$2.)$ Consider the expected returns, standard deviations, Sharpe ratios, and correlation matrix for three stocks:

$\backslash$table$[[,,,$Correlation Matrix ${}_{ij},],[$Stock$,E(R_i),{}_i,$Stock $1,$Stock $2,$Stock $3,$Sharpe$],[1,0\mathrm{.}13,0\mathrm{.}21,1\mathrm{.}00,0\mathrm{.}10,0\mathrm{.}35,0\mathrm{.}476],[2,0\mathrm{.}16,0\mathrm{.}22,0\mathrm{.}10,1\mathrm{.}00,0\mathrm{.}72,0\mathrm{.}591],[3,0\mathrm{.}24,0\mathrm{.}59,0\mathrm{.}35,0\mathrm{.}72,1\mathrm{.}00,0\mathrm{.}356]]$

Use the Solver function in Excel to find the portfolio weights, portfolio expected return $E(r_P),$ portfolio standard deviation ${}_P,$ and Sharpe ratio for the following optimal portfolios:

a$.)$ The risky asset portfolio that minimizes standard deviation for a target expected return of $18\%.$ Do not constrain short$-$sales.

b$.)$ The risky asset portfolio that maximizes the Sharpe ratio, $\frac{E(r_P)-r_f}{{}_P}.$ Do not constrain short sales. Assume a risk$-$free rate of $3\%.$