Dynamic Trading with Predictable Returns and Transaction Costs ∗ Nicolae Gârleanu and Lasse

This paper derives in closed form the optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean-reversion speeds. The optimal updated portfolio is a linear combination of the existing portfolio, the optimal portfolio absent trading costs, and the optimal portfolio based on future expected returns and transaction costs. Predictors with slower mean reversion (alpha decay) get more weight since they lead to a favorable positioning both now and in the future. We implement the optimal policy for commodity futures and show that the resulting portfolio has superior returns net of trading costs relative to more naive benchmarks. Finally, we derive natural equilibrium implications, including that demand shocks with faster mean reversion command a higher return premium. We are grateful for helpful comments from Darrell Duffie, Pierre Collin-Dufresne, Andrea Frazzini, Esben Hedegaard, Anthony Lynch, Ananth Madhavan (discussant), Andrei Shleifer, and Humbert Suarez, as well as from seminar participants at Stanford Graduate School of Business, University of California at Berkeley, Columbia University, NASDAQ OMX Economic Advisory Board Seminar, University of Tokyo, and the Journal of Investment Management Conference. Gârleanu is at Haas School of Business, University of California, Berkeley, NBER, and CEPR; e-mail: [email protected]. Pedersen (corresponding author) is at New York University, NBER, and CEPR, 44 West Fourth Street, NY 10012-1126; e-mail: [email protected], http://www.stern.nyu.edu/∼lpederse/. Active investors and asset managers — such as hedge funds, mutual funds, and proprietary traders — try to predict security returns and trade to profit from their predictions. Such dynamic trading often entails significant turnover and trading costs. Hence, any active investor must constantly weigh the expected excess return to trading against the risk and costs of trading. An investor often uses different return predictors, e.g., value and momentum predictors, and these have different prediction strengths and mean-reversion speeds, or, said differently, different “alphas” and “alpha decays.” The alpha decay is important because it determines how long the investor can enjoy high expected returns and, therefore, affects the trade-off between returns and transactions costs. For instance, while a momentum signal may predict that the IBM stock return will be high over the next month, a value signal might predict that Cisco will perform well over the next year. The optimal trading strategy must consider these dynamics. This paper addresses how the optimal trading strategy depends on securities’ current expected returns, the evolution of expected returns in the future, their risks and correlations, and their trading costs. We present a closed-form solution for the optimal portfolio rebalancing rule taking these considerations into account. The optimal trading strategy is intuitive: The best new portfolio is a combination of 1) the current portfolio (to reduce turnover), 2) the optimal portfolio in the absence of trading costs (to get part of the best current risk-return trade-off), and 3) the expected optimal portfolio in the future (a dynamic effect). Said differently, the best portfolio is a weighted average of the current portfolio and a “target portfolio” that combines portfolios 2) and 3). Consistent with this decomposition, an investor facing transaction costs trades more aggressively on persistent signals than on fast mean-reverting signals: the benefits from the former accrue over longer periods, and are therefore larger. As is natural, transaction costs inhibit trading, both currently and in the future. Thus, target portfolios are conservative given the signals, and trading towards the target portfolio is slower when transaction costs are large. The key role played by each return predictor’s mean reversion is an important implication