The 4% Rule vs Monte Carlo Simulation
Quick answer: The 4% rule is a rule of thumb that grew out of two historical studies of how long a portfolio lasted when a fixed amount, raised each year for inflation, was withdrawn from it. A Monte Carlo model can rerun the same arithmetic over thousands of simulated return sequences. Run on this site's default return assumptions, which use 1971 to 2025 real returns and a mix of 60/40 stocks and bonds, a 30-year plan that withdraws the 4% rule's amount ended with money in about 95% of the simulated paths. That is a description of the model, not a statement about your retirement.
If you want to try other rates yourself, the Monte Carlo simulation retirement calculator on the home page takes a spending figure, a mix and a horizon and shows the result in the same way. The allocation changes described under "what changes the result most" further down are easy to try in the free Monte Carlo retirement calculator too.
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.
Where the rule came from
The rule of thumb is usually summed up in one sentence: in the first year of retirement, take 4 percent of the starting portfolio, then raise that dollar amount each year with inflation. The shorthand hides two separate pieces of research, and it helps to look at what each of them actually said.
Bengen, 1994 (primary reading)
The first is an article by William Bengen in the Journal of Financial Planning. We read the Financial Planning Association's 2004 reprint of the October 1994 piece, so that is a reprint and not the original typeset issue. Everything below attributed to it is as the reprint's text reads.
Bengen says he relied on actual historical performance of investments and inflation from the Ibbotson 1992 Yearbook. His first illustrative retirement date was 1 January 1926, with later clients starting each following year. The text we read does not state the last year of data used, so we do not print one. The illustration in his first figure used a mix of half intermediate-term Treasury notes and half common stocks, which he described as an arbitrary mix chosen for illustration. Elsewhere he tested five mixes against first-year withdrawals of 1 to 8 percent, assuming continual rebalancing.
The method is simple to state. The first-year withdrawal is a percentage of the starting portfolio, and later withdrawals are the prior year's amount adjusted for inflation. His charts cap portfolio life at 50 years, and his planning test asks for a minimum of 30 years. In the 50/50 test, a 3 percent first-year withdrawal never gave less than 50 years of portfolio life. A 4 percent first-year withdrawal was not exhausted before 33 years in any past case and lasted 50 years or more in most. A 4.25 percent withdrawal could exhaust a portfolio in as little as 28 years, and at 5 percent the effects become pronounced, with some late-1960s and early-1970s starters having only about 20 years.
What did he suggest in practice? The reprint's practical rule for a client aged 60 to 65 is "about 4 percent". He recommends 50 to 75 percent in stocks, treats the work as applying to a tax-deferred account, and says that a taxable account might change the conclusion. Notice what the primary text does not contain: the rule is not stated as a law, it is one author's reading of past American returns.
The Trinity study, 1998 (primary reading)
The second piece is a February 1998 article in the AAII Journal by Cooley, Hubbard and Walz, which people usually call the Trinity study. We read the article's text through a web reading tool, not from a PDF, and two readings agreed on the points below.
The study says its results rest on annual stock and bond returns from 1926 to 1995, with a second view that starts in 1946. It tested five stock and bond mixes, from all stocks to all bonds, payout periods of 15, 20, 25 and 30 years, and annual withdrawal rates from 3 to 12 percent. It defines a "portfolio success rate" as the share of past payout periods that a portfolio supported. The article text says 3 percent and 4 percent withdrawal rates are extremely unlikely to exhaust any stock and bond portfolio over the payout periods in its main table. It adds that a 5 percent rate still gives reasonably high success rates in the inflation-adjusted case.
The study is also candid about limits: it did not adjust for taxes or transaction costs, and it says it is unknown whether the full-period or the post-war table is more representative of the future. It adds that adjusting withdrawals for inflation sharply lowers many success rates.
A word about numbers. The exact 30-year success cells for the 4 and 5 percent rates sit in a table that was an image on the page, and we could not read it, so this page prints no figure from that table. One secondary source, a 2008 AAII article by Reichenstein, reports that a 50/50 portfolio at a 4 percent withdrawal survived 95 percent of the 30-year periods in 1926 to 1995. That is a second-hand report of a figure, and we label it that way. A later paper by Guyton and Klinger also summarizes the two earlier pieces: Bengen finding rates between 4.1 and 4.58 percent depending on the stock mix, and the Trinity work finding a 4.0 percent rate nearly always successful over 30-year periods between 1926 and 1995. Again, that is a secondary description.
