ATR position sizing: risk per trade, the stop multiple, and the size it implies

Position sizing is the part of a trading decision that is arithmetic rather than opinion. Four numbers produce one instruction: how much of the account is at risk on the trade, how far away the stop sits, how large the position therefore is, and what that position costs if the stop is reached. None of the four requires a view about where the price is going. All four can be written down before the order is placed, and checked afterwards by anyone holding a calculator.

The stop distance is where the Average True Range enters. A stop placed at a fixed number of currency units is a different risk in a quiet instrument from the same stop in a volatile one; a stop placed at a fixed multiple of ATR is the same multiple of the same measure in both. That is the whole argument for using ATR, and it is a modest argument. ATR converts a stop from a price into a unit of recent movement. It does not tell you which way the price will go, how likely the stop is to be reached, or whether the trade is worth taking.

What follows is the arithmetic on one position, worked to the cent: an account, a risk percentage, a fourteen-bar ATR and a two-ATR stop, producing a share count, a notional and a cost per stop-out. Then the same arithmetic under a moving ATR, where the interesting number is not the size but the size you would have held if you had not looked.

What ATR measures, and what it does not

The Average True Range is a smoothed average of the true range, and the true range is the largest of three distances on each bar: the high minus the low, the high minus the previous close, and the previous close minus the low. The second and third matter on gaps. A bar that opens below yesterday’s close and never trades above the previous close has a true range larger than its own high-to-low span, and a measure built on high minus low alone would understate the move.

Two conventions then produce the average. The simple version takes the mean of the last n true ranges. Wilder’s version, which is what most platforms call ATR, seeds with that mean and then recurses: each new value is (13 × the previous ATR + today’s true range) ÷ 14 at the default length of fourteen. The recursion gives every past true range a weight that decays geometrically, with the weight falling to half after 9.35 bars at that length — the half-life of (13/14)ⁿ. A fourteen-bar simple mean instead drops the fifteenth observation entirely and weights the rest equally. The two will not agree, and the difference is a choice rather than an error. Whichever is used, the interval and the convention belong in the note: a daily two-ATR stop and an hourly two-ATR stop are different distances, and a Wilder ATR and a simple ATR of the same length are different numbers.

The measure is a summary of dispersion over a window. It says nothing about direction, nothing about the shape of the distribution inside the window, and nothing about what happens after it. A market that trended 3 per cent in one direction every day for fourteen days has a large ATR and no two-way movement at all; a market that oscillated in a tight band for a month has a small one. A stop sized off ATR is a stop sized off recent movement, and the assumption underneath it — that the next few bars resemble the last fourteen — is an assumption, not a measurement.

The four numbers, in order

The sequence is fixed because each figure feeds the next, and computing them out of order is how a sizing sheet ends up with a size that does not match its stated risk.

Risk per trade, in the reporting currency. Account equity × the risk fraction. A half a per cent of a $100,000 account is $500. This is a policy number, and it should be written down as one: not “small”, not “conservative”, but 0.50 per cent.

Stop distance, in price. ATR × the multiple. At an ATR of 2.40 and a multiple of two, the stop sits 4.80 below the entry.

Size. Risk per trade ÷ stop distance. $500 ÷ 4.80 is 104.17 shares, and the fraction is the part most sheets get wrong: the size is a division, so a wider stop always produces a smaller position for the same risk.

The rounded size, and the residue. Whole shares, contracts or lots, and the difference between the risk the rounded size carries and the risk intended. 104 shares at 4.80 is $499.20, which is $0.80 — 0.16 per cent — under the stated risk. That residue is harmless at this size and becomes material when the instrument is expensive: a position of nine shares where the division said 9.4 can carry 4 per cent less risk than intended, and it should be reported rather than absorbed.

Table 1 sets the four out on one position, with the checks a reader can run in one pass.

Table 1. The sizing arithmetic for one illustrative long position: equity, risk fraction, ATR, multiple and entry, and every figure derived from them. Source: constructed for this piece; the account, the instrument and the series are illustrative and describe no market.

