Statistical Risk Models

TL;DR

This paper provides algorithms and source code for constructing statistical risk models, including methods for fixing the number of risk factors using eRank, and efficient eigen decomposition of covariance matrices, aimed at practical applications.

Contribution

It introduces complete algorithms and source code for statistical risk modeling, notably a non-iterative eigen decomposition method and eRank-based risk factor determination.

Findings

eRank method yields results similar to previous approaches

Eigen decomposition algorithm is computationally efficient with linear complexity

Algorithms are designed for practical, pedagogical use

Abstract

We give complete algorithms and source code for constructing statistical risk models, including methods for fixing the number of risk factors. One such method is based on eRank (effective rank) and yields results similar to (and further validates) the method set forth in an earlier paper by one of us. We also give a complete algorithm and source code for computing eigenvectors and eigenvalues of a sample covariance matrix which requires i) no costly iterations and ii) the number of operations linear in the number of returns. The presentation is intended to be pedagogical and oriented toward practical applications.