Optimal Trend Following Trading Rules

Document Type

Article

Publication Date

5-2016

Abstract

This paper is concerned with the optimality of a trend following trading rule. The underlying market is modeled like a bull-bear switching market in which the drift of the stock price switches between two states: the uptrend (bull market) and the down trend (bear market). We consider the case when the market mode is not directly observable and model the switching process as a hidden Markov chain. This is a continuation of our earlier study reported in Dai et al. [Dai M, Zhang Q, Zhu Q (2010) Trend following trading under a regime-switching model. SIAM J. Fin. Math. 1:780–810] where a trend following rule is obtained in terms of a sequence of stopping times. Nevertheless, a severe restriction imposed in Dai et al. [Dai M, Zhang Q, Zhu Q (2010) trend following trading under a regime-switching model. SIAM J. Fin. Math. 1:780–810] is that only a single share can be traded over time. As a result, the corresponding wealth process is not self-financing. In this paper, we relax this restriction. Our objective is to maximize the expected log-utility of the terminal wealth. We show, via a thorough theoretical analysis, that the optimal trading strategy is trend following. Numerical simulations and backtesting, in support of our theoretical findings, are also reported.

Published Citation

Min Dai, Zhou Yang, Qing Zhang, Qiji Jim Zhu (2016) Optimal Trend Following Trading Rules. Mathematics of Operations Research 41(2):626-642. https://doi.org/10.1287/moor.2015.0743

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