$2.$ 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 $5\%.$ The probability distribution of the risky funds is as follows:

Expected Return Stock Fund $($S$)8\%$

Bond Fund $($B$)13\%$

The correlation between the fund returns is $\mathrm{.}30.$

Standard deviation $12\%$

$20\%$

$($a$)$ First, tabulate $($i$.$e$.,$ draw a table$)$ the investment opportunity set using invest$-$ ment proportions for the stock fund of zero to $100\%$ in increments of $20\%.$ Then, draw the investment opportunity set of the two risky funds.

$($b$)$ Show all the M$-$V efficient investment strategies on your graph.

$($c$)$ Draw a tangent from the risk$-$free rate to the opportunity set. What does your graph show approximately for the optimal portfolio$$s expected return and standard deviation?

$1$

$($d$)$ The tangency portfolio yields a return of $11\%$ and a std dev of $14\mathrm{.}2\%.$ What are the weights of stock and bond funds in the tangency portfolio?

$($e$)$ Calculate the Sharpe Ratio of the CAL that crosses from the tangency line.

$($f$)$ You require that your complete portfolio yield an expected return of $17\mathrm{.}7\%,$ and that it be efficient.

i$.$ What is the standard deviation of your portfolio?

ii$.$ What is the proportion of your total money invested in the T$-$bill fund and

each of the risky funds?