Financial Applications of Random Matrix Theory: a short review

TL;DR

This paper reviews how Random Matrix Theory has been applied to finance, covering theoretical results and practical uses like portfolio optimization and risk estimation over the past decade.

Contribution

It provides a comprehensive overview of recent theoretical developments and their applications in financial markets, guiding future research in the field.

Findings

The Marcenko-Pastur spectrum is fundamental in financial data analysis.

Random Matrix Theory aids in improving portfolio optimization.

Eigenvalue statistics help in risk estimation.

Abstract

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum and its various generalisations, random SVD, free matrices, largest eigenvalue statistics, etc.) as well as some concrete applications to portfolio optimisation and out-of-sample risk estimation.