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Beta and CAPM A portfolio that combines the risk-free asset and the market portfolio has an expected return of 9 percent and a standard deviation of 13 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 12 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .45 correlation with the market portfolio and a standard deviation of \(\mathbf{4 0}\) percent?

Standard Deviation and Beta There are two stocks in the market, stock \(\boldsymbol{A}\) 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. 1\. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why? 2\. What are the expected return and standard deviation of a portfolio consisting of 70 percent of stock \(A\) and 30 percent of stock \(B\) ? 3\. What is the beta of the portfolio in part (b)?