Tag Info

When $x_i$ is the return of the $i$th asset, the returns of portfolio $\vec{w}$ are $\sum_i w_i x_i$. The covariance of the returns of two portfolios, $\vec{w}$ and $\vec{v}$ are then $$\sum_i \sum_j w_i v_j \operatorname{cov}\left(x_i, x_j\right).$$ Now note that $\Sigma_{i,j} = \operatorname{cov}\left(x_i,x_j\right)$. The rest is confirming that this ...