Lab notebook · chapter 7 of 7 · page 2 of 3

Breadth continued

Result — 112 large caps, 447 sampled days, 2016–2026

score correlation IC correlation
signals in catalog 31 31
effective breadth 8.40 5.57
√breadth (the multiplier) 2.90× 2.36×
√31 if independent 5.57× 5.57×
top-3 eigenvalue share 53.9% 65.5%
mean |correlation| 0.207 0.300
clusters at |r| ≥ 0.5 6 (one holds 24) 5 (one holds 25)

Twenty-five of the thirty-one signals form a single cluster. Momentum, reversal, moving averages, RSI, Bollinger, drawdown depth, close location, volatility and skew are all chained together at |r| ≥ 0.5. Only negative_skew and rev_1d stand alone, with vol_trend/volume_shock and illiquidity/small_dollar_vol as two-name pairs — and that second pair is one of the duplicates planted as a control.

Some correlations are near-identities the labels concealed: mom_1m vs rev_21d is −0.97 (they are the same number with opposite signs), mom_12_1 vs mom_accel is −0.94, lowvol_60 vs downside_dev is +0.97.

No signal has a measurable edge

signals at |t| ≥ 2 0 (1.6 expected by chance at 5%)
best |t| 1.55 (downside_dev)
signs matching their a-priori prior 13/31 — binomial p = 0.24, i.e. a coin flip
mean individual |IC| 0.0140
mean individual IC (signed) −0.0058

t-stats are deflated by √(horizon/stride) for overlapping forward windows. Without that correction they would be twice as large, which is the difference between "nothing here" and two apparent discoveries.