Combining Many Weak Signals

A single well-researched signal typically has a monthly information coefficient — the correlation between the signal's ranking and subsequent returns — somewhere around 0.02 to 0.05. That is a weak predictor by any everyday standard; it means the signal explains well under 1% of the cross-sectional variance in next month's returns. And yet firms build entire businesses on stacks of signals exactly this weak. The reason is that combining many weakly correlated weak signals produces a much stronger composite than any one of them alone — this is the entire logic behind running a broad research effort rather than searching for one brilliant predictor.

Why weak signals add up to something strong

If you had one coin that was biased 51-49 toward heads, betting on it once is barely better than a coin flip. But if you had a thousand independent 51-49 biased coins and bet on the majority vote of all of them, you would win with very high confidence — the individual noise cancels while the individual bias accumulates. Signal blending works the same way.

$IC_{\text{combined}} \approx IC_{\text{avg}} \cdot \sqrt{N}$

In words: if you combine $N$ signals of similar individual quality ($IC_{\text{avg}}$) that are uncorrelated with each other, the combined IC scales with the square root of the count. Ten independent signals each with IC 0.03 combine, roughly, to an IC near 0.03 × √10 ≈ 0.095 — more than three times any single signal, from ingredients that were each individually mediocre.

The critical, easy-to-miss word is uncorrelated. If the ten signals are all variants of the same underlying idea — cheapness measured five different ways — they move together, the noise does not cancel, and you get something closer to one signal's worth of information dressed up as ten.

What actually determines the blend's quality

Two numbers matter more than any individual signal's IC: how many genuinely distinct signals you have, and how correlated they are with each other. This pair is often called the strategy's breadth — not the count of signals, but the count of independent bets they represent. Ten signals with pairwise correlation of 0.7 might have an effective breadth closer to two or three; ten signals with pairwise correlation near 0.1 have an effective breadth close to ten.

This is why research teams organise signal families by mechanism (value, momentum, quality, flow, sentiment) rather than by dataset — two signals built from completely different raw data can still be highly correlated if they're both, underneath, proxies for the same underlying phenomenon, while two signals from the same dataset can be nearly independent if they capture different aspects of it.

A worked example

A desk has five candidate signals, each with a monthly IC around 0.03. Combined naively (equal-weighted), the actual realised combined IC is 0.055 — not the 0.03 × √5 ≈ 0.067 that full independence would predict, because the average pairwise correlation among the five is about 0.25, not zero.

Dropping the two most correlated signals (a pair with 0.6 correlation to each other, largely redundant) and adding a genuinely different sixth signal from an unrelated data source drops the raw count to four but raises the realised combined IC to 0.071 — fewer ingredients, more independence, and a better result. This is the standard trade a research team makes constantly: it is often correct to remove a signal that "works" on its own, because its marginal contribution to the blend, given what else is already in it, is negative or near zero.

Drag the correlation up toward 1: watch how little new information a second signal adds once it moves in lockstep with the first. Drag it down toward 0: that's the regime where adding signals is genuinely free lunch, in the "the whole is greater than the sum of its parts" sense.