Survivability Model

The survivability model combines decay and other risk factors to estimate the fraction of headline yield that can realistically be captured.

Survivability Score

The survivability score $S$ is a composite metric on [0, 100] that captures:

1. Decay factor — How much funding persists over horizon
2. Sign-flip risk — Probability of funding direction change
3. Historical stability — Variance in funding rate series

Where the exact functional form weights these components based on empirical analysis.

Mirage Ratio

The mirage ratio $M$ quantifies the gap between headline and survivable APR:

Equivalently:

Interpretation

Survivable APR

Survivable APR is the expected achievable yield after accounting for persistence:

Or directly:

Mirage APR

The portion of yield that won't survive:

This is the "mirage" — the yield that looks real but won't materialize.

Survivability Components

1. Decay Component

Based on half-life and holding horizon:

2. Sign-Flip Component

Penalizes high sign-flip probability:

3. Stability Component

Based on funding rate variance:

Lower variance indicates more stable funding.

Combined Score

The final survivability score combines components:

With weights determined by empirical optimization against realized outcomes.

Example Calculation

Given:

• $APR_f = 120\%$
• $t_{half} = 36$ hours
• Horizon = 24 hours
• $\rho_{flip} = 0.15$

Step 1: Calculate decay factor

• $\lambda = \ln(2) / 36 = 0.0193$
• $D(24) = (1 - e^{-0.0193 \times 24}) / (0.0193 \times 24) = 0.74$

Step 2: Estimate survivability

• $S \approx 65$ (combining decay, flip, stability)

Step 3: Calculate mirage ratio

• $M = 1 - 0.65 = 0.35$ (35%)

Step 4: Survivable APR

• $APR_{surv} = 120\% \times 0.65 = 78\%$

Practical Guidance