Residualised Return Targets After a Risk Model

A model that predicts "tech stocks will do well next quarter" during a broad tech rally isn't discovering anything — every stock in the sector went up together because of a shared market and sector move, and a model rewarded for calling that correctly is being rewarded for rediscovering beta, not for finding a genuine, stock-specific edge. If the eventual goal is a market-neutral, sector-neutral portfolio that doesn't take directional bets on things everyone already knows about, then training the model on raw returns wastes its capacity on exactly the part of the return that a risk model would neutralize away anyway.

Residualising the target

A residualised return target regresses the raw forward return on a set of known risk factors (market beta, sector, size, value, and whatever else a standard risk model uses) and keeps only the leftover — the residual — as the label:

$$r_{i,t+1} = \beta_1 F_{1,t+1} + \beta_2 F_{2,t+1} + \dots + \varepsilon_{i,t+1} ,$$

where $F_1, F_2, \dots$ are the known factor returns (market, sector, size, etc.), the $\beta$'s are the stock's exposures to each, and $\varepsilon_{i,t+1}$ is what's left over after those known effects are subtracted out. In plain English: the residual is the part of the stock's move that a standard risk model couldn't already explain — genuinely stock-specific, and exactly the piece a portfolio that's already hedged for market and sector exposure actually cares about predicting.

Why train on the residual rather than the raw return

If a stock-picking model is going to be deployed inside a market-neutral, sector-neutral portfolio construction process that already hedges out factor exposures, then whatever predictive power the model found in the factor part of the return gets cancelled out at the portfolio level anyway — that part of the model's "accuracy" was never going to translate into money. Training directly on the residual means every unit of model performance measured during research corresponds to alpha that will actually survive the hedging step in production, rather than reporting an inflated accuracy number driven by factor bets that get neutralized later.

Worked example: separating stock-specific from sector-wide moves

Suppose a semiconductor stock returns $+6\%$ next month. A risk model attributes $+4\%$ of that to the broad market factor and $+1.5\%$ to the semiconductor sector factor, leaving a residual of $6\% - 4\% - 1.5\% = 0.5\%$. If every other stock in the semiconductor sector also returned around $+5.5\%$ that month (mostly market and sector-driven), a model trained on raw returns would see this stock as a strong "up" case, indistinguishable from its sector peers. Trained on the residual, the model instead sees a small, genuinely stock-specific $+0.5\%$ — modest, but the part that's actually attributable to something about this company rather than the sector-wide tailwind every peer also enjoyed, and the only part a sector-neutral portfolio construction process would actually be able to monetize.

The line above shows fitted values versus residuals for a simple regression — residualising a return target is the same operation at the security level: subtract what a risk model's factors explain, and keep only what's left as the label.

What this means in practice

Residualised targets are standard in institutional quant research precisely because most real portfolios are risk-managed and factor-hedged before they ever reach a trading desk — reporting or optimizing on raw-return accuracy without accounting for that hedging step overstates how much of a model's apparent skill will actually convert into portfolio-level alpha.