Why the S&P 500 is not Gaussian

I'm trying to keep up with Taleb's new technical book, but I have neither his background in trading nor mathematical rigor. In a previous life I was a physicist; they are notorious for skipping math steps based on intuition, expecting mathematicians will prove their intuition correct.

I may do some out loud thinking here, starting with a TL&DR of this chart.

The book Statistical Consequences of Fat Tails is here: https://www.academia.edu/37221402/STATISTICAL_CONSEQUENCES_OF_FAT_TAILS_TECHNICAL_INCERTO_COLLECTION_

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Which brings us to the S&P chart. If it was Gaussian, it should stay under the blue line. It's not even close, so it must a scarier distribution. But what's in the chart?

Well we can plough through 3 pages of Taleb's math, or check Wikipedia for (non nuclear war) MAD: "In other words, for a normal distribution, mean absolute deviation is about 0.8 times the standard deviation"

That's where the sqrt(π/2) blue line comes from. QED-ish; not a normal distribution.

@sjors You lost me at "Why" :/

https://www.amazon.com/Fooled-Randomness-Hidden-Markets-Incerto/dp/0812975219

Sjors Provoost@sjors@m.sprovoost.nl@michaelfolkson @stephanlivera for your reading pleasure 🙂