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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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    Citations

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    Cited by:

    1. Gianluca De Nard & Robert F. Engle & Bryan Kelly, 2024. "Factor-Mimicking Portfolios for Climate Risk," Financial Analysts Journal, Taylor & Francis Journals, vol. 80(3), pages 37-58, July.
    2. Elliot Beck & Damian Kozbur & Michael Wolf, 2023. "Hedging Forecast Combinations With an Application to the Random Forest," Papers 2308.15384, arXiv.org, revised Aug 2023.
    3. Olivier Ledoit & Michael Wolf, 2022. "Markowitz portfolios under transaction costs," ECON - Working Papers 420, Department of Economics - University of Zurich, revised Sep 2024.
    4. Jin Yuan & Xianghui Yuan, 2023. "A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation," SAGE Open, , vol. 13(2), pages 21582440231, June.
    5. Jean-Philippe Bouchaud & Iacopo Mastromatteo & Marc Potters & Konstantin Tikhonov, 2022. "Excess Out-of-Sample Risk and Fleeting Modes," Papers 2205.01012, arXiv.org.
    6. Esra Ulasan & A. Özlem Önder, 2023. "Large portfolio optimisation approaches," Journal of Asset Management, Palgrave Macmillan, vol. 24(6), pages 485-497, October.
    7. Jiang, Yifu & Olmo, Jose & Atwi, Majed, 2024. "Dynamic robust portfolio selection under market distress," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
    8. Anatolyev, Stanislav & Pyrlik, Vladimir, 2022. "Copula shrinkage and portfolio allocation in ultra-high dimensions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    9. Yan Zhang & Jiyuan Tao & Zhixiang Yin & Guoqiang Wang, 2022. "Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

    More about this item

    Keywords

    dynamic conditional correlations; factor models; large-dimensional asymptotics; Markowitz’s portfolio selection; rotation equivariance;
    All these keywords.

    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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