Monte Carlo vs Historical Retirement Simulation
Quick answer: A historical simulation takes the plan you describe and runs it through each real stretch of past years, one start year at a time. A Monte Carlo simulation instead draws thousands of random return sequences that share the statistical shape of the past. Both are models of the same data, and both can be wrong in different ways. On one example plan, a $40,000 yearly withdrawal from $1,000,000 for 30 years, the replay of every start year since 1928 lasted in 94% of the windows, and the Monte Carlo run on the same dataset lasted in 92% of its paths.
You can see the random-draw side of this in the Monte Carlo simulation retirement calculator, which uses the same dataset described below.
Education, not financial advice. This page explains a method and shows what a model produced from stated assumptions. It does not tell you what to buy, sell, save or spend. For your own situation, ask a qualified professional.
Two ways to ask the same question
Imagine you want to know whether a retirement plan could have survived the past. There are two honest ways to go about it.
The first is to take history literally. Pick a start year, say 1950, apply that year's real stock and bond returns, then the next year's, and so on until the plan's horizon ends. Then do it again from 1951, and again from 1952. Each run is a real, consecutive stretch of years, and the result is the share of those stretches in which the money lasted. People usually call this a historical simulation or a backtest. A replay is the plainest name for it.
The second is to treat the past as a source of ingredients and not a script. You measure how large a typical year's return was, how much it varied, and how stocks and bonds moved relative to each other. Then you let a computer generate many new sequences with those same properties, run the plan through each one, and count. That is Monte Carlo. If the idea is new to you, what a Monte Carlo simulation is walks through the steps.
Neither is a prediction. Both answer "what would the plan have done under these inputs?", and they differ in what the inputs are: real years in a real order for the replay, and invented years with real statistics for the simulation.
What a replay does well
A replay keeps things the simulation has to guess at. Bad years in history came in clusters, good years came in clusters, and stocks and bonds sometimes moved together and sometimes apart. All of that is in the data in its true order, so a replay inherits it without anyone having to model it.
It is also easy to explain and hard to argue with. When a replay says that a plan ran out of money in a particular window, you can name the start year and look at what happened. That concreteness is its great virtue.
What a replay cannot do
A replay can only show you what happened. The dataset this site uses, Aswath Damodaran's annual returns workbook from NYU Stern, runs from 1928 through 2025, which is 98 years. Fitting a 30-year retirement into that range gives 69 start years at most, and no start year later than 1996, because later windows would run past the end of the data.
Those windows overlap heavily. A window that starts in one year shares 29 of its 30 years with the window that starts the year after. The 69 windows are therefore not 69 independent trials. In a span of 98 years there is room for only about three 30-year retirements that do not overlap, and the dataset's own period is one short chapter of American market history. A replay cannot tell you what would have happened under a sequence that never occurred, such as a bad decade that started a few years later than the bad decade that did occur.
A replay is also sensitive to which years you include. Restrict it to windows that begin in 1971 or later, matching the 55 years behind this calculator's default assumptions, and the sample shrinks to 26 windows.
What Monte Carlo does well, and what it assumes
A simulation can generate far more sequences than history holds, including orderings that never happened. That helps with a question a replay handles poorly: how sensitive is the result to the order of returns? On this site, the 5,000 paths in a default run each draw a different order, and the page on sequence of returns risk shows why that order matters.
It also lets you change an assumption and see the effect at once. Lower the average stock return by a point, widen the spread of returns, or shift the mix, and the whole result updates. A replay has no knob for "what if the future average is a point lower than the past?" because the average is whatever the data says.
But a simulation pays for that flexibility with assumptions of its own. This model draws each year's returns from a lognormal distribution fitted to the average, spread and correlations of the dataset, and it draws each year separately from the previous one. If real markets tend to show runs of weak years, the model will understate them. If real returns have fatter tails than the fitted shape, it will understate the extremes. The methodology page lists these choices. The line between the two approaches is thus not "real vs fake". A replay trusts the data's order and a simulation trusts the data's summary statistics.
Same data, both ways
The cleanest comparison holds the data and the plan fixed, then changes only the method. Here is the plan, used as a hypothetical example: a 60/40 mix of stocks and bonds, a starting balance of $1,000,000, and $40,000 a year in today's dollars held flat in real terms for 30 years, with each year's withdrawal taken at the start of the year. Withdrawing 4 percent of the starting balance and then keeping its buying power steady is the structure behind the 4% rule, and that page gives the background.
The replay result: of 69 windows that begin in 1928 or later, 65 lasted the full 30 years, which is 94%. The windows that failed began in 1965, 1966, 1968, 1969. All four are clustered within a five-year stretch, and because neighbouring windows share most of their years, they are best read as one rough period seen from four starting points, not four unrelated failures. The worst of them, in the sense that its money ran out soonest, started in 1966.
