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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
PROBLEM SETS
1.
2. If the security’s correlation coefficient with the market portfolio doubles
(with all other variables such as variances unchanged), then beta, and therefore the
risk premium, will also double. The current risk premium on the security is: 14% –
Price = Dividend/Discount rate
b. False. Investors require a risk premium only for bearing systematic
( )β [ ( ) ]
.12
.18 .06β [.14 .06] β 1.5
.08
P f P M f
P P
E r r E r r= + ´ -
= + ´ - ® = =
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
5. According to the CAPM, $1 Discount Stores requires a return of 13% based on its
Everything $5 requires a return of 10% based on its systematic risk level of β = 1.0.
7. Correct answer is choice a. Beta is a measure of systematic risk. Since only
8. The appropriate discount rate for the project is:
Using this discount rate:
10
1
$15
NPV $40 $40 [$15
1.224
t
t=
=- + =- + ´
å
The internal rate of return (IRR) for the project is 35.73%. Recall from your
9. a. Call the aggressive stock A and the defensive stock D. Beta is the sensitivity
of the stock’s return to the market return, i.e., the change in the stock return
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
.02 .38 .06 .12
β 2.00 β 0.30
.05 .25 .05 .25
A D
- - -
= = = =
- -
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
b. With the two scenarios equally likely, the expected return is an average of the
two possible outcomes:
c. The SML is determined by the market expected return of [0.5 × (.25 + .05)] =
15%, with βM = 1, and rf = 6% (which has βf = 0). See the following graph:
Expected Return - Beta Relationship
0
5
10
15
20
25
30
35
40
0
0.5
1
1.5
2
2.5
3
Beta
Expected Return
SML
D
M
A
A
The equation for the security market line is:
d. Based on its risk, the aggressive stock has a required expected return of:
The analyst’s forecast of expected return is only 18%. Thus the stock’s alpha is:
αA = actually expected return – required return (given risk)
Similarly, the required return for the defensive stock is:
The analyst’s forecast of expected return for D is 9%, and hence, the stock has
a positive alpha:
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
αD = Actually expected return – Required return (given risk)
The points for each stock plot on the graph as indicated above.
10. Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return
11. Possible. If the CAPM is valid, the expected rate of return compensates only for
systematic (market) risk, represented by beta, rather than for the standard deviation,
12. Not possible. The reward-to-variability ratio for Portfolio A is better than that of
the market. This scenario is impossible according to the CAPM because the CAPM
predicts that the market is the most efficient portfolio. Using the numbers supplied:
.16 .10 .18 .10
0.5 0.33
.12 .24
A M
S S
- -
= = = =
Portfolio A provides a better risk-reward trade-off than the market portfolio.
13. Not possible. Portfolio A clearly dominates the market portfolio. Portfolio A has
both a lower standard deviation and a higher expected return.
14. Not possible. The SML for this scenario is: E(r) = 10 + β × (18 – 10)
Portfolios with beta equal to 1.5 have an expected return equal to:
The expected return for Portfolio A is 16%; that is, Portfolio A plots below the
15. Not possible. The SML is the same as in Problem 14. Here, Portfolio A’s required
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
17. Since the stock’s beta is equal to 1.2, its expected rate of return is:
1 1 0 1
1
0
$50 $6
( ) 0.18 $53
$50
D P P P
E r P
P
-
+- +
= ® = ® =
18. The series of $1,000 payments is a perpetuity. If beta is 0.5, the cash flow should be
discounted at the rate:
If, however, beta is equal to 1, then the investment should yield 16%, and the price
paid for the firm should be:
a. To determine which investor was a better selector of individual stocks we look
at abnormal return, which is the ex-post alpha; that is, the abnormal return is
b. If rf = 6% and rM = 14%, then (using the notation alpha for the abnormal
return):
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
investor appears to have tilted his portfolio toward underpriced stocks.
c. If rf = 3% and rM = 15%, then:
Here, not only does the second investor appear to be the superior stock
selector, but the first investor’s predictions appear valueless (or worse).
21. a. Since the market portfolio, by definition, has a beta of 1, its expected rate of
return is 12%.
c. Using the SML, the fair expected rate of return for a stock with β = –0.5 is:
( ) 0.05 [( 0.5) (0.12 0.05)] 1.5%E r = + - ´ - =
The actually expected rate of return, using the expected price and dividend for
next year is:
$41 $3
( ) 1 0.10 10%
$40
E r +
= - = =
Because the actually expected return exceeds the fair return, the stock is
underpriced.
22. In the zero-beta CAPM the zero-beta portfolio replaces the risk-free rate, and thus:
You should invest in this fund because alpha is positive.
b. The passive portfolio with the same beta as the fund should be invested 80%
in the market-index portfolio and 20% in the money market account. For this
portfolio:
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
24. a. We would incorporate liquidity into the CCAPM in a manner analogous to the
way in which liquidity is incorporated into the conventional CAPM. In the
latter case, in addition to the market risk premium, expected return is also
b. As in part (a), nontraded assets would be incorporated into the CCAPM in a
fashion similar to part (a). Replace the market portfolio with consumption
While ownership of a privately held business is analogous to ownership of an
illiquid stock, expect a greater degree of illiquidity for the typical private
The same general considerations apply to labor income, although it is
probable that the lack of liquidity for labor income has an even greater impact
CFA PROBLEMS
1. a. Agree; Regan’s conclusion is correct. By definition, the market portfolio lies on
the capital market line (CML). Under the assumptions of capital market theory, all
portfolios on the CML dominate, in a risk-return sense, portfolios that lie on the
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
b. Nonsystematic risk is the unique risk of individual stocks in a portfolio that is
Disagree; Wilson’s remark is incorrect. Because both portfolios lie on the
Markowitz efficient frontier, neither Eagle nor Rainbow has any nonsystematic
risk. Therefore, nonsystematic risk does not explain the different expected returns.
2. E(r) = rf + β × [E(r M ) − rf ]
If the forecast rate of return is less than (greater than) the required rate of return,
then the security is overvalued (undervalued).
Therefore, Furhman Labs is overvalued and Garten Testing is undervalued.
3. a.
5. d.
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
9. d. [You need to know the risk-free rate]
10. Under the CAPM, the only risk that investors are compensated for bearing is the
risk that cannot be diversified away (systematic risk). Because systematic risk
11. a. McKay should borrow funds and invest those funds proportionately in
Murray’s existing portfolio (i.e., buy more risky assets on margin). In addition
b. McKay should substitute low-beta stocks for high-beta stocks in order to
reduce the overall beta of York’s portfolio. By reducing the overall portfolio
beta, McKay will reduce the systematic risk of the portfolio and, therefore,
reduce its volatility relative to the market. The security market line (SML)
12. a.
Expected Return Alpha
b. i. Kay should recommend Stock X because of its positive alpha, compared to
Stock Y, which has a negative alpha. In graphical terms, the expected
ii. Kay should recommend Stock Y because it has higher forecasted return and
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CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
Stock X: (14% 5%)/36% = 0.25
The market index has an even more attractive Sharpe ratio than either of the
When a stock is held as a single stock portfolio, standard deviation is the
relevant risk measure. For such a portfolio, beta as a risk measure is irrelevant.
Although holding a single asset is not a typically recommended investment
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