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$)15\%32\%$

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

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

Required:

a$.$ What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of $12\%?$

b$.$ Calculate the standard deviation of the portfolio which yields an expected return of $12\%.$