Factor Decay and Half-Life

Factor decay is the rate at which a factor's predictive power dissipates over time. A factor with a 6-week half-life loses half its signal value in 6 weeks; another factor with a 6-month half-life retains usable predictive power across a quarterly rebalance. Choosing rebalance frequency without knowing factor half-life is the single most common preventable cause of "the backtest looked good but live trading didn't."

What "decay" actually measures

For a cross-sectional factor (value, momentum, quality, etc.), decay is the rate at which the rank order of stocks by factor score predicts subsequent rank order of returns. If you sort stocks by factor today and look at how well that ordering still predicts returns N days later, the predictive correlation (the Information Coefficient or IC — see IC) erodes as N increases. The half-life is the N at which the IC falls to half its value at N=0.

The intuition: factor signals are themselves prices in disguise. Once the factor publishes a name as "cheap," some flow of capital toward that name begins. The signal gets arbitraged away at a rate proportional to how much capital pays attention. Fast-decay factors (momentum, short-term reversal) get arbitraged quickly. Slow-decay factors (quality, value on multi-year horizons) take longer.

Estimating half-life from IC time series

FM103's Factor Decay sub-pill fits an exponential decay to the IC computed at successive horizons:

The estimation is per-factor, period-by-period, then aggregated to a median half-life across the backtest. The engine uses Spearman rank correlation (Spearman 1904) for IC rather than Pearson, because rank correlation is robust to the cross-sectional outliers and non-normality that plague factor distributions.

Interpretation table

• Half-life < 1 week: Factor decays before a typical retail rebalance can capture it. Either rebalance daily/intraday (transaction costs become decisive) or change factor.
• Half-life 1–4 weeks: Monthly or bi-weekly rebalance. Typical for momentum and short-term reversal.
• Half-life 1–3 months: Quarterly rebalance survives. Typical for earnings revisions, post-earnings drift (Bernard & Thomas 1989).
• Half-life 6–18 months: Semi-annual or annual rebalance. Classic value factors, F-Score (Piotroski 2000).
• Half-life > 18 months: Annual or buy-and-hold appropriate. Quality, asset growth, accruals.

The "half-life shorter than rebalance" diagnostic

The single most useful one-line readout in FM103: "Your momentum factor has a 2-week half-life and you're rebalancing quarterly." Translation: by the time you rebalance, the momentum signal you saw at the prior rebalance has decayed by ~16x (~ln(2) · 12 / 2). You are trading stale signals.

The fix is rarely "rebalance more often" — that path leads to turnover that eats the gross edge. The fix is usually "use a slower factor" or "blend factors with compatible half-lives." A momentum-value blend with quarterly rebalance is incoherent; momentum needs faster rebalance, value tolerates slower. Pick one cadence and one factor archetype that matches it.

Decay vs. half-life confusion

Two related numbers come up:

• Mean reversion half-life (in stochastic methods literature) measures how fast a deviation from a long-term mean reverts — the speed at which mu pulls a process back. Standard for OU processes; estimated from the AR(1) coefficient φ via HL = ln(2) / (1 − φ).
• Factor decay half-life (here) measures how fast a cross-sectional ranking loses predictive power. Same math (exponential decay) but applied to IC, not to a single time series.

See Half-Life from AR(1) and OU Process for the derivation.

What can go wrong

• Too few periods. Half-life estimation is noisy with N < 12 rebalances. A backtest with 4 quarterly periods produces a half-life estimate with a standard error larger than the estimate itself.
• Regime mixing. Half-life can differ across macro regimes. A median across regimes obscures the variance. The Regime-Conditional sub-pill is the place to look.
• Universe survivorship. If the historical universe is the today-current S&P 500, the factor will look healthier than it really was — survivorship biases factor IC upward (Brown, Goetzmann, Ibbotson & Ross 1992).