Consider two stocks, A and B$.$ Expected returns on these stocks are:

$\frac{?}{\text{b}\text{a}\text{r}}(r{)}_A=10\mathrm{.}79\%\frac{,}{b}ar(r{)}_B=13\mathrm{.}80\%.$

Standard deviations of their returns are:

${}_A=21\mathrm{.}83\%,{}_B=34\mathrm{.}29\%.$

Returns on these two stocks are uncorrelated with each other. Use the above to answer the following $($A$)-($D$).$

Suppose the risk$-$free interest rate is $4\mathrm{.}03\%.$ If you were to form a portfolio of A and B only, with the expected

return of $15\mathrm{.}00\%,$ what would be the standard deviation of this portfolio's return?

$\%$ B$)$ What is the lowest possible standard deviation you can achieve by forming a portfolio of A and B only? C$)$ What is the highest Sharpe ratio $($in $\%)$ you can achieve using a portfolio of A and B only? D$)$Alice is a mean$-$variance optimizer. Her objective is to maximize the following function of the mean $()$ and the variance $()$ of her portfolio return:

What fraction of her portfolio $($in $\%)$ should Alice invest in the risk$-$free asset?