You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of $10\%$ and a standard deviation of $16\%.$ The other is a fund that is actively managed by your broker. This fund has an expected return of $16\%$ and a standard deviation of $20\%.$ The risk$-$free rate is currently $7\%.$ What is the maximum fee your broker could charge and still leave you as well off as if you had invested in the passive market fund? $($Assume that the fee would be a percentage of the investment in the broker's fund, and would be deducted at the end of the year.$)$