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

Author

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  • Hanene Ben Salah

    (IMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique, BESTMOD - Business and Economic Statistics MODeling - ISG - Institut Supérieur de Gestion de Tunis [Tunis] - Université de Tunis, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Mohamed Chaouch

    (UAEU - United Arab Emirates University)

  • Ali Gannoun

    (IMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique)

  • Christian de Peretti

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Abdelwahed Trabelsi

    (BESTMOD - Business and Economic Statistics MODeling - ISG - Institut Supérieur de Gestion de Tunis [Tunis] - Université de Tunis)

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.

Suggested Citation

  • Hanene Ben Salah & Mohamed Chaouch & Ali Gannoun & Christian de Peretti & Abdelwahed Trabelsi, 2018. "Mean and median-based nonparametric estimation of returns in mean-downside risk portfolio frontier," Post-Print hal-01300673, HAL.
    • Handle: RePEc:hal:journl:hal-01300673
    DOI: 10.1007/s10479-016-2235-z
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    References listed on IDEAS

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    1. Ang, James S., 1975. "A Note on the E, SL Portfolio Selection Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 849-857, December.
    2. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    3. Javier Estrada, 2004. "Mean-Semivariance Behaviour: An Alternative Behavioural Model," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 3(3), pages 231-248, December.
    4. 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.
    5. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
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    Cited by:

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    2. Alessia Naccarato & Andrea Pierini & Giovanna Ferraro, 2021. "Markowitz portfolio optimization through pairs trading cointegrated strategy in long-term investment," Annals of Operations Research, Springer, vol. 299(1), pages 81-99, April.
    3. Rutkowska-Ziarko, Anna & Markowski, Lesław & Pyke, Christopher & Amin, Saqib, 2022. "Conventional and downside CAPM: The case of London stock exchange," Global Finance Journal, Elsevier, vol. 54(C).
    4. Chinnadurai Kathiravan & Murugesan Selvam & Sankaran Venkateswar & S. Balakrishnan, 2021. "Investor behavior and weather factors: evidences from Asian region," Annals of Operations Research, Springer, vol. 299(1), pages 349-373, April.
    5. Fr'ed'eric Butin, 2020. "Generalized distance to a simplex and a new geometrical method for portfolio optimization," Papers 2009.08826, arXiv.org.
    6. Anna Rutkowska-Ziarko & Lesław Markowski, 2022. "Accounting and Market Risk Measures of Polish Energy Companies," Energies, MDPI, vol. 15(6), pages 1-21, March.
    7. Christian de Peretti, 2015. "A New Approach in Nonparametric Estimation of Returns in Mean-Downside Risk Portfolio frontier," Post-Print hal-02095499, HAL.
    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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    Keywords

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