Monte Carlo simulation is a statistical method that, instead of relying on a single 'average' scenario, generates thousands of possible future paths for your portfolio. Each path takes into account random market fluctuations – bull and bear markets, different yearly returns. The result is a distribution of possible final portfolio values, not just one number.
In investing, nobody knows the future. But we can estimate the range of possible outcomes, assuming that the future will be somewhat similar to the past in terms of average return and volatility. Monte Carlo takes these parameters and creates a realistic range of scenarios.
Instead of asking: 'How much will I have in 20 years if the market averages 7%?' – Monte Carlo asks: 'In 90% of cases my capital will be between X and Y, and in half of the cases above Z.' That is much more practical.
02Percentiles
How to read percentiles: p10, p50 (median), p90
After running a Monte Carlo simulation (e.g., 10,000 paths), the results are sorted from worst to best. Percentiles divide this set into one hundred equal parts.
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p10 (10th percentile)
This is the result that is better than 10% of all paths. In other words: in 10% of scenarios the outcome is worse than p10, and in 90% it is better. p10 is often considered a pessimistic scenario – good to know to prepare for tough times.
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p50 (median)
The middle result – exactly half of the paths are better, half are worse. This is the realistic, central scenario. Unlike the arithmetic mean, the median is not distorted by extreme values (very good or very bad outcomes).
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p90 (90th percentile)
The result that is better than 90% of paths – only 10% of simulations achieve this or higher. This is an optimistic scenario, showing the potential in favorable market conditions.
Example: A simulation for a portfolio of $100,000 after 20 years might show: p10 = $180,000, median = $320,000, p90 = $580,000. This means that in 80% of cases the outcome will be between $180,000 and $580,000, and in half of the cases it will exceed $320,000.
The wider the range between p10 and p90, the higher the risk (volatility) of the portfolio. A narrow range means more predictable outcomes.
03Median
Median – the middle of possible scenarios
The median (p50) is the most important value from a Monte Carlo simulation. Why? Because unlike the arithmetic mean, the median is not pulled upward by a few extremely good years. It gives a more realistic picture of what you can expect in a typical case.
In finance, the average annual return is often used, but that average can be misleading – if you lose 50% one year and then gain 100%, the arithmetic average is 25%, but your capital returned to the starting point. The median accounts for such sequences and gives a fairer picture.
320 000 zł
Median (p50) – typical expected outcome
280 000 zł
Arithmetic mean – may be higher than median
In the Investiq calculator, we show the median as the main result – this is what you should use for long‑term planning.
04Importance
Why is Monte Carlo important for investors?
1
Understanding risk
Monte Carlo shows not only the 'average' outcome but also the distribution of possible results. You can see how large the gap can be between pessimistic and optimistic scenarios.
2
Financial planning
Thanks to percentiles, you can estimate what capital is realistic in a pessimistic scenario (p10). If that lower outcome still meets your goals, your plan is safe.
3
Avoiding the illusion of certainty
A single linear projection (e.g., '7% per year') can give a false sense of security. Monte Carlo reminds us that the future is uncertain, but we can prepare for it.
Key lesson: even if the median shows growth, in a pessimistic scenario (p10) you might have a loss or low return. Diversification and a long horizon shift the distribution to the right – they increase the median and narrow the range.
05Chart
How to interpret the Monte Carlo chart in the calculator
In the Investiq calculator, after calculating results you will see a Monte Carlo chart. The X‑axis shows years, the Y‑axis shows portfolio value. There are three lines on the chart:
Lower line (p10) – pessimistic scenario; only 10% of simulations end worse.
Middle line (p50 / median) – central scenario; half of simulations end better, half worse.
Upper line (p90) – optimistic scenario; only 10% of simulations end better.
Between p10 and p90 lies 80% of all possible outcomes. The wider this corridor, the higher the risk (volatility). You can also see individual paths – each represents one random market scenario.
Practical tip: when analyzing your portfolio, always look at the median (p50) as the most realistic outcome. If p10 is acceptable for you (does not ruin your plans), it means your strategy is well prepared for worse years.