Portfolio choice with return predictability and small trading frictions

Abstract

This paper studies a portfolio choice problem of a utility-maximizing investor with return predictability and small liquidity costs. By adopting a logarithmic-return assumption, our asymptotic expansion around small liquidity costs provides the closed-form expressions for the first-order approximation of the value function and the associated almost-optimal trading strategy. The almost-optimal trading strategy indicates that the investor should trade toward the optimal frictionless portfolio, instead of directly adopting it. The approximated value function effectively captures the utility loss derived from the investor's inability to adopt the optimal frictionless portfolio directly over time. Finally, our numerical analysis indicates that the investor's utility loss is sensitive to the specifications of the return-predicting factors and that the investor's trading behaviors under the logarithmic-return and arithmetic-return assumptions can differ remarkably over a medium to a long investment horizon.