Binary vs Continuous Labels for Alpha Models

Some alpha research pipelines label a stock's next-month outcome as simply 1 (it beat the median) or 0 (it didn't), and train a classifier on that. Others label the same outcome with the actual return, $+2.3\%$ or $-0.7\%$, and train a regressor to predict the number directly. Both are legitimate choices built from identical underlying data, but they ask the model to solve genuinely different problems, and the choice has real consequences for how noisy the training signal is and how the model's output can be used downstream.

What each framing throws away or keeps

A binary label collapses the outcome down to a single bit — did the stock end up above some threshold (the cross-sectional median, zero, a peer group average) or not. This is easier to model (many robust, well-understood classification tools exist) and easier to evaluate (accuracy, precision, a confusion matrix), and it's naturally more robust to a handful of extreme outliers, since a $+40\%$ month and a $+2\%$ month both just become "1" if both clear the threshold. But it throws away magnitude entirely — a model can't distinguish "barely crossed the threshold" from "blew past it by a mile," which matters if you ever want to size a bet rather than just decide its direction.

A continuous label (the actual return, or a risk-adjusted version of it) keeps the full magnitude information, letting a regression model in principle learn not just direction but conviction — useful for position sizing. The cost is that continuous financial returns are noisy and fat-tailed, and a squared-error loss on raw returns can be dominated by a small number of extreme observations, making the fitted model chase noise in the tails rather than learning the more reliable, smaller everyday signal.

Worked example: the same five stocks, two ways

Take the five next-month returns $+8\%, +1\%, -2\%, +3\%, -6\%$, with the cross-sectional median at $+1\%$. As binary labels (above vs. at-or-below median): stock A ($+8\%$) → 1, stock B ($+1\%$) → 0 (at the median, not above), stock C ($-2\%$) → 0, stock D ($+3\%$) → 1, stock E ($-6\%$) → 0. A classifier trained on this treats A's dramatic $+8\%$ and D's modest $+3\%$ as identical, equally-weighted positive examples. As continuous labels, the model instead sees the full spread $+8, +1, -2, +3, -6$, preserving the fact that A's move was nearly three times the size of D's — information a portfolio construction step that sizes positions by conviction would want to use, but which a squared-error loss will also let A's outsized number dominate the fitting process more than D's.

Explore how classifier flexibility trades off against overfitting above — a binary alpha label sets up exactly this kind of classification problem, in contrast to a regression problem where the "boundary" is replaced by a continuous fitted surface.

A middle ground: multi-class or ordinal labels

Some pipelines split the difference by using a small number of ordinal buckets (say, quintiles of return: strong down, down, flat, up, strong up) rather than a single binary split or a fully continuous number. This keeps some magnitude information — the model still distinguishes a strong mover from a modest one — while remaining more robust to a single extreme observation dominating the loss than a fully continuous target would be.

What this means in practice

Binary and ordinal framings are common for signals meant to feed a rank-and-select portfolio construction process, where only the direction or coarse ranking matters; continuous targets are preferred when the downstream use genuinely needs magnitude, such as conviction-weighted position sizing, provided the training loss and label construction are made robust enough to fat tails (winsorizing, rank transforms) to avoid being dominated by extreme outcomes.