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There are two stocks in the market, Stock A and Stock B. The price of Stock A today is $81. The price of Stock A next year will be $70 if the economy is in a recession, $93 if the economy is normal, and $103 if the economy is expanding. The probabilities of recession, normal times, and expansion are .26, .54, and .20, respectively. Stock A pays no dividends and has a correlation of .76 with the market portfolio. Stock B has an expected return of 14.6 percent, a standard deviation of 34.6 percent, a correlation with the market portfolio of .30, and a correlation with Stock A of .42. The market portfolio has a standard deviation of 18.6 percent. Assume the CAPM holds.
Problem (a) If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why?
Problem (b) What are the expected return and standard deviation of a portfolio consisting of 70 percent of Stock A and 30 percent of Stock B?
Problem (c) What is the beta of the portfolio in part (b)? How would you expect this portfolio's rate of return to change if the overall market rose by an extra 7%?
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