Multiple Risky Assets, Transaction Costs and Return Predictability: Implications for Portfolio Choice

Abstract

Our paper contributes to the dynamic portfolio choice and transaction cost literatures by considering a multiperiod CRRA individual who faces transaction costs and who has access to multiple risky assets, all with predictable returns. We numerically solve the individual’s multiperiod problem in the presence of transaction costs and predictability. In particular, we characterize the investor’s optimal portfolio choice with proportional and fixed transaction costs, and with return predictability similar to that observed for the U.S. stock market. We also perform some comparative statistics to better understand the nature of the no-trade region with more than one risky asset. Throughout our focus is on the case with two risky assets. We also perform some utility comparisons. The calibration exercise reveals some interesting results about the relative attractiveness of the three equity portfolios calibrated.

With proportional transaction costs and i.i.d. returns, we numerically find the rebalancing rule to be a no-trade region for the portfolio weights with rebalancing to the boundary. With zero correlation, the no-trade region is a rectangle irrespective of the investor’s age. When the correlation of the risky assets is non-zero, the no-trade region becomes a parallelogram. With positive correlation, the parallelogram distorts the associated rectangle in such a way as to take advantage of the associated substitutability across the two assets that the positive correlation induces. The converse is true for negative correlation. Turning to the allocations with return predictability, our numerical results strongly suggest that it is the conditional return correlation that determines the nature of the distortion to the no-trade parallelogram. Irrespective of the investor’s age, the distortion always mirrors the no-trade parallelogram distortion that we find in the i.i.d. case for return correlation of the same sign. The no-trade region is always larger late in life than early in life. However, the difference in no-trade area between early and late in life is less pronounced when returns are predictable, consistent with intuition that the benefits from rebalancing today are more short-lived when returns are predictable than in the i.i.d. case.