[btilly]

The key principle is that you get CLT when a bunch of random factors add. Which happens in lots of places.

In finance, the effects of random factors tend to multiply. So you get a log-normal curve.

As Taleb points out, though, the underlying assumptions behind log-normal break in large market movements. Because in large movements, things that were uncorrelated, become correlated. Resulting in fat tails, where extreme combinations of events (aka "black swans") become far more likely than naively expected.

[srean]

Some correlations are fine though, there are versions of CLT that applies even when there are benign correlations.

https://en.wikipedia.org/wiki/Central_limit_theorem#Dependen...

I know you know that and were just simplifying. Just wanted this fact to be better known for practitioners. Your comment on multiplicative processes is spot on.

I say more here

https://news.ycombinator.com/item?id=47437152

It's bit of a shame that these other limiting distributions are not as tractable as the Gaussian.

[btilly]

Absolutely. The effect of straightforward correlations is a change in the variance, which can be measured in finance.

The effect of the nonlinear changing correlations is that future global behavior can't be predicted from local observations without a very sophisticated model.