What Is a Monte Carlo Simulation?
A Monte Carlo simulation is a way of studying uncertainty by running a model thousands of times, each time with different random inputs. Instead of predicting one outcome, it produces a distribution of possible outcomes, so an investor can see how likely different results are. The method is named after the Monte Carlo casino in Monaco, a nod to the role of chance in the calculations.
In investing, the model is often a projection of a portfolio's future value. Analysts specify assumptions such as expected average returns, volatility, inflation, and the amount withdrawn or contributed each year. The simulation then draws random returns for each year, based on those assumptions, and records the ending value. Repeating this process many times yields a spread of results.
How It Works
The basic steps are:
- Define the model, including the variables and how they relate to one another.
- Assign each uncertain variable a probability distribution, often based on historical data.
- Draw random values for each variable and calculate the outcome.
- Repeat the process many times and summarize the results.
The output is usually expressed as percentiles or probabilities. For example, a result might show the portfolio value at the 10th, 50th, and 90th percentiles, or the share of trials in which savings lasted through a planned retirement.
Why It Matters to Investors
Monte Carlo analysis highlights risk that a single average-return projection hides. Two portfolios with the same average return can produce very different ranges of outcomes, and the simulation makes that difference visible. Many retirement planning tools use this approach to estimate the chance of running out of money.
The method has limits. Results depend heavily on the assumed distributions, and historical patterns may not repeat. Returns are often modeled as independent from year to year, which may not match real markets. A simulation estimates probabilities under its assumptions; it does not guarantee any outcome.
Updated October 19, 2026. For general education only; not financial, tax or legal advice.