Problem $6-19$

You manage a risky portfolio with an expected rate of return of $18\%$ and a standard deviation of $29\%.$ The T$-$bill rate is $5\%.$ Your client's degree of risk aversion is $A=2\mathrm{.}5,$ assuming a utility function $U=E(r)-\frac{1}{2}A{}^2.$

a$.$ What proportion, $y,$ of the total investment should be invested in your fund? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

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b$.$ What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

$\backslash$table$[[$Expected return,$\%],[$Standard deviation,$\%$