Exercise $\backslash$#$3($Slides $19-32$: Chapter $6$: Capital Allocation$)$

Consider a risky portfolio with an expected return of $\backslash (10\mathrm{.}5\backslash \%\backslash )$ and standard deviation of $\backslash (18\backslash \%\backslash ).$ Assume the risk$-$free rate is $\backslash (3\mathrm{.}5\backslash \%\backslash )$ and you have a risk aversion factor of $3.$

$($a$)$ Assuming you allocate $\backslash (80\backslash \%\backslash )$ in the risky portfolio and the remaining in the riskfree asset, compute the complete portfolio's Expected Return, Standard Deviation, and Sharpe Ratio.

$($b$)$ What percentages of your money must be invested in the risky portfolio and the risk$-$free asset, respectively, to form a portfolio with an expected return of $\backslash (8\backslash \%\backslash )?$

$($c$)$ What percentages of your money must be invested in the risky portfolio and the risk$-$free asset, respectively, to form a portfolio with a standard deviation of $\backslash (15\backslash \%\backslash )?$

$($d$)$ With risk aversion factor of $3,$ what percentages of your money must be invested in the risky portfolio and the risk$-$free asset, respectively, to maximize your utility function?