Bitcoin Power-Law Collateral Model

Financing $100k/yr borrowing against Bitcoin

How large a stack keeps loan-to-value ≤ 50% even if price sits at the Porkopolis power law 16.5ᵗʰ-percentile support band — while drawing tranches as needed and capitalising interest, indefinitely.

Assumptions

Result

Required BTC stack
BTC
Binding moment (peak LTV)
LTV at trend price, that date
Stack value today @ trend

Liabilities vs. collateral value (USD)

log scale
collateral @ trend collateral @ 16.5ᵗʰ pctile accrued liabilities

Loan-to-value over time

LTV if price at 16.5ᵗʰ pctile (stress) LTV if price on trend

Phase 0 · Accumulation via DCA

How long until you can start borrowing?

Save monthly into Bitcoin at the trend price, starting today. Every month your stack grows; every month the required stack for the strategy above shrinks (because trend price climbs). Wait for them to cross.

DCA Strategy

Handover

Time to "ready to borrow"
Stack accumulated by then
Total USD invested via DCA
Stack value at handover @ trend

Required stack vs. accumulated stack

log scale
required stack (if borrowing starts then) accumulated via DCA crossover = "ready to borrow"

Method. Trend = a·xᵇ with a=1.728×10⁻¹⁷, b=5.76, x = days since genesis (3 Jan 2009), calibrated to Porkopolis's published year-end table. Stress price = (multiple)·trend; Porkopolis's rarely-breached floor ≈ 0.42×, so the 16.5ᵗʰ-pctile 1-σ support is taken near 0.42×. Liabilities draw one tranche every few months from today and compound interest monthly; nothing is ever repaid. Required stack = maxₜ [ liabilities(t) ÷ (maxLTV · stress price(t)) ].
DCA logic. Each month, the slider amount buys BTC at k·trend price, where k is the "effective price paid" slider (default 0.80×). Because Bitcoin spends roughly half its time below trend and DCA captures the harmonic mean of visited prices, real cycle-aware DCA historically pays ~0.7–0.85× of trend, not 1.0×. Set k=1.0× for trend-only buying. For any candidate borrow-start date S, the model re-runs the LTV stress simulation starting at S and finds the smallest stack that survives it. The handover is the first month where accumulated ≥ required.
Disclaimer. This model is for informational purposes only. Not financial advice. Every number presented depends on an unproven assumption: that Bitcoin's historical "power-law" price trend continues for decades. It may not. This strategy uses leverage — borrowing against Bitcoin and letting interest compound without repaying. If Bitcoin's price falls far enough, your loan can be liquidated and you can lose your entire stack. Bitcoin has repeatedly dropped 70%+ in the past. Outputs marked "forever" are illustrative only and assume conditions that have never been tested over a real retirement horizon. Do not make financial decisions based on this tool.

CC0 1.0 Universal