Standard Deviation and Beta There are two stocks in the market, Stock A and Stock B . The price of Stock A today is $75. The price of Stock A next year will be

$64 if the economy is in a recession, $87 if the economy is normal, and $97 if the economy is expanding. The probabilities of recession, normal times, and expansion are .2, .6, and .2, respectively. Stock A pays no dividends and has a correlation of .7 with the market portfolio. Stock B has an expected return of 14 percent, a standard deviation of 34 percent, a correlation with the market portfolio of .24, and a correlation with Stock A of .36. The market portfolio has a standard deviation of 18 percent. Assume the CAPM holds.

a. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why?

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 ?

c. What is the beta of the portfolio in part (b)?