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Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimization

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  • Bongiorno, Christian
  • Challet, Damien

Abstract

Portfolio optimization requires sophisticated covariance estimators that are able to filter out estimation noise. Non-linear shrinkage is a popular estimator based on how the Oracle eigenvalues can be computed using only data from the calibration window. Contrary to common belief, NLS is not optimal for portfolio optimization because it does not minimize the right cost function when the asset dependence structure is non-stationary. We instead derive the optimal target. Using historical data, we quantify by how much NLS can be improved. Our findings reopen the question of how to build the covariance matrix estimator for portfolio optimization in realistic conditions.

Suggested Citation

  • Bongiorno, Christian & Challet, Damien, 2023. "Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimization," Finance Research Letters, Elsevier, vol. 52(C).
    • Handle: RePEc:eee:finlet:v:52:y:2023:i:c:s1544612322005608
    DOI: 10.1016/j.frl.2022.103383
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    1. Christian Bongiorno & Damien Challet, 2021. "Covariance matrix filtering with bootstrapped hierarchies," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-13, January.
    2. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    3. Joel Bun & Romain Allez & Jean-Philippe Bouchaud & Marc Potters, 2015. "Rotational invariant estimator for general noisy matrices," Papers 1502.06736, arXiv.org, revised Oct 2016.
    4. Liusha Yang & Romain Couillet & Matthew R. McKay, 2015. "A Robust Statistics Approach to Minimum Variance Portfolio Optimization," Papers 1503.08013, arXiv.org.
    5. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    6. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
    7. Christian Bongiorno & Damien Challet & Gr'egoire Loeper, 2021. "Cleaning the covariance matrix of strongly nonstationary systems with time-independent eigenvalues," Papers 2111.13109, arXiv.org, revised Mar 2023.
    8. repec:hal:wpaper:hal-02612262 is not listed on IDEAS
    9. De Nard, Gianluca & Engle, Robert F. & Ledoit, Olivier & Wolf, Michael, 2022. "Large dynamic covariance matrices: Enhancements based on intraday data," Journal of Banking & Finance, Elsevier, vol. 138(C).
    10. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    11. Christian Bongiorno & Damien Challet, 2022. "Reactive global minimum variance portfolios with k-BAHC covariance cleaning," The European Journal of Finance, Taylor & Francis Journals, vol. 28(13-15), pages 1344-1360, October.
    12. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    13. Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
    14. repec:hal:wpaper:hal-03481441 is not listed on IDEAS
    15. Ester Pantaleo & Michele Tumminello & Fabrizio Lillo & Rosario Mantegna, 2011. "When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1067-1080.
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    Cited by:

    1. Mörstedt, Torsten & Lutz, Bernhard & Neumann, Dirk, 2024. "Cross validation based transfer learning for cross-sectional non-linear shrinkage: A data-driven approach in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(2), pages 670-685.

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