Question $2(25$ points$)$ Assume there are initially only two assets in which to invest, A and B$.$ Further assume no shortsale restrictions and that short$-$sale proceeds can be used to invest. The expected return of the market portfolio is given below. Market Portfolio Expected return rate $\backslash (=14\backslash \%\backslash )$ The expected return and standard deviation of return of asset $\backslash ($ A $\backslash )$ and asset $\backslash ($ B $\backslash )$ are as follows: Asset A Expected return rate $\backslash (=18\backslash \%,\backslash$sigma$=0\mathrm{.}10\backslash )$ Asset B Expected return rate $\backslash (=12\backslash \%,\backslash$sigma$=0\mathrm{.}06\backslash )$ Assume that correlation coefficient between the returns of assets $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ is $-0\mathrm{.}75,$ i$.$e$.,\backslash (\backslash$rho$\_\{$A B$\}=-\backslash )0\mathrm{.}75.($a$)(5$ points$)$ What is the composition of the market portfolio? That is$,$ determine the weight of asset A and asset B in the market portfolio. $($b$)(5$ points$)$ What is standard deviation of return of the market portfolio? $($c$)(5$ points$)$ What is the Sharpe ratio of the market portfolio if the risk$-$free rate is $\backslash (4\backslash \%\backslash )?($d$)(5$ points$)$ Assuming that the risk$-$free rate as well as the borrowing rate is $\backslash (4\backslash \%\backslash ),$ a client, with total wealth $\backslash (\backslash$$ $100,000\backslash ),$ wants a portfolio with an expected return of $\backslash (20\backslash \%\backslash ).$ How could you achieve the client's objective using the market portfolio? $($e$)(5$ points$)$ What is the standard deviation of the portfolio created in part $($d$)?$