INITIAL BALANCE / S&P 500
Give the first hour a scale.
Measure the opening range against the movement already priced in.
93.4%Narrowest fifth · close inside ±1σ
54.7%Widest fifth · close inside ±1σ
In the S&P 500 study, the narrowest fifth of opening-hour ranges finished inside ±1σ on 93.4% of sessions. The widest fifth did so on 54.7%. The groups were ranked by the opening-hour high–low range divided by the one-sided 1σ band width.
READING THE FINDING
Normalizing the Initial Balance puts the first hour into the day’s volatility context. The study does not publish exact quintile cutoffs or group counts, so these groups cannot be turned into precise live thresholds from the paper alone. Use the first hour of the US cash session, with the correct daylight-saving mapping.