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...

In spite of the widespread popularity of trend-following investing, little is still known about optimal trend-following with transaction costs. A few existing studies consider this question using a continuous-time model within the stochastic optimal control theory framework. However, despite...

We start this paper by presenting compelling evidence of short-term momentum in the excess returns on the S&P Composite stock price index. For the first time ever, we assume that the excess returns follow an autoregressive process of order p, AR(p), and evaluate the parameters of this process....

In this paper, a result for bivariate normal distributions (Sheppard, 1899) from statistics is transformed into a financial asset context in order to build a tool which could translate a correlation matrix into an equivalent probability matrix and vice versa. This way, the correlation...