Working out your liquidation price

Liquidation happens when the equity backing a position falls to the maintenance margin the venue requires for it. Equity is your posted margin plus or minus the profit and loss so far. The maintenance requirement is a small percentage of the current position value, often around half a percent on a deep market and considerably higher on a long-tail one. Set those two equal and solve for the price, and you have the level.

Write the entry price as P, the position size in coin units as Q, the margin as M and the maintenance margin rate as m. Equity at some price X is M plus Q times X minus P. The requirement is m times Q times X. Setting them equal and rearranging gives the liquidation price as P minus M over Q, all divided by one minus m. The term M over Q is your margin per coin, which is the buffer expressed in price units, and the division by one minus m is the maintenance requirement pulling the level slightly closer to you.

Take BTC at one hundred thousand, one thousand dollars of isolated margin at ten times leverage, and a maintenance rate of half a percent. The notional is ten thousand dollars, so the size is nought point one BTC. Margin per coin is one thousand divided by nought point one, which is ten thousand. One hundred thousand minus ten thousand is ninety thousand, divided by nought point nine nine five gives ninety thousand four hundred and fifty two. So the position is closed at about ninety thousand four hundred and fifty, a fall of nine point five five percent. Without maintenance margin the answer would have been exactly ninety thousand, the naive one over leverage rule, and the maintenance requirement cost you four hundred and fifty dollars of room.

For a short the equity is M plus Q times P minus X, and the same rearrangement gives P plus M over Q, divided by one plus m. With the same inputs that is one hundred and ten thousand divided by one point zero zero five, which is one hundred and nine thousand four hundred and fifty three, a rise of nine point four five percent. The short is liquidated on a slightly smaller percentage move than the long, because the maintenance requirement is charged on the position value and the position value grows as the price moves against a short.

The number on the ticket at entry is not a constant.

• Funding is deducted from margin, so the level creeps toward you on every settlement you pay
• Adding margin pushes it away: in the worked long, another five hundred dollars moves it from about ninety thousand four hundred and fifty to about eighty five thousand four hundred and thirty
• Adding size pulls it closer, because margin per coin falls
• Maintenance rates are tiered on most venues and rise with position size, so scaling in can widen the requirement
• Under cross margin, profit and loss on unrelated positions changes the equity backing this one

Everything above assumes isolated margin, where the position has its own allocation. Under cross margin the whole balance backs every position, so there is no meaningful per-position liquidation price: there is an account-level condition that depends on all of them at once. The displayed per-position figure under cross margin is a projection that assumes nothing else changes, which in a correlated selloff is precisely the assumption that fails.