Monte Carlo (Portfolio)
Quick Definition
A statistical simulation technique that models thousands of random market scenarios to estimate the probability of a portfolio meeting its goals.
What Is Monte Carlo (Portfolio)?
Monte Carlo Simulation (Portfolio Analysis)
Monte Carlo simulation is a statistical modeling technique that runs thousands of randomized scenarios to estimate the probability of different portfolio outcomes. Instead of assuming a fixed average return, it models the uncertainty and randomness inherent in financial markets.
How Monte Carlo Simulation Works
- Define inputs: Portfolio size, allocation, withdrawal rate, time horizon
- Set parameters: Expected return, volatility, inflation, correlations for each asset class
- Run simulations: Generate 1,000-10,000+ random return sequences
- Analyze results: Calculate probability of success (not running out of money)
Example Simulation Output
Scenario: $1,000,000 portfolio, 4% withdrawal rate, 30-year retirement, 60/40 allocation
| Percentile | Ending Balance | Interpretation |
|---|---|---|
| 95th (best case) | $3,200,000 | Exceptional markets |
| 75th | $1,800,000 | Above-average outcomes |
| 50th (median) | $950,000 | Most likely result |
| 25th | $320,000 | Below-average but viable |
| 5th (worst case) | $0 (depleted at year 24) | Portfolio runs out |
Success Rate: 87% of simulations lasted 30+ years
Monte Carlo vs Simple Projections
| Method | Assumes | Output | Limitation |
|---|---|---|---|
| Linear projection | Fixed 7% return every year | Single outcome | Ignores volatility |
| Historical backtesting | Past returns repeat | Limited scenarios | Only tests past periods |
| Monte Carlo | Random returns within parameters | Probability distribution | Only as good as assumptions |
What the Results Tell You
- 90%+ success rate — Your plan is robust, likely conservative
- 80-90% success rate — Solid plan with reasonable margin
- 70-80% success rate — Acceptable but consider backup plans
- Below 70% — Plan needs adjustment (save more, spend less, or work longer)
Key Variables That Matter Most
- Sequence of returns — Early losses hurt far more than late losses
- Withdrawal rate — Each 0.5% increase significantly reduces success probability
- Time horizon — Longer retirements require lower withdrawal rates
- Asset allocation — Too conservative or too aggressive both reduce success rates
Why It Matters
Monte Carlo simulation gives investors a realistic probability of success rather than a false sense of certainty from a single projection. It reveals how vulnerable a plan is to bad luck (poor early returns) and helps identify the optimal balance between spending and safety. Most comprehensive financial plans now include Monte Carlo analysis.
Monte Carlo (Portfolio) Example
- 1A financial planner runs 10,000 Monte Carlo simulations showing an 88% probability that a client's $1.2M portfolio lasts 35 years at a 3.8% withdrawal rate.
- 2Monte Carlo analysis reveals that reducing withdrawal from 4.5% to 4.0% increases the 30-year success rate from 72% to 89%.
Related Terms
4% Rule
A retirement guideline suggesting you can withdraw 4% of your portfolio in year one, adjusted for inflation annually, with high confidence of lasting 30 years.
Withdrawal Rate
The percentage of a retirement portfolio withdrawn annually to fund living expenses, critical for determining how long savings will last.
Sequence of Returns Risk
The risk that the timing of poor investment returns early in retirement can permanently damage portfolio longevity.
Asset Allocation
The strategic distribution of an investment portfolio across different asset classes — such as stocks, bonds, and cash — to balance risk and return based on goals and time horizon.
Risk Budgeting
A portfolio construction method that allocates a total risk budget across assets or strategies, ensuring each contributes a defined amount of risk.
Asset Allocation
The process of dividing investments among different asset classes like stocks, bonds, and cash to balance risk and reward.
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