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

Rupendra Yadav, Amita Sharma, Aparna Mehra

TL;DR

The paper tackles the fragility of mean-variance portfolios caused by estimation errors in mean returns and the covariance matrix. It integrates five mean shrinkage and eleven covariance shrinkage estimators into MV and GMV frameworks, then evaluates their performance across six global markets using a rolling-window approach. A super-efficiency DEA ranking scheme assesses portfolios on return and risk-adjusted metrics, comparing shrinkage-based portfolios against five benchmark optimization strategies. Key findings show that GMV with the Ledoit-Wolf two-parameter covariance estimator (COV2) often yields universal best performance, while MV with COV2 and the sample mean (SM) excels for return-oriented investors; these shrinkage-based approaches generally outperform traditional benchmarks, highlighting practical guidance for portfolio construction across market regimes.

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.

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

TL;DR

The paper tackles the fragility of mean-variance portfolios caused by estimation errors in mean returns and the covariance matrix. It integrates five mean shrinkage and eleven covariance shrinkage estimators into MV and GMV frameworks, then evaluates their performance across six global markets using a rolling-window approach. A super-efficiency DEA ranking scheme assesses portfolios on return and risk-adjusted metrics, comparing shrinkage-based portfolios against five benchmark optimization strategies. Key findings show that GMV with the Ledoit-Wolf two-parameter covariance estimator (COV2) often yields universal best performance, while MV with COV2 and the sample mean (SM) excels for return-oriented investors; these shrinkage-based approaches generally outperform traditional benchmarks, highlighting practical guidance for portfolio construction across market regimes.

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.
Paper Structure (19 sections, 7 equations, 1 figure, 6 tables)

This paper contains 19 sections, 7 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Motivation and Background
  3. Objective and Approach
  4. Mean-Variance and Global Minimum-Variance Portfolio Optimization Models
  5. Shrinkage Estimators
  6. Shrinkage Estimator for Mean
  7. Shrinkage Estimators for Covariance Matrix
  8. Super-efficiency DEA Model
  9. Data and Empirical Set-up
  10. Sample Data and Sample Period
  11. Rolling Window Scheme
  12. Methodology
  13. Result Discussion
  14. Assessment for Group A
  15. Assessment for Group B
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Efficiency scores distribution framed over different datasets and varying out-of-sample period size of the five benchmark models (MV & GMV with sample estimates, CVaR, MAD, MM) and the universal best-performing models corresponding to the groups A, B, and C.