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Monte Carlo simulation: definition and example

A method that generates thousands of possible paths from your rules, to see the range of outcomes instead of a single scenario. Each path is a possible future, not a forecast.

Chart of a Monte Carlo simulation of 1,000 one-year paths for $10,000 in bitcoin, with a median of $14,381 and a p5-p95 range from $6,884 to $30,752.
Monte Carlo simulation: 1,000 one-year paths resampled from BTC daily returns from October 2022 to October 2026.Chart licensed under CC BY 4.0: you may reuse it with the credit “Metena (metena.app)”.

Definition

A backtest tells only one story: the one that happened. Monte Carlo builds thousands of others by reshuffling the observed moves, to see the range of what could have happened.

The result is a distribution, not a forecast. The simulation assumes the future resembles the past it uses; it contains no event that is not in that past.

How to read the chart

Each thin green line is a simulated path of $10,000 invested in bitcoin for a year (120 of the 1,000 simulated are drawn). The scale is logarithmic.

The bright line is the median: half the paths end above it. The dotted gold lines frame 90% of the scenarios, between the 5th and 95th percentiles.

Worked example

1,000 one-year paths, built by drawing bitcoin’s real daily returns between October 2022 and October 2026 at random. After a year, the median is $14,381, the 5th percentile $6,884 and the 95th $30,752. 20.5% of paths end below the starting $10,000.

In Metena

Metena’s backtest runs a Monte Carlo simulation on your strategy and shows percentiles of return, Sharpe and maximum drawdown, so you judge how solid a result is rather than a single number.

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Related terms

Percentile (p5, p95)
The 5th percentile is the value below which 5% of simulated scenarios fall; the 95th is the value only 5% exceed. They bound the low and high scenarios.
Backtest
Replaying a strategy on past data to measure what it would have delivered. Useful for testing rules, but the past does not predict the future.
Volatility
The size of an asset’s price swings. High volatility means large moves, up as well as down.
Stress test
Simulating your rules through a historical shock, such as the March 2020 crash, the LUNA collapse or the FTX bankruptcy, to see what they would have absorbed.

Related guides

How to read a crypto backtest without being fooled
Return, maximum drawdown, overfitting, Monte Carlo: how to read the results of a crypto strategy backtest, with real bitcoin examples.

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Educational content. It is not investment advice. Crypto-assets carry a high risk that can go as far as the total loss of capital.