Optimal trend-following rules in two-state regime-switching models

Academic research on trend-following investing has almost exclusively focused on testing various trading rules’ profitability. However, all existing trend-following rules are essentially ad hoc, lacking a solid theoretical justification for their optimality. This paper aims to address this gap in the literature. Specifically, we examine the optimal trend-following when the returns follow a two-state process, randomly switching between bull and bear markets. We show that if a Markov model governs the return process, it is optimal to follow the trend using the Exponential Moving Average rule. However, the Markov model is unrealistic because it does not represent the bull and bear market duration times correctly. It is more sensible to model the return process by a semi-Markov model where the state termination probability increases with age. Under this framework, the optimal trend-following rule resembles the Moving Average Convergence/Divergence rule. We confirm the validity of the semi-Markov model with an empirical study demonstrating that the theoretically optimal trading rule outperforms the popular 10-month Simple Moving Average and 12-month Momentum rules across a universe of international markets.