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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 mu
by btilly 7mo ago
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.
- deleted 7mo ago[deleted]
- srean 7mo agoSome 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#Dependent_processes 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 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 7mo agoAbsolutely. 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.