Assume that a risky portfolio has an expected return of $15\%$ and standard deviation of $20\%,$ whereas the risk$-$free asset has a return of $5\%.$ Further, suppose that the borrowing rate that your client faces is $10\%.$ Also, suppose your client has a risk$-$ aversion parameter, A $=4.$

$($a$)$ Draw the CAL.

$($b$)$ What is the reward$-$to$-$volatility ratio in the lending range? What is the reward$-$ to$-$volatility ratio in the borrowing range? Which one is higher, and why?

$($c$)$ Suppose your client initially has all her money invested in a risk$-$free asset. What is the required rate of return for her to stay on the same indifference curve while taking on an investment with a standard deviation of $15\%?$

$($d$)$ Draw the indifference curve where U $=0\mathrm{.}1$ for this investor. Label at least $3$ points on the indifference curve.

$($e$)$ What is the optimal capital allocation to the risky asset for this investor?