Plain record › Study 25

Do price gaps between shares that move together close faster than a reshuffle of the same moves?

Study 25 · Inconclusive · recorded 1 October 2026 · answer: Not settled · full paper with figures

The question

The pairs, counted in study twenty-one, are shares of one industry and size whose prices moved together for two years; we then watch their price gap for a year. When the gap moves two standard deviations from its usual level, does it return within half of one inside 20 trading days more often than the same moves in random order?

Rules fixed before the result

We fixed in advance the pairs, the trigger at two standard deviations, the close at half of one, the 20-day horizon and 10,000 reshuffles, and required at least 200 gaps, 40 in each of three periods and 100 pair-years, a pair watched for a year, no pair over 10% of gaps. The closing share counted as faster above the highest 2.5% of shuffled shares, slower below the lowest 2.5%, otherwise not separated. Seven side checks were set, none deciding.

Data and method

For each pair formed in 2014 to 2020, the gap is the difference of the two shares' log prices, measured against its mean and standard deviation in the year before the watched year, 2016 to 2022. A gap event starts when the gap first moves beyond two standard deviations and closes if it returns within half of one inside 20 trading days. The reshuffle keeps each pair-year's daily moves and starting point but removes any pull back.

The answer

Of 664 widened gaps, 13.4% closed within 20 trading days. Shuffling the same moves put the middle 95% of closing shares between 11.5% and 16.8%, and the actual share fell inside that range, so it was not separated from a random order of the same moves; the result is not settled. All seven side checks gave the same reading. Most gaps stayed open after 20 trading days under both the actual and the shuffled moves. We had expected faster closing, at low confidence, so the result differed from our expectation.

Main estimate

0.134 fraction (95% range 0.115 to 0.168), from 664 observations

What it changes

Nothing changed. Pairs of shares gained no support from this study and were not carried to a planned study.

How it was made

Run took 38 minutes; independent code review: approve; the recorded calculation reruns to the same result.

Fingerprints

plan dbf10e864ceed01a46330a6ba485436671d439a94c7b0499acba3c4b43bb7f4b
result a61f548b9f4ee50eccd1a20798c039e4e249263e23a0bebe69aec537fbf18490

Exploratory work on development data; not a performance claim.