BL-SD-010: Cross-Sectional Residual Reversion

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-07

Venue: Bybit perpetuals Programme: I Verdict: FALSIFIED Axis of death: Idea Transferability: UNIVERSAL

1. Identification

Designed and settled the same day. The thesis was named the family's best candidate on entry, ranked first of three for a stated reason: the same proven relative mean-reversion family that had produced the platform's only live-validated edge at the time, but computed cross-sectionally rather than pairwise, which was expected to reach statistical power in days rather than weeks because every symbol produces a signal on every bar.

2. Economic thesis

Each bar, a symbol's return over a lookback window minus the equal-weight basket's mean return over the same window is its idiosyncratic residual. A residual that has moved further from the basket than its peers is assumed to be over-extended and expected to revert; a position is opened long the most negative residuals and short the most positive, dollar and beta neutral by construction, and closed at a fixed horizon.

Who is forced to lose. The design record does not name one. It argues from a statistical property of the price panel, that a symbol's idiosyncratic move should mean-revert toward the basket, rather than from a mechanism that compels a specific counterparty to transact against its own interest at the moment of reversion. This absence is not corrected in this retelling; it is carried forward as a defect of the original thesis and is returned to in section 13.

3. Falsifiable claim

No single quoted pre-registration sentence predates the measurement in the source record; the design document states its validation criterion in narrative form. Reproduced as closely as the source allows:

Cross-sectional residual mean-reversion, entered on a causal residual z-score and held to a fixed horizon, produces a positive net expectation across a small, principled parameter grid, on both a 15-minute and a 1-hour panel, net of an 11 basis point fee and a 4 basis point spread cost, and beats a random-symbol control matched on real price dynamics.

4. Mathematical specification

Notation per BL-D-011. Universe of N liquid Bybit perpetuals, prices P[t,i].
 
Causal lookback return, strictly using data at or before t:
 
  ret_{i,t}(L)  =  log P_{i,t}  -  log P_{i,t-L}
 
Cross-sectional residual, demeaned across the universe at bar t:
 
  resid_{i,t}   =  ret_{i,t}(L)  -  mean_j ret_{j,t}(L)
 
Cross-sectional z-score, at bar t only:
 
  z_{i,t}       =  ( resid_{i,t} - mean_i resid_{i,t} ) / std_i resid_{i,t}
                =  resid_{i,t} / std_i resid_{i,t}      (residuals sum to zero
                    across i by construction, so the numerator's mean term
                    vanishes)
 
Market-neutral level (the PnL unit, not the signal):
 
  spread_{i,t}  =  log P_{i,t}  -  mean_j log P_{j,t}
 
Entry, fire at t when, for symbol i:
 
  entry_z <= |z_{i,t}| < entry_z_max      entry_z = 1.5, entry_z_max = 3.0
  direction  d_i = +1 (long) if z_{i,t} < 0,  -1 (short) if z_{i,t} > 0
 
Exit, fixed horizon:
 
  at bar  t + hold,  hold in {6, 12, 24} bars.  Positions that cannot
  complete the full horizon before the data ends are dropped, not
  partially scored.
 
Sizing:
 
  one unit notional per leg, equal weight, dollar-neutral by construction
 
Cost, per leg, round trip:
 
  c_rt  =  2 * fee_per_fill  +  spread_cost_bps
        =  2 * 5.5  +  4.0  =  15.0 bps
 
Net per leg:
 
  r_net,i(t)  =  d_i * ( spread_{i,t+hold} - spread_{i,t} ) * 1e4  -  c_rt

Causality holds by construction and is pinned by an explicit no-look-ahead property test in the instrument's own test suite. ret_{i,t}(L) is a function of P_{i,t} and P_{i,t-L} only, both at or before t. resid_{i,t} and z_{i,t} demean and scale across the cross-section at bar t alone, using no information from any bar after t. The row of z at bar t never depends on any price after t; every term entering the signal at t is measurable with respect to F_t.

5. Operating envelope

6. Instrument

The cross-sectional reversion primitive, built test-driven-first, 24 unit tests at the time of this measurement including an explicit no-look-ahead property test. Harness: a dedicated backtest runner, executed in an ephemeral container against a public data feed, leaving the live shadow process untouched.

The naive interval construction is stated here as a limitation rather than corrected retroactively. The finding below is decisive enough, NET in the hundreds of basis points against noise, that a correlation-aware re-treatment would not plausibly change the sign of the verdict, but that is a judgement stated here, not a re-measurement.

A first version of the null in this instrument's development shuffled the time index directly rather than the symbol selection, and manufactured an apparent edge of roughly +2,200 basis points from a series that contained none, from the same family of defect as a look-ahead bias. It was replaced before any result was reported, with the random-symbol, real-price control described above.

7. Results

Neither timeframe produced a single configuration clearing its round-trip cost. The least-negative reported figure across all 18 configuration-by- timeframe cells is -96 basis points, which remains substantially negative even before any cost is credited back. The random-symbol control behaved as expected on both timeframes, which establishes that the harness measures a real absence of edge rather than a broken measurement.

