Dynamic Consumption and Portfolio Decisions with Time Varying Asset Returns

Abstract

In this article, the authors study dynamic consumption and portfolio decisions by using dynamic programming that allows them to compute, with sufficient accuracy, the decision variables and the consumption-wealth ratio at any point of the state space. The dynamic decision problem is first analytically and numerically solved for a simple model with constant returns. Then the authors solve a model with dynamic consumption and portfolio decisions when time-varying returns are calibrated from the low-frequency components of U.S. time series financial data. The implications of the change of investor’s risk aversion, the change of returns, and the time horizon are explored for the consumption decisions, the consumption–wealth ratio, the asset allocation, and the path of wealth.