91Ó°ÊÓ

Portfolio Expected Return You own a portfolio that is \(\mathbf{4 0}\) percent invested in stock \(\boldsymbol{X}, 35\) percent in stock \(Y\), and 25 percent in stock \(Z\). The expected returns on these three stocks are 11 percent, 17 percent, and 14 percent, respectively. What is the expected return on the portfolio?

Portfolio Expected Return You have \(\$ \mathbf{1 0 , 0 0 0}\) to invest in a stock portfolio. Your choices are stock \(X\) with an expected return of 16 percent and stock \(Y\) with an expected return of 10 percent. If your goal is to create a portfolio with an expected return of 12.9 percent, how much money will you invest in stock \(X\) ? In stock \(\boldsymbol{r}\) ?

Calculating Expected Returns A portfolio is invested 15 percent in stock \(G\), 65 percent in stock \(J\), and 20 percent in stock \(K\). The expected returns on these stocks are 8 percent, 15 percent, and 24 percent, respectively. What is the portfolio's expected return? How do you interpret your answer?

Calculating Portfolio Betas You own a portfolio equally invested in a risk- free asset and two stocks. If one of the stocks has a beta of 1.85 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

Using CAPM A stock has a beta of 1.25, the expected return on the market is 12 percent, and the risk-free rate is 5 percent. What must the expected return on this stock be?

Using CAPM A stock has a beta of .92 and an expected return of 10.3 percent. A risk-free asset currently earns 5 percent. 1\. What is the expected return on a portfolio that is equally invested in the two assets? 2\. If a portfolio of the two assets has a beta of \(\mathbf{5 0}\), what are the portfolio weights? 3\. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? 4\. If a portfolio of the two assets has a beta of 1.84, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.

Reward-to-Risk Ratios Stock \(Y\) has a beta of 1.35 and an expected return of 14 percent. Stock \(Z\) has a beta of .85 and an expected return of 11.5 percent. If the risk-free rate is 5.5 percent and the market risk premium is 6.8 percent, are these stocks correctly priced?

Portfolio Standard Deviation Security \(F\) has an expected return of 10 percent and a standard deviation of 26 percent per year. Security \(G\) has an expected return of 17 percent and a standard deviation of 58 percent per year. 1\. What is the expected return on a portfolio composed of 30 percent of security \(F\) and \(\mathbf{7 0}\) percent of security \(G\) ? 2\. If the correlation between the returns of security \(F\) and security \(G\) is .25, what is the standard deviation of the portfolio described in part (a)?

Portfolio Standard Deviation Suppose the expected returns and standard deviations of stocks \(\boldsymbol{A}\) and \(\boldsymbol{B}\) are \(\mathrm{E}\left(\boldsymbol{R}_A\right)=.13, \mathrm{E}\left(\boldsymbol{R}_{\boldsymbol{B}}\right)=.19, \sigma_A=.38\), and \(\sigma_B=.62\), respectively. 1\. Calculate the expected return and standard deviation of a portfolio that is composed of \(\mathbf{4 5}\) percent \(A\) and 55 percent \(B\) when the correlation between the returns on \(A\) and \(B\) is .5. 2\. Calculate the standard deviation of a portfolio that is composed of 40 percent \(A\) and 60 percent \(B\) when the correlation coefficient between the returns on \(A\) and \(B\) is -.5 . 3\. How does the correlation between the returns on \(\boldsymbol{A}\) and \(\boldsymbol{B}\) affect the standard deviation of the portfolio?

CML The market portfolio has an expected return of 12 percent and a standard deviation of 19 percent. The risk-free rate is 5 percent. 1\. What is the expected return on a well-diversified portfolio with a standard deviation of 7 percent? 2\. What is the standard deviation of a well-diversified portfolio with an expected return of 20 percent?