Monte Carlo Probability of Success in Retirement: What It Really Means

This analysis draws on research by Derek Tharp and Justin Fitzpatrick published at Kitces.com, and on Michael Kitces’s writing there on Monte Carlo analysis. We’d recommend reading them in full.

How a Monte Carlo Simulation Turns a Plan Into One Number

The method is named for the casino in Monaco, and it is what the name suggests: a disciplined way of rolling dice many times and counting the results. A retirement simulation starts with the household’s plan, meaning what it owns, how that money is invested, what it intends to spend, and the income it can count on, such as Social Security or a pension. It then needs a model of the markets: an average return for each kind of investment, a measure of how widely returns swing around that average (the standard deviation), how the investments tend to move together, and an assumption for inflation.

One trial. The software takes out the first year’s spending, applies a return drawn at random from that model, and moves on to the next year, repeating until it reaches the end of the plan, often age 95 or later. One pass is one possible retirement.

Thousands of trials. It then repeats the whole process, often 1,000 times, and in some tools as few as 250 or as many as 10,000 or more, each time with a fresh set of random returns. Some trials begin with a strong decade and some with a weak one; some string several bad years together and some never see one.

The count. Every trial in which the money lasted to the end of the plan counts as a success, and the probability of success is the share of trials that succeeded. Some tools set the bar higher, counting a trial as a success only if it also finishes with a target amount left for heirs or charity, which lowers the number for the same plan.

Because the count comes from a finite number of random trials, the number itself carries some noise. In our worked example below, running the identical plan 50 times with 1,000 trials each, and a fresh set of random draws each time, produced results anywhere from 79.9% to 87.5%. With 10,000 trials, 20 reruns landed between 82.6% and 84.3%. With 1,000 trials, a plan that moves from 84% to 82% between two reviews may have changed, or the dice may simply have landed differently.

A Worked Example: What Sits Inside an 83% Plan

To make this concrete, we ran our own simulation for a hypothetical Texas couple, both 65. They have $2,000,000 invested and plan to spend $130,000 a year in today’s dollars, with $50,000 of it coming from Social Security. That leaves $80,000 a year, or 4% of the portfolio, to come from savings, held flat after inflation for 30 years, to age 95. Each year’s withdrawal comes out at the start of the year, and each year’s return, after inflation and fees, is drawn at random from a bell curve with a simple average of 4% (about 3.5% a year compounded) and a standard deviation of 10%, independently of every other year. Social Security rises with inflation, and taxes are left out to keep the arithmetic visible. These are illustrative assumptions for a balanced portfolio, not a forecast and not a recommendation for anyone’s plan.

Of 10,000 simulated retirements, 8,310 paid every year’s spending through age 94, a probability of success of about 83%. The other 1,690, about 17%, ran short. Opening up those two groups shows how much the single number blends together. Of the failures, 149 ran out before 85 and 1,541 ran out between 85 and 95. Of the successes, 2,683 ended with less than $1 million in today’s dollars, 1,993 with between $1 million and $2 million, and 3,634 with more than $2 million, more than the couple started with. In 1,384 of them, the portfolio finished above $4 million, double its starting value after inflation.

What the Number Counts as a Failure

A failure in most simulations means one thing: at some point before the end of the plan, the portfolio could not cover the year’s spending in full. The count does not say when that happened, by how much the household fell short, or what it lived on afterward. Justin Fitzpatrick made the point at Kitces.com in 2021: the failure column lumps a shortfall in the middle of retirement together with one a year or two before the end, and the same failure rate means far less for a household living mostly on Social Security and pensions than for one living mostly on its portfolio.

When. In our example, failures came late. Of the 1,690, about 91% ran short at 85 or later, and more than half, about 56%, at 90 or later; the median failure arrived at 90. A failure at 91 after 26 years of full spending is a very different event from one at 78, the earliest in our example, yet the score counts them the same.

