets in combination with the market portfolio of all risky securities.

– In reality, a tremendous amount of trading occurs each day.


• Excessive Trading and Overconfidence– Overconfidence Bias• Investors believe they can pick winners and losers

when, in fact, they cannot; this leads them to trade too much.

– Sensation Seeking• An individual’s desire for novel and intense risk-taking

experiences.

Figure 13.3 NYSE Annual ShareTurnover, 1970–2008

Source: www.nyxdata.com

Figure 13.4 Individual Investor Returns Versus Portfolio Turnover

Source: B. Barber and T. Odean, “Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors,” Journal of Finance 55 (2000) 773–806.)


• Individual Behavior and Market Prices– If individuals depart from the CAPM in random

ways, then these departures will tend to cancel out.

– Individuals will hold the market portfolio in aggregate, and there will be no effect on market prices or returns.

13.4 Systematic Trading Biases

• Hanging on to Losers and the Disposition Effect– Disposition Effect• When an investor holds on to stocks that have lost

their value and sell stocks that have risen in value since the time of purchase.

13.4 Systematic Trading Biases (cont’d)

• Investor Attention, Mood, and Experience– Studies 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 returns.

– Sunshine generally has a positive effect on mood, and studies have found that stock returns tend to be higher when it is a sunny day at the location of the stock exchange.


• Investor Attention, Mood, and Experience– Investors appear to put too much weight on their

own experience rather than considering all the historical evidence.

– As a result, people who grew up and lived during a time of high stock returns are more likely to invest in stocks than people who experienced times when stocks performed poorly.


• Herd Behavior– When investors make similar trading errors

because they are actively trying to follow each other’s behavior

• Informational Cascade Effects– Where traders ignore their own information

hoping to profit from the information of others


• Implications of Behavioral Biases– If individual investors are engaging in strategies

that earn negative alphas, it may be possible for more sophisticated investors to take advantage of this behavior and earn positive alphas

13.5 The Efficiency of the Market Portfolio

• Trading on News or Recommendations– Takeover Offers• If you could predict whether the firm would ultimately

be acquired or not, you could earn profits trading on that information

Figure 13.5 Returns to Holding Target Stocks Subsequent to Takeover Announcements

Source: Adapted from M. Bradley, A. Desai, and E. H. Kim, “The Rationale Behind Interfirm Tender Offers: Information or Synergy?” Journal of Financial Economics 11 (1983) 183–206.

13.5 The Efficiency of the Market Portfolio (cont’d)

• Trading on News or Recommendations– Stock Recommendations• Jim Cramer makes numerous stock recommendations

on his television show, Mad Money– For stocks with news, it appears that the stock price correctly

reflects this information the next day, and stays flat (relative to the market) subsequently

– On the other hand, for the stocks without news, there appears to be a significant jump in the stock price the next day, but the stock price then tends to fall relative to the market, generating a negative alpha, over the next several weeks

Figure 13.6 Stock Price Reactionsto Recommendations on Mad Money

Source: Adapted from J. Engelberg, C. Sasseville, J. Williams, “Market Madness? The Case of Mad Money,” SSRN working paper, 2009.


• The Performance of Fund Managers– Numerous studies report that the actual returns

to investors of the average mutual fund have a negative alpha

– Superior past performance is not a good predictor of a fund’s future ability to outperform the market

Figure 13.7 Estimated Alphas for U.S. Mutual Funds (1975–2002)

Source: Adapted from R. Kosowski, A. Timmermann, R. Wermers, H. White, “Can Mutual Fund ‘Stars’ Really Pick Stocks? New Evidence from a Bootstrap Analysis,” Journal of Finance 61 (2006): 2551–2596.

Figure 13.8 Before and After Hiring Returns of Investment Managers

Sources: A. Goyal and S. Wahal, “The Selection and Termination of Investment Management Firms by Plan Sponsors,” Journal of Finance 63 (2008): 1805–1847 and with J. Busse, “Performance and Persistence in Institutional Investment Management,” Journal of Finance, forthcoming.


• The Winners and Losers– The average investor earns an alpha of zero,

before including trading costs– Beating the market should require special skills or

lower trading costs• Because individual investors are likely to be at a

disadvantage on both counts, the CAPM wisdom that investors should “hold the market” is probably the best advice for most people

13.6 Style-Based Anomalies and the Market Efficiency Debate

• Size Effect– Excess Return and Market Capitalizations• Small market capitalization stocks have historically

earned higher average returns than the market portfolio, even after accounting for their higher betas

– Excess Return and Book-to-Market Ratio• High book-to-market stocks have historically earned

higher average returns than low book-to-market stocks

Figure 13.9 Excess Return of Size Portfolios, 1926–2008

Source: Data courtesy of Kenneth French.

