Using the special case of two stocks, and the equation down below,

explain in detail how you could get the graph $($next page on the righ$-$hand side$),$ where the correlation is negative $1.$

Show all your work $($equations$,$ and relevant explanations$).$

$\backslash$sigma $\_($p$)^(2)=$w$\_($A$)^(2)\backslash$sigma $\_($A$)^(2)+$w$\_($B$)^(2)\backslash$sigma $\_($B$)^(2)+2$w$\_($A$)$w$\_($B$)\backslash$sigma $\_($A$,$B$)$

The general equation for many stock portfolio

Portfolio Variance $=\backslash$sum$\_($i$=1)^$N $\backslash$sum$\_($j$=1)^$N w$\_($i$)$w$\_($j$)\backslash$sigma $\_($i$,$j$)$

W$\_($i$)$ is the weight of asset i in the portfolio

$($same for j$).$

$\backslash$sigma $\_($i$,$j$)$ is the covariance between assets i and j$.$

For a two$-$asset portfolio, this formula is:Risk vs$.$ return for Feasible Portfolios $r_p$

vs$.{}_P$Risk vs$.$ return for Feasible Portfolios $r_p$

$vs.{}_P$

Case $1$: ${}_{AB}=+1$

Case $2$: ${}_{AB}=0$

Case $3$: ${}_{AB}=-1$

Actual Efficient Frontier