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maths in book
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tschm committed Dec 17, 2024
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12 changes: 6 additions & 6 deletions README.md
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Expand Up @@ -80,9 +80,9 @@ We offer a `SampleCovariance` class as seen above.
Factor risk models use the projection of the weight vector into a lower
dimensional subspace, e.g. each asset is the linear combination of $k$ factors.

```math
$$
r_i = \sum_{j=1}^k f_j \beta_{ji} + \epsilon_i
```
$$

The factor time series are $f_1, \ldots, f_k$. The loadings are the coefficients
$\beta_{ji}$.
Expand All @@ -94,15 +94,15 @@ 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
$$
Var(r) = Var(\beta^T w) + Var(\epsilon w)
```
$$

We assume the residual returns are uncorrelated and hence

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

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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2 changes: 1 addition & 1 deletion book/_config.yml
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Expand Up @@ -13,7 +13,7 @@ parse:
# needed for plotly
sphinx:
config:
mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
mathjax_path: https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML
html_js_files:
- https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js

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