Monte Carlo Retirement Calculator

A retirement projection that uses one average return gives one answer, and that answer hides the thing most likely to hurt a retiree: the order in which good and bad years arrive. A Monte Carlo simulation replaces the single average with thousands of possible market histories. Each history, or path, is a run of yearly returns drawn at random from a distribution you describe with two numbers, an expected return and a volatility. The plan is run through every path, and the result is a count: in how many paths did the money pay the spending you asked for, every year, to the end?

This calculator runs 10,000 paths. Everything is in today’s dollars, so returns are after inflation and spending keeps its buying power without an inflation input. Each year the model takes that year’s spending, subtracts any Social Security or pension that has started, withdraws the rest at the start of the year, and grows what remains by that year’s return less the fee. A path fails in the first year the balance cannot cover the withdrawal. The share of paths that never fail is the success rate.

It is a single-purpose tool. For a steady-return projection, a worst-years-first stress test and the question of which account to draw from, use the retirement withdrawal calculator. If you are still saving and want to know whether the balance will be there on day one, start with the retirement savings calculator or the guide to how much you need to retire.

Illustrative example: the people and figures below are hypothetical, not real clients. Numbers are calculated from the stated assumptions.

The calculator opens on a $1,000,000 portfolio, $40,000 of spending a year (4% of the starting balance), a 30-year retirement and no other income. The portfolio is 60% stocks, 35% bonds and 5% cash, which under the long-run assumptions described below has an expected real return of 5.8% a year with volatility of 12.3%, less a fee of 0.25%.

Start with the projection most people have seen. If the portfolio earned exactly 5.8% above inflation every year, the plan would never be in doubt: after 30 years of withdrawals it would hold $1,966,414 in today’s dollars. Now let the returns vary. Across 10,000 simulated paths, 90.5% paid the full $40,000 every year and 947 ran short. Among the paths that ran short, the median ran out in year 26, and the earliest in year 13.

The median path ends with $1,369,844, well under the steady-return figure. That gap is not bad luck. Volatility lowers the rate at which money compounds: a portfolio that averages 5.8% a year with 12.3% volatility grows at a median of about 4.8% a year after the fee. An average-return projection quietly uses the higher number.

Read across the last row. One path in ten ends above $4,826,952, more than 4 times the starting balance in real terms. One in ten ends below $17,342. The same plan, the same assumptions, and an outcome anywhere from an empty account to a large estate.

The chart of balances by year shows five lines: the 10th, 25th, 50th, 75th and 90th percentiles. Each point is a ranking of all 10,000 paths in that one year. The 10th-percentile line at year 20 is the balance that 10% of paths were below at that moment; it is not the history of any single unlucky path. Real paths cross the lines constantly, falling below the 25th percentile after a bad stretch and climbing back.

Three things are worth looking for:

• The width. The fan widens every year because good and bad returns compound. In the example, the middle half of paths spans $791,776 to $1,457,084 after 10 years and $499,685 to $2,784,105 after 30.
• The direction of the median. A median that rises in today’s dollars, as it does here, means the typical path is spending less than the portfolio earns. A median that slopes down means the plan is designed to consume capital, which can be intended.
• Where the lower lines reach zero. Paths that have run out are counted as $0, so when the failure rate passes 10% the 10th-percentile line sits on the axis. In the example 9.5% of paths fail, so that line ends at $17,342.

The percentile lines are in today’s dollars. The account statements along any of these paths would show larger numbers, because they include inflation.

There is no agreed threshold. Published research tends to work with a target and solve for spending: Morningstar’s annual study, for example, looks for the highest starting withdrawal that lasts 30 years in 90% of its simulations, and for 2026 puts it at 3.9%. Targets between about 80% and 95% are commonly quoted. The right number for a household depends on how much of the spending is optional and what else stands behind it.

Pushing the rate toward 100% has a price. In the example, cutting spending from $40,000 to $30,000 raises the success rate from 90.5% to 98.5%. It also raises the median ending balance from $1,369,844 to $2,076,616. To protect against the worst 9.5% of paths, the household spends $10,000 less in every year of every path, including the large majority in which the money was never at risk. A very high success rate is, for most paths, a plan to leave a lot unspent.

