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The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation
[Design-Free Estimation of Variance Matrices]

Author

Listed:
  • Olivier Ledoit
  • Michael Wolf

Abstract

Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz’s portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance matrix certainly will not do. In this article, we review our work in this area, going back 15+ years. We have promoted various shrinkage estimators, which can be classified into linear and nonlinear. Linear shrinkage is simpler to understand, to derive, and to implement. But nonlinear shrinkage can deliver another level of performance improvement, especially if overlaid with stylized facts such as time-varying co-volatility or factor models.

Suggested Citation

  • Olivier Ledoit & Michael Wolf, 2022. "The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation [Design-Free Estimation of Variance Matrices]," Journal of Financial Econometrics, Oxford University Press, vol. 20(1), pages 187-218.
    • Handle: RePEc:oup:jfinec:v:20:y:2022:i:1:p:187-218.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbaa007
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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