A Robust Statistics Approach to Minimum Variance Portfolio Optimization

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.

References in corpus (2)

• High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: Risk underestimation
• Large Dimensional Analysis of Robust M-Estimators of Covariance with Outliers

Cited by in corpus (7)

• Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions
• Statistical inference for the EU portfolio in high dimensions
• Large Dimensional Analysis of Robust M-Estimators of Covariance with Outliers
• Large-dimensional behavior of regularized Maronna's M-estimators of covariance matrices
• Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio
• Linear pooling of sample covariance matrices
• High-dimensional covariance matrix estimators on simulated portfolios with complex structures