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CAPM and Expected Return

The following table shows betas for several companies. Calculate each stock`s expected rate of return using the CAPM. Assume the risk-free rate of interestis 5 percent. Use a 9 percent risk premium for the market portfolio.

CAPM and Expected Return. Stock A has a beta of .5 and investors expect it to return 5 percent. Stock B has a beta of 1.5 and investors expect it to return 13 percent. Use the CAPMto find the market risk premium and the expected rate of return on the market.

23. CAPM and Expected Return. If the expected rate of return on the market portfolio is 14 percent and T-bills yield 6 percent, what must be the beta of a stock that investors expect to return 10 percent?

24. Project Cost of Capital. Suppose General Mills is considering a new investment in the common stock of a publishing company. Which of the betas shown in the table in problem 21 is most relevant in determining the required rate of return for this venture? Explain why the expected return to General Mills stock is not the appropriate required return.

25. Risk and Return. True or false? Explain or qualify as necessary. a. The expected rate of return on an investment with a beta of 2 is twice as high as the expected rate of return of the market portfolio.

b. The contribution of a stock to the risk of a diversified portfolio depends on the market risk of the stock.

c. If a stock`s expected rate of return plots below the security market line, it is underpriced.

d. A diversified portfolio with a beta of 2 is twice as volatile as the market portfolio.

e. An undiversified portfolio with a beta of 2 is twice as volatile as the market portfolio.

26. CAPM and Expected Return. A mutual fund manager expects her portfolio to earn a rate of return of 12 percent this year. The beta of her portfolio is .8. If the rate of return available on risk-free assets is 5 percent and you expect the rate of return on the market portfolio to be 15 percent, should you invest in this mutual fund?

27. Required Rate of Return. Reconsider the mutual fund manager in the previous problem. Explain how you would use a stock index mutual fund and a risk-free position in Treasury bills (or a money market mutual fund) to create a portfolio with the same risk as the manager`s but with a higher expected rate of return. What is the rate of return on that portfolio?

28. Required Rate of Return. In view of your answer to the preceding problem, explain why a mutual fund must be able to provide an expected rate of return in excess of that predicted by the security market line for investors to consider the fund an attractive investment opportunity.

29. CAPM. We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, .2.

a. If the interest rate on Treasury bills is 5 percent and the expected return on the market portfolio is 15 percent, what is the expected return on the shares of the law firm according to the CAPM?

b. Suppose you invested 90 percent of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio?

30. Leverage and Portfolio Risk. Footnote 4 in the material asks you to consider a borrow-and invest strategy in which you use $1 million of your own money and borrow another $1 million to invest $2 million in a market index fund. If the risk-free interest rate is 4 percent and the expected rate of return on the market index fund is 12 percent, what is the risk premium and expected rate of return on the borrow-and-invest strategy? Why is the risk of this strategy twice that of simply investing your $1 million in the market index fund?

1 See Figure 4.16. Anchovy Queen`s beta is 1.0.

2 A portfolio`s beta is just a weighted average of the betas of the securities in the portfolio. In this case the weights are equal, since an equal amount is assumed invested in each of the stocks in Table 4.9. The average beta of these stocks is (1.07 + 1.14 + .88 + .61 + .97 + 1.30

+ .92 + 1.33 + 1.33 + 1.20)/10 = 1.07.

3 The standard deviation of a fully diversified portfolio`s return is proportional to its beta. The standard deviation in this case is .5 АГАз 20 = 10 percent.