Overfitting Impact Models to Sparse Trade Data
Market impact models are often fit using a firm's own trades, which for large or illiquid names can be a tiny, unrepresentative sample, and a flexible model fit to that sparse data can look accurate in-sample while making unreliable predictions live.
Market impact models estimate how much a trade will move the price, usually as a function of order size relative to typical volume. Large-cap, liquid names generate thousands of trades to fit against, but a mid-cap name a desk trades only a few times a month might supply just a handful of data points. Fitting a model with several free parameters — say, a curve with separate terms for temporary and permanent impact plus interactions with volatility — to a dozen trades risks the model memorizing the quirks of those specific trades rather than learning the true relationship between size and cost.
The symptom is a model that fits its own training trades almost perfectly but produces wild or overconfident cost estimates for new trades in the same name, especially at sizes outside the narrow range it happened to see. The fix is usually to simplify: fewer parameters, pooling data across similar names to borrow strength, or shrinking estimates toward a sensible prior rather than trusting a thinly-supported fit.
A flexible impact model fit to a handful of trades in an illiquid name can fit that history almost exactly while being nearly useless for predicting the next trade's cost — sparse data calls for a simpler model, not a more flexible one.
Fitting a four-parameter impact curve to 8 historical trades in a thinly-traded stock will nearly always produce a curve that passes through those 8 points closely, but predicts wildly different costs for a 9th trade of a size it hasn't seen.
Related concepts
Practice in interviews
Further reading
- Kissell, The Science of Algorithmic Trading and Portfolio Management (ch. 11)