Monte Carlo Simulation

A mathematical technique that uses repeated random sampling to model the probability of different outcomes in a process that cannot easily be predicted.

A Monte Carlo simulation is a computerized mathematical technique used to model the probability of different outcomes in systems that are highly unpredictable. By running thousands or millions of simulated trials using random variables based on historical probability distributions, it helps investors and analysts quantify risk and uncertainty rather than relying on a single, static estimate. In finance, this technique is widely applied to portfolio planning, retirement forecasting, and option pricing. Instead of assuming a constant annual return (such as a flat 7% return every year), the simulation introduces random variability to mimic real-world market volatility. This allows investors to see a wide spectrum of potential future paths and assess the likelihood of extreme events, such as a severe market drawdown. Investors care about Monte Carlo simulations because they provide a realistic, probabilistic view of financial goals. For example, a simulation can estimate the probability that a retiree's portfolio will survive for 30 years under various market conditions. A key pitfall for investors is "garbage in, garbage out"—if the underlying assumptions about asset volatility, correlation, or average returns are inaccurate or based on too short of a historical window, the simulation's output will be highly misleading.

An investor wants to test if their $1,000,000 retirement portfolio will last 30 years with a $50,000 annual withdrawal. Instead of assuming a fixed 6% annual return, a Monte Carlo simulation runs 10,000 trials, randomly varying annual returns based on historical stock and bond volatility. If the portfolio remains above $0 at the end of 30 years in 8,200 of those trials, the simulation indicates an 82% probability of success (8,200 / 10,000 = 0.82) and an 18% probability of running out of money.