Risk Analysis
Monte Carlo Sim Calculator
Simulate thousands of market paths for your portfolio.
Input Parameters
Adjust variables to stress-test your strategy.
10 YEARS
7%
15%
2000
Invested
$70,000
Median
$101,134
Worst 10%
$68,038
Loss Prob.
12.0%
Scenario Distributions
Visualizing 10–90 percentile outcomes.
Random Sample Trajectories
Each line represents one possible future.
Bear Case (10th)
$68,038
Only 10% of simulations ended below this level.
Expected (Median)
$101,134
The 50/50 line where half of outcomes are better/worse.
Bull Case (90th)
$155,146
Optimistic scenario with only 10% chance of being exceeded.
Glossary & Formulas
Key Terms
- Volatility (Risk)
- The standard deviation of expected annual returns, representing market fluctuation. Higher volatility means wider potential outcomes.
- Simulations
- The number of independent randomized market paths generated by the model to determine the statistical likelihood of outcomes.
- Median Outcome (50th Percentile)
- The middle projected value. In 50% of the simulated paths, your portfolio performed better, and in 50% it performed worse.
- Bull Case (90th Percentile)
- An optimistic market scenario where only 10% of simulations ended up with a higher portfolio balance.
- Bear Case (10th Percentile)
- A pessimistic market scenario where only 10% of simulations ended up with a lower portfolio balance.
Model Used
This calculator simulates monthly returns using a standard normal distribution (Box-Muller transform) to apply random shocks to the expected return.
Monthly Mean (μ) = Annual APY / 12
Monthly Volatility (σ) = Annual Volatility / √12
Random Return = μ + (σ × Z)
- Z: A random standard normal variable generated for each specific month in each simulation path.
- Random Return: The simulated percentage growth or loss for a single month.
- Compounding: The portfolio value is multiplied by (1 + Random Return) sequentially for every month of the horizon.