*4.1. Data and Software*

The empirical back-testing was based on intraday data from the S&P 500 from January 1998–December 2015. This highly liquid stock market includes the stocks of the 500 leading blue chip companies that offer high-quality commodities and generally-accepted services. Since the S&P 500 index captures 80 percent of the total U.S. market capitalization (S&P Dow Jones Indices 2015), this dataset represents a fundamental test for any potential capital market anomaly. To be in line with Stübinger and Endres (2018), we applied a two-step process with the objective of removing any survivor bias from the database. First, we used the information list from QuantQuote (2016) to build a binary constituent matrix for S&P 500 shares from January 1998–December 2015. The 4527 rows characterize the trading days considered, and the 984 columns show the stocks that were ever in the S&P 500. Each element of this matrix displays a "1" if the corresponding company is part of the S&P 500 index on the corresponding day, otherwise a "0". The sum of each row is about 500 because on each trading day, there are approximately 500 stocks in the index. Second, the complete archive of minute-by-minute prices from January 1998–December 2015 was downloaded from QuantQuote (2016). The corresponding stock exchange was open from Monday to Friday from 9:30–16:00 Eastern time. Consequently, the price time series of a share includes 391 data points per day. We followed Stübinger and Endres (2018) and adjusted the data by stock splits, dividends, and other corporate actions. By performing these two steps, our study design is in a position to map the constituents of the S&P 500 and the corresponding price time series completely.

The presented methodology and all relevant evaluations were implemented in the statistical programming language R (R Core Team 2019). For computation-intensive calculations, we used both the general-purpose programming language C++ and on-demand cloud computing platforms with virtual computer clusters that are available 24/7 via the Internet.
