Which one of the following is correct?

a. XYZ is overpriced.

b. XYZ is fairly priced.

c. XYZ™s alpha is .25%.

d. XYZ™s alpha is .25%.

31. What is the expected return of a zero-beta security?

a. Market rate of return.

b. Zero rate of return.

d. Negative rate of return.

www.mhhe.com/bkm

d. Risk-free rate of return.

32. Capital asset pricing theory asserts that expected returns are best explained by:

a. Economic factors

b. Specific risk

c. Systematic risk

d. Diversification

33. According to CAPM, the expected rate of return of a portfolio with a beta of 1.0 and an

alpha of 0 is:

a. Between rM and rf .

b. The risk-free rate, rf .

Bodie’Kane’Marcus: II. Portfolio Theory 7. Capital Asset Pricing © The McGraw’Hill

Essentials of Investments, and Arbitrage Pricing Companies, 2003

Fifth Edition Theory

256 Part TWO Portfolio Theory

c. (rM rf).

d. The expected return on the market, rM.

The following table shows risk and return measures for two portfolios.

Average Annual Standard

Portfolio Rate of Return Deviation Beta

R 11% 10% 0.5

S&P 500 14% 12% 1.0

34. When plotting portfolio R on the preceding table relative to the SML, portfolio R lies:

a. On the SML.

b. Below the SML.

c. Above the SML.

d. Insufficient data given.

35. When plotting portfolio R relative to the capital market line, portfolio R lies:

a. On the CML.

b. Below the CML.

c. Above the CML.

d. Insufficient data given.

36. Briefly explain whether investors should expect a higher return from holding portfolio A

versus portfolio B under capital asset pricing theory (CAPM). Assume that both

portfolios are fully diversified.

Portfolio A Portfolio B

Systematic risk (beta) 1.0 1.0

Specific risk for each

individual security High Low

37. Assume that both X and Y are well-diversified portfolios and the risk-free rate is 8%.

Portfolio Expected Return Beta

X 16% 1.00

Y 12% 0.25

www.mhhe.com/bkm

In this situation you could conclude that portfolios X and Y:

a. Are in equilibrium.

b. Offer an arbitrage opportunity.

c. Are both underpriced.

d. Are both fairly priced.

38. According to the theory of arbitrage:

a. High-beta stocks are consistently overpriced.

b. Low-beta stocks are consistently overpriced.

c. Positive alpha investment opportunities will quickly disappear.

d. Rational investors will pursue arbitrage consistent with their risk tolerance.

Bodie’Kane’Marcus: II. Portfolio Theory 7. Capital Asset Pricing © The McGraw’Hill

Essentials of Investments, and Arbitrage Pricing Companies, 2003

Fifth Edition Theory

257

7 Capital Asset Pricing and Arbitrage Pricing Theory

39. A zero-investment portfolio with a positive alpha could arise if:

a. The expected return of the portfolio equals zero.

b. The capital market line is tangent to the opportunity set.

c. The law of one price remains unviolated.

d. A risk-free arbitrage opportunity exists.

40. The APT differs from the single-factor CAPM because the APT:

a. Places more emphasis on market risk.

b. Minimizes the importance of diversification.

c. Recognizes multiple unsystematic risk factors.

d. Recognizes multiple systematic risk factors.

41. An investor takes as large a position as possible when an equilibrium price relationship

is violated. This is an example of:

a. A dominance argument.

b. The mean-variance efficient frontier.

c. Arbitrage activity.

d. The capital asset pricing model.

42. The feature of APT that offers the greatest potential advantage over the simple CAPM

is the:

a. Identification of anticipated changes in production, inflation, and term structure of

interest rates as key factors explaining the risk-return relationship.

b. Superior measurement of the risk-free rate of return over historical time periods.

c. Variability of coefficients of sensitivity to the APT factors for a given asset over

time.

d. Use of several factors instead of a single market index to explain the risk-return

relationship.

43. In contrast to the capital asset pricing model, arbitrage pricing theory:

a. Requires that markets be in equilibrium.

b. Uses risk premiums based on micro variables.

c. Specifies the number and identifies specific factors that determine expected returns.

d. Does not require the restrictive assumptions concerning the market portfolio.

www.mhhe.com/bkm

Bodie’Kane’Marcus: II. Portfolio Theory 7. Capital Asset Pricing © The McGraw’Hill

Essentials of Investments, and Arbitrage Pricing Companies, 2003

Fifth Edition Theory

258 Part TWO Portfolio Theory

STANDARD & POOR™S

1. In the previous chapter, you used data from Market Insight to calculate the beta

of Apple Computer (AAPL). Now let™s compute the alpha of the stock in two

consecutive periods. Estimate the index model regression using the first two years

of monthly data. (You can get monthly T-bill rates to calculate excess returns from

the Federal Reserve website at http://www.federalreserve.gov/releases/h15/data.

htm.) The intercept of the regression is Apple™s alpha over that 2-year period.

