A State-Variable Decomposition Approach for Solving Portfolio Choice Problems

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