A Robust Statistics Approach to Minimum Variance Portfolio Optimization


We have a tendency to study the design of portfolios below 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 giant portfolios, the amount of obtainable market returns is usually of similar order to the amount of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market knowledge typically contain outliers that, if not correctly handled, might any corrupt the covariance estimation. We tend to address these shortcomings by finding out the performance of a hybrid covariance matrix estimator based on Tyler’s strong M-estimator and on Ledoit-Wolf’s shrinkage estimator whereas assuming samples with significant-tailed distribution. Employing recent results from random matrix theory, we have a tendency to develop the same estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing on-line the shrinkage intensity. Our portfolio optimization technique is shown via simulations to outperform existing strategies both for synthetic and real market knowledge.

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