The Effect of Fat Tails on Rules for Optimal Pairs Trading

Pairs trading, a popular investing strategy, is often carried out using the meanreverting Ornstein-Uhlenbeck equation as a cornerstone. The random variables which determine the underlying stochastic process are customarily assumed to follow a normal distribution, despite the well-known fact that in Finance random variables are more prone to reach extreme values than Gaussians. In this article we check the reliability of the referred normality assumption, and we analyse the impact that fat-tailed (Lévy stable, generalized hyperbolic and non-centered t-student) distributions have on the optimal orders for pairs trading of stocks and cryptocurrencies. We find that the normal distribution suits very poorly to the spread residuals, being the t-student and hyperbolic distributions more appropriate choices. We also find that the optimal trading rules are strongly influenced by the distribution chosen to fit the residuals, as are the risk measures (the impact on the expected performance being moderate). In addition, we investigate the effect of Poisson events on the optimal trading rules of pairs and single products, which has a decisive influence on the stop-loss orders for the former and profit-taking for the latter