How it works
Each simulation steps through your plan month by month. Every month it adds your saving, then draws a random return for stocks and for bonds from a bell-shaped (log-normal) distribution with the yearly return and volatility you set, and grows each part of the portfolio by it. The portfolio is rebalanced back to your stock and bond mix every month. After thousands of runs, the simulator sorts the final values and reports the 10th, 50th and 90th percentiles: one run in ten ended below the "bad case", half ended above the middle outcome, one in ten above the "good case".
The point is not the middle number, which a simple compound interest calculator can give you. It is the spread. Two plans with the same average can feel very different if one of them has a one-in-ten chance of ending with half as much.
What it leaves out
Real markets have fatter tails than a bell curve: crashes like 2008 happen more often than the model expects, and returns are not independent from month to month. The simulator also ignores fees, taxes and inflation, and assumes you keep saving every month even in a crash. Treat the bad case as optimistic and the goal probability as a rough guide.
Examples
Sequence risk. Two investors each earn the same average return over 20 years, but one gets the crash in year 1 and the other in year 19. The second ends with far less, because the crash hits when the account is biggest. Run the simulator with large monthly savings, then with a large starting amount and no savings, and compare how wide the bands get near the end.
Stocks versus bonds. With the default assumptions, moving from 80% stocks to 40% stocks lowers the middle outcome but raises the bad case relative to the middle, which is what a bond allocation buys you. See our guide to hedging a stock portfolio.
Explain it like I'm 13
Imagine you could play out your savings plan 5,000 times, like replaying a video game level, and each time the market has a different mood: some years great, some terrible. Afterwards you line up all 5,000 endings. The one in the middle is your "typical" result, and the ones near the bottom show how bad things could reasonably get. That's a Monte Carlo simulation, named after the casino.
Questions
What is a Monte Carlo simulation?
A way to see the range of possible outcomes by running thousands of random versions of the future. Each run draws a different sequence of monthly returns, and together they show how likely each result is.
Are the default returns a forecast?
No. They are round numbers close to long-run U.S. history before inflation: about 9% a year with 16% volatility for stocks, 4.5% with 6% volatility for high-quality bonds. Change them to test your own assumptions.
Why do results change slightly each time?
Every run uses new random numbers. With 5,000 runs the percentiles move only a little; the overall picture stays the same.
Does it include inflation, fees or taxes?
No. Results are in future dollars before fees and taxes. Lower the expected returns to allow for them, for example by about 2.5 points for inflation.
Questions about this article? Pal reads it with you and answers in plain English.