On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index

TLDR

This article explores the distributional properties of market index returns using Tukey’s g and h distributions. The authors develop simple, outlier‑robust estimates of skewness and elongation. They show that over long periods the market index follows a skewed, elongated g×h distribution, provide functional forms for these distributions, and note implications for portfolio strategies and pricing models that incorporate higher moments. © 1988 University of Chicago.

Abstract

This article is an exploratory investigation of the distributional properties of market index returns using J. W. Tukey's g and h distributions. Specifically, it is shown that over sufficiently long periods of time, the distribution of the market index is adequately explained as a skewed, elongated (g x h) distribution. Estimates of skewness and elongation are developed that are easy to calculate and are robust with respect to outliers. Functional forms for the appropr iate distributions are provided. The findings reported here have implications for understanding skewness and elongation, developing appropriate portfolio strategies, and devising pricing models incorporating higher moments. Copyright 1988 by the University of Chicago.