$1.$ Consider the following securities:

Risky security: E$($R$)=20\%$ and $\backslash$sigma $=20\%.$

Risk$-$free security: Rf $=15\%,$ which is also the borrowing rate.

You want to construct a portfolio combining the risky security and the risk$-$free security to get an expected return of $25\%.$

$($a$)$ What weights would you need to put in the risky and the risk$-$free securities to earn an expected return of $25\%?$

$($b$)$ What is the standard deviation of this portfolio?

$($c$)$ What is the reward$-$to$-$variability ratio?

$($d$)$ Draw the capital allocation line $($CAL$).$ Label the points and the axes clearly.