Equilibrium pairs trading under delayed cointegration

Abstract

Cointegration analysis is an econometric tool used to identify equilibrium among assets and construct a pairs trading portfolio. The discrete-time vector error correction model (VECM) for identifying cointegration includes lag difference terms as explanatory variables, thus permitting delayed adjustment of the deviations from equilibrium. The continuous-time limit of the VECM becomes a stochastic delay differential equation. We investigate the dynamic open-loop equilibrium mean–variance pairs trading strategy under such a delayed cointegration model. The existence and uniqueness results for the equilibrium are offered. We prove in general that the equilibrium strategy can lead to statistical arbitrage under certain conditions that are related to the roots of the corresponding characteristic equation. We obtain an explicit solution for a case with distributed delay. Our empirical study demonstrates the superiority of our strategy over its Markovian counterpart when the model selection result prefers a high-order VECM.