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$)20\%30\%$

Bond fund $($B$)1215$

The correlation between the fund returns is $0\mathrm{.}10.$

Tabulate the investment opportunity set of the two risky funds $($use a similar table as below$)$:

Proportion

in Stock Fund Proportion

in Bond Fund Expected

Return Standard

Deviation

$0\mathrm{.}00\%100\mathrm{.}00\%$

$17\mathrm{.}3982\mathrm{.}61$

$20\mathrm{.}0080\mathrm{.}00$

$40\mathrm{.}0060\mathrm{.}00$

$45\mathrm{.}1654\mathrm{.}84$

$60\mathrm{.}0040\mathrm{.}00$

$80\mathrm{.}0020\mathrm{.}00$

$100\mathrm{.}000\mathrm{.}00$

If the risk free rate is $8\%,$ what is the optimal risky portfolio $($the tangency portfolio, i$.$e$.$ what are its weights, return and variance$)?$

Portfolio invested in the stock

Portfolio invested in the bond

Expected return

Standard deviation

What is the minimum variance portfolio?

Plot the efficient frontier and the CML on a graph. Identify the minimum variance and the tangency portfolio on it$.$