Conditional and Interaction Signals
Momentum often works only when a market is actually trending, and value often works only when a stock isn't cheap for a good reason — a signal's edge frequently depends on a second variable, and modeling that dependence directly usually beats averaging over it.
Prerequisites: Conditioning a Signal on the Volatility Regime, Nonlinear Signal Transformations
A signal's average IC over many years can hide the fact that the signal only actually works under certain conditions. Momentum — buying recent winners — tends to work well when a market is trending and tends to reverse sharply during a crash, when yesterday's winners are exactly the crowded positions that get sold first. A single average IC across both regimes understates how strong the signal is when conditions are right, and overstates how safe it is when they're not.
A conditional signal or interaction signal makes this dependence explicit by combining two variables rather than averaging over the second one: instead of "momentum" alone, the model uses "momentum, given that realized volatility is currently low" or "momentum multiplied by trend strength." Mechanically this can be as simple as multiplying two normalized signals together (an interaction term) or as involved as fitting separate models per regime and switching between them.
When a signal's effectiveness genuinely depends on the level of a second variable, blending the two into a single average-case model throws away real information — an interaction or conditional formulation captures a strong effect in the regime where it holds and correctly mutes it in the regime where it doesn't, rather than reporting one washed-out number for both.
Splitting a signal by regime
Worked example
A 12-month momentum signal is tested across ten years, split by whether trailing realized volatility was above or below its median. In low-volatility periods, momentum's IC is 0.08 — strong. In high-volatility periods, its IC is −0.01 — essentially useless, consistent with momentum crash risk during sharp reversals. Averaged across the full sample without conditioning, the signal reports an IC of about 0.035, which understates its usefulness in calm markets and hides that it's actively unhelpful in stressed ones.
An interaction model multiplies the momentum z-score by a low-volatility indicator (1 in the calm regime, 0 in the stressed regime), so the position sizes down to nothing exactly when the historical data says the edge disappears. Backtesting this conditional version against the unconditional one, the realized Sharpe ratio over the ten years improves meaningfully — not because the underlying momentum effect got any stronger, but because capital was withdrawn from the regime where it was actually negative.
Conditioning a signal on a second variable adds a parameter (where to split, or how to weight the interaction) that must itself be chosen out-of-sample — picking the regime boundary that happens to look best in the backtest is a subtle form of overfitting. Choose the conditioning variable because there's a mechanism connecting it to the signal's edge (momentum crashes are a documented, structural phenomenon), not because a grid search over possible splits found one that worked historically.
Related concepts
Practice in interviews
Further reading
- Grinold and Kahn, Active Portfolio Management (ch. 9)