Monte Carlo Equity Curve Simulator
A Monte Carlo equity curve simulator resamples the percentage returns you enter with replacement, compounds 5,000 reproducible hypothetical paths and summarizes terminal equity and maximum drawdown percentiles. It describes one conditional resampling model; it does not predict future returns, verify the sample or identify a safe risk level.
Enter one comparable return sample
Use 10 to 1,000 same-basis percentage returns. Keep frequency, costs, strategy definition and observation selection consistent.
A positive starting amount used only to scale the hypothetical paths.
Enter 10 to 1,000 signed percentage returns separated by commas or new lines. Every value must be greater than -100%.
A whole-number horizon from 1 to 1,000 sampled observations.
A path is counted when equity reaches or falls below this entered fraction of starting equity.
Conditional path distribution
Entered Strategy Robustness 1.0.0.
On smaller screens, scroll horizontally to inspect the complete calculation table.
| Terminal percentile | Equity |
|---|
How the Monte Carlo equity paths are calculated
Drawdown = (Running peak − Current equity) ÷ Running peak × 100
Each trade draws one entered return with replacement
Version 1.0.0 derives a deterministic seed from the normalized inputs. A Mulberry32 generator then selects one index from the entered return sample for every simulated trade. Because selection is with replacement, an observation can appear repeatedly in one path or not at all.
Every path compounds the sampled percentage returns from the same entered starting equity. The engine retains each terminal equity and each path’s deepest running-peak percentage drawdown, sorts the 5,000 values and applies disclosed Type-7 linear interpolation to the requested percentiles.
The terminal percentiles summarize endpoints under this one empirical draw-pool assumption. The maximum-drawdown percentiles summarize each path’s deepest decline. Neither distribution includes an outcome absent from the entered sample, unless it arises through compounding or ordering.
Worked example from the audited fixture
The audited constant-return fixture starts at 1,000, enters ten observations of +10%, samples three trades per path and uses a 50% floor.
- Every random draw is +10%, so every path is 1,000 × 1.10 × 1.10 × 1.10 = 1,331. The 5th, median and 95th terminal percentiles are therefore all 1,331.
- Equity never falls below its running peak, so both reported maximum-drawdown percentiles are 0%. No path ends below start or touches the 500 floor.
Reproduce it: select “Load audited example” above. The engine retains full precision and rounds only visible output.
How to interpret the result
- The median terminal value is the middle of the 5,000 seeded endpoints, not the most likely future account value.
- The 5th and 95th terminal percentiles show the central 90% span of this simulated set. They are not a confidence interval for actual future equity.
- The 95th-percentile maximum drawdown is exceeded by about 5% of these simulated path maxima under this seed and model. It is not the maximum possible loss.
- A zero floor-hit percentage means none of the 5,000 modeled paths touched the entered floor. It does not prove that a real account cannot do so.
Assumptions and limits
- Sampling individual returns with replacement does not preserve autocorrelation, volatility clustering, trade grouping or regime order.
- The model does not add spread, commission, financing, slippage or gaps unless those effects are already represented consistently in every entered return.
- A selected or incomplete sample can make every output misleading even when the arithmetic is correct.
- Five thousand seeded paths produce a reproducible finite estimate, not an exhaustive probability distribution.
- No risk fraction, position size, optimal setting, profitability forecast, quality grade, signal or recommendation is produced.
Monte Carlo vs bootstrap vs walk-forward efficiency
These tools answer separate questions. Monte Carlo summarizes hypothetical resampled paths, bootstrap estimates uncertainty around one entered statistic, and walk-forward efficiency compares entered IS and OOS rates. None substitutes for audited records, a documented test design or execution evidence.
| Measure | Evidence entered | Question answered | Main boundary |
|---|---|---|---|
| Monte Carlo equity | Entered percentage returns | Seeded terminal-equity and drawdown path distribution | Not a forecast or exhaustive loss boundary. |
| Bootstrap expectancy | Entered signed outcomes | Percentile interval for resampled arithmetic means | Not a next-trade prediction interval. |
| Walk-forward efficiency | Entered IS and OOS window results | Aggregate OOS result rate divided by aggregate IS result rate | Not an optimisation or robustness verdict. |
| Risk of ruin | Assumed win rate, payoff and fixed risk | Finite-horizon threshold-hit estimate | A separate parametric two-outcome model. |
Frequently asked questions
- It samples the entered percentage returns with replacement, compounds 5,000 seeded hypothetical paths and summarizes their terminal equity and maximum drawdown distributions.
- No. The output is conditional on the entered sample, horizon, seed and resampling method and is not a real-world forecast.
- Version 1.0.0 hashes the normalized inputs into a fixed 32-bit seed, so identical inputs reproduce the same 5,000 paths.
- Every simulated trade draws one observation from the entered return pool, and the same observation can appear repeatedly or not at all in one path.
- It is the Type-7 95th percentile of the 5,000 path-level maximum drawdown values, not the maximum possible future loss.
- It means none of the 5,000 modeled paths reached the entered equity floor; it does not prove a real account cannot reach it.
- No. Individual-return resampling does not preserve original ordering, serial dependence, trade groups or changing market regimes.
- No. Risk of Ruin is a separate parametric fixed-fraction two-outcome model; this page resamples an empirical percentage-return pool.
Sources and methodology
- Trading Blox — Monte Carlo simulations — Documents equity-curve reordering and sampling-with-replacement methods.
- CFTC — Commodity trading systems — Official warning about the inherent limitations of hypothetical trading results.
The immutable implementation contract fixes the seed, resampling count, quantile convention, duration weighting, invalid states and permanent exclusions so later copy or layout edits cannot silently alter the arithmetic.
Continue the path-risk review
Verify the execution records behind your sample
Before treating any return, outcome or window result as net and comparable, confirm which spread, commission, financing, conversion and execution conventions apply to the broker entity and account used. These browser calculations do not retrieve statements or certify that entered records are complete.
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