Understanding Monte Carlo Simulations for Retirement

Why a Single Forecast Falls Short

Most retirement calculators give you one number. Plug in your savings rate, expected return, and retirement age — and out pops a single projected pot. The problem? Markets don't move in straight lines.

A 7% average annual return sounds reassuring, but the sequence of those returns matters enormously. Two retirees with identical average returns can end up in wildly different positions depending on when the good and bad years fall.

This is known as sequence-of-returns risk, and it's one of the most important — and most overlooked — factors in retirement planning. Research by William Bengen in 1994 first highlighted the importance of withdrawal sequencing, leading to the widely cited "4% rule" — itself a product of historical simulation analysis.

Where Monte Carlo Comes From

The Monte Carlo method has its origins in the 1940s at the Los Alamos National Laboratory, where physicists Stanislaw Ulam and John von Neumann developed it while working on nuclear weapons research. Ulam, recovering from an illness and playing solitaire, realised that rather than trying to calculate the probability of winning through combinatorics, it was far easier to simply play hundreds of games and observe the results.

He and von Neumann formalised this into a computational technique: use repeated random sampling to estimate outcomes that are too complex to solve analytically. They codenamed it "Monte Carlo" after the famous casino in Monaco — a nod to the role of chance and randomness at the heart of the method.

"The first thoughts and attempts I made to practice [the Monte Carlo method] were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires." — Stanislaw Ulam, Adventures of a Mathematician (1976)

The technique was initially used for neutron diffusion calculations, but its applications quickly spread. By the 1960s, Monte Carlo methods were being used in operations research, engineering, and physics. The financial services industry adopted them from the 1970s onwards, initially for options pricing and risk modelling, and later for retirement planning and portfolio analysis.

Today, Monte Carlo simulation is a standard tool in quantitative finance, used by pension funds, wealth managers, and financial planning software — including Scenarios.

How Monte Carlo Simulation Works

Instead of producing one forecast, a Monte Carlo simulation runs thousands of scenarios — typically 1,000 or more — each using randomly generated inputs drawn from historical patterns or assumed distributions.

For retirement planning, this means each simulation generates a different sequence of investment returns, inflation rates, and other variables. Some sequences are favourable, others are punishing. The result isn't a single number — it's a distribution of outcomes: a range showing what might happen under good conditions, average conditions, and difficult ones.

The question isn't "will I have enough?" — it's "what's the probability that I'll have enough?"

This shift in framing is powerful. It moves retirement planning from false precision to honest uncertainty. You can see this in action for free with your own numbers.

The mathematics behind it

At its core, Monte Carlo simulation relies on the law of large numbers: as you increase the number of random trials, the average of the results converges on the expected value. With 1,000 simulations, you get a statistically robust picture of the range of possible outcomes.

Each simulation typically models returns as random draws from a distribution. A common approach uses geometric Brownian motion — the same mathematical framework behind the Black-Scholes options pricing model — where each year's return is drawn from a log-normal distribution characterised by a mean (expected return) and standard deviation (volatility).

Scenarios uses this parametric approach, generating correlated random returns for each asset class based on calibrated mean and volatility assumptions. A correlation matrix — applied via Cholesky decomposition — ensures that the simulated behaviour between asset classes (e.g. equities moving together, bonds providing diversification) reflects real-world relationships.

Sequence-of-Returns Risk

Why does running multiple simulations matter so much? Because of sequence-of-returns risk — the risk that poor returns early in retirement disproportionately damage your portfolio, even if average returns over the full period are reasonable.

Consider two retirees who both experience an average 7% annual return over 25 years:

• Retiree A gets strong returns in the first decade and poor returns later. Their portfolio grows early, and later losses are absorbed by a larger base.
• Retiree B gets poor returns first and strong returns later. Their portfolio shrinks early while they're making withdrawals, and even strong later returns can't recover the lost ground.

Same average return. Vastly different outcomes.

This was demonstrated empirically by Michael Kitces and Wade Pfau in their research on retirement income sustainability, and it's the central reason why single-point forecasts are misleading for retirees.

The problem with compound interest calculators

Most online retirement tools are essentially compound interest calculators. You enter a return assumption — say 7% — and they compound it forward in a straight line. The output feels precise: "You'll have £1.2 million at age 65."

But that precision is an illusion. A compound interest calculator assumes you'll earn exactly the same return every single year. It can't model the reality that markets crash, recover, stagnate, and boom in unpredictable sequences. It can't account for the fact that a -20% year early in retirement is far more damaging than the same -20% year a decade later.

Worse, it gives you a single number — which feels like an answer, but is really just one of thousands of possible outcomes. It's like checking the weather forecast for one day and assuming every day for the next 25 years will be the same.

Monte Carlo simulation captures this by testing your plan against thousands of different sequences, giving you a realistic picture of the range of outcomes rather than a single misleading average.

How Scenarios Uses Monte Carlo

When you build a plan in Scenarios, we run 1,000 simulations across your full financial picture — pensions, ISAs, GIAs, cash, and property. Each simulation applies:

• Randomised real equity returns drawn from historical UK and global data
• Inflation variability rather than a fixed assumption
• Your specific tax position including Income Tax, Capital Gains Tax, and Dividend Tax
• Your withdrawal strategy and account drawdown order

The output is a probability-weighted view of your retirement. You can see your median outcome, but also your 10th percentile (a tough scenario) and 90th percentile (an optimistic one).

What the Numbers Actually Mean

When Scenarios tells you there's an 85% chance your money lasts to age 95, it means that in 850 out of 1,000 simulated futures, your portfolio survived. In the other 150, it didn't.

That's not a guarantee. But it's a far more honest and useful answer than "you need £X to retire."

It's worth noting that Monte Carlo results are sensitive to the assumptions that go in. The choice of return distribution, the correlation between asset classes, and the inflation model all affect the output. No model perfectly predicts the future — but a well-constructed simulation gives you a framework for thinking about uncertainty rather than ignoring it.

The Practical Takeaway

Monte Carlo simulation doesn't eliminate uncertainty — nothing can. But it quantifies it. And that changes the conversation from guesswork to informed decision-making.

Instead of asking "do I have enough?", you can ask:

• What happens if I retire two years earlier?
• How much does increasing my pension contribution by £200/month improve my odds?
• What if inflation runs hotter than expected for a decade?
• How does changing my withdrawal order between ISA and pension affect my success rate?

These are the questions that actually matter. And they're exactly the kind of questions a probability-based approach can answer. You can build your own plan for free and see how Monte Carlo simulation applies to your specific situation.

Further Reading

• Ulam, S. (1976). Adventures of a Mathematician. University of California Press.
• Bengen, W. (1994). "Determining Withdrawal Rates Using Historical Data." Journal of Financial Planning, 7(4), 171–180.
• Kitces, M. & Pfau, W. (2015). "Reducing Retirement Risk with a Rising Equity Glide Path." Journal of Financial Planning, 28(1), 38–45.
• Metropolis, N. & Ulam, S. (1949). "The Monte Carlo Method." Journal of the American Statistical Association, 44(247), 335–341.
• Mandelbrot, B. & Hudson, R. (2004). The (Mis)Behaviour of Markets. Profile Books.