A regime-switching model of stock returns with momentum and mean reversion

A vast body of empirical literature documents the existence of short-term momentum and medium-term mean reversion in various financial markets. However, few theoretical models explain these two common phenomena. A Markov model, wherein the return process randomly switches between bull and bear states, can reproduce many stylized facts of financial asset returns, excluding the mean reversion. An important limitation of the Markov model is that the state termination probability does not depend on age. We develop a semi-Markov model wherein, following the empirical evidence, the state termination probability increases with age. We demonstrate that this model induces short-term return momentum and subsequent reversal. We calibrate our model to real-world data and show that the empirical results agree with our theoretical model.