Optimal Convergence Trade Strategies∗

Convergence trades exploit temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced assets. This paper studies optimal convergence trades under both recurring and non-recurring arbitrage opportunities represented by continuing and ‘stopped’ cointegrated price processes and considers both fixed and stochastic (Poisson) horizons. We demonstrate that conventional long-short delta neutral strategies are generally suboptimal and show that it can be optimal to simultaneously go long (or short) in two mispriced assets. We also find that the optimal portfolio holdings critically depend on whether the risky asset position is liquidated when prices converge. Our theoretical results are illustrated using parameters estimated on pairs of Chinese bank shares that are traded on both the Hong Kong and China stock exchanges. We find that the optimal convergence trade strategy can yield economically large gains compared to a delta neutral strategy.