Discrete hierarchy of sizes and performances in the exchange-traded fund universe

TL;DR

This paper uncovers a discrete size hierarchy in the ETF universe, revealing a log-periodic structure and an inverse size effect where larger ETFs outperform smaller ones, based on detailed statistical analysis.

Contribution

It introduces a novel classification of ETFs into seven size layers based on a multiplicative ratio and analyzes their size distribution and performance patterns.

Findings

Seven size layers with a ratio of 3.5 in market capitalization

Larger ETFs show stronger intra- and inter-layer similarity

Large ETFs outperform small ETFs in 2014 and 2015

Abstract

Using detailed statistical analyses of the size distribution of a universe of equity exchange-traded funds (ETFs), we discover a discrete hierarchy of sizes, which imprints a log-periodic structure on the probability distribution of ETF sizes that dominates the details of the asymptotic tail. This allows us to propose a classification of the studied universe of ETFs into seven size layers approximately organized according to a multiplicative ratio of 3.5 in their total market capitalization. Introducing a similarity metric generalising the Herfindhal index, we find that the largest ETFs exhibit a significantly stronger intra-layer and inter-layer similarity compared with the smaller ETFs. Comparing the performance across the seven discerned ETF size layers, we find an inverse size effect, namely large ETFs perform significantly better than the small ones both in 2014 and 2015.