Monte Carlo Simulation
Why single predictions are misleading
Instead of asking “what will my portfolio be worth?”, Monte Carlo asks: “what are all the things that could happen?” And it answers by simulating thousands of possible futures.
Markets are random. Not completely random — there's a general drift upward over time — but the path is unpredictable. A single forecast line gives you one possible future. Monte Carlo simulation gives you thousands, showing the full range of outcomes you might experience.
This is perhaps the most honest way to think about future returns: not as a number, but as a distribution of possibilities.
How it works
- Start with a principal amount and assumptions about expected return and volatility
- Each month, the portfolio changes by: drift + random shock (using geometric Brownian motion)
- Repeat this hundreds or thousands of times, each with different random shocks
- Collect all the outcomes and compute percentile bands — the range within which most outcomes fall
The model uses: dS = S × (μ dt + σ √dt × Z), where μ is expected return, σ is volatility, and Z is a random normal variable. This is the standard model used in quantitative finance.
Educational content only — not investment advice, recommendations, or a suggestion to act. Past performance is not indicative of future results. Your decisions are your own. Full disclaimer.
Why this matters
Single forecast
“Your portfolio will be worth $25,000 in 10 years.” Precise but misleading. It ignores the enormous uncertainty inherent in markets.
Distribution of outcomes
“There's a 90% chance your portfolio will be between $8,000 and $50,000.” Less precise, but honest about the range of possibilities.
See it in action
Adjust the parameters and watch the simulation run. Click Re-run to generate a fresh set of random paths — notice how the distribution changes each time (but the bands stay similar).
Adjust parameters
Median Outcome
$18.6K
5th Percentile
$6.8K
95th Percentile
$48.9K
Prob. of Loss
14%
500 Simulated Paths — Percentile Bands
What to notice:
- Click Re-run multiple times — the bands stay roughly similar even though every path is different
- Increase volatility — the fan spreads wider. Higher uncertainty = wider range of outcomes
- Extend the time horizon — the band widens further. Uncertainty grows with time
- Set return to 0% — even with no expected growth, volatility alone creates a spread of outcomes
- Probability of loss decreases with longer time horizons (if expected return > 0) — time diversifies risk
Your turn
Think about predictions you've seen. When someone says “the market will return 10% this year” — that's a single line. What does the full distribution look like? How wide is the band of possible outcomes?
The lesson from Monte Carlo isn't that we can't predict anything — it's that honest predictions are distributions, not numbers. Anyone who gives you a precise forecast without uncertainty bands is either oversimplifying or selling you something.
Reflect in your JournalWhat you've learned
- -Monte Carlo simulation runs thousands of possible futures — showing the distribution of outcomes, not just one prediction.
- -The fan chart shows percentile bands: 90% of simulated outcomes fall between the 5th and 95th percentile lines.
- -Volatility controls the width of the fan. Higher uncertainty = wider range of possible outcomes. Time also widens the fan.
- -Probability of loss typically decreases with longer time horizons (if expected return > 0) — but never reaches zero.
- -Honest predictions are distributions, not numbers. A precise forecast without uncertainty bands is always oversimplified.
Want to test this?
Many experienced investors suggest practicing with a paper money account on a reputable broker before risking real capital. Many brokers offer free simulated trading environments where you can test strategies with real market data and no financial risk.
Paper trading lets you build confidence, understand execution, and see how a strategy behaves in real time — without the emotional weight of real money on the line.
Important
Everything on this platform is educational and didactic in nature. We do not provide investment advice, financial advisory, or recommendations to buy or sell any financial instrument. Past performance is not indicative of future results. All strategies shown are historical simulations for learning purposes only. Always do your own research and consult a qualified financial advisor before making investment decisions.
Educational content · Not investment advice or recommendations
We're educators, not advisors. Your decisions are your own. Disclaimer