Chapter 6—Risk, Return and the Capital Asset Pricing Model
MULTIPLE CHOICE
1. The “feasible set” and “efficient set” differ because:
a.
the feasible set considers all portfolios of risky stocks, whereas the efficient set includes
only stock portfolios with minimum risk for a given level of expected return
b.
the feasible set plots the expected return and standard deviation for all possible portfolios
while the efficient set consists of only those portfolios offering the lowest expected return
for a given level of standard deviation
c.
the feasible set consists of all possible portfolios of assets, whereas the efficient set
includes only those portfolios which maximize expected returns for any given level of
volatility
d.
the feasible set contains portfolios in which the correlation between assets lies between 1.0
and –1.0, whereas the efficient set contains portfolios of assets with correlations that are
always less than one
e.
the feasible set will always be a subset of the efficient set
2. Uncle Bill is less risk averse than most investors. He would like to create a portfolio with a lower
standard deviation and a higher expected return than the market portfolio. You would tell Bill:
a.
this is impossible in equilibrium
b.
to borrow funds at the risk-free rate and invest them in the market portfolio
c.
to invest more of his wealth in the risk-free security than in the market portfolio
d.
to allocate funds between the market portfolio and the risk-free asset such that his
portfolio will lie to the right of the market portfolio on the CML
e.
to find the portfolio at the point of tangency between the efficient set and the CML
3. If the riskless rate increases, the optimal risky portfolio will have a __________ expected return and a
__________ standard deviation.
a.
higher; lower
b.
lower; higher
c.
lower; lower
d.
higher; higher
e.
superior; suboptimal
4. Consider the Capital Market Line. Given that the expected return on the market portfolio is Rm%, the
risk-free rate is Rf%, and the standard deviation of the market portfolio is sm%, the market price of
risk would be:
a.
ans1
b.
ans2
c.
ans3
d.
ans4
e.
ans5
5. According to the CAPM, the lower a security’s beta, the __________ its exposure to systematic risk
and the __________ its expected return.
a.
greater; lower
b.
greater; higher
c.
lower; lower
d.
lower; higher
e.
greater; greater
6. Alice is considering two stocks. Stock A has a beta of b1 while Stock B has a beta of b2. The risk
premium on the market portfolio is rm% and the risk-free rate is rf%. Alice believes the expected
return on stock B would be twice as high as the expected return on A, and therefore she should invest
in Stock B. Which of the following statements is true?
a.
Alice is incorrect regarding B’s expected return and would increase her exposure to
systematic risk more by investing in A than B.
b.
Alice is incorrect regarding B’s expected return; however, B does provide a higher
expected return than A.
c.
Alice is incorrect regarding B’s expected return; however, she will not be affected by
systematic risk if she holds a diversified portfolio and could invest in either B or A.
d.
Alice is correct regarding B‘s expected return and would increase her exposure to
systematic risk by investing in B.
e.
Alice is correct regarding B‘s expected return and should put all her wealth in B.
7. GoodBuy stock has a beta of b. The expected return on GoodBuy is Er%, while the expected return on
the market portfolio is only Rm%. The risk-free rate is Rf%. Because GoodBuy lies __________ the
SML, it is considered __________.
a.
below; overpriced
b.
below; underpriced
c.
above; underpriced
d.
above; overpriced
e.
on; correctly priced
8. If the slope of the Security Market Line is slope% and the expected return on the market portfolio is
p%, the risk free rate __________ and the market risk premium __________.
a.
is rf%; is p%
b.
is rf%; is slope%
c.
is slope%; is p%
d.
is rf%; can’t be determined unless the standard deviation of the market portfolio is known
e.
is slope%; can’t be determined without knowing j
9. In equilibrium, if all investors will hold some combination of the market portfolio and the risk-free
asset (according to the CAPM). An asset with higher variance and lower expected return than what
could be obtained on the CML can survive:
a.
if it lies below the SML and is therefore underpriced
b.
if it is strongly correlated with all other assets
c.
if it has a beta over 1.0
d.
if it weakly covaries with the market
e.
only if it lies on the efficient frontier
10. Company XYZ has an R-squared and of r1 and b1, respectively. Company ABC has an R-squared
and of r2 and b2, respectively. This suggests:
a.
Company ABC has a larger risk premium than Company XYZ
b.
