CHAPTER 25—PORTFOLIO THEORY AND ASSET PRICING MODELS
TRUE/FALSE
1. The slope of the SML is determined by the value of beta.
2. If you plotted the returns of Selleck & Company against those of the market and found that the slope
of your line was negative, the CAPM would indicate that the required rate of return on Selleck’s stock
should be less than the risk-free rate for a well-diversified investor, assuming that the observed
relationship is expected to continue in the future.
3. If the returns of two firms are negatively correlated, then one of them must have a negative beta.
4. A stock with a beta equal to −1.0 has zero systematic (or market) risk.
5. It is possible for a firm to have a positive beta, even if the correlation between its returns and those of
another firm are negative.
6. In portfolio analysis, we often use ex post (historical) returns and standard deviations, despite the fact
that we are interested in ex ante (future) data.
7. If investors are risk averse and hold only one stock, we can conclude that the required rate of return on
a stock whose standard deviation is 0.21 will be greater than the required return on a stock whose
standard deviation is 0.10. However, if stocks are held in portfolios, it is possible that the required
return could be higher on the low standard deviation stock.
8. The CAPM is a multi-period model which takes account of differences in securities’ maturities, and it
can be used to determine the required rate of return for any given level of systematic risk.
9. The SML relates required returns to firms’ systematic (or market) risk. The slope and intercept of this
line can be influenced by managerial actions.
10. The Y-axis intercept of the SML indicates the return on an individual asset when the realized return on
an average (b = 1) stock is zero.
11. We will almost always find that the beta of a diversified portfolio is less stable over time than the beta
of a single security.
12. Arbitrage pricing theory is based on the premise that more than one factor affects stock returns, and
the factors are specified to be (1) market returns, (2) dividend yields, and (3) changes in inflation.
MULTIPLE CHOICE
13. You have the following data on three stocks:
Stock
Standard Deviation
Beta
A
0.15
0.79
B
0.25
0.61
C
0.20
1.29
As a risk minimizer, you would choose Stock ____ if it is to be held in isolation and Stock ____ if it is
to be held as part of a well-diversified portfolio.
a.
A; B.
b.
B; C.
c.
C; A.
d.
C; B.
e.
A; A.
14. Which is the best measure of risk for an asset held in isolation, and which is the best measure for an
asset held in a diversified portfolio?
a.
Standard deviation; correlation coefficient.
b.
Beta; variance.
c.
Coefficient of variation; beta.
d.
Beta; beta.
e.
Variance; correlation coefficient.
15. Which of the following is NOT a potential problem with beta and its estimation?
a.
Sometimes, during a period when the company is undergoing a change such as toward
more leverage or riskier assets, the calculated beta will be drastically different than the
“true” or “expected future” beta.
b.
The beta of “the market,” can change over time, sometimes drastically.
c.
Sometimes the past data used to calculate beta do not reflect the likely risk of the firm for
the future because conditions have changed.
d.
There is a wide confidence interval around a typical stock’s estimated beta.
e.
Sometimes a security or project does not have a past history which can be used as a basis
for calculating beta.
16. Stock A’s beta is 1.5 and Stock B’s beta is 0.5. Which of the following statements must be true about
these securities? (Assume market equilibrium.)
a.
Stock B must be a more desirable addition to a portfolio than Stock A.
b.
Stock A must be a more desirable addition to a portfolio than Stock B.
c.
The expected return on Stock A should be greater than that on Stock B.
d.
The expected return on Stock B should be greater than that on Stock A.
e.
When held in isolation, Stock A has greater risk than Stock B.
17. For markets to be in equilibrium (that is, for there to be no strong pressure for prices to depart from
their current levels),
a.
The past realized rate of return must be equal to the expected rate of return; that is, .
b.
The required rate of return must equal the realized rate of return; that is, r = .
c.
All companies must pay dividends.
d.
No companies can be in danger of declaring bankruptcy.
e.
The expected rate of return must be equal to the required rate of return; that is, = r.
18. Which of the following statements is CORRECT?
a.
The slope of the CML is ( M − rRF)/bM.
b.
All portfolios that lie on the CML to the right of M are inefficient.
c.
All portfolios that lie on the CML to the left of M are inefficient.
d.
The slope of the CML is ( M − rRF)/M.
e.
The Capital Market Line (CML) is a curved line that connects the risk-free rate and the
market portfolio.
19. In a portfolio of three different stocks, which of the following could NOT be true?
a.
The riskiness of the portfolio is greater than the riskiness of one or two of the stocks.
b.
The beta of the portfolio is less than the betas of each of the individual stocks.
c.
The beta of the portfolio is greater than the beta of one or two of the individual stocks’
betas.
d.
The beta of the portfolio cannot be equal to 1.
e.
The riskiness of the portfolio is less than the riskiness of each of the stocks if they were
held in isolation.
