Monte Carlo position sizing: how many futures contracts per account?

Contents

1. How does Monte Carlo simulation decide contract count?
2. Which trade list do you feed into the simulation?
3. Why keep margin and tick value in the model?
4. Which drawdown percentile should you use?
5. How do you simulate the same trades at 1, 2 and 3 contracts?
6. Can Monte Carlo calculate risk of ruin across trials?
7. How do you turn the result into contracts per account size?
8. Frequently asked questions
9. References

How does Monte Carlo simulation decide contract count?

Monte Carlo position sizing reshuffles your strategy's own closed-trade list thousands of times, reads the maximum drawdown that most of those reshuffled histories stay under, adds the margin each open contract needs, and sets the contract count so that both fit inside the share of the account you decided to risk before you ran anything.

Monte Carlo simulation is a method that answers a question by running the same random process many times and counting the results, named by Metropolis and Ulam (1949). In trading, the random process is the order of your trades. Think of a deck of cards where each card is one closed trade. The sum of the deck is fixed, so the total profit does not change when you shuffle. What changes is how many losing cards you can turn over in a row. That run of losses is the drawdown, and it is the number that decides how many contracts an account can carry.

The chain has five steps. Take the closed trades after costs. Reshuffle their order a thousand times or more. Record the maximum drawdown of each reshuffled history. Read the drawdown that most trials stay under. Divide that figure, plus margin, into the part of the account you are willing to lose. The free Monte Carlo drawdown simulator runs the middle steps from a pasted trade list. For the reshuffle itself, start with what Monte Carlo simulation is, with a futures example; for the drawdown side, read why a Monte Carlo backtest usually shows a worse max drawdown than the original.

Which trade list do you feed into the simulation?

Feed in the closed trades of one real backtest, after commission and slippage, at one contract. The simulation can only rearrange what you give it. A trade list without costs produces a drawdown that is too shallow, and a list from a backtest with several contracts has to be divided back to one contract before the scaling in the later sections works.

The worked input for this article is a run from AlphaPrime (Valynox) on NQ daily bars from the start of 2019 to the end of June 2025, long and short, one contract. It uses an Average True Range rule as its only entry and exit, a stand-in built from a standard indicator, not a Monte Carlo rule itself. It is the one candidate the search kept out of 1,024 it tried, chosen for its return against its drawdown, and picking the kept one after the fact flatters its numbers. Nothing here says the rule earned that money or that a reader can expect it; the list is used only as raw material for the reshuffle.

The max drawdown of $96,430 in that table is one ordering of 172 trades, the ordering that the calendar happened to produce. Shuffle the same 172 trades and a different ordering gives a different drawdown. Some orderings cluster the losses and dig deeper; some spread them out and stay shallower. The single figure from the backtest is one point inside that spread, and there is no reason to expect it to be the deepest. The closed-trade list that feeds the reshuffle is the one AlphaPrime's Performance Report prints trade by trade, next to the drawdown that this one calendar order produced.

Two checks on the input before you shuffle. The trade count matters: 172 trades is a modest sample, and the reshuffle cannot invent trades that are not there, so a short list gives a narrow and over-confident spread. And the order of trades should not carry information the shuffle destroys: a strategy whose losses come in natural clusters, as trend rules often do in sideways markets, may see a real drawdown deeper than the shuffled ones. Bailey, Borwein, López de Prado and Zhu (2014) show why the best of many candidates carries an optimistic bias, which is one more reason to treat the kept run's own drawdown as a floor, not a ceiling.

Why keep margin and tick value in the model?

Keep both in, because the account carries the drawdown and the margin at the same time, and leaving either out makes the contract count look safer than it is. Tick value is the dollar amount one minimum price step of the contract is worth; it is what turns a point move on the chart into a dollar loss in the account. Maintenance margin is the money the exchange and broker require you to hold for every open contract; it is locked while the position is open and is not available to absorb losses.

