Entropy and efficiency of the ETF market

TL;DR

This paper measures the information efficiency of ETF markets using Shannon entropy on high-frequency data, accounting for various market regularities, and finds volatility significantly impacts market regularity.

Contribution

It introduces a methodology to isolate true market inefficiencies from regularities like intraday patterns and microstructure effects using entropy analysis.

Findings

Low entropy correlates with high relative tick size.

Volatility accounts for 62% of market regularity.

Microstructure effects contribute 20% to regularity.

Abstract

We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-minute and 5-minute price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate true inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure.