Optimal Trend-Following With Transaction Costs

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 being theoretically the most appropriate, this approach makes the problem intractable analytically, and the numerical solutions are extremely complex. In this paper, we suggest a discrete-time model that represents an acceptable compromise between theoretical simplicity and practical relevance. On the one hand, we formulate a partly tractable optimization problem that can be solved numerically using standard and efficient optimization methods. On the other hand, we demonstrate that our model produces a satisfactory solution that substantially reduces trading costs. Under reasonable assumptions about the trend process, we show that the optimal trend-following rule is very much like the popular simple moving average crossover rule. Thus, our model justifies using the crossover rules in practice. Historical simulations show that the empirical evidence is in satisfactory agreement with our theoretical model