Optimal Trend-Following With Transaction Costs

42 Pages Posted: 22 Nov 2022

See all articles by Valeriy Zakamulin

Valeriy Zakamulin

University of Agder - School of Business and Law

Javier Giner

University of La Laguna - Faculty of Economics, Business and Tourism

Date Written: November 20, 2022

Abstract

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.

Keywords: stock market, trend-following, transaction costs, simple moving average, moving average crossover

JEL Classification: G11, G17

Suggested Citation

Zakamulin, Valeriy and Giner, Javier, Optimal Trend-Following With Transaction Costs (November 20, 2022). Available at SSRN: https://ssrn.com/abstract=4282126 or http://dx.doi.org/10.2139/ssrn.4282126

Valeriy Zakamulin (Contact Author)

University of Agder - School of Business and Law ( email )

Service Box 422
Kristiansand, N-4604
Norway
+47 38141039 (Phone)

HOME PAGE: http://vzakamulin.weebly.com/

Javier Giner

University of La Laguna - Faculty of Economics, Business and Tourism ( email )

Camino La Hornera s/n
La Laguna, Tenerife, 38071
Spain
+34 922317102 (Phone)

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