File 03 — The Monte Carlo Fan
The Monte Carlo Fan
Ten thousand futures from one set of odds — and the gap between the average and yours.
One set of odds, rolled forward hundreds of times, every possible future fanned out from today. Then turn a single dial — how wild each year is — and watch the trick Taleb built a career on: crank the turbulence and the average future soars while the typical one sinks, sometimes below where it started. Same odds, two destinies. The shaded band holds the middle 80%; the red line is you. This is the picture behind “The Average Is a Liar,” drawn out over years.
One set of odds, rolled forward four hundred times. Every faint line is a future your money could have — same rules, different luck. The shaded band holds the middle 80% of them; the red line is the typical outcome, the dashed line the average. Now reach for the second dial.
calm ·········· ● ·········· storm — the same expected return, but crank the wildness and the average pulls away from the life you actually get.
The average future
$27k
what a brochure would quote
The typical future
$20k
the middle path — closer to yours
After 20 years the middle 80% of futures land between $7.2k and $55k. 21% of them end below the $10k you started with, and the luckiest 10% hold 31% of all the money in the picture.
A calm fan: here the typical future and the average sit close together, so the mean isn’t lying to you. Push the volatility dial up and watch them split — that gap is where averages start to deceive.
Model: geometric Brownian motion, the standard textbook Monte Carlo for prices — each step multiplies wealth by a random draw, so returns compound. The median grows with the drift minus half the variance; that ½σ²is the “volatility drag” the second dial is really moving. Illustrative, not a forecast of any real asset.