Definition
Monte Carlo simulation is a stochastic modeling technique that generates many possible outcomes by repeatedly drawing random values from specified probability distributions, then summarizes the resulting distribution to characterize what could happen.
Why it matters
Monte Carlo simulation is the dominant stochastic method in retirement analytics. When an analyst reports a probability that a plan will succeed, a percentile band on projected income, or a distribution of terminal balances, the underlying computation is almost always a Monte Carlo simulation. Understanding how the method works, what it assumes, and where its output is most and least reliable is what lets a reader interpret the resulting probability figures rather than treating them as forecasts.
How it works
A Monte Carlo simulation begins with a model that produces an outcome from a specified set of inputs and a specification of probability distributions for the inputs treated as uncertain. The simulation draws one value from each specified distribution using a random-number generator, runs the model to produce one path, and records the outcome. It then repeats the process, typically ten thousand times or more, producing a distribution of outcomes across the sampled paths. The distribution is summarized through statistics of interest: the median, the tenth and ninetieth percentiles, the fraction of paths that meet a specified success criterion. Consider a 20-year retirement projection with annual returns drawn from a normal distribution (mean 5 percent, standard deviation 12 percent), starting balance $500,000, annual withdrawals $30,000: a Monte Carlo simulation might find that in 85 percent of ten thousand simulated paths the balance remains positive through year 20, with the median terminal balance near $250,000 and a wide dispersion around it. The accuracy of the summary statistics depends on the number of paths (more paths reduce sampling noise) and on the validity of the input distributions (well-chosen distributions produce meaningful output; poorly chosen distributions produce confident-looking output about the wrong question).
In practice
An individual encountering a Monte Carlo output should ask what distributions the simulation assumed, how those distributions were calibrated, how many paths were run, and what the output actually reports. A "probability of success" figure is a summary of the fraction of paths meeting a specified criterion, not a probability in any deeper sense; changing the input distributions changes the figure. The individual should also understand that Monte Carlo simulation typically holds mortality either deterministic (planning to a fixed age) or stochastic (drawing age at death from a survival distribution), and that the two treatments produce meaningfully different plan-success figures for the same portfolio parameters. The method is powerful when its assumptions are disclosed and interpreted honestly, and less useful when its output is presented as a forecast.
Related terms
- Stochastic modeling
- Deterministic modeling
- Deterministic versus stochastic projection
- Geometric Brownian motion
- Standard deviation
- Variance
- Probability of ruin
- Sequence of returns risk