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:

The correlation between the fund returns is $.30.$

$($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?

$($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?