Company XYZ has a higher correlation coefficient with the market than Company ABC
c.
Company ABC has a lower percentage of its variability explained by the variability in the
market’s return
d.
Company XYZ has lower systematic risk and greater unsystematic risk than ABC
e.
Company XYZ has greater systematic and unsystematic risk than Company ABC
11. The Fama-French model asserts that a firm’s exposure to SMB and HML risk are important in
explaining expected returns. Which of the following is consistent with the F-F model?
a.
a firm with a negative size beta and an average book-to-market beta has high expected
returns
b.
a firm with an average size beta and a positive book-to-market beta has low expected
returns
c.
a firm that has a positive size beta and a positive book-to–market beta has high expected
return
d.
a new internet company with a low book value of equity, but high market value of equity
and high returns
e.
none of the above
12. A portfolio is __________ if it offers the highest expected return among the group of portfolios with
equal or less volatility.
a.
inefficient
b.
minimum variance
c.
efficient
d.
the feasible set
e.
optimal risky
13. The __________ tells us the composition of the optimal portfolio from a theoretical standpoint.
a.
CAPM
b.
efficient frontier
c.
market portfolio
d.
single-factor model
e.
two-fund separation principle
14. The search for the composition of the optimal portfolio begins when investors form estimates of the
__________ for all risky assets in the economy.
a.
expected returns
b.
standard deviations
c.
covariances
d.
all of the above
e.
none of the above
15. The __________ quantifies the relationship between the expected return and standard deviation for
portfolios consisting of the risk-free asset and the optimal risky portfolio.
a.
SML
b.
APT
c.
CAPM
d.
CML
e.
F-F Model
16. Which of the following is a serious flaw with the CAPM?
a.
expected returns on assets are inherently unobservable
b.
CAPM is a one-period model
c.
no investment is truly risk free
d.
market portfolio is unobservable
e.
all of the above are serious flaws
17. The __________ argues that stock returns are best explained by a three-factor model.
a.
APT
b.
Fama-French model
c.
M & M model
d.
CAPM
e.
Harry Markowitz model
18. What really distinguishes the Fama-French approach from both the CAPM and the APT is that it is an
entirely empirical attempt to model __________.
a.
book value
b.
asset returns
c.
beta
d.
low-beta stocks
e.
the benefits of diversification
19. Economists adopt the assumption of __________ as a way to consider how the market will reach
equilibrium.
a.
homogeneous expectations
b.
inefficient portfolios
c.
efficient frontiers
d.
feasible sets
e.
efficient markets
20. Richard has $money to invest, but he is willing to borrow money to increase the size of his investment.
How much should Richard borrow to construct a portfolio with an expected return of er% if the
risk-free rate is rf% and the expected return of the optimal portfolio is eop%?
a.
$ans1
b.
$ans2
c.
$ans3
d.
$ans4
e.
$ans5
21. Adding real estate should move the efficient frontier __________ relative to including only stocks.
a.
down and to the left
b.
up and to the left
c.
down and to the right
d.
up and to the right
22. According to a survey conducted by Graham and Harvey, corporate finance practitioners and
investment professionals __________ make substantial use of the CAPM.
a.
do, do
b.
do, do not
c.
do not, do
d.
do not, do not
23. When its returns are regressed on the market’s, a stock with a high beta will have a __________ term
in the regression.
a.
high intercept
b.
low intercept
c.
high slope
d.
low slope
24. The market portfolio includes
a.
Stocks
b.
Real estate
c.
Bonds
d.
All risky assets
25. Consider an asset that currently plots below the security market line,
a.
The asset is underpriced given its level of risk and its price should rise until it plots on the
SML
b.
The asset is underpriced and its beta will decrease until it plots on the SML
c.
The asset is overpriced given its level of risk and its price should decrease until it plots on
the SML
d.
The asset is overpriced and its beta will increase until it plots on the SML
26. Empirical tests have raised concerns about the CAPM, including:
a.
The risk-free rate has poor proxies
b.
The risk-free rate is relatively stable
c.
The CAPM is silent whether short-term or long-term risk-free rates should be used
d.
Empirical test have little concern about the risk-free interest rate
27. Two researchers, using the CAPM, generate different estimates for the same stock. Examining these
results the likely source of the difference is:
a.
The researchers select different proxies for risk-free interest rates
b.
