Optimality of Momentum and Reversal

We develop a continuous-time asset price model to capture short-run momentum and long-run reversal. By studying a dynamic asset allocation problem, we derive the optimal investment strategy in closed form and show that the combined momentum and reversal strategies are optimal. We then estimate the model to the S&P 500 and demonstrate that, by taking the timing opportunity with respect to trend in return and market volatility, the optimal strategies outperform not only pure momentum and pure mean reversion strategies, but also the market index and time series momentum strategy. Furthermore we show that the optimality also holds for the out-of-sample tests and with short-sale constraints and the outperformance is immune to market states, investor sentiment and market volatility