Most losing accounts are not destroyed by bad entries. They are destroyed by good entries taken in the wrong size, where a single trade that was supposed to cost one per cent of the account costs eight, and the next four trades are taken in a hurry to win it back.
Position sizing is the arithmetic that stops that happening. It is one division. The reason it is worth an article is that the version of the division most people use is subtly wrong, and the error always runs in the same direction: the real loss is bigger than the one you budgeted for.
The decision position sizing actually makes
Before you can size anything you have to fix three things, and only one of them is a market question:
- How much of the account you are willing to lose on this trade. A policy choice. The market has no opinion about it.
- Where the trade is wrong. That is the stop price: the level at which the reason you took the trade no longer holds.
- Where you are getting in. The entry price.
Everything else follows. The size is not an input you choose and then hope about — it is an output, computed from those three. If you find yourself deciding the size first and then looking for a stop that justifies it, you are not sizing a position, you are picking a number and decorating it.
The formula
Write R for the money you are risking, d for the distance from entry to stop, and q for the
number of units to buy or sell. The naive version everyone learns first is.
Being stopped out moves the price by d against you on q units, so it costs q × d, which is
R. That is the whole idea, and for a spot trade at a venue that charges nothing it is exact.
It is not exact anywhere else, because opening and closing the position both cost a fee. With a
taker fee rate f charged on notional at each fill, a position of q units pays q × entry × f to
open and q × stop × f to close at the stop. The real cost of being stopped out is.
Set that equal to your budget R and solve for q.
That is the formula. The fee term sits in the denominator, so it makes the position slightly smaller — which is exactly right, because the fee is part of what losing costs, and paying it out of the same budget is the only way the worst case comes out equal to the number you chose.
Worked example: a long with no fees
Round numbers first, so the shape is visible.
| Input | Value |
|---|---|
| Account equity | 10,000 |
| Risk | 1% |
| Entry | 100 |
| Stop | 96 |
| Side | Long |
| Fee rate | 0% |
The arithmetic, in order:
R = 10,000 × 1/100 = 100
d = |100 − 96| = 4
q = 100 / 4 = 25 units
notional = 25 × 100 = 2,500
stop dist = 4/100×100 = 4%
worst case = 25 × 4 = 100So: a 10,000 account, risking 1%, with the stop 4% away, buys 2,500 of exposure. Note that the notional is a quarter of the account even though the risk is one hundredth of it. That ratio is what the stop distance buys you, and it is why a tight stop is not automatically a conservative trade — a tight stop with a fixed risk budget means a larger position, and a larger position is more sensitive to slippage and to a gap through the stop.
The reward targets are quoted in multiples of the risk, called R-multiples. One R is one stop distance in the profitable direction: 104, then 108, then 112. Quoting targets this way is useful because it makes trades comparable across instruments and sizes. “I made 2R” means something. “I made 340” means nothing until you know what was risked.
Worked example: a short with fees and leverage
Now the realistic case, where the fee term does work.
| Input | Value |
|---|---|
| Account equity | 25,000 |
| Risk | 1.5% |
| Entry | 2,000 |
| Stop | 2,080 |
| Side | Short |
| Leverage | 5× |
| Fee rate | 0.05% per fill |
R = 25,000 × 1.5/100 = 375
d = |2,000 − 2,080| = 80
f = 0.05/100 = 0.0005
fee/unit = 0.0005 × (2,000
+ 2,080) = 2.04
q = 375 / (80 + 2.04)
= 375 / 82.04 = 4.570941
notional = 4.570941 × 2,000
= 9,141.88
margin = 9,141.88 / 5
= 1,828.38
fees = 4.570941 × 2.04 = 9.32
worst = 4.570941 × 80 + 9.32
= 365.68 + 9.32 = 375.00The worst case comes out at exactly the 375 that was budgeted, which is the point of the exercise.
Now do it the naive way and compare. Ignoring fees, q = 375 / 80 = 4.6875 units, a notional of
9,375. Being stopped out of that position costs:
4.6875 × 80 = 375.00
price move
4.6875 × 0.0005
× (2,000 + 2,080) = 9.5625
actual loss = 384.56Nine and a half units of overshoot on a 375 budget: 2.6% more than intended. On one trade that is noise. The reason it matters is that it is not random noise — it is a bias, in the same direction, on every trade, forever, and it scales with how often you trade and how much you pay in fees. A trader taking several trades a day at a high fee tier is running a permanently larger book than their own risk policy describes, and will not find out until a bad run makes the gap visible.
