**6. Conclusions**

In this paper, we presented an integrated statistical arbitrage strategy based on overnight price gaps and implemented it on high-frequency data of the S&P 500 stocks from January 1998–December 2015. In this context, we made four contributions to the literature. The first contribution relates to the developed trading framework based on a jump-diffusion model: we are in a position to capture jumps, mean-reversion, volatility clusters, and drifts. Our approach identifies overnight price gaps based on the jump test of Barndorff-Nielsen and Shephard (2004) and exploits temporary market anomalies by corresponding investments. In a preliminary study, we confirmed the assumption of mean-reverting overnight gaps with the aid of the S&P 500 index. The second contribution focuses on the value-add of our strategy. Therefore, we benchmarked it against well-known quantitative strategies from the same research area, namely the naive S&P 500 buy-and-hold strategy, fixed threshold strategy, general volatility strategy, and reverting volatility strategy. The third contribution is based on our large-scale empirical study on a sophisticated back-testing framework. Our strategy produced statistically- and economically-significant returns of 51.47 percent p.a. after transaction costs; the benchmarks were outperformed. The fourth contribution focuses on the profitable and robust performance results also in the last part of our sample period. Our findings posited a severe challenge to the semi-strong form of market efficiency even in recent times.

We identified three possible directions for further research: First, the event study and the back-testing framework should be conducted in other equity universes. Second, the exit signal of the strategy should be determined for each stock individually. Third, a multivariate model could be developed that takes into account the common interactions between stocks.

**Author Contributions:** J.S. and L.S. conceived of the research method. The experiments were designed by J.S. and performed by L.S. The analyses were conducted and reviewed by J.S. and L.S. The paper was initially drafted by J.S. and revised by L.S. It was refined and finalized by L.S. and J.S.

**Funding:** We are grateful to the "Open Access Publikationsfonds", which has covered 75 percent of the publication fees.

**Acknowledgments:** We are further grateful to Ingo Klein and two anonymous referees for many helpful discussions and suggestions on this topic.

**Conflicts of Interest:** The authors declare no conflict of interest.