How much. When the portfolio runs dry, Social Security keeps paying. In our example, spending would fall from $130,000 to the $50,000 Social Security provides, a cut of about 62%, which is severe. Now consider a second couple with $1,000,000 invested and $90,000 of Social Security, spending the same $130,000. Their $40,000 a year from savings is also 4% of the portfolio, so under the same assumptions their probability of success is identical, about 83%. But if their portfolio runs dry, spending falls to $90,000, a cut of about 31%. Same number, very different stakes. As Derek Tharp has put it at Kitces.com, the probability of success says nothing about the magnitude of failure, and the share of spending covered by income that does not depend on markets caps how deep a failure can go. That is one reason the Social Security decision, covered in our article on when to claim Social Security, matters for the floor of a plan as well as its total.

What the household did about it. A simulation that counts failures assumes the household kept spending the same amount, year after year, until the money was gone. Real households watching a portfolio shrink rarely behave that way. They trim the travel budget, delay a project, or give a little less for a few years, often well before the account reaches zero. The score treats the household as if it never looked.

What the Number Counts as a Success

The other side of the count gets less attention. Every trial in which the money lasted is a success, whether it finished with a few dollars or a few million. In our example, one in ten successes finished with less than about $307,000, a plan that worked with little to spare. The median success finished with about $1.7 million, and more than four in ten successes ended with more than the couple started with.

Michael Kitces has suggested that the probability of success is better described as a probability of excess, the likelihood of having money left over, because the score makes no distinction between finishing with a dollar and finishing with millions. For a household, that excess has a cost. It is the family trip that stayed on the someday list, the help with a first home that came later than it could have, and the gifts made through an estate rather than during life, when the giver could see what they did. Justin Fitzpatrick has noted at Kitces.com that one could say a 100% probability of success is a 100% risk of underspending. In our experience, spending and giving too little is the more common problem, as we explain in our article on risk-based spending guardrails.

Pushing the number higher is not free. In our example, cutting the withdrawal from $80,000 to $70,000 a year lifts the probability of success from about 83% to about 92%. That is $10,000 a year less spending and giving, every year for 30 years, to buy protection against shortfalls that mostly arrive in the 90s.

Chasing the last few points also means leaning on the least reliable part of the simulation. Tharp has argued that a single score works like a game’s high score, nudging households to push it toward 100% even when that cuts against their goals for spending and giving. And at the very top of the scale, the number rests on a handful of extreme trials. In Fitzpatrick and Tharp’s 2022 tests, the spending a simulation treated as risk free kept falling as trials were added, because more random draws produce more extreme losing streaks, a result they read as an artifact of the method rather than a fact about markets.

The Assumptions Behind the Percentage

A probability of success is only as meaningful as the assumptions underneath it, and small changes in those assumptions move the number more than most people expect. Holding everything else in our example the same:

Return. At a simple average real return of 3.5% instead of 4%, the plan reads about 77%; at 3%, about 69%. At 4.5%, it reads about 88%, and at 5%, about 92%. Each half point of assumed return, a gap well within the range of reasonable disagreement about the future, moves the number by four to eight points in this example.

Volatility. With a standard deviation of 8%, the plan reads about 91%; with 12%, about 76%. Two simulations with the same average return can differ by double digits depending only on how bumpy the ride is assumed to be.

Spending. Raising the withdrawal from $80,000 to $90,000 drops the plan to about 70%. At $100,000, it reads about 56%. The $10,000 between 83% and 70% is less than 8% of this couple’s total budget.

Horizon. Ending the plan at 90 instead of 95 lifts the number to about 93%; extending it to 100 lowers it to about 73%. The same couple, with the same money, gets three different scores depending on how long the plan assumes they will live. We lean toward setting the horizon at a fixed age adjusted for health and family history, and updating it as health changes.