A low rate is not automatically a broken plan either. “Failure” in the model means the portfolio could not pay one year’s spending in full with no change of course in the years before. A household that would trim travel after a poor decade is not running the plan the constant-spending rule describes. That is what the guardrail setting is for.

The table falls slowly at first and then quickly: half a point of extra spending costs 2.8 points of success between 3% and 3.5%, and 11.8 points between 5% and 5.5%.

Sequence-of-returns risk is the risk that poor returns arrive early, while the portfolio is at its largest and withdrawals have barely begun. Money withdrawn after a fall is taken out at low prices and is not there for the recovery. The same poor years late in retirement do far less damage, because less depends on them.

The simulation makes this measurable. Sort the 10,000 example paths by their compound return over the first 10 years and split them into five equal groups. Every group faces the same assumptions; they differ only in luck during the opening decade.

In the worst fifth, where the first decade returned a median of 0.2% a year after inflation, only 58.6% of paths lasted. In the best fifth, 100% did. Of the plan’s 947 failures, 87% come from the bottom group. A retiree cannot choose the decade they retire into, which is why the practical responses to this risk are about what to do if the first years go badly, not about predicting them.

A success rate looks precise and is not. It is a restatement of the return and volatility you entered, and modest changes to either move it a long way. For the example plan:

One percentage point less return takes the plan from 90.5% to 82.3%; two points less takes it to 70.3%. Nobody knows the next 30 years’ real return to within a point. The honest way to use the tool is to run a cautious case and a hopeful one and read the result as a range.

The mix matters in both directions

Holding fewer stocks lowers volatility, and it also lowers the return that funds the withdrawals. Under the default assumptions the second effect wins once the stock share gets low:

This table inherits every limit of the model, and one in particular: the stock assumption is the average of an unusually good century for US shares. It shows how the arithmetic works. It does not show which mix suits a particular household.

The 4% rule comes from historical backtesting. William Bengen’s 1994 study, and the Trinity study that followed in 1998, took the actual sequence of US returns and asked what starting withdrawal, raised with inflation each year, would have survived every 30-year retirement on record. The answer was about 4% of the starting balance for portfolios holding roughly half to three-quarters in stocks.

Backtesting uses returns that really happened, in the order they happened, so it keeps features a simple simulation lacks: crashes followed by recoveries, long inflationary stretches, the way stocks and bonds actually moved together. Its weakness is the size of the sample. A century of data holds only about three 30-year periods that do not overlap, and all of them come from one country whose markets did unusually well.

Monte Carlo trades realism for breadth. It can produce 10,000 retirements, including sequences worse than anything in the record, and it lets you change the assumptions. But every path comes from the distribution you chose. If the expected return is too high, all 10,000 paths are too rosy together.

The two approaches land close to each other here because this calculator’s defaults are built from the same history: a 4% withdrawal for 30 years succeeds in 90.5% of paths, and would be 92.2% with no fee. Treat the 4% rule as one row of the spending table above, the row that corresponds to one set of assumptions, and not as a law.

Enter the same balance and spending into two Monte Carlo tools and the answers can differ by 20 points or more. Neither is necessarily wrong. The usual reasons, roughly in order of size:

• Return assumptions. Historical averages, a firm’s own forecast and a user-entered figure can differ by two or three points a year. The table above shows what two points do.
• Nominal or real. A 6% return with 3% inflation is about a 2.9% real return. A tool that asks for return and inflation separately is not using the same number as one that asks for a real return.
• Fees and taxes. Some tools deduct them, some assume you already have.
• How returns are generated. Independent draws from a bell curve, draws from a lognormal curve, reshuffled historical years, or models in which bad years make good years more likely all produce different tails.
• What counts as failure and how spending behaves. Running out in the final year, dipping below a floor, or cutting spending along the way are scored differently.
• The number of paths. With 1,000 paths, a rate near 91% carries a sampling margin of about ±1.9 points; with 10,000 it is about ±0.6.

