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Diversifiable Risk

Risk and Return. True or false? Explain or qualify as necessary.

a. Investors demand higher expected rates of return on stocks with more variable rates of return.

b. The capital asset pricing model predicts that a security with a beta of zero will provide an expected return of zero.

c. An investor who puts $10,000 in Treasury bills and $20,000 in the market portfolio will have a portfolio beta of 2.0.

d. Investors demand higher expected rates of return from stocks with returns that are highly exposed to macroeconomic changes.

e. Investors demand higher expected rates of return from stocks with returns that are very sensitive to fluctuations in the stock market.

2. Diversifiable Risk. In light of what you`ve learned about market versus diversifiable (unique) risks, explain why an insurance company has no problem in selling life insurance to individuals but is reluctant to issue policies insuring against flood damage to residents of coastal areas. Why don`t the insurance companies simply charge coastal residents a premium that reflects the actuarial probability of damage from hurricanes and other storms?

3. Unique vs. Market Risk. Figure 4.14 plots monthly rates of return from 1993 to 1999 for the Snake Oil mutual fund. Was this fund well-diversified? Explain.

4. Risk and Return. Suppose that the risk premium on stocks and other securities did in fact rise with total risk (that is, the variability of returns) rather than just market risk. Explain how investors could exploit the situation to create portfolios with high expected rates of return but low levels of risk.

5. CAPM and Hurdle Rates. A project under consideration has an internal rate of return of 14 percent and a beta of .6. The risk-free rate is 5 percent and the expected rate of return on the market portfolio is 14 percent.

a. Should the project be accepted?

b. Should the project be accepted if its beta is 1.6?

c. Why does your answer change?

6. CAPM and Valuation. You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those cash flows are uncertain.

a. Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-free rate is 5 percent and the expected rate of return on the market portfolio is 15 percent?

b. By how much will you overvalue the firm if its beta is actually .6?

7. CAPM and Expected Return. If the risk-free rate is 6 percent and the expected rate of return on the market portfolio is 14 percent, is a security with a beta of 1.25 and an expected rate of return of 16 percent overpriced or underpriced?

8. Using Beta. Investors expect the market rate of return this year to be 14 percent. A stock with a beta of .8 has an expected rate of return of 12 percent. If the market return this year turns out to be 10 percent, what is your best guess as to the rate of return on the stock?

9. Unique vs. Market Risk. Figure 4.15 shows plots of monthly rates of return on three stocks versus the stock market index. The beta and standard deviation of each stock is given beside its plot.

a. Which stock is riskiest to a diversified investor?

b. Which stock is riskiest to an undiversified investor who puts all her funds in one of these stocks?

Consider a portfolio with equal investments in each stock. What would this portfolio`s beta have been?

d. Consider a well-diversified portfolio made up of stocks with the same beta as Exxon What are the beta and standard deviation of this portfolio`s return? The standard deviation of the market portfolio`s return is 20 percent.

e. What is the expected rate of return on each stock? Use the capital asset pricing model with a market risk premium of 8 percent. The risk-free rate of interest is 4 percent.