Risk and position size

Leverage: what it is, and what it does to the numbers

Leverage is not a strategy, a style or a level of courage. It is a ratio between the size of your exposure and the collateral behind it, and every consequence it has follows from that one ratio. This lesson explains all of them and recommends nothing.

About 12 minutes to read. Free, no account.

What we will not do in this lesson

Before the arithmetic, the position this school takes, stated once and plainly. We will never tell you what multiplier to use. Not here, not in a signal, not if you ask.

That is not caution about liability. It is that the choice depends entirely on things we do not know and cannot know: what fraction of your money is in this account, whether the rest of your income is secure, what you owe, who depends on you, how you behave after a run of losses, what your exchange charges, what its maintenance requirement is, and how much of your attention this will have at four in the morning. Anybody who names a number for you without knowing those things is not giving you advice, they are guessing in front of you. That includes anybody confident, anybody with a large audience, and us.

What we can do - and what this lesson does completely - is show you the arithmetic, so that whatever number you choose, you know in advance what it does. A reader who understands the mechanics and picks their own setting is in a different situation from a reader who copied one, even if the two numbers happen to match.

The three numbers, and the ratio between two of them

Leverage involves three quantities. Keep them separate and the whole subject becomes arithmetic.

Notional - the size of the exposure, units times price. This is what moves when price moves, and what fees and funding are charged on.
Margin - the collateral the exchange holds against the position. Notional divided by the leverage.
Leverage - the ratio between them, which is not a separate thing from the other two. Choosing any two fixes the third.

The definitions

notional   =  units  x  price
margin     =  notional  /  L
L          =  notional  /  margin

Take the position from the sizing lesson: 800 units at 1.2500, so 1,000 of notional. Here is what different values of L do to the collateral, and to nothing else:

The same 1,000 of exposure, at four values of L

L =  2      margin  =  1,000 / 2    =  500
L =  5      margin  =  1,000 / 5    =  200
L = 10      margin  =  1,000 / 10   =  100
L = 20      margin  =  1,000 / 20   =   50

in all four rows the position is 800 units at 1.2500,
and a 0.0100 move in price makes or loses 8

Read that last line carefully, because it is the single most misunderstood fact about leverage. The multiplier did not change the profit or loss in currency at all. A move of one cent is worth 8 in every row. What changed is how much collateral is tied up - and therefore how far price can travel against you before the collateral is gone.

The distance to zero, computed

If margin is notional divided by L, then an adverse move of 1/L of the notional loses the entire margin. That is the whole of it:

The adverse move that erases the margin

loss in currency  =  notional  x  adverse move
margin            =  notional  /  L

equal when the adverse move  =  1 / L

L =  2    ->  50.00%
L =  5    ->  20.00%
L = 10    ->  10.00%
L = 20    ->   5.00%
L = 50    ->   2.00%
L = 100   ->   1.00%

Work one row through on the position above, at L = 5, so margin is 200.

A 5% move and a 20% move, against 200 of margin

price 1.2500 -> 1.1875     (down 5.00%)
  loss  0.0625 x 800    =  50
  that is 50 / 200      =  25% of the margin

price 1.2500 -> 1.0000     (down 20.00%)
  loss  0.2500 x 800    =  200
  that is 200 / 200     =  100% of the margin

A 20% fall in the price of the coin removed 100% of the collateral. The coin did something ordinary; the account did something final. That is what the multiplier does: it converts a routine move in the market into a total loss of what you posted. At larger values of L the move required is smaller, and at L = 100 a 1% move does it - a distance many coins cover in minutes.

Liquidation happens before the margin reaches zero

Exchanges do not wait for your collateral to reach exactly zero, because by then they would be carrying the loss. They close the position when equity falls to a maintenance margin - a small percentage of notional, which varies by venue, by instrument and by position size. Call that rate m.

Liquidation distance

liquidated when equity falls to  m x notional

loss available  =  margin - m x notional
                =  notional x (1/L - m)

so the adverse move that liquidates  =  1/L - m

Put numbers in. Take m = 0.5% of notional, which is 5 on the 1,000 position, and work two values of L.

Where the position is closed for you

L =  5    margin  200    maintenance  5
  loss available   =  200 - 5          =  195
  as a move        =  195 / 1,000      =  19.50%
  price           =  1.2500 - 195/800  =  1.00625

L = 20    margin   50    maintenance  5
  loss available   =   50 - 5          =   45
  as a move        =   45 / 1,000      =   4.50%
  price           =  1.2500 -  45/800  =  1.19375

Now compare the second row with the stop from the first lesson. That stop sat at 1.2000, which is 4.00% below entry. The liquidation price is 1.19375, which is 4.50% below entry. The stop and the liquidation are half a percent apart. A wick of the kind the stop lesson measured - 0.64% past the stop on an ordinary candle - reaches the liquidation price. And a liquidation is not an exit at your stop: it is a forced market exit, with a fee, at whatever the book offers, at the worst moment, and it takes the whole margin rather than the amount you planned to risk.

