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 $63 if the economy is in a recession, $83 if the economy is normal, and $96 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 .8 with the market portfolio. Stock B has an expected return of 13 percent, a standard deviation of 34 percent, a correlation with the market portfolio of .25, and a correlation with stock A of .48. 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)?
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