Suppose you manage an equity fund with the following securities$.$ Use the following data to help build an optimal risky portfolio deploying the Treynor$-$Black Model.

$\backslash$table$[[$Input Data,$\backslash$table$[[$Vought$],[$International$]],$LexCorp,$\backslash$table$[[$Hammer$],[$Industries$]],\backslash$table$[[$Roxxon$],[$Energy$]]],[$Alpha$,1\mathrm{.}20\%,0\mathrm{.}60\%,1\mathrm{.}60\%,2\mathrm{.}50\%],[$Beta$,0\mathrm{.}877,1\mathrm{.}015,1\mathrm{.}63,1\mathrm{.}25],[$Residual Standard Deviation,$21\mathrm{.}70\%,14\mathrm{.}80\%,21\mathrm{.}30\%,25\mathrm{.}70\%],[,,,,],[$Market Data,,,,$],[$Expected Return,S&P $500,$Treasury Bills,,$],[$Standard Deviation,$12\mathrm{.}00\%,3\mathrm{.}00\%,,],[,24\mathrm{.}00\%,0\mathrm{.}00\%,,],[$Required:$,,,,],[$Note: Use cells A$2$ to C$11$ from the given information to complete this question.,,,,$]]$

Using the information in the table above, using the Treynor$-$Black model, please take all necessary steps to create an optim portfolio, including discovering initial individual weights and the beta$-$adjusted active portfolio weight. Then, calculate the premium and variance of the optimal risky portofolio.

$\backslash$table$[[$Active Positions,$\backslash$table$[[$Vought$],[$International$]],$LexCorp,$\backslash$table$[[$Hammer$],[$Industries$]],\backslash$table$[[$Roxxon$],[$Energy$]]],[$Initial Position $($Not Scaled$),,,,],[$Scaled Initial Position,,,,$]]$