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n. 1. Suppose the risk-free rate goes up to 7%. What effect would higher interest rates have
on the SML and on the returns required on high-risk and low-risk securities?
Answer: The SML is shifted higher, but the slope is unchanged.
Here we have plotted the SML for betas ranging from 0 to 2.0. The base case
Answer: When investors’ risk aversion increases, the SML is rotated upward about the
y-intercept, which is rRF. Suppose rRF remains at 4 percent, but now rM increases to 12
o. Your client decides to invest $1.4 million in Blandy stock and $0.6 million in
Gourmange stock. What are the weights for this portfolio? What is the
portfolio’s beta? What is the required return for this portfolio?
Answer: The portfolio’s beta is the weighted average of the stocks’ betas:
There are two ways to calculate the portfolio’s expected return. First, we can use
the portfolio’s beta and the SML:
Mini Case: 6 - 2
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in part.
Second, we can find the weighted average of the stocks’ expected returns:
rp=
n
1i
iirw
p. Jordan Jones (JJ) and Casey Carter (CC) are portfolio managers at your firm.
Each manages a well-diversified portfolio. Your boss has asked for your opinion
regarding their performance in the past year. JJ’s portfolio has a beta of 0.6 and
had a return of 8.5%; CC’s portfolio has a beta of 1.4 and had a return of 9.5%.
Which manager had better performance? Why?
Answer: To evaluate the managers, calculate the required returns on their portfolios using the
SML and compare the actual returns to the required returns, as follows:
Portfolio Manager
JJ CC
Portfolio beta = 0.7 1.4
Notice that JJ’s portfolio had a higher return than investors required (given the
q. What does market equilibrium mean? If equilibrium does not exist, how will it
be established?
Answer: Market equilibrium means that marginal investors (the ones whose trades determine
Mini Case: 6 - 3
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
Market price = Intrinsic value
Market equilibrium also means that the expected return a security must equal its
required return (which reflects the security’s risk).
^
r
= r
If the market is not in equilibrium, then some assets will be undervalued and/or
some will be overvalued. If this is the case, traders will attempt to make a profit by
r. What is the Efficient Markets Hypothesis (EMH) and what are its three forms?
What evidence supports the EMH? What evidence casts doubt on the EMH?
Answer: The EMH is the hypothesis that securities are normally in equilibrium, and are
“priced fairly,” making it impossible to “beat the market.”
Weak-form efficiency says that investors cannot profit from looking at past
Semistrong-form efficiency says that all publicly available information is
Strong-form efficiency says that all information, even inside information, is
Most empirical evidence supports weak-form EMH because very few trading
Most empirical evidence supports the semistrong-form EMH. For example, the
Mini Case: 6 - 4
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
In addition, there are times when a market becomes overvalued. This is often
Mini Case: 6 - 5
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
Web Appendix 6B
Calculating Beta Coefficients With a Financial Calculator
Solutions to Problems
6B-1 a.
c. 1. Stand-alone risk as measured by would be greater, but beta and hence systematic
2. CAPM assumes that company-specific risk will be eliminated in a portfolio, so the
d. 1. The stock's variance and would not change, but the risk of the stock to an investor
Web Solutions: 6B - 6
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
(%)r
Y
2. Because of a relative scarcity of such stocks and the beneficial net effect on portfolios
e. The following figure shows a possible set of probability distributions. We can be
We can also say on the basis of the available information that Y is smaller than M;
Stock Y’s market risk is only 62% of the “market,” but it does have company-specific
Stock Y has b = 0.62, while the average stock (M) has b = 1.0; therefore,
A disequilibrium exists—Stock Y should be bid up to drive its yield down. More likely,
Web Solutions: 6B - 7
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
g. The beta would decline to 0.53. A decline indicates that the stock has become less risky;
6B-2 a.
The slope of the characteristic line is the stock’s beta coefficient.
Slope =
M
i
r
r
Run
Rise
.
SlopeA = BetaA =
20.1500.29
20.1500.29
= 1.0.
Web Solutions: 6B - 8
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
The graph of the SML is as follows:
The equation of the SML is thus:
c. Required rate of return on Stock A:
Required rate of return on Stock B:
C
r
ˆ
Return on Stock C if it is in equilibrium:
Web Solutions: 6B - 9
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
C
r
ˆ
A stock is in equilibrium when its required return is equal to its expected return.
Web Solutions: 6B - 10
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
