A Heuristic For Fat-Tailed Stock Market Returns*
16 Pages Posted: 5 Dec 2023 Last revised: 7 May 2024
Date Written: June 21, 2024
Abstract
Large negative equity rates of return are known to occur more frequently than they should under the Gaussian normal distribution. Stock return distributions are usually kurtotic, roughly as if they were drawn from Student T-distributions with 2-5 degrees of freedom. A very easy adjustment to assess the probability of extreme losses is first to adjust the Z-score using-1.25-log(-Z). Thus, for example, one should expect a stock return that is 17 standard deviations below the mean as often as one would expect to see a draw that is |-1.25-log(17) ≈-4| standard deviations below the mean under a normal distribution.
Keywords: Tail Risk
JEL Classification: G11
Suggested Citation: Suggested Citation