Dynamic Asset Allocation Strategies Using a Stochastic Dynamic Programming Approach∗

A major investment decision for individual and institutional investors alike is to choose between different asset classes, i.e., equity investments and interest-bearing investments. The asset allocation decision determines the ultimate risk and return of a portfolio. The asset allocation problem is frequently addressed either through a static analysis, based on Markowitz’ mean-variance model, or dynamically but often myopically through the application of analytical results for special classes of utility functions, e.g., Samuelson’s fixed-mix result for constant relative risk aversion. Only recently, the full dynamic and multi-dimensional nature of the asset allocation problem could be captured through applications of stochastic dynamic programming and stochastic programming techniques, the latter being discussed in various chapters of this book. The paper reviews the different approaches to asset allocation and presents a novel approach based on stochastic dynamic programming and Monte Carlo sampling that permits one to consider many rebalancing periods, many asset classes, dynamic cash flows, and a general representation of investor risk preference. The paper further presents a novel approach of representing utility by directly modeling risk aversion as a function of wealth, and thus provides a general framework for representing investor preference. The paper shows how the optimal asset allocation depends on the investment horizon, wealth, and the investor’s risk preference and how it therefore changes over time depending on cash flow and the returns achieved. The paper demonstrates how dynamic asset allocation leads to superior results compared to static or myopic techniques. Examples of dynamic strategies for various typical risk preferences and multiple asset classes are presented.