Publisher: WM STUDIOS. Last updated: 21 August 2026.
An average path describes no real path
The simplest calculation applies a constant return, year after year. It produces a smooth curve, pleasant to read, and resembling no lived experience: markets do not rise by the same amount every year.
A Monte Carlo simulation approaches the problem differently. Instead of one path it draws thousands, picking a return at random each year from a distribution that has been chosen. Each path is one possible history; together they form a spread of outcomes.
What you gain is not precision but shape. You see how widely the outcomes scatter. What you do not gain is any certainty about which one will occur.
What a percentile means, and what it does not
Results are usually read as percentiles. A sentence such as « in 10 % of simulations the capital runs out before the end of the term » is often misread.
It means precisely this: among the draws performed, under the assumptions chosen, one in ten ends that way. That is a property of the model, not a probability about your life. The model knows nothing of your actual circumstances, and its distribution is a choice rather than an observation.
Two practical consequences. First, a percentile is never better than the assumption that produced it: change the distribution and the figure changes. Second, the extreme cases are the least reliable of the set, because they rest on the small number of draws in the tails, precisely where the usual models describe reality least well.
Sequence risk: the same average return, two different outcomes
This is the most important mechanism to grasp, and it is purely arithmetic.
Take ten annual returns and apply them to a capital of 300,000 € from which 15,000 € is withdrawn at the start of each year. The two sequences below contain exactly the same ten returns, with the same arithmetic mean of 7.9 %. Only their order differs.
| Sequence | Order of returns | Capital after 10 years |
|---|---|---|
| Bad years early | −18, −8, +14, +6, +12, +10, +22, +8, +15, +18 | 311,222 € |
| Bad years late | +18, +15, +8, +22, +10, +12, +6, +14, −8, −18 | 421,681 € |
A gap of 110,459 €, or 35 %, from the same returns and the same average. Nothing changed but the order.
And here is the proof that the effect comes from the interaction with withdrawals: with no withdrawals at all, both orders give exactly the same result, 602,432 €. Multiplication is commutative, so the order of the factors is irrelevant. It is the withdrawals that break that symmetry, because taking a fixed sum from a reduced capital consumes a larger share of the portfolio.
This is why an average return, taken alone, says almost nothing about a situation involving withdrawals. And it is also why a simulation that draws whole paths contributes something that an average return calculation cannot.
What the model leaves out or simplifies
The list is long, and every item moves the result.
- Inflation. A nominal capital says nothing about what it will buy. A projection in current euros and the same one in constant euros tell two different stories.
- Fees. Management, brokerage and wrapper fees are charged every year, including bad ones, and compound just as returns do.
- Taxation. It depends on the wrapper, the holding period, the household's situation, and it changes over time. Any tax assumption over thirty years is a convention.
- Your life. A change of job, a birth, a separation, an unexpected expense, an inheritance: these often weigh more than market returns, and no model draws them at random.
- The horizon. A projection stops at a date you set. That choice alone determines a large part of the result.
- Correlations and distribution tails. The usual models assume a statistical regularity that crises contradict: bad years arrive more clustered, and more severely, than a smooth law assumes.
- The model itself. Choosing a distribution is already deciding the outcome. That risk, known as model risk, is not reduced by any number of additional draws.
Why two simulators do not give the same figure
It is not that one of them is faulty. A simulation result is entirely determined by its assumptions, and there are many: the average return chosen, volatility, the probability law, the treatment of inflation, fees, taxation, the horizon, the timing of contributions and withdrawals, the number of draws.
A one point difference in the return assumption, or two years in the horizon, is enough to move the percentiles substantially. Comparing two results therefore only makes sense once the assumptions have been compared first. A simulator that does not display them is a simulator you cannot read.
On fixed rate withdrawal rules
Simple rules circulate that consist of withdrawing a fixed percentage of the initial capital each year. They are convenient, and this page recommends none of them.
What is useful to know is what such rules are: the result of historical studies, run on a given market, over a given period, for a given retirement length and a given portfolio composition. In other words a retrospective finding within a precise perimeter, not a general law.
Transposing such a finding to another market, another era, another duration, another tax regime or another composition steps outside what the study actually measured. The sequence risk described above also explains why a fixed rate behaves very differently depending on when you start: the same rule applied in two consecutive years does not produce the same history.
The useful conclusion is not a figure but a question: which perimeter does this number come from, and is my case inside it?
What PulseMyPortfolio does, and does not do
The application lets you build a projection from assumptions that you enter: starting capital, contributions, withdrawals, horizon, average return, volatility. It shows the spread of outcomes alongside the assumptions used, so that the figure stays readable.
What it does not do, and will not do: it proposes no assumption as being the right one, recommends no investment and no allocation, computes no « required » capital, and does not tell you whether or when you might stop working. Nor does it ask for your investor profile.
Results are indicative estimates, dependent on the assumptions entered, and constitute neither a forecast nor a guarantee. Every calculation runs on your device.
Sources and framework
The warning principles adopted on this page and in the application voluntarily align with those the general regulation of the Autorité des marchés financiers, the French markets regulator, imposes on information about future performance: rest on reasonable assumptions, do not rely on simulations of past performance, and state clearly that a simulated performance does not prejudge future results. WM STUDIOS is neither an investment services provider nor a regulated investment adviser; this alignment is voluntary.
- Autorité des marchés financiers: regulation and investor information.
The return sequences in the example are fictional and chosen to illustrate an ordering effect. They represent no market, no period and no investment, and are not a return assumption.
Further reading
The page on calculating net worth describes the starting point of any projection, and the one on tracking dividends explains why only total return is coherent. The frequently asked questions cover how the application works.