Leverage & Liquidation Engines

We keep saying “leveraged” — now let’s make it exact. Leverage is the lever that makes perps thrilling and lethal in equal measure, and it leads directly to the most important number a perp trader watches: the liquidation price, the level at which the engine forcibly closes you out. This lesson derives that price from first principles, distinguishes the two margin modes, and opens up the keeper-bot machinery that enforces it.

Leverage: a small lever moving a big weight

Analogy. Leverage is a crowbar. A short crowbar (low leverage) moves a small rock with a forgiving margin for error. A long crowbar (high leverage) moves a boulder with the same effort — but the tip whips violently, and a tiny slip at your hand becomes a huge swing at the rock. The longer the lever, the more you move per unit of effort, and the less room you have before it slips out of control.

Definition. Leverage is the ratio of your position’s notional to the margin backing it:

$\text{leverage} = \frac{\text{notional}}{\text{margin}}.$

Equivalently, your margin is a fraction $1/\text{leverage}$ of the notional. At 10×, you back $10,000 of exposure with $1,000 of collateral; your margin is 10% of notional.

Why it cuts both ways. Your PnL is measured on the notional, but your survival is measured on the margin. A 1% adverse move on a $10,000 notional is a $100 loss — which is 10% of your $1,000 margin. So a price move of $x\%$ becomes a margin move of $x\% \times \text{leverage}$. Crank leverage to 50× and a mere 2% adverse move wipes out your entire margin. This is the seed of the liquidation price.

Initial margin, maintenance margin, and the liquidation price

Two margin thresholds govern a position:

• Initial margin — the collateral required to open the position. At 10× leverage, initial margin is 10% of notional. It sets your maximum leverage.
• Maintenance margin — the minimum equity you must keep, as a fraction of notional, to keep the position open. It’s smaller than initial margin (e.g. 0.5%). When your equity falls to the maintenance margin, you’re liquidated.

The liquidation price, derived. Your position equity is margin + unrealized PnL. For a long with entry price $P_0$, notional $N$ (in asset units $q$, so $N = q P_0$), and margin $M$, the equity at price $P$ is

$\text{equity} = M + q\,(P - P_0).$

Liquidation triggers when equity falls to the maintenance requirement $m \cdot q P$ (maintenance fraction $m$ of current notional). Setting equity equal to that and solving for the liquidation price $P_\text{liq}$:

$M + q(P_\text{liq} - P_0) = m\, q\, P_\text{liq}.$

For a quick, accurate-enough approximation, ignore the tiny $m P_\text{liq}$ term against $P_0$ and note $M = qP_0/\text{lev}$. The price has to fall by about

$\frac{P_0 - P_\text{liq}}{P_0} \approx \frac{1}{\text{lev}} - m$

before you’re liquidated. In words: a long is liquidated after an adverse move of roughly (1 ÷ leverage − maintenance fraction). A short is the mirror image — liquidated after an adverse move up of the same size.

Worked example: the full liquidation arithmetic

Let’s nail every digit. You go long 1 BTC perp at $30,000, posting $3,000 margin (so leverage = 30,000 / 3,000 = 10×). Maintenance margin is 0.5% of notional.

Step 1 — the survivable move. Liquidation move ≈ 1/lev − m = 1/10 − 0.005 = 0.10 − 0.005 = 0.095 = 9.5%.

Step 2 — the liquidation price. Price must fall 9.5% from $30,000:

$P_\text{liq} \approx 30{,}000 \times (1 - 0.095) = 30{,}000 \times 0.905 = \$27{,}150.$

So if BTC’s mark touches roughly $27,150, the engine liquidates the long.

Step 3 — sanity check via equity. At $27,150, the loss is 1 × (30,000 − 27,150) = $2,850. Equity = margin − loss = 3,000 − 2,850 = $150. Maintenance requirement = 0.5% × notional ≈ 0.005 × 27,150 ≈ $136. Equity ($150) has fallen to roughly the maintenance floor ($136) — confirming the trigger is right around there.

Step 4 — the bankruptcy price. Keep falling to where equity hits zero: that’s the bankruptcy price, 30,000 − 3,000 = $27,000. The gap between liquidation ($27,150) and bankruptcy ($27,000) is the engine’s working room — the cushion it needs to actually close the position before equity goes negative. If it can’t close in that window, the position goes bankrupt and the insurance fund (next lesson) eats the shortfall.

Drag the meter below: set 10× and you’ll see a liquidation around $27,150 with a ~9.5% buffer; push leverage toward 100× and watch the buffer collapse to a fraction of a percent.

Isolated vs cross margin: how far a loss can reach

A crucial risk choice: which collateral backs the position?

• Isolated margin. Only the margin you assigned to this position is at risk. If it’s liquidated, you lose that margin and nothing else — the blast radius is contained. Great for ring-fencing a degenerate high-leverage punt.
• Cross margin. Your entire account balance backs the position. That gives a much wider buffer (the liquidation price is far further away, because all your equity defends it), but a single bad position can drain your whole account. It’s more capital-efficient and survives deeper drawdowns, at the cost of correlated blow-up risk.

Analogy. Isolated margin is putting $200 of chips on one table and leaving your wallet in the hotel safe — you can only lose the $200. Cross margin is dumping your whole wallet on the table — you can ride out a bad streak that would have busted the $200 stake, but a catastrophic hand can take everything.

The liquidation engine: keepers, partial liquidation, and the close

When the mark price hits your liquidation level, who actually closes you, and how? In DeFi, there’s no broker to call — the work is done by a liquidation engine plus a swarm of keeper bots.

• Keepers / liquidator bots. Permissionless actors who monitor every open position. The instant a position’s mark crosses its liquidation threshold, they race to submit the liquidation transaction. Their incentive is a liquidation fee or penalty carved out of the position’s remaining margin (and on-chain, this is a flavor of the liquidation MEV you may have met in the MEV course — landing the liquidation first is worth money).
• Partial vs full liquidation. A good engine doesn’t always nuke the whole position. Partial liquidation closes just enough of the position to restore the maintenance buffer, leaving the trader with a smaller, healthy position rather than wiping them out — gentler, and it reduces market impact. Full liquidation closes everything, used when the position is too far gone or too small to partially unwind.
• The bankruptcy / insurance handoff. The engine tries to close the position in the window between the liquidation price and the bankruptcy price. If the market is moving too fast (a gap or a thin book) and it closes below bankruptcy, the position has gone negative — and the shortfall is covered by the insurance fund, the subject of the next lesson.

Why the maintenance margin exists at all: it’s the engine’s head start. By triggering liquidation while you still have a sliver of equity (not at zero), the engine gives keepers time and price room to actually execute the close before your loss becomes the protocol’s loss. The maintenance margin is the buffer that protects everyone else from your blow-up.

You can now compute a liquidation price in your head and explain who pulls the trigger. But we left a dangling thread: what happens when the engine can’t close in time and a position goes negative? That shortfall has to land somewhere. Next: the insurance fund that absorbs bad debt, and auto-deleveraging (ADL) — the last-resort mechanism that socializes losses onto the most-profitable traders when even the insurance fund runs dry.