Learn
Monte Carlo vs. historical backtest
How retirement simulations work, and how to read success rates
A success rate is the share of simulated retirements in which your money lasts through your planned retirement period without hitting zero. When Calcifir reports an “87% success rate,” that is the question it answers. Two methods can run the simulation. A historical backtest replays real market history, and a Monte Carlo simulation draws thousands of random futures from statistics of that history. They answer slightly different questions.
Knowing which one you are looking at, and what each can and cannot tell you, changes how you should read the number. A 90% success rate from a Monte Carlo run is not the same as a 90% rate from a historical backtest, even if they point in the same direction.
Example: two lenses on the same rateExample
Take a 30-year retirement at a 4.0% withdrawal rate. Drag the slider to see how the two methods estimate the odds. In these examples they track each other closely, with Monte Carlo a touch lower because it can generate sequences worse than anything in the historical record.
The figures are illustrative examples of how to read a success rate, not results from your plan. The real rate depends on the portfolio mix, taxes and spending. Your own figures are on the Confidence page.
Historical backtest
94%
Illustrative · 1,497 overlapping windows · only ~5 independent
Monte Carlo
91%
Illustrative · 10,000 synthetic paths
In these examples the two estimates sit about 3 points apart. A larger gap is worth investigating: it means one method is picking up downside the other isn't. The examples assume a 30-year horizon with no mid-retirement spending adjustments.
Example figures from a sample household. Build your plan →
How a historical backtest works
A historical backtest tests your plan against every actual market sequence since 1871, using Shiller's long-run US stock and bond return data. For a 30-year retirement, the test steps forward one month at a time: Feb 1871–Jan 1901, then Mar 1871–Feb 1901, then Apr 1871–Mar 1901, and so on through 1,497 overlapping 30-year windows. The last runs Oct 1995 to Sep 2025. Each window is a complete real-world retirement, with the 1929 crash, the stagflation of the 1970s, the dot-com bust and 2008.
That 1,497 counts windows, not independent evidence, and the difference matters more than almost anything else on this page. Because the step is one month, any two adjacent windows share 359 of their 360 months: 99.7% of the identical market history. The whole record runs 1871 to 2025, about 155 years, which holds only about five 30-year stretches that do not overlap at all.
Five is the honest sample size. The 1,497 is those same five stretches counted over and over at one-month offsets. Treating them as 1,497 independent tests makes any success rate, or confidence range, look far more precise than the data can support.
The success rate is the percentage of those windows where your portfolio never hit zero before the end of the period. A 94% historical success rate over 30 years would mean roughly 90 of those 1,497 windows failed. That is not 90 independent failures.
At the 4% rule the failures collapse into essentially two episodes: retiring into the late 1920s, and retiring into the mid-1960s. Shift a start date by a single month and you get another “failure” assembled from almost exactly the same market data.
Strengths
- +Uses real historical sequences, including actual crashes: 1929, 1966, 2000, 2008
- +Preserves real autocorrelation: bad years sometimes cluster, just as they did historically
- +Anchored in actual economic history. Every data point is real.
- +Results are interpretable: you can see which periods failed and why
Weaknesses
- −Severely limited sample size. The engine builds 1,497 overlapping 30-year windows, but ~155 years of data contains only about five that don't overlap. Counting the overlapping ones as independent overstates how precisely any historical success rate is known.
- −US-centric. The 20th century was the American century, and survivorship bias is real.
- −Cannot model “worse than history” scenarios: if future conditions are more severe than any historical period, the backtest won't show it
- −Past sequences do not have to repeat in the same order
How a Monte Carlo simulation works
Monte Carlo simulation does not replay history. It generates thousands of synthetic return sequences from statistical properties of historical returns, typically the mean, standard deviation and correlations of annual real returns. From those properties, it creates 10,000 or more random 30-year (or 40- or 50-year) return paths and counts how many of them allow your portfolio to survive.
The appeal is sample size. The historical backtest can offer only about five truly independent 30-year stretches, because its 1,497 windows are those same five re-counted at one-month offsets. Monte Carlo gives you 10,000 or 100,000 paths that really are independent of one another, though all of them are generated from that same historical record. That lets the simulation explore the full statistical distribution of outcomes, including tails that may be worse than any individual year in recorded history.
Strengths
- +Unlimited sample size: 10,000+ runs give richer statistical coverage
- +Can model tail risks more extreme than anything in the historical record
- +Can model parameter uncertainty, for example by running the simulation with varying mean return assumptions
- +Easy to layer on CAPE-based adjustments (CAPE is the cyclically adjusted price-to-earnings ratio, a stock-valuation measure) or stress scenarios that shift the distribution
Weaknesses
- −The normal-distribution version assumes returns are normally distributed: markets have fat tails and skewness that a Gaussian model understates
- −Most variants do not preserve real-world autocorrelation: crashes and recoveries have structure that random draws miss
- −Can be optimistic if variance is underestimated, or pessimistic if mean return is set too conservatively
- −Results depend heavily on the parameter assumptions: garbage in, garbage out
Monte Carlo variants Calcifir supports
Normal distribution
Draws each year's return from a normal distribution parameterized by historical mean and standard deviation. It is fast and transparent but underweights tail events.