The last row is the identity that makes the whole table usable without a share count. Position size as a percentage of equity is the risk percentage divided by the stop distance expressed as a percentage of price: 0.50 ÷ 4.80 gives 10.42 per cent, which is the $10,400 notional against the $100,000 account. Any sizing sheet whose notional and whose stated risk fail that division has a number in a label that is not in the computation. It is the fastest check available, and it catches the commonest error in the family: a size computed on risk and then adjusted upwards for conviction.

The multiple is a choice; the size is an output

The stop multiple is the one free parameter in the chain, and it is a decision about tolerance rather than a measurement. A one-ATR stop is inside the range of an ordinary bar; a three-ATR stop is outside it. Neither is correct, and the arithmetic does not choose. What the arithmetic does is price the choice, because the multiple fixes the distance and the distance fixes the size.

Table 2. The same $500 risk and the same ATR of 2.40 at five stop multiples: distance, raw size, traded size, risk realised after rounding, notional, and notional as a percentage of the $100,000 account. Source: computed from Table 1.

Three readings of that table are worth stating plainly.

The risk column is flat within 0.5 per cent across all five rows, which is the point of the method: the stop moves, the size absorbs the move, and the risk stays where the policy put it. A trader who holds the size at 104 shares and varies the multiple is not sizing: at a 1.0 ATR stop those shares risk $249.60, and at a 3.0 ATR stop $748.80 — a threefold range in the loss on the same position, against the same stated $500.

The notional column is not flat, and it is the column that decides how much of the account is exposed to a gap. At a one-ATR stop the position is 20.8 per cent of equity; at three ATRs it is 6.9 per cent. Both carry $500 of stated risk, and they do not carry the same exposure: the tight-stop position is three times larger, and a gap through a tight stop is a larger loss in currency than the same gap through a wide one. Sizing to risk controls the scheduled loss and leaves the unscheduled one to the notional.

The rounding column shows why a share-based instrument cannot deliver the risk exactly. Across the five rows the realised risk runs from $496.80 to $499.20 — a 0.5 per cent spread around a $500 target, purely from rounding down. On a $40 instrument with 25 shares the same procedure would miss by several per cent in one direction, and the sheet should say so instead of printing $500.

What the stop costs when volatility moves

Volatility is not a constant, and the interesting property of ATR sizing is what it does when the measure moves. Table 3 holds the account, the risk and the multiple fixed and moves the ATR through a factor of four, first recomputing the size as the method requires, then showing the risk carried by an unchanged position of 104 shares.

Table 3. The same 2.0 ATR stop and $500 risk at six levels of ATR. The left group recomputes size; the right group holds the 104 shares from Table 1 and reports the risk that position carries. Source: computed from Table 1.

A volatility doubling from 2.40 to 4.80 halves the size, from 104 shares to 52, and halves the notional with it. The stated risk does not move. That is the method working as designed, and it has a cost that is easy to state and easy to miss: the position that the method allows in a quiet market is four times the position it allows in a violent one, so a strategy’s returns are concentrated in the calm periods by construction. Whether that is desirable is a question about the strategy, not about the arithmetic.

The right-hand columns are the more useful half. A position of 104 shares sized when ATR was 2.40 carries $748.80 of risk when ATR reaches 3.60 — 49.76 per cent more than the policy permits — and $998.40 at an ATR of 4.80, which is 1.9968 times the stated risk. Nothing about the position changed. The stop did not move, the entry did not move; the market’s ordinary daily range doubled, and a stop two such ranges away is now twice as far in currency as it was when it was placed. This is the mechanism behind the sentence every risk note contains and most sizing sheets ignore: the loss you take is not the loss you sized for unless the stop is re-derived when the measure moves.

There are three ways to handle it, and each has a price. Re-size when ATR moves: the position shrinks as volatility rises, which locks in the risk and forces a sale into a wider market. Widen the stop and keep the size: the risk grows by the ratio of the new ATR to the old, which is the column above. Keep the stop and the size and accept the drift: the position carries whatever the market’s dispersion implies, and the risk figure in the note is a historical statement rather than a current one. The choice belongs in the policy, in writing, because the default — doing nothing and reading the same risk number — is the third option taken silently.

