The question
When a listed company files a priced prospectus to sell shares, do its shares afterwards trail companies like it? The question matters to anyone who prices new issues, holds companies that issue often, or wants to know whether markets absorb new supply quickly.
What was already known
Weak returns after share offerings are among the longer-standing observations in empirical finance, documented in academic work since the mid-1990s. What has been argued over ever since is less whether a gap appears than whether it is real: results depend heavily on the benchmark chosen, on how long-horizon returns are averaged, and on how often the same company issues. This investigation does not claim a new effect. It asks whether the gap survives a stricter procedure: rules fixed before any outcome is seen, comparison companies matched on industry and size, the same companies measured on ordinary dates, and uncertainty measured by resampling whole companies rather than individual sales.
How the investigation unfolded
- Study 45 · 10 October · stoppedRegistered the question with a required precision: able to detect a 3-point gap over the month and a 10-point gap over the year. The year could only reach 19. By its own rule the study stopped before looking at any return after a sale.
- Study 46 · 10 October · diagnosisAsked why, still without looking at outcomes. Found the cause and a measurement that fixed it.
- Study 47 · 11 October · the answerRe-registered the question with the new measurement and answered it.
- Study 52 · 13 October · the follow-upTested whether the result was confined to drug and biotechnology companies, which issue often.
The data
Sales were taken from the regulator's public filing indexes: a company's first priced prospectus in 90 days, filed from 2014 to 2022, at least 180 days after its shares entered the records. That gave 2,190 sales by 745 companies. Each sale was matched with five comparable companies in the same industry with similar trading size that had filed no such prospectus within a year. Companies that later disappeared stay in the data. For the comparison on ordinary dates, the same companies were measured on 5,757 windows with no sale within a year either side.
The filings do not say whether new shares, holders' shares or other securities were sold, so all are counted as one family of events.
Study 45: a plan that stopped itself
Before any return after a sale was computed, the plan fixed its minimums (at least 400 sales by 150 companies, enough in each of three periods) and the precision it needed. It then measured that precision on data from before the sales. The month passed. The year did not: the smallest one-year gap the test could reliably detect was 19 points, against the 10 required. The study stopped and recorded no answer, as its rules said it must. It had put the chance of a stop of any kind at 15%.
A stop is a result. A study that runs anyway on a test too blunt for its question produces a reassuring "no effect" that means nothing.
Study 46: diagnosing the obstacle
The follow-up asked a narrow question: can the one-year test be made precise enough on the same sales, and if so, how? It fixed in advance what would count as each possible cause: faulty prices, a few extreme cases, or companies whose years are simply that volatile. It still did not look at any return after a sale.
- Not bad data. Of the 16 most extreme cases, only one failed a check of the price series, against none of the 44 least extreme.
- A few enormous rises. 14 of those 16 were driven by the selling company's own rise in the year before the sale, very large. A handful of such moves dominated the average.
- The fix. Comparing growth on a logarithmic scale, where a tenfold rise and a 90% fall carry equal weight, cut the smallest detectable effect from 19 to 5.8 points. Pulling the extremes in also passed (7.4); using the comparables' median barely helped (18.5). The order in which remedies would be tried was fixed in advance, with the log scale first.
- A further finding. The same companies' ordinary years were noticeably less spread than the years before their sales, so later plans take their precision check from ordinary years.
Changing the scale made the one-year test precise enough
Smallest one-year effect the test could reliably detect, in percentage points. Shorter is better; the plan required 10 or less.
Show the numbers
| Measure | Smallest detectable effect (points) |
|---|---|
| Plain returns (as planned) | 19.0 |
| Comparables' median | 18.5 |
| Extremes pulled in (1%) | 7.4 |
| Log scale (adopted) | 5.8 |
| Required by the plan | 10.0 |
The change is not free. The log scale measures the gap in a typical holder's growth of wealth, not in average returns, and more volatile shares grow more slowly on it even with equal expected returns. Study 47 therefore reports both scales and adds volatility back as a check.
Study 47: the answer
The question was registered again on the new measurement, with its precision checked first: the test could now detect 1.7 points over the month and 4.1 log points over the year, inside the bounds of 3 and 10. The plan listed seven competing explanations, what each predicted, and the answer it expected. It expected a lasting shortfall, with low confidence.
- Month: shares trailed their comparable companies by 4.4 points (95% range 3.4 to 5.5).
- Year: 25 log points behind (19 to 31). In plain returns, 12 points (7 to 17). With each share's volatility added back, still 24 log points.
- No recovery: the gap deepened at every horizon measured, from the first day to the end of the year.
The gap opens at once and keeps widening for a year
Average return of the selling company minus its five comparable companies, in percentage points, plain-return scale. Horizons are evenly spaced, not to scale. Vertical bars show 95% ranges where the study computed them.
Show the numbers
| Trading day | Average gap (points) | 95% range |
|---|---|---|
| 1 | −2.54 | — |
| 5 | −3.03 | −3.63 to −2.44 |
| 10 | −3.51 | −4.27 to −2.76 |
| 21 | −4.41 | −5.46 to −3.42 |
| 42 | −5.25 | — |
| 63 | −5.87 | — |
| 126 | −7.76 | — |
| 189 | −8.29 | — |
| 252 | −12.06 | −16.67 to −7.20 |
The gap belongs to the sale, not to the kind of company
The same companies measured on ordinary dates, at least a year from any sale, show no gap. Dots are averages; lines are 95% ranges.
