You estimate that a passive portfolio, for example, one invested in a risky portfolio that mimics the S&P $500$

stock index, offers an expected rate of return of $12\%$ with a standard deviation of $28\%.$ You manage an

active portfolio with expected return $17\%$ and standard deviation $38\%.$ The risk$-$free rate is $6\%.$ Your client's

degree of risk aversion is $A=3\mathrm{.}0.$

a$.$ If he chose to invest in the passive portfolio, what proportion, $y,$ would he select? $($Do not round

intermediate calculations. Round your answer to $2$ decimal places.$)$

Proportion of $y$

b$.$ What is the fee $($percentage of the investment in your fund, deducted at the end of the year$)$ that you can

charge to make the client indifferent between your fund and the passive strategy affected by his capital

allocation decision $($i$.$e$.,$ his choice of $y)?($Do not round intermediate calculations. Round your answer to $2$

decimal places.$)$

Fee

$3\mathrm{.}02\%$ per year