The pairwise rule predicted this one
what you'll learn · Why score-stage composition of decorrelated parents stacked where mixed-stage composition of higher-correlation parents interfered, and what this confirms about the pairwise rule as a pre-test.
Picked the most-decorrelated top-arm pair (+0.71 correlation), composed them at the score stage, and shipped the result. The composite beat both parents AND baseline — the first composite-arm result this session to do all three. The empirical confirmation closes the loop the matrix opened: low pairwise correlation predicts composite stacking.
PR #742’s pairwise-correlation note named the next experiment:
The most-decorrelated arm pair on this synthetic:
three_clock_vol_regimevsvol_weightedat +0.72. Or:three_clock_momentumvsvol_weightedat +0.71.A composite of those two parents would have the lowest expected correlation — the highest stack probability the matrix can predict.
PR #744 shipped XsThreeClockVolWeightedMomentumStrategy —
three_clock_momentum × vol_weighted composed at the score
stage. PR #746 ran the experiment.
The result
mean stdev max
baseline: +0.957 1.335 +2.879
vol_weighted (parent 1): +0.930 1.180 +2.723
three_clock_momentum (parent 2):+0.918 1.191 +2.934
three_clock_vol_weighted: +1.058 1.216 +3.347 ← above all threeThe composite beats both parents AND baseline. First composite-arm result this session where the composite tops baseline on a 10-seed run.
The deltas:
- Δ vs
vol_weighted: +0.128 - Δ vs
three_clock_momentum: +0.140 - Δ vs baseline: +0.101
- max: +3.347 (highest of the four)
What the pairwise rule predicted
PR #710’s discipline rule, in three bands:
| Correlation | Composite outcome |
|---|---|
| over 0.95 | almost certainly interferes (composite IS parent) |
| 0.5 – 0.8 | marginally stack or flat |
| under 0.3 | stacks (different signals) |
three_clock_momentum × vol_weighted at +0.71 was the
most-decorrelated top-arm pair — the highest-stack-probability
candidate the matrix could predict from the existing arms.
The empirical outcome: stacked, by +0.10 to +0.14 Sharpe across all three comparison points.
The score-stage vs mixed-stage distinction
This composite worked. The previous composite
(three_clock_portfolio_vol, PR #738) didn’t. The pattern:
| Composite | Stage | Pairwise corr (parent) | Outcome |
|---|---|---|---|
three_clock_portfolio_vol |
score × portfolio | +1.00 | interferes |
three_clock_vol_weighted |
score × score | +0.71 | stacks |
The portfolio-stage composition added no information because the
portfolio gate rarely fired in this synthetic — portfolio_scale = 1.0 most of the time, so the composite’s per-seed sharpe
sequence was identical to the score-only parent’s.
The score-stage composition added information because the vol-normaliser applied PER SYMBOL, changing the relative ranking of the cross-sectional bucket. The two parents see different aspects of the same data; combining them changed which symbols landed in the top/bottom quantile.
What this rules out
-
Not “score-stage always stacks.” The
three_clock_vol_regimecomposite (PR #661, also score-stage) interfered on single-signal data — both parents were finding the same edge. Score-stage is a necessary but not sufficient condition for stacking. -
Not “decorrelated always stacks.” The +0.71 pair stacked here. The +0.78 pair (
three_clock_momentumvsthree_clock_vol_regime) might not — they’re score-stage too, but both built around the three-clock signal. The matrix predicts; the experiment confirms. -
Not “this beats baseline by a meaningful margin.” +0.101 vs baseline is well below stdev 1.216. Statistically the composite ties baseline at this seed count. The direction (above, not below) is the load-bearing observation; the magnitude needs more seeds.
The refined rule
PR #710’s original:
When proposing a composite arm, compute the parents’ pairwise correlation first.
PR #742’s first refinement:
Compute the would-be composite’s correlation with each parent.
PR #746’s confirming evidence + a third refinement:
Same-stage composition (score × score) can stack if parents are decorrelated. Mixed-stage composition (score × portfolio) tends to interfere unless the second-stage intervention actually fires often on the data.
Combined rule:
Composite stacks if and only if:
- Parents have low pairwise correlation (under 0.5), AND
- The composition is same-stage (both parents intervene at the same layer — score, gate, portfolio), OR
- The cross-stage intervention fires frequently enough on the data that its per-seed contribution is non-zero.
The next experiment
The matrix shows other decorrelated pairs worth testing:
three_clock_vol_regime × vol_weightedat +0.72 — similar shape to this PR’s result.vol_weighted × ts_momentumat +0.72 — different score shape; ts_momentum is per-symbol-threshold.three_clock_vol_regime × ts_momentumat +0.27 — the LOWEST pairwise correlation across the top arms.
The +0.27 pair is the highest-stack-probability candidate the matrix predicts. Whether stacking continues into the under-0.3 band or saturates is the natural follow-up — out of scope for this note.
Closing
The pairwise rule worked as a pre-test for the first time this session. The matrix predicted; the experiment confirmed; operators get a cheap signal for which composites are worth building. Real-data verification is still the next required test — synthetic results don’t survive contact with real markets without independent confirmation. The matrix and the discipline rules survive; the specific Sharpe number needs real bars.