Monte Carlo Retirement Calculator

What the Monte Carlo retirement calculator does

The Monte Carlo retirement calculator estimates how likely a retirement portfolio is to support your withdrawals when investment returns arrive unevenly. The year-to-year variation, not only the average, decides whether savings last. The calculator simulates 2,000 retirements and tells you in how many of them the money lasts the full period, together with the 10th, 50th and 90th percentile of the balance left at the end.

Why a single average return misleads

Most simple retirement calculators apply a fixed return, say six percent, identically every year. That hides the main risk in retirement: a run of poor returns early on, combined with ongoing withdrawals, can drain the portfolio before markets recover.

This is sequence-of-returns risk. Two retirees can earn the same average return over thirty years and end up in completely different situations because of the order in which good and bad years arrive. Someone who hits a downturn in the first years of drawdown sells assets at low prices to fund spending, leaving less capital to benefit from the recovery. Because every simulated path meets its good and bad years in a different order, a Monte Carlo simulation shows this risk.

How the simulation works

At the start of each simulated year every path pays your withdrawal. The rest of the balance then earns a return drawn from a normal distribution whose mean is your expected return and whose standard deviation is your volatility. A path whose balance at the start of a year is smaller than the withdrawal has run out of money: it stays at zero and counts as a failure. A single simulated year cannot lose more than the whole balance.

The random numbers come from a pseudo-random generator with a fixed seed, so the same inputs always replay the same 2,000 paths. The paths come in mirrored pairs: every random shock is used once as drawn and once with its sign flipped, a standard technique that keeps the simulation from leaning towards lucky or unlucky draws. When you change an input, all paths are recalculated with the same underlying shocks, so any difference comes from your change.

With volatility set to zero every path earns exactly the expected return and the calculator reproduces the classic drawdown formula, shown in the results as the ending balance at a constant return. Comparing that figure with the simulated median shows how much the ups and downs cost a retiree who keeps withdrawing through them.

Reading the results

The probability that the money lasts is the share of the 2,000 paths that pay every withdrawal in full for the number of years you entered. At 80%, one simulated retirement in five ran out of money before the end.

Half the paths end above the median ending balance and half below, counting a path that ran out as zero. The median is usually well below the constant-return balance, because a path that suffers early losses while withdrawing rarely catches up. The 10th percentile shows what a bad sequence could leave, and it is zero when more than one path in ten runs out. The 90th percentile shows the upside, and the gap between the two shows how much your outcome depends on luck.

The chart plots the 10th, 50th and 90th percentile of the balance year by year, so you can see when the weak paths begin to run dry.

How to use the calculator

1. Enter your starting portfolio balance at the beginning of retirement.
2. Enter the amount you plan to withdraw each year.
3. Enter your expected average annual return.
4. Enter the volatility of that return.
5. Enter the number of years the portfolio must last.

The tool shows the probability of success, the three ending balances, the constant-return comparison and the fan chart.

Testing a plan

• Lower the annual withdrawal and watch the probability climb. Small reductions in spending have a large effect, because money not withdrawn keeps compounding.
• Reduce the volatility to model a more conservative asset mix. A calmer portfolio narrows the fan, trading some upside for a stronger worst case, though it usually comes with a lower expected return.
• Extend the years to see how a longer retirement raises the risk. More time lets money compound but also gives a bad sequence more chances to hurt.

Limits of the model

Each simulated year is independent of the one before and follows a normal distribution, so the model has no fat tails, no crashes beyond what a bell curve allows and no replay of real market history. The withdrawal stays fixed in nominal terms, and the model ignores inflation, taxes, fees and the flexibility real retirees show when markets fall. At very high volatility a normal draw can fall below minus 100%; such a year is counted as a total loss.

The 2,000 paths are a sample, so the probability carries a sampling error of about one percentage point and the percentiles a few percent. Use the calculator to compare plans, see how sensitive your outcome is to volatility, and find a withdrawal that keeps the probability of success where you are comfortable.

This article is general information only and is not financial advice.

About This Monte Carlo Retirement Calculator

Use this Monte Carlo retirement calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.