One factor, two lines, one cut.
The margin
Every name carries a beta to the market and a volatility of its own. The market carries one volatility. For a basket of dollar values v, the margin is
market = (Σ βᵢ·vᵢ)² · σm² does not diversify idio = Σ (vᵢ·εᵢ)² diversifies as 1/√n margin = k · √(market + idio)
Two values of k. One to open — to borrow or to withdraw — and a lower one to hold, so an account that was allowed to open has room before it can be cut. At launch σm is 5% over the margin horizon, k is 3 to open and 2.2 to hold. All of it is governed; none of it is in the code.
The margin is homogeneous: double the basket, double the margin. Everything about liquidation follows from that one property.
Three baskets of a hundred thousand
| Basket | Margin to open | Haircut | Borrows |
|---|---|---|---|
| AAPL alone | 25,455 | 25.4% | 74,544 |
| AAPL + MSFT + NVDA | 23,685 | 23.7% | 76,314 |
| AAPL + SPY + QQQ | 17,932 | 17.9% | 82,067 |
Three technology names share a factor, so they diversify little. An index and a stock share less, so they diversify more. The rule does not know which sector a name is in; it knows its beta and its own noise.
The two lines
V₀ is the value of the names with a fresh price; V₁ the value of every name that has a price at all. M₀ is the margin of the fresh basket at the opening k; M₁ the margin of the whole basket at the holding k.
to open debt ≤ V₀ − M₀ to hold debt ≤ V₁ − M₁ else liquidable power V₀ − M₀ − debt health (V₁ − M₁) / debt
A late print holds a position but cannot open one. A feed that answers nothing freezes the liquidation of every account that holds its name, until the governor repoints it.
The cut
A liquidator repays r and receives r·(1 + b) of value, taken from every name in proportion. The basket keeps its shape, so its margin ratio does not climb after the cut. Because the margin is homogeneous, the largest r that still leaves the account at a target health h has a closed form:
F = V₁ − M₁ denom = h − F·(1+b)/V₁ r_max = denom > 0 ? (h·D − F)/denom : D
When the slice would be the whole basket, the liquidator takes it all for V₁/(1 + b) and the rest of the debt is written off — against the scribe's reserves first, the lenders after. At launch b is 5% and h is 1.10.
One liquidation, played out
A scroll holds 100 AAPL at 200, 100 SPY at 600 and 100 TSLA at 300 — 110,000 USDG — and borrows to the limit. Then TSLA halves.
- 1.Before the fall
Margin to open 24,565 (22.3%). The scroll borrows 85,434.
- 2.TSLA at 150
The basket is worth 95,000. Margin to hold 13,384; the free equity F is 81,615, below the debt. Health 0.955. Liquidable.
- 3.The closed form
r_max = 62,458. The liquidator repays that and takes 65,581 of value — 69.0% of every name, at 5% over.
- 4.After the cut
Debt 22,976, basket 29,418, health 1.100 — the target, to the rounding. 31.0% of every name is still on the scroll, in the same proportions as before.