Volatility-Scaled Return Targets

A model trained across both a sleepy utility stock and a wild small-cap biotech, using raw forward returns as its target, faces an awkward problem: the biotech's routine, unremarkable 5% daily swings dwarf the utility's genuinely notable 1% move, so a squared-error loss will fixate almost entirely on getting the biotech's giant, mostly-random swings a little less wrong, while barely bothering to learn anything about the quieter, more predictable utility stock. Volatility-scaled targets fix this by expressing each return relative to that asset's own typical size of move, so the loss function treats a surprising move as surprising regardless of which asset it happened to occur in.

How the scaling works

A volatility-scaled target divides the forward return by a measure of that asset's recent volatility, typically an estimate like a trailing realized or exponentially weighted standard deviation of returns:

$$z_t = \frac{r_{t+1}}{\hat{\sigma}_t} ,$$

where $r_{t+1}$ is the forward return being labeled, and $\hat{\sigma}_t$ is the volatility estimate computed using only data available up to time $t$. In plain English: instead of asking the model to predict "how big was the return," you ask it to predict "how many typical-sized moves was this return, relative to how much this specific asset normally moves" — a question whose scale is comparable across a sleepy utility and a wild biotech, even though their raw return sizes are nowhere close.

Worked example: two stocks, one shared model

Suppose the utility stock has a trailing daily volatility of 0.5% and today's forward return is $+1.0\%$; the biotech has a trailing daily volatility of 6% and today's forward return is $+9\%$. The raw returns make the biotech's move look nine times larger. But the volatility-scaled targets are $1.0 / 0.5 = 2.0$ for the utility and $9 / 6 = 1.5$ for the biotech — on a relative basis, the utility's move was actually the more surprising one (two standard deviations versus 1.5), which is exactly the comparison a shared cross-sectional model needs to make sensible use of both stocks' data. Training on raw returns, a squared-error loss would have devoted almost all its attention to the biotech's much larger absolute number and effectively ignored the utility's genuinely more unusual move.

Why this matters for cross-sectional models

Pooling many assets into one model (rather than training a separate model per asset) is one of the main ways machine learning adds value in alpha research — more data, shared structure. But pooling only works if the target is on a comparable footing across assets; otherwise the highest-volatility names dominate the loss and the model effectively becomes a specialist in whichever handful of names move the most, at the expense of everything else. Volatility scaling is the standard fix, playing the same role for return targets that per-series scaling plays for general forecasting targets.

Try widening the standard deviation above and picture the same absolute move landing at very different points on a wide versus narrow distribution — volatility scaling recenters every asset's return onto a common, standardized version of that same picture.

What this means in practice

Volatility-scaled targets are near-universal in cross-sectional equity and futures alpha models, since the alternative — pooling raw returns across assets of very different typical volatility — reliably produces models that are secretly just volatility-chasers. The main design choice is the lookback and weighting used to estimate $\hat{\sigma}_t$, which must use only past information to avoid leaking the very volatility that's partly determined by the return being predicted.