CALC TOOL

Monte Carlo Investment Risk Simulator

Simulate up to 5,000 possible futures for a portfolio and see value at risk, Sharpe ratio, drawdown and stress tests. Runs in your browser. For information only, not financial advice.

Investment Risk SimulatorAZRS QuickFix

For information only, not financial advice. Results come from a statistical model with the assumptions you set. Real markets can behave differently and past performance does not predict future returns.

Portfolio Settings

Investment Details

Initial Investment $10,000

Time Horizon 10 yrs

Annual Contribution $0

Contribution Growth/yr 0%

Market Parameters

Expected Return/yr 7%

Annual Volatility (σ) 15%

Simulation Paths

Mode

Asset Allocation

Quick Preset

100% Private & Free
All math runs in your browser. No data ever sent to servers.

Simulation Results

Ready to Simulate

Configure your portfolio and click Run Simulation to see full risk analysis with 6 live charts.

How It Works

Real Financial Math, Explained

We use Geometric Brownian Motion — the same model behind Black-Scholes — running entirely in your browser.

Core Formulas Used in This Simulator

Rₜ = (μ − σ²/2) + σ·Z

GBM log-return each year. μ = expected return, σ = volatility, Z = standard normal random variable (Box-Muller transform)

Vₜ₊₁ = (Vₜ + C) × eᴿᵗ

Portfolio value update. V = current value, C = annual contribution, eᴿᵗ = exponential growth factor preventing negative prices

Sharpe = (μ − rƒ) / σ

Risk-adjusted return ratio. rƒ = 2% risk-free rate. Above 1.0 is excellent, 0.5–1.0 acceptable, below 0.5 poor.

VaR₉₅ = Initial − P5(finals)

Value at Risk at 95% confidence, as this tool computes it: your initial investment minus the 5th-percentile final portfolio value. 5% of simulated outcomes end worse than this. A negative loss figure means even the 5th-percentile outcome finished above your starting amount. Contributions and withdrawals are not subtracted.

Monte Carlo Simulation

Instead of a fixed 7% growth rate, we simulate thousands of random market paths using real statistical distributions — showing the full range of possible futures.

Geometric Brownian Motion

GBM is the gold standard in quantitative finance for modeling asset prices. It captures compounding, volatility, and log-normal returns — the same math behind Black-Scholes options pricing.

Asset Allocation Engine

Adjust your mix across 5 asset classes with real historical return and volatility data. Weighted portfolio parameters are computed automatically from your allocation.

Value at Risk (VaR)

VaR at 95% confidence tells you: in 95% of simulated scenarios the final value is at or above the 5th-percentile outcome, so the loss versus your initial investment is no larger than this figure. It is a statistical estimate from the model, not a guarantee.

Historical Stress Testing

See how your portfolio survives the 2008 Financial Crisis, COVID crash, Dot-com bust, 1970s stagflation, and more — with recovery time projections.

Completely Private

All simulation calculations run in JavaScript in your browser, and the amounts you enter are not sent to our server. No account or login is needed.

Frequently Asked Questions

A Monte Carlo simulation generates thousands of random market scenarios based on your expected return and volatility. Instead of assuming a straight 7% growth every year, it shows the full range of possible outcomes — from unlucky to lucky — giving you a realistic probability-based picture of risk.

GBM is the mathematical model most commonly used in quantitative finance to simulate asset prices. It models returns as log-normally distributed, ensuring prices can't go negative and compounding is correct. The formula Rₜ = (μ − σ²/2) + σ·Z is its core. This is the same math behind the Black-Scholes options pricing model.

VaR at 95% confidence, as computed here, is your initial investment minus the 5th-percentile final value. In 95% of simulated scenarios the portfolio finishes no further below your starting amount than this. If the tool shows $3,000 at risk on a $10,000 portfolio, 5% of simulated outcomes ended more than $3,000 below your starting amount at the end of the time horizon.

The Sharpe Ratio measures return per unit of risk. Above 1.0 is excellent, 0.5–1.0 is acceptable, and below 0.5 suggests poor risk-adjusted return. It's (Return − Risk-Free Rate) ÷ Volatility, using 2% risk-free.

Both measure risk-adjusted return. Sharpe divides by total volatility (up and down). Sortino only penalizes downside volatility — it's considered more realistic since investors only care about losing money, not winning. Higher Sortino is always better.

Withdrawal mode simulates drawing money from your portfolio each year instead of adding to it. It calculates ruin probability — the chance your portfolio hits $0. This is the most critical metric for retirement planning.