The Black Swan: The Impact of the Highly Improbable · chapter 7 · id the-black-swan-c7-06-under-gaussian-assumptions-his
“Under Gaussian assumptions, historical market events repeatedly produce sigma calculations that are mathematically impossible: the 1987 crash (20-25 sigma), the 2008 financial crisis (multiple days of 5-8 sigma moves), and the COVID-19 crash of March 2020 all exceed the probabilities the model assigns.”
holdsconfidence: high⚠ extracted by pipeline, re-audit pending
Receipts
RCM Alternatives: The 1987 Crash and the 300 Mile Tall Mansource alive
A 25-sigma event under a normal distribution has a probability of approximately 1 in 10^135. For comparison, the universe has existed for approximately 10^17 seconds. The equivalent in human height would be a person 300 miles tall.
Extreme Events in Finance: LTCM Crisissource alive
The August 1998 Russian crisis produced multiple days with market moves of 4-7 standard deviations. Under Gaussian assumptions, such clustering should be essentially impossible.
Mandelbrot (2001), 'Scaling in Financial Prices', Yalecheck errored — retry queued
Financial markets exhibit fat-tailed distributions where extreme events occur with far greater frequency than Gaussian models predict. The cumulative evidence from decades of market data conclusively rejects the normal distribution for financial returns.
This claim is a stable, citable object. If you can falsify a verdict, tell us — corrections are loud here.