Position Sizing Formula: Worked Examples and Drawdown Odds
How to turn money at risk and a stop distance into a position size, with forex examples that match AlphaScala's calculators plus share and futures examples. A 10,000-sequence simulation shows how often each risk-per-trade level reaches a 20% or 50% drawdown.
The position sizing formula is: position size = money at risk ÷ (stop distance × value of one unit of that distance). Money at risk is your balance times the percentage you accept losing. Forex traders convert the result into lots through pip value; stock and futures traders get shares or contracts directly. Round down, never up.
The same four steps size any instrument, and AlphaScala's position size calculator runs them for currency pairs:
- Set the money at risk by multiplying the balance by the risk percentage. A $10,000 account at 1%, the calculator's default, has $100 at risk.
- Measure the stop distance in the instrument's own unit: pips for currency pairs, price points for shares and futures.
- Price one unit of that distance in your account currency. In forex that is pip value per unit; for shares and futures it is the dollar value of one point, which is $1 per share or the exchange-set value per contract.
- Divide the money at risk by stop distance × unit value, then round down to a size your broker accepts.
A volatility-based stop, such as a multiple of average true range, changes only step 2. A wider stop gives a smaller position for the same money at risk.
Every account and trade in the examples below is hypothetical, and the arithmetic is not a trade idea or personalized advice. Leveraged products can lose money fast: the risk disclosure US futures brokers must hand customers under CFTC rule 17 CFR 1.55 warns that you "may sustain a total loss of the funds that you deposit" and "may incur losses beyond these amounts."
Forex position size: from pip value to lots
AlphaScala's position size calculator and pip value calculator share one convention. A pip is 0.0001 on most pairs and 0.01 on pairs quoted in Japanese yen, and pip value is converted from the quote currency into the account currency through the US dollar.
money_at_risk = balance × risk% ÷ 100
pip_value_per_unit = pip_size × (quote currency → account currency rate)
units = money_at_risk ÷ (stop_pips × pip_value_per_unit)
lots = units ÷ 100,000 (standard), 10,000 (mini) or 1,000 (micro)
EUR/USD on a dollar account
These are the calculator's default inputs: a $10,000 balance, 1% risk, EUR/USD and a 30-pip stop.
- Money at risk is $10,000 × 1% = $100.
- Pip value per unit is $0.0001. The quote currency is the account currency, so no conversion is needed.
- Loss per unit at the stop is 30 × $0.0001 = $0.003.
- The position is $100 ÷ $0.003 = 33,333 units, which is 0.3333 standard lots or 33.33 micro lots, with a pip value of $3.33 at that size.
If your broker takes lots in steps of 0.01, round down to 0.33 lots (33,000 units) and the loss at the stop becomes $99.00. Rounding up to 0.34 lots would put $102 at risk and break the 1% limit.
USD/JPY on a euro account
A yen pair on a euro account needs a two-step currency conversion, from yen to dollars and from dollars to euros. Take a €5,000 balance, 1% risk (€50), USD/JPY and a 40-pip stop.
- Pip size is 0.01 because the quote currency is yen, so one pip on one unit is ¥0.01.
- At the rates in AlphaScala's price table at 09:00 UTC on October 22, 2026 (USD/JPY 157.044 and EUR/USD 1.12345, sourced from TwelveData), ¥0.01 is worth €0.00005668. One standard lot moves ¥1,000 per pip, or €5.67.
- Loss per unit at the stop is 40 × €0.00005668 = €0.0022672.
- The position is €50 ÷ €0.0022672 = 22,053 units, or 0.2205 standard lots. Rounded down to 0.22 lots, the loss at the stop is €49.88.
The euro figures move with the exchange rate. The calculator recomputes them from the latest snapshot in AlphaScala's price table, which a scheduled job refreshes every three hours.
Why margin is a different number from risk
The 0.33-lot EUR/USD position controls €33,000, about $37,074 at the 09:00 UTC rate of 1.12345. At 1:30 leverage, the default in AlphaScala's forex margin calculator, the broker holds about $1,236 as margin. The loss at the stop is still $99.
Leverage decides how much cash the broker ties up, while the stop and the size decide what you lose. In July 2019 the UK's Financial Conduct Authority said firms selling CFDs to retail clients would be required to limit leverage to between 30:1 and 2:1.
Shares and futures contracts from the same formula
Stock position size in shares
For shares, each dollar of stop distance costs $1 per share held, so the formula shortens to money at risk ÷ (entry − stop).
Take a $25,000 account risking 1%, which puts $250 at risk. With an entry at $48.20 and a stop at $46.90, the risk per share is $1.30, so the position is 192 shares (192.3 rounded down). The loss at the stop is $249.60, and the position is worth $9,254, or 37% of the account.
Position value is an output of the formula, not an input.
