Group Aggregation Features

A single stock's raw return doesn't tell you much on its own — was the whole sector up 3% that day, making this stock's 2% gain actually below average? A raw daily volume of 5 million shares means something completely different for a mega-cap versus a micro-cap. Comparing a value to its own history or to its peers, rather than looking at it in isolation, is often where the real predictive signal lives, and that comparison is built by aggregating within groups.

The idea: summarize the group, then compare the individual to it

Pick a grouping key — sector, exchange, calendar day, account, order type — and a variable you care about. Compute a group-level statistic (mean, median, standard deviation, rank) of that variable within each group, then attach that group statistic back onto every row belonging to the group, so each individual observation can be compared against its peers.

$$x^{\text{rel}}_i = x_i - \bar{x}_{g(i)}$$

In plain English: take a stock's own value $x_i$, subtract the average value $\bar{x}$ computed only over the group $g(i)$ that row belongs to (its sector, say), and the result is how far above or below its peer group the stock sits — a feature that's often far more informative than the raw level. The same pattern works with group standard deviation (to standardize), group rank (percentile within the group), or group count (how crowded the group is).

Worked example: sector-relative return

Five tech-sector stocks post daily returns of 3%, 1%, -2%, 4%, and 2%; five energy-sector stocks post 5%, 6%, 4%, 5%, and 7%. The tech-sector mean is $(3+1-2+4+2)/5 = 1.6\%$; the energy-sector mean is $(5+6+4+5+7)/5 = 5.4\%$. A tech stock that returned 3% has a sector-relative return of $3 - 1.6 = 1.4\%$ — solidly above its peers. An energy stock that returned 5% has a sector-relative return of $5 - 5.4 = -0.4\%$ — actually below its peers, despite a higher raw return than every tech stock. Without the group aggregation, a raw-return-only model would have ranked the energy stock ahead of the tech stock; the sector-relative feature reverses that ranking, which is often the more economically meaningful comparison for a stock-picking model.

What this means in practice

Group aggregation features are the workhorse behind cross-sectional signals in equity models: sector-neutral returns, industry-relative valuation ratios, exchange-relative bid-ask spreads. They also compress high-cardinality categoricals (sector, exchange) into a small number of numeric summary columns instead of one-hot columns per category. The one danger is computing the group statistic using information that wouldn't have been available at the time — including a stock's own future return in the sector average it's compared against, or computing the aggregate over the full dataset rather than only prior data, both of which leak future information into a feature meant to represent a contemporaneous or historical comparison.