On Single Point Forecasts for Fat Tailed Variables

tags: [ taleb , finance , src:paper , src:podcast ]

src: paper via EconTalk.

Using tools from extreme value theory (EVT), Cirillo and Taleb [1] determined that pandemics are patently fat tailed (with a tail exponent patently in the heaviest class: \(α < 1\)) — a fact that was well known (and communicated by Benoit Mandelbrot) but not formally investigated.

Pandemics are fat-tailed.

Random variables with unstable (and uninformative) sample moments may still have stable tail properties centrally useful for inference and risk taking.

RVs with undefined first (and second) moments are still parameterizable (e.g. Cauchy, and stable distributions).

From Wiki:

Many—notably Benoît Mandelbrot as well as Nassim Taleb—have noted this shortcoming of the normal distribution model and have proposed that fat-tailed distributions such as the stable distributions govern asset returns frequently found in finance.

For matters of survival, particularly when systemic, under such classes as multiplicative pandemics, we require “evidence of no harm” rather than “evidence of harm”.

Basically, if you have a fat-tailed distribution, and don’t have enough data to determine the properties of this particular sample, then expect the worst (since your sample moments are uninformative).

He then goes on to explain how, with fat-tailed distributions, confidence levels of the moments are too large to be practically useful (since second moments are so large).