Several other assumptions sit underneath many simulations without much discussion. Many hold inflation at a single fixed rate. We lean toward weighting inflation risk more heavily than one fixed rate implies, though the case on the other side is real: the Federal Reserve targets 2%, and inflation has stayed low for long stretches. Many assume spending stays flat after inflation, while the research we cover in our article on the retirement spending smile finds that real spending tends to fall about 1% a year on average, so for many households a flat assumption builds in a hidden margin, though a budget that is almost all essentials may stay flat for decades. And some planners lower their return assumptions when stock valuations are high, which lowers the spending a simulation will support, often by more than it appears. In Tharp’s 2017 analysis, lowering the assumed real return of a portfolio of 60% stocks and 40% Treasury bills from its historical 5.9% to 2% left half of all simulated retirements worse than anything in U.S. market history, for reasons the next section explains. We lean toward keeping valuations out of the withdrawal rate a plan starts from; at most, they inform some investment decisions at the margins, and a weak decade is handled through reviews and adjustments set in advance. The counterargument deserves a fair hearing: high starting valuations have tended to be followed by weaker returns over the next decade, and Tharp himself cautions that ignoring them is not automatically the better choice.

Random Years Versus Real Markets

Many Monte Carlo models, including our example, draw each year’s return independently of the last, the way one roll of the dice has no memory of the one before. Real markets have not behaved quite that way. Over short stretches they have shown some momentum, with losing years tending to cluster, which makes the early run of bad years that does so much damage, a risk we explain in our article on sequence-of-returns risk, more likely than independent draws imply. Over longer stretches they have tended to recover after deep slumps, a pattern independent draws leave out. Those two habits pull the simulation in opposite directions, depending on where in the range a plan sits.

Near the top of the scale, where the score depends on the worst trials, the simulation is harsher than history. A bell curve is often faulted for missing extreme events, and over days and months markets do produce more of them than a bell curve predicts. Over whole years, the picture changes: Tharp found in 2017 that annual returns for a portfolio of 60% stocks and 40% Treasury bills since 1871 showed no statistically significant departure from a bell curve, and Kitces has noted that the bigger miss in annual data has been on the upside, the occasional extraordinary year. Over decades, the missing recoveries matter more. In Tharp’s comparison, with 10,000 trials using the same history’s average return and volatility, about 6.5% of simulated retirements were worse than the worst one on record, so the 4.08% starting withdrawal that had survived every historical period read only about 93.5% in the simulation.

In the middle of the range, and in tests against what actually happened, the error has run the other way. Fitzpatrick and Tharp’s 2022 comparison, which we walk through in our guardrails article, found Monte Carlo somewhat more generous than history between about 40% and 90%, a gap they tentatively linked to the short-term momentum that independent draws leave out. Their 2023 study asked a different question: how well forecasts made at the time matched what happened next. Producing a probability of success each month from 1951 through 2002 for 200 simple income plans lasting 20 years, they found the traditional approach, one set of assumptions built from the prior 30 years of returns, overconfident above 50% and most of all between about 70% and 97%: of every 100 plans it put at 95%, about 20 rather than 5 turned out to be spending too much. That does not contradict the 93.5% result, which compared two methods using the same long-run averages; in the 2023 test, part of the miss came from the trailing averages themselves. Historical analysis and a regime-based Monte Carlo, which sets different assumptions for the next decade and for the long run, had roughly 25% less forecasting error. No method came close to perfect, and even historical analysis was somewhat overconfident above 50%, though far less so.

Some models address the independence problem by drawing whole blocks of historical years at a time, so streaks survive. None of these approaches sees the future. Each is a different way of describing uncertainty, with its own blind spots, and the fact that every one of them errs is its own argument for revisiting a plan rather than trusting any single reading.

One Projection or an Ongoing Plan

Tharp has pointed out that the probability of success answers a specific question: if the household charged forward blindly, spending exactly as planned no matter what happened, in what share of simulated futures would the money last? For a one-time projection, where nobody will look again, that is the right question, and a high number is a reasonable thing to want.

