A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long$-$term bond fund, and the third is a money market fund that provides a safe return of $8\%.$ The characteristics of the risky funds are as follows:

Expected Return Standard Deviation

Stock fund $($S$)21\%28\%$

Bond fund $($B$)1218$

The correlation between the fund returns is $0\mathrm{.}9.$

Required:

a$-1.$ What are the investment proportions in the minimum$-$variance portfolio of the two risky funds?

a$-2.$ What are the expected value and standard deviation of the minimum$-$variance portfolio rate of return?