Persistence & Decay

Funding rates are mean-reverting. This section models how quickly funding decays and how to estimate persistence.

Half-Life Model

Funding rates exhibit exponential decay toward historical mean. We model this with a half-life parameter:

Where $\lambda$ is the exponential decay coefficient.

Equivalently:

Decay Factor

The decay factor for a holding horizon $h$ is:

This represents the average fraction of initial funding rate captured over the holding period.

Interpretation

Half-Life Estimation

Half-life is estimated from historical funding rate series using:

1. Autocorrelation analysis — Measure rate of correlation decay
2. Mean reversion speed — Fit exponential model to rate series
3. Regime detection — Identify stable vs. volatile periods

Estimation Window

Default estimation uses a 14-day rolling window of 8-hour funding observations (42 data points).

Sign-Flip Risk

Beyond magnitude decay, funding can flip sign — switching from positive to negative (or vice versa).

The sign-flip share $\rho_{flip}$ is estimated from historical funding:

High sign-flip share indicates unstable funding direction.

Decay-Adjusted PnL

Raw funding PnL over horizon $h$:

Decay-adjusted PnL:

Example

Given:

• $APR_f = 100\%$
• Position = $10,000
• Horizon = 24 hours
• $t_{half} = 24$ hours

Then:

• PnL_{raw} = 100\% \times 10000 \times \frac{24}{8760} = \27.40$
• $D(24) = 0.63$
• PnL_{decay} = 27.40 \times 0.63 = \17.26$

The decay adjustment reduces expected PnL by 37%.

Practical Implications

1. Short horizons — Less affected by decay, but more by fees
2. Long horizons — Decay dominates; need high half-life opportunities
3. Half-life threshold — Generally require $t_{half} > h$ for meaningful capture