Lesson 10 of 20 · 7 min
What a Monte Carlo simulation actually does, step by step
It generates thousands of possible paths from stated assumptions and counts what happened in them.
Monte Carlo sounds sophisticated and is mechanically simple. It is a way of answering questions about a distribution you cannot write down, by generating a large number of examples from it and counting.
The procedure, in full:
- State the assumptions: a starting value, an expected return, a volatility, a time horizon, and a step size.
- Draw a random number for the first step, scaled to the volatility and the length of the step.
- Apply it to the starting value to get the value after one step.
- Repeat until the horizon is reached. That completes one path.
- Record whatever you care about along that path — the ending value, the lowest point reached, whether a threshold was crossed.
- Do the whole thing thousands of times, then summarise: percentiles, frequencies, medians.
That is genuinely all of it. There is no forecasting step and no cleverness. Its value is that it handles questions closed-form mathematics cannot, particularly path-dependent ones: what fraction of paths ever touched a level, rather than what fraction ended below it.
The output for the standard setup used throughout this track — $600,000 collateral, $300,000 balance, 70 percent threshold, three years, 7 percent drift, 20 percent volatility, 10,000 runs — has a median ending collateral value of about $702,000, a fifth percentile of about $402,000 and a ninety-fifth of about $1,267,000. The distribution is wide and right-skewed, which is why the mean of about $753,000 sits well above the median.
The critical caveat, which lesson 12 develops: every number above is a property of the assumptions, not of the world. A simulation cannot discover fat tails that its random-number generator was not given.
Key terms
- Monte Carlo simulation
- Generating many random paths from stated assumptions and summarising the results. Answers questions no formula can.
- Path
- One complete simulated history from start to horizon. Path-level detail is what makes the method useful.
- Right skew
- A distribution with a long upper tail, which pulls the mean above the median. Compounding produces it naturally.
Worked example
Ten thousand runs of the standard setup
Collateral $600,000, balance $300,000, threshold 70%, three years, monthly steps, 7% drift, 20% volatility, 10,000 runs.
- 5th percentile ending collateral
- $402,000
- 25th percentile
- $561,000
- Median
- $702,000
- 75th percentile
- $897,000
- 95th percentile
- $1,267,000
- Mean
- $753,000
Above the median — the distribution is right-skewed.
The middle answer is $702,000 and the plausible range spans $402,000 to $1,267,000. Reporting only the mean would have been the least representative single number available.
Check yourself
In the standard simulation the mean ending value is $753,000 and the median is $702,000. Why is the mean higher?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.