What is a Monte Carlo simulation?

The standard retirement calculator runs a single projection. You enter your numbers, pick an average return (say 7%), compound forward, see if you run out of money before you run out of years. The answer is a clean yes or no. It's also misleading, because real markets don't deliver the average every year. They deliver something different each year, and the order in which the good and bad years arrive matters a lot.

A Monte Carlo simulation tests the plan against thousands of randomly-generated sequences of annual returns. Each sequence has roughly the same long-run average but a different order. Some sequences front-load the bad years (which is dangerous for a retiree). Some front-load the good years (which is forgiving). The simulation counts how many of those thousands of sequences leave you with money at the end, and reports the percentage.

That percentage (the success rate) is more honest than a yes/no answer. A plan that succeeds 95% of the time is genuinely robust. A plan that succeeds 60% of the time may average out fine, but you wouldn't bet your retirement on a coin flip plus a small edge.

Concretely: pick your inputs (starting balance, annual contributions, retirement age, annual spending, mean return, return volatility, inflation). The simulator generates 10,000 different sequences of annual returns. Each return is drawn from a normal distribution around your mean and standard deviation. For each sequence, the simulator steps through your retirement year by year: apply that year's return, add contributions if you're still working, subtract inflation-adjusted spending if you're retired, repeat until life expectancy. Count how many sequences end with money still in the account.

Worked example. Two retirees, both with $1M, both planning to spend $50,000/year inflation-adjusted for 30 years, both at a 7% mean return with 15% standard deviation. They make identical decisions and have identical assumptions. The only difference: random luck. In a Monte Carlo run, one retiree might end with $3.5M (lucky markets in the first decade compounded well). Another might run out of money at year 22 (early-decade losses she never recovered from). The two retirees' fates were determined by sequence-of-returns risk, not by anything in their plan.

The output of a Monte Carlo simulation is a distribution, not a number. RetireWise reports the 10th percentile (bad-luck case), the 25th, the median (50th), the 75th, and the 90th, plus the percentage of trials that didn't run out (the success rate). A retirement plan with a 95th percentile of $5M but a 10th percentile of $0 has wildly different downside than one with a 95th percentile of $2M and a 10th percentile of $500K, even if both medians look similar.