Our own tools illustrate it. The Monte Carlo mode of the retirement withdrawal calculator opens on a 6% return before inflation, 3% inflation and 12% volatility. Put the after-inflation equivalent of those figures into this page, with no fee, and the example plan succeeds in 62.8% of paths instead of 90.5%, close to what that page shows. The plan did not change. The assumed real return fell from 5.8% to 2.9%.

Random sampling is a much smaller effect. The published set of 10,000 paths and five others put the example between 90.1% and 90.5%. This page always uses the same set, so a change in the result always comes from a change in your inputs.

Constant spending is the harshest rule a plan can follow: it withdraws the same real amount in the year after a crash as in the year after a boom. The guardrail option here is deliberately simple. In any year that starts with the portfolio below a set fraction of its starting value, in today’s dollars, spending is cut by a set percentage. When the portfolio is back above the line, full spending returns. The defaults are a 10% cut below 80% of the starting value.

On the example plan, that rule lifts the success rate from 90.5% to 94.2%. At $50,000 of spending (5%), it lifts it from 72.7% to 80.3%, and a 20% cut takes it to 87.5%.

The improvement is paid for in spending, and the simulation shows how often. At 4%, the rule is triggered at least once in 52% of paths, and in those paths the median time at reduced spending is 13 years. At 5% it is triggered in 65% of paths for a median of 16 years. A guardrail does not make a spending level safe. It converts some of the risk of running out into a larger chance of living on less for a long stretch, and the second number deserves as much attention as the first.

Published guardrail methods are more elaborate than this one. They usually raise spending after strong markets as well as cutting it after weak ones, and they set the triggers by the current withdrawal rate. This calculator models the cutting half only.

Income that arrives whatever markets do reduces what the portfolio has to deliver, and that is the amount exposed to sequence risk. The calculator subtracts other income from spending from the year it starts.

Take the same $1,000,000 portfolio with $70,000 of spending. With no other income that is a 7% withdrawal, and 29.7% of paths last. Add a $30,000 Social Security benefit from year 1 and the portfolio only has to find $40,000: the result is the 90.5% of the opening example.

Now suppose that benefit is the amount at a full retirement age of 67, and it is held until 70 instead. Delayed retirement credits add 8% of the full benefit for each year of waiting, for anyone born in 1943 or later, so it becomes $37,200 from year 4. The portfolio carries the full $70,000 for 3 years and $32,800 after that, and 94.0% of paths last. The early years are heavier and the remaining decades lighter. Whether that trade suits a household turns on health, a spouse’s benefit and taxes, none of which this page models; the Social Security break-even calculator works through the filing ages.

In the model, a failed path is abrupt: full spending one year, nothing the next. In the example the median failed path reaches that point in year 26, and the earliest in year 13. But the trouble is visible long before. The paths that fail are overwhelmingly the ones whose first decade went badly, and by year 10 a tenth of all paths hold less than $604,954 of the original $1,000,000 in real terms while still drawing $40,000. That is a withdrawal rate of 6.6% or more on what is left, with 20 years to go.

Few households would watch that happen for fifteen years without acting, which is the main reason a simulated failure rate overstates the chance of actually running out and understates the chance of having to change plans. The adjustments households and their advisers commonly discuss are these. They are described as information about how each one works, not as advice to do any of them.

• Spending cuts. Temporary reductions after poor markets, which is what the guardrail setting approximates. They work best when a meaningful share of the budget is discretionary.
• Delaying Social Security. A larger inflation-adjusted benefit for life lowers the withdrawal the portfolio must sustain in later decades, at the cost of larger withdrawals before it starts.
• Annuitising a floor. Exchanging part of the portfolio for guaranteed lifetime income, so that essential bills do not depend on markets. The income is typically fixed in dollars, so inflation erodes it, and the money is no longer available for other uses or heirs. The annuity payout calculator shows what a lump sum pays out over a set period.
• A cash reserve. Holding a few years of spending in cash, Treasury bills or a CD ladder so that withdrawals need not come from stocks after a fall. A reserve lowers the portfolio’s expected return. This model can only represent it as a larger cash share of a fixed mix, so it will not show any benefit from choosing what to sell.
• Where withdrawals come from. Taxes are outside this model, but the order in which accounts are drawn changes how much of each withdrawal is spendable. See the guide to retirement withdrawal order.