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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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1 change: 1 addition & 0 deletions book/_config.yml
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Expand Up @@ -8,6 +8,7 @@ only_build_toc_files: true
parse:
myst_enable_extensions:
# for conversion of the maths
- amsmath
- dollarmath

# needed for plotly
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