When returns are partially predictable and trading is costly, utility-maximizing investors track a target portfolio at a constant trading speed. The target portfolio is optimal for a frictionless market, where asset returns are scaled back to account for trading costs and volatilities are adjusted to proxy the “execution risk” of holding assets that are costly to trade and exposed to volatile states. The trading speed solves an optimal execution problem, which describes how the legacy portfolio inherited from the past is traded toward the target portfolio in an optimal manner. Unlike for period-by-period mean-variance preferences, the target portfolio hedges changes in investment opportunities, and both it and the trading speed are linked and depend on execution risk. We set the problem out first in an “absolute” framework—price shocks independent of the price level, and investors have CARA preferences—and then in a “relative” framework, with price shocks scaled by price levels and CRRA preferences. We illustrate the practical implications of these results in a model where market return predictions are based on a short-term momentum and a long-term value signal. This paper was accepted by Kay Giesecke, finance. Funding: X. Shi acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) through Discovery Grant RGPIN-2024-04569 and Discovery Launch Supplement DGECR-2024-00444. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.05913 .
Muhle‐Karbe et al. (Tue,) studied this question.