The researchers use different methods for determining beta
c.
The researchers have different expected holding periods for the stock
d.
At least one researcher does not understand the CAPM
28. In addition to the market-risk premium and a market-to-book factor the Fama and French model adds
a.
A low P/E factor
b.
A small-firm size factor
c.
A large-firm size factor
d.
A high P/E factor
29. In addition to the market-risk premium and a firm-size factor the Fama and French model adds
a.
A low P/E factor
b.
A high market-to-book factor
c.
A low market-to–book factor
d.
A high P/E factor
30. Why should practitioners be concerned about the problems and nuances of the empirical tests of the
CAPM?
a.
These problems are sufficient to discredit the CAPM
b.
None of the empirical tests actually test the theoretical model, leaving its validity intact
c.
Practitioners only need to know how to use CAPM
d.
The challenges empirical researchers face testing the CAPM are very similar to the
challenges that practitioners face employing the CAPM
MATCHING
Match the following terms with their best descriptions:
a.
CAPM
b.
APT
c.
Fama-French
1. is based on an individual asset’s covariance with the market portfolio
2. shows that differences in returns on portfolios of large and small stocks and portfolios of high
book-to-market and low book-to-market stocks help explain why some stocks have high average
returns while other stocks have low average returns
3. assumes all investors have homogenous expectations
4. provides a theoretical apparatus to model asset prices
5. investors can buy or sell short a large number of traded assets
6. asset returns are driven by many (unidentified) factors representing systematic risks
7. for each factor influencing returns, there is an associated risk premium
8. the only determinant of a stock’s expected return is its beta
9. an empirical attempt to model asset prices
Match the following terms with their best descriptions:
a.
CAPM
b.
APT
c.
Fama-French Model
d.
CML
e.
market price of risk
10. offers no guidance about what factors should be important
11. quantifies the relationship between the expected return and standard deviation of a portfolio
12. entirely empirical attempt to model asset prices
13. investors try to maximize
14. a single-factor model
SHORT ANSWER
1. Both beta and R-square provide a measure of how an asset is related to the market. Provide a brief
discussion of the similarities and differences between these two measures.
2. Critically discuss the following comment:
“I have no interest in investing internationally. The U.S. market has outperformed international
markets in many years. Because virtually no combination of international investments can outperform
a solely U.S. investment portfolio, I will not diversify internationally.“
3. You are combining a risky asset with an investment in risk-free U.S. Treasury bills with one year to
maturity. The U.S. Treasury bills offer a rf percent rate of return. The risky asset has an expected
return of er percent and a standard deviation of s percent over the next year. If your total funds are $m
and you invest $i in the risky asset, calculate your portfolio expected return and standard deviation.
4. Describe how the efficient frontier changes when a risk-free investment opportunity is available. Why
is the ‘old efficient frontier’ no longer efficient?
5. Sketch the security market line and directly calculate the slope as the rise over the run from the
intercept to the location of the market portfolio on the line. Before calculating the relevant ratio, be
sure to first determine the expected return and beta of both the risk-free investment and the market
portfolio.
6. Assume the risk-free rate of return is 4 percent. A given risky asset has a beta of 0, and a standard
deviation of 22 percent.
What is the required rate of return to this risky asset?
Explain the somewhat puzzling result that an asset with a standard deviation of 22 percent has
the expected return that you found in part a.
The fair rate of return on a zero-beta investment is the risk-free rate, or 4 percent.
can be diversified away.
7. You observe a scatter plot with a risky asset’s return on the vertical axis and the market return on the
horizontal axis. The plot of points displays no discernable pattern, being randomly distributed around
the origin of the graph.
What will be the estimated beta in this case?
What will be the estimated regression intercept?
the estimated beta will be zero.
The regression intercept will be given by the sample mean of the stock’s returns. In this case it
will be close to zero.
8. Consider a stock that plots above the Security Market Line. If you held a large well-diversified
portfolio, explain the impact of adding a small amount of this stock to your portfolio. If all investors
shared your view, would they wish to add this stock to their portfolios? How would these decisions
affect the market price and the required return to this particular stock?
9. Explain the two-fund separation principle.
10. Risky asset A has an expected return of Er% and the risk-free asset has a return of 5%. How can you
construct a portfolio of these two assets with an expected return of rp%?
