AXOQUANT
AXOQUANT
Working paper
A tradeable structural relationship needs an enforcer: an agent contractually or legally obliged to push prices back together, whose obligation does not depend on the relationship having held before. The obligation has to come from a document — a prospectus, a treaty, a statute, a contract — and it has to name a party and a trigger. Statistical co-movement has no such agent. Its persistence is a bet that a past correlation regime continues, which is exactly the bet a composition null prices, and the word "cointegration" does not distinguish the two cases. The mechanism does.
This paper states the taxonomy we admit at authoring, the cross-market gradient that motivates it, and the correction that matters most — enforcement is necessary and not sufficient. Three separate named, documented, contractual obligations we screened were fully discharged and paid nobody. The rule that follows is an admission test rather than a hypothesis: measure the dislocation against round-trip cost before spending research time. It also states the cost of the method. Six campaigns support the principle; the sample is two asset classes and a handful of books, and it is written into a campaign charter as an admission rule, not as settled science.
§1
Five classes are admitted. Each is stated as a class, because the instrument is never the finding — the obligation is. A candidate must name its row, the party the obligation binds, the document the obligation comes from, the dated or conditional trigger, and the event that would end it. A seed that cannot fill those fields is not rejected; it is reclassified as a control and it runs as one.
| Enforcer class | Obligated party | Trigger that binds |
|---|---|---|
| Prospectus rebalance mandate | the fund's issuer or responsible entity | every dealing day's close, per the constitutive document |
| Defended band with a formal intervention obligation | the monetary authority, and in a two-sided arrangement its counterparty | the quoted rate reaching a published band edge |
| Share-class legal identity | the issuer | a conversion right or an identical cash-flow claim, on its stated terms |
| Contract convergence | the contract and its clearing house | the dated settlement |
| Index tracking mandate | the fund | the index's dated reconstitution or effective date |
The classes are enumerated, not recalled. A standing census reads obligations out of primary documents — prospectuses and central-bank pages — and holds a verbatim-verified quote against each: 35 obligations enumerated at its first version (2026-08-02), 33 of them screened against round-trip cost, and 17 coverage holes named in the record rather than left implicit. An enumeration is not a verdict. A row that clears cost is an unpriced candidate, which is arithmetic and necessary-not-sufficient; §3 is what happens to candidates that clear it.
One finding from building the census is worth publishing against ourselves: the regulatory document collection we already held contained none of the primary prospectus or central-bank texts the census needed. A corpus that cannot produce the document behind an obligation is a corpus about obligations, not of them. The gap is logged as a version-two item.
§2
The screen is the same in every market. Test cointegration on a training window, then require the relationship to stay stationary on a later window it was not selected from. The baseline is the set of correlation-only candidates put through the identical gate, so the comparison is against the market's own rate of accidental persistence rather than against zero.
The result is ordinal and the ordering is the finding. Three asset classes, lettered A, B and C here rather than named, because a list of the markets we screen is live information even when every individual result in it is dead. In A, statistical cointegration persists well above its own random baseline. In B it persists above its baseline by a smaller margin. In C the record calls the gap statistically indistinguishable from chance. So statistical relationships are abundant in one asset class, present in a second, and arbitraged away in a third.
The reading is not that one market is inefficient and another is efficient. It is that a statistical relationship is a decaying asset whose half-life is set by how many participants can see it, while an enforced one is not — arbitraging an enforced relationship away requires the enforcer to stop enforcing. That is why enforced structure survives in all three and statistical structure survives in one.
Abundance is also not specificity. The best-known statistical relationship in currencies passed our survivability gate with a stable Sharpe and was refused at the specificity gate at p = 0.62 against a beta-adjusted null: the carry factor, correctly named, and published as such on the method page. A relationship can be real, persistent, and still be someone else's factor.
§3
This is the strongest correction to our own published stance, and it is why this paper exists rather than the abstract it replaces. A real enforcer can be entirely priced in. The obligation is discharged perfectly, on time, by a party that has no choice — and there is nothing left on the table. Three cases, each a named, documented, contractual obligation, each measured, each paying nobody.
