Q#$9.[20$ Points$]$ A pension fund manager is considering three mutual funds. The first is a stock

fund, the second is a long$-$term government and corporate bond fund, and the third is a T$-$bil

money market fund that yields a rate of $8\%.$ The correlation between the fund returns is $\mathrm{.}10.$ The

probability distribution of the risky funds is as follows:

A$.$ What are the investment proportions in the minimum$-$variance portfolio of the two risky

funds, and what is the expected value and standard deviation of its rate of return?

B$.$ Tabulate and draw the investment opportunity set of the two risky funds. Use

investment proportions for the stock fund of zero to $100\%$ in increments of $20\%.$

C$.$ Draw a tangent from the risk$-$free rate to the opportunity set. What does your graph

show for the expected return and standard deviation of the optimal portfolio?

D$.$ Solve numerically for the proportions of each asset and for the expected return and

standard deviation of the optimal risky portfolio.

E$.$ What is the Sharpe ratio of the best feasible CAL?

F$.$ You require that your portfolio yield an expected return of $14\%,$ and that it be efficient,

on the best feasible CAL.

What is the standard deviation of your portfolio?

What is the proportion invested in the T$-$bill fund and each of the two risky

funds?

G$.$ If you were to use only the two risky funds, and still require an expected return of $14\%,$

what would be the investment proportions of your portfolio? Compare its standard

deviation to that of the optimized portfolio in Problem F$.$ What do you conclude?