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.