How Monte Carlo Simulations Are Actually Built

Retirement software commonly reports a probability of success derived from a simulation. Knowing how those simulations are constructed explains what the number can and cannot tell anyone.

The engine generates paths, not forecasts

A simulation draws a sequence of returns for each year of a plan from a statistical distribution, applies the plan's cash flows, and records whether the money lasted.

Repeating that thousands of times produces a distribution of outcomes, and the reported figure is the share of runs in which the plan did not run out.

No path is a prediction. The exercise is describing the range of results a set of assumptions can produce, which is a different claim from saying what will happen.

The input assumptions carry the result

Expected return, volatility and the correlations between asset classes are chosen by whoever configured the model, usually from historical data over a selected period.

Small changes to those inputs move the reported probability substantially, which is why two tools can produce very different figures for the same household.

Inflation is modeled separately, and whether it is treated as fixed or as a variable with its own distribution changes the spread of outcomes considerably.

Independence between years is a strong simplification

Basic implementations draw each year independently, which means the model contains no tendency for weak periods to be followed by stronger ones or for volatility to cluster.

Real market history shows both patterns, so independent draws can understate the chance of a prolonged difficult stretch while overstating the chance of extreme isolated years.

More elaborate approaches sample blocks of historical sequences or model changing regimes, at the cost of introducing further assumptions.

The failure definition is binary and unrealistic

A run is generally counted as a failure if the portfolio reaches zero at any point, regardless of whether that happened in the third year or the thirty-second.

It also assumes the household kept spending on schedule while watching the balance fall, which almost nobody does.

Because real households adjust, the reported failure rate describes an unmanaged plan, and models that incorporate spending rules produce a different and usually more forgiving picture.

The number is a comparison tool

The useful application is relative: comparing two allocations, two spending levels or two claiming choices under identical assumptions.

Read that way, the model answers which change moves the plan in which direction, which is far more robust than the absolute figure.

Interpreting a specific output against a specific household's circumstances is work for a qualified financial professional, and the assumptions behind any tool should be visible before its result is relied on.