Optimal Convergence Trading

Optimal Convergence Trading

Vladislav Kargin∗ January 14, 2004

Abstract 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.

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Introduction

Arbitrageurs are people who detect inconsistencies in asset prices and invest in them hoping that the inconsistencies will be eliminated. The waiting time is often uncertain and since the arbitrageur depends on the willingness of other people to lend him money, the irrationality of creditors may lead to great debacles long before prices converge to consistent values. The notorious story of the arbitrage fund LTCM that lost 90 percent of its value on “riskless” deals illustrates the importance of credit constraints. So what policy should the arbitrageur pursue when creditors impose borrowing constraints? In particular, can the arbitrageur allocate the available funds in such a way as to eliminate all the long-run risk? If this risk elimination is possible, the mispricings should be equally attractive to risk-averse as well as risk-neutral investors. However, a popular view

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