IC Decay Curves and Signal Half-Life

A single information coefficient number — say, IC = 0.05 at a one-day horizon — tells you a signal predicts next-day returns somewhat. It doesn't tell you whether that predictive power is gone by day two, or still meaningfully present a month later. That distinction matters enormously for how you actually trade the signal: a signal whose IC evaporates in a day needs to be traded (and retraded) daily, while one that stays predictive for a month can be held with far less turnover and far lower transaction costs. The IC decay curve — computing the IC separately at each forecast horizon from 1 day out to, say, 60 days — makes this visible directly, and its half-life summarizes it in a single number.

An analogy: how long a weather forecast stays useful

A weather forecast issued this morning is highly accurate for this afternoon, somewhat accurate for tomorrow, and nearly useless for three weeks out — its accuracy decays smoothly with the forecast horizon, not all at once. An IC decay curve is the same idea applied to a trading signal: instead of asking "is this signal accurate," you ask "how accurate is it 1 day out, 5 days out, 20 days out," and plot the answer as a curve. Just as a weather forecast's "useful horizon" tells a farmer how far ahead to plan around it, a signal's IC half-life tells a portfolio manager how long to hold a position built on it before the signal's edge has decayed away.

The measurement, one symbol at a time

For each forecast horizon $h$ (in trading days), compute the cross-sectional information coefficient between the signal measured today and the return realized from today to $h$ days later: $\text{IC}(h) = \text{corr}(s_t, r_{t \to t+h})$, averaged across many dates $t$. Plotting $\text{IC}(h)$ against $h$ typically shows a curve that starts at its highest value for small $h$ and decays toward zero as $h$ grows — the signal's information content is "used up" as the market incorporates it into prices.

The half-life is the horizon $h_{1/2}$ at which the decay curve has fallen to half its starting value: $\text{IC}(h_{1/2}) = \text{IC}(1)/2$ (or sometimes defined relative to the peak IC if that occurs after horizon 1). If the decay is roughly exponential, $\text{IC}(h) \approx \text{IC}(0) \cdot e^{-\lambda h}$, the half-life relates directly to the decay rate: $h_{1/2} = \ln(2)/\lambda$.

Worked example: fitting a decay curve

Suppose a value signal's measured IC at horizons of 1, 5, 20, 40, and 60 days is 0.08, 0.075, 0.05, 0.03, and 0.015 respectively. This decays much more slowly than a typical short-term reversal signal, which might show IC of 0.06 at 1 day, dropping to 0.01 by day 5 and near zero by day 10. Fitting an exponential curve to the value signal's points gives a decay rate of roughly $\lambda \approx 0.023$ per day, implying a half-life of $\ln(2)/0.023 \approx 30$ days — a signal that's still meaningfully predictive a full month out. For the reversal signal, fitting the same way gives $\lambda \approx 0.55$ per day, a half-life of about $\ln(2)/0.55 \approx 1.3$ days — a signal that must be rebalanced almost daily to capture most of its edge before it's gone.

What this means in practice

The decay curve and half-life directly inform portfolio construction: a signal with a short half-life needs frequent rebalancing to capture its edge, which means it must clear a higher transaction-cost hurdle to be worth trading at all, while a signal with a long half-life can be traded with low turnover and is more forgiving of trading costs and implementation delay. Combining signals with different half-lives in one portfolio — a fast-decaying reversal signal alongside a slow-decaying value signal — is common precisely because they call for different trading frequencies, and understanding each one's own decay curve is what makes it possible to size and schedule trades sensibly instead of over- or under-trading a given signal relative to how quickly its information actually decays.