New answers tagged statistical-finance
1
The variance of the portfolio is $$ V_p=\sum_i \sum_j w_i w_j Cov(r_i,r_j)$$
because of the properties of $Cov(\cdot,\cdot)$ we can rewrite this as $$ V_p=\sum_i w_i Cov(r_i,\underbrace{\sum_j w_j r_j}_{R_P})$$ where $R_p$ is the return on the portfolio. So we have
$$ V_p=\sum_i w_i Cov(r_i,R_p)$$ QED
(And it is true of every portfolio, not just the ...
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