On the Market-Neutrality of Optimal Pairs-Trading Strategies

TL;DR

This paper investigates the conditions under which optimal pairs-trading strategies are market-neutral, providing a theoretical foundation for the practical use of market-neutral pairs-trading in financial markets.

Contribution

It establishes a sharp well-posedness condition for the stochastic control problem and shows this condition is necessary and sufficient for market-neutrality in pairs-trading.

Findings

Well-posedness condition for the control problem

Market-neutrality is characterized by the same condition

Theoretical justification for market-neutral pairs-trading

Abstract

We consider the problem of optimal investment in a market with two cointegrated stocks and an agent with CRRA utility. We extend the findings of Liu and Timmermann [The Review of Financial Studies, 26(4):1048-1086, 2013] by paying special attention to when/if the associated stochastic control problem is well-posed and providing a verification result. Our new findings lead to a sharp well-posedness condition which is, surprisingly, also the necessary and sufficient condition for the optimal investment to be market-neutral (i.e. having offsetting long/short positions in the stocks). Hence, we provide a theoretical justification for market-neutral pairs-trading which, despite having a strong practical relevance, has been lacking a theoretical ground.