$(1)$ Ms$.$ Johns manages a mutual fund. Her fund has an annual standard deviation of $15\%.$ Her

competitor is running a mutual fund with an expected return of $8\%$ and an annual standard

deviation of $10\%.$ The risk$-$free rate is $2\%.$ What should her expected return be if she would like

to outperform her competitor according the Sharpe ratio? $($use Excel$)$

$(2)$ Thomas manages an investment firm. His firm's investments have beta of $0\mathrm{.}7.$ The market

risk premium is $6\%,$ and the risk$-$free rate in the economy is $2\%.$ Thomas presents you the

following offer: "Let me manage your portfolio and I'll provide an annual return of $7\%($this

return is gross, i$.$e$.,$ before management fees$).$ I'll only charge management fees of $1\%."$ Would

you take his investment offer? $(6$ pts$)$