Monte Carlo Simulation Replaces One Guess With Ten Thousand
Rather than projecting a single path, the method runs many random ones and reports the distribution. Its usefulness depends entirely on assumptions that stay hidden.
The Idea
A conventional projection assumes a single set of inputs and produces a single answer. A retirement plan assuming 7 percent annual returns produces one number for the balance in thirty years.
That number is wrong with near certainty, because returns will not be 7 percent every year. The sequence matters, and the projection has no way to express that.
Monte Carlo simulation instead draws each year's return randomly from an assumed distribution, runs the full path, and repeats the process thousands of times. The output is a distribution of outcomes rather than a point.
What It Adds
The output can answer questions the single path cannot. What proportion of scenarios run out of money before the horizon. What the range of outcomes looks like at the tenth and ninetieth percentiles. How the probability of success changes if the withdrawal rate falls by half a percent.
The single projection answers what happens if everything goes as assumed. The simulation answers how often things go badly enough to matter, which is the question actually being asked.
Sequence Risk
The most valuable thing it exposes is sequence of returns risk: the order of returns matters enormously when money is being withdrawn.
Two retirees experiencing identical average returns over thirty years can have completely different outcomes depending on when the poor years occurred. Early losses combined with withdrawals deplete the capital that would have participated in the later recovery.
A single path projection using an average return cannot represent this at all, because averaging removes the ordering. The simulation captures it naturally, since some of its random paths place the bad years early.
Where It Misleads
| Assumption | Typical treatment | Reality |
|---|---|---|
| Return distribution | Normal | Fat tails, extreme years more common |
| Year to year independence | Independent draws | Some mean reversion and momentum |
| Correlations | Fixed | Rise sharply in crises |
| Expected return | Historical average | May not describe the future |
| Behaviour | Plan followed exactly | People change plans under stress |
The correlation assumption is the most consequential in portfolio work. Diversification is modelled using historical correlations, and correlations between risk assets tend to rise toward one during severe declines. A simulation using average historical correlations therefore understates how bad the worst scenarios are, in exactly the scenarios that determine whether the plan survives.
The Precision Illusion
Running more simulations produces a smoother, more precise looking distribution. It does not produce a more accurate one.
Ten thousand paths drawn from a wrong distribution give a very precise description of a wrong model. The number of runs affects sampling noise in the output and has no bearing on whether the assumptions were right.
Reporting an 87 percent probability of success implies a confidence the underlying assumptions cannot support. The honest interpretation is that this plan fails in a meaningful minority of modelled scenarios, and that the model itself is uncertain.
Using It Well
Vary the assumptions and see how much the conclusion moves. If reducing the expected return by one percentage point changes success probability dramatically, the plan is fragile regardless of what the headline figure says.
Use distributions with fat tails rather than normal ones. Include a deliberate stress path with poor early returns rather than relying on random draws to generate one. And read the output as a comparison between choices rather than as a forecast, since it is far more reliable at ranking options than at estimating absolute probabilities.
The Bottom Line
Monte Carlo simulation replaces a single projection with a distribution of outcomes, which surfaces sequence risk and the range of possibilities that averages conceal. Its results are entirely determined by assumed distributions and correlations that are known to be wrong in specific directions. Treat the output as a tool for comparing decisions under uncertainty, not as a probability you can rely on.