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maths in book
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tschm committed Dec 17, 2024
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Expand Up @@ -92,15 +92,11 @@ factor space. The variance for a position $w$ is the sum of the variance of the
systematic returns explained by the factors and the variance of the
idiosyncratic returns.

```math
Var(r) = Var(\beta^T w) + Var(\epsilon w)
```
$$Var(r) = Var(\beta^T w) + Var(\epsilon w)$$

We assume the residual returns are uncorrelated and hence

```math
Var(r) = y^T \Sigma_f y + \sum_i w_i^2 Var(\epsilon_i)
```
$$Var(r) = y^T \Sigma_f y + \sum_i w_i^2 Var(\epsilon_i)$$

where $\Sigma_f$ is the covariance matrix of the factors and $Var(\epsilon_i)$
is the variance of the idiosyncratic returns.
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