# Do Ten Weak Signals Combine into a Strong One? — The Premise Behind IR = IC × √Breadth
- Source: FoldAlpha Research (https://app.foldalpha.com/en/research/weak-signal-combination) · Published: 2026-09-03 · Series: Myth Testing 16

When [Article 14](/en/research/why-momentum-quality) 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:

| Signal | IC | t | Read |
|---|---|---|---|
| 12-month momentum | +0.013 | 0.98 | weak |
| 3-month momentum | -0.001 | -0.04 | 0 |
| **Low volatility** | **-0.026** | -1.56 | **opposite to the literature** |
| **Lottery effect** | **-0.019** | -1.42 | **opposite to the literature** |
| 52-week high | -0.008 | -0.55 | opposite |
| Revenue YoY | +0.059 | 1.54 | strongest |

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):

| Signal | S&P500 | S&P400+600 |
|---|---|---|
| Low volatility | -0.026 | -0.024 (reverse sign reproduced) |
| Lottery effect | -0.019 | -0.008 (reverse sign reproduced) |
| **Revenue YoY** | **+0.059 (t 1.5)** | **-0.119 (t -2.6)** |
| Short-term reversal | +0.005 | +0.023 (t 1.8) |

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)

| Configuration | CAGR | IR 2011–19 | IR 2020–24-01 | IR 2024-02 onward | MDD |
|---|---|---|---|---|---|
| Baseline, 10 stocks, monthly (current) | **38.7%** | **1.60** | 1.26 | 1.41 | -27% |
| Baseline, 30 stocks, monthly | 26.7% | 1.50 | 1.21 | 1.28 | **-21%** |
| Combined, 10 stocks, monthly | 10.1% | 1.23 | 0.68 | 0.13 | -21% |
| Baseline, 10 stocks, weekly | 28.3% | 1.14 | 0.82 | 1.39 | -37% |
| S&P500 | 14.1% | 1.14 | 0.69 | 1.58 | -24% |

- **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

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This article documents tests on historical data for informational purposes only. It is not investment advice or a recommendation to buy or sell any security. Past test results do not guarantee future returns.