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1

Sure. Your CAPM will tell you there's significant positive alpha in Tech and significant negative in Energy! Which makes total economic sense... Except do the same for the last 5 years excluding 2020; and you might/will get largely the same result. Tech boomed; and Energy sucked for years before Covid ;-) So if you're serious about measuring the Covid effect,...

5

This is the result of the Sherman-Morrison inversion for the sum of an invertible matrix and an outer product. You will find this (and many other helpful methods) in the Matrix Cookbook. Specifically, this is equation 160 on p 18:  \left(\boldsymbol{A}+\boldsymbol{bc}^T\right)^{-1}=\boldsymbol{A}^{-1}-\frac{\boldsymbol{A}^{-1}\boldsymbol{bc}^T\boldsymbol{A}...

1

Comparing 8.1 and 8.3 we see that $\sigma_p$ is replaced by $\rho_{jM}\sigma_j$. Importantly it is NOT replaced by $σ_j$ as hasty thinking might have led us to guess: "just replace $p$ by $j$ in the subscripts of 8.1 and it would still work, right?" No, that would be wrong. 8.3 shows that what matters for expected return is not $σ_j$, the ...

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