A Random Matrix Approach to Credit Risk

TL;DR

This paper uses Random Matrix Theory to analyze how correlations in credit portfolios impact diversification and loss distribution tails, revealing that even zero-mean correlations significantly affect risk estimates.

Contribution

It introduces a novel application of Random Matrix Theory to model correlation effects in credit risk, providing analytical bounds on loss distribution impacts.

Findings

Correlations limit diversification effects.

Correlations significantly alter loss distribution tails.

Randomly fluctuating correlations provide a lower bound for risk estimation.

Abstract

We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.