Dynamic Cointegrated Pairs Trading: Time-Consistent Mean-Variance Strategies

Cointegration is a useful econometric tool for identifying assets which share a common equilibrium. Cointegrated pairs trading is a trading strategy which attempts to take a profit when cointegrated assets depart from their equilibrium. This paper investigates the optimal dynamic trading of cointegrated assets using the classical mean-variance portfolio selection criterion. To ensure rational economic decisions, the optimal strategy is obtained over the set of time-consistent policies from which the optimization problem is enforced to obey the dynamic programming principle. We solve the optimal dynamic trading strategy in a closed-form explicit solution. This analytical tractability enables us to prove rigorously that cointegration ensures the existence of statistical arbitrage using a dynamic time-consistent meanvariance strategy. This provides the theoretical grounds for the market belief in cointegrated pairs trading. Comparison between time-consistent and precommitment trading strategies for cointegrated assets shows the former to be a persistent approach, whereas the latter makes it possible to generate infinite leverage once a cointegrating factor of the assets has a high mean reversion rate.