Target-Seeking Decompositions of Multi-Period Optimal Portfolios

Abstract

We identify decompositions of multi-period optimal portfolios, in which each subportfolio is dedicated to achieving a single investment target, in dynamic models with Von Neumann-Morgenstern preferences and diffusion asset returns (“Merton’s problem”). These decompositions rest on recognizing the equivalence between Merton’s problem and a generalized Mean-Variance Optimization problem. We show that the special properties of the component sub-portfolios facilitate empirical implementation of dynamic asset allocation, and provide new insights into how multi-period optimal portfolios can be constructed. A practical application is examined, which entails a “divide-and-conquer” approach for long-term investors, like pension funds, to develop asset allocation strategies.

Keywords: Portfolio Management, Portfolio Decomposition, Merton’s Problem, Multiperiod, Asset Allocation, Dynamic Programming, Mean Variance Optimization, Zero-Cost Portfolios, Long-term Investments

JEL Classification: G11