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_
First thing to understand is that there's hierarchy of statistical distributions, our high school friend Gaussian being near the friendly bottom.
Unless you understand the underlying process, like in some areas of physics, you can measure all you like, but you can't prove something is in the lower left. You can however *disprove* it, often with a single observation (after you check your instruments). Falsification at work.
As you disprove friendly distributions like Gaussian, you move up.
@sjors You lost me at "Why" :/
@stevenroose maybe just start with Fooled by Randomness; no math. I read Talebs books out of order and read this one last. Funny to notice how he suddenly became much friendlier 🙂
https://www.amazon.com/Fooled-Randomness-Hidden-Markets-Incerto/dp/0812975219
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.
https://en.wikipedia.org/wiki/Average_absolute_deviation#Mean_absolute_deviation_around_a_central_point