Monte Carlo Portfolio Simulator
Traditional financial planning relies on static average returns, which dangerously obscures sequence-of-returns risk. A Monte Carlo simulation uses random sampling governed by historical drift and volatility to generate thousands of possible future paths, revealing the true distribution of potential outcomes.
The 'Drift' (μ)
Standard Deviation (σ)
Enter parameters and click run to generate paths.
Simulation Results (Year )
While the average annualized return is , the volatility drag of means the median outcome is lower than a simple linear projection. Use the Kelly Criterion to optimize risk-adjusted returns based on these distributions.
Understanding the Math: Geometric Brownian Motion
This simulator uses Geometric Brownian Motion (GBM), the standard continuous-time stochastic process used in quantitative finance to model stock prices (and the foundational assumption of the Black-Scholes model).
The equation is: dS = μS dt + σS dW
Where:
dS: The change in the asset price.μ(Drift): The expected annual return.σ(Volatility): The standard deviation of the returns.dW: A Wiener process (Brownian motion), representing the random market shock drawn from a normal distribution.
Volatility Drag
One of the most important concepts revealed by Monte Carlo simulation is volatility drag (variance drain). Notice that if you input an 8% return and a 20% volatility over 20 years, the median (50th percentile) outcome is significantly lower than a naive calculation of 100,000 * (1.08)^20.
Because a 50% loss requires a 100% gain to break even, volatility geometrically degrades compound returns. The actual expected compound annual growth rate (CAGR) approaches μ - (σ²/2). To understand the historical maximum pain a strategy has endured, check our Drawdown Analyzer. To estimate the worst-case scenario over a specific time horizon, use the Value at Risk (VaR) calculator.
Limitations of Standard GBM
Standard Monte Carlo using GBM assumes log-normal returns. However, real financial markets exhibit fat tails (kurtosis) and skewness—extreme events happen much more frequently than a normal distribution suggests. If you are modeling complex AI trading strategies that might suffer from overfitting, standard GBM might underestimate the risk of a black swan event. Advanced models incorporate jump-diffusion or utilize Hidden Markov Models for regime detection to switch volatility states dynamically.