A thousand futures in one chart: reading a Monte Carlo simulation without fooling yourself
4 min read by Opthest
Nobody knows the return of the next twenty years — and any tool that hands you one as a single number is lying. A Monte Carlo simulation starts from the opposite admission: we don’t know which future we’ll get, but we can generate thousands of plausible ones and watch how they spread. The result isn’t a line — it’s a fan. And a fan is read in a way that instinct, trained on forecasts, almost always gets wrong. Here are the right questions.
Why a fan and not a line?
Because a single path would be a lie dressed up as a chart. A simulation draws, year after year, random returns consistent with the portfolio’s expected return, volatility and correlations, and compounds them out to the horizon. Then it repeats the whole thing thousands of times — serious practice is ten thousand or more — producing thousands of different stories. The fan is all of them at once: narrow at the start, where chance has had little time to diverge, and steadily wider to the right, because uncertainty accumulates. That trumpet shape is the message: the future isn’t a point, it’s a widening interval.
Is that line down the middle the “predicted” result?
No — and this is the most common mistake. The median line is the 50th percentile: half the scenarios finish above it, half below. It is not a promise, not the “base case” to count on — it’s simply where the deck cuts in half. Anyone planning with their head looks elsewhere: at the 25th or 10th percentile, the unlucky-but-far-from-impossible scenarios. The useful question isn’t “what will I have, on average?” but “if things go badly one time in ten, where do I land — and can I live with it?”. It’s the same discipline as the math of recovery: you design from the downside, not from the average.
I re-run it and get different numbers. Is it broken?
No — it’s working exactly as it should. Monte Carlo is random sampling: two runs of ten thousand paths will give a slightly different median, a tail a little longer or shorter. What does not change, when the count is high enough, is the shape — the width of the fan, the order of magnitude of the percentiles. If instead the results lurch visibly from one run to the next, you simply have too few paths: below a thousand or so the extreme metrics turn unstable and the chart stops saying anything reliable. Precision is bought with the number of simulations, not with luck.
What if the future doesn’t look like the past?
Here is the real limit, and it’s only honest to name it. A simulation is worth exactly as much as the assumptions you feed it: nudge the expected return or volatility by a point and the fan shifts. Worse, the classic model draws returns from a bell curve, which understates extremes. Markets have fat tails — over roughly ninety years the U.S. index has had years below −30% and years above +50% more often than a Gaussian predicts. Translation: the “official” fan tends to be too narrow on both catastrophes and windfalls. Serious simulations know this and stress it — fatter tails, real historical sequences, bad runs placed at the start — precisely because the order in which returns arrive, not just their average, decides a plan’s fate.
So what’s it for, if it predicts nothing?
It turns uncertainty from a shapeless dread into something legible. It doesn’t tell you what will happen; it tells you how exposed you are to what might — the margin between a plan and the edge of the cliff, how much changes if you add a hundred a month, shorten the horizon, carry more risk. It’s a tool to interrogate a choice, not to receive one ready-made. It is not a recommendation about what to buy, and no percentile is a guarantee: the decision, and the uncertainty you choose to bear, remain yours.
A Monte Carlo simulation isn’t a crystal ball — it’s a map of how rough the road can get. It doesn’t tell you where you’ll arrive; it tells you how close to the edge you’re driving.