The Bitcoin Safe Withdrawal Rate at Any Entry Residual

William Bengen's 4% rule is the most widely-cited number in retirement planning. From a 50/50 U.S. equity-bond portfolio, you can safely withdraw 4% per year for 30 years at ~95% reliability. What's the Bitcoin analogue?

We asked it in the natural Bitcoin dimension: at any starting log-residual against the power-law trend, what is the maximum USD withdrawal from 1 BTC that survives a 30-year retirement at 99% in-model reliability?

Parameterizing by residual (rather than by calendar date or current price) makes the answer scenario-invariant to time and directly measures the sequence-of-returns sensitivity that equity retirement analysis worries about: does entry valuation matter?

The Answer

990,000 simulated paths. 6 inflation scenarios. 3 horizons. 15 entry residuals from 0.52× trend to 2.51× trend.

Under any realistic inflation assumption at the 30-year horizon, 1 BTC supports a retirement income that beats the Bengen 4% rule applied to a $500,000 equity portfolio — by a factor of 5 to 7×. At 99% in-model reliability.

1 BTC at current trend is approximately $131k. 1 BTC at deep bear is approximately $69k. Either way, the annual safe withdrawal exceeds $20,000.

The Flat Curve

Here is the surprising part. The SWR99 curve is nearly flat across entry residuals in every scenario at 30 years.

Bear entry (0.52× trend): $20.2k/year under 7% M2 stress.
Peak bull (2.51× trend): $21.3k/year under 7% M2 stress.
Spread: $1.1k/year, roughly 5%.

Entry valuation does not meaningfully affect dollar-denominated 30-year retirement capacity. The dominant determinant is the inflation escalator, not the entry valuation, not fat-tail shape, not floor stochasticity.

Mechanism: OU mean-reversion with an 11-month half-life. Bear entries quickly revert to trend and spend the remaining 28+ years drawing from the same stationary distribution as bull entries. The early drawdown burns more BTC per dollar at bear entries, but the window is short and the effect integrates away over 30 years.

The Bengen Inversion

Expressed as a percentage of initial nominal stack value, the picture flips.

Every cell beats the Bengen 4% rule — by factors of 1.6× to 7.3×. But notice the direction: higher percentage SWR at worse entry valuations. That is the opposite of equity wisdom, which penalizes high-CAPE entries.

The mechanism is mean-reversion alpha. A bear-entry path is expected to revert toward trend, giving the retiree a source of return the equity literature has no analogue for. Bull entries start above trend, mean-reversion drags them back down, and they get no such free ride.

Under the Bitcoin power law, the equity advice "don't retire into a high-valuation market" is backwards. The percentage you can safely withdraw is largest at the worst-looking entry points.

When Horizon Matters

At 30 years, entry residual is a non-factor. At 100 years, it matters modestly under M2 stress.

Under 7% M2 escalation at 100 years, bear-entry SWR99 drops from $20k to $16k while bull-entry SWR99 holds near $20k. The reason is that 100 years crosses the horizon at which the power-law trend CAGR decelerates below the 7% escalator — around year 63 from the simulation start. Past that point, bear-entry paths that haven't fully recovered from early drawdowns are no longer rescued by strong trend compounding in the late horizon.

For standard retirement planning, this is a non-issue. A 30-year retirement horizon terminates well inside the adoption-phase regime where trend compounding dominates. For century-long asset-preservation horizons, the paper recommends using shorter-horizon numbers as the primary plan and treating long-horizon results as scenario analysis.