For Challenge Problems $27,28$ and $29$: You estimate that a passive portfolio, that is$,$ one invested in a risky portfolio that mimics the S&P $500$ stock index, yields an expected rate of return of $13\%$ with a standard deviation of $25\%.$ You manage an active portfolio with expected return $18\%$ and standard deviation $28\%.$ The risk$-$free rate is $8\%.$

Draw the CML and your funds' CAL on an expected return$-$standard deviation diagram.

a$.$ What is the slope of the CML$?$

b$.$ Characterize in one short paragraph the advantage of your fund over the passive fund.

$28.$ Your client ponders whether to switch the $70\%$ that is invested in your fund to the passite portfolio.

a$.$ Explain to your client the disadvantage of the switch.

b$.$ Show him the maximum fee you could charge $($as a percentage of the investment in your fund, deducted at the end of the year$)$ that would leave him at least as well off investing in your fund as in the passive one. $($Hint: The fee will lower the slope of his CAL by reducing the expected return net of the fee.$)$