20. You have the following data on (1) the average annual returns of the market for the past 5 years and
(2) similar information on Stocks A and B. Which of the possible answers best describes the historical
betas for A and B?
Years
Market
Stock A
Stock B
1
0.03
0.16
0.05
2
−0.05
0.20
0.05
3
0.01
0.18
0.05
4
−0.10
0.25
0.05
5
0.06
0.14
0.05
a.
bA > +1; bB = 0.
b.
bA = 0; bB = −1.
c.
bA < 0; bB = 0.
d.
bA < −1; bB = 1.
e.
bA > 0; bB = 1.
21. Which of the following statements is CORRECT?
a.
The typical R2 for a stock is about 0.94 and the typical R2 for a portfolio is about 0.6.
b.
The typical R2 for a stock is about 0.3 and the typical R2 for a large portfolio is about 0.94.
c.
The typical R2 for a stock is about 0.94 and the typical R2 for a portfolio is also about 0.94.
d.
The typical R2 for a stock is about 0.6 and the typical R2 for a portfolio is also about 0.6.
e.
The typical R2 for a stock is about 0.3 and the typical R2 for a portfolio is also about 0.3.
22. Which of the following statements is CORRECT?
a.
The characteristic line is the regression line that results from plotting the returns on a
particular stock versus the returns on a stock from a different industry.
b.
The slope of the characteristic line is the stock’s standard deviation.
c.
The distance of the plot points from the characteristic line is a measure of the stock’s
market risk.
d.
The distance of the plot points from the characteristic line is a measure of the stock’s
diversifiable risk.
e.
“Characteristic line” is another name for the Security Market Line.
23. Which of the following statements is CORRECT?
a.
Richard Roll has argued that it is possible to test the CAPM to see if it is correct.
b.
Tests have shown that the risk/return relationship appears to be linear, but the slope of the
relationship is greater than that predicted by the CAPM.
c.
Tests have shown that the betas of individual stocks are stable over time, but that the betas
of large portfolios are much less stable.
d.
The most widely cited study of the validity of the CAPM is one performed by Modigliani
and Miller.
e.
Tests have shown that the betas of individual stocks are unstable over time, but that the
betas of large portfolios are reasonably stable over time.
24. Assume an economy in which there are three securities: Stock A with rA = 10% and A = 10%; Stock
B with rB = 15% and B = 20%; and a riskless asset with rRF = 7%. Stocks A and B are uncorrelated
(rAB = 0). Which of the following statements is most CORRECT?
a.
The expected return on the investor’s portfolio will probably have an expected return that
is somewhat below 10% and a standard deviation (SD) of approximately 10%.
b.
The expected return on the investor’s portfolio will probably have an expected return that
is somewhat below 15% and a standard deviation (SD) that is between 10% and 20%.
c.
The investor’s risk/return indifference curve will be tangent to the CML at a point where
the expected return is in the range of 7% to 10%.
d.
Since the two stocks have a zero correlation coefficient, the investor can form a riskless
portfolio whose expected return is in the range of 10% to 15%.
e.
The expected return on the investor’s portfolio will probably have an expected return that
is somewhat above 15% and a standard deviation (SD) of approximately 20%.
25. You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks. The portfolio
beta is equal to 1.12. You have decided to sell a coal mining stock (b = 1.00) at $5,000 net and use the
proceeds to buy a like amount of a mineral rights company stock (b = 2.00). What is the new beta of
the portfolio?
a.
1.1139
b.
1.1700
c.
1.2311
d.
1.2927
e.
1.3573
26. Your mother’s well-diversified portfolio has an expected return of 12.0% and a beta of 1.20. She is in
the process of buying 100 shares of Safety Corp. at $10 a share and adding it to her portfolio. Safety
has an expected return of 15.0% and a beta of 2.00. The total value of your current portfolio is $9,000.
What will the expected return and beta on the portfolio be after the purchase of the Safety stock?
rp bp
a.
11.69%; 1.22
b.
12.30%; 1.28
c.
12.92%; 1.34
d.
13.56%; 1.41
e.
14.24%; 1.48
27. Suppose that (1) investors expect a 4.0% rate of inflation in the future, (2) the real risk-free rate is
3.0%, (3) the market risk premium is 5.0%, (4) Talcott Inc.’s beta is 1.00, and (5) its realized rate of
return has averaged 15.0% over the last 5 years. Calculate the required rate of return for Talcot Inc.
a.
10.29%
b.
10.83%
c.
11.40%
d.
12.00%
e.
12.60%
28. A stock you are holding has a beta of 2.0 and the stock is currently in equilibrium. The required rate of
return on the stock is 15% versus a required return on an average stock of 10%. Now the required
return on an average stock increases by 30.0% (not percentage points). The risk-free rate is unchanged.
By what percentage (not percentage points) would the required return on your stock increase as a
result of this event?
a.
