You manage a risky portfolio with expected rate of return of $12\%$ and standard deviation of $28\%.$ The T$-$bill rate is $2\%.$

Your client$$s degree of risk aversion is A $=3\mathrm{.}5.$

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?