The stop is an instruction, not a price

Every figure above treats the stop as an execution price. It is not. A stop is an instruction to send a market order once a level trades, and the fill is whatever the book offers when the order arrives. In a liquid instrument during continuous trading the difference is a tick or two. Overnight, at a halt, or in the first minutes after a release, it can be the whole move.

Take the Table 1 position: 104 shares, entry 100.00, stop 95.20, intended loss $499.20. If the instrument opens at 92.10 — a gap of 3.10 through the stop, which is 1.29 ATRs at the ATR of 2.40 — the filled loss is 104 × 7.90 = $821.60, which is 1.6432 times the intended risk, or 64.32 per cent more. An opening print at 90.00 gives $1,040, or 2.08 times. Each ATR of gap through the stop adds 104 × 2.40 = $249.60, so a gap the size of the whole stop distance doubles the loss before any slippage is counted.

This is the part of the arithmetic that a tight stop makes worse, not better. The tighter the stop, the larger the position for a given risk, and the larger the position, the more each unit of gap costs. A one-ATR stop produces a position twice the size of a two-ATR stop for the same $500, so an overnight gap of one ATR through either stop costs twice as much in the first case. The multiple is not a dial that reduces risk; it moves risk between the scheduled column and the unscheduled one.

Two further limits belong in the same note. A stop does not bound the loss for a position that cannot be exited — a halted instrument, a limit-down session, a contract at expiry. And the arithmetic above assumes one position; ten positions each sized at 0.50 per cent carry 5 per cent of the account at risk if they are unrelated, and considerably more if they are the same factor bought ten ways. Per-trade risk is a number about one line, and the number that matters at the portfolio level is a correlation-weighted sum that this sheet does not compute.

What the arithmetic cannot do

The method produces a size. It does not produce a reason, and the honest statement of its limits is longer than the method itself.

ATR is backward-looking by construction, and the sizing assumes the next bars resemble the window. When a regime changes — a quiet instrument becoming volatile, a news cycle arriving, a session’s liquidity thinning — the ATR that produced the size lags the change, which is exactly when the size is most wrong.

The multiple carries no probability. A stop at two ATRs is not a 95 per cent stop, or any other percentage; the frequency with which a price travels two ATRs against a position is a property of the distribution, and the distribution is precisely what the fourteen-bar average does not measure. Sizing does not reduce the number of losses, the size of a losing run, or the chance that the first four trades are all stopped; it makes each of those losses the same size, which is a different and smaller claim. Twenty consecutive full losses at 0.50 per cent apiece is a 10.00 per cent linear drawdown, and 9.54 per cent compounded — $90,461.05 on this account — and no sizing rule changes whether twenty are possible, only what each one costs.

Finally, the arithmetic is silent on whether the trade should exist. A position sized at exactly the policy risk is a well-formed position and may still be a bad one. Nothing in the four numbers tests the reason for the entry, and a sizing sheet that leads with the size invites the reader to skip that question.

What a sizing sheet costs

Two engine calls produce the numbers: indicator, for the true range and the ATR with its convention and interval stated, and verify, to cross-check the price the sheet uses against a second observation within 0.1 per cent — a stale price moves the stop distance, and the stop distance is the divisor. At the published $0.006125 on Base that is $0.012250, a figure that is published rather than measured while the analyst services are pending review.

Three model calls draft the sheet at DeepSeek’s measured $0.00700: one to state the policy and the assumptions, one to assemble the table, one to write the paragraph that says what the stop would cost on a gap. That is $0.021000, so one sizing sheet is $0.033250.

Twelve a month, on a book of positions, is 24 engine calls ($0.147000) and 36 model calls ($0.252000): $0.399000, or $0.033250 a sheet and $4.79 over twelve months. At the metered ceiling of $0.00955 the model line rises to $0.343800 and the month to $0.490800, 23 per cent more; on Qwen at a flat $0.00875 the model line is $0.315000 and the month $0.462000, 15.8 per cent more. The 0.50 USDC opening balance is seventy-one calls at $0.00700 and a sheet is five paid calls, so the balance holds fourteen sheets. The document parts that render the sheet carry no published per-call price and sit outside every total here.

