R = Mean + Volatility x Z
Each simulation generates random annual returns using a normal distribution with your specified mean return and volatility (standard deviation).
Monte Carlo simulation is a computational technique that uses random sampling to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. In investing, it runs thousands of hypothetical scenarios using randomized returns based on expected performance and volatility to project a range of possible portfolio outcomes over a given time horizon.
Unlike simple compound interest calculations that assume a fixed annual return, Monte Carlo simulation accounts for the randomness and uncertainty inherent in financial markets. Each simulation generates a unique path of annual returns drawn from a normal distribution, producing a distribution of final portfolio values that reflects real-world uncertainty.
The median outcome represents the middle result across all simulations -- half of scenarios ended above this value and half below. The 10th and 90th percentiles provide a range of likely outcomes, representing the pessimistic and optimistic scenarios respectively. A wider gap between these percentiles indicates higher uncertainty in outcomes.
The probability of loss shows what percentage of simulations resulted in a final value below your initial investment. This is a key risk metric -- a lower probability of loss suggests a more conservative investment profile. The best and worst case values show the extreme ends of the simulation distribution.
Monte Carlo simulations assume returns follow a normal (Gaussian) distribution, which may not fully capture real-world market behavior such as fat tails, skewness, or black swan events. Actual market returns often exhibit larger extreme moves than a normal distribution predicts, meaning real risk may be higher than simulated.
The quality of simulation results depends heavily on the accuracy of input assumptions. If your expected return or volatility estimates are significantly off, the simulation outputs will be misleading. Additionally, Monte Carlo simulation does not account for transaction costs, taxes, changing market conditions, or behavioral factors that affect real investment outcomes.