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When Optimal Pairs Trading Is Well-Posed and Market-Neutral

Article arXiv papers · Author: Bahman Angoshtari
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Summary

This study examines optimal investment in two cointegrated stocks for an investor with constant relative risk aversion utility. It extends earlier stochastic-control work by focusing on whether the optimization problem is well-posed and by supplying a verification result for the proposed solution.

The central finding is a sharp condition: the problem is well-posed exactly when the optimal positions form a market-neutral long-short portfolio. This provides a theoretical basis for market-neutral pairs trading under the model considered. The excerpt reports a theoretical result rather than empirical evidence, and it does not state the condition’s formula or explain how robust the conclusion is to different utility functions, market assumptions, or trading costs.

Key ideas

  • The model studies optimal investment in a pair of cointegrated stocks under CRRA utility.
  • The analysis checks well-posedness of the stochastic control problem and provides verification.
  • A single sharp condition determines whether the problem is well-posed.
  • That condition is also necessary and sufficient for offsetting long and short positions.
  • The result gives theoretical support for market-neutral pairs trading within the stated model.

Tags

EquitiesPairs tradingMean reversionPortfolio construction
Full text
# On the Market-Neutrality of Optimal Pairs-Trading Strategies


# On the Market-Neutrality of Optimal Pairs-Trading Strategies









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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.