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:

The correlation between the fund returns is $\mathrm{.}15.$ Stock Fund $($s$)$ Expected Return is $15\%$ and Standard Deviation is $32\%$ Stock Fund $($B$)$ Expected Return is $9\%$ and Standard Deviation is $23\%$

$1.$ Tabulate and draw the investment opportunity set of the two risky funds. Use investment

proportions for the stock fund of $0\%$ to $100\%$ in increments of $20\%.$ What expected return

and standard deviation does your graph show for the minimum$-$variance portfolio?

$2.$ What is the reward$-$to$-$volatility ratio of the best feasible CAL?

$3.$ Suppose now that your portfolio must yield an expected return of $12\%$ and be efficient,

that is$,$ on the best feasible CAL.

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

b$.$ What is the proportion invested in the T$-$bill fund and each of the two risky funds

$4.$ If you were to use only the two risky funds and still require an expected return of $12\%,$

what would be the investment proportions of your portfolio? Compare its standard

deviation to that of the optimal portfolio in the previous problem. What do you conclude?