The replay result for windows beginning in 1971 or later: 26 of 26 lasted, or 100%, with failing start years of none.
The Monte Carlo result on the same plan, with 5,000 paths: under the default assumptions, which come from 1971 to 2025 real returns, it lasted in 95% of the paths. Under the longer 1928 to 2025 assumptions, it lasted in 92%.
| Method | Sample | Result | Share that lasted | Failing start years |
|---|---|---|---|---|
| Historical replay, every 30-year window from 1928 | 69 windows | 65 lasted | 94% | 1965, 1966, 1968, 1969 |
| Historical replay, windows starting 1971 or later | 26 windows | 26 lasted | 100% | none |
| Monte Carlo, 1971–2025 assumptions | 5,000 trials | 95% | not applicable | |
| Monte Carlo, 1928–2025 assumptions | 5,000 trials | 92% | not applicable |
What this number leaves out. It comes from a model with the assumptions shown, in annual steps and after-inflation returns. It does not model taxes, health or long-term care costs, inflation that differs from the model, or how you would act in a bad year. See what a Monte Carlo simulation cannot see.
How to read the gap
The two methods land within a few points of each other here. The 1971-and-later replay reads 100% against the simulation's 95%. The all-windows replay reads 94% against 92%. Those differences are small enough that they could come from several places at once, and the data cannot say which.
Part of the gap is just the random-draw noise: with a fixed seed and 5,000 paths, the same default scenario moves within a narrow band when the seed changes, as the page on the good Monte Carlo success rate explains. Part of it is that the replay tests only the years that happened, whereas the simulation also tests orderings that did not, including some worse ones. And part is the fitted shape: a fitted bell curve of returns is smoother than the actual set of 55 or 98 numbers behind it.
Notice the direction. The replay confined to 1971 and later is the only figure above that reads as clean. A narrow window of history can look perfect because it contains no failing start, and that tells you about the sample as much as about the plan. A Monte Carlo score of 95% on the same years leaves room for the bad openings the sample happened not to contain.
Other tools that replay history
Free tools that replay history exist; FIREcalc and cFIREsim are two names that come up often, and we have not reviewed them, so this page says nothing about how they work or how their results compare with ours. If you try one, check the same things you would check anywhere: which years of data it uses, whether returns are real or nominal, how it treats taxes and fees, and how it defines success. The page on how to pick a Monte Carlo retirement calculator turns those into a ten-point list.
Choosing between them, or using both
Because each has a blind spot the other does not, they tend to be used together. A replay is a sanity check: if a simulation says a plan is nearly certain to last and the replay shows several real failing start years, one of the two is telling you something about the inputs. A simulation is a stress test: if a replay shows no failures but the simulation shows a meaningful share, the simulation is asking what happens when the order is less friendly than the sample.
When the two disagree a lot, the most useful move is usually to find out why, not to pick whichever number you prefer. Common causes include a different dataset, a different definition of success, a replay that uses nominal returns while the simulation uses real ones, or different treatment of withdrawals, like taking them at the start of the year in one and at the end in the other. A model whose assumptions are on screen makes that search shorter, which is part of why the retirement Monte Carlo calculator lists its means, spreads and correlations beside every result.
What this can't tell you
This page can't tell you which method is right for your situation, or whether your own retirement would have survived any start year. Our replay is a simple one: a fixed mix, real returns, a flat real withdrawal, no taxes or costs, and a single dataset of annual returns. A replay built differently, from monthly data or a different country, would produce different counts. We also cannot tell you how a different tool's replay would look, because we have not looked. And nothing here says that a score near the ones above means a plan will hold; both numbers describe the past and a model of it.
Questions readers ask
Is a historical simulation more realistic than Monte Carlo?
It is more literal, which is not always the same as more realistic. A replay keeps real clusters of good and bad years, but it can only show the few sequences that occurred, and overlapping windows make the sample look larger than it is. A simulation is flexible, but it rests on fitted assumptions.
Why do overlapping windows matter?
A window starting one year later shares nearly all of its years with the one before, so their results move together. Sixty-nine windows therefore carry far less independent information than sixty-nine separate trials would. Treat the historical success rate as a rough summary of a few distinct periods, not as a precise percentage.
Can both methods give a high score and still be misleading?
Yes. If both use the same dataset, they share its limits: a small number of years, one country, annual steps and real returns. Agreement between them shows that the arithmetic is consistent, which is useful, but it does not show that the future will resemble the data.
Which one does this calculator use?
The calculator on the home page is a Monte Carlo model. The historical replay figures on this page and the page about the 4% rule were computed from the same dataset for comparison, and they are fixed examples, not a feature of the calculator.