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# Capital Asset Pricing Model Questions

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Consider the following information:

Stock A Stock B T-bills
Beta 0.6 1.2 0.0
Expected return, % 5.0 8.0 2.0

(a) Assuming that all stocks are priced correctly according to the CAPM, compute the expected return on the market portfolio.

(c) Is it possible for a stock to have a negative standard deviation in returns? Explain.

(d) Consider two separate stocks: the returns on the stock of AppleCo have a standard deviation of 32% and a beta of 0.9; the returns on the stock of BananaCo have a standard deviation of 20% and a beta of 1.2. Which company's stock should provide a greater return to investors? Why?

All work and formulas are needed to understand the logic behind. Thank you!

#### Solution Summary

The article addresses common introductory finance questions regarding the Capital Asset Pricing Model, Sharpe Ratios, and expected returns of stocks.

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## Investments: Expected return, volatility, beta and risk premium, PV of cash flow, hedge

1. Compute the expected return and volatility of return for a portfolio that has a portfolio share of 0.9 in the S&P 500 and 0.1 in an emerging market index. The S&P 500 has a volatility of return of 15 percent and an expected return of 12 percent. The emerging market has a return volatility of 30 percent and an expected return of 10 percent. The correlation between the emerging market index return and the S&P 500 is 0.1.

2. If the S&P 500 is a good proxy for the market portfolio in the CAPM, and the CAPM applies to the emerging market index, use the information in previous question to compute the beta and risk premium for emerging market index.

3. A firm has an expected cash flow of \$500 million in one year. The beta of the common stock of the firm is 0.8 and this cash flow has the same risk as the firm as a whole. Using a risk-free rate of 5 percent and a risk premium on the market portfolio of 6 percent, what is the present value of the cash flow? If the beta of the firm doubles, what happens to the present value of the cash flow?

4. Using the data in the previous question, consider how hedging the cash flow against systematic risk might affect the firm. If management wants to eliminate the systematic risk of the cash flow completely, how could it do so? How much would the firm have to pay investors to bear the systematic risk of the cash flow?

5. Consider problem 3. To hedge the firm's systematic risk, management has to pay investors to bear this risk. Why is it that the value of the firm for shareholders does not fall when the firm pays other investors to bear the cash flow's systematic risk?

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