*4.2. Formation Period*

In the formation period, we considered all S&P 500 stock constituents. Therefore, we (i) conducted the BNS jump test based on past returns (ii) applied the jump detection scheme in the case of rejecting the null hypothesis, and (iii) selected the top stocks for the subsequent trading period. This subsection describes the outlined three-step logic.

In the first step, we executed the BNS jump test based on both the 390 intraday returns of the last trading day and the overnight return, i.e., the percentage change of the price from 16:00 of the last day to 9:30 of the current trading day. Specifically, we determined the *z*-statistic of Huang and Tauchen (2005) (see Equation (18)). If the null hypothesis was rejected, at least one jump emerged in the underlying security during the considered period. If the null hypothesis was not rejected, no jump emerged in the underlying security during the considered period. Consequently, we did not consider this stock in our back-testing framework.

In the second step, we applied the jump identification method of Andersen et al. (2010) to ensure that we only selected stocks possessing overnight gaps (see Section 2.2). Therefore, we considered only stocks that incorporate a significant overnight gap.

In the third step, we followed Miao (2014) and Stübinger and Endres (2018) and selected the most suitable shares for the out-of-sample trading period. Our algorithm attempted to find stocks possessing the most meaningful jump last night. For this purpose, we selected the top stocks, that possesses overnight gaps in the sense of Andersen et al. (2010), with the highest *z*-statistic of Huang and Tauchen (2005). The top 10 stocks were transferred to the trading period (see Section 4.3) 1.

<sup>1</sup> If less than 10 shares satisfied the condition of Andersen et al. (2010), we traded accordingly less. However, this case is extremely rare.