One of these looked like a trade until the entry was moved. Measured with the signal and the entry sharing a bar, it was positive in every calendar year of its sample. Lagged a single bar, the sign flipped in all five years and a block bootstrap put P( mean ≤ 0 ) = 0.9997. In a separate case the same defect inflated a steelman result roughly fivefold — five-sixths of the apparent edge was stale prints and bid-ask noise reverting. A one-bar entry lag is now enforced by the harness on everything, not applied by convention.
The correction runs on our own exhibits too. An earlier demonstration of this principle — an enforced-tracking book that had passed both gates — was withdrawn in 2026-07 when a fills-level audit found the book had not traded the instruments its labels claimed. Three further routing defects were excavated beneath it. The principle is restated here without that exhibit, and the withdrawal is left in the record rather than edited out; the audit chain that caught it is the stronger exhibit anyway.
§4
Enforcement earns a candidate a screen, not a slot. Before any cluster time is spent, a seed must clear three things, on data observable before the analysis window:
The rule in one line: enforcement without dislocation pre-classifies as a control. It runs, it is reported, and it is not treated as a candidate. The band case is the class property in miniature — a defended band pays when it is wide and defended episodically, and does not pay when it is narrow and continuously honoured. The obligation is identical in both. The tradeable room is not.
The rule was not derived; it was extracted from an audit we did not enjoy.
§5
Every class in Table 1 has a termination event. Bands are re-set or abandoned; prospectuses are amended; share classes collapse or merge; contracts are delisted; index methodologies change. The obligation that makes the book tradeable is also the single point at which it fails, and it fails discontinuously.
In-sample statistics are structurally blind to this. A bootstrap resamples the path it was given; it cannot contain a break that is absent from its sample, so every bootstrap-sized leverage number on an enforced book is answering a question about a world in which the enforcer never stopped. Enforced books therefore take scenario-sized leverage instead: the historical break is imposed by hand on the band or the mandate and the position is sized to survive it. The 2015 franc break is the reference scenario — a defended floor that had held for years gapped through every stop in minutes. The mechanics of that sizing rule sit in Gate L.
The second half of the rule is operational. Every enforced book registers a same-day kill trigger on its own enforcement mechanism: a change to the arrangement retires the book the day it is announced, not the day the P&L notices. A book whose thesis is a document must be killed by that document changing.
Two further limits, stated rather than buried. Enforcement guarantees the relationship; it guarantees neither the size of the dislocation nor the depth at which it can be filled, so capacity remains a separate first-class measurement and a specific book can be perfectly enforced and too thin to fund. And n is small. Six campaigns point one way, on two asset classes and a handful of books. This is the best organizing prior we have, and it is written into a campaign charter as an admission rule precisely so that its own controls can refute it.
§6
Mechanism-first authoring does not scale the way a tournament does. Each seed needs a primary document, a named party, a trigger, a cost screen and a mechanism-nulling placebo. A tournament authors thousands of candidates in the time that takes, and for a while we ran both and let the tournament set the pace.
The defence of the slow method is a measurement, not a preference. We planted dislocations of known size into calibrated synthetic series and swept them upward until our pair search started finding them. At the dislocation scales real contractual obligations actually pay, the search's power is near zero: the detection floor sits above the signal. A gate whose power curve begins above the dislocations real mechanisms offer is not conservative; it is blind, and every kill verdict it issued below that floor has an unknown false-negative rate. The floor's value, the planted scales and the power curves are withheld as instrument calibration; the direction and the existence of the measurement are published.
Two consequences follow. The tournament is the moonshot channel, not the discovery channel — it is where breadth is bought, not where obligations are found. And the corroborating anecdote is the one that should have been obvious years earlier: our best-validated enforced-structure book arrived through mechanism-first authoring, not through the search that was built to find it.
One qualifier, because the instrument that produced the floor has not finished its own examination. The generator behind those power curves owes an out-of-sample moment-match table — vol clustering persistence, tail index, cross-sectional dispersion, autocorrelation at the horizons we trade. A generator that cannot pass its own moment-match test is not a null, and a verdict resting on it is provisional. Until that table lands, the detection floor is our best measurement of the pipeline's eyes and not a validated one. That instrument, and what it returned when we ran it against ourselves, is the 2026-08 working paper We measured our own instrument.