You manage a risky portfolio with an expected rate of return of $19\%$ and a standard deviation of $31\%.$ The T$-$bill rate is $5\%.$

Your client$$s degree of risk aversion is A $=2\mathrm{.}8.$

Required:

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

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