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Robust Portfolio Optimization Using Pseudodistances

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  • Aida Toma
  • Samuela Leoni-Aubin

Abstract

The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature.

Suggested Citation

  • Aida Toma & Samuela Leoni-Aubin, 2015. "Robust Portfolio Optimization Using Pseudodistances," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-26, October.
    • Handle: RePEc:plo:pone00:0140546
    DOI: 10.1371/journal.pone.0140546
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    References listed on IDEAS

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    1. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    2. Beatriz Vaz de Melo Mendes & Ricardo Pereira Câmara Leal, 2005. "Robust multivariate modeling in finance," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 1(2), pages 95-106, June.
    3. Toma, Aida & Leoni-Aubin, Samuela, 2010. "Robust tests based on dual divergence estimators and saddlepoint approximations," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1143-1155, May.
    4. Cédric Perret-Gentil & Maria-Pia Victoria-Feser, 2005. "Robust Mean-Variance Portfolio Selection," FAME Research Paper Series rp140, International Center for Financial Asset Management and Engineering.
    5. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
    6. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    7. Gervini, Daniel, 2002. "The influence function of the Stahel-Donoho estimator of multivariate location and scatter," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 425-435, December.
    8. Victor DeMiguel & Francisco J. Nogales, 2009. "Portfolio Selection with Robust Estimation," Operations Research, INFORMS, vol. 57(3), pages 560-577, June.
    9. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    10. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
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    Cited by:

    1. Pichler, Alois & Schlotter, Ruben, 2020. "Entropy based risk measures," European Journal of Operational Research, Elsevier, vol. 285(1), pages 223-236.
    2. Giuseppe Pandolfo & Carmela Iorio & Roberta Siciliano & Antonio D’Ambrosio, 2020. "Robust mean-variance portfolio through the weighted $$L^{p}$$ L p depth function," Annals of Operations Research, Springer, vol. 292(1), pages 519-531, September.
    3. David Quintana & Roman Denysiuk & Sandra García-Rodríguez & Antonio Gaspar-Cunha, 2017. "Portfolio implementation risk management using evolutionary multiobjective optimization," Post-Print hal-01881379, HAL.

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