Now repeat this exercise using the next two years of monthly data. This will give

you alpha and beta estimates for two consecutive time periods. Finally, repeat this

regression exercise for several (e.g., a dozen) other firms.

2. Given your results for question 1, we can now investigate the extent to which beta

in one period predicts beta in future periods and whether alpha in one period

predicts alpha in future periods. Regress the beta of each firm in the second

period against the beta in the first period. (If you estimated regressions for a

dozen firms in question 1, you will have 12 observations in this regression.) Do the

same for the alphas of each firm.

3. We would expect that beta in the first period predicts beta in the next period, but

that alpha in the first period has no power to predict alpha in the next period.

(The regression coefficient on first-period beta will be statistically significant, but

the coefficient on alpha will not be.) Why does this expectation make sense? Is it

borne out by the data?

WEBMA STER

Beta Coefficients

Go to www.mhhe.com/edumarketinsight. Click on Monthly Valuation Data. The report

summarizes seven months of data related to stock market activity and contains several

comparison reports to the market indexes. Pull the monthly valuation data for General

Electric, The Home Depot, Johnson and Johnson, Honeywell, and H.J. Heinz.

After reviewing the reports, answer the following questions:

1. Which of the firms are low-beta firms?

2. Does the beta coefficient for these low-beta firms make sense given what type of

firms they are? Briefly explain.

3. Describe the variation in the reported beta coefficients over the seven months

www.mhhe.com/bkm

of data.

SOLUTIONS TO 1. The CML would still represent efficient investments. We can characterize the entire population by

two representative investors. One is the “uninformed” investor, who does not engage in security

>

Concept analysis and holds the market portfolio, while the other optimizes using the Markowitz algorithm

with input from security analysis. The uninformed investor does not know what input the informed

CHECKS

investor uses to make portfolio purchases. The uninformed investor knows, however, that if the

other investor is informed, the market portfolio proportions will be optimal. Therefore, to depart

from these proportions would constitute an uninformed bet, which will, on average, reduce the

efficiency of diversification with no compensating improvement in expected returns.

Bodie’Kane’Marcus: II. Portfolio Theory 7. Capital Asset Pricing © The McGraw’Hill

Essentials of Investments, and Arbitrage Pricing Companies, 2003

Fifth Edition Theory

259

7 Capital Asset Pricing and Arbitrage Pricing Theory

2. Substituting the historical mean and standard deviation in Equation 7.1 yields a coefficient of risk

aversion of

E(rM) rf .085

A* 2.1

2

0.202

M

This relationship also tells us that for the historical standard deviation and a coefficient of risk

aversion of 3.5, the risk premium would be

2

0.202

E(rM) rf A* 3.5 0.14 14%

M

3. 1.25, 1.15. Therefore, given the investment proportions, the portfolio beta is

Ford GM

wFord wGM (0.75 1.25) (0.25 1.15) 1.225

P Ford GM

and the risk premium of the portfolio will be

E(rP) rf P[E(rM) rf] 1.225 8% 9.8%

4. a. The alpha of a stock is its expected return in excess of that required by the CAPM.

E(r) {rf [E(rM) rf]}

12 [5 1.0(11 5)] 1

XYZ

13 [5 1.5(11 5)] 1%

ABC

b. The project-specific required rate of return is determined by the project beta coupled with the

market risk premium and the risk-free rate. The CAPM tells us that an acceptable expected rate

of return for the project is

rf [E(rM) rf] 8 1.3(16 8) 18.4%

which becomes the project™s hurdle rate. If the IRR of the project is 19%, then it is desirable.

Any project (of similar beta) with an IRR less than 18.4% should be rejected.

5. The least profitable scenario currently yields a profit of $10,000 and gross proceeds from the

equally weighted portfolio of $700,000. As the price of Dreck falls, less of the equally weighted

portfolio can be purchased from the proceeds of the short sale. When Dreck™s price falls by more

than a factor of 10,000/700,000, arbitrage no longer will be feasible, because the profits in the worst

state will be driven below zero.

To see this, suppose Dreck™s price falls to $10 (1 1/70). The short sale of 300,000

shares now yields $2,957,142, which allows dollar investments of only $985,714 in each of the

other shares. In the high real interest rate, low inflation scenario, profits will be driven to zero.

Stock Dollar Investment Rate of Return (%) Dollar Return

Apex $ 985,714 20 $ 197,143

Bull 985,714 70 690,000

www.mhhe.com/bkm

Crush 985,714 20 197,143

Dreck 2,957,142 NA* 690,000

Total $ 0 $ 0