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$)15\%34\%$

Bond fund $($B$)9\%25\%$

The correlation between the fund returns is $0\mathrm{.}13.$

What is the expected return and standard deviation for the minimum$-$variance portfolio of the two risky funds? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. $($Do not round intermediate calculations and round your final answers to $2$ decimal places.$)$

What is the Sharpe ratio of the best feasible CAL? $($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$

Suppose now that your portfolio must yield an expected return of $12\%$ 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.$)$