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A Monte Carlo Method for Optimal Portfolios

Authors

  • Jérôme B. Detemple,

  • Ren Garcia,

  • Marcel Rindisbacher

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    • * Jérôme B. Detemple is at Boston University, School of Management and CIRANO; René Garcia is at Université de Montréal, Department of Economics and CIRANO; and Marcel Rindisbacher is at University of Toronto, Rotman School of Management and CIRANO. The paper was presented at Boston University, Boston College, CIRANO, McMaster University, MIT, NYU (Stern), NYU (Courant), University of Rochester, University of Waterloo, PUC (Rio de Janeiro), York University, The Fields Institute, MITACS general meeting (Toronto), Optimization Days 1999 (Montréal), EFA 1999 (Helsinki), NFA 1999 (Calgary), AFA 2000 (Boston), CMS 2000 (Vancouver), and the 2001 Financial Mathematics conference at UCLA (IPAM). We thank an anonymous referee and the editor, Rick Green, for very useful comments. The paper has also benefited from the suggestions of Helyette Geman, Jacob Sagi, Jun Liu, Larry Epstein, Steve Figlewski, Alex Shapiro, Anthony Lynch, Stan Pliska, Toby Daglish, Martin Gonzales Eiras, David Menagarishvili, and Mark Loewenstein. Financial support from the Network of Centers of Excellence (MITACS) is gratefully acknowledged.

Abstract

This paper proposes a new simulation-based approach for optimal portfolio allocation in realistic environments with complex dynamics for the state variables and large numbers of factors and assets. A first illustration involves a choice between equity and cash with nonlinear interest rate and market price of risk dynamics. Intertemporal hedging demands significantly increase the demand for stocks and exhibit low volatility. We then analyze settings where stock returns are also predicted by dividend yields and where investors have wealth-dependent relative risk aversion. Large-scale problems with many assets, including the Nasdaq, SP500, bonds, and cash, are also examined.

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