Suppose you are a fund manager, managing an active fund with an expected return of $14\%$ and a standard deviation of $20\%.$ The risk$-$free rate is $2\%.$

You are advising a risk averse client who has mean$-$variance preferences and would like to invest in a combination of the risk$-$free asset and your active fund. They currently have a passive portfolio with an expected return of $8\%$ and a standard deviation of $12\%.$ The sharpe ratios for the active fund and passive portfolio are $0\mathrm{.}6$ and $0\mathrm{.}5$ respectively. Using this information could you answer the question: What is the fee $($as a percentage of the investment in your fund$)$ you could charge your client to make them indifferent between investing in your active fund or the passive portfolio? $[10$ pts$/45$pts$]$