A Monte Carlo Method for Optimal Portfolios

52 Pages Posted: 16 Nov 2000

See all articles by Jerome Detemple

Jerome Detemple

Boston University - Department of Finance & Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO)

René Garcia

Université de Montréal - CIREQ - Département de sciences économiques; University of Montreal

Marcel Rindisbacher

Questrom School of Business, Boston University; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Multiple version iconThere are 2 versions of this paper

Date Written: April 2000

Abstract

This paper provides (i) new results on the structure of optimal portfolios, (ii) economic insights on the behavior of the hedging components and (iii) simulation-based methods for numerical implementation of allocation rules. The core of our approach relies on closed-form solutions for functionals of diffusion processes which simplify their numerical simulation and facilitate the computation and simulation of the hedging components of optimal portfolios. One of our procedures relies on a variance-stabilizing transformation of the underlying process which eliminates stochastic integrals from the representation of random variables in hedging terms and ensures the existence of an exact weak approximation scheme. This improves the performance of Monte-Carlo methods in the numerical implementation of portfolio rules derived on the basis of probabilistic arguments. Our approach is flexible and can be used even when the dimensionality of the set of underlying state variables is large. We implement the procedure for a class of bivariate and trivariate models in which the uncertainty is described by diffusion processes for the market price of risk (MPR), the interest rate (IR) and other relevant factors. After calibrating the models to the data we document the behavior of the portfolio demand and the hedging components relative to the parameters of the model such as risk aversion, investment horizon, speeds of mean-reversion, IR and MPR levels and volatilities. We show that the hedging terms are important and cannot be ignored for asset allocation purposes. Risk aversion and investment horizon emerge as the most relevant factors: they have a substantial impact on the size of the optimal portfolio and on its economic properties for realistic values of the models' parameters.

JEL Classification: G11, G13, G23, C61, C63

Suggested Citation

Detemple, Jerome and Garcia, René and Rindisbacher, Marcel, A Monte Carlo Method for Optimal Portfolios (April 2000). Available at SSRN: https://ssrn.com/abstract=228844 or http://dx.doi.org/10.2139/ssrn.228844

Jerome Detemple (Contact Author)

Boston University - Department of Finance & Economics ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
(617) 353-4297 (Phone)
(617) 353 6667 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

René Garcia

Université de Montréal - CIREQ - Département de sciences économiques ( email )

C.P. 6128, succursale Centre-Ville
3150, rue Jean-Brillant, bureau C-6027
Montreal, Quebec H3C 3J7
Canada
514-985-4014 (Phone)

University of Montreal ( email )

United States

Marcel Rindisbacher

Questrom School of Business, Boston University ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States
617 353 4152 (Phone)
617 353 999 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

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