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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$)16\%40\%$

Bond fund $($B$)10\%31\%$

The correlation between the fund returns is $0\mathrm{.}12.$

Suppose now that your portfolio must yield an expected return of $13\%$ and be efficient, that is$,$ on the best feasible CAL.

Required:

a$.$ What is the standard deviation of your portfolio? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$-1.$ What is the proportion invested in the T$-$bill fund? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$-2.$ What is the proportion invested in each of the two risky funds? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$