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Asymptotic analysis of different covariance matrices estimation for minimum variance portfolio

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  • Linda Chamakh

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, Global Markets Quantitative Research - BNP Paribas)

  • Emmanuel Gobet

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Philippe Lemor

    (Global Markets Quantitative Research - BNP Paribas)

Abstract

In dynamic minimum variance portfolio, we study the impact of the sequence of covariance matrices taken in inputs, on the realized variance of the portfolio computed along a sample market path. The allocation of the portfolio is adjusted on a regular basis (every H days) using an updated covariance matrix estimator. In a modelling framework where the covariance matrix of the asset returns evolves as an ergodic process, we quantify the probability of observing an underperformance of the optimal dynamic covariance matrix compared to any other choice. The bounds depend on the tails of the returns, on the adjustment period H, and on the total number of rebalancing times N. These results provide asset managers with new insights into the optimality of their choice of covariance matrix estimators, depending on the depth of the backtest N H and the investment period H. Experiments based on GARCH modelling support our theoretical results.

Suggested Citation

  • Linda Chamakh & Emmanuel Gobet & Jean-Philippe Lemor, 2021. "Asymptotic analysis of different covariance matrices estimation for minimum variance portfolio," Working Papers hal-03207061, HAL.
    • Handle: RePEc:hal:wpaper:hal-03207061
    Note: View the original document on HAL open archive server: https://hal.science/hal-03207061
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    References listed on IDEAS

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    1. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
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