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

Author

Listed:
  • Hanene Ben Salah

    (BESTMOD Laboratory
    Université Claude Bernard Lyon 1, Institut de Science Financière et d’Assurances, LSAF EA2429
    IMAG)

  • Mohamed Chaouch

    (United Arab Emirates University)

  • Ali Gannoun

    (IMAG)

  • Christian Peretti

    (Université Claude Bernard Lyon 1, Institut de Science Financière et d’Assurances, LSAF EA2429)

  • Abdelwahed Trabelsi

    (BESTMOD Laboratory)

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.

Suggested Citation

  • Hanene Ben Salah & Mohamed Chaouch & Ali Gannoun & Christian Peretti & Abdelwahed Trabelsi, 2018. "Mean and median-based nonparametric estimation of returns in mean-downside risk portfolio frontier," Annals of Operations Research, Springer, vol. 262(2), pages 653-681, March.
    • Handle: RePEc:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-016-2235-z
    DOI: 10.1007/s10479-016-2235-z
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    3. D. Pla-Santamaria & M. Bravo, 2013. "Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips," Annals of Operations Research, Springer, vol. 205(1), pages 189-201, May.
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    8. Xie, Nan & Wang, Zongrun & Chen, Sicen & Gong, Xu, 2019. "Forecasting downside risk in China’s stock market based on high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 530-541.

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