Figure 13.10 Excess Return of Book-to-Market Portfolios, 1926–2008

Source: Data courtesy of Kenneth French.

13.6 Style-Based Anomalies and the Market Efficiency Debate (cont’d)

• Size Effect– Size Effects and Empirical Evidence• Data Snooping Bias

– Given enough characteristics, it will always be possible to find some characteristic that by pure chance happens to be correlated with the estimation error of average returns

Example 13.2

Alternative Example 13.2A

• Problem

– Suppose two firms, ABC and XYZ, are both expected to pay a dividend stream of $2.2 million per year in perpetuity.

– ABC’s cost of capital is 12% per year and XYZ’s cost of capital is 16%.

– Which firm has the higher market value?

– Which firm has the higher expected return?

Alternative Example 13.2A

• Solution

– ABC has an expected return of 12%.

– XYZ has an expected return of 16%.

ABC

$2,200,000Market Value $18,333,333

.12

XYZ

$2,200,000Market Value $13,750,000

.16

Alternative Example 13.2B

• Problem

– Now assume both stocks have the same estimated beta, either because of estimation error or because the market portfolio is not efficient.

– Based on this beta, the CAPM would assign an expected return of 15% to both stocks.

– Which firm has the higher alpha?

– How do the market values of the firms relate to their alphas?

Alternative Example 13.2B

• Solution

– αABC = 12% - 15% = -3%

– αXYZ = 16% - 15% = 1%

– The firm with the lower market value has the higher alpha.


• Momentum– Momentum Strategy• Buying stocks that have had past high returns and

(short) selling stocks that have had past low returns


• Implications of Positive-Alpha Trading Strategies– The only way positive-alpha strategies can persist in a market is

if some barrier to entry restricts competition• However, the existence of these trading strategies has

been widely known for more than 15 years– Another possibility is that the market portfolio is not efficient,

and therefore a stock’s beta with the market is not an adequate measure of its systematic risk.


• Implications of Positive-Alpha Trading Strategies– Proxy Error• The true market portfolio may be efficient, but the

proxy we have used for it may be inaccurate

– Behavioral Biases• By falling prey to behavioral biases, investors may hold

inefficient portfolios


• Implications of Positive-Alpha Trading Strategies– Alternative Risk Preferences and Non-Tradable

Wealth• Investors may choose inefficient portfolios because

they care about risk characteristics other than the volatility of their traded portfolio

13.7 Multifactor Models of Risk• The expected return of any marketable security is:

– When the market portfolio is not efficient, we have to find a method to identify an efficient portfolio before we can use the above equation. However, it is not actually necessary to identify the efficient portfolio itself.

– All that is required is to identify a collection of portfolios from which the efficient portfolio can be constructed.

[ ] ( [ ] ) effs f s eff fE R r E R r

13.7 Multifactor Models of Risk (cont’d)

• Using Factor Portfolios– Given N factor portfolios with returns RF1, . . . , RFN,

the expected return of asset s is defined as:

– β1…. βN are the factor betas.

1 21 2

1

[ ] ( [ ] ) ( [ ] ) ( [ ] )

( [ ] )

F F FNs f s F f s F f s FN f

NFN

f s FN fn

E R r E R r E R r E R r

r E R r


• Using Factor Portfolios– Single-Factor Model• A model that uses one portfolio

– Multi-Factor Model• A model that uses more than one portfolio in the

model

• The CAPM is an example of a single-factor model while the Arbitrage Pricing Theory (APT) is an example of a multifactor model


• Using Factor Portfolios– A self-financing portfolio can be constructed by

going long in some stocks and going short in other stocks with equal market value

– In general, a self-financing portfolio is any portfolio with portfolio weights that sum to zero rather than one


• Using Factor Portfolios– If all factor portfolios are self-financing then:

1 21 2

1

[ ] [ ] [ ] [ ]

( [ ])

F F FNs f s F s F s FN

NFN

f s FNn

E R r E R E R E R

r E R


• Selecting the Portfolios– Market Capitalization Strategy• A trading strategy that each year buys a portfolio of

small stocks and finances this position by short selling a portfolio of big stocks has historically produced positive risk-adjusted returns. – This self-financing portfolio is widely known as the small-

minus-big (SMB) portfolio.


• Selecting the Portfolios– Book-to-market Ratio Strategy• A trading strategy that each year buys an equally-

weighted portfolio of stocks with a book-to-market ratio less than the 30th percentile of NYSE firms and finances this position by short selling an equally-weighted portfolio of stocks with a book-to-market ratio greater than the 70th percentile of NYSE stocks has historically produced positive risk-adjusted returns. • This self-financing portfolio is widely known as the

high-minus-low (HML) portfolio.


