Blending by Family, Then Across Families

A signal library rarely has forty independent ideas — it has, say, eight value variants, six momentum variants, five quality variants, and so on, because once a researcher finds a working idea, close variations of it are cheap to generate. Blend all forty flat, with equal or optimised weights, and the families with the most members quietly get the most total weight, whether or not that family deserves it.

The flat-blend trap

If value has eight highly correlated variants and momentum has two, an equal-weighted flat blend puts roughly 20% of total weight on momentum and 80% on value — not because value is four times better, but because it has four times the headcount. The blend ends up looking almost entirely like a value signal wearing a diversified-looking label.

Two-stage blending

The fix is hierarchical: first combine the signals within each family into a single family score (equal-weighted is usually fine here, since within-family signals tend to be similar enough that little is lost). Then combine the resulting family scores — now one score per family, regardless of how many raw signals went into it — into the final blend. This makes the number of underlying variants within a family irrelevant to how much weight the family gets, and lets the researcher set family-level weights deliberately, based on judgement about which economic idea deserves how much say.

A worked example

A library has 5 value variants (average pairwise correlation 0.8), 2 momentum variants (correlation 0.3), and 3 quality variants (correlation 0.6). Flat equal weighting gives value roughly 50% of total weight, momentum 20%, quality 30% — an accident of headcount. Blending within family first, then averaging the three resulting family scores equally, gives each economic idea exactly one-third of the say, which is what the researcher actually intended when calling these "three signal families" in the first place.