Most households, though, revisit their plan. For them, Tharp argues, the probability of success overstates the risk of running out, because a household watching its plan can adjust before a shortfall becomes severe. His research also found that when spending is updated regularly to hold a target probability, spending over a retirement follows the markets far more than the target chosen, apart from where it starts, and the target mostly tilts the plan toward income now or toward wealth left later; in our terms, toward spending and giving during life or toward legacy. In an ongoing plan, the number works less like a measure of risk and more like a dial between today and legacy.

In Tharp’s 2021 analysis of a hypothetical retired couple with a $200,000 legacy goal, walked through every 30-year period of market history since 1871 with spending reset each month to hold a constant probability, median spending rarely differed by more than about $1,000 a month (roughly 15% of the 95% plan’s starting spending) between a plan held at 95% and one held at 20%. What differed was the money left at the end, where the 95% plan averaged nearly three times the couple’s legacy goal. The trade runs the other way too: a plan that starts higher has further to fall, and in one period beginning in 1944, spending under the 50% plan fell at its low point by nearly half from where it started, against about a fifth under the 95% plan.

Reframing failure as adjustment helps, but only partly. Kitces has suggested that a probability of failure would be better called a probability of adjustment, since a plan that heads off course usually forces a change rather than a catastrophe. He has also described a client couple whose plan read 60%: where he saw a 40% chance of failure, they heard a 60% chance of never needing to change a thing, and with very flexible spending, they were ready to trim if markets turned. Tharp later showed that the phrase can mean two very different things. One is the share of simulated retirements in which, looking back, a cut would have been needed to avoid running out, which is simply the failure rate. The other is the chance that a household following a dynamic plan, one that adjusts spending as results change, would cut at some point without the benefit of hindsight, which is far higher. Walking the same hypothetical couple through the same history in 2022, he counted how often each target called for a cut below the couple’s starting spending at some point. Holding 70% called for such a cut in 99.57% of those periods. Holding 95% did so in about 96%, and even at 95%, about 15% of periods saw spending fall 35% or more below where it started.

Holding a constant probability is not a practical way to spend, as Tharp himself notes, and buffers before any change, like the guardrails set in advance that we describe in our guardrails article, are designed to avoid much of that churn. The lesson carries over anyway: a household whose plan will be monitored can expect adjustments, mostly small, and the useful conversation is about which ones, how large, and when, in dollars. Tharp has also suggested that many advisors already work this way informally, with thresholds they keep in their heads, such as trimming if the number falls to 70% and raising spending if it climbs to 99%; writing those lines down in dollars, in advance, is what turns a score into a plan.

Questions Worth Asking About Any Probability of Success

What are the assumptions? The average return, the volatility, the inflation rate, and whether fees are taken out first. A number quoted without its assumptions is half a sentence.

What counts as a failure? Running out entirely, or falling below a target left for heirs? Any year with a shortfall, or only the end? Two plans can read the same percentage and mean different things.

What happens after a failure? How much of the spending would still be covered by Social Security, a pension, or other income that does not depend on markets, and how deep would the cut be?

What spending path and horizon does it assume? Flat spending to 95 is a common default, but not a description of most retirements. For couples, it matters whether the plan models the first death, when one Social Security check stops and, usually from the year after the death, the survivor files under single brackets, a shift we cover in our article on the widow’s tax penalty. We lean toward modeling the first death in every couple’s plan.

Will the plan be updated, and what happens if it drifts? A one-time number and a number that will be revisited mean different things. If the plan will be updated, the more useful questions are how often, what would trigger a change, and how large that change would be.

How We Think About It

We lean toward treating a probability of success as a technical measurement, not a grade. As Tharp has suggested, it belongs behind the scenes, where it can inform the plan, rather than at the center of the conversation, where a single percentage tends to be heard as a pass or a fail. Fitzpatrick, drawing on the risk-communication work of Peter Sandman, has argued that the words do part of the damage: failure calls up a sudden catastrophe, while for a monitored plan that starts somewhat conservatively, the real risk is chronic and controllable: occasional, mostly small adjustments a household can see coming. It is the same reason we question any single number for retirement readiness, as we explain in our article on how much you need to retire.

