Glossary term
Monte Carlo (toy)
Definition
Many made-up paths under assumed drift and volatility (geometric Brownian motion). A teaching fan, not a forecast.
How it works
A Monte Carlo simulation runs the same assumptions many times with different random draws and reads the spread of results. The classroom version uses geometric Brownian motion: each step multiplies the value by exp((μ − σ²/2)·dt + σ·√dt·Z), where μ is the assumed drift, σ the assumed volatility and Z a random draw from a standard normal distribution.
The output is a fan of paths and a few percentiles, such as the 5th, 50th and 95th ending values. The classroom fixes the random seed, so the same fan appears on every screen. That is deliberate: if the picture reshuffled on each load, the spread would feel like decoration, and you could refresh until you liked the picture.
Worked example
Start with a hypothetical $100,000, assume 6% drift and 15% volatility for ten years. The median ending multiplier is exp((0.06 − 0.15²/2) × 10) = exp(0.4875) = 1.628, so a median near $162,800. The mean ending value is $100,000 × exp(0.06 × 10) = about $182,200.
Now keep 6% drift and raise volatility to 35%. The median multiplier is exp((0.06 − 0.35²/2) × 10) = exp(−0.0125) = 0.988, a median of about $98,800, below the start, while the mean stays near $182,200. Both numbers are correct and they answer different questions.
Hypothetical, for education only. Not a recommendation and not a prediction.
Common mistake
The mistake is treating the middle of the fan as the middle of the future. It is the middle of a cloud generated from two numbers someone typed in, and different inputs move it obediently. A toy like this is useful for seeing that spread exists, that volatility subtracts from compounding, and that the median and the mean can disagree. It is not a projection of any account.