BL-SD-014: Spread Momentum, the Inverse of Cointegration

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-07

Venue: Bybit Programme: I Verdict: NOT PROVEN Blocking axis: Power Transferability: N/A, verdict not settled

1. Identification

Produced as salvage from the falsification of Strategy B, on the same pairs and the same causal walk-forward harness, rather than from a separate design cycle.

2. Economic thesis

Where BL-SD-013 bet that a diverged spread reverts to its mean, this hypothesis bets the opposite: that at extreme divergence, the spread continues moving away from the mean rather than back toward it, and that riding the continuation captures a return the fade hypothesis was giving away.

The separability evidence that motivated the test was measured before the inversion was built. Trades that had diverged under the original strategy carried a higher entry z-score than trades that had reverted, resolved faster, and were concentrated in trending, meme, or narrative-driven tokens, while reverted trades were concentrated in established alts. All three signals point the same way: at extreme divergence, the spread has momentum rather than mean reversion.

Who is forced to lose. As with its parent hypothesis, no structural forced loser is named. The thesis is a statistical inversion of a mechanism that itself never named one, and that absence carries forward unchanged.

3. Falsifiable claim

No claim was pre-registered as a separate document before this test was run; it inherits the decision rule of the walk-forward harness used to settle BL-SD-013, applied in the reverse direction. Reproduced from the verdict record:

If the momentum configuration's walk-forward net expected value is positive with a t-statistic at or above 2, on the same clean pairs and the same causal fitting, the spread carries a tradeable continuation edge rather than a reversion edge.

4. Mathematical specification

Notation per BL-D-011. Same pair set and same causal fitting as BL-SD-013.
 
beta_t(L), alpha_t(L), mu_t(L), sigma_t(L)   as in BL-SD-013 section 4,
                                              fit on the trailing window [t-L, t-1] only
 
signal, entry:
  spread_t = log p_{i,t} - beta_t(L) * log p_{j,t} - alpha_t(L)
  z_t      = ( spread_t - mu_t(L) ) / sigma_t(L)
  fire at t when |z_t| >= entry_z; direction = +sign(z_t)     [ride the divergence, inverted sign vs BL-SD-013]
 
exit:
  |z_t| >= cont_z   (continuation realised, take profit)
  |z_t| <= rev_stop_z   (reverted against the position, stop)
  hold >= max_hold bars   (timeout)
 
sizing: one unit each leg, dollar-neutral pair, hedged at entry beta_t0(L), frozen
cost:   c_rt = 11.0 * (1 + beta_t(L)) bps  +  leg_spread of 6.0 bps
 
Best configuration tested: entry_z = 2.5, cont_z = 3.5, rev_stop_z = 1.5, max_hold = 12 bars (48h)

Causality is inherited directly from the corrected harness in BL-SD-013 section 4: every fitted quantity uses only the trailing window ending at t, and the position is hedged and evaluated against entry-time parameters rather than refitted quantities. No new look-ahead surface was introduced by inverting the direction of the bet.

5. Operating envelope

6. Instrument

BL-IS-003, the same instrument that falsified the parent fade hypothesis, run with the momentum simulator rather than the fade simulator. No new tool was built; the momentum test exists specifically to determine whether the falsification instrument, having just killed one strategy, was also capable of confirming its opposite rather than simply tending to produce negative results.

7. Results

The best configuration inverts the parent hypothesis's loss into a positive median and mean return with a majority win rate, but the t-statistic of 1.80 does not clear the pre-registered bar of 2.

8. Verdict, blocking axis, and transferability

Verdict: NOT PROVEN. Axis: power. Transferability: not applicable; the record's transferability classification is reserved for FALSIFIED and CLOSED verdicts.

The interval around this result is not reported as spanning zero explicitly in the source, but the t-statistic of 1.80 is, by the pre-registered rule itself, insufficient to confirm an edge. This is recorded as a lead rather than a falsification and rather than a confirmed edge, precisely to avoid the error this record treats as a distinct failure mode: labelling an underpowered result as either a kill or a win poisons any decision that later inherits the label.

The temptation to treat this as a validated replacement for the just-retired parent strategy was named explicitly at the time it arose and was not acted on. The threshold held.

9. Cost and capacity analysis

Cost is embedded in the reported net figures, using the same schedule as BL-SD-013. No separate gross figure is preserved. Capacity was not measured, and was never reached, since the result did not clear the bar that would have justified further investment in measuring it.

10. Envelope sensitivity and reopening conditions

Binding parameter: statistical power, not cost or mechanism sign.

Reversal condition:  a live or forward-tested sample sufficient to raise the
                      t-statistic from 1.80 to 2.0 or above at the same point
                      estimate, or a materially larger point estimate at the
                      existing sample size. Neither was pursued.

Unlike BL-SD-013, this result cannot be classified as universal or envelope-bound, because it was never settled in either direction. What would resolve it is more data on the same specification, gathered forward rather than mined from the same walk-forward window the point estimate was drawn from, since re-testing on the same data would be horizon shopping.

What would reopen it: a forward shadow of the specification in section 4, accumulated to a sample large enough to move the t-statistic decisively past 2, with the microstructure substrate the verdict record recommends, tick-exact divergence detection rather than four-hour close z-scores, in place of the slower construction used here.

What would not reopen it: re-running the same three configurations on the same historical window. That would not add information; it would repeat the measurement that already produced the underpowered result.

11. Reference implementation

BL-IS-003, run through its momentum-continuation path, published as walk_forward_momentum in 05_INSTRUMENTS/src/walk_forward.py. Six of that module's 26 cases cover this path specifically; the rest cover the reversion path and the shared fold geometry. This hypothesis was never deployed to a shadow instrument in its own right, so no separate engine module exists to publish.

Publishing that path found the ordering defect recorded in BL-IS-000 section 6 a second time. The current-bar sanity checks on the fitted hedge ratio sat ahead of the open-position branch and skipped past it on failure, exactly as they did in the reversion path, so a continuation exit, a reversion stop or a timeout could fail to fire on a bar whose own trailing fit was degenerate. The exits read frozen entry-bar parameters and never read the current fit, which is why the guard did not belong there. Both paths are fixed and one test pins each.

The finding generalises past this instrument. A guard placed ahead of a branch it does not belong to travels with the loop it sits inside, so it gets copied wherever that loop is copied. Finding one is a reason to read every other loop in the same file rather than to close the item, and that is how the second one surfaced here.

No result in this dossier moves. The defect is latent: it changes an exit only on a bar where the trailing fit is degenerate, and no such bar occurs in the measured sample.

12. Evidence register

13. Lessons extracted

This hypothesis is cited in BL-IN-003 section 7 as the case for holding a statistical threshold under pressure: the programme had just lost its flagship stat-arb strategy and had, in hand, a promising-looking replacement produced by the very instrument that had killed the first one. Recording it as NOT PROVEN rather than confirming it on a t-statistic of 1.80 was the correct outcome precisely because the incentive ran the other way.

No rule number is attached to this hypothesis specifically; the discipline it exercises, refusing to promote an underpowered result under pressure, is the general standard this record applies throughout rather than a rule this hypothesis produced on its own.

14. Cross-references

BL-SD-013 for the parent hypothesis and the shared harness. BL-IN-003 section 7 for the narrative of the decision not to confirm this result under pressure. BL-D-009 rule on the distinction between a lead and an edge. BL-SD-000 ledger row SPR-MOM.

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