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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 probability distributions of the risky funds are:

Expected Return Standard Deviation

Stock fund $($S$)15\%36\%$

Bond fund $($B$)9\%27\%$

The correlation between the fund returns is $0\mathrm{.}15.$

Required:

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