We lean toward basing our risk analysis on historical returns rather than Monte Carlo, treating history as a record of what has happened rather than a promise of what will, and toward not showing clients a score at all. What we lean toward showing instead is the risk of overspending and of underspending, how often a raise or a cut would have come along historically, and the spending decision tree in dollars: what the household can spend now, and the portfolio values at which spending would change. That approach, described in our guardrails article, is built on the research Tharp and Fitzpatrick published at Kitces.com. Plans for retired clients are typically updated about twice a year, and any adjustment is set out in advance, in dollars.

We lean toward keeping part of the margin of safety in where spending starts, below the plan’s best guess of what the money can support, and placing the rest elsewhere: in those regular reviews, in spending lines set in advance, in a horizon set with health and family history in mind, in a legacy goal, and in a separate plan for long-term care, which we cover in our article on funding long-term care.

When a household brings us a probability of success from another plan, we lean toward reading it through the questions above rather than taking it at face value. A high number can be a sign of room as much as a sign of safety: room to spend more on the trips and the time with family, and room to give more while the giver can see the gift land. For a household whose budget is mostly core spending, or whose income floor is low, a high number may be exactly the margin it wants. A lower number may call for a closer look at the assumptions and the floor before it calls for any change. Either way, the starting point is what the money is for, which is why every plan we build begins with a Statement of Financial Purpose.

Common Questions

What is a good Monte Carlo probability of success?

There is no single right number. A probability of success depends on the assumptions behind it, on how severe a shortfall would be, and on whether the plan will be updated. For a one-time projection that nobody will revisit, a high number protects against a shortfall no one will see coming. For a plan reviewed regularly, Derek Tharp’s research at Kitces.com suggests the target works more like a setting that tilts a plan toward income now or toward what is left later, and James Yaworski, also writing at Kitces.com, has suggested matching it to a household’s willingness and ability to adjust, including how much of what it draws from savings is discretionary. In our hypothetical example of a couple, both 65, with $2,000,000 invested and $130,000 a year of spending, $50,000 of it from Social Security, the plan read about 92% withdrawing $70,000 a year from savings and about 70% withdrawing $90,000.

Does a 70% probability of success mean a 30% chance of running out of money?

Only if nothing ever changes. The 30% are the simulated retirements in which the starting spending, held fixed for the whole plan, would have run the portfolio short at some point, often late in life. The number says nothing about how deep the shortfall would be, and income such as Social Security would keep paying. A household that reviews its plan would usually see trouble coming and could adjust before a shortfall became severe, so the more useful question is how often an adjustment would come and how large it would be.

Why does my probability of success change every time the plan is updated?

Markets moved, the household is a year older, spending changed, or the assumptions were revised. Part of any change can also be noise from the random draws themselves, especially when the simulation runs only 1,000 trials, so a move of a point or two between reviews may mean nothing at all.

How many simulations does a Monte Carlo analysis need?

Enough that random noise is small next to the decisions the number informs. Each run draws fresh random returns, so the result moves even when nothing in the plan has changed. In our hypothetical example of a couple, both 65, with $2,000,000 invested and $130,000 a year of spending, $50,000 of it from Social Security, 50 runs of 1,000 trials each ranged from 79.9% to 87.5%, while 20 runs of 10,000 trials ranged from 82.6% to 84.3%. Measured in dollars, the noise is smaller than it looks: in Fitzpatrick and Tharp’s 2022 tests of 250 to 100,000 trials, the spending a plan supports typically varied by only about 1% to 2% from run to run at 1,000 trials, except at the extremes. Once the noise is that small, the assumptions matter far more than the trial count.