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Annals of Operations Research

, Volume 262, Issue 2, pp 653–681 | Cite as

Mean and median-based nonparametric estimation of returns in mean-downside risk portfolio frontier

  • Hanene Ben Salah
  • Mohamed Chaouch
  • Ali Gannoun
  • Christian de PerettiEmail author
  • Abdelwahed Trabelsi
S.I.: Financial Economics

Abstract

The downside risk (DSR) model for portfolio optimisation allows to overcome the drawbacks of the classical Mean–Variance model concerning the asymmetry of returns and the risk perception of investors. This model optimization deals with a positive definite matrix that is endogenous with respect to portfolio weights. This aspect makes the problem far more difficult to handle. For this purpose, Athayde (2001) developed a new recursive minimization procedure that ensures the convergence to the solution. However, when a finite number of observations is available, the portfolio frontier presents some discontinuity and is not very smooth. In order to overcome that, Athayde (2003) proposed a mean kernel estimation of the returns, so as to create a smoother portfolio frontier. This technique provides an effect similar to the case in which continuous observations are available. In this paper, Athayde model is reformulated and clarified. Then, taking advantage on the robustness of the median, another nonparametric approach based on median kernel returns estimation is proposed in order to construct a portfolio frontier. A new version of Athayde’s algorithm will be exhibited. Finally, the properties of this improved portfolio frontier are studied and analysed on the French Stock Market.

Keywords

Downside risk Kernel method Mean nonparametric estimation Median nonparametric estimation Portefolio efficient frontier Semi-variance 

Notes

Acknowledgments

Christian de Peretti gratefully acknowledges financial support of the Global Risk Institute in Financial Services (Toronto).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Hanene Ben Salah
    • 1
    • 2
    • 3
  • Mohamed Chaouch
    • 4
  • Ali Gannoun
    • 3
  • Christian de Peretti
    • 2
    Email author
  • Abdelwahed Trabelsi
    • 1
  1. 1.BESTMOD LaboratoryLe BardoTunisia
  2. 2.Université Claude Bernard Lyon 1, Institut de Science Financière et d’Assurances, LSAF EA2429LyonFrance
  3. 3.IMAGMontpellier Cedex 05France
  4. 4.Department of StatisticsUnited Arab Emirates UniversityAl AinUAE

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