Optimal Trend Following Rules in Two-State Regime-Switching Models

Academic research on trend-following investing has almost exclusively been focused on testing the profitability of various trading rules. However, all existing trend-following rules are ad-hoc rules whose optimality has never been justified theoretically. The goal of this paper is to fill this gap in the literature. Specifically, this paper examines the optimal trend-following rules when the returns follow a two-state process that randomly switches between bull and bear markets. We show that if the returns are modeled by a Markov switching model, it is optimal to follow the trend using the Exponential Moving Average. In a more realistic case where the returns are modeled by a semi-Markov switching model (SMSM) where the state duration times exhibit positive duration dependence, the optimal trend-following rule is somewhat similar to the Moving Average Convergence/Divergence rule. We confirm the validity of the SMSM by an empirical study that uses the data on the S\&P 500 and Dow Jones Industrial Average indices. We demonstrate that the theoretically optimal trading rule outperforms the popular 10-month Simple Moving Average and 12-month Momentum rules