You are managing a mutual fund which reports an expected return of $15\%,$ a variance of$.0\mathrm{.}0784,$ and a beta of $1\mathrm{.}4.$ The current T$-$bill rate is $5\%$ and the S&P$500$ stock index $($as the market index$)$ reports an expected return of $10\%$ and a variance of $0\mathrm{.}04.$ If one of your investors decides to invest $80\%$ of her portfolio in your fund and the rest in a T$-$bill money market fund, what is the Treynor ratio of your client's portfolio?

A$.0\mathrm{.}116$

B$.0\mathrm{.}071$

C$.0\mathrm{.}356$

D$.0\mathrm{.}057$