Monte Carlo Tools
Equity Curve Monte Carlo Simulator
Investment Education, Research & Tools for Smarter Decisions.
Enter your strategy's win rate, average win, average loss, and trade count to simulate thousands of possible equity paths. The tool shows the median outcome, realistic performance ranges, and the worst-case scenarios you need to plan for, replacing false precision with an honest distribution.
Direct Answer
An equity curve Monte Carlo simulator generates thousands of randomized equity paths from a strategy's win rate, average win, average loss, and trade count, replacing a single historical backtest with a distribution of plausible outcomes. Instead of trusting one lucky (or unlucky) sequence of trades, it reports the median result alongside realistic best-case and worst-case ranges. That range, not the single backtested curve, is what should inform position sizing and risk tolerance decisions.
Tool
Enter your strategy parameters above and click Run Simulation to see the distribution of outcomes.
Uses synthetic data computed from user-entered parameters only. Does not use real market data.
How to Use This Tool
Enter your strategy's win rate as a percentage (e.g., 52 for a 52% win rate). Enter the average winning trade size and average losing trade size as positive percentages of trading capital (e.g., "2.0" means the average win returns 2% of capital; "1.2" means the average loss costs 1.2%). Enter the number of trades in your typical trading period. The simulation paths field controls how many alternative equity paths to generate, more paths give more stable percentile estimates. Click Run Simulation.
The tool generates each simulated path by drawing trades randomly with your specified win probability and applying the win or loss return to the running capital (compound sizing). It then computes the terminal return, max drawdown, and Sharpe-proxy for each path and reports the distribution across all paths. Expectancy per trade is computed as (win rate × avg win) − (loss rate × avg loss); the simulation's median terminal return should approximate (1 + expectancy)^n − 1 for the given number of trades.
Compare where your historical backtest result falls within the simulated distribution. If your backtest showed a terminal return of +45% and the median simulation path shows +31%, your historical backtest result was in the top 20-25% of outcomes by luck of trade sequence, adjust your live expectations accordingly toward the median.
Understanding the Outputs
Expectancy per trade: The expected dollar-profit per trade as a percentage of capital, calculated as (win rate × avg win) − (loss rate × avg loss). Positive expectancy is necessary but not sufficient for long-run success, you also need sufficient capital to survive the inevitable losing sequences. A strategy with expectancy of +0.4% per trade sounds small but compounds to +55% over 100 trades at the median.
Median terminal return: The middle simulated outcome across all paths. Half of simulated paths finish above this level and half finish below. This is the most honest representation of the strategy's typical outcome, not the average (which is distorted by extreme positive paths) and not the historical backtest result (which may have been path-lucky).
10th, 90th percentile range: The 80% probability band of terminal returns. If you ran this strategy many times over the specified number of trades, approximately 80% of runs would end within this range. Paths outside this range (best 10% and worst 10%) represent unusually lucky and unusually unlucky sequences.
5th percentile max drawdown: The worst drawdown level that 5% of paths exceeded, meaning 95% of simulated paths had a max drawdown better than this level. Use this as the conservative stress case for position sizing: ensure you can survive this drawdown level without being forced to stop trading.
Assumptions and Limitations
- Independent trades assumed: The simulator draws each trade's outcome independently. Real strategies may have streaky wins or losses due to market regime autocorrelation, this tool cannot model that serial dependence.
- Binary win/loss assumed: Each trade is modeled as either a full win (at the specified average win percentage) or a full loss (at the specified average loss percentage). Real strategies have variable trade sizes; this approximation simplifies the distribution.
- Compound (percentage) position sizing: Each trade's outcome is applied as a percentage of current capital, meaning wins compound and losses reduce the capital base for subsequent trades. Fixed-dollar sizing would produce different terminal return distributions.
- No transaction costs: The tool does not deduct commissions or slippage. In practice, these reduce expectancy and should be incorporated into the average win and loss figures before running the simulation.
Four Numbers Are Not a Strategy
A win rate, an average win, an average loss and a trade count describe a strategy in four numbers, and a strategy is not four numbers. The simulation treats every trade as an independent draw with fixed characteristics, which is a useful simplification and a poor description of most real records, where results cluster and the size of wins and losses shifts with conditions.
Used inside that limitation, the tool answers something genuinely valuable: how different the path could have looked with identical underlying statistics. Seeing the spread of outcomes consistent with one set of inputs is the fastest cure for treating a single equity curve as destiny.
The inputs deserve scepticism of their own. Averages computed from a short record are unstable, and a handful of unusual results can dominate an average win or loss enough to distort everything downstream of it.
