Signal and Noise in Financial Correlation Matrices

TL;DR

This paper applies Random Matrix Theory to analyze financial correlation matrices, demonstrating that meaningful correlations can be identified even within the 'random' spectrum, impacting portfolio optimization strategies.

Contribution

It introduces a method to distinguish true correlations from noise in financial data using eigenvalue spectrum analysis based on Random Matrix Theory.

Findings

Correlations can be measured in the 'random' part of the spectrum.

Eigenvalue spectrum analysis reveals meaningful information in financial correlation matrices.

Implications for improving portfolio optimization by accounting for noise in correlation estimates.

Abstract

Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to analyze a particular case of the correlations in financial series and to show that contrary to earlier claims, correlations can be measured also in the ``random'' part of the spectrum. Implications for the portfolio optimization are briefly discussed.