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Robust estimation of covariance and its application to portfolio optimization

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  • Huo, Lijuan
  • Kim, Tae-Hwan
  • Kim, Yunmi

Abstract

Outliers can have a considerable influence on the conventional measure of covariance, which may lead to a misleading understanding of the comovement between two variables. Both an analytical derivation and Monte Carlo simulations show that the conventional measure of covariance can be heavily influenced in the presence of outliers. This paper proposes an intuitively appealing and easily computable robust measure of covariance based on the median and compares it with some existing robust covariance estimators in the statistics literature. It is demonstrated by simulations that all of the robust measures are fairly stable and insensitive to outliers. We apply robust covariance measures to construct two well-known portfolios, the minimum-variance portfolio and the optimal risky portfolio. The results of an out-of-sample experiment indicate that a potentially large investment gain can be realized using robust measures in place of the conventional measure.

Suggested Citation

  • Huo, Lijuan & Kim, Tae-Hwan & Kim, Yunmi, 2012. "Robust estimation of covariance and its application to portfolio optimization," Finance Research Letters, Elsevier, vol. 9(3), pages 121-134.
    • Handle: RePEc:eee:finlet:v:9:y:2012:i:3:p:121-134
    DOI: 10.1016/j.frl.2012.06.001
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    Cited by:

    1. Fotis Papailias & Dimitrios Thomakos, 2015. "Covariance averaging for improved estimation and portfolio allocation," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 29(1), pages 31-59, February.
    2. Galvani, Valentina & Gubellini, Stefano, 2013. "Mean–variance dominant trading strategies," Finance Research Letters, Elsevier, vol. 10(3), pages 142-150.
    3. Kim, Yunmi & Kim, Tae-Hwan & Ergün, Tolga, 2015. "The instability of the Pearson correlation coefficient in the presence of coincidental outliers," Finance Research Letters, Elsevier, vol. 13(C), pages 243-257.
    4. Anja Vinzelberg & Benjamin R. Auer, 2022. "Unprofitability of food market investments," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(7), pages 2887-2910, October.
    5. R. P. C. Leal & B. V. M. Mendes, 2013. "Assessing the effect of tail dependence in portfolio allocations," Applied Financial Economics, Taylor & Francis Journals, vol. 23(15), pages 1249-1256, August.
    6. Xidonas, Panos & Mavrotas, George & Hassapis, Christis & Zopounidis, Constantin, 2017. "Robust multiobjective portfolio optimization: A minimax regret approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 299-305.
    7. Ramesh Adhikari & Kyle J. Putnam & Humnath Panta, 2020. "Robust Optimization-Based Commodity Portfolio Performance," IJFS, MDPI, vol. 8(3), pages 1-16, September.
    8. Xidonas, Panos & Hassapis, Christis & Soulis, John & Samitas, Aristeidis, 2017. "Robust minimum variance portfolio optimization modelling under scenario uncertainty," Economic Modelling, Elsevier, vol. 64(C), pages 60-71.

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    More about this item

    Keywords

    Covariance; Robust estimation; Median;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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