For the E-mini Nasdaq-100 (NQ), CME Group lists a contract size of $20 times the index and a minimum tick of 0.25 index points worth $5.00, so one full index point is $20 per contract. A backtest that was built with the correct point value already reports trades in dollars, and the shuffle works on those dollars directly. Check that setting once before you trust the list; a backtest set to the wrong point value gives a drawdown that is wrong by the same factor. Exchanges can change tick size, point value and margin, so confirm them on the exchange's contract page; the free futures contract calculator shows tick value and point value side by side.

Margin is often the larger of the two blocks for an index future, which surprises traders who size only by drawdown. The sizing rule in the later sections treats one contract as a package: its share of the simulated drawdown plus its margin, both scaling together.

Which drawdown percentile should you use?

Size to the 95th percentile of the simulated maximum drawdown, not to the median and not to the single drawdown of the original backtest. A percentile is the value that a given share of the trials stay under; the 95th percentile is the drawdown that 95 of every 100 reshuffled histories did not exceed. Magdon-Ismail and Atiya (2004) show that the expected maximum drawdown grows with the length of the record, so the longer you plan to trade, the further to the right the real-life figure drifts; the 95th percentile builds in part of that drift.

Each candidate line has a clear reason to reject it:

Sizing line	What it is	Why it is or is not the right line
Median (50th percentile)	Half the trials were deeper	Too kind: you accept a coin flip on whether the real drawdown is worse
Original backtest drawdown	One ordering, the calendar's	No special status; often sits near the middle of the spread
95th percentile	19 of 20 trials stayed under it	Covers most orderings and still leaves a tradeable contract count
Worst trial	One freak ordering	Moves every time you rerun the shuffle and would leave you trading almost nothing

The worst trial deserves one more word. It depends on how many trials you ran: a thousand shuffles produce a milder worst case than ten thousand, because more draws reach further into the tail. A sizing line that changes with the number of trials is not a line you can write down in advance. The 95th percentile settles quickly as trials increase, which is exactly what a pre-written rule needs.

How do you simulate the same trades at 1, 2 and 3 contracts?

Multiply every trade result by the contract count, and the 95th-percentile drawdown and the margin both scale in a straight line while the account stays the same size. Two contracts of the same rule produce exactly twice the dollar result of each trade, because entries and exits are at the same prices; the shuffle therefore does not need to be rerun. Scale the one-contract percentile and the one-contract margin, and compare each total with the fixed risk share of the account.

The risk share is the part of the account you decided, before running anything, that this strategy may lose in a deep drawdown while still holding its margin. It is your choice and should be written down in advance. An account that runs several strategies gives each one a smaller share.

Note what happens to the bars as the account grows. Doubling the account doubles the line but leaves the bars where they are, so the contract count rises in steps, not smoothly. This is why the last section rounds down to a whole contract rather than quoting a fraction.

Can Monte Carlo calculate risk of ruin across trials?

Yes: count the share of trials in which the account falls below a ruin line you wrote down before running, and that share is the risk of ruin for that contract count. Risk of ruin is the probability that the account loses a set fraction of its starting value before it recovers, usually a fraction at which you would stop trading the strategy. The ruin line is a loss level, not a drawdown percentile; it might be half the account, or whatever point at which you would stop.

1. Write the ruin line down first. A line chosen after seeing the trials is a line fitted to the trials.
2. Run the shuffle once at one contract and keep every trial's full equity path, not only its max drawdown.
3. For each contract count, scale every path by the contract count and count the trials that cross the ruin line at any point.
4. Divide by the number of trials. The result is the risk of ruin at that contract count.

The share rises steeply once contracts pass what the 95th-percentile drawdown allows. At one contract the ruin line sits far beyond the right tail of the drawdown spread, and almost no trial reaches it. Each extra contract stretches the spread by one more unit, and because the tail of a drawdown distribution is thin, a small stretch sweeps in a large share of trials at once. In the hypothetical figure below, the share is a fraction of one percent at one contract, a few percent at two, and about a fifth of all trials at three; the trader's pre-written limit of two percent is crossed between one and two contracts, the same boundary the drawdown comparison found.

