Kurtosis as Peakedness: The Phoenix from the Ashes

Foundations for Scientific Investing, Eighth Edition, January 2019

12 Pages Posted: 26 Sep 2016 Last revised: 5 Feb 2019

See all articles by Timothy Falcon Crack

Timothy Falcon Crack

University of Otago - Department of Accountancy and Finance

Date Written: January 1, 2019

Abstract

It has recently been argued that we should no longer associate peakedness with kurtosis (Westfall, 2014). The main part of the argument is based on a decomposition of kurtosis into terms associated with the center or with the tails of a distribution. Simple empirical, simulated, and analytical counter arguments are given to show that this decomposition is incorrect, because it is inconsistent with Pearson’s (1902, 1905) basic thesis. In fact, the level of kurtosis of a distribution is typically strongly influenced by the shape of the center of the distribution. We must, however, be cautious in describing the excess kurtosis of a symmetric distribution as a function of its peakedness relative to a normal distribution with the same variance — because of a mistake by Pearson that has often been overlooked.

Keywords: kurtosis, peakedness, fat tails, Pearson, Westfall

JEL Classification: C46, C58, G12

Suggested Citation

Crack, Timothy Falcon, Kurtosis as Peakedness: The Phoenix from the Ashes (January 1, 2019). Foundations for Scientific Investing, Eighth Edition, January 2019, Available at SSRN: https://ssrn.com/abstract=2841538

Timothy Falcon Crack (Contact Author)

University of Otago - Department of Accountancy and Finance ( email )

Dunedin
New Zealand

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