*Article* **Statistical Arbitrage with Mean-Reverting Overnight Price Gaps on High-Frequency Data of the S&P 500**

### **Johannes Stübinger \* and Lucas Schneider**

Department of Statistics and Econometrics, University of Erlangen-Nürnberg, Lange Gasse 20, 90403 Nürnberg, Germany; lucas.schneider@fau.de

**\*** Correspondence: johannes.stuebinger@fau.de

Received: 27 February 2019; Accepted: 26 March 2019; Published: 1 April 2019

**Abstract:** This paper develops a fully-fledged statistical arbitrage strategy based on a mean-reverting jump–diffusion model and applies it to high-frequency data of the S&P 500 constituents from January 1998–December 2015. In particular, the established stock selection and trading framework identifies overnight price gaps based on an advanced jump test procedure and exploits temporary market anomalies during the first minutes of a trading day. The existence of the assumed mean-reverting property is confirmed by a preliminary analysis of the S&P 500 index; this characteristic is particularly significant 120 min after market opening. In the empirical back-testing study, the strategy delivers statistically- and economically-significant returns of 51.47 percent p.a.and an annualized Sharpe ratio of 2.38 after transaction costs. We benchmarked our trading algorithm against existing quantitative strategies from the same research area and found its performance superior in a multitude of risk-return characteristics. Finally, a deep dive analysis shows that our results are consistently profitable and robust against drawdowns, even in recent years.

**Keywords:** computational finance; asset pricing models; overnight price gaps; financial econometrics; mean-reversion; statistical arbitrage; high-frequency data; jump-diffusion model
