Entropy and Efficiency of the ETF Market

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.

Exchange traded funds in Europe and the US

“…Their results show that investors may not get the exposure in broad markets they seek from international leveraged ETFs and tend to be exposed to the U.S. market, especially in the short term horizon. Similar findings were found byCalcagnile et al (2019); ETFs that track indices of markets that are closed during the ETFs' trading time could not rely on a simultaneous evolution of the corresponding indices.…”

“…The size of tracking errors is found to be correlated with the low return of the underlying index and low volume of the leveraged ETF. Furthermore, the regression analysis shows negative serial 49 Volatility smile is a common graph shape that results from plotting the strike price and implied volatility of a group of options with the same underlying asset and expiration date. The volatility smile is so named because it looks like a smiling mouth.…”

“…They conclude that the impact of ETF rebalancing on late-day returns and volatility is not economically significant. Finally, Deng et al (2014) find that leverage in exchange traded funds can affect the 'crookedness' of volatility smiles49 .…”

Efficiency of the Moscow Stock Exchange before 2022

“…Before estimating the degree of market efficiency, we need to get