Replicating the properties of hedge fund returns ∗ Nicolas Papageorgiou, Bruno R´ emillard, Alexandre Hocquard HEC Montr´ eal April 8, 2008 Abstract In this paper, we implement a multi-variate extension of Dybvig (1988) Payoff Distribution Model that can be used to replicate not only the marginal distribution of most hedge fund returns but also their dependence with other asset classes. In addition to proposing ways to overcome the hedging and compatibility inconsistencies in Kat and Palaro (2005), we extend the results of Schweizer (1995) and adapt American options pricing techniques to evaluate the model and also derive an optimal dynamic trading (hedging) strategy. The proposed methodology can be used as a benchmark for evaluating fund performance, as well as to replicate hedge funds or generate synthetic funds. Key Words: Hedge Funds, Hedging, Replication, Copula, Gaussian mixtures. J.E.L. classification: G10, G20, G28, C16 * Corresponding author: Nicolas Papageorgiou, Finance Department, HEC Montr´ eal, 3000 Cote Sainte- Catherine, Montreal,QC, H3T 2A7, Canada. All the authors are at HEC Montr´ eal and can be reached at firstname.lastname@hec.ca. This work is supported in part by the Fonds pour la formation de chercheurs et l’aide ` a la recherche du Gouvernement du Qu´ ebec, by the Fonds qu´ eb´ ecois de la recherche sur la soci´ et´ e et la culture, by the Natural Sciences and Engineering Research Council of Canada and by Desjardins Global Asset Management. The authors would also like to thank Frank Leclerc, Aziz Sor´ e, Gauthier Webanck and Hugues Langlois. 1