Hidden Noise Structure and Random Matrix Models of Stock Correlations

TL;DR

This paper uncovers a new correlation structure in stock return noise linked to key market factors, introduces refined random matrix models, and highlights biases in traditional risk estimation methods.

Contribution

It reveals a novel noise correlation structure, develops advanced random matrix models incorporating heavy tails, and identifies biases in standard risk cleaning procedures.

Findings

Residual noise has a structured correlation linked to top factors

Noise band consists of multiple subbands that do not fully mix

Traditional risk estimation can be biased even in stationary conditions

Abstract

We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise band is composed of multiple subbands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering. We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription.