Optimal Investment and Consumption with Return Predictability and Execution Costs

Abstract

We provide a closed-form solution to an optimal investment and consumption problem for a constant absolute risk aversion (CARA) agent, who faces execution costs when trading correlated risky assets with return predictability. The optimal investment strategy indicates that the agent should trade gradually toward a dynamic aim portfolio, which is an adjusted Merton portfolio with modifications to account for the persistence of the return predicting signals and the execution costs. The optimal consumption strategy is quadratic in the return predicting signals and linear in the agent’s wealth. Our numerical studies show that the execution costs diminish the importance of asset return predictability on the agent’s optimal investment strategy, thereby confirming the conjecture raised by Liu (2004). In addition, the presence of the intermediate consumption leads to a more aggressive aim portfolio than the case without consumption.

Keywords: Continuous-time investment and consumption problem; Return predictability; Linear temporary price impact; Execution costs; Utility maximization.

JEL Classification: G11, G12