A tighter stop on the same stock would produce more shares and a larger position value with the same $250 at risk. The same arithmetic sizes a spot crypto position in coins.
When a stop fills below the stop price
The formula sizes the planned loss; it cannot cap a gap. The SEC's Understanding Order Types investor bulletin says that when the stop price is reached, "a stop order becomes a market order," and the execution price "can deviate significantly from the stop price due to the demand for a stock and the prices of available liquidity."
If the stock in the example opened at $44.00 after overnight news, the 192 shares would lose $806.40, which is 3.2% of the account rather than 1%. A stop-limit order avoids an unexpected fill price, but the same bulletin says the limit price "may prevent the order from being executed."
Futures position size in contracts
Futures contracts replace pip value with the exchange's dollar value per point:
contracts = money_at_risk ÷ (stop_in_points × dollars_per_point)
CME's rules for the Micro E-mini S&P 500 future (MES) value each contract at $5 times the S&P 500 index, with a minimum move of 0.25 index points "equal to $1.25 per contract" (CME submission 19-140 to the CFTC, April 2019). The same filing sets an offset ratio of 10 MES contracts to one E-mini S&P 500 (ES) contract, and CME's rule for options on one ES future says "each Index point shall represent $50.00 per option contract" (CME filing to the CFTC, April 2022). Ten micros to one ES puts ES at $50 per point.
Take a $50,000 account risking 1% ($500) with a 12-point stop:
| Contract | Dollars per point | Loss per contract at 12 points | Contracts for $500 at risk | Loss at the stop |
|---|---|---|---|---|
| MES | $5 | $60 (48 ticks × $1.25) | 8 (8.33 rounded down) | $480 |
| ES | $50 | $600 | 0 (0.83 rounded down) | No trade at 1% |
One ES contract on that stop would put $600, or 1.2% of the account, at risk. The arithmetic leaves two ways to keep the 1% limit: trade the micro contract, or pass on the trade.
How often 0.5%, 1%, 2% and 5% risk per trade reach a 20% or 50% drawdown
The formula fixes the loss on one trade. A run of trades is a different question, so on October 22, 2026 AlphaScala simulated 10,000 sequences of 200 trades at each risk level. For background on picking the percentage itself, see how much capital to risk per trade.
How the 10,000-sequence simulation works
- Two hypothetical systems share a 1.5:1 reward:risk ratio. System A wins 50% of trades, an expectancy of +0.25R per trade, where R is the amount risked. System B wins 40%, exactly the break-even win rate at 1.5:1, so its expectancy is zero before costs.
- Each trade risks a fixed percentage of current equity, the way the calculator sizes off whatever balance you enter. A win adds 1.5 times the amount risked and a loss removes exactly the amount risked.
- There are no spreads, commissions, slippage or gaps in the model, and trades are independent of each other. Costs and gaps would push every drawdown figure higher, and several correlated open positions behave like one larger position.
- Maximum drawdown is the largest peak-to-trough fall in equity across the 200 trades. The same 10,000 win/loss sequences are reused at every risk level, so the rows differ only by position size. The code ran in Python with NumPy 2.2.6 (seed 20261022), and a rerun with a different seed moved no probability by more than 1.1 percentage points.
System A: 50% win rate at 1.5:1
| Risk per trade | Drawdown of 10%+ | Drawdown of 20%+ | Drawdown of 50%+ | Median worst drawdown |
|---|---|---|---|---|
| 0.5% | 0.9% | 0 of 10,000 | 0 of 10,000 | 4.4% |
| 1% | 35.1% | 0.6% | 0 of 10,000 | 8.7% |
| 2% | 97.2% | 29.7% | 0 of 10,000 | 16.9% |
| 5% | 100% | 99.8% | 15.7% | 38.7% |
| 8.3% (half Kelly) | 100% | 100% | 74.0% | 57.7% |
| 16.7% (full Kelly) | 100% | 100% | 99.98% | 86.5% |
Moving from 1% to 2% risk raised System A's chance of a 20% drawdown from 0.6% to 29.7%, about 50 times higher, even though the system makes money on average.
System B: 40% win rate at 1.5:1, no edge
| Risk per trade | Drawdown of 10%+ | Drawdown of 20%+ | Drawdown of 50%+ | Median worst drawdown |
|---|---|---|---|---|
| 0.5% | 40.6% | 1.7% | 0 of 10,000 | 9.0% |
| 1% | 93.0% | 37.0% | 0 of 10,000 | 17.5% |
| 2% | 99.99% | 91.5% | 9.9% | 32.9% |
| 5% | 100% | 100% | 84.6% | 66.7% |
Without an edge, a bigger size did not improve the typical result. System B's median ending balance fell from 99.6% of the starting balance at 0.5% risk to 69.1% at 5%, and the share of sequences that finished below the start rose from 52.3% to 63.5%.
