Simulate thousands of market futures, instantly.
Monte Carlo simulation runs thousands of randomized market scenarios to show you the realistic range of outcomes for a long-term portfolio — not just an average, but the full distribution of risk and return.
Example output
$10,000 initial — 30 year horizon
7% expected annual return · 15% volatility
Distribution of final portfolio values
Research supported by
- UMass Boston
- Oracle Research
- Undergraduate Research Fellowship
See the full picture, not just the average.
Most financial projections give you a single number. Monte Carlo simulation gives you thousands — so you can understand the real range of outcomes before committing to a strategy.
Built on rigorous financial mathematics.
The simulator is grounded in the same models used in academic research and professional quantitative finance — not simplified assumptions.
Geometric Brownian Motion
Each simulation path is generated using GBM — the standard model in quantitative finance — which captures both the expected drift of returns and their random volatility.
Customizable Parameters
Set your initial investment, time horizon, expected annual return, and volatility. Every input is adjustable so you can model your specific situation.
10,000 Simulations
Each run generates 10,000 independent market paths in milliseconds, giving you a statistically robust distribution rather than a single projected outcome.
Inflation Adjustment
Toggle between nominal and real (inflation-adjusted) returns to understand what your portfolio is actually worth in future purchasing power.
Annual Contributions
Model dollar-cost averaging by adding regular annual contributions to your portfolio. See how consistent investing amplifies long-term outcomes.
Open Methodology
Every assumption and formula is documented and reproducible. This is academic research — the math is transparent and available for peer review.
Ready to model your portfolio?
Set your parameters, run 10,000 simulations, and see the full distribution of where your investments could go.
Why this exists.
Most people never invest because the numbers feel abstract. This simulator makes them concrete.
How the simulator works.
Inputs go in, 10,000 randomized market paths come out. Here is exactly what happens in between.
The Inputs
Everything the simulator lets you configure before running a scenario.
- Initial investment amount
- Annual contribution (optional)
- Expected annual return (%)
- Annual volatility / std. deviation (%)
- Time horizon (years)
- Inflation adjustment toggle
- Number of simulation paths (up to 10,000)
The Model
Each simulation path is generated using Geometric Brownian Motion — the standard stochastic process in quantitative finance.
- dS = μS dt + σS dW (GBM formula)
- Wiener process for random shocks
- Log-normal return distribution
- Independent paths — no autocorrelation
- Supports real & nominal return modes
- Validated against historical S&P 500 data
The Outputs
What the simulator produces after running all paths.
- Full return distribution histogram
- 10th / 50th / 90th percentile paths
- Probability of loss at horizon
- Median and mean final portfolio value
- Confidence interval band chart
- Conservative / moderate / aggressive comparison
- Downloadable results (coming soon)
Frequently asked questions
Have a question about the methodology? Reach out directly.
What is Monte Carlo simulation?
What does volatility mean in this context?
How is this different from a compound interest calculator?
Monte Carlo simulation is a computational method that runs thousands of randomized scenarios to model uncertain outcomes. Instead of predicting a single future, it generates a full distribution of possibilities — giving you a probabilistic picture of where your investments could land.
Volatility (σ) is the annualized standard deviation of log returns. It controls how wide the distribution of outcomes spreads. A higher σ means more randomness in each simulated year, which compresses the median outcome and widens the gap between the 10th and 90th percentile paths.
A compound interest calculator assumes a fixed, guaranteed return every year. This simulator models the randomness of real markets: some years are up 30%, others down 40%. Variance reduces the median outcome significantly compared to the deterministic projection — a phenomenon called volatility drag.
What mathematical model powers each simulation path?
What is a confidence interval in the output?
Who funded this research?
Each path is generated using Geometric Brownian Motion (GBM), the standard stochastic process in quantitative finance. The formula dS = μS dt + σS dW models continuous price evolution with a deterministic drift (μ) and a random Wiener shock (σ dW), producing log-normally distributed returns.
The confidence band shows the range between the 10th and 90th percentile simulation paths at every point in time. 80% of all simulated portfolios fall within this band. The median (50th percentile) path runs through the center. It is not a prediction — it is a probability-weighted envelope.
This project was funded by Oracle through UMass Boston's Undergraduate Research Fellowship. The research was self-initiated: the project proposal, supervisor, and research scope were all identified independently. It is an open-methodology project with no commercial interest.
Why 10,000 simulations?
Does the simulator account for inflation?
Can I use this simulator for real financial decisions?
10,000 paths provide statistically robust convergence. Below ~1,000 runs, percentile estimates are noisy and unstable. At 10,000, the law of large numbers stabilizes the distribution so that the 10th, 50th, and 90th percentile paths are reliable and reproducible across runs.
Yes. When inflation adjustment is toggled on, the simulator deflates each nominal return path by a fixed inflation rate, converting outputs to real (purchasing-power-adjusted) dollars. This makes a meaningful difference over long horizons: a nominal $1M in 30 years is worth far less in today's dollars.
This tool is for educational and research purposes only. It models idealized market behavior and does not account for taxes, fees, behavioral factors, or correlated market events. It is designed to build intuition about long-term investing — not to replace a licensed financial advisor.