A Heuristic For Fat-Tailed Stock Market Returns*

16 Pages Posted: 5 Dec 2023 Last revised: 22 Jun 2024

See all articles by Ivo Welch

Ivo Welch

University of California, Los Angeles (UCLA); National Bureau of Economic Research (NBER)

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

Welch, Ivo, A Heuristic For Fat-Tailed Stock Market Returns* (June 21, 2024). Available at SSRN: https://ssrn.com/abstract=4630509 or http://dx.doi.org/10.2139/ssrn.4630509

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