146 Berk/DeMarzo ? Corporate Finance, Second Edition
If risk were eliminated by holding stocks for 20 years, you would expect to find similar returns for all four periods, which you do not.
10-27. What is an efficient portfolio?
An efficient portfolio is any portfolio that only contains systemic risk; it contains no diversifiable risk.
10-28. What does the beta of a stock measure?
Beta measures the amount of systemic risk in a stock
10-29. You turn on the news and find out the stock market has gone up 10%. Based on the data in
Table 10.6, by how much do you expect each of the following stocks to have gone up or down: (1) Starbucks, (2) Tiffany & Co., (3) Hershey, and (4) Exxon Mobil.
Beta*10% Starbucks 10.4% Tiffany & Co. 16.4% Hershey 1.9% Exxon Mobil 5.6%
10-30. Based on the data in Table 10.6, estimate which of the following investments do you expect to
lose the most in the event of a severe market down turn: (1) A $1000 investment in eBay, (2) a $5000 investment in Abbott Laboratories, or (3) a $2500 investment in Walt Disney.
For each 10% market decline, eBay down 10%*1.93 = 19.3%, 19.3% × 1000 = $193 loss; Abbott down 10%*.18 = 1.8%, 1.8% × 5000 = $90 loss; Disney down 10%*.96 = 9.6%, 9.6% × 2500 = $240 loss; Disney investment will lose most.
10-31. Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%.
a. Calculate the beta of a firm that goes up on average by 43% when the market goes up and
goes down by 17% when the market goes down. b. Calculate the beta of a firm that goes up on average by 18% when the market goes down and
goes down by 22% when the market goes up. c. Calculate the beta of a firm that is expected to go up by 4% independently of the market. a.
Beta?43???17?60? Stock???1.5
? Market30???10?40b. Beta?? Stock?18?22?40????1
? Market30???10?40c. A firm that moves independently has no systemic risk so Beta = 0
?2011 Pearson Education
Berk/DeMarzo ? Corporate Finance, Second Edition 147
10-32. Suppose the risk-free interest rate is 4%.
a. i. Use the beta you calculated for the stock in Problem 31(a) to estimate its expected return.
ii. How does this compare with the stock’s actual expected return?
b. i. Use the beta you calculated for the stock in Problem 31(b) to estimate its expected return.
ii. How does this compare with the stock’s actual expected return? a. E[RM] = ? (30%) + ? (–10%) = 10%
i.. E[R] = 4% + 1.5 (10% – 4%) = 13% ii. Actual Expected return = (43% – 17%) / 2 = 13% ii. Actual l expected Return = (–22% + 18%) / 2 = –2%
b. i. . E[R] = 4% – 1(10% – 4%) = -2%
10-33. Suppose the market risk premium is 5% and the risk-free interest rate is 4%. Using the data in
Table 10.6, calculate the expected return of investing in
a. Starbucks’ stock. b. Hershey’s stock. c. Autodesk’s stock. a. 4%+1.04 × 5% = 9.2% b. 4% + 0.19 × 5% = 4.95% c. 4% + 2.31 × 5% = 15.55%
10-34. Given the results to Problem 33, why don’t all investors hold Autodesk’s stock rather than Hershey’s stock?
Hershey’s stock has less market risk, so investors don’t need as high an expected return to hold it. Hershey’s stock will perform much better in a market downturn.
10-35. Suppose the market risk premium is 6.5% and the risk-free interest rate is 5%. Calculate the
cost of capital of investing in a project with a beta of 1.2.
Cost of Capital?rf???E?Rm??rf??5?1.2?6.5??12.8%
10-36. State whether each of the following is inconsistent with an efficient capital market, the CAPM, or
both:
a. A security with only diversifiable risk has an expected return that exceeds the risk-free
interest rate. b. A security with a beta of 1 had a return last year of 15% when the market had a return of
9%. c. Small stocks with a beta of 1.5 tend to have higher returns on average than large stocks with
a beta of 1.5. a. This statement is inconsistent with both. b. This statement is consistent with both.
c. This statement is inconsistent with the CAPM but not necessarily with efficient capital markets.
?2011 Pearson Education
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