Modelling skewness and elongation in financial returns: the case of exchange-traded funds

Recent studies have documented the importance of asymmetry and tail-fatness of returns on portfolio-choice, asset-pricing, value-at-risk and option-valuation models. This article explores the nature of skewness and elongation in daily Exchange-traded Fund (ETF) return distributions using g, h and (g � h) distributions. These exploratory data analytic techniques of Tukey (1977) reveal patterns that are hidden from a cursory glance at conventional measures for skewness and elongation. The g, h and (g � h) distributions provide parameter estimates that indicate substantial variation in skewness and elongation for individual ETFs; nonetheless, some trends are discovered when the funds are grouped by fund size and style of investing. Monte Carlo simulations suggest that these exploratory techniques are able to capture patterns found in commonly used Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family of models.