The following data apply to Problems $4$ through $10$: 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 $6\%.$

The probability distribution of the risky funds is as follows:

$*Tableat$ picture.

The correlation between the fund returns is $0\mathrm{.}13.$

$4.$ 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?

$5.$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 $20\%.$

$6.$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?

$7.$Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky porfolio.

$8.$What is the Sharpe ratio of the best feasible CAL?

$9.$You require that your portfolio yields an expected return of $11\%,$ and that it be efficient, on the

best feasible CAL.

a$.$ What is the standard deviation of your portfolio?

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

$10.$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 porffolio? Compare its standard deviation to that of

the optimized portfolio in Problem $9.$ What do you conclude?