Do shares that close just below a whole-number price earn less the next session than shares just above?
Study 81 · Changed a rule or plan · recorded 2 November 2026 · answer: Yes · full paper with figures
The question
Each session we compare shares whose closing price sits one to five hundredths below a whole number with shares one to five hundredths above one, holding the day's own return fixed, and ask whether the first group earns less the next session, against the market fund. We also ask whether the same gap is smaller around prices ending in .50.
Rules fixed before the result
Fixed before any return from these years was formed: the answer is yes only if the gap's 95% range lies wholly below zero and reaches 0.06 percentage points a session, the smallest gap worth a screen note, and the same gap around prices ending in .50 is clearly smaller. If the range lies below zero but either other condition fails, the answer is partly. At least 1,000 sessions were needed, and checks on earlier years had to pass first.
Data and method
Each session, among shares priced at five or more in US currency, one least-squares fit of the next session's return over the market fund on seven price-position groups and the day's own return gives the gap between the just-below and just-above groups, averaged over sessions. The range allows for correlation between nearby sessions. Before these years were read, the method matched the earlier exploratory figures, and reshuffling the groups on earlier years showed its false-alarm rate within its target.
The answer
Yes. Over 1,258 sessions from 2018 to 2022, shares closing just below a whole-number price earned 0.121 percentage points less the next session than shares just above (95% range 0.086 to 0.156 less), beyond the gap of 0.06 set in advance as the smallest gap worth a screen note. Around prices ending in .50 the gap was 0.059 (0.022 to 0.097), smaller by 0.062 (0.009 to 0.115); at the quarter marks it was 0.006 the other way (0.023 less to 0.035 more). It appeared overnight, 0.046 (0.026 to 0.065), and during the day, 0.075 (0.044 to 0.106). In this sample it was larger under a price of twenty than above, 0.165 against 0.082, by 0.082 (0.010 to 0.154), and in the thinnest third by trading value than the most liquid third, 0.210 against 0.083, by 0.129 (0.038 to 0.219).
Main estimate
-0.121 percentage points (95% range -0.156 to -0.086), from 1258 observations
What it changes
The result supports a note, for the record only, on every screen that admits shares by a whole-number price: a floor at five admits shares closing just above it and refuses those just below, where this gap sits. The next question in this area is how orders gather at whole numbers, which needs order-book data we do not hold. No trading decision changes.
What remains uncertain
These years were used before, by studies 57 and 58, so this is a check inside our development data, not an independent test. Each session counts once, so shares moving together on the same date are allowed for, but the larger gaps among cheaper and thinly traded shares were read one at a time, with no joint guard against chance. Without quote data, closes at the buying or selling quote cannot be separated directly.
How it was made
Run took 66 minutes; independent code review: approve; the recorded calculation reruns to the same result.
Fingerprints
plan 6c34db8236d11abf2586972a6f1729a8e1e6ce59ee79e00d8dcee0a119783504 result 6ce2931d7ea62684ed309d0e55d0b5beeca977a48041d3043ee68c376b4676a9
Exploratory work on development data; not a performance claim.