Bootstrap resampling
Instead of a mathematical distribution, this approach resamples randomly from the actual year-by-year historical returns. Each synthetic sequence is assembled from real years in random order. This preserves fat tails while still generating many more paths than a historical backtest.
Block bootstrap
Resamples multi-year blocks of consecutive historical years (five-year blocks) instead of single years. This preserves serial correlation (momentum, mean reversion and multi-year drawdowns) that single-year resampling shuffles away. A block that starts in one of the last four years wraps round to 1872, so every year is drawn equally often and the average return matches the one the projection uses.
Regime-switching
Splits the record at its median stock return into stronger and weaker years and switches between the two at the rate history switched. Since 1872 a strong year was followed by another strong year exactly half the time, and so was a weak one. So on this record the switching carries almost no memory: its years arrive no more clustered than bootstrap resampling's. It reads the record as a loop, counting 2024 as followed by 1872, so it too draws every year equally often.
How the two methods compare on the same scenario
The chart below shows illustrative success rates from each method for the classic 4% rule over a 30-year retirement. They are round numbers, not outputs of your plan, and the real rates move with the portfolio mix, taxes and spending. Your own figures are on the Confidence page. The two methods give similar but not identical answers, and that gap is useful information.
Illustrative success rate: 4% withdrawal, 30-year retirement
In these examples the gap is about 3 percentage points. Monte Carlo can run lower than the backtest because it can generate sequences worse than anything that actually occurred historically.
Illustrative divergence across withdrawal rates and horizons
These are illustrative examples, not engine results. The two methods tend to diverge more at higher withdrawal rates and longer horizons, which are the scenarios where stress-testing matters most.
How to read success rates
A success rate is not a literal chance of going broke. A 90% historical success rate does not mean “you have a 10% chance of going broke.” It means 10% of historical 30-year periods ended with the portfolio depleted before the period was over, assuming no adjustments were made.
In real life, virtually no retiree follows a rigid rule with zero adjustment for 30 years. Real people cut spending in bad markets, pick up occasional work, or adjust when they see their portfolio eroding, so the actual behavioral risk is lower than the model suggests. The simulation's job is to show you the guardrails, not to predict your exact outcome.
Historically very robust
The failures at this success rate are typically the worst starting years in the record: retiring just before the 1929 crash, or in the mid-1960s. Those plans might well have lasted if spending had been reduced modestly in the worst years. At this level, your plan is as resilient as the historical record allows.
Solid, with a flex plan
Depending on the portfolio mix, this range can include the classic 4% rule outcome for 30-year retirements. It is considered the consensus “safe withdrawal rate” zone. The sensible addition is a guardrail rule: if your portfolio drops meaningfully in the first five years, reduce spending 10–15% for a year or two. Simulations of rules like this, such as Guyton and Klinger (2006), find they cut failure rates substantially.
Meaningful risk: plan for flexibility
At this success rate, your withdrawal rate is high enough that adverse sequences produce real stress. That is not necessarily disqualifying. If you have part-time income potential, a flexible budget, or plans to downsize, you can absorb what the model says is a 15–25% failure rate. Going in with no contingency plan at this level is risky.
High risk: reconsider the withdrawal rate
Below 75%, the withdrawal rate is likely too aggressive for the time horizon. You can reduce the withdrawal rate (lower spending or more savings), shorten the horizon in the model (planning for a legacy instead of full depletion), or model a flexible strategy like Guyton-Klinger that cuts spending in bad stretches. This is not a number to rationalize away.
In a simulation, “failure” is not the same as going broke
“Failure” means the portfolio hits zero before the end of the modeled period under the rigid withdrawal rule. In reality, retirees adjust. They spend less in bad years, pick up occasional work, sell a vacation home, or adjust expectations. The simulation assumes no behavioral response, which can understate how a flexible retiree fares. It also leaves out costs it does not model (see “What the model does not capture” below). Treat the success rate as a test of one rigid rule, not as a lower bound or a literal prediction.
Which method should you use?
Use both. They are complementary lenses, not competing answers to the same question.
Use historical backtest to understand what actually happened
If you want to know how your plan would have fared across real market history, with real crashes, real recoveries and real economic regimes, use a historical backtest. Every data point is something that actually occurred. And because the failures are specific historical periods, you can investigate them: what happened in 1929, and would I have handled it differently?
Use Monte Carlo to stress-test against scenarios worse than history
The US market delivered exceptional returns over the past 150 years. That is partly good policy and institutional strength, and partly survivorship bias: we are looking at one of history's great economic success stories. Monte Carlo can generate paths worse than anything in that record, such as 20-year bear markets, persistent inflation or prolonged low-return environments. If you want to plan more conservatively than history shows, Monte Carlo is the better tool.
