Problem $2.$ Your uncle, has asked you for some financial advice. His retirement savings are currently invested as follows: $$20,000$ in the riskless asset, $$40,000$ in GM stock and $$40,000$ in Microsoft stock. He wants to know if this is a sensible portfolio. You decide to analyze it based on the CAPM model.

You look in a Beta Book and find that GM stock has a Beta of $1\mathrm{.}1$ and the $R^2$ of the regression is $0\mathrm{.}40.$ Microsoft stock has a Beta of $0\mathrm{.}8$ and the $R^2$ of the regression is $0\mathrm{.}30.$ Suppose further that the correlation between the return to GM stock and the return to Microsoft stock is $0\mathrm{.}3.$

If $r_f$ is $4\%$ and the expected excess return on the market $E(r_M)-r_f$ is $6\%,$ what is the expected return on his portfolio?

If the market return has a standard deviation of $20\%,$ compute the variance and standard deviation of his current portfolio. $($Hint: use the information in the $R^2$ values to calculate the standard deviation of each stock return. Then use the information about the correlations between the two stock returns to calculate the portfolio standard deviation.$)$Assuming that the CAPM is correct, find an efficient portfolio consisting of the riskless asset and the market portfolio that has the same return standard deviation as your Uncle's current portfolio. What is the expected return on this portfolio? How does it compare to the expected return of his current portfolio?