Chapter 13
Investor Behavior and Capital Market
Efficiency
13–1. Assume that all investors have the same information and care only about expected return and
volatility. If new information arrives about one stock, can this information affect the price and
return of other stocks? If so, explain why.
13–2. Assume that the CAPM is a good description of stock price returns. The market expected return
is 8% with 8% volatility and the risk-free rate is 4%. New news arrives that does not change any
of these numbers but it does change the expected return of the following stocks:
a. At current market prices, which stocks represent buying opportunities?
b. On which stocks should you put a sell order in?
Chapter 13/Investor Behavior and Capital Market Efficiency 189
Neither stock pays dividends. Assume you are an investor with the disposition effect, you bought
at time 1, and now it is time 3. Assume throughout this question that you do no trading (other
than what is specified) in these stocks.
a. Which stock(s) would you be inclined to sell? Which would you be inclined to hold on to?
b. How would your answer change if right now is time 6?
c. What if you bought at time 3 instead of 1 and today is time 6?
d. What if you bought at time 3 instead of 1 and today is time 5?
13-13. Suppose that all investors have the disposition effect. A new stock has just been issued at a price
of $60, so all investors in this stock purchased the stock today. A year from now the stock will be
taken over, for a price of $72 or $48 depending on the news that comes out over the year. The
stock will pay no dividends. Investors will sell the stock whenever the price goes up by more than
10%.
a. Suppose good news comes out in 6 months (implying the takeover offer will be $72). What
equilibrium price will the stock trade for after the news comes out, that is, the price that
equates supply and demand?
b. Assume that you are the only investor who does not suffer from the disposition effect and
your trades are small enough to not affect prices. Without knowing what will actually
transpire, what trading strategy would you instruct your broker to follow?
13-14. Davita Spencer is a manager at Half Dome Asset Management. She can generate an alpha of
1.55% per year on up to $93 million. After that her skills are spread too thin, so she cannot add
value and her alpha is zero. Half Dome charges a fee of 1.14% per year on the total amount of
money under management (at the beginning of each year). Assume that there are always
investors looking for positive alpha and no investor would invest in a fund with a negative alpha.
In equilibrium, that is, when no investor either takes out money or wishes to invest new money,
a. What alpha do investors in Davita’s fund expect to receive?
b. How much money will Davita have under management?
c. How much money will Half Dome generate in fee income?
13-15. Allison and Bill are both mutual fund managers, although Allison is more skilled than Bill. Both
have $100 million in assets under management and charge a fee of 1%/year. Allison is able to
generate a 2% alpha before fees and Bill is able to generate a 1% alpha before fees.
a. What is the alpha investors earn in each fund (that is, the alpha after fees are taken out)?
b. Which fund will experience an inflow of funds?
190 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
c. Assume that both managers have exhausted the supply of good investment opportunities and
so they will choose to invest any new funds received in the market portfolio and so those
funds will earn a zero alpha. How much new capital will flow into each fund?
d. Once the new funds have stopped flowing, what is the alpha before and after fees of each
fund? Which fund will be larger?
e. Calculate each manager’s compensation once the capital has stopped flowing. Which
manager has higher compensation?
13–16. Assume the economy consisted of three types of people. 56% are fad followers, 41% are passive
investors (they have read this book and so hold the market portfolio), and 3% are informed
traders. The portfolio consisting of all the informed traders has a beta of 1.55 and an expected
return of 15%. The market expected return is 11%. The risk-free rate is 6%.
a. What alpha do the informed traders make?
b. What is the alpha of the passive investors?
c. What is the expected return of the fad followers?
d. What alpha do the fad followers make?
13–17. Explain what the size effect is.
192 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
c.
Rank
Firm Name
Market Value
Cost of Capital
Portfolio
All Firms
1
B1
$1180.72
0.08
0.08
2
B2
$803.28
0.12
3
B3
$742.42
0.13
4
S1
$118.07
0.08
5
S2
$80.33
0.12
6
S3
$74.24
0.13
–0.13
Portfolio All
–4.90%
d.
Rank
Firm Name
Market Value
Cost of Capital
Portfolio
All Firms
1
S3
$74.24
0.13
0.13
2
B3
$742.42
0.13
3
S2
$80.33
0.12
4
B2
$803.28
0.12
5
S1
$118.07
0.08
6
S1
$118.07
0.08
–0.08
Portfolio All
4.90%
13–20. Consider the following stocks, all of which will pay a liquidating dividend in a year and nothing
in the interim:
a. Calculate the expected return of each stock.
b. What is the sign of correlation between the expected return and market capitalization of the
stocks?
Beta
Return
13–21. In Problem 19, assume the risk-free rate is 3% and the market risk premium is 7%.
a. What does the CAPM predict the expected return for each stock should be?
Chapter 13/Investor Behavior and Capital Market Efficiency 193
b. Clearly, the CAPM predictions are not equal to the actual expected returns so the CAPM
does not hold. You decide to investigate this further. To see what kind of mistakes the
CAPM is making, you decide to regress the actual expected return onto the expected return
predicted by the CAPM. What is the intercept and slope coefficient of this regression?
c. What are the residuals of the regression in (d)? That is, for each stock, compute the
difference between the actual expected return and the best fitting line given by the intercept
and slope coefficient in (b).
d. What is the sign of the correlation between the residuals you calculated in (e) and market
capitalization?
e. What can you conclude from your answers to part (b) of the previous problem and part (d)
of this problem about the relation between firm size (market capitalization) and returns?
(The results do not depend on the particular numbers in this problem. You are welcome to
verify this for yourself by redoing the problems with another value for the market risk
premium, and by picking the stock betas and market capitalizations randomly.)
Market
Capitalization
($ million)
Total
Liquidating
Dividend ($
million)
Beta
Expected Return
CAPM
Error
Residual +
Intercept
Just Residual
Stock A
800
1000
0.77
0.25
0.0839
0.1661
0.18430808
0.08337312
Stock B
750
1000
1.46
0.33333333
0.1322
0.20113333
0.22982353
0.12888858
Stock C
950
1000
1.25
0.05263158
0.1175
–0.0648684
–0.0393684
–0.1403034
Stock D
900
1000
1.07
0.11111111
0.1049
0.00621111
0.02897663
–0.0719583
Risk Free rate
Market Risk Premium
Correlation
Slope
Intercept
Intercept
Correlation
3%
7.00%
–0.9984206
0.78297881
0.10093495
0.10093495
–0.9968741
13–22. Explain how to construct a positive-alpha trading strategy if stocks that have had relatively high
returns in the past tend to have positive alphas, and stocks that have had relatively low returns
in the past tend to have negative alphas.
13–23. If you can use past returns to construct a trading strategy that makes money (has a positive
alpha), it is evidence that market portfolio is not efficient. Explain why.
13–24. Explain why you might expect stocks to have nonzero alphas if the market proxy portfolio is not
highly correlated with the true market portfolio, even if the true market portfolio is efficient.
13–25. Explain why, if some investors are subject to systematic behavioral biases while others pick
efficient portfolios, the market portfolio will not be efficient.
