Monte Carlo Simulation for Investing

Here's the uncomfortable truth about investing: nobody knows what the market will do next year. Not your advisor, not CNBC, not the best quant on Wall Street. So how do you plan for a future you can't predict?

You simulate thousands of them and see what patterns emerge. That's Monte Carlo simulation.

What Is a Monte Carlo Simulation?

Named after the casino city (fitting for a technique about probability), Monte Carlo simulation runs your portfolio through thousands of possible future scenarios based on historical return patterns.

Instead of saying "the market averages 10% a year," it asks: "Given that returns vary wildly from year to year, what are the realistic range of outcomes for YOUR portfolio over the next 20 years?"

How It Works (No PhD Required)

1. Start with your portfolio. Your actual tickers, allocations, and investment amount.
2. Pull historical data. How did these assets actually behave? What were the returns, volatility, and correlations?
3. Generate random scenarios. Using the statistical properties from step 2, create thousands of possible future return paths. Each path is different, but all are statistically plausible.
4. Run your portfolio through each scenario. See where you end up after 10, 20, or 30 years across all those paths.
5. Analyze the distribution. What's the median outcome? What's the worst 5% of outcomes? The best 5%?

The result is a probability fan — a visualization showing the range of where your portfolio could end up, with confidence bands.

Why It Matters More Than Average Returns

Averages lie. The stock market "averages" about 10% per year over long periods. But nobody experiences the average.

Consider two investors who both averaged 10% over 20 years:

• Investor A: Earned 10% every single year (this never happens)
• Investor B: Earned +30%, -15%, +25%, -10%... averaging 10% (this is reality)

They have the same average return, but Investor B's actual ending wealth is lower because of volatility drag — the mathematical reality that losses hurt more than gains help. Lose 50%, and you need a 100% gain just to break even.

Monte Carlo captures this because it models the path of returns, not just the destination.

Sequence of Returns Risk

This is where Monte Carlo becomes essential for retirees and anyone drawing down a portfolio.

If the market crashes 30% in your first year of retirement while you're withdrawing 4%, the combined hit to your portfolio may be unrecoverable — even if the market roars back later. The same crash happening 15 years into retirement barely matters.

Monte Carlo reveals this by showing scenarios where early crashes devastate the portfolio vs. scenarios where they don't. It puts a probability on "will I run out of money?"

What the Results Tell You

A typical Monte Carlo output shows percentile bands:

• 95th percentile: The optimistic scenario (only 5% of simulations did better)
• 75th percentile: Things went well
• 50th percentile (median): The most typical outcome
• 25th percentile: Things didn't go great
• 5th percentile: Near-worst case (only 5% of simulations did worse)

The spread between the 5th and 95th percentile tells you how uncertain your outcome is. A narrow spread means your portfolio is relatively predictable. A wide spread means you're on a wilder ride.

How Many Simulations?

Most financial tools run 1,000 to 10,000 simulations. Why so many? Because with only 100 runs, the results are noisy — run it again and you'll get meaningfully different numbers. At 10,000 runs, the percentiles stabilize.

There's no magic number, but 5,000+ simulations give reliable results for planning purposes.

Limitations (Honest Assessment)

Monte Carlo is powerful but not perfect:

• Past ≠ Future. Simulations are based on historical return distributions. If the future is fundamentally different (and it might be), the simulations are miscalibrated.
• Correlation shifts. Assets that were uncorrelated in normal times can become highly correlated in a crisis (2008 proved this). Basic Monte Carlo may miss this.
• Fat tails. Real market returns have more extreme events than a normal distribution predicts. Black swans happen more than the math suggests.
• False precision. "87.3% probability of success" sounds scientific but implies more certainty than the model deserves. Think in ranges: "high 80s" is more honest.

Despite these limitations, Monte Carlo is far better than a single projection or an "average return" calculation. It forces you to think probabilistically about your future.

When to Use Monte Carlo

• Retirement planning: "What withdrawal rate gives me a 90% success probability over 30 years?"
• Goal planning: "What's the probability I'll have $500K in 15 years with my current strategy?"
• Portfolio comparison: "Does an 80/20 or 60/40 allocation give me a higher probability of meeting my goal?"
• Stress testing: "How does my portfolio behave in the worst 5% of scenarios?"