How a Monte Carlo simulation works
The idea is simple: when a result depends on many uncertain inputs that interact in ways no single formula can capture, run the model many times with random inputs and study the spread of results.
In retirement planning, the tangled problem is decades of uneven returns meeting withdrawals, taxes and Inflation. A straight-line financial projection assumes the same return every year, which hides sequence of returns risk completely. A Monte Carlo simulation replaces that single path with many, in four steps:
- Set return assumptions: an average and a volatility, or standard deviation, for each part of your asset allocation, plus how the parts move together.
- Draw a random return for every year of the plan from those assumptions.
- Run the plan’s income, spending, withdrawals and taxes through that path and record how it ends.
- Repeat hundreds or thousands of times, then count how many paths paid for every year.
How to read Monte Carlo results
The headline is usually a probability of success: the share of paths in which the plan paid for everything through its final year. An 83% result means 17% of simulated futures ran short at some point if spending never changed. It does not mean a 17% chance of going broke, because real households cut back, delay purchases or work longer when markets fall, and failing paths often run short only late in the plan.
Look past the headline to three other readings. Percentile bands show the range of balances each year: the 10th percentile is a poor outcome and the 50th the middle one. The timing of failures shows whether trouble tends to arrive at 75 or at 95. The size of shortfalls shows whether a failing path misses by a few thousand dollars or by years of spending.
A result is often more useful for planning responses than as a grade, for example by setting a dynamic spending rule that trims withdrawals if the portfolio falls below a set level.
Monte Carlo simulation vs. historical backtesting
A historical backtest runs a plan through each real stretch of past returns in its original order, so it captures actual crashes, inflation spells and recoveries. But it has only a few dozen heavily overlapping periods to learn from, and it can never show a sequence worse than the ones that happened.
A parametric Monte Carlo simulation invents new sequences, including ones worse than history, but only from the averages, volatility and correlations you give it. Many tools draw returns from a bell-shaped normal distribution, which can make extreme years rarer than they have been in real markets, and they draw each year independently, which breaks up streaks such as a decade of high inflation.
A middle path, often called bootstrapping, draws real historical years in a new random order, and block bootstrapping draws whole multi-year stretches to keep streaks intact. Because each method has blind spots, a plan that holds up under several is more trustworthy than a high score from any one of them.
Limits and common mistakes
A simulation is only as good as its inputs, and a result printed to one decimal place can look far more precise than it is. FINRA generally bars broker-dealers from projecting investment performance but allows investment analysis tools that show the likelihood of outcomes, provided they describe their method, key assumptions and limitations, and state plainly that the projections are hypothetical, may vary with each use and guarantee nothing. Common mistakes:
- Treating the return assumption as a detail. In the example below, a one-point lower average cuts the success rate from about 83% to about 69%.
- Running too few paths. At 1,000 paths, an 83% result carries a sampling margin of about ±2.3 points on its own.
- Ignoring fees and taxes, which overstates what the plan can spend.
- Ending the plan too early, which hides longevity risk behind a flattering score.
- Comparing scores across different tools; compare plans within one tool and one set of settings.
Illustrative numbers
A 30-year Monte Carlo test of a $1 million portfolio
- Paths
- Complete simulated lifetimes, often 1,000 or more
- Average
- The assumed mean yearly return
- Standard deviation
- The assumed volatility of yearly returns
- z
- A random draw from a standard normal distribution, new each year
The return line describes the common parametric version; bootstrap versions draw real historical years instead.
Starting portfolio and spending$1,000,000; $40,000 a year, raised with inflation, for 30 years
Return assumption, after inflationAverage 4%, standard deviation 10%, from a bell curve
One sample year with z = −1.54% + (−1.5 × 10%) = −11%
Paths that lasted all 30 yearsAbout 83%
Median ending balanceAbout $640,000 at today’s prices
Same plan with a 3% average returnAbout 69% of paths lasted
Sampling margin if you ran 1,000 pathsAbout ±2.3 points
These figures come from 200,000 simulated paths, with spending withdrawn at the start of each year; $40,000 from $1 million is a 4% starting withdrawal rate. A one-point change in the assumed return moved the answer 14 points, far more than any sampling noise, so the inputs deserve more scrutiny than the headline.
At a glance
Four ways to test a retirement plan against uncertain markets
| Method | Where yearly returns come from | Strength | Blind spot |
|---|---|---|---|
| Straight-line projection | One fixed average every year | Clear baseline for taxes and cash flow | Shows no volatility or sequence risk |
| Historical backtest | Real past years in their original order | Real crashes, inflation spells and recoveries | Few independent periods; cannot go beyond history |
| Parametric Monte Carlo | Random draws from an assumed average, volatility and correlation | Thousands of new sequences, including worse-than-history ones | Only as good as its assumptions; bell curves can understate extreme years |
| Bootstrap or block resampling | Real historical years or multi-year blocks in a random order | Keeps real returns and inflation while creating new sequences | Cannot produce a year worse than the worst on record |
Put it in your plan
Monte Carlo in MoneyWhatIf
MoneyWhatIf’s Monte Carlo view is Plan Resilience. Instead of drawing returns from a bell curve, it deals reshuffled historical years from an index or a 60/40 blend, by default in 20-year stretches that never repeat a calendar year within a run, and reruns the full plan, taxes and withdrawals included, 100, 300 or 500 times. It reports the share of runs that never went short with a Wilson 95% give-or-take, counts runs that needed a home sale separately, and draws 10th to 90th percentile bands. Any run can be opened as a full projection.
Common questions
Monte Carlo FAQs
What is a good Monte Carlo success rate?
There is no universal number. A higher target buys more protection against poor markets but means spending less in most futures and often leaving a large balance unspent. A lower one supports more spending but relies on your willingness to cut back if markets disappoint. It helps to decide in advance what you would change, and when, if the rate fell, then judge the result with those responses in mind.
Why do Monte Carlo results change each time I run them?
Each run draws a new set of random returns, so the percentage shifts slightly unless the tool fixes its random seed. FINRA requires broker-dealer tools of this kind to explain that results may vary with each use and over time. More paths shrink the noise: around an 83% success rate, the sampling margin is about ±7 points with 100 paths, ±2.3 with 1,000 and ±0.7 with 10,000.
Is Monte Carlo better than the 4% rule?
They do different jobs. The 4% rule is a starting withdrawal rate drawn from historical backtests of 30-year retirements. A Monte Carlo simulation tests your particular plan, with its own spending, income, taxes, horizon and portfolio, against many possible markets. It can also test the 4% rule itself, or any other safe withdrawal rate, under assumptions different from the past, such as lower future returns.
Why is it called a Monte Carlo simulation?
The method came from physics, not finance. The mathematician Stanislaw Ulam conceived it in 1946, and at Los Alamos his colleague Nicholas Metropolis named it after the gambling resort of Monte Carlo, partly because Ulam had an uncle who borrowed money to go gambling there. It is now used wherever an answer depends on many uncertain inputs, from engineering reliability and project cost estimates to option pricing and weather forecasts.