11. Calculate the expected return of a stock with a b beta if the expected return on the market portfolio is
em % and the risk free rate is rf %.
12. Describe the predictions of the CAPM.
13. Explain the statement: “Some portfolios are better than others.“
14. The risk-free rate of return is rf percent, the expected rate of return on the market portfolio is rm %,
and R & R stock has a beta of b. Determine the required rate of return on R & R stock if the expected
inflation rate increases by i percent and real returns on both the risk-free asset and the market portfolio
remain constant.
15. How would you interpret a stock beta of 1.7?
16. What are the variables that affect the variance of a portfolio of stocks?
17. What might investors do if they find a stock above the Security Market Line?
18. What are the primary tasks that someone wanting to implement the Arbitrage Pricing Theory for a
practical purpose would have to perform?
19. What are the risk factors suggested by the Fama-French model?
20. Carol invests $money of her own money and $borrow in borrowed funds in an asset with an expected
return of r% and a standard deviation of s%. What is the standard deviation of her new portfolio?
21. The risk-free asset pays rf%, the market portfolio’s expected return is rm%, and its standard deviation
is s%. What is the slope of the capital market line?
22. The expected return on Jill Corporation is er%, and its beta is b. The risk-free rate is rf%, and the
expected return on the market portfolio is rm%. Does the asset lie on, above, or below the Security
Market Line? Explain.
23. Suppose you believe the following factors drive stock returns: unexpected changes in the weather,
unexpected movement in the Dow Jones Industrial Average, and unexpected shifts in the price of
butter. The weather risk premium is rw%, the risk premium on the DJIA is rd%, and the risk premium
on butter is rb%. If the stock of Fog Corporation is sensitive to the above factors and has a weather
beta of bw, DJIA beta of bd, and a butter beta of bb, what is the expected return on this stock if the
risk-free rate is rf%?
24. Is the expected return on a stock with a beta of b2, three times the expected return on a stock with a
beta of b1?
25. Comment on the following claim: “If Stock X lies below the efficient frontier, no one should hold
stock X.”
26. Explain how the presence of a risk-free asset changes the nature of portfolio choice.
27. Suppose that market interest rates are negatively correlated with overall market returns. If one views
the CAPM investment horizon as 3 months, what could be said about the beta of 10 year T-bonds?
28. How might the portfolio selection problem change if interest rates for borrowing were greater than
those for lending? A graph may help.
29. What are some possible sources of information regarding stock expected returns, variances and
covariances?
30. Prove that when a portfolio is combined with a risk-free asset, the expected return of the combination
is an affine (linear) function of the standard deviation. You may take as given formulas for expected
return and variance of portfolios with two assets.
31. Briefly describe two challenges faced by those who would empirically test the CAPM.
32. What are some factors involved in determining frequency and total time period of data when
estimating a stock’s beta?
ESSAY
1. We understand that unsystematic risk can be diversified away in a portfolio. Do you believe that firms
should invest in a large number of unrelated projects to offer their investors a diversified stock return?
Provide at least one scenario supporting both a positive and negative answer to this question.
2. Carefully distinguish between systematic and unsystematic risk, and explain why the market rewards
only one type of risk. How do the three leading asset-pricing models discussed in this chapter quantify
the notion of systematic risk?
3.
Common stock
Expected
return
Standard
deviation of returns
Correlation coefficient between
returns on stock
& the market portfolio
1
e1 %
s1 %
cor1
2
e2 %
s2 %
cor2
3
e3 %
s3 %
cor3
1
2
3
The standard deviation (S. D.) for the market portfolio is sm%, the risk-free rate is rf%, and the market
risk premium is mrp%. Estimate the beta for each stock and use the CAPM to determine which stocks
appear to be attractive investments.
4. You have two portfolios to select from. Portfolio 1 has an E(R) = r1% with a standard deviation of
s1% and portfolio 2 has an E(R) = r2 % with a standard deviation of s2%. If the risk-free rate is rf%
which portfolio is optimal?
5. What information is found by estimating a regression line of a stock?
6. “I understand that there is a direct relationship between risk and expected return. Because I am a
long-term investor and less risk averse than other investors, I will invest all of my funds in a single
risky asset.”
Critically evaluate this statement and offer an alternative strategy that should offer higher returns for
this investor without higher risk.