Paper: arXiv 2601.20643

Authors: Rupendra Yadav, Amita Sharma, Aparna Mehra

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a comprehensive empirical study comparing 16 different shrinkage estimators for mean and covariance across six diverse stock markets using rolling out-of-sample backtests. Its use of Super-Efficiency Data Envelopment Analysis (DEA) to evaluate portfolio efficiency across multiple risk-return investor profiles provides strong empirical depth and structured analysis.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Mitigate estimation error in MV & GMV portfolio models using shrinkage estimators"] --> B["Inputs & Test Setup:<br>6 Real-World Equity Datasets<br>Rolling Window Methodology"]
    
    B --> C["Parameter Estimation:<br>5 Expected Return Shrinkage Estimators<br>11 Covariance Shrinkage Estimators"]
    
    C --> D["Portfolio Strategy & Evaluation:<br>Construct MV & GMV Portfolios<br>Rank via Super-Efficient Data Envelopment Analysis (DEA)"]
    
    D --> E["Benchmarking:<br>Compare top ranked shrinkage portfolios against Sample MV/GMV, MiniMax, CVaR, & MAD"]
    
    E --> F["Key Findings:<br>1. GMV + Ledoit-Wolf COV2 is optimal for general investors<br>2. MV + COV2 + Sample Mean suits return-oriented investors"]

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1 of 68 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.