A pension fund manager is considering three mutual funds. The rst is a stock fund,

the second is a long$-$term government and corporate bond fund, and the third is a short$-$

term money market fund that yields a rate of $8\%.$ The probability distribution of the risky

funds is as follows:

Expected Return Standard Deviation

Stock fund $($S$)20\%30\%$

Bond fund $($B$)12\%15\%$

The correlation between the fund returns is $0\mathrm{.}10.$

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?