BL-IS-015: Concentration Decomposition

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-07

1. What it measures

Whether a pooled result is a property of the whole sample or a property of a small part of it wearing the whole sample's average.

The instrument decomposes a set of trade-level results by instrument, by liquidity class as a proxy for regime, and by exclusion of the extremes, and reports a confidence interval for each slice rather than a single pooled figure. R-19 requires the decomposition before any verdict is issued; this instrument is what makes running it routine rather than exceptional.

2. Why it exists

A verdict was once issued on a sample of 39,250 dislocation events that cleared every gate a normal review would apply: sample size, statistical process, a healthy recording container. Decomposed by instrument, 87 percent of those events came from a single low-grade listing that a live strategy's own universe filter would have refused to trade [BL-IN-004]. The verdict was retracted. R-19 is the rule that decomposition produced.

The near miss that produced this specific instrument was quieter. A post-verdict review of the H-R1 primary result asked whether its mean concealed structure the way the dislocation sample had. Symbol concentration had been checked for a related characterisation, G2, and came back clean at 2.75 percent. It had not been checked for H-R1 itself. Running the check after the fact, rather than before the verdict, is the gap this instrument closes: the same decomposition, applied by default rather than by request.

3. Interface

summarise(net, bars, label) -> slice_report
  net      net result per trade, in basis points
  bars     entry bar index per trade, used to collapse same-timestamp legs
           into portfolio-level observations before computing the interval
  returns  n, boot-mean, CI95 and p against zero from a moving-block
           bootstrap [BL-IS-001], plus median, trimmed mean, win rate and sd

The instrument calls summarise once on the pooled sample, once per liquidity tertile, once with the top instrument excluded, and once with the top and bottom one percent of trades excluded, and reports all of them side by side. It computes no return of its own; every input is a result already produced by the measurement under review.

4. A worked result

Applied to the H-R1 primary sample, symbol concentration came back clean: the busiest single instrument carried 0.82 percent of trades, the top ten carried 7.99 percent, on 43,209 trades across 154 symbols [E-0022]. Nothing in the contamination class that closed BL-IN-004 was present here.

The decomposition by liquidity tertile told a different story from the pooled figure:

The pooled interval spans zero and settles nothing. The high-liquidity slice does not: its interval sits entirely below zero, the one subgroup of three where the bootstrap rejects a null of no effect. A verdict drawn from the pooled row alone would have missed that the result is not uniform across the universe it was measured on.

Excluding the busiest instrument moved almost nothing, n=42,856, boot mean -9.15, confirming the pooled figure was never a concentration artifact in the BL-IN-004 sense. Excluding the extreme one percent of trades on each side moved a great deal, boot mean +20.14, CI95 [5.81, +33.39] on 42,343 trades, which is a tail-sensitivity finding rather than a concentration finding and is reported as a separate row rather than folded into the same number.

5. What this does and does not settle

None of the rows above is a verdict. The instrument is descriptive by design: it answers why a pooled figure looks the way it does, not whether a favourable slice constitutes an edge. Selecting the high-liquidity slice's negative finding, or the tail-trimmed slice's positive one, as a new specification after seeing this table would be p-hacking performed one step downstream of the usual place, and every candidate this decomposition surfaces is treated as exactly that: a candidate requiring its own pre-registration and its own sample, never a standing conclusion.

The same discipline, applied inside a different instrument rather than as a separate pass, is what rejected the one market-making candidate that appeared to survive an adverse-selection screen: 72.5 percent of its result traced to a single day [BL-IS-006 section 7]. The check is the same shape wherever it runs; only the axis of decomposition changes.

6. What it does not do

It does not correct for having looked. Running this decomposition and then treating any favourable subgroup as a finding reintroduces the multiplicity problem R-05 exists to close, at the subgroup level instead of the specification level.

It does not compute a result. Every number it reports depends on a measurement instrument that already ran; this one only regroups and re-intervals that output.

It does not tell a reader which axis to decompose along. Liquidity tertile was the axis chosen for H-R1 because it is the mechanical driver of cost and capacity on this substrate; a different substrate or a different hypothesis may need a different axis, and choosing the wrong one can hide the same structure it is meant to reveal.

7. Cross-references

BL-D-009 rule R-19. BL-IN-004 for the incident that produced the rule. BL-IS-001 for the bootstrap this instrument calls. BL-IS-006 section 7 for the same check applied to a different axis. The concentration diagnostic. Evidence E-0022.

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