A pension fund manager is considering the following three mutual funds,

i$.$ A risk$-$free money market fund with $8\%$ return,

ii$.$ a stock fund $($S$)$ with E$($RS$)=20\%$ and standard deviation $\backslash$sigma $[$E$($RS$)]=30\%,$

iii. a bond fund $($B$)$ with E$($RB$)=12\%$ and standard deviation $\backslash$sigma $[$E$($RB$)]=15\%,$

The correlation coefficient between the stock and bond funds is $\backslash$rho S$,$B$=0\mathrm{.}10$

A$.$ What are the investment proportions in the minimum$-$variance portfolio $($MVP$)$ of S and B and what are the expected return E$($Rp$)$ and the standard deviation $\backslash$sigma $[$E$($RP$)]$ of this MVP$?(4$ points$)$

B$.$ Tabulate and draw the investment opportunity set of the risky funds, S and B$.$ Use investment proportions for Stock fund of $0\%$ to $100\%$ in increments of $20\%.(4$ points$)$

C$.$ Draw a tangent from the risk$-$free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal portfolio? $(4$ points$)$

D$.$ Compute the weights of each asset and the expected return and the standard deviation of the optimal risky portfolio. $(4$ points$)$

E$.$ What is the Sharpe ratio of the best possible CAL? $(4$ points$)$