A pairs trading strategy based on linear state space models and the Kalman filter

Abstract

Among many strategies for financial trading, pairs trading has played an important role in practical and academic frameworks. Loosely speaking, it involves a statistical arbitrage tool for identifying and exploiting the inefficiencies of two long-term, related financial assets. When a significant deviation from this equilibrium is observed, a profit might result. In this paper, we propose a pairs trading strategy entirely based on linear state space models designed for modelling the spread formed with a pair of assets. Once an adequate state space model for the spread is estimated, we use the Kalman filter to calculate conditional probabilities that the spread will return to its long-term mean. The strategy is activated upon large values of these conditional probabilities: the spread is bought or sold accordingly. Two applications with real data from the US and Brazilian markets are offered, and even though they probably rely on limited evidence, they already indicate that a very basic portfolio consisting of a sole spread outperforms some of the main market benchmarks.

Keywords:

• Kalman filter
• Mean-reverting conditional probabilities
• Pair
• Pairs trading
• Spread
• State space models
• Statistical arbitrage

Acknowledgements

Our sincere thanks go to the referees, whose comments, requirements and suggestions were invaluable for improving this paper. We are also truly grateful to Cristiano Fernandes, Adrien Nguyen Huu and Paulo Cezar Carvalho for their very constructive comments. All remaining errors are ours.

Notes

No potential conflict of interest was reported by the authors.