Shrinkage Estimators for Mean and Covariance: Evidence on Portfolio Efficiency Across Market Dimensions

TL;DR

This study evaluates shrinkage estimators for mean and covariance in portfolio optimization, demonstrating that certain shrinkage methods, especially Ledoit Wolf's COV2, improve portfolio performance across different market conditions.

Contribution

It provides a comprehensive empirical comparison of multiple shrinkage estimators for mean and covariance, identifying optimal models for various investor profiles.

Findings

GMV with Ledoit Wolf COV2 is most effective for broad investors.

MV with COV2 and sample mean suits return-focused investors.

Shrinkage estimators outperform traditional methods in diverse scenarios.

Abstract

The mean-variance model remains the most prevalent investment framework, built on diversification principles. However, it consistently struggles with estimation errors in expected returns and the covariance matrix, its core parameters. To address this concern, this research evaluates the performance of mean variance (MV) and global minimum-variance (GMV) models across various shrinkage estimators designed to improve these parameters. Specifically, we examine five shrinkage estimators for expected returns and eleven for the covariance matrix. To compare multiple portfolios, we employ a super efficient data envelopment analysis model to rank the portfolios according to investors risk-return preferences. Our comprehensive empirical investigation utilizes six real world datasets with different dimensional characteristics, applying a rolling window methodology across three out of sample testing periods. Following the ranking process, we examine the chosen shrinkage based MV or GMV portfolios against five traditional portfolio optimization techniques classical MV and GMV for sample estimates, MiniMax, conditional value at risk, and semi mean absolute deviation risk measures. Our empirical findings reveal that, in most scenarios, the GMV model combined with the Ledoit Wolf two parameter shrinkage covariance estimator (COV2) represents the optimal selection for a broad spectrum of investors. Meanwhile, the MV model utilizing COV2 alongside the sample mean (SM) proves more suitable for return oriented investors. These two identified models demonstrate superior performance compared to traditional benchmark approaches. Overall, this study lays the groundwork for a more comprehensive understanding of how specific shrinkage models perform across diverse investor profiles and market setups.