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

Author

Listed:
  • Hanene Ben Salah

    (IMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique, Laboratoire BESTMOD ISG Tunis - ISG Tunis, LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon, UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Mohamed Chaouch

    (LVIC - Laboratoire Vision et Ingénierie des Contenus - DIASI (CEA, LIST) - Département Intelligence Ambiante et Systèmes Interactifs - LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies - DRT (CEA) - Direction de Recherche Technologique (CEA) - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay)

  • Ali Gannoun

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

  • Christian de Peretti

    (ECL - École Centrale de Lyon - Université de Lyon, LSAF - 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.

Suggested Citation

  • Hanene Ben Salah & Mohamed Chaouch & Ali Gannoun & Christian de Peretti & Abdelwahed Trabelsi, 2016. "Mean and median-based nonparametric estimation of returns in mean-downside risk portfolio frontier," Post-Print hal-04875563, HAL.
    • Handle: RePEc:hal:journl:hal-04875563
    DOI: 10.1007/s10479-016-2235-z
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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. Anna Rutkowska-Ziarko & Lesław Markowski, 2022. "Accounting and Market Risk Measures of Polish Energy Companies," Energies, MDPI, vol. 15(6), pages 1-21, March.
    4. Andrea Rigamonti & Katarína Lučivjanská, 2024. "Mean-semivariance portfolio optimization using minimum average partial," Annals of Operations Research, Springer, vol. 334(1), pages 185-203, March.
    5. 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.
    6. Christian de Peretti, 2015. "A New Approach in Nonparametric Estimation of Returns in Mean-Downside Risk Portfolio frontier," Post-Print hal-02095499, HAL.
    7. Saker Sabkha & Christian Peretti & Dorra Hmaied, 2019. "On the informational market efficiency of the worldwide sovereign credit default swaps," Journal of Asset Management, Palgrave Macmillan, vol. 20(7), pages 581-608, December.
    8. 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).
    9. 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.
    10. Fr'ed'eric Butin, 2020. "Generalized distance to a simplex and a new geometrical method for portfolio optimization," Papers 2009.08826, arXiv.org.

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