A State-Variable Decomposition Approach for Solving Portfolio Choice Problems

51 Pages Posted: 9 Mar 2008

See all articles by Lorenzo Garlappi

Lorenzo Garlappi

University of British Columbia (UBC) - Sauder School of Business

Georgios Skoulakis

University of British Columbia (UBC) - Division of Finance

Date Written: February 2008

Abstract

In this paper, we develop a new method for the solution of dynamic portfolio choice problems. Our approach consists of decomposing each state variable into a sum of its conditional mean and the corresponding zero-mean shock. Such a state variable decomposition (SVD) allows efficient computation of the conditional expectations required for the solution of the dynamic optimization problem. Under commonly used distributional assumptions for the state variable shocks (e.g., normality or lognormality), this decomposition allows closed-form evaluation of such expectations, thus avoiding computationally intensive quadrature or simulation-based techniques. Our approach can easily handle intermediate consumption, multiple risky assets, multiple state variables, portfolio constraints, non-expected utility preferences as well as portfolio problems in which wealth is not a redundant state variable. We illustrate the accuracy of the method by comparing our solution to either the analytical solution, whenever available, or the solution obtained by quadrature methods. Finally, we employ our method to solve a large-scale strategic asset allocation problem with recursive preferences and predictable asset returns similar to the one solved by Campbell, Chan, and Viceira (2003) via log-linear approximation. Our approach allows us to impose realistic no borrowing and short-selling constraints and its precision, unlike that of the log-linear approximation, does not rely on the elasticity of intertemporal substitution being close to unity. The versatility of our approach makes it a suitable solution method for a wide range of dynamic problems in finance and economics.

Keywords: dynamic portfolio choce, approximation techniques

JEL Classification: G110

Suggested Citation

Garlappi, Lorenzo and Skoulakis, Georgios, A State-Variable Decomposition Approach for Solving Portfolio Choice Problems (February 2008). EFA 2008 Athens Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1102604 or http://dx.doi.org/10.2139/ssrn.1102604

Lorenzo Garlappi (Contact Author)

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

Georgios Skoulakis

University of British Columbia (UBC) - Division of Finance ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

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