A Robust Statistics Approach to Minimum Variance Portfolio Optimization

TL;DR

This paper introduces a robust portfolio optimization method that combines Tyler's M-estimator and Ledoit-Wolf's shrinkage estimator, improving risk estimation accuracy for large, heavy-tailed financial datasets.

Contribution

It develops a new hybrid covariance estimator and a consistent risk estimator using random matrix theory, enhancing portfolio optimization under heavy-tailed distributions.

Findings

Outperforms existing methods on synthetic data

Effective with real market data

Handles outliers and heavy tails well

Abstract

We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market data often contain outliers which, if not correctly handled, may further corrupt the covariance estimation. We address these shortcomings by studying the performance of a hybrid covariance matrix estimator based on Tyler's robust M-estimator and on Ledoit-Wolf's shrinkage estimator while assuming samples with heavy-tailed distribution. Employing recent results from random matrix theory, we develop a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity. Our portfolio optimization method is shown via simulations to outperform existing methods both for synthetic and real market data.