The free risk of ruin calculator reaches a similar figure from a different direction, using win rate, payoff ratio and risk per trade instead of the trade list. When the two routes disagree widely, the trade list usually holds the explanation: a few very large losses that an average-based formula smooths away.

How do you turn the result into contracts per account size?

Divide the account's risk share by the sum of the 95th-percentile drawdown and the margin per contract, then round down to a whole number. The steps, in order:

1. Export the closed-trade list of a one-contract backtest with commission and slippage included.
2. Write down the risk share, the ruin line and the ruin limit before running anything.
3. Reshuffle the list a thousand times or more and record each trial's max drawdown and equity path.
4. Read the 95th-percentile max drawdown for one contract.
5. Look up the current maintenance margin per contract on the exchange's contract page.
6. Divide the risk share by (drawdown + margin) and round down.
7. Check the risk of ruin at that contract count against your pre-written limit; if it fails, drop one contract.
8. If the rule has a fixed stop, also take the count the free position size calculator gives from the stop distance and the account risk per trade, and trade the smaller of the two counts. The drawdown-based count protects the account across a run of losses; the stop-based count protects it on a single trade.

Rerun the division whenever the margin changes, whenever you add trades to the list, and whenever the account moves enough to cross a step. The margin and the trade list change the denominator; the account changes the numerator; the risk share should not change at all once written.

The one test to run next: take your own one-contract trade list, run it through the simulator, and write down two contract counts, one from the backtest's single max drawdown and one from the 95th percentile. If they differ by a whole contract, the single drawdown was hiding orderings that your account could not have carried. If you prefer to see every step of the shuffle, building the Monte Carlo simulation in Excel walks through it cell by cell.

Frequently asked questions

What is Monte Carlo position sizing?

Monte Carlo position sizing is a way of choosing how many contracts to trade by reshuffling a strategy's own closed trades many times and reading how deep the drawdown gets in most of the reshuffled histories. The contract count is then the largest number at which that drawdown, plus the margin for each contract, still fits inside the share of the account you decided to risk. It uses the trades you already have rather than a formula built from averages.

How many Monte Carlo trials do I need for position sizing?

A thousand reshuffles is enough for the 95th percentile to settle; more trials change it very little. The worst trial, by contrast, keeps getting worse as you add trials, which is one reason not to size to it. What limits accuracy more than the trial count is the number of real trades in the list: a short list gives a narrow, over-confident spread no matter how many times you shuffle it.

Should I size to the 95th or the 99th percentile of drawdown?

The 95th percentile is the usual choice because it is stable across reruns and leaves a contract count you can actually trade. The 99th percentile is closer to the worst trial, moves more between runs, and often cuts the contract count by a whole contract for little change in the risk of ruin. If you want extra protection, lower the risk share of the account instead of moving the percentile.

Does reshuffling the trades change the strategy's win rate or profit?

No. Every reshuffled history contains the same trades, so the total profit, the win rate, the profit factor and the average trade are identical in every trial. Only the order changes, and with it the deepest run of losses. That is why the method is useful for sizing and not for judging whether the strategy has an edge.

Can Monte Carlo calculate the risk of ruin for a futures strategy?

Yes. Write down a ruin line, such as a 50 percent loss of the account, before running. Then count how many reshuffled equity paths cross that line at any point and divide by the number of trials. Repeat for each contract count; the share rises sharply once the contract count exceeds what the 95th-percentile drawdown and margin allow.

References

• Metropolis, N., & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335–341.
• Magdon-Ismail, M., & Atiya, A. F. (2004). Maximum Drawdown. Risk, 17(10), 99–102.
• Bailey, D. H., Borwein, J., López de Prado, M., & Zhu, Q. J. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance. Notices of the American Mathematical Society, 61(5), 458–471.
• CME Group. E-mini Nasdaq-100 Futures contract specifications (contract size $20 × index, minimum tick 0.25 index points = $5.00). cmegroup.com/markets/equities/nasdaq/e-mini-nasdaq-100.contractSpecs.html