Do one company's returns against comparable companies, at different dates, move together more than earlier studies assumed?
Study 51 · Changed a rule or plan · recorded 13 October 2026 · answer: Partly · full paper with figures
The question
Each earlier study comparing a company's return with comparable companies of the same industry and similar trading size assumed, when checking the smallest effect it could detect, that two returns of the same company are correlated at one tenth. We measured it over the month after and the year after the start of each quarter, and after those studies' events.
Rules fixed before the result
Fixed in advance: each horizon reads at or under 0.10, between 0.10 and 0.25, or above 0.25 by where its whole 95% range lies. The year has its own rule if the month is at or under 0.25, the year lies wholly above the month's upper edge (0.10 if the month read at or under 0.10, else 0.25), and non-overlapping windows lie below the full year. It needed 2,000 ordinary-date windows from 300 companies each holding two or more.
Data and method
We rebuilt four earlier studies' companies, events and ordinary dates exactly, and took each window's return against comparable companies of the same industry and similar trading size over the month after and the year after; a company appearing in several studies counts once. We measured how much of the returns' spread lies between companies rather than within them, with a range from resampling whole companies 2,000 times, and read the year again on windows that do not overlap.
The answer
Partly. Over the month after the start of each quarter, the correlation between two returns of the same company was 0.01 (95% range from just below zero to 0.026), at or under the one tenth assumed. Over the year after it was 0.21 (0.18 to 0.25), because windows of one year starting a quarter apart share most of their trading days; on windows that do not overlap it was about 0.10 (0.05 to 0.14), wholly below the full year. After the four earlier studies' events the year read 0.27 (0.22 to 0.32), and the year's value differed between the groups of companies studied. At these values the earlier studies' checks of the smallest effect they could detect all stay within their limits, the closest at 0.096 against 0.12.
Main estimate
0.010 ratio (95% range -0.006 to 0.026), from 10924 observations
What it changes
By the rule fixed in advance, later plans keep one tenth for the month, while the year is set pair by pair: about 0.15 for two years of one company that do not overlap, more for two that share trading days. The earlier studies' checks would hold at any correlation up to about 0.85, well above the measured range, so their conclusions stand as recorded.
What remains uncertain
These windows and events were studied before, in studies forty-seven, forty-eight, forty-nine and thirty-nine, and this plan was fixed after their counts were seen. The year's value differed between the groups of companies, and companies on the same dates share a second dependence, measured here as near zero and not treated in the checks. One development sample, 2013 to 2022.
How it was made
Run took 121 minutes; independent code review: approve; the recorded calculation reruns to the same result.
Fingerprints
plan 3945da0b892d499e8cac7c3034ea943cfbdc82156b8d714c579c22f584a397e2 result 284b6aa2def390c73363082a3692c0ad8f1522895a9394e65e80e593014ab536
Exploratory work on development data; not a performance claim.