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 $14\%$ with a standard deviation of $26\%.$ You manage an active portfolio with expected return $17\%$ and standard deviation $20\%.$ The

risk$-$free rate is $5\%.$ Your client's degree of risk aversion is $A=2\mathrm{.}1.$

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

$\%$ per year