Amplification Ratio Scaling Dynamics
A mathematical exploration of how leverage ratios scale.
In the vacuum
- Amplification ratio
- 0.0%
- Bitcoin reserve
- $10B
- Notional preferred outstanding
- $0B
- Reserve vs. original
- 1×
This example is shown in a theoretical vacuum for conceptual sake.
Vacuum conditions
- BTC price holds still.
- Preferred stock holds par.
- All capital raised goes straight to Bitcoin.
In a vacuum where all things hold still, 100% amplification requires infinite issuance.
Chart data as a table
| Doubling | Issued | Bitcoin reserve | Notional preferred outstanding | Amplification ratio | Reserve vs. original |
|---|---|---|---|---|---|
| Start | $0B | $10B | $0B | 0.0% | 1× |
| 1 | $10B | $20B | $10B | 50.0% | 2× |
| 2 | $20B | $40B | $30B | 75.0% | 4× |
| 3 | $40B | $80B | $70B | 87.5% | 8× |
| 4 | $80B | $160B | $150B | 93.8% | 16× |
| 5 | $160B | $320B | $310B | 96.9% | 32× |
| 6 | $320B | $640B | $630B | 98.4% | 64× |
| 7 | $640B | $1.28T | $1.27T | 99.2% | 128× |
| 8 | $1.28T | $2.56T | $2.55T | 99.6% | 256× |
Dividend coverage
- Amplification ratio
- 0.0%
- Bitcoin reserve
- $10B
- Notional preferred outstanding
- $0B
- Dividend rate
- 10.0%
- Annual obligation
- $0B
- Dividend coverage
- ∞
This example is shown in a theoretical vacuum for conceptual sake.
Vacuum conditions
- BTC price holds still.
- Preferred stock holds par.
- All capital raised goes straight to Bitcoin.
In the vacuum, all things held still at a 10% dividend rate, you would never be able to get below 10 years of dividend coverage.
Dividends paid outside the reserve
Chart data as a table
| Amplification ratio | Notional preferred outstanding | Bitcoin reserve | Annual obligation | Dividend coverage |
|---|---|---|---|---|
| 50.0% | $10B | $20B | $1B | 20.0 years |
| 75.0% | $30B | $40B | $3B | 13.3 years |
| 90.0% | $90B | $100B | $9B | 11.1 years |
| 95.0% | $190B | $200B | $19B | 10.5 years |
| 99.0% | $990B | $1T | $99B | 10.1 years |
Outside the vacuum
- Amplification ratio
- 50.0%
- Bitcoin reserve
- $20B
- Notional preferred outstanding
- $10B
- Dividend rate
- 10.0%
- Dividend coverage
- 20.0 years
before the price move: $20B Bitcoin reserve, $10B notional preferred outstanding
This example is shown in a theoretical vacuum for conceptual sake.
Vacuum conditions
BTC price holds still.- Preferred stock holds par.
- All capital raised goes straight to Bitcoin.
If the Bitcoin price goes up, amplification goes down. If the Bitcoin price goes down, amplification goes up.
| Bitcoin price change | Amplification ratio | Bitcoin reserve |
|---|---|---|
| 200.0% | $5B | |
| 100.0% | $10B | |
| 66.7% | $15B | |
| 50.0% | $20B | |
| 40.0% | $25B | |
| 33.3% | $30B | |
| 28.6% | $35B |
True North contributors include professionals affiliated with Strive, Inc. (Nasdaq: ASST), a Bitcoin treasury company and issuer of SATA preferred stock. True North maintains editorial independence. All analysis reflects True North's views, not those of any affiliated entity. Coverage of all digital credit instruments follows the same analytical methodology regardless of issuer. This is not financial advice.
Disclaimer: All figures on this page are hypothetical and do not model any specific security. This tool is for informational and educational purposes only. It does not constitute investment advice, a recommendation, or a solicitation to buy or sell any security. Always verify data from primary sources before making investment decisions.
Methodology
Definition: Amplification ratio = perpetual preferred notional / BTC reserve. Written A = N / B, with N the notional preferred outstanding and B the Bitcoin reserve, both in billions of dollars. The model carries no debt, so preferred notional is the whole senior claim; the glossary definition of the amplification ratio counts debt and preferred stock together.
Assumptions: Amplification ratio scaling in a vacuum · perpetual preferred at par · every dollar raised buys Bitcoin · Bitcoin held flat. Stage 2 also assumes dividends are paid outside the reserve. Stage 3 relaxes the first vacuum condition and lets the Bitcoin price move.
In the vacuum: starting from a $10B reserve, reaching amplification A takes N = 10·A / (1 − A) of issuance, and the reserve becomes B = 10 + N. Each doubling issues the current reserve, so A′ = (A + 1) / 2. As A approaches 100%, N grows without bound.
Dividend coverage: at dividend rate c the annual obligation is c·N, and coverage in years is B / (c·N) = 1 / (c·A). As A approaches 100%, coverage falls toward a floor of 1/c years. The rate steps by 0.5 percentage points between 2.0% and 15.0%.
Outside the vacuum: a $20B reserve at amplification A0 carries N = 20·A0 of preferred notional. After a Bitcoin price change p the reserve is 20(1 + p), amplification is A0 / (1 + p), and coverage is 20(1 + p) / (c·N). The move changes the reserve, not the notional.
Data sources: none. Every figure is a hypothetical parameter of the model; the page reads no market prices, holdings, or instrument data.
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