BL-SD-044: Variance Reduction, Twelve Weighting Variants

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-08

Venue: Bybit perpetuals Programme: II Verdict: CLOSED Axis of death: Method Transferability: UNIVERSAL

1. Identification

H-X3 is not a hypothesis and carries no falsifiable claim of its own. It is the check that had to run before the programme decided whether the H-X2 result was worth the sealed held-out era, and the record keeps it as a dossier because the check itself, and its negative result, shaped that decision.

2. Economic thesis

No new mechanism. H-X2 already stated it and named the forced loser. This pass tests a narrower, procedural question: does the same mechanism, measured on the same 569 fragile rebalances, produce a materially tighter estimate under a different bucket width, universe restriction, or weighting scheme than the one pre-registered.

The distinction matters because a tighter standard error is not evidence about the market, only about the estimator. A programme that treats a lower standard error, found after a disappointing result, as grounds to prefer a different specification has stopped testing a thesis and started searching for a friendlier one. This pass exists to run that search, if it was going to happen anyway, honestly and in the open.

Who is forced to lose, if the effect were real. Unchanged from BL-SD-043: leveraged holders liquidated in a single name at the moment the broader market is thinnest.

3. Falsifiable claim

No claim was pre-registered for this pass on its own terms. It is governed by the standing rule that a search over specifications, run after a result disappoints, may not be reported as if it were the original test:

4. Mathematical specification

Notation per BL-D-011. Base residual signal and fragility conditioning
identical to BL-SD-043 (H-X2) section 4: causal 24h residual, trailing-
median fragility gate, dollar-neutral construction, 24h non-overlapping
rebalance. The 569 fragile, traded rebalances are the same set of events
in every cell below; only the bucket, universe, and weight change.
 
bucket_k   in { 0.10, 0.20, 0.25, 0.33, 0.40 }   fraction per leg
universe_j in { A: liquid half, A2: full 154-symbol universe }
weight_m   in { equal,
                inverse-sigma:  w_i(t) = (1/sigma_i(t)) / sum_i(1/sigma_i(t)),
                z-rank:         w_i(t) = z_i(t) / sum_i |z_i(t)|  }
 
Ranking and bucket membership at each t use only information observable
at t, per BL-SD-043 section 4. Position is dollar-neutral, long the low
bucket and short the high bucket, sign convention fixed in BL-SD-043.
 
Exit: open[t+1+H], H = 24h, unchanged across every cell.
 
Cost: c_rt = 8.85 bps round trip, BL-FM-002 section 3.3, scaled by the
      turnover realised in that specific cell.

Causality holds by construction. Every cell reweights or rebuckets the same causal signal at the same causal timestamp; none introduces a look-ahead term, and the fragility gate that determines which 569 rebalances trade is identical across all twelve cells, so no cell can gain an edge by trading a different, more favourable set of events.

5. Operating envelope

6. Instrument

The variance and liquidity cell map, built on the pinned cross-sectional module shared with H-X1 and H-X2. It re-executes the H-X2 fragility gate and sweeps bucket width, universe, and weighting scheme against the fixed event set, reporting every cell rather than the single best one.

7. Results

None of the eleven variants exceeds the pre-registered cell's t-statistic of 1.715, the highest in the sweep. The cell most often cited as this pass's headline figure, the liquid-half decile-0.10 restriction, is weaker on both dimensions: net 5.962 at t=0.697 against the pre-registered cell's 6.850 at t=1.715. Restricting the universe and tightening the bucket, the two most intuitive levers for reducing name-level noise, both moved the estimate away from significance. Rank-based weighting fares worst: both z-rank cells return the only negative point estimates in the table.

A diagnostic run alongside the sweep measured pairing quality directly: median beta-gap across pairs 49.34 bps, with 75.92 percent of pairs exceeding 50 bps. A dollar-neutral pair meant to isolate an idiosyncratic move is carrying a median beta mismatch of that size in every one of the twelve cells, because none of them touches how pairs are formed.

8. Verdict, axis of death, and transferability

Verdict: CLOSED. Axis: method. Transferability: UNIVERSAL.

Twelve reweighting and rebucketing variants were tested against the fixed event set that produced H-X2's inconclusive primary result, and none improved on the pre-registered specification's t-statistic. The pre-registered cell was, itself, the best cell in the sweep.

The axis is method rather than power or cost: the finding is not about this construction's envelope but that searching for a lower-standard-error specification, after the pre-registered one fails to clear significance, is not a source of edge, across five bucket widths, two universe definitions, and three weighting schemes. Transferability is UNIVERSAL: no envelope substitution rescues a result that a wider or narrower search over the estimator itself could not improve.

9. Cost and capacity analysis

Best cell (pre-registered), net       +6.85 bps, t=1.715, n=569
Widest cell (0.40 cutoff), net        +1.62 bps, t=0.611, n=569
Cost range across cells               6.76 to 8.01 bps, turnover-scaled

Cost is not the binding constraint in any cell; the round trip is close to flat across the sweep because the underlying event count and holding period never change. Capacity was not separately assessed in this pass; it is addressed in BL-SD-043 section 9 and carries forward unchanged.

10. Envelope sensitivity and reopening conditions

Binding parameter: none in the usual envelope sense. The only lever this pass could pull was which specification to report, and that lever is the one the discipline forecloses.

Reversal condition: none available without re-opening the pre-registration
process. A cell that appeared to clear significance would itself require
fresh pre-registration and a fresh quota charge before it could be
treated as evidence, per the standing rule this pass exists to enforce.

No cost, capital, or latency substitution applies: none of the twelve cells failed on cost, capital, or latency. They failed to improve on a specification already measured honestly.

11. Reference implementation

The trailing volatility gauge the sweep weights on is published as trailing_sigma in 05_INSTRUMENTS/strategies/python/src/fragility_conditioning.py, with the rest of the conditioning layer, and the portfolio arithmetic as 05_INSTRUMENTS/src/cross_sectional.py, shared with BL-SD-042 and BL-SD-043. The cell map itself remains scheduled.

The gauge reads the window ending before the bar it labels and never the bar itself, which is what allows it to size a position taken at that bar. On a 24-hour rebalance grid its 30-rebalance window is 30 days, matching the liquidity window this family uses elsewhere, and a test confirms a volatility spike belongs only to the windows that follow it.

12. Evidence register

13. Lessons extracted

The clean result here is negative and worth exactly as much as a positive one would have been. A search for a lower standard error, run honestly and disclosed in full rather than reported as a single best cell, found nothing to prefer over the pre-registered specification. That outcome is what let the programme proceed to BL-SD-045 with the original H-X2 construction intact, rather than one quietly optimised against its own disappointing result.

The beta-gap diagnostic is carried forward as an open item. A median pair-level beta mismatch of 49 basis points, present identically across all twelve cells because none touches pair formation, is a candidate explanation for the base construction's standard error. It was not pursued further here, because doing so would itself require a fresh pre-registration this pass was explicitly built not to spend.

14. Cross-references

BL-SD-043 for the H-X2 construction this pass characterises. BL-SD-045 for the hypothesis this pass cleared to proceed toward the sealed era. BL-D-002 on the distinction between a pre-registered test and a post-hoc specification search. BL-SD-000 ledger row H-X3.

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