The gap between them is useful signal
In the illustrative example above, the historical backtest gives 94% and Monte Carlo gives 91%. That is close enough to suggest reasonable agreement. When two methods diverge significantly, say 90% vs 75%, one is picking up something the other isn't. A large gap often signals a scenario where the historical record has been relatively favorable but statistical modeling suggests meaningful downside tails. That divergence is “model risk” and deserves investigation.
Why the first decade matters most
Both methods show the same thing: the order of returns in your first decade matters most. A 4% withdrawal from a $1M portfolio produces different outcomes depending on whether markets go up or down in years 1–10.
If you retire into a strong bull market, early gains build a buffer against later downturns. If you retire into a bear market, withdrawals in down years lock in losses and deplete capital that can never recover. This is called sequence-of-returns risk. It is the main reason the 4% rule sometimes fails even when long-run average returns look fine.
The practical implication
Your first five years of retirement are when your plan is most vulnerable. If markets deliver poor returns in that window, consider a flexible strategy that can cut spending by 10–15% before the damage compounds. That is why Guyton-Klinger guardrails, CAPE-based rules and variable percentage withdrawal strategies exist: they all have built-in mechanisms to reduce spending when portfolio stress is detected early.
How the two methods treat clustered bad years
A historical backtest preserves the actual autocorrelation of returns, meaning how closely one year follows the last. Bad years in the historical record were sometimes followed by more bad years, as in the 1966–1982 stagflation era. Monte Carlo that draws one year at a time does not capture this clustering. The normal distribution, bootstrap resampling and regime-switching all draw each year without regard to the last, and the switching rate on this record is a coin flip. Block bootstrap does keep runs of bad years together, by drawing five consecutive real years at a time.
How we test your plan
Two independent engines answer the same question. One draws simulated forward futures from the market record. The other replays every real retirement start since 1871 in the order it happened. Your plan headlines one of them and the other corroborates. Both numbers stand, and we never average them. Neither is the safe one: an engine that looks cautious at one success threshold looks generous at another.
Both engines include Medicare income surcharges. Each run charges the Medicare Part B and D income-related surcharge (IRMAA) your retirement income puts you in range of, off the income of two years before, as Medicare sets it from your tax return two years earlier.
Assumptions in force. The results run on your return model, inflation, fees and spending. Your expected return, inflation and fee assumptions are changed on their own pages. What Confidence changes and saves is your spending strategy, the early-withdrawal penalty switch, which markets your plan is tested against, and how many futures we test. See every assumption →
Data vintage. Real market history runs from 1871 to 2025. Through September 2023 it is Robert Shiller’s published series, which has not been updated since; later months come from FRED, the St. Louis Fed’s data service (inflation, the 10-year Treasury yield and the S&P 500 price), with a constant dividend yield, and carry no CAPE (valuation) reading.
What the model does not capture.
- Personal shocks: a single catastrophic expense, fraud, or another financial event outside the modeled paths.
- Behavior under stress: the model assumes you follow the strategy, but real retirees often deviate in a downturn.
- Policy changes: future tax law, Social Security reform, or Medicare changes beyond today’s rules.
- Scripted market crashes inside retirement: a “Market downturn” event you add moves the balance you retire on, but the simulations generate their own market paths, so a scripted crash isn’t replayed inside them. Every other event kind (spending, income, home, care) flows through in full.
- State and local tax: each state’s brackets, deductions, credits and retiree exclusions are modeled. A local income tax is modeled only when you pick your locality on People.
- Three ways to spend that the engine does not run: smoothing between last year’s spending and a share of savings (the endowment rule), a cash bucket set aside for the first years (savings are drawn by account type, in your draw order), and a floor bought with an annuity (Social Security and pensions are the guaranteed floor).
- Health-insurance subsidies for dependents: the credit before Medicare prices the benchmark for you and your partner only, and only when People marks your premium full price.
Related topics
Sources
- Online Data: U.S. Stock Markets 1871-Present and CAPE Ratio. Robert J. Shiller, Yale University.
- Consumer Price Index for All Urban Consumers: All Items in U.S. City Average (CPIAUCNS). U.S. Bureau of Labor Statistics, via FRED, Federal Reserve Bank of St. Louis.
- Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity, Quoted on an Investment Basis (GS10). Board of Governors of the Federal Reserve System, via FRED, Federal Reserve Bank of St. Louis.
- S&P 500 (SP500). S&P Dow Jones Indices, via FRED, Federal Reserve Bank of St. Louis.
- Determining Withdrawal Rates Using Historical Data. William P. Bengen, Journal of Financial Planning, 1994.
- Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable. Philip L. Cooley, Carl M. Hubbard and Daniel T. Walz, AAII Journal, 1998.
- Decision Rules and Maximum Initial Withdrawal Rates. Jonathan T. Guyton and William J. Klinger, Journal of Financial Planning, 2006.
- 2026 Medicare Costs (income-related monthly adjustment amounts). Centers for Medicare & Medicaid Services, 2026.
Written by Jordan Arlan
Jordan is the founder of Calcifir and builds the planner these articles explain. About Calcifir
Published April 23, 2026 · Last reviewed November 14, 2026