The 1.6× Floor Rule

We test the 1.6× Floor Rule — the claim that a 50% LTV Bitcoin-backed loan is structurally safe when entry price is at or below 1.6× the power law floor — against 13 years of daily price data. Across 1,982 qualifying entry points (price ≥ $1), the 730-day liquidation rate is zero. Above the threshold, 58.6% of entries result in liquidation within 730 days.

The rule is not merely conservative: every floor multiple from 1.0× to 1.6× shows zero failures; failures begin at 1.7× (0.18%). The rule’s zero-failure property derives from the structural floor truncation documented in the companion paper The Reflecting Barrier: the liquidation price of any below-1.6×-floor loan sits below the power law floor, which has never been closed below in 15 years of post-2010 data.

Prior Work on Bitcoin-Collateralised Lending Risk

Bitcoin-backed lending emerged as a significant financial product category between 2018 and 2022, with platforms including BlockFi, Nexo, Ledn, Unchained Capital, and Celsius extending loans collateralised by Bitcoin holdings. The collapse of multiple centralised lenders in 2022 — most prominently Celsius Network (July 2022, approximately $4.7 billion in customer claims) and BlockFi (November 2022, following the FTX contagion) — produced a body of evidence on the failure modes of Bitcoin-backed lending.

Post-mortem analyses identify a common pattern: platforms extended loans at LTV ratios and liquidation thresholds that did not account for the structural properties of Bitcoin’s price distribution. Celsius maintained lending books with effective LTV ratios approaching 80% during market peaks, with liquidation triggers at 85–90% LTV. When Bitcoin declined 75% from its November 2021 ATH, these positions were systematically underwater.

The academic literature on cryptocurrency lending risk is sparse. Cong et al. (2021) model crypto lending markets with endogenous price crashes, finding that leverage constraints are binding during downturns. Gudgeon et al. (2020) analyse DeFi liquidation cascades, showing that fixed LTV thresholds without reference to underlying asset volatility structures produce systemic risk. Neither paper incorporates a structural floor constraint of the type the Bitcoin power law provides.

This paper contributes the first empirical test of a floor-anchored loan safety rule against the full historical Bitcoin price series. The key departure from prior work is that the safe zone is defined not in terms of price levels or ATH multiples, but in terms of the price’s relationship to the power law floor — a structural boundary with independently verified truncation properties.

Rule Derivation

At 50% loan-to-value, the liquidation threshold on standard lending platforms is 80% LTV, corresponding to a liquidation price of 0.625 × entry price. For the liquidation price to remain below the power law floor, the entry price must satisfy:

liquidation_price < floor_price
0.625 × entry < floor
entry < 1.60 × floor

This geometric relationship scales across LTV ratios. The table below reports the safe entry ceiling for each standard LTV tier at today’s floor price ($55,828). The current price ($66,848) is at 1.20× floor — well inside the 50% LTV safe zone.

Floor_current = 0.432× trend. Today’s floor: $55,828. Today’s price: $66,848 (1.20× floor, inside safe zone at 50% LTV).

Empirical Test

We test the rule against all daily closing prices in the dataset where price ≥ $1 (n = 5,184 days, excluding pre-2011 exchange artifact data). For each entry day, we compute the floor price using floor_current = 0.432 × trend, classify whether the entry satisfies price ≤ 1.60 × floor, and record whether any price within the subsequent 730 calendar days falls below 0.625 × entry price.

A 730-day (2-year) test window is used because it covers approximately one full halving cycle of potential price decline, including the sustained bear markets that have characterised each cycle. Loans that survive 730 days without liquidation are classified as passing regardless of longer-term price trajectory.

Results

Zero failures across 1,982 safe-zone entries. Of 1,982 entry days satisfying the 1.6× rule, none resulted in a 730-day price touching the liquidation threshold. The contrast with the unsafe zone is stark: 2,032 of 3,468 entries above 1.6× floor (58.6%) were liquidated within the test window.

The zero-failure property holds across the entire safe zone from 1.0× to 1.6× floor. Failures begin precisely at 1.7× floor (0.18%).

Stress Test: The Closest Calls

Although no safe-zone entry resulted in liquidation, the closest calls are instructive for understanding the rule’s margin of safety. The rule works with single-digit margins above the liquidation price during two of the most severe bear markets in Bitcoin history.

The 2015-07-12 entry at $310 is the most instructive: the liquidation price was $194, and the subsequent cycle minimum was $209 on 2015-08-24 — only $15 (7.9%) above the threshold. The floor held at $242 on that date, providing a $15 buffer above the $194 liquidation price. This was the 2015 cycle capitulation bottom, the closest the power law floor has ever been tested in a loan context.

The 2022 entries (LUNA/FTX bear market) show similar structure: entries near $23,000 had liquidation prices near $14,500, and Bitcoin bottomed near $15,800 during the FTX contagion — above the floor of approximately $14,700 on those dates.

These stress tests demonstrate that the zero-failure result is not achieved with large comfortable margins. The floor held during two of the most severe bear markets in Bitcoin’s history (2015 cycle bottom: −87% from peak; 2022 FTX contagion: −77% from peak) with single-digit percentage margins above the liquidation threshold. The rule works because the floor holds.

Mechanism: Why the Rule Works

The 1.6× floor rule’s zero-failure property derives directly from the power law floor’s structural truncation. As demonstrated in the companion paper The Reflecting Barrier (Scale Invariant Capital, 2026), the Bitcoin residual distribution shows 81% fewer observations below the conservative floor than a normal distribution predicts (χ² = 203.9, p < 10⁻⁵⁰). The floor has zero daily closes below it in post-2010 reliable price data under the conservative definition.

The causal chain is simple: a loan entered below 1.6× floor has a liquidation price below the floor. The floor has never closed below. Therefore the loan has never been liquidated.

This is not a statistical regularity — it is a mechanical consequence of the floor’s documented structural properties. The two papers are complementary: the Reflecting Barrier establishes why the floor holds; the 1.6× Floor Rule establishes what that means for loan safety.

Limitations

Intraday prices. The test uses daily closes. Lending platforms that mark positions to intraday prices may liquidate loans that would not appear as failures in this test. The March 2020 flash crash briefly traded below the published floor without closing there — an intraday test would show different results for that episode.

Floor definition sensitivity. The test uses floor_current (0.432× trend). Under the conservative floor (0.314×), the safe-zone ceiling at 50% LTV would be at 0.502× trend — a narrower zone with fewer qualifying entries but even stronger historical backing.

Platform-specific LTV ratios. Liquidation ratios vary by platform. Ledn uses 80% LTV for liquidation on standard loans. The 0.625× multiplier assumes a 50% initial LTV with 80% liquidation trigger. Users on platforms with different structures should recompute the safe entry ceiling using the formula in the derivation section.

Future floor validity. The zero-failure result depends on the power law floor continuing to hold. The floor’s holding probability and truncation properties are documented empirically but are not guaranteed forward-looking. The Reflecting Barrier paper estimates that the truncation has strengthened across cycles, which supports forward extrapolation, but no structural guarantee is possible.