Optimal Time Series Momentum

We develop a continuous-time asset price model to capture the time series momentum documented recently. The underlying stochastic delay differential system facilitates the analysis of effects of different time horizons used by momentum trading. By studying an optimal asset allocation problem, we find that the performance of time series momentum strategy can be significantly improved by combining with market fundamentals and timing opportunity with respect to market trend and volatility. Furthermore, the results also hold for different time horizons, the out-of-sample tests and with short-sale constraints. The outperformance of the optimal strategy is immune to market states, investor sentiment and market volatility.