Statistical arbitrage with optimal causal paths on high-frequency data of the S&P 500

Abstract

This paper develops the optimal causal path algorithm and applies it within a fully-fledged statistical arbitrage framework to minute-by-minute data of the S&P 500 constituents from 1998 to 2015. Specifically, the algorithm efficiently determines the optimal non-linear mapping and the corresponding lead–lag structure between two time series. Afterwards, this study explores the use of optimal causal paths as a means for identifying promising stock pairs and for generating buy and sell signals. For this purpose, the established trading strategy exploits information about the leading stock to predict future returns of the following stock. The value-add of the proposed framework is assessed by benchmarking it with variants relying on classic similarity measures and a buy-and-hold investment in the S&P 500 index. In the empirical back-testing study, the trading algorithm generates statistically and economically significant returns of 54.98% p.a. and an annualized Sharpe ratio of 3.57 after transaction costs. Returns are well superior to the benchmark approaches and do not load on any common sources of systematic risk. The strategy outperforms in the context of cryptocurrencies even in recent times due to the fact that stock returns contain substantial information about the future bitcoin returns.

Keywords:

• Finance
• Optimal causal path
• Statistical arbitrage
• Lead–lag structure
• High-frequency trading
• Cryptocurrency

JEL classification:

• C1
• C5
• C6
• G1
• G12

Acknowledgments

The author has benefited from many helpful discussions with Sylvia Endres, Ingo Klein, Julian Knoll, Sandra Romeis, and the anonymous referee.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 Thanks to Kenneth R. French for providing all relevant data for these models on his website.