Improving Cointegration-Based Pairs Trading Strategy with Asymptotic Analyses and Convergence Rate Filters

Abstract

A pairs trading strategy (PTS) constructs a mean-reverting portfolio whose logarithmic value moves back and forth around a mean price level. It makes profits by longing (or shorting) the portfolio when it is underpriced (overpriced) and closing the portfolio when its value converges to the mean price level. The cointegration-based PTS literature uses the historical sample mean and variance to establish their open/close thresholds, which results in bias thresholds and less converged trades. We derive the asymptotic mean around which the portfolio value oscillates. Revised open/close thresholds determined by our asymptotic mean and standard derivations significantly improve PTS performance. The derivations of asymptotic means can be extended to construct a convergence rate filter mechanism to remove stock pairs that are unlikely to be profitable from trading to further reduce trading risks. Moreover, the PTS literature oversimplifies the joint problem of examining a stock pair’s cointegration property and selecting the fittest vector error correction model (VECM). We propose a two-step model selection procedure to determine the cointegration rank and the fittest VECM via the trace and likelihood ratio tests. We also derive an approximate simple integral trading volume ratio to meet no-odd-lot trading constraints. Experiments from Yuanta/P-shares Taiwan Top 50 Exchange Traded Fund and Yuanta/P-shares Taiwan Mid-Cap 100 Exchange Traded Fund constituent stock tick-by-tick backtesting during 2015–2018 show remarkable improvements by adopting our approaches.