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Covariance matrix filtering and portfolio optimisation: the Average Oracle vs Non-Linear Shrinkage and all the variants of DCC-NLS

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  • Christian Bongiorno
  • Damien Challet

Abstract

The Average Oracle, a simple and very fast covariance filtering method, is shown to yield superior Sharpe ratios than the current state-of-the-art (and complex) methods, Dynamic Conditional Covariance coupled to Non-Linear Shrinkage (DCC+NLS). We pit all the known variants of DCC+NLS (quadratic shrinkage, gross-leverage or turnover limitations, and factor-augmented NLS) against the Average Oracle in large-scale randomized experiments. We find generically that while some variants of DCC+NLS sometimes yield the lowest average realized volatility, albeit with a small improvement, their excessive gross leverage and investment concentration, and their 10-time larger turnover contribute to smaller average portfolio returns, which mechanically result in smaller realized Sharpe ratios than the Average Oracle. We also provide simple analytical arguments about the origin of the advantage of the Average Oracle over NLS in a changing world.

Suggested Citation

  • Christian Bongiorno & Damien Challet, 2023. "Covariance matrix filtering and portfolio optimisation: the Average Oracle vs Non-Linear Shrinkage and all the variants of DCC-NLS," Papers 2309.17219, arXiv.org.
    • Handle: RePEc:arx:papers:2309.17219
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    1. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    2. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    3. 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.
    4. Gianluca De Nard & Olivier Ledoit & Michael Wolf, 2021. "Factor Models for Portfolio Selection in Large Dimensions: The Good, the Better and the Ugly [Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 236-257.
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