A decision rule

One instruction comes out of all of this, and it is about what gets written down before the order rather than about the order.

Publish five numbers per position, in this order: the risk in the reporting currency and the fraction of equity it represents; the ATR, with its length, interval and convention; the stop distance in ATR multiples and in price, with the stop price; the size after rounding, and the residue against the intended risk; and the notional as a percentage of equity. Those five make the position checkable by a second person in under a minute, because the risk percentage divided by the stop percentage must equal the notional percentage.

Then publish the two numbers the trade will actually produce. The loss if the stop fills at the stop, and the loss if it fills one ATR worse. The first is the plan; the second is what the plan costs when the market does not cooperate, and it is the number that decides whether the notional is acceptable — not the first.

Then re-derive when ATR moves by more than a stated amount. A table like Table 3 is the argument: the same 104 shares carried $499.20 of risk at an ATR of 2.40 and $748.80 at an ATR of 3.60. A policy that does not name the threshold at which the position is re-sized has not decided this question, and the default answer is the wrong column.

What the rule does not contain is a view on direction, a probability that the stop is reached, or a claim that a sized position is a good one. It contains four numbers and the sentence that says what they leave out. For a sheet that will be read at the moment of a decision, that is the right length.

Method note

The account, the ATR, the entry price and every series behind Table 3 are constructed for this piece and labelled illustrative; they describe no instrument and no market observation. The arithmetic is stated so that it can be reproduced: stop distance = ATR × multiple = 2.40 × 2.0 = 4.80; size = 500.00 ÷ 4.80 = 104.1667, traded at 104 whole units; risk at 104 = 104 × 4.80 = $499.20; notional = $10,400.00, which is 10.40 per cent of $100,000 and equals the risk fraction divided by the stop fraction, 0.50 ÷ 4.80 = 10.4167 per cent before rounding. The gap figures are 104 × (100.00 − open) for opens of 95.20, 92.10 and 90.00; the drawdown figures are 20 × $500 = $10,000 linear and $100,000 × 0.995²⁰ = $90,461.05 compounded. Wilder’s recursion weight is 13/14 at the default length and its half-life is ln 0.5 ÷ ln (13/14) = 9.35 bars. Engine prices are the published $0.006125 per basic operation on Base from catalog.json, read 31 October 2026; the analyst services are pending review and return no 402 quote, so that price is published rather than measured. Model prices are measured from the live 402 handshake’s exact amount on Base on 31 October 2026 at a short prompt and max_tokens: 1000: $0.00700 for deepseek-v4-flash, $0.00955 at about 3,000 tokens, and $0.00875 for qwen3.8-flash at both lengths. Monthly counts are planning assumptions. Nothing here is a forecast of price, a statement about the probability of any level being reached, a claim that any method produces a return, or investment advice.

The pillar is Finance and markets on x402 — three engines, four jobs, one price. The role that produces a sizing sheet is trade_analyst, which measures a supplied series into indicators, a composite signal and a level at which the view fails, and which will not produce a forward-looking return or call a rule profitable. The compute is bought at x402.press/services/deepseek/ with a second model at x402.press/services/qwen/; the measured handshake is reviewed at DeepSeek: per-call chat completions over x402, and the two endpoints against each other at Inference endpoints compared. A sizing sheet is one half of an exposure decision; the other half is the arithmetic in FX exposure for importers, where the position is a payable and the hedge ratio is the size. And the number a stop is really made of — the break-even the position has to clear — is set out in Breakeven inflation explained, which is the same subtraction applied to a different pair of prices.

x402.review is written and edited by N.P. Vincent. The publication is connected to x402.press, which sells the services reviewed here; that interest is disclosed on every piece that touches a service, and it is stated here rather than left to inference.

Filed under Jobs · Tags: position-sizing, atr, risk, trading