Retirement Monte Carlo Simulator

Understanding the retirement Monte Carlo simulator — concept and principle

A steady-return projection hides the fact that markets go up and down, and the order of good and bad years can make or break a retirement. A Monte Carlo simulation runs thousands of random return paths and counts how often the money lasts. It shows the success rate, the chance of running out and the range of ending balances.

How it is calculated

• Each year's real return is drawn at random from a normal distribution with your average return μ and volatility σ.
• At the start of each year the withdrawal W (constant in real terms) is taken, then the rest grows: B ← (B − W)(1 + R).
• A path fails if the balance reaches zero before the final year.
• Success rate = paths that last ÷ number of simulations; ending values are sorted to read the 10th, 50th and 90th percentiles.
• Withdrawal rate = W ÷ starting portfolio.

The principle

Two retirees with the same average return can have very different outcomes: losses early in retirement, while withdrawals are being taken, shrink the base that later gains must rebuild. This sequence-of-returns risk is invisible in an average. Simulating many plausible sequences turns the question "will my money last?" into a probability. The normal model is a simplification: real returns have fatter tails and periods of persistent good or bad performance.

Worked example

Default inputs: $1,000,000, first-year withdrawal $40,000, average real return 5%, volatility 12%, 30 years, 2,000 simulations.

1. Withdrawal rate: 40,000 ÷ 1,000,000 = 4%.
2. Each of 2,000 paths draws 30 random returns, such as +17%, −8%, +5%.
3. In the run shown, 1,704 of 2,000 paths last 30 years: success rate 85.2%, chance of running out 14.8%.
4. Ending values: 10th percentile $0, median about $992,958, 90th percentile about $3,981,632.

Because returns are random, each run gives slightly different figures, typically within a couple of percentage points.

How to read the result

Many planners treat a success rate of roughly 80–90% as reasonable when you are willing to cut spending in bad years, and aim higher if spending is inflexible. A wide gap between bad and good cases shows how much is left to chance. Lowering the withdrawal rate, accepting flexible spending or adding guaranteed income raises success.

Common mistakes

• Entering a nominal return while the withdrawal is meant to be in real terms.
• Reading a 100% success rate as a guarantee.
• Ignoring taxes and fees, which lower the effective return.

Frequently asked questions

What success rate is good enough?

There is no single standard; 80–90% is common if you can adjust spending, higher if you cannot.

Why does the result change slightly each time?

Each run uses new random numbers; more simulations make the estimate more stable.

Is a 0% bad-case ending value alarming?

It means at least 10% of paths ran out, which matches a success rate below 90%.

Sources: Bengen, W. P., "Determining Withdrawal Rates Using Historical Data", Journal of Financial Planning (1994) · Glasserman, P., Monte Carlo Methods in Financial Engineering (2003)