A Control-Theoretic Feedback Method for Pairs Trading

Summary

This paper presents a general pairs-trading algorithm framed as a feedback-control problem. It allows the trader to choose a broad class of spread functions and adjusts investment levels dynamically as that spread changes. Rather than relying on restrictive assumptions about stock-price processes and spread forms, the method defines a pair as tradeable when the spread and price process together satisfy a mean-reversion condition. For such cases, the authors prove that the algorithm produces positive expected account growth.

The paper also reports tests on historical trading data, fitting stock pairs to a commonly used spread function, and describes simulation results as showing robust growth without very large drawdowns. These results support the method in the tested setting, but the supplied description gives no specific performance figures or details about costs, execution, or out-of-sample validation. The theoretical growth result is conditional on the stated mean-reversion condition; it is not a guarantee for arbitrary pairs or live trading.

Key ideas

• The algorithm adjusts investment levels dynamically using a chosen spread function as feedback.
• A stock pair qualifies as tradeable when the spread and price process satisfy a mean-reversion condition.
• The authors prove positive expected account growth under that condition.
• Historical-data tests and simulations report robust growth without very large drawdowns.
• The evidence described does not establish live performance or account for unspecified trading costs and execution details.

Tags

# A General Framework for Pairs Trading with a Control-Theoretic Point of View


# A General Framework for Pairs Trading with a Control-Theoretic Point of View









Pairs trading is a market-neutral strategy that exploits historical correlation between stocks to achieve statistical arbitrage. Existing pairs-trading algorithms in the literature require rather restrictive assumptions on the underlying stochastic stock-price processes and the so-called spread function. In contrast to existing literature, we consider an algorithm for pairs trading which requires less restrictive assumptions than heretofore considered. Since our point of view is control-theoretic in nature, the analysis and results are straightforward to follow by a non-expert in finance. To this end, we describe a general pairs-trading algorithm which allows the user to define a rather arbitrary spread function which is used in a feedback context to modify the investment levels dynamically over time. When this function, in combination with the price process, satisfies a certain mean-reversion condition, we deem the stocks to be a tradeable pair. For such a case, we prove that our control-inspired trading algorithm results in positive expected growth in account value. Finally, we describe tests of our algorithm on historical trading data by fitting stock price pairs to a popular spread function used in literature. Simulation results from these tests demonstrate robust growth while avoiding huge drawdowns.

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