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 $24\%.$ You manage an active portfolio with expected return $17\%$ and standard

deviation $29\%.$ The risk$-$free rate is $8\%.$ Your client's degree of risk aversion is $A=2\mathrm{.}9.$

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

your answer to $2$ decimal places.$)$

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

Intermedlate colculations. Round your answer to $2$ decimal places.$)$