Modelling a range of outcomes instead of one
A single average return hides the range. Simulating many volatile paths shows the spread of outcomes, and the spread is usually much wider than people expect.
What this calculator does
- Simulates many possible investment paths using a mean return and a volatility assumption.
- Reports the median outcome and the 10th, 25th, 75th and 90th percentiles.
- Estimates the probability of reaching a target and of running out entirely.
- Replaces a single point projection with a distribution.
How the calculation works
Instead of applying one return every year, the simulation draws a different random return for each year of each path, from a distribution defined by the mean return and volatility you enter. Running a thousand such paths produces a thousand different endings, and the useful information is in their spread rather than in any single one. The median is the middle outcome — half of the paths did better, half worse — and it sits below the mean because a few very good paths pull the average up without being typical. The percentiles describe the range: the 10th is a poor but entirely plausible outcome, the 90th a good one. The probability of ruin counts the paths that hit zero, which is the number that matters most when withdrawals are being taken. Presenting a distribution rather than a point estimate is the whole purpose, because a single projection implies a precision that volatile markets do not offer.
The rule
For each of many paths, and each year: value = (value + contribution − withdrawal) × (1 + a return drawn at random from a distribution with the given mean and volatility). The endings are then sorted into percentiles.
Step by step
- Draw a random annual return from the distribution defined by the mean and volatility.
- Apply contributions or withdrawals for the year, then the return.
- Repeat for every year of the horizon to complete one path.
- Repeat for the number of simulated paths requested.
- Sort the outcomes and report the median, the percentiles, and how many paths reached the target or hit zero.
Worked example
£100,000 invested with £12,000 added each year for twenty years, assuming a 7% mean return with 15% volatility, against a £1,000,000 target, over a thousand simulated paths.
What was entered
| Initial investment | £100,000 |
|---|---|
| Annual contribution / savings | £12,000 |
| Annual retirement spending | £0 |
| Expected mean return | 7% a year |
| Annual volatility | 15% |
| Simulation timeframe | 20 years |
| Number of simulated paths | 1,000 |
| Target wealth goal | £1,000,000 |
The arithmetic
- The median outcome is about £779,979 — half the paths finished above this and half below.
- The 10th percentile is about £415,590 and the 90th about £1,529,945, a spread of more than a million pounds on identical inputs.
- Only 33.1% of paths reached the £1,000,000 target, despite the mean return of 7% suggesting it should be close.
- No path ran out of money, because contributions are being added and nothing is withdrawn.
- The mean outcome of about £908,349 is well above the median, because a minority of very strong paths pull the average up.
- The gap between the mean and the median is exactly why a single average-return projection misleads.
What the calculator returns
| Median outcome | £779,978.56 |
|---|---|
| 10th percentile | £415,589.99 |
| 90th percentile | £1,529,945.06 |
| Chance of reaching the target | 33.1% |
| Chance of running out | 0% |
| Mean outcome | £908,349.49 |
Key assumptions
- Annual returns are drawn independently from a distribution defined by the mean and volatility you enter.
- Contributions and withdrawals happen once a year.
- The simulation is reproducible, so the same inputs always produce the same distribution.
Limitations
- The model assumes returns are independent from year to year and follow a well-behaved distribution. Real markets show crashes, recoveries and correlations that such a model understates, so the true tails are usually fatter than the simulation suggests.
- Everything depends on the mean and volatility you supply. Those are assumptions, not knowledge, and the output inherits all their uncertainty.
- Inflation is not applied unless the mean return you entered is a real return.
- Tax and charges are not modelled, and both reduce every path.
- A probability from a simulation is a property of the model, not a fact about the future.
- This is a projection, not advice.
Common questions
Why is the median lower than the mean?
Why did only a third of paths reach the target when the mean return was 7%?
Does a 0% chance of ruin mean it is safe?
Can I rely on these probabilities?
Related calculators
- Investment Growth Calculator — Compare the single average-return projection this distribution replaces.
- Safe Withdrawal Rate Calculator — See what the same assumptions imply for a withdrawal rate, without volatility.
- FIRE Calculator — Test how robust a financial independence target is to a poor sequence of returns.
Official sources
Every figure in this guide was checked against the sources below. Where a source could not confirm a figure, it is marked as requiring verification rather than presented as settled.
- Investing beginner's guide: understanding risk — MoneyHelperInvestment risk, volatility and the range of possible outcomes
- Pension Wise: free pension guidance — MoneyHelperFree impartial guidance on pension options, available from age 50