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<p>Estimating large-dimensional covariance matrices is central to portfolio optimization, yet standard shrinkage methods are often vulnerable to outliers and market stress. This paper addresses this gap by introducing a robust linear shrinkage estimator (RSLS), which combines robustness against extreme returns with shrinkage toward a structured sparse target. We benchmark RSLS against robust and non-robust alternatives through synthetic experiments - covering regime shifts, market efficiency, PRIAL comparisons, and index tracking - and empirical analysis on Nifty 50 and S&amp;P 50 datasets. The results indicate that RSLS and RNL consistently outperform non-robust estimators, with robust methods delivering lower portfolio variance during crisis periods such as the 2008 crash and COVID-19 pandemic. Our findings also show that incorporating linear shrinkage and a robust covariance estimator (RSLS) can yield higher Sharpe Ratios, when compared to shrinkage methods which do not account for robustness. Our findings underscore the value of robustness in covariance estimation for both practitioners and regulators. For portfolio managers, robust estimators can yield more stable allocations. For policy-makers, their superior performance, especially for fat-tailed distributions, suggests a possible future role in strengthening risk management efforts and reducing vulnerability during incidents of financial risk.</p>

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Robust Linear Shrinkage Estimator for Highly Volatile Times

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Sumanjay Dutta,
  • Parthajit Kayal

摘要

Estimating large-dimensional covariance matrices is central to portfolio optimization, yet standard shrinkage methods are often vulnerable to outliers and market stress. This paper addresses this gap by introducing a robust linear shrinkage estimator (RSLS), which combines robustness against extreme returns with shrinkage toward a structured sparse target. We benchmark RSLS against robust and non-robust alternatives through synthetic experiments - covering regime shifts, market efficiency, PRIAL comparisons, and index tracking - and empirical analysis on Nifty 50 and S&P 50 datasets. The results indicate that RSLS and RNL consistently outperform non-robust estimators, with robust methods delivering lower portfolio variance during crisis periods such as the 2008 crash and COVID-19 pandemic. Our findings also show that incorporating linear shrinkage and a robust covariance estimator (RSLS) can yield higher Sharpe Ratios, when compared to shrinkage methods which do not account for robustness. Our findings underscore the value of robustness in covariance estimation for both practitioners and regulators. For portfolio managers, robust estimators can yield more stable allocations. For policy-makers, their superior performance, especially for fat-tailed distributions, suggests a possible future role in strengthening risk management efforts and reducing vulnerability during incidents of financial risk.