The theory was confirmed; the inputs are empty
Equal-weighting N independent signals should multiply IC by √N_eff. It did:
| combined IC | −0.0130 (t = −0.55) |
| lift over mean signed IC | 2.22× |
| lift predicted from IC breadth 5.57 | 2.36× |
The breadth machinery works about as advertised — it just amplified a negative number.
How well it works is less precise than that 6% gap suggests, and the small-cap replication below is what shows it: the denominator is a mean IC of −0.006, close enough to zero that the ratio is unstable. Across both universes the combination lifts by 2.2–3.7× against a prediction of 2.4–2.5×. That confirms the framework directionally — combining is worth roughly what the eigenvalues say, not √31 and not nothing — but the large-cap agreement to within 6% was luck, not precision.
The arithmetic that follows is unforgiving. At the measured IC of 0.014, a usable IR needs about 1,300 independent bets a year for IR 0.5, or 5,100 for IR 1.0. What 31 signals actually supply:
| bets/yr | IR | years to t=2 | |
|---|---|---|---|
| 5.57 breadth × monthly | 67 | 0.11 | 305 |
| 5.57 breadth × weekly | 290 | 0.24 | 70 |
| 8.40 breadth × weekly | 437 | 0.29 | 47 |
And weekly rebalancing was already ruled out by the turnover work — costs eat it. Adding more price-derived signals does not fix this. Going from 3 signals to 31 bought effective breadth of 5.57; the marginal signal is adding roughly 0.2 of a bet, and the shortfall is two orders of magnitude.
Anything that changes the answer has to be genuinely orthogonal information — not another transformation of the same OHLCV series that every one of these 31 signals is computed from. That is the only remaining place an LLM could plausibly help: as a source of new features from text, not as a decision maker over the same prices.
Small caps replicate it
Same 31 signals, 110 small caps, same window — as a check that this is not a large-cap artifact. It is not.
| large | small | |
|---|---|---|
| effective breadth (IC) | 5.57 | 6.19 |
| effective breadth (score) | 8.40 | 8.85 |
| largest cluster at |r| ≥ 0.5 | 25 of 31 | 24 of 31 |
| signals at |t| ≥ 2 | 0 | 1 |
| mean individual IC (signed) | −0.0058 | −0.0039 |
| combined IC | −0.0130 | −0.0145 |
| combination lift | 2.22× | 3.71× |
| lift predicted | 2.36× | 2.49× |
The same pairs top the matrix in both universes — mom_1m/rev_21d at −0.97,
lowvol_60/downside_dev at +0.97 — which is what a structural result looks
like rather than a fitted one.
The one signal reaching |t| ≥ 2 is illiquidity at +2.06 (IC +0.0289).
Against 1.6 expected by chance across 31 tests, one hit is not a discovery. And
it is the same self-defeating trade the capacity work already ran into: the
measured trade-weighted spread on this universe is 14.27 bps, several times
the edge on offer. The one signal that shows up is the one we cannot harvest.