What the rule quietly assumes
Seen side by side, the two studies share a set of assumptions that are easy to forget when the rule is quoted in a sentence.
- A fixed schedule. The withdrawal is set on day one and then moves only with inflation. It does not respond to the portfolio. Real people tend to spend differently as markets move and as life changes.
- A fixed horizon. Both studies used a set number of payout years. Thirty years is a common choice, and a retirement that starts at 55 or runs past 95 asks a different question.
- A fixed mix. A steady allocation, rebalanced continually in Bengen's tests, is easier to model than the way people actually hold and adjust their money.
- One country's history. Both used American returns from the twentieth century, a period that included a few very good decades.
- No taxes or costs. Both treat the money as a single pot, and the Trinity article says outright that it ignored taxes and transaction costs.
- Success means not running out. Neither tells you how much would be left, or what the spending felt like on the way.
None of these is a flaw, since every study has to hold something still. They are a reminder that the "4 percent" in the rule of thumb is the output of a particular design, and that moving any of the pieces moves the answer.
The same rule in a Monte Carlo model
A Monte Carlo model keeps the rule's arithmetic and changes what feeds it. Instead of replaying the American years one after another, it draws many random sequences of yearly returns that match the average, spread and relationships of stocks and bonds in a dataset. If the idea of random draws is new, what a Monte Carlo simulation is walks through it step by step.
Here is the comparison this site's calculator can make. The example below is a $1,000,000 portfolio, a 60/40 mix of stocks and bonds, and spending of $40,000 a year in today's dollars, held for 30 years. The returns are real, meaning after inflation, so a flat $40,000 stands for steady buying power.
Under the default assumptions, which come from the Damodaran annual dataset covering 1971 through 2025 (55 years), the plan lasted all 30 years in about 95% of the simulated paths. Swap in the longer 1928 to 2025 dataset (98 years) and the same plan lasted in about 92%. The two numbers differ because the longer dataset contains a different set of years, with a different average and a wider spread, and the model is only as steady as the data it is given. Both come from a seeded run of 5,000 paths, so a different seed would move them by a point or two.
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 rate and horizon move the result
The table below keeps the 60/40 mix and the example starting balance of $1,000,000, and varies the withdrawal rate and the number of years. All of it is under the default assumptions, 1971 to 2025 real returns.
| Starting rate | 20 years | 25 years | 30 years | 35 years | 40 years |
|---|---|---|---|---|---|
| 3% ($30,000 a year) | 100% | 100% | 99% | 99% | 98% |
| 3.5% ($35,000 a year) | 100% | 99% | 98% | 96% | 94% |
| 4% ($40,000 a year) | 100% | 98% | 95% | 91% | 87% |
| 4.5% ($45,000 a year) | 99% | 95% | 89% | 83% | 78% |
| 5% ($50,000 a year) | 96% | 89% | 80% | 73% | 67% |
| 6% ($60,000 a year) | 86% | 71% | 59% | 50% | 44% |
In this example, reading across a row, the lesson is how much the horizon matters. At a 4.0 percent rate on that balance, the plan lasted in 100% of the paths over 20 years, 95% over 30 years and 87% over 40 years. Reading down a column shows the rate effect. For 30 years, a 3.5 percent rate ($35,000 a year on that balance) gave 98%, a 4.5 percent rate ($45,000) gave 89%, a 5.0 percent rate ($50,000) gave 80%, and a 6.0 percent rate ($60,000) gave 59%. The score falls slowly at first and then faster.
This is the point where a one-line rule and a simulation part ways in how they talk. The rule gives one rate, and the simulation gives a surface: for any rate and any horizon, a number. You may read that surface differently from the way the rule's authors did, and that is fine.
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.
Historical windows against random draws
Both data sets here are the same annual returns, so the comparison is fair in one respect: only the method differs. Using the same dataset, the same 60/40 mix, the same $1,000,000 and the same $40,000 held flat in real terms, as an example of the method, we replayed every 30-year window that began in 1928 or later and ended by 2025. That gave 69 windows, and 65 of them lasted the full 30 years, a historical success rate of 94%. The windows that did not last began in 1965, 1966, 1968, 1969.
