Ensembling Alpha Models

No single model predicts stock returns well. A momentum model has an information coefficient — the correlation between its predictions and actual outcomes — that might sit around 0.03 to 0.05 in a good month, meaning it's right slightly more often than a coin flip, weighted by conviction. That's not a rounding error away from useless; a great model in this business is a persistently, barely-better-than-random model, run at scale across thousands of bets. The practical consequence is that no single model is ever "the" signal — quant shops build several imperfect models, on different features, different horizons, sometimes different architectures, and combine their outputs. Ensembling is the discipline of doing that combination well, because doing it badly (equal-weighting everything, or picking last quarter's best performer) throws away most of the benefit.

Why combining beats picking

Two models that are each weakly predictive but make different mistakes produce a combined signal stronger than either alone — this is the same diversification arithmetic that shows up everywhere in portfolio construction, applied to signals instead of assets. If model A's information coefficient is $IC_A$ and model B's is $IC_B$, and their prediction errors have correlation $\rho$, the combined signal's IC is higher than either individual one whenever $\rho$ is meaningfully below 1 — models that agree perfectly add nothing by being combined, and models that disagree the most (while still each having real skill) add the most.

Worked example. Model A is a value-momentum linear model with $IC_A = 0.04$; model B is a tree-based model on alt-data features with $IC_B = 0.03$ (see Tree-Based Cross-Sectional Return Models). Their predictions, measured across the same stock universe over the same period, have a correlation of $\rho = 0.15$ — mostly independent, because they're built from almost entirely different inputs. A simple equal-risk-weighted blend of two signals with these ICs and correlation produces a combined IC of roughly

$IC_{\text{blend}} = \sqrt{\frac{IC_A^2 + IC_B^2 + 2\rho\, IC_A IC_B}{2(1+\rho)}} \times \sqrt{2}$

which for these numbers works out to about 0.045 — modestly above even the better individual model, not because either model got smarter, but because the blend's errors partially cancel. If instead $\rho$ had been 0.8 (the two models mostly agreeing), the blended IC would come out barely above 0.04: two highly correlated models add almost nothing over the better one alone.

How the weights actually get set

Naive equal-weighting ignores that models differ in skill and overlap. A more disciplined approach weights each model roughly in proportion to its own IC, divided through by its correlation with the rest of the ensemble — a model that's individually weaker but adds real diversification can deserve more weight than a stronger model that's redundant with three others already in the blend. In practice this is estimated the same way a covariance matrix is estimated for asset returns, and suffers the same problem: the weighting matrix is noisy, especially with few historical observations relative to the number of models, so many shops shrink the estimated weights toward equal-weighting rather than trusting the optimizer's raw output.

What erodes it

Ensembling's benefit depends on the models staying genuinely different. If several models are all retrained on overlapping feature sets, or several teams independently discover the same alt-data source, the ensemble's effective diversification collapses even though it looks like five models on paper — five correlated views of the same signal, not five independent ones (the same crowding dynamic covered in Factor Crowding). Ensembles are also slower to adapt: a genuinely broken model still contributes weight until enough live data accumulates to downweight it, so an ensemble can drag a bad model's losses along for longer than a single-model strategy would.