Modeling momentum and reversals

Stock prices are well known to exhibit behaviors that are difficult to model mathematically. Individual stocks are observed to exhibit short term price reversals and long term momentum, while their industries only exhibit momentum. Here we show that individual stocks can be modeled by simple mean reverting processes in such a way that these behaviors are captured, the model is arbitrage free, and market informational efficiency is preserved. Simulation shows that in such a market, when mean reversion is sufficiently high, strategies which use reversals would substantially outperform buy and hold strategies.