Monte Carlo vs historical simulation for retirement
Monte Carlo invents thousands of futures by drawing returns at random from a distribution you specify; historical simulation replays sequences that actually happened, in the order they happened. One gives you a large sample of futures that never occurred; the other gives a small sample of futures that did.
Both exist to answer the same question a single projected line cannot: not "when do I reach my number?" but "how often does the money last once I start spending it?"
Why either method exists
A deterministic projection applies one average return every year. That is adequate while you are saving, because you are adding money and the average is roughly what you get. It becomes misleading the moment you start withdrawing, because the order of returns starts to matter: selling during a fall permanently removes shares that would otherwise have recovered. Two retirements with the same average return and the same spending can end thirty years apart on that basis alone.
Simulation exists to expose that ordering effect. The two families differ only in where they get their orderings from.
The two methods, side by side
| Monte Carlo | Historical simulation | |
|---|---|---|
| Where returns come from | Drawn at random from a distribution you set (typically a mean and a standard deviation) | Real recorded market returns, replayed in their actual order |
| Sample size | As many as you like — thousands of runs | Limited by history; overlapping start years, so runs are not independent |
| Handles ordering | Yes, but randomly generated ordering | Yes, and the ordering genuinely occurred |
| Main weakness | Inherits your distribution: a normal curve understates extremes and treats each year as independent | One economic history, heavily overlapping — and the future need not resemble it |
| Best at | Exploring a wide space of possibilities, stress-testing spending rules | Asking "would this plan have survived the actual bad periods?" |
The weakness people underestimate in Monte Carlo
A standard Monte Carlo draws each year independently from a normal distribution. Real markets break both halves of that:
- Extremes are more common than a normal curve predicts. Crashes of a size the model treats as vanishingly rare have happened repeatedly within a century.
- Years are not independent. Bad years cluster, and long stretches of poor real returns are precisely the pattern that ruins a withdrawal plan. Independent draws scatter the bad years politely across the horizon, which is the friendliest possible arrangement for a retiree.
The consequence is not that Monte Carlo is useless — it is that a 90% success rate from a normal model is a statement about that model, and the real world has a slightly fatter left tail than it assumes.
The weakness people underestimate in historical replay
Replaying real data sounds unimpeachable, and it has a genuine advantage: returns, inflation and their correlation all move together exactly as they did. But the sample is much smaller than it looks. A century of data yields only a handful of genuinely independent thirty-year retirements — the rest overlap and share most of their years. And it is one country's economic history, over a period that included an unusually favourable stretch for its equities.
What a success rate does not tell you
"90% success" means 90% of the simulated sequences did not hit zero before the horizon ended. It is not the probability that your retirement will work. It is conditional on the assumptions, the dataset or distribution, the spending rule and the horizon length — and it says nothing about how the failures failed. A plan that fails at year 29 of 30 is not the same as one that fails at year 8, and a single percentage hides that difference completely.
It also assumes you would carry on spending unchanged while your portfolio halved, which almost nobody does. Flexible-spending rules routinely lift a mediocre success rate into a comfortable one — not because the markets improved, but because the model stopped assuming you would ignore them.
So which should you use?
- Use a deterministic projection to find your date. That is what it is good at.
- Use simulation to test the retirement, not the accumulation. The question is survival, not arrival.
- Run both methods if the tool offers them, and treat a large gap as information. If one says 95% and the other 70%, the honest reading is that the answer is sensitive to method — which is itself worth knowing.
- Check what the "historical" data actually is. Tools differ enormously here, and the label alone tells you nothing.
What Ember does, stated plainly
Ember runs a Gaussian Monte Carlo — returns drawn from a normal distribution around your expected real return, at a volatility you set — and reports a success rate with the caveats above.
It also offers a second mode that replays a fixed return series in order, so you can see the ordering effect directly. That series is illustrative: it is not real market data, and Ember does not present it as evidence about what any market did. Tools built on real recorded datasets — the well-known free simulators use actual long-run US series — do something Ember currently does not, and if that is what you need, use them alongside this. Replacing the illustrative series with a real, versioned dataset is on Ember's roadmap, and this page will change the day it lands.
Saying so costs a marketing line and buys the only thing that matters in a planning tool: that when it does tell you something, you can believe it.
See both, on your own numbers
Ember shows the projection and the simulation side by side, with every assumption editable.
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