You survey a client and you conclude that this client$$s level of $$risk aversion$$ is commensurate with a target standard deviation $=15\%.($This means that the client would want to allocate funds into a portfolio with a standard deviation greater than this number$).$ You can allocate your client$$s wealth into a corporate bond fund, a common stock fund, and a U$.$S$.$ T$-$ Bills $($risk $-$free$),$ with the following means and standard deviations:

Bond fund $14\%$

Common stock $21\%$

U$.$S$.$ T$-$Bill $(5\%$

$20\%39\%0\%$

The correlation between the stock fund and the bond fund is $=0\mathrm{.}4.$

Find the proportions $($weights$)$ the investor should allocate into the common stock fund $($&$),$ the bond

fund $(),$ and the risk$-$free asset $)$ so that the investor achieves the maximum return given the $#

desired target standard deviation $=\%.$ Hints:

A$)$ First find the weights $$& and $$$ that form the optimal risky portfolio.

B$)$ Next, find the expected return $((")*+)(")*+$ and standard deviation of the optimal risky

portfolio you found in A$).$

C$)$ Finally, obtain what proportion should be assigned into the optimal risky portfolio in A$)$ and the

risk$-$free asset such that the target standard deviation $!=15\%$ is achieved.

D$)$ Now find the expected return and standard deviation of the final portfolio from C$).$