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Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization

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  • Szilard Pafka
  • Marc Potters
  • Imre Kondor

Abstract

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate the spectrum of large exponentially weighted random matrices (whose upper band edge needs to be known for the implementation of the estimation) analytically, by a procedure analogous to that used for standard random matrices. Finally, we illustrate, on empirical data, the superiority of the newly introduced estimator in a portfolio optimization context over both the method of exponentially weighted moving averages and the uniformly-weighted random-matrix-theory-based filtering.

Suggested Citation

  • Szilard Pafka & Marc Potters & Imre Kondor, 2004. "Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization," Papers cond-mat/0402573, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0402573
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    1. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    2. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
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    Cited by:

    1. Mahsa Ghorbani & Edwin K P Chong, 2020. "Stock price prediction using principal components," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    2. Sebastien Valeyre & Denis S Grebenkov & Sofiane Aboura, 2019. "Emergence of correlations between securities at short time scales," Post-Print hal-02343888, HAL.
    3. S. Valeyre & D. S. Grebenkov & S. Aboura, 2018. "Emergence of correlations between securities at short time scales," Papers 1807.05015, arXiv.org.
    4. Martins, André C.R., 2007. "Non-stationary correlation matrices and noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 552-558.
    5. Zdzisław Burda & Andrzej Jarosz & Maciej Nowak & Jerzy Jurkiewicz & Gabor Papp & Ismail Zahed, 2011. "Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1103-1124.
    6. Svensson, Jens, 2007. "The asymptotic spectrum of the EWMA covariance estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 621-630.
    7. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2007. "Randomly generating portfolio-selection covariance matrices with specified distributional characteristics," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1610-1625, March.
    8. Gilles Zumbach, 2011. "Empirical properties of large covariance matrices," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1091-1102.
    9. Mahsa Ghorbani & Edwin K. P. Chong, 2022. "A dimension reduction method for stock-price prediction using multiple predictors," Operational Research, Springer, vol. 22(3), pages 2859-2878, July.
    10. Vincent Tan & Stefan Zohren, 2020. "Estimation of Large Financial Covariances: A Cross-Validation Approach," Papers 2012.05757, arXiv.org, revised Jan 2023.
    11. Alejandro Rodriguez Dominguez, 2022. "Portfolio Optimization based on Neural Networks Sensitivities from Assets Dynamics respect Common Drivers," Papers 2202.08921, arXiv.org, revised Dec 2022.

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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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