Optimal Dynamic Momentum Strategies

Abstract

We explicitly solve for the optimal dynamic trading strategy between a riskless asset and a risky asset with momentum. The optimal portfolio weight depends not only on the momentum, as in Merton’s (1971) framework, but also on the historical price path; this contrasts with Merton. Due to their path dependence, optimal portfolio weights have a wide distribution for a given level of momentum; for example, investors may short the risky asset if it has rebound price paths but leverage if it has hump-shaped price paths. This effect tends to be the most significant after large price swings. Path dependence is solved with explicit formulas and presented with heuristic statistics.

Keywords: momentum, optimal trading strategy, path dependence.

JEL Classification: C32, G11