Nothing here accounts for a strategy ceasing to work, for costs changing, or for how the person running it behaves during the worst stretch in the simulated set.
Frequently Asked Questions
Why does the median result differ from the arithmetic expectancy?
The arithmetic expectancy (win rate × avg win − loss rate × avg loss) estimates the average return per trade. But with compound percentage sizing, the geometric growth, which determines terminal wealth, is lower than arithmetic due to volatility drag. A strategy with +0.5% expectancy per trade will have a median terminal return slightly below (1.005)^N due to the variance of trade returns reducing compound growth. This is the standard relationship between arithmetic mean return and geometric mean return.
What is a realistic number of simulation paths?
2,000 paths provides stable estimates for the 10th and 90th percentile outputs. For the 5th percentile max drawdown estimate, 5,000 paths is preferred for better precision. The simulator caps at 10,000 paths for browser performance. For research-grade analysis at the 1st percentile, run 50,000+ paths in a dedicated environment.
How do I include transaction costs in the simulation?
Subtract your estimated transaction cost per trade from the average win and add it to the average loss before entering values. If your average win is 2.2% gross and you pay 0.05% in commissions each way (0.1% round trip), enter 2.2 − 0.1 = 2.1% as the average win. If your average loss is 1.1% gross, enter 1.1 + 0.1 = 1.2% as the average loss.
Can I use this tool for a strategy with many small wins and occasional large losses?
Yes. Enter the average win as a small percentage (e.g., 0.8%) and the average loss as a larger percentage (e.g., 3.0%). The simulation will reflect the negative skew of such a strategy, most paths will end with modest positive returns, but a minority will experience very deep drawdowns from the large loss events. This pattern is typical of premium-selling or mean-reversion strategies.
Why is the 5th percentile max drawdown much worse than I expected?
The 5th percentile max drawdown reflects the worst 5% of simulated trade sequences, where the strategy happened to run into an unusually long string of consecutive losses early in the sequence, depleting capital before gains could compound. With compound sizing, early large losses hit a full capital base; the resulting drawdown can be much deeper than the arithmetic average would suggest. This is the correct answer to "what is a realistic bad-case scenario," and it is typically more severe than naive intuition suggests.
Does the simulator assume each trade is independent of the one before it?
Yes. Each simulated trade is drawn without reference to what preceded it, which means any real tendency for winners or losers to cluster is absent from the output. Strategies that add to positions after a win, reduce size after a loss, or trade a signal that persists across several entries all violate that assumption. Where clustering is genuinely present, the simulated paths will show smoother sequences and shallower drawdowns than the strategy is capable of producing.
What happens to the output when the win rate and average win came from very few trades?
The inputs carry the uncertainty of the sample they came from, and the simulator treats them as exact. Twenty trades give a win rate whose true value could plausibly sit several percentage points either side, and the output distribution is built as though that ambiguity did not exist. The result looks precise while resting on estimates that are not. Running the simulation across a range of plausible input values shows how much of the output is assumption.
Should the trade count be the historical number or a forward-looking one?
It depends what the run is for. Using the historical count produces a distribution comparable to the backtest that generated the inputs, which is the right setup for asking whether the recorded result was ordinary or fortunate. Using an expected forward count, such as the trades anticipated over the coming year, produces a distribution about the period ahead. Mixing the two, by using historical inputs with a forward count and reading it as a forecast, overstates what the exercise supports.
Can the simulator represent a strategy that varies position size between trades?
Not directly. It works from a single average win and average loss, which implicitly treats every trade as the same size. A strategy that sizes by volatility, by conviction, or by remaining capital produces a distribution of trade outcomes that a single pair of averages cannot describe. Expressing wins and losses as percentages of equity rather than as fixed amounts is a partial workaround, since it at least keeps compounding consistent across paths.
References
- Vince, R. (1992). The Mathematics of Money Management. Wiley. Covers compound growth, drawdown as a function of bet size and win rate, and path dependency in compounded sequences.
- Tharp, V. K. (2006). Trade Your Way to Financial Freedom, 2nd ed. McGraw-Hill. Chapter 11 covers expectancy calculation and its role in strategy evaluation.
- Pardo, R. (2008). The Evaluation and Optimization of Trading Strategies, 2nd ed. Wiley. Chapter 9 covers Monte Carlo simulation for strategy validation.
Educational Disclaimer
This tool is for educational purposes only. Simulation results are based solely on user-entered parameters and a simplified statistical model, they do not represent or predict actual future trading performance. Trading involves risk, including the possible loss of all capital. Consult a qualified financial professional before making trading decisions.