What a Monte Carlo Simulation Does, and What It Assumes

Why anybody does this

Ramesh has been given a retirement projection: contribute this much, earn this rate, and the money lasts. It is a single line on a chart and he has noticed the problem with it. Markets do not deliver the same return every year, and the order in which they deliver it changes the answer — sometimes drastically, once withdrawals have begun. That effect is measured on the Indian record in sequence risk before and after withdrawals begin.

A Monte Carlo simulation addresses this directly. Rather than one assumed path, it generates many — each a different sequence of yearly returns — runs the plan through each, and reports the share that succeeded. Instead of "you will have this much" the answer becomes "the plan worked in this proportion of the runs".

That is a real improvement. It replaces a false precision with a distribution, and it makes the order of returns visible instead of assuming it away.

Where the returns come from, which is the whole question

To generate ten thousand futures, the simulation needs a rule for producing a year's return. That rule is the entire content of the exercise, and it is almost never displayed alongside the result.

There are broadly two approaches, and each has a specific weakness.

Draw from a statistical distribution. Pick an average return and a spread, and generate years at random from it. This is clean and fast, and it embeds two assumptions that are known to be wrong: that returns follow that particular shape, and that each year is independent of the last. Real markets produce extreme moves more often than the common shapes predict, and they cluster — turbulent periods follow turbulent periods. A simulation built this way will understate how often several bad years arrive together, which is precisely the scenario the exercise exists to examine.

Draw from actual history. Sample real past years, or real sequences of them. This keeps the true shape and, if whole stretches are sampled, some of the clustering. Its weakness is different: the history is short, so the same few episodes are drawn repeatedly. Ten thousand runs built from one country's few decades are ten thousand rearrangements of a small amount of evidence, not ten thousand independent futures.

Either way, the number of runs is not evidence of anything. It is a statement about how long the computer ran. A weak assumption simulated a million times is a weak assumption with a smooth-looking histogram in front of it.

The four assumptions to ask about

Whenever you are shown one of these outputs, four inputs decided it and none is usually visible.

The expected return. If it was estimated as an average of historical years, it is too high for a projection, because an average exceeds the rate that actually compounds — the identity in why an average return can mislead you. This single error is enough to turn a failing plan into a passing one.

The variability, and whether bad years cluster. Covered above. Independence is the default and it is the assumption most likely to be flattering.

Inflation. Whether it is modelled at all, whether it varies, and whether it is correlated with returns. A plan that succeeds in money terms and fails in purchasing power has not succeeded.

Costs and tax. Frequently omitted entirely, and both are certain in a way returns are not.

If the answer to "what did you assume?" is not available, the output is not interpretable, however many runs it reports.

Reading a success rate honestly

A headline like "the plan succeeded in most runs" needs two more questions before it means anything.

What counted as success? Usually "the money did not run out before a specified age". That definition treats running out one year early and running out fifteen years early as the same failure, and it treats dying with an enormous unspent surplus as an unqualified success. Neither matches what anybody actually wants.

What did the failures look like? This is the more useful question and it is rarely answered. A plan that fails narrowly and late, in ways a modest spending adjustment would fix, is in a very different position from one that fails early and catastrophically. The share of runs that failed tells you nothing about which kind they were.

The most useful output from one of these exercises is not the success rate at all. It is sensitivity: which input, changed slightly, moves the answer most. That tells you where to direct attention, and it is robust to the modelling assumptions in a way the headline number is not.

What it is genuinely good for

Comparing options under one consistent set of assumptions — retiring two years later against spending slightly less, say. The absolute numbers may be unreliable and the ranking usually survives, because both options were run through the same flawed model.

Making variability visible. A client who has seen the spread of outcomes understands their plan better than one shown a single line, even if the spread itself is imperfectly estimated.

And finding the fragile input, as above.

What to take away

A Monte Carlo simulation converts one confident wrong answer into a distribution of answers whose shape depends entirely on assumptions you were not shown. That is progress, and it is not certainty.

Ask what generates a year's return, whether bad years are allowed to cluster, whether inflation, costs and tax are in there, and what counted as success. Then use it for comparison and for sensitivity, and treat the success percentage as the least informative number on the page.