Orthogonalising Signals Before Blending

Blending five alpha signals sounds like diversification, but if three of the five are all, at heart, different flavors of the same momentum idea, the "blend" doesn't actually combine five independent views — it just gives momentum a triple vote. A weighted average of correlated signals concentrates risk rather than spreading it, and it inflates a backtest's apparent breadth of ideas without adding any genuinely new information. Orthogonalisation is the step that fixes this: before blending, strip each signal of the part it shares with the others, so what remains is only each signal's unique, non-overlapping contribution.

The idea: keeping only what's new

Picture three analysts giving you stock recommendations. If two of them are secretly reading the same research report and just phrasing it differently, listening to "three opinions" is really listening to one opinion twice with a extra voice. To get real diversification, you'd want to ask each analyst "what do you believe that the others don't already believe" — their unique contribution, net of the shared view. Orthogonalising signals does exactly this mathematically: it regresses each signal on the others and keeps only the residual, the part uncorrelated with (orthogonal to) everything else already in the blend.

Concretely, to orthogonalise signal $x_2$ with respect to signal $x_1$, regress $x_2$ on $x_1$:

$$x_2 = \alpha + \beta x_1 + x_2^{\perp},$$

and keep the residual $x_2^{\perp}$ — the part of $x_2$'s variation left over once its linear relationship with $x_1$ has been removed. In plain English: $x_2^{\perp}$ is what signal 2 says that signal 1 doesn't already say; blending $x_1$ with $x_2^{\perp}$ (rather than raw $x_2$) means the two combined signals no longer double-count the shared component. With more than two signals this generalizes to sequentially orthogonalising each new signal against everything already included, or, equivalently, decomposing the whole signal set with something like principal component analysis and blending the resulting uncorrelated components instead.

Worked example: three momentum-family signals

Suppose 1-month, 6-month, and 12-month price momentum have pairwise correlations around 0.75 — all three are largely the same underlying bet on trend persistence at slightly different horizons. A naive equal-weighted blend of all three effectively triples the weight on "trend persistence" relative to any other signal in the portfolio, such as a value signal that's uncorrelated with all three. Orthogonalising: keep 1-month momentum as is; regress 6-month momentum on 1-month and keep only the residual (the part of medium-term trend not explained by the short-term reading); regress 12-month momentum on both and keep only its residual. The resulting three orthogonalised components — each capturing a genuinely distinct horizon of trend information rather than an overlapping copy — can now be blended with weights that reflect their individual quality, without one underlying idea silently dominating the mix through sheer repetition.

What this means in practice

Skipping orthogonalisation before blending is one of the most common ways a "multi-factor" model quietly becomes a one-factor model in disguise — the backtest shows five signals contributing, but risk is concentrated in whatever theme those signals happen to share. Checking pairwise correlations among candidate signals before blending, and orthogonalising or otherwise decorrelating anything above a modest threshold (commonly around 0.5–0.6), is a cheap step that meaningfully changes both the diversification and the interpretability of the resulting blend.