Those figures can be checked without a simulation. The median sequence wins 80 of its 200 trades, the expected count at a 40% win rate, and at a fixed dollar risk 80 wins of 1.5R and 120 losses of 1R net exactly zero. Sized at 5% of current equity, the same 80 gains of 7.5% and 120 losses of 5% compound to 1.075^80 × 0.95^120 = 69.1% of the start. Exact binomial odds of finishing below the start are 53.1% at 0.5% risk and 64.2% at 5% risk, within 0.8 percentage points of the simulated shares.
Prop-firm rules change the question, and the FTMO risk-per-trade simulation looks at that case.
Losing streaks behind those drawdowns
When each trade risks a fixed percentage of current equity, the number of straight losses needed to reach a given drawdown is fixed arithmetic:
| Risk per trade | Losses in a row to a 20% drawdown | Losses in a row to a 50% drawdown |
|---|---|---|
| 0.5% | 45 | 139 |
| 1% | 23 | 69 |
| 2% | 12 | 35 |
| 5% | 5 | 14 |
Long losing runs are common over 200 trades. The exact probabilities below come from a Markov chain over the current run length, not from the simulation:
| At least one losing run of | 50% win rate | 40% win rate |
|---|---|---|
| 5 trades | 96.6% | 99.95% |
| 8 trades | 32.0% | 75.0% |
| 10 trades | 9.0% | 38.0% |
| 12 trades | 2.3% | 15.4% |
Ten straight losses in one particular ten-trade window have a 0.1% chance at a 50% win rate (0.5 to the 10th power). Over 200 trades, the chance of at least one 10-loss run is 9.0%, about 90 times higher. At 5% risk, five straight losses cost 22.6% of the account, and a system that wins half its trades has a 96.6% chance of at least one such run in 200 trades.
Kelly criterion and what full Kelly does to drawdowns
J. L. Kelly Jr. described the bet size that maximizes the long-run growth rate of capital in "A New Interpretation of Information Rate" (Bell System Technical Journal, July 1956). For a trade that wins R times the amount risked with probability W, and loses the amount risked otherwise, maximizing that growth rate gives:
kelly_fraction = W − (1 − W) ÷ R
For System A that is 0.5 − 0.5 ÷ 1.5 = 16.7% of equity per trade, and a numerical search over the expected log-growth function returned the same 0.1667. For System B the fraction is zero: with no edge, Kelly sizes the trade at nothing.
Full Kelly hit a 50% drawdown in 99.98% of System A's sequences, with a median worst drawdown of 86.5%. Half Kelly still reached 50% in 74.0% of them. Both rows assume the win rate and payoff are known exactly, and the fraction rises with both inputs. If System A's true win rate were 45% rather than 50%, its Kelly fraction would be 8.3%, so sizing at the computed 16.7% would be double the true Kelly. A typical sequence at that true win rate, 90 wins in 200 trades, ends at 2.80 times its starting balance at 8.3% risk and at 1.03 times at 16.7%. How to calculate win rate covers how many trades it takes before an observed win rate can be told apart from break-even.
FAQ
What is the formula for position size?
Position size = money at risk ÷ (stop distance × value of one unit of that distance), where money at risk is balance × risk percentage. In forex the unit value is pip value per unit of the base currency. For shares and futures it is the dollar value of one point: $1 per share, or the contract's dollars per point. Round the result down.
How many lots is 1% risk on a $10,000 account?
On EUR/USD with a USD account, 1% is $100, so a 30-pip stop gives 0.33 standard lots and a 20-pip stop gives 0.5 lots. On USD/JPY the answer also moves with the USD/JPY rate, because a pip on one standard lot is worth ¥1,000 rather than a fixed $10. At 157.044, the 09:00 UTC rate on October 22, 2026, that pip was worth $6.37, so a 30-pip stop gave 0.52 lots.
Is 2% risk per trade too much?
The simulation answers with probabilities rather than a yes or no. For a system winning 50% of trades at 1.5:1, 2% risk produced a 20% drawdown in 29.7% of 200-trade sequences, against 0.6% at 1% risk. For a break-even system, 2% risk produced a 20% drawdown in 91.5% of sequences. Where the line sits for you depends on your measured edge and the drawdown you can sit through.
Should position size be rounded up or down?
Down, because rounding up puts more than the planned amount at risk. In the EUR/USD example, rounding 0.3333 lots down to 0.33 puts $99 at risk at the stop, while rounding up to 0.34 puts $102 at risk, above the $100 limit. Shares and contracts follow the same rule: 192.3 shares becomes 192, and 8.33 MES contracts becomes 8.
Drafted with AI writing tools and published without an individual editor review. Figures, prices and dates may be out of date; check them against the primary sources before relying on them. Educational content only, not personalized financial advice.