Passive vs Active Retirement Under Power-Law Growth

The Bengen 4% rule sets the safe withdrawal rate as a fixed percentage of the starting portfolio value. Bitcoin offers a different anchor: the power-law floor, which grows at a known, decelerating rate.

The question this paper asks: if we anchor the initial withdrawal not to the starting portfolio value but to the next twelve months of floor growth in dollars — and inflate from there — what coverage percentage maintains a target confidence over a retirement horizon, with and without active cycle-aware rules?

Anchoring to floor growth means the rule self-calibrates to where the retiree sits on the power-law curve. An early-cycle retiree gets a richer initial dollar withdrawal than a late-cycle retiree without any hand-tuning — because the dollar value of one year of floor growth is itself the slow-moving, model-anchored reference.

The Coverage Rule

For 1 BTC at trend on 2026-05-04, twelve months of floor growth is $21,873. We call this the 100% coverage withdrawal. Higher coverage = more lifestyle. Lower = more bequest.

Across the full 40–140% coverage sweep at 30,000 paths per cell, the rule that emerges:

Inflation matters more than horizon. Going 3% → 6% costs ~13–15 percentage points of safe coverage at any confidence level. Going 30y → 50y costs only 2–4 pp. Product tiers should branch on inflation assumption first.

The Endowment Tier

Sub-100% coverage isn't a "safer 100%." It's a different product altogether.

At 80% coverage ($17,498/yr per BTC), ruin is functionally zero across all four tested combinations — including 50 years at 6% inflation, where ruin is just 0.12%. And the median surviving path retains 0.36 to 0.47 BTC of the starting 1 BTC after the full horizon.

Even the unlucky tenth-percentile surviving path at 50y / 6% inflation ends with 0.22 BTC and ~$52M nominal. The strategy operates as a perpetual endowment: the asset cannot be exhausted in any reasonable scenario, and the surplus accumulates as bequest.

At 6% inflation, the 80% tier also delivers a 60× reduction in ruin probability versus the 100% tier — the dial between 80% and 100% is a wealth-preservation knob at low inflation, and a survival-and-preservation knob at high inflation.

The Playbook Uplift

Layer the wealth playbook on top of the same withdrawal stream:

• Borrow living expenses while spot is below 1.6× floor (~0.69× trend) at 10% APR
• Pay all debt at the first crossing of trend
• Sell 50% of remaining stack at each of 1.5×, 2×, 3× trend (each tier fires once per cycle)
• Redeploy all remaining fiat into BTC at the first crossing of trend going down
• Recycle every cycle

Same coverage. Same starting BTC. Same model. The ruin numbers collapse:

The playbook adds approximately +50 percentage points of safe coverage at 99% confidence. The natural default product tier shifts from 100% (passive) to 150% (active) — with 99.5%+ survival at both 3% and 6% inflation over 30 years.

At 99% confidence (3% infl, 30y), the passive holder can withdraw ~104% of forward floor growth (~$22.8k/yr per BTC). The Storm Years Playbook operator can withdraw ~180% (~$39.4k/yr per BTC). Same in-model reliability target. Different product.

The Stress Test

Following an external A− review citing "model dependency disguised as structural inevitability," we ran a four-batch hostile-reviewer sensitivity battery:

1. Borrow APR doubled (10% → 15% → 20%) — tests counterparty-risk widening
2. Cycle peaks capped at 2× trend — tests "no more 2× tops" world
3. β decay 0.001/yr — tests power-law exponent weakening (~25% lower trend at year 30)
4. Parameter bootstrap (20 draws of β, cycle σ, floor mean) — tests parameter uncertainty

The Standard tier (150% coverage) ruin under each stress, both inflation regimes:

The +50pp / Standard-tier / 99% confidence claim survives every stress in both inflation regimes. Bootstrap 95% credible interval for ruin: [0.01%, 0.24%] at 3% inflation, [0.15%, 0.86%] at 6%. Both safely under the 1%-ruin / 99%-confidence threshold the product is positioned on.

Surprise finding: peak compression at 2× trend barely affects the 150% tier. At 150% coverage the playbook's safety derives from the 1.5× tier and the trend-redeploy mechanic, both of which survive a 2× cap. The 200% Aggressive tier is sensitive to all four stresses and requires explicit parameter-uncertainty disclosure.

The Product Ladder

Two ladders fall out of the data. The passive variant is a wealth-preservation tool. The active variant is the Storm Years Playbook.

* Aggressive tier confidence is at baseline parameters. Bootstrap p95 worst case: 83%. Disclose explicitly.

The default product is the Standard tier: 150% coverage, 99%+ confidence in both inflation regimes, defended against four orthogonal stress tests. Each 5pp drop in confidence buys you ~14pp coverage under passive hold, ~25pp under the playbook. The playbook approximately doubles the elasticity of confidence to lifestyle dollars.