Estimating Alpha Half-Life

A decay curve is a picture; a half-life is a number you can put in a spec document. It answers one question precisely: how long until this signal has lost half of what it started with? That single number drives rebalance frequency, position sizing, and how nervous to be about lag in the pipeline.

Turning a curve into a half-life

Most decay curves are roughly exponential — IC falls off at a constant proportional rate rather than a constant absolute one. If $IC(t)$ is the information coefficient $t$ days after the signal fires, an exponential fit looks like

$IC(t) = IC(0) \cdot e^{-\lambda t}$

where $\lambda$ is the decay rate. The half-life $t_{1/2}$ is the time at which $IC(t) = IC(0)/2$, which solves to

$t_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}$

In words: fit how fast the log of the IC falls in a straight line against time, read off the slope as $\lambda$, and divide 0.693 by it. You don't need calculus to use this in practice — a spreadsheet regression of $\ln(IC(t))$ against $t$ gives you $\lambda$ directly as the negative of the slope.

A worked example

A momentum signal starts at $IC(0) = 0.040$. Measured IC at day 10 is 0.028. Taking logs: $\ln(0.028/0.040) = \ln(0.70) \approx -0.357$. Since $IC(t)/IC(0) = e^{-\lambda t}$, that gives $-\lambda \cdot 10 = -0.357$, so $\lambda \approx 0.0357$ per day. Half-life is then $0.693 / 0.0357 \approx 19.4$ days.

That number is directly actionable: a rebalance every 4–5 days uses roughly a quarter of the half-life, keeping most of the signal's power while still refreshing before too much decays away. A weekly rebalance (7 days) is defensible too, and would cost less in turnover for a modest give-up in freshness. A monthly rebalance, at over a full half-life, would mean trading on a signal that has already lost more than half its original information by the time it's acted on again.