For this question, you want to round up to two digits for the final answer. If the final answer is in

percentage form, round up to the nearest basis point.

Assume that the hypothetical investor has the following utility function

$U=E[r]-\frac{A}{2}$Var$(r)=E[r]-\frac{A}{2}{}^2$

There are two risky assets available. Their mean and variance are given by: $E[r^A]=5\%,{}_A=$

$15\%,E[r^B]=10\%,{}_B=28\%.$

Risk$-$free rate is given by $r^f=3\%.$

$($a$)$ What are the Sharpe ratios of $r^A$ and $r^B?$

$($b$)$ Assume that $A=1,$ calculate the utility index of $r^A,r^B,$ and $r^f.$ Which one gives the highest

utility score?

$($c$)$ Assume that $A=2,$ calculate the utility index of $r^A,r^B,$ and $r^f.$ Which one gives the highest

utility score?

$($d$)$ Assume that $A=5,$ calculate the utility index of $r^A,r^B,$ and $r^f.$ At $A=5,$ are $r^A$ and $r^B$

attractive as individual assets?