Monte Carlo simulation
A Monte Carlo simulation generates thousands of possible paths for a portfolio, each with random returns consistent with its historical volatility and correlations. Instead of a single answer it returns a distribution of outcomes with their probabilities, which lets you talk about scenarios rather than predictions. It is only as good as the assumptions feeding it.
How it is calculated
There is no closed formula: it is brute force. You take the portfolio's past behaviour — average return and volatility —, simulate thousands of possible paths over the horizon you care about, and sort the outcomes. With 10,000 one-year simulations, the outcome ranked 500th from the bottom is the 5th percentile: 5 % of scenarios sit below it. If that value is −18 %, the reading is that in 95 % of the simulated paths the portfolio does not fall more than 18 % over the year. The number of simulations matters less than it seems; the input assumptions matter enormously.
The figures in the example are invented and rounded so the arithmetic can be redone by hand. They are not data from any real company.
What it is NOT
It is not a prediction. It is a way of showing the range of outcomes that follow from a set of assumptions, and it is worth no more than those assumptions. If returns are assumed to follow a normal bell curve, the simulation will understate large drawdowns, because markets produce them more often than that curve allows. Ten thousand paths drawn on a wrong hypothesis are ten thousand wrong paths.
See also
See it on real data
Celsmar computes this from the accounts companies file with their regulator, and shows which line every figure comes from. Free to start, no card.
Definition for informational purposes. It is not financial advice nor a recommendation to buy or sell.