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...

This paper assumes that the market returns follow a two-state Markov process that randomly switches between bull and bear states. We show that in this case, the exponential moving average (EMA) represents the optimal trend-following rule. The paper provides the analytical solution to the optimal...

A vast body of empirical literature documents the existence of short-term momentum and medium-term mean reversion in various financial markets. By contrast, there is still a great shortage of theoretical models that explain the presence of these two common phenomena. We develop a semi-Markov...