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 sure rate of $5\mathrm{.}5\%.$ The correlation between the fund returns is $0\mathrm{.}15.$ The probability distributions of the risky funds are:

Expected Return Standard Deviation

Stock fund $($S$)15\%32\%$

Bond fund $($B$)9\%23\%$

$8.$ Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of $0\%$ to $100\%$ in increments of $20\%.$ What expected return and standard deviation? $9.$ Draw a tangent from the risk$-$free rate to the opportunity set.

What does your graph show for expected return and standard deviation of the optiman risk portfolio? $.$ What is the Sharpe ratio of the best feasible CAL? $11.$Suppose now that your portfolio must yield an expected return of $12\%$ and be efficient, that is$,$ 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?