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, 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

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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.

Date: 2016-06-23
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Published in Annals of Operations Research, 2016, 262 (2), pp.653-681. ⟨10.1007/s10479-016-2235-z⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04875563

DOI: 10.1007/s10479-016-2235-z

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