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 rate of $8\%.$ The probability distribution of the risky funds is as follows:

Expected Return, Standard Deviation

Stock Fund $($S$)$: $20\%,30\%$

Stock Fund $($B$)$ :$12\%,15\%$

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

a$.$ Draw a tangent line from the risk$-$free rate to the investment opportunity set. What does your graph roughly show for the expected return and standard deviation of the optimal portfolio?

$($ Show calculations $)$