The Dispersion Bias

TL;DR

This paper identifies a bias in the estimation of eigenvectors of financial covariance matrices that affects portfolio risk assessment and proposes a novel correction method with theoretical guarantees.

Contribution

It introduces a new eigenvector bias correction method that improves covariance matrix eigenvector estimation beyond existing regularization techniques.

Findings

Bias distorts minimum variance portfolio weights

Risk forecasts are severely underestimated without correction

The proposed method improves eigenvector estimation accuracy

Abstract

Estimation error has plagued quantitative finance since Harry Markowitz launched modern portfolio theory in 1952. Using random matrix theory, we characterize a source of bias in the sample eigenvectors of financial covariance matrices. Unchecked, the bias distorts weights of minimum variance portfolios and leads to risk forecasts that are severely biased downward. To address these issues, we develop an eigenvector bias correction. Our approach is distinct from the regularization and eigenvalue shrinkage methods found in the literature. We provide theoretical guarantees on the improvement our correction provides as well as estimation methods for computing the optimal correction from data.