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Capital distribution and portfolio performance in the mean-field Atlas model

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  • Benjamin Jourdain

    ()
    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Université Paris Est (UPE) - École des Ponts ParisTech (ENPC), INRIA Paris-Rocquencourt - MATHRISK - INRIA - École des Ponts ParisTech (ENPC) - Université Paris-Est Marne-la-Vallée (UPEMLV))

  • Julien Reygner

    ()
    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Université Paris Est (UPE) - École des Ponts ParisTech (ENPC), LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot)

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    Abstract

    We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of companies grows to infinity. Then, we discuss the long-term capital distribution. We recover the Pareto-like shape of capital distribution curves usually derived from empirical studies, and provide a new description of the phase transition phenomenon observed by Chatterjee and Pal. Finally, we address the performance of simple portfolio rules and highlight the influence of the volatility structure on the growth of portfolios.

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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00921151.

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    Date of creation: 20 Aug 2014
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    Handle: RePEc:hal:wpaper:hal-00921151

    Note: View the original document on HAL open archive server: http://hal-enpc.archives-ouvertes.fr/hal-00921151
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    Related research

    Keywords: Stochastic Portfolio Theory; Capital distribution curves; Rank-based models; Mean-field Atlas model; Growth rate; Size effect;

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    1. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Annals of Finance, Springer, vol. 9(3), pages 439-454, August.
    2. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Papers 1302.3870, arXiv.org.
    3. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
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