Monte Carlo Simulation

Monte Carlo simulation runs thousands of random scenarios to estimate the range of possible outcomes for a portfolio or financial plan. Instead of using a single expected return, it models uncertainty.

How It Works:

1. Define inputs (expected return, volatility, time horizon, withdrawals)
2. Generate thousands of random return sequences
3. Calculate outcomes for each sequence
4. Analyze the distribution of results

Retirement Planning Example:

• $1M portfolio, 4% annual withdrawal, 30-year horizon
• 10,000 simulations with randomized returns
• Result: 85% probability of not running out of money

Interpreting Results:

Success Rate	Interpretation	Action
>95%	Very safe	Plan is robust
85-95%	Comfortable	Minor adjustments may help
75-85%	Moderate risk	Consider reducing withdrawals
<75%	High risk	Significant changes needed

Advantages over Simple Projections:

• Accounts for sequence of returns risk (order matters for withdrawals)
• Models volatility drag (geometric vs arithmetic returns)
• Provides probability ranges rather than single outcomes
• Captures worst-case scenarios that simple averages miss

Limitations:

• Assumes historical return distributions continue
• Cannot model black swan events accurately
• Garbage in, garbage out — results depend on input assumptions
• May give false precision (85.3% vs 86.1% is meaningless)

Tools for Individual Investors:

• Portfolio Visualizer (free)
• Vanguard Retirement Nest Egg Calculator
• FIRECalc (uses historical data instead of random sampling)