standard deviation ${}_p=15\%.$

can allocate

Bills $($risk $-$free$),$ client's wealth into a corporate bond fund, a greater than this number$).$ You

$($he following means and standard deviations: with then stock fund, and a U$.$S$.$ T$.$

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

Find the proportions $($weights$)$ the investor should allocate into the common stock fund $(w_5),$ the bond

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

desired target standard deviation ${}_P=15\%$

Hints:

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

B$)$ Next, find the expected return $E(R_{\text{r}\text{i}\text{s}\text{k}\text{y}}){}_{\text{r}\text{i}\text{s}\text{k}\text{y}}$ 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 ${}_p=15\%$ is achieved.

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