36.10%
b.
38.00%
c.
40.00%
d.
42.00%
e.
44.10%
29. Calculate the required rate of return for the Wagner Assets Management Group, which holds 4 stocks.
The market’s required rate of return is 15.0%, the risk-free rate is 7.0%, and the Fund’s assets are as
follows:
Stock
Investment
Beta
A
$ 200,000
1.50
B
300,000
−0.50
C
500,000
1.25
D
1,000,000
0.75
a.
10.67%
b.
11.23%
c.
11.82%
d.
12.45%
e.
13.10%
30. Consider the information below for Postman Builders Inc. Suppose that the expected inflation rate and
thus the inflation premium increase by 2.0 percentage points, and Postman acquires risky assets that
increase its beta by the indicated percentage. What is the firm’s new required rate of return?
Beta:
1.50
Required return (rs)
10.20%
RPM:
6.00%
Percentage increase in beta:
20%
a.
14.00%
b.
14.70%
c.
15.44%
d.
16.21%
e.
17.02%
Old rs = rRF + b(RPM): 10.2% = rRF + 1.5(6.0%): rRF = 10.2% − 9.0% = 1.20%
31. Assume that the market is in equilibrium and that stock betas can be estimated with historical data.
The returns on the market, the returns on United Fund (UF), the risk-free rate, and the required return
on the United Fund are shown below. Based on this information, what is the required return on the
market, rM?
Year
Market
UF
2008
−9%
−14%
2009
11%
16%
2010
15%
22%
2011
5%
7%
2012
−1%
−2%
rRF: 7.00%;
rUnited: 15.00%
a.
10.57%
b.
11.13%
c.
11.72%
d.
12.33%
e.
12.95%
Old beta:
1.50
Old rs = rRF + b(RPM)
10.20%
RPM
6.00%
Percentage increase in beta:
20%
32. You are given the following returns on “the market” and Stock F during the last three years. We could
calculate beta using data for Years 1 and 2 and then, after Year 3, calculate a new beta for Years 2 and
3. How different are those two betas, i.e., what’s the value of beta 2 − beta 1? (Hint: You can find betas
using the Rise-Over-Run method, or using your calculator’s regression function.)
Year
Market
Stock F
1
6.10%
6.50%
2
12.90%
−3.70%
3
16.20%
21.71%
a.
7.89
b.
8.30
c.
8.74
d.
9.20
e.
9.66
PROBLEM
33. Security A has an expected return of 12.4% with a standard deviation of 15%, and a correlation with
the market of 0.85. Security B has an expected return of −0.73% with a standard deviation of 20%, and
a correlation with the market of −0.67. The standard deviation of rM is 12%.
a.
To someone who acts in accordance with the CAPM, which security is more risky, A or B?
Why? (Hint: No calculations are necessary to answer this question; it is easy.)
b.
What are the beta coefficients of A and B? Calculations are necessary.
c.
If the risk-free rate is 6%, what is the value of rM?
34. You plan to invest in Stock X, Stock Y, or some combination of the two. The expected return for X is
10% and X = 5%. The expected return for Y is 12% and Y = 6%. The correlation coefficient, rXY, is
0.75.
a.
Calculate rp and p for 100%, 75%, 50%, 25%, and 0% in Stock X.
b.
Use the values you calculated for rp and p to graph the attainable set of portfolios. Which
part of the attainable set is efficient? Also, draw in a set of hypothetical indifference curves
to show how an investor might select a portfolio comprised of Stocks X and Y. Let an
indifference curve be tangent to the efficient set at the point where rp = 11%.
c.
Now suppose we add a riskless asset to the investment possibilities. What effects will this
have on the construction of portfolios?
d.
Suppose rM = 12%, M = 4%, and rRF = 6%. What would be the required and expected return
on a portfolio with P = 10%?
e.
Suppose the correlation of Stock X with the market, rXM, is 0.8, while rYM = 0.9. Use this
information, along with data given previously, to determine Stock X’s and Stock Y’s beta
coefficients.
f.
What is the required rate of return on Stocks X and Y? Do these stocks appear to be in
equilibrium? If not, what would happen to bring about an equilibrium?
35. Stock A has an expected return rA = 10% and A = 10%. Stock B has rB = 14% and B = 15%. rAB = 0.
The rate of return on riskless assets is 6%.
a.
Construct a graph that shows the feasible and efficient sets, giving consideration to the
existence of the riskless asset.
b.
Explain what would happen to the CML if the two stocks had (a) a positive correlation
coefficient or (b) a negative correlation coefficient.
c.
Suppose these were the only three securities (A, B, and riskless) in the economy, and
everyone’s indifference curves were such that they were tangent to the CML to the right of
the point where the CML was tangent to the efficient set of risky assets. Would this represent
a stable equilibrium? If not, how would an equilibrium be produced?
Calculations:
