Optimal trend-following trading rules

24 Oct 2016. NUS mathematicians have provided a theoretical justification of trend-following trading strategies.

Prof DAI Min from the Department of Mathematics in NUS and his co-authors have provided a theoretical justification of trend-following strategies in a bull-bear switching market. The idea is to catch a bull market at its early stage, ride the trend, and liquidate the position at the first evidence of the subsequent bear market. Numerical experiments were conducted to validate the theoretical results and demonstrate how they perform in an actual marketplace.

Traditional trading strategies can be classified into three categories: (i) buy and hold; (ii) contra-trend, and (iii) trend-following. There is a large body of literature devoted to theoretical justifications of the buy-and-hold strategy and the contra-trend strategy. However, very little research exists for the trend-following strategy. In practice, a trend-follower often employs moving averages to determine the general direction of the market and to generate trading signals. Nevertheless, rigorous mathematical analysis is absent, because the moving averages are non-Markovian.

Prof Dai and his co-authors considered a bull-bear switching market with partial information and generated trade signals using the conditional probabilities of the bull phase, given up-to-date stock prices. The optimal buying and selling times are given in terms of a sequence of stopping times determined by two threshold curves. They showed that the optimal strategy is indeed a trend-following system characterised by the threshold curves which can be obtained through solving a system of associated Hamilton-Jacobi-Bellman equations.

 

36. Dai Min MAT 20160828 1

Figure shows the Shanghai Stock Exchange Composite Index 2001-2012: Trend-following trading (Green) vs. Buy-and-hold (Blue).

 

References

Dai M*; Yang Z*; Zhang Q*; Zhu QJJ*, "Optimal Trend Following Trading Rules" MATHEMATICS OF OPERATIONS RESEARCH Volume: 41 Issue: 2 Pages: 626-642 DOI: 10.1287/moor.2015.0743 Published: 2016

Dai M*; Zhang Q*; Zhu QJ*, "Trend Following Trading under a Regime Switching Model" SIAM JOURNAL ON FINANCIAL MATHEMATICS Volume: 1 Issue: 1 Pages: 780-810 DOI: 10.1137/090770552 Published: 2010