Monte Carlo methodology: how Portfolio Lab simulates wealth paths

In depth5 min read · updated 24 October 2026 · 6 sources

This Monte Carlo methodology describes the Monte Carlo page: from a portfolio's monthly returns it builds thousands of possible future paths on which contributions or withdrawals run. The page shows the range of outcomes and how often the money lasts. The basics are covered in the article Monte Carlo simulation.

Return basis

The basis is the monthly returns of the selected portfolio from the grid over the common period of its securities, reset to the target weights every month, without costs and without inflows or outflows. At least twelve months are required; the results only become meaningful with many years that include crises. The page shows the historical return p.a. (arithmetic mean × 12) and volatility p.a. (× √12) of this basis.

Four ways to draw returns

The simple bootstrap following Efron (1979) keeps the actual distribution of monthly returns with all its extremes, but destroys patterns over time. The block bootstrap, based on the principle of Kunsch (1989), preserves them within a year, such as phases of high volatility or trends. The block length is fixed at twelve months; unlike the stationary bootstrap of Politis and Romano (1994), it does not vary. A 30-year series therefore consists of 30 drawn annual blocks.

The parametric methods draw monthly returns μ + σ × z. With your own assumptions, the return p.a. / 12 and the volatility p.a. / √12 apply (defaults 6% and 12% p.a., i.e. 0.5% and 3.46% per month). For the t distribution, z is divided by √(5/3) so that the variance stays the same; in exchange, large swings occur more often. This is closer to real markets, whose returns have fat tails (Mandelbrot 1963). Monthly returns below −99% are capped at −99%.

How a path runs

Each path starts with the initial wealth (default 100,000) and runs through the horizon (default 30 years, up to 60) month by month: first the drawn return, then the inflow or outflow at the end of the month. The amount is in today's purchasing power and, if set, rises with a fixed inflation rate (default 2% p.a., per month (1.02)^(1/12) − 1 = 0.165%). Once wealth falls to zero, it stays there; there is no borrowing.

The simulation runs 2,000 paths (selectable from 500 to 10,000) with a fixed starting value (seed) for the random number generator: the same inputs always produce the same paths. This lets you compare two settings without chance getting in the way.

Results

• Percentiles 10, 25, 50, 75 and 90 of wealth per month as a fan chart, nominal and real (divided by the price level at fixed inflation). The table shows reference years, every five years for horizons of 10 years or more.
• Success rate: the share of paths that end with more than zero. With withdrawals, this is the probability that the money lasts until the end, under the model's assumptions.
• Time of depletion: for paths that fall to zero, the year in which this happens.
• Distribution of final values: histogram up to the 99th percentile, so that a few outliers do not blow up the chart.
• Return per path: the time-weighted return p.a. of the drawn months, independent of inflows and outflows.

How precise is a success rate?

A success rate from 2,000 paths is itself an estimate. Its standard error is √(p × (1 − p) / n): at p = 90% and n = 2,000 that is 0.67 percentage points, so a 95% band runs from about 88.7% to 91.3%. Differences of one percentage point between two settings are therefore hard to interpret. Because of the fixed seed, however, both variants draw the same returns as long as only amounts or inflation change. That makes the comparison much steadier. Far larger than this random error is the model error: which history is drawn and which return is assumed often shifts the rate by ten points or more.

Monte Carlo, backtest and financial goals

The backtest shows exactly one path (the one that actually happened) with costs, taxes and rebalancing. Monte Carlo reshuffles the same history and asks how things would have turned out in a different order; in exchange, costs and taxes are left out. Financial goals combine both for concrete goals, with taxes on sales. Putting all three side by side shows whether a plan only works in the one historical order or in many others as well.

Limitations

• The future need not resemble the past: the bootstrap only knows months that have already happened.
• Inflation is fixed. In reality it fluctuates and is linked to returns.
• No taxes or costs; financial goals include taxes on sales.
• A success rate of 90% does not mean “safe”: in every tenth path the money runs out. How much the order of returns matters is shown in the article sequence risk.

Monte Carlo methods in finance go back to Boyle (1977); a standard reference on errors and variance reduction is Glasserman (2003).

This page describes how Portfolio Lab calculates; past results are not a forecast. All terms in the glossary.