Do Ten Weak Signals Combine into a Strong One? — The Premise Behind IR = IC × √Breadth

When Article 14 argued that "there is no share left for individuals in the public-data factor space," a natural objection followed — then what do WorldQuant and Renaissance live on? Isn't factor mining precisely the straightforward approach?

Fair. Their method rests on the fundamental law of active management: IR = IC × √(number of independent bets). Even if a single signal has an IC of 0.02, combining thousands of them and turning the book over daily lets breadth manufacture IR. We can test a scaled-down version of that.

Pre-registration (fixed before looking at results)

• Ten signals, signs specified in advance from the literature, not changed after seeing performance: 12-month momentum (excluding the most recent month), 6-month, 3-month (+); 1-month return (−, short-term reversal); 3-month volatility (−, low volatility); close / 52-week high (+); maximum daily return over the past month (−, lottery effect); share of positive months out of 12 (+); GP/A (+); revenue YoY (+)
• Combination: per-date percentile rank × sign → simple average. No weight optimization
• Configurations: {combined 10 signals, baseline (the same 5 signals used in live operation)} × N{10, 20, 30} × {monthly, weekly} = 12, all reported
• Costs: 0.2% round trip. Decision rule: a combined or breadth configuration must beat the baseline in all three sub-periods before adoption is even considered

Result 1 — There was no signal to begin with

S&P500, 189 monthly periods over 2011–2026, IC (Spearman) after applying the signs:

Every one of them |IC| < 0.06, t < 1.6. In US large caps over 2011–2026, the high-volatility names and the names with a history of spikes rose more — the opposite of the textbook.

Result 2 — The signs flipped in the holdout

The same signals with the same signs, applied to data that had not been looked at when the S&P500 results were produced (S&P400+600, 1,069 stocks):

The strongest signal became the strongest inverse signal in another universe. That is what a signal with an IC of 0.02–0.06 actually is — a t of 1.5 in one place can be a t of -2.6 in another.

Result 3 — Portfolios (net of costs)

• The combination failed. Equal-weighting signals whose signs had flipped diluted the momentum, and after 2020 it trails even the index. Pre-registration is what keeps us from saying "just drop those three" — doing so would be an ex-post selection
• Breadth did not raise IR. Going from 10 to 30 stocks improves MDD from -27 to -21, but IR goes 1.39 → 1.30. If IC is zero, no amount of √breadth makes it anything other than zero.
• Weekly rebalancing is plainly worse. Costs of 2–2.5% per year plus noise. MDD -37%
• In small and mid caps (S&P400+600) the baseline strategy itself is inferior to large caps, at IR 0.75 and MDD -34%

So why does it work for WorldQuant?

For breadth to work, a positive out-of-sample IC is the precondition. Their thousands of signals come from alternative data and tick data, turn over daily, and are executed at costs measured in basis points. In what we have — monthly prices and financials for large caps — the textbook anomalies were already zero or reversed in sign. There was no raw material for breadth to amplify. And the baseline strategy (momentum 3/6/12 + quality, 10 stocks, monthly) beat every alternative it was compared against across all three periods.

Limitations

• Survivorship bias from current index constituents (the baseline arm's CAGR of 38.7% cannot be trusted as an absolute figure; only arm-to-arm comparison is meaningful)
• No volume-based signals included (the price data carries no volume)
• Financial features exist only from 2022 onward; earlier periods are treated as neutral