• Selecting the Portfolios– Past Returns Strategy• Each year, after ranking stocks by their return over the

last one year, a trading strategy that buys the top 30% of stocks and finances this position by short selling bottom 30% of stocks has historically produced positive risk-adjusted returns. – This self-financing portfolio is widely known as the prior one-

year momentum (PR1YR) portfolio. » This trading strategy requires holding the portfolio for a

year and the process is repeated annually.


• Selecting the Portfolios– Fama-French-Carhart (FFC) Factor Specifications

11

[ ] ( [ ] ) [ ]

[ ] [ ]

Mkt SMBs f s Mkt f s SMB

HML PR YRs HML s PR YR

E R r E R r E R

E R E R

Table 13.1 FFC Portfolio Average Monthly Returns, 1926–2008

Example 13.3

Example 13.3 (cont'd)

Alternative Example 13.3

• Problem

– You are considering making an investment in a project in the semiconductor industry.

– The project has the same level of non-diversifiable risk as investing in Intel stock.

Alternative Example 13.3• Problem (continued)

– Assume you have calculated the following factor betas for Intel stock:

– Determine the cost of capital by using the FFC factor specification if the monthly risk-free rate is 0.5%.

1

0.171

0.432

0.419

0.121

MktINTC

SMBINTC

HMLINTC

PR YRINTC

Alternative Example 13.3• Solution

– The annual cost of capital is .0099691 × 12 = 11.96%

11

[ ] ( [ ] ) [ ]

[ ] [ ]

Mkt SMBs f s Mkt f s SMB

HML PR YRs HML s PR YR

E R r E R r E R

E R E R

[ ] 0.5% (0.171)(.64%) (0.432)(0.17%)

(0.419)(0.53%) (0.121)(0.76%)sE R

[ ] .005 .0010944 .0007344 .0022207 .0009196sE R

[ ] .0099691sE R


• The Cost of Capital Using the Fama-French-Carhart Factor Specification– Although it is widely used in research to measure

risk, there is much debate about whether the FFC factor specification is really a significant improvement over the CAPM


• The Cost of Capital Using the Fama-French-Carhart Factor Specification– One area where researchers have found that the FFC factor

specification does appear to do better than the CAPM is measuring the risk of actively managed mutual funds

• Researchers have found that funds with high returns in the past have positive alphas under the CAPM. When the same tests were repeated using the FFC factor specification to compute alphas, no evidence was found that mutual funds with high past returns had future positive alphas.

13.8 Methods Used In Practice

• There is no clear answer to the question of which technique is used to measure risk in practice—it very much depends on the organization and the sector.

– There is little consensus in practice in which technique to use because all the techniques covered are imprecise.

Figure 13.11 How Firms Calculate the Cost of Capital

Source: J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 60 (2001): 187–243.

lecture Quiz

1. If investors buy a stock with a positive alpha, what is the likely effect on its price and expected return?

2. How can an uninformed investor guarantee themselves a non-negative alpha?

3. Why is the high trading volume observed in markets inconsistent with the CAPM equilibrium?

lecture Quiz (cont’d)

4. What are some of the systematic behavioral biases that individual investors fall prey to?

5. If fund managers are so smart, why do the returns on their funds not have positive alphas?

6. What does the existence of a positive-alpha trading strategy imply about market efficiency?

lecture Quiz (cont’d)

7. What is the advantage of a multi-factor model over a single factor model?

8. What is the most popular method used by corporations to calculate the cost of capital?

9. What other techniques do corporations use to calculate the cost of capital?

Appendix

• Building a Multifactor Model– Assume that there are two portfolios that can be

combined to form an efficient portfolio. • These are called factor portfolios and their returns are

denoted as RF1 and RF2. The efficient portfolio consists of some (unknown) combination of these two factor portfolios, represented by portfolio weights x1 and x2:

Appendix (cont’d)

• Building a Multifactor Model– To see if these factor portfolios measure risk,

regress the excess returns of some stock s on the excess returns of both factors:

– This statistical technique is known as a multiple regression.

Appendix (cont’d)

• Building a Multifactor Model– A portfolio, P, consisting of the two factor

portfolios has a return of:

– which simplifies to:

Appendix (cont’d)

• Building a Multifactor Model– Since εi is uncorrelated with each factor, it must

be uncorrelated with the efficient portfolio:

Appendix (cont’d)

• Building a Multifactor Model– Recall that risk that is uncorrelated with the

efficient portfolio is diversifiable risk that does not command a risk premium. Therefore, the expected return of portfolio P is rf , which means αs must equal zero.• Setting αs equal to zero and taking expectations of both

sides, the result is the following two-factor model of expected returns:

Learning Objectives

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