Assume that you manage a risky portfolio with an expected rate of return of $18\%$ and a standard deviation of $28\%.$ The T$-$bill rate is $8\%.$ Your client$$s degree of risk aversion is A $=3\mathrm{.}5,$ assuming a utility function U $=$ E$($r$)-(1)/(2)$A$\backslash$sigma $^2.$

a$)$ What proportion, y$,$ of the total investment should be invested in your fund?

b$)$ What is the expected value and standard deviation of the rate of return on your client$$s optimized portfolio?