$4-$ The following data apply to Problems $4.$a through $4.$g: 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$-$bill money market fund that yields a rate of $8\%.$

The probability distribution of the risky funds is as follows: $(3$ Points$)$

The correlation between the fund returns is $\mathrm{.}10.$

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.

f$\mathrm{.}1.$ What is the standard deviation of your portfolio?

f$\mathrm{.}2.$ 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?