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?