How position size follows from stop distance

The three numbers the calculation needs 

Size is the one term in a trade that is settled before the market has any say in it. Where price goes next is not chosen by the trader, whether a stop is reached is not chosen by the trader, and what the spread happens to be at that moment is not chosen by the trader. The number of lots, contracts or shares written on the ticket is chosen in full and in advance, and it is the only term of which that is true. The calculation below turns the two figures the previous lessons produced into that number.

• The risk amount. The money the position is intended to cost if the stop is reached, stated in the currency the account is denominated in. The previous lesson described where this figure comes from, and why no fraction of equity is put forward here as the correct one.
• The stop distance. How far the stop level sits from the entry, in whatever unit the instrument moves in: pips for a currency pair, dollars per ounce for a metal, points for an index, quote currency per share for a shares CFD. Where on the chart that level sits is a separate question, and a later lesson in this module treats it.
• The value of one unit of that distance, per unit of size. What one pip is worth per lot, what a one dollar move is worth per gold lot, what one index point is worth per contract. The orders module worked this figure out for each of those cases, and it is taken as given here.

Multiplying the second figure by the third produces an intermediate number worth naming, because the whole calculation turns on it: the cost of reaching the stop on one unit of size. One lot, one contract, one share. It is a money amount, it is fixed the moment the stop distance is fixed, and it knows nothing about how large the position will be. Once it exists, the rest is a single division.

The division that produces the size 

1. The stop distance is multiplied by the value of one unit of that distance, giving the cost of reaching the stop on one unit of size.
2. The risk amount is divided by that cost, giving a size in whatever unit the instrument is dealt in.
3. The result is rounded to a size the instrument actually permits, because lots, contracts and shares are dealt in stated increments rather than continuously.
4. The rounded size is multiplied back by the cost per unit, which restates what reaching the stop now costs and shows whether the rounding moved that figure above or below the risk amount.

The fourth step is the one most often skipped, and the one that keeps the arithmetic honest. A division rarely lands on a permitted increment, so the size dealt is almost never the size the formula produced. Rounding down leaves the realised cost below the amount intended. Rounding up leaves it above, and on a coarse increment that overshoot is not always small. Multiplying back converts an assumption about it into a number.

The calculation in a currency pair 

A currency pair is the simplest case because the third input is the one the orders module spent a whole lesson on. Pip value per lot is already a money amount in the account currency, so the two multiplications collapse into one and the division follows immediately.

The last two rows are the point of the block rather than a flourish. Reaching the stop and moving the same distance the other way produce the same magnitude with the opposite sign, because the size term is common to both. Sizing sets the scale of every outcome at once. It does not set the loss and leave the gain alone, and no arrangement of the arithmetic can make it do so.

The same division in gold 

Gold is quoted per troy ounce and moves in cents rather than pips, and the contract covers a number of ounces rather than a number of currency units. That changes the name of the middle term and nothing else. The distance is stated in dollars per ounce, the value of one dollar of movement per lot follows from the contract size, and the division is unchanged.

Half a lot is a real answer, not a rounding failure, and this is where an instrument's minimum increment starts to bind. A contract dealt in hundredths of a lot absorbs the result exactly. A contract dealt in whole lots cannot, and the risk amount then has no size that expresses it: the nearest permitted sizes sit either side of the intended cost, and one of them is above it.

The same division on an index 

An index contract states an amount of money per index point, so the first multiplication has already been performed by whoever wrote the contract. The distance is a count of points, the value per point is read from the specification, and the division produces a number of contracts. Index contracts are frequently dealt in whole numbers, so this is where the rounding step does visible work.

Neither rounded figure equals the risk amount, and no care in the earlier steps makes them equal. That is the ordinary condition of the calculation rather than a defect in it. The rounding step makes the discrepancy a known number instead of an unexamined one, and on a coarse increment the gap between the nearest permitted size below and the nearest above is a substantial fraction of the risk amount itself.

The same division in a shares CFD 

A shares CFD is conventionally written on a stated number of shares, and the smallest increment of the quote is an increment of the share price itself. The value of one unit of distance per share is therefore one unit of the quote currency, which makes this the most transparent case of all: the cost of reaching the stop on one share is the stop distance, and nothing else.

The contract value row is included because it is the figure the risk calculation says nothing about. A stop distance of a few per cent of the share price produces a contract value many times the risk amount, and it is the contract value that the margin requirement is assessed against. A size that satisfies the risk calculation is therefore not automatically a size the account can support: margin is a separate constraint, computed on the contract value rather than on the stop, and where the two give different answers the smaller size binds.

Why a wider stop produces a smaller position 

The stop distance sits in the denominator, so size moves inversely with it: doubling the distance halves the size, quartering it quadruples the size. This is the relationship that most often runs the wrong way round in practice, because a wide stop feels cautious and a tight stop feels aggressive, whereas in the arithmetic the width of the stop is not a measure of caution at all. Caution lives in the risk amount. The stop distance only decides how that fixed amount is divided up.

Read across the four sizes and the last two rows do not move. That invariance is the purpose of the calculation. A stop placed where the chart suggests rather than where the arithmetic would prefer costs the same as any other stop, because the size absorbs the difference. It also means size is not a statement of conviction. It is a consequence of a distance, and a trade with a tight stop is not a larger commitment than one with a wide stop, however different the two tickets look.

What the arithmetic does not settle 

The calculation produces an intended cost, not a guaranteed one, and the gap between those two words is where most of the trouble in this topic lives. A stop is an instruction to close a position once price reaches a specified level. It is not a guarantee of the level at which the closing trade is done. In fast markets, on a gap, or where a session opens away from where it closed, a position can close materially worse than the level specified, and the realised cost is then larger than the risk amount by however far the fill sat from the stop. A later lesson in this module deals with the standard and guaranteed varieties of the order.

Three further limits are worth stating plainly. The third input is not always stable: pip value in an account whose currency differs from the quote currency depends on a conversion rate that moves while the position is open, so a cost calculated at the outset is an estimate rather than a fixed term. The calculation is also silent about the other positions an account holds, and several positions each sized to the same risk amount can be exposed to the same underlying move, which is the subject of a later lesson. And it says nothing about how often a stop is reached, which is not something the arithmetic can know and not something this page puts a figure on.

Why the calculation comes before the order 

An order ticket asks for a size. It does not ask for a risk amount, it does not ask for a stop distance, and it does not compute the relationship between them. Nothing in the mechanics of placing an order requires the calculation to have happened, which is precisely why the order in which the two are done is the whole matter.

Performed first, the calculation has three inputs and one unknown, and it resolves. Performed after a size has been dealt, the size is no longer unknown and the only free term left is the stop distance. The arithmetic then runs backwards and yields a stop distance that makes the existing size cost the intended amount, which is a level selected by division rather than by anything on the chart. The same equation is solved either way. What differs is which term is allowed to dictate the others, and a stop derived from a size chosen by feel is a stop placed wherever that feeling landed. Tools for the arithmetic itself sit on the cost calculator, though the ordering problem is procedural and no tool addresses it.

A second reason is less obvious. Once a position is open its value changes continuously, and arithmetic performed while watching a number move is arithmetic performed under conditions nobody would choose for accuracy. All three inputs are knowable before anything is dealt. Writing them down before the ticket is opened removes the calculation from the moment when it is hardest to do, and the last lesson in this module deals with the behavioural failures that make that moment as unreliable as it is.

Where practitioners disagree 

The formula itself is not controversial. Four things around it are, and a reader will meet all four. The first is whether size follows the stop at all. The tradition described here fixes the risk amount and lets size vary; an older convention fixes the size and lets the risk vary, on the grounds that a constant size makes trades comparable and keeps dealing simple where increments are too coarse for a fine answer. The objection is direct: with size constant, the cost of reaching the stop varies with the stop distance, and stop distances vary with conditions, so the risk carried is set by whatever the market happens to be doing rather than by any decision.

The second is what the risk amount is a fraction of. Recalculating it from current equity before every trade makes the money amount shrink after losses and grow after gains, which is arithmetically consistent but means the size of a trade depends on the results of trades that have nothing to do with it. Holding a fixed money amount instead keeps sizing stable and independent, at the cost of that amount drifting as a proportion of the account, upward exactly when the account is smaller. Both conventions are widely used and neither removes the risk of loss.

The third is whether costs belong inside the risk amount. One convention deducts spread and commission from the risk amount before the division, leaving the arithmetic to size the price movement alone; another treats the risk amount as a price risk budget and accounts for costs separately, on the grounds that mixing the two makes neither figure readable. The fourth is the rounding rule. Rounding down is the more commonly stated convention because it errs below the intended cost, but it is not universal, and on a coarse increment it can produce a size at which the fixed costs of dealing are large relative to what is being risked. None of the four is settled, and a document presenting any of them without its objection is presenting a preference as a finding.