$4)$ You form two risky portfolios A and B by investing in Stocks D$,$ E$,$ and F$.$

a$)$ You invest $1/4$ of your money in Stock D and $3/4$ in Stock E$.$ The correlation between Stock D and Stock E is $0\mathrm{.}2$ while the standard deviation of Stock D is $40\%$ and the standard deviation of Stock E is $20\%.$ Figure out the expected return and the standard deviation of the risky portfolio A$.($Please use the expected return of $13\%$ for Stock D and the average return of $9\%$ for Stock E$.)(35$points$)$

b$)$ You invest $2/3$ of your money in Stock E and $1/3$ in Stock F$.$ The covariance between Stock E and Stock F is $0\mathrm{.}008$ while the standard deviation of Stock E is $20\%$ and the standard deviation of Stock F is $25\%.$ Figure out the expected return and the standard deviation of the risky portfolio B$.($Please use the average return of $9\%$ for Stock E and $12\%$ for Stock F$.)(35$points$)$

C$)$ Given the risk$-$free rate of $4\%,$ figure out the Sharpe ratio for Portfolios A and B and choose a better portfolio. $(25$points$)$