Limit the replay to windows that start in 1971 or later, matching the years behind the default assumptions, and there are 26 windows, with 26 lasting, or 100%. The failing start years are none.
| 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 |
Notice how close the numbers sit, and also how the narrower sample reads as perfect. A historical replay and a Monte Carlo run answering the same question gave 94% and 92% for the long dataset, and 100% and 95% for the default one. The replay can say nothing about a path that never happened, and the simulation can say nothing it was not told about the relationship between one year and the next. Overlapping windows also make the replay look more solid than it is: 69 windows are not 69 independent trials, because neighbouring windows share most of their years. The page on Monte Carlo vs historical simulation takes up that comparison in more detail.
The worst start in this replay was 1966, the year whose 30-year window ran out of money soonest. If you want to see what a weak opening decade does to a plan, the page on sequence of returns risk uses that same year and a made-up example side by side.
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.
What changes the result most
Several choices move the Monte Carlo answer by more than people expect.
The stock share. Holding the example fixed ($40,000 a year, 30 years, the default dataset), the plan lasted in 89% of paths with 30 percent in stocks and 70 percent in bonds, 95% with 60/40, 95% with 80/20 and 94% with all stocks. The curve is flat near the middle. The lowest-stock mix did worse in this dataset, where bonds averaged 2.5% a year after inflation against 8.4% for stocks, which is a statement about these years and not a law.
The years in the dataset. As shown above, the long dataset and the default one are three points apart for the same plan.
The horizon. For example, going from 30 to 40 years cut the 4.0 percent row noticeably, while the 3.0 percent row hardly moved. How long you plan for is one of the largest levers, and the page on how long your money will last in retirement looks at that directly.
How the spending is defined. The rule holds spending flat in real terms. A plan where spending falls with age, or where Social Security covers part of it, is a different plan, and a withdrawal rate drawn from the portfolio alone will describe it poorly. The safe withdrawal rate page looks at what happens when the withdrawal responds to the market.
How to use the rule without over-reading it
As a rule of thumb, 4 percent works as a unit of measure. It is a convenient way to ask "what would it take?" because dividing a yearly spending number by 0.04 gives a rough portfolio size to compare against. As a unit, it is useful in conversation. As a prediction, it is far weaker.
When you meet the figure in a headline or on a forum, it can be worth checking five things: which data it came from, what horizon it assumed, whether taxes were counted, whether withdrawals were fixed or flexible, and what counted as success. When a simulation produces a different number, the cause is usually one of those five, not an error.
And when a calculator gives a success rate near the one the rule suggests, the good Monte Carlo success rate page covers what that kind of number does and does not mean, without telling you what to aim for.
What this can't tell you
This page can't tell you what withdrawal rate fits your life. It cannot tell you whether the next thirty years will look more like the years in either dataset, or whether the lowest-return decades ahead will be milder or harsher than anything on record. It has no view of your taxes, your health costs, the other income you may have, or how you would respond if markets fell early in your retirement. The historical studies it cites are close to thirty years old, and we did not look for later work that might have revised them. The results above come from a model with annual steps and real returns, and a different model, even on the same data, would give different numbers.
Questions readers ask
Is the 4% rule the same as a 4 percent success rate?
No, and for example the two can differ a lot. The rule names a starting withdrawal, 4 percent of the opening balance, which is then raised with inflation. A success rate is a separate measure: the share of tested periods or simulated paths in which the money lasted. The two are linked only through the assumptions behind a given study or model.
Why does the Monte Carlo result differ from the historical result?
They use different procedures. A replay runs each real 30-year window once, in order. A simulation draws thousands of random sequences from the dataset's averages and spreads. Their answers land close together here, but the overlap in the historical windows and the independence of the random draws push them apart in small ways.
Did the Trinity study say 4 percent always worked?
Its text says 3 and 4 percent rates were extremely unlikely to exhaust the portfolios in its main table. It did not claim certainty, it said it ignored taxes and costs, and it said it was unknown which period best represents the future. A second-hand report puts one 30-year cell at 95 percent.
Does a longer retirement need a lower rate?
In this model, yes, as the example table shows: at the same rate, more years mean a lower share of paths that last. The table above shows the 4.0 percent row falling as the horizon grows. How much lower depends on the dataset and the mix, and the model cannot say what fits any one person's horizon.