diff --git a/README.md b/README.md index e9fdc366..5930950a 100644 --- a/README.md +++ b/README.md @@ -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 $\beta_{ji}$. @@ -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. diff --git a/book/_config.yml b/book/_config.yml index 31fe2db1..9a2a2796 100644 --- a/book/_config.yml +++ b/book/_config.yml @@ -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