Month · percentage points
Year · log points (about a percentage for small values)
Show the numbers
| Window | After the sale | Ordinary dates |
|---|---|---|
| Month, points | −4.41 (−5.46 to −3.42) | +0.46 (−0.75 to +1.75) |
| Year, log points | −24.8 (−30.8 to −19.4) | −0.5 (−3.6 to +2.6) |
Seven explanations, tested against the figures
The plan named each explanation's distinguishing prediction before the result. Each one's distinguishing prediction failed, two of them with caveats. The record chooses none.
| Explanation | What it predicted | What was found |
|---|---|---|
| Temporary supply pressure | A dip in the first weeks that recovers within the year | Contradicted No recovery; the gap kept widening for a year. |
| Managers sell when shares are dear | A larger gap after a larger run-up before the sale | Contradicted The opposite: the gap was smaller after a larger run-up (slope +0.16, range 0.06 to 0.26). The same companies show a similar slope on ordinary dates, so it may reflect these companies rather than the sale. |
| Weaker companies, sale or no sale | A gap on ordinary dates as well | Contradicted No gap on ordinary dates. Caveat: those dates sit at least a year from any sale, so a weakness confined to years around sales would not show. |
| Mixed-up kinds of filing | No gap overall, a gap in one kind | Contradicted Every kind of filing trails. |
| No effect | No gap at the sizes that matter | Contradicted |
| Size mismatch | The gap moves when size is measured before the sale | Contradicted Barely moved. |
| Volatility, not returns | The gap vanishes on plain returns or with volatility added back | Contradicted Still behind on both. |
The cause therefore stays open. The record narrows it: the gap is tied to the sale, lasts at least a year, and is not explained by timing, size, volatility or the kind of company.
How robust
The plan named its alternative analyses before any result and fixed that none could change the reading. Each was reported as if it were the main analysis.
Every alternative analysis, and every period, points the same way
One-year gap in log points. The alternatives were listed in the plan before any result; none could change the reading.
Show the numbers
| Analysis | Year gap (log points) | 95% range |
|---|---|---|
| Registered measure | −24.8 | −30.8 to −19.4 |
| Volatility added back | −24.3 | −31.7 to −17.6 |
| Delisted firms dropped | −26.1 | −32.5 to −20.3 |
| Three comparables | −24.4 | −30.2 to −18.6 |
| Size before the sale | −23.8 | −30.1 to −18.2 |
| Ranges by calendar month | −24.8 | −29.9 to −19.5 |
| First sale per company only | −18.5 | −24.1 to −12.9 |
| Extremes trimmed | −23.9 | −29.2 to −19.1 |
| 30-day gap rule, not 90 | −27.1 | −34.7 to −20.2 |
| Filed 2014–2016 | −26.9 | −36.2 to −17.9 |
| Filed 2017–2019 | −20.1 | −31.5 to −10.1 |
| Filed 2020–2022 | −28.4 | −34.3 to −22.4 |
Study 52: is it one industry?
Drug and biotechnology companies sell shares often and are volatile, so the result could have been theirs alone. Study 52 split the same sales by industry, with rules fixed in advance and the same resampling draws as study 47, which reproduced its figures exactly.
Not a biotech story
Both groups trail by similar amounts; the difference between them could not be told apart from zero.
Month · percentage points
Year · log points
Show the numbers
| Group | Month (points) | Year (log points) |
|---|---|---|
| Drug and biotechnology | −4.7 (−6.6 to −2.8) | −22 (−30 to −15) |
| All other industries | −4.2 (−5.4 to −3.0) | −26 (−35 to −19) |
Both groups trail over the month and the year; neither shows a gap on ordinary dates. The difference between them is imprecise: drug and biotechnology could be up to 7 log points deeper or 15 shallower. So large differences are ruled out and small ones are not. In 2017–2019 alone, the drug and biotechnology gap was measured but its range did not lie wholly below zero.
What it means, and what it does not
- It means that, on this development data and under rules fixed in advance, shares of companies that sell stock trail comparable companies for at least a year, and the gap is tied to the sale rather than to the kind of company.
- It does not mean the gap could be captured in trading. Costs, timing of information and short-selling limits were not studied.
- It does not identify the cause. It rules out several and leaves the rest open. The next registered question is how the gap splits by kind of sale, and whether it grows with the sale's size.
Limits and disclosures
- Development data only. Nothing here has been confirmed on data set aside for confirmation, and no outside expert has reviewed it.
- The same sales were studied four times. Each plan was fixed before its own outcome, but studies 46, 47 and 52 were designed knowing earlier figures from these sales.
- A design gap cost a study. Earlier studies had already shown extreme values in company returns, and a fallback measure could have been registered in study 45. It was not. Plans must now register one in advance.
- A change of scale is a change of question. The log measure is about a typical holder's wealth, not average returns. Both are reported.
- Dependence across companies. Ranges resample whole companies, but sales by different companies in the same week share market and industry shocks that this does not capture.
- Industry codes are each company's current code, not its code at the time of the sale.
- A person in the loop. A written owner direction, prompted by an idle gap in the queue, named study 47 as the next study. Its design, rules and reading were the engine's.
Written by hand from the four studies' published records and result files; every figure is taken from those records. Exploratory research on historical data: not investment advice, a trading recommendation or a performance claim. Each study has its own page: 45, 46, 47, 52.