Optimal Convergence Trading

TL;DR

This paper analyzes optimal convergence trading strategies for credit-constrained investors in mispriced assets modeled by Ornstein-Uhlenbeck processes, deriving policies that balance risk and mispricing correction.

Contribution

It introduces a framework for optimal convergence trading under credit constraints, deriving explicit policies and analyzing their properties.

Findings

Optimal differentiable policy is linear in mispricing.

Threshold policy recommends immediate investment when mispricing > 0.

Investments remain risky even in the long run.

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 credit-constrained arbitrageurs should be risk-neutral if they are to engage in convergence trading.