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

Hanene Ben Salah, Mohamed Chaouch, Ali Gannoun (), Christian de Peretti and Abdelwahed Trabelsi
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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, LSAF - 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
Abdelwahed Trabelsi: BESTMOD - Business and Economic Statistics MODeling - ISG - Institut Supérieur de Gestion de Tunis [Tunis] - Université de Tunis

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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.

Keywords: Downside risk; Kernel method; Mean nonparametric estimation; Median nonparametric estimation; Portefolio efficient frontier; Semi-variance (search for similar items in EconPapers)
Date: 2018-03
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Published in Annals of Operations Research, 2018, 262 (2), pp.653-681. ⟨10.1007/s10479-016-2235-z⟩

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Journal Article: Mean and median-based nonparametric estimation of returns in mean-downside risk portfolio frontier (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01300673

DOI: 10.1007/s10479-016-2235-z

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