How leverage multiplies both directions

Results on margin are the price move times L. That is the attraction, and the arithmetic is symmetrical in a way the marketing never is.

A 3% move, measured against the margin

notional 1,000, a 3% move is 30 either way

L =  2   margin  500   ->  30 /  500  =   6% of margin
L =  5   margin  200   ->  30 /  200  =  15% of margin
L = 10   margin  100   ->  30 /  100  =  30% of margin
L = 20   margin   50   ->  30 /   50  =  60% of margin

the same 30. up or down.

Both columns are real. A multiplier that turns a 3% move into 60% of the margin does it in both directions, and the previous lesson explains why that is not a fair trade: the two directions are symmetrical in percent and not in consequence. Losing 60% of the margin requires 150% to undo. Losing 100% of it ends the position entirely, and no subsequent gain applies to a position that no longer exists.

That asymmetry is the entire argument, and it is arithmetic rather than temperament. Upside is multiplied and recoverable; downside is multiplied and, at the end, absorbing. The multiplier shortens the distance to a state you cannot trade your way out of.

Where leverage interacts with position sizing

Here is the part that resolves most confusion. If you size by stop distance the way the second lesson describes, the notional is already decided before leverage enters the picture. Your risk amount and your stop fixed it. Leverage then only decides how much collateral has to sit behind that notional, and how close the liquidation price is.

Used that way, a multiplier is a statement about collateral efficiency, and the only question it raises is whether the liquidation price is far enough beyond your stop that the stop is what actually ends the trade. That is a computation you can do, with the formula above and your venue’s maintenance rate, before you open anything.

The damage happens when leverage is used the other way round - as a way to hold a larger notional than the account would otherwise support. Watch what that does with every other number held constant.

The same account, the same stop, a larger notional

account 4,000, stop 4.00% below entry

notional   1,000   ->  4.00% of 1,000   =   40 at stake
                       as a share of the account  =  1.0%

notional  10,000   ->  4.00% of 10,000  =  400 at stake
                       as a share of the account  =  10.0%

the stop did not move. the risk went up ten times.

Nothing about the chart changed between those two rows. The stop is in the same place for the same reason. The only difference is the size of the position, and ten of those losses in a row is the 5% column from the drawdown lesson twice over. Leverage did not create that risk - the position size did. Leverage made the position size possible, which is why the two subjects cannot be taught apart.

The decision, and whose it is

So: what should you use? We do not know, and we are not going to pretend otherwise. We do not know what this account is to you. The arithmetic on this page is complete and it is the same arithmetic a desk uses; the inputs are facts about your life.

What we will say is what the arithmetic says, in four lines, none of which is a recommendation.

The adverse move that erases your collateral is 1/L, and liquidation comes slightly before that, at 1/L minus the maintenance rate.
The loss in currency from a price move does not depend on L at all. Only the collateral behind it and the distance to liquidation do.
If your liquidation price is close to your stop, the stop is decorative - the exchange decides the outcome, not your plan.
The direction that compounds against you is the one that ends in a position that no longer exists, and the recovery arithmetic of the previous lesson does not apply to it.

If you take one thing from this module, take this: compute your liquidation price before you open the position, write it next to your stop, and look at the gap between them. If that gap is uncomfortable, the arithmetic has told you something, and it told you before it cost anything. See the risk disclaimer.

The terms, defined

Leverage (L): The ratio of notional to margin. Not a separate quantity - fixing any two of notional, margin and L fixes the third.
Notional: Units times price: the exposure that actually moves with the market, and the base fees and funding are charged on.
Margin: The collateral held against the position, equal to notional divided by L. What a liquidation takes.
Maintenance margin (m): The minimum equity an exchange requires, as a rate on notional. It varies by venue, instrument and position size.
Liquidation: The exchange closing the position when equity reaches the maintenance level. A forced market exit with a fee, not an exit at your stop.
Liquidation distance: 1/L minus m, as a fraction of the entry price. Shorter in practice, because fees and funding are deducted from margin.
Funding: A periodic payment between long and short holders of a perpetual contract, charged on notional and paid out of margin, in whichever direction the rate sits.

What this means in practice

Say the three quantities separately: notional, margin, leverage. Two of them fix the third.
Remember that the currency result of a price move does not depend on the multiplier. Only the collateral and the liquidation distance do.
Compute the liquidation price before opening, from your own venue’s maintenance rate, and write it beside your stop.
Treat fees and funding as deductions from margin that move the liquidation price closer while you hold.
Size from the stop first. If leverage is deciding your position size rather than your collateral, the order of operations is backwards.
Choose your own setting, from your own circumstances, and distrust anybody who names one for you - including anybody who sounds certain.

Nothing in this lesson is financial advice or an instruction to trade. See the risk disclaimer. We never recommend a leverage setting - that decision is yours.