Monte Carlo Simulation for Trading Systems

Your equity curve is one hand of cards dealt from a much larger deck. Monte Carlo simulation reshuffles that deck a few thousand times so you can see the drawdowns, the flat stretches, and the blow-ups your particular run happened to dodge — before a prop firm’s daily loss limit finds them for you.

Why one equity curve is one lucky path

The curve you have is a single ordering of your trades. Had the same trades arrived in a different sequence — same win rate, same average win and loss, just shuffled — your peak drawdown could have been twice as deep or half as shallow. Nothing about your edge changed; only luck of the draw did.

That is the trap. Traders read a smooth backtest as proof of safety when it is really one sample from a distribution of possible histories. A prop-firm account can survive the friendly ordering and fail the unfriendly one on identical trades. Monte Carlo exists to show you the unfriendly orderings on purpose, so you size and plan for them instead of meeting them by surprise.

Resampling trades to build outcome distributions

The mechanics are simple enough to trust:

Take your list of closed-trade results, ideally as R-multiples so they are size-independent.
Draw a new sequence of N trades from that list — either by shuffling the existing set (permutation) or by sampling with replacement (bootstrap).
Compound that sequence into an equity path and record the outcome and the worst drawdown along the way.
Repeat a few thousand times.

Sampling with replacement is usually the better choice: it lets an unlucky path draw three of your worst losers back to back, which permutation of a fixed set caps artificially. The output is not one number but a full distribution — of final equity, of maximum drawdown, of time spent underwater. That distribution is the honest description of your system.

Feed it clean inputs. If your win rate and average win/loss are themselves noisy estimates from too few trades, the simulation inherits that noise. Nail down your expectancy first so the deck you are shuffling reflects a real edge and not a lucky sample.

Reading the drawdown percentile bands

The most useful output is the maximum drawdown distribution. Sort every simulated run’s worst drawdown and read the percentiles:

The median (50th) is a typical bad patch — expect to live through this routinely.
The 95th percentile is a rough stress level: 1 in 20 histories were worse.
The 99th percentile is your “plan for it” number for a funded account with hard limits.

A frequent shock: the drawdown you already survived often sits near the median, not the tail. That means deeper drawdowns are not exotic — they are ordinary futures you simply haven’t reached yet. Compare the 95th and 99th percentile depths against a firm’s trailing threshold using the prop-firm drawdown calculator, and if the tail breaches the limit, the account is under-capitalized for the strategy no matter how good the average looks. Because most prop programs trail the drawdown on your peak rather than your starting balance, read the trailing drawdown explainer before you interpret these bands.

Risk of ruin and the worst-case tail

Risk of ruin falls straight out of the simulation: the fraction of runs that hit your account-death threshold — a firm’s max loss line, or a personal stop — before recovering. If 4% of paths breach the limit, that is a 1-in-25 chance of losing the account on this strategy at this size, luck alone.

The tail is where accounts actually die, so look past the average:

Depth — how deep does the worst 1% go?
Duration — how long do the worst runs stay underwater? A survivable drawdown that lasts 200 trades can still break a challenge’s time window or your patience.
Recovery — from the tail low, what does climbing back require? Size that against the drawdown recovery calculator, because the gain needed to recover grows non-linearly with depth.

Position sizing from the Monte Carlo output

This is the payoff. Instead of picking risk-per-trade from feel, dial it until the 99th-percentile drawdown sits comfortably inside the hardest limit you trade under, with margin to spare. Halve your risk and the whole drawdown distribution roughly halves with it — a direct, quantified lever.

The logic:

Pick the tightest constraint across every account you run.
Set per-trade risk so the tail drawdown clears it with room for costs and slippage.
Re-run whenever your win rate or payoff drifts — the safe size moves with the edge.

Shibiki turns that chosen ceiling into a hard risk limit enforced at the broker, not a note in your journal. The size Monte Carlo says is survivable becomes a rule the EA holds even on a day your discipline doesn’t. And if you run the same strategy copied across several prop accounts, the simulation’s tail is the number that keeps a correlated bad streak from taking all of them out at once.

Pitfalls: independence and stationarity

Monte Carlo is only as honest as its assumptions, and two of them bite:

Independence. Basic resampling assumes each trade is independent of the last. If you add to losers, scale in, or your losses cluster in choppy regimes, real drawdowns run deeper than the shuffle predicts. Block-bootstrap resampling — drawing short runs of consecutive trades — preserves some of that clustering.
Stationarity. Shuffling assumes tomorrow’s trades come from the same distribution as the ones you fed in. Markets change. A simulation built on a trending quarter will understate the pain of the chop that follows.

Treat the percentile bands as a stress test, not a forecast. They tell you how fragile your system is to bad luck given its historical behavior — which is exactly the question a funded trader should be asking. Just don’t mistake a clean simulation for a promise about the future.