Where leverage actually enters
Look again at the short example. Leverage appears exactly once, in the margin line.
It does not appear in q at all. This surprises people, and it is the single most useful thing on
this page: leverage does not change your risk. The stop does. Leverage changes how much
collateral the venue demands to hold the position open. The same 4.570941 units at 5× ties up
1,828.38 of margin; at 10× it ties up 914.19; at 1× it ties up the full 9,141.88. In all three
cases, being stopped out costs 375.
What leverage genuinely changes is your distance to liquidation, and that is a separate constraint you have to check separately. If the exchange’s maintenance margin would liquidate the position before price reaches your stop, your stop is decorative — the venue closes you first, at a worse price, with a fee. High leverage is dangerous because it moves the liquidation price inside the stop, not because it magically enlarges the loss on a position whose stop was honoured.
The mistakes that actually cost money
Sizing from margin instead of from the stop
“I put 500 into the trade at 10× so I am risking 500.” That is the liquidation loss, not the
planned loss, and it only describes what happens if the position is never closed. The planned loss
is q × d plus fees, and it can be far smaller or far larger than the margin posted. Margin is a
collateral question. Risk is a stop question.
Ignoring the round-trip fee
Covered above. Two fills, both charged, both paid out of the same budget.
Moving the stop after entry
Every number on this page assumes the stop is honoured. Widening a stop because price is approaching it converts a 1% loss into an unbounded one, and it does so at the exact moment you are least able to think about it clearly. If you would not have taken the trade with the wider stop — and you would not have, because the wider stop implies a smaller position and a worse reward-to-risk — then widening it mid-trade is a new trade you never analysed.
Treating correlated positions as independent
Five 1% positions in five different assets that all move together is not five 1% risks. It is one 5% risk wearing a disguise. The formula sizes one position at a time and has no idea the others exist; the correlation check is yours to do.
Choosing a risk percentage that only survives a good run
The percentage is a policy choice, so choose it against a losing streak rather than a winning one.
Risking a fixed percentage of current equity, the account after n consecutive losses is the
starting equity times (1 − riskPercent/100)ⁿ:
| Risk per trade | After 5 losses | After 10 losses | After 20 losses |
|---|---|---|---|
| 1% | −4.9% | −9.6% | −18.2% |
| 2% | −9.6% | −18.3% | −33.2% |
| 5% | −22.6% | −40.1% | −64.2% |
Ten losses in a row is not exotic. A strategy that wins half its trades produces a run that long sooner or later, given enough trades, and it will do so at the worst possible moment for your confidence rather than a convenient one. Note also that drawdowns are asymmetric: recovering from −20% needs +25%, and recovering from −50% needs +100%. The maths punishes the deep hole far more than it rewards the deep run.
This is arithmetic about a hypothetical sequence of losses. It is not a prediction, and no risk percentage makes a losing strategy profitable — it only decides how long the account survives while you find out which kind you have.
What the formula does not model
Being explicit about this matters more than the formula itself.
- Slippage. The fill you get is not the price you clicked, especially on a stop order in a fast market. The model assumes both fills land exactly on the quoted prices.
- Gaps. A stop is an instruction to sell at market once a level trades, not a guarantee of that level. A weekend gap or a liquidation cascade can fill you far past it.
- Partial fills and scaling. One entry, one exit, one price each.
- Funding. A perpetual position held across funding intervals pays or receives funding, which the sizing model ignores entirely. That belongs in the profit-and-loss calculation instead — see a profit-and-loss calculation that starts once the position is open.
- Maker versus taker fees. One rate, applied to both fills. If you enter with a resting order and exit with a stop, you are paying two different rates.
Every one of these pushes the real loss in the same direction: worse than modelled. Treat the computed worst case as a floor, not a ceiling.
This is educational material, not financial advice, and nothing here is a recommendation to take any position. Trading leveraged products can cost you more than you put in.