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Expected Returns

Calculating Beta. Following are several months` rates of return for Tumblehome Canoe Company. Prepare a plot like Figure 4.7. What is Tumblehome`s beta?

Expected Returns. Consider the following two scenarios for the economy, and the returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.

a. Find the beta of each stock. In what way is stock D defensive?

b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.

c. If the T-bill rate is 4 percent, what does the CAPM say about the fair expected rate of return on the two stocks?

d. Which stock seems to be a better buy based on your answers to (a) through (c)?

12. CAPM and Cost of Capital. Draw the security market line when the Treasury bill rate is 10 percent and the market risk premium is 8 percent. What are the project costs of capital for new ventures with betas of .75 and 1.75? Which of the following capital investments have positive NPVs?

CAPM and Valuation. You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are: Based on the behavior of the firm`s stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 5 percent and that the expected rate of return on the market portfolio is 15 percent, what is the net present value of the project?

14. CAPM and Cost of Capital. Reconsider the project in the preceding problem. What is the project IRR? What is the cost of capital for the project? Does the accept Јreject decision using IRR agree with the decision using NPV?

15. CAPM and Valuation. A share of stock with a beta of .75 now sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4 percent, and the market risk premium is 8 percent. If the stock is perceived to be fairly priced today, what must be investors` expectation of the price of the stock at the end of the year?

16. CAPM and Expected Return. Reconsider the stock in the preceding problem. Suppose investors actually believe the stock will sell for $54 at year-end. Is the stock a good or bad buy? What will investors do? At what point will the stock reach an ¬equilibrium ­ at which it again is perceived as fairly priced?

17. Portfolio Risk and Return. Suppose that the S&P 500, with a beta of 1.0, has an expected return of 13 percent and T-bills provide a risk- free return of 5 percent.

a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .5; (iv) .75; (v) 1.0?

b. Based on your answer to (a), what is the trade-off between risk and return, that is, how does expected return vary with beta?

c. What does your answer to (b) have to do with the security market line relationship?

18. Portfolio Risk and Return. Suppose that the S&P 500, with a beta of 1.0, has an expected return of 15 percent and T-bills provide a risk- free return of 5 percent.

a. How would you construct a portfolio from these two assets with an expected return of 12 percent?

b. How would you construct a portfolio from these two assets with a beta of .4?

c. Show that the risk premiums of the portfolios in (a) and (b) are proportional to their betas.

19. CAPM and Valuation. You are considering the purchase of real estate which will provide perpetual income that should average $50,000 per year. How much will you pay for the property if you believe its market risk is the same as the market portfolio`s? The T-bill rate is 5 percent, and the expected market return is 12.5 percent.

20. Risk and Return. According to the CAPM, would the expected rate of return on a security with a beta less than zero be more or less than the risk-free interest rate? Why would in vestors be willing to invest in such a security? Hint: Look back to the auto and gold example.