Optimal Convergence Trading

This article examines arbitrage investment in a mispriced asset when the mispricing follows the Ornstein-Uhlenbeck process and a credit-constrained investor maximizes a generalization of the Kelly criterion. The optimal differentiable and threshold policies are derived. The optimal differentiable policy is linear with respect to mispricing and risk-free in the long run. The optimal threshold policy calls for investing immediately when the mispricing is greater than zero with the investment amount inversely proportional to the risk aversion parameter. The investment is risky even in the long run. The results are consistent with the belief that creditconstrained arbitrageurs should be risk-neutral if they are to engage in convergence trading. Myron [Scholes] once told me they are sucking up nickels from all over the world. But because they are so leveraged that amounts to a lot of money. Merton Miller about the essence of arbitrage.