You manage a risky portfolio with an expected rate of return of $17\%$ and a standard deviation of $28\%.$ The T$-$bill rate is $7\%.$

Your client's degree of risk aversion is $A=2\mathrm{.}0.$

Required:

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

b$.$ What are the expected value and standard deviation of the rate of return on your client's optimized portfolio?