The finding that gives this hypothesis its successor is the fifth row. The identical selection rule, reversed in direction only, is positive and partially significant on the 1-hour panel. The cross-section carries real, extractable information; the direction the original thesis assumed, that an over-extension reverts, is the wrong sign of it.

8. Verdict, axis of death, and transferability

Verdict: FALSIFIED. Axis: Idea. Transferability: UNIVERSAL.

Zero of eighteen configuration-by-timeframe cells clear the round-trip cost, and the least-negative of them remains negative by a wide margin even before any cost is credited back: crediting the full 15.0 basis point round trip to the -96 basis point reading leaves -81 basis points gross. BL-D-002 section 4 asks whether the result would be positive under arbitrarily favourable envelope parameters. Here it would not, because the sign of the underlying relationship is wrong, not merely too small to clear a fee.

The mirror-direction result confirms this reading rather than merely suggesting it. If the failure were a power problem, the reversed selection would not be expected to show a clean, partially significant positive result on the same data and the same grid. It does, which means the market this panel was drawn from rewards continuation of an idiosyncratic move over this horizon range, not reversion of it. The reversal thesis is falsified on the mechanism, and the transferability classification is universal because no substitution of cost, capital, or execution channel changes the sign of a relationship that is measured, not merely underpowered.

9. Cost and capacity analysis

Round-trip cost assumed                    15.0 bps
Least-negative configuration, net          -96.0 bps
Least-negative configuration, gross        approximately -81.0 bps

Cost is not the binding constraint. A 15.0 basis point round trip is immaterial against a result whose least favourable reading is more than five times that magnitude before any cost is applied. Capacity was not measured; the hypothesis failed on mechanism before frequency or size became a relevant question.

10. Envelope sensitivity and reopening conditions

No binding parameter exists to name, because the finding is a sign reversal in the underlying relationship, not a magnitude shortfall against cost.

Reversal condition:  none computable.

Setting the round-trip cost to zero and crediting it back to every reported configuration does not turn a single one of the eighteen cells positive. The defect is in the direction of the idiosyncratic price relationship over this horizon range, not in the fee paid to trade it, which is exactly the reasoning BL-D-002 section 4 applies to distinguish a universal falsification from an envelope-bound closure.

What would reopen it: none identified for the reversal direction specifically. The mirror-direction result already answers the natural follow-up, whether the cross-section carries information at all, in the affirmative, and that follow-up is carried forward as its own pre-registered hypothesis in BL-SD-011 rather than folded into this one.

What would not reopen it: a different fee tier or execution channel. The sign of the relationship, not the cost of trading it, decided this result.

11. Reference implementation

Published as 05_INSTRUMENTS/strategies/python/src/cross_sectional_reversion.py, with 28 tests. The module retains both a "reversal" and a "momentum" mode as an exact mirror of each other by construction, because the momentum mode is the signal this dossier's own results motivated as a separate, pre-registered hypothesis rather than a retroactive relabelling of this one.

Writing the mirror down as an equation is what makes the pair legible. Because the two modes share one selection rule and differ only in sign, per trade

net_momentum  =  -net_reversal  -  2 * (fee + spread_cost)

exactly. Both directions pay the full round trip, so flipping the bet does not flip the cost. Two things follow. The two modes cannot both be profitable. And a gross edge that merely fails to clear cost in one direction fails by twice as much in the other.

This dossier measured net between -96 and -558 basis points across nine configurations, none positive. The identity says the momentum mirror was settled at that moment, and BL-SD-011 measured it regardless, because a pre-registered hypothesis is closed by measurement rather than by algebra. The published test suite pins the identity, since the algebra only holds if the implementation matches it.

Two ordering rules in the module are worth a reader's attention because neither is cosmetic. Exits are processed before entries on every bar, so a symbol closing at t cannot re-open at t. The entry band's upper bound is exclusive, so a fresh position is never opened at the level that would stop it out. Both came out of the cointegration work, where the overlap between those two produced a six-minute churn cycle.

12. Evidence register

13. Lessons extracted

This hypothesis produced R-03 in the rules register: a naive time-shuffle null, tried first during the instrument's own development, manufactured an apparent 2,200 basis point edge from a series that contained none. It was caught and replaced before any result was reported, but the near-miss is the reason a matched null, one that shares timing, turnover, and exposure with the strategy and destroys only the association between signal and outcome, is now mandatory rather than a matter of instrument-author discretion.

The absence of a named forced loser, noted in section 2, is preserved here rather than retrofitted. A hypothesis argued from a statistical property of a price panel, without naming a counterparty compelled to transact against its own interest, is structurally closer to an observed pattern than to a thesis, and this hypothesis's death on the idea axis rather than on power is consistent with that gap having been real rather than cosmetic.

14. Cross-references

BL-SD-011 for the mirror-direction successor this dossier's own results motivated. BL-SD-012 for the sibling approach proposed the same day against the same substrate. BL-D-009 section 2 for R-03, produced by this hypothesis's instrument development. BL-D-011 section 3 for the causality constraint this measurement's signal satisfies. BL-SD-000 ledger row XSEC-REV.

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