Against a recent level, do wide gaps between paired shares close more often than chance?
Study 38 · Changed a rule or plan · recorded 4 October 2026 · answer: Yes · full paper with figures
The question
Chance here means each pair's own daily moves put in random order many times, which keeps how much the pair moves but removes any pull back. Study twenty-five, judging each gap against a year-old level, could not tell how often gaps closed apart from chance; we ask whether a level set over the last sixty trading sessions can.
Rules fixed before the result
Fixed before any recent-level gap was measured: at least 200 gaps in all, 40 in each period and 100 pair-years (one pair watched over one calendar year, a pair counting once per year it is used), with no pair holding over a tenth of the gaps. The gaps close faster than chance if the share closed lies above the 250th highest of 10,000 reshuffled shares, slower if below the 250th lowest, otherwise neither. We expected neither, at low confidence.
Data and method
On the same matched pairs of shares as study twenty-five, in development data up to 2022, each pair's price gap was measured against its usual level and spread over the last sixty trading sessions, not a year-old level. A gap of two or more standard deviations counted as closed if it came back within half of one within twenty sessions. The share closed was compared with 10,000 reshuffles of each pair's own daily moves, which remove any pull back.
The answer
Yes, a little more often than chance allows: 531 of 1,548 wide gaps (about 34%) closed within twenty sessions, above the reshuffles' range of about 28% to 33% (median about 30%), and only 2 of the 10,000 reshuffles reached that share. Every minimum set in advance was met. We had expected the gaps to close no more often than the reshuffles, at low confidence, so the result differs from our expectation. Most of the rise over study twenty-five is the new yardstick itself: measured against the recent level, the reshuffled moves alone closed about 30% of gaps, where against a year-old level study twenty-five's reshuffles closed about 14%; the actual moves take it from about 30% to about 34%.
Main estimate
0.343 fraction (95% range 0.279 to 0.327), from 1548 observations
What it changes
Study twenty-five, which judged each gap against a year-old level, could not tell the share of gaps that closed apart from the share that chance alone gives. This result reopens work on these pairs, but only as a finding on development data. The next question on pairs must first tell a pull back towards the recent level apart from short-lived swings back and forth in the daily moves, which the reshuffle removes along with any pull.
What remains uncertain
The result covers only study twenty-five's pairs, about half utilities, and comes mostly from 2021-2022: in 2019-2020 the share of 247 gaps that closed was within the reshuffles' range. A 120-session level or 40-session horizon does not separate gaps from reshuffles, and reshuffling in runs of five narrows the margin. Pairs share dates and often an industry, each reshuffled separately, so that range may be too narrow; untested short-lived swings back and forth in daily moves could explain the result.
How it was made
Run took 99 minutes; independent code review: approve; the recorded calculation reruns to the same result.
Fingerprints
plan 3881b640968027a1f0e4e184a7e307cc53c75e7d32977ed377b916aafd53b532 result 9f45004587981c1218b53c9605aa2650ef141ad14905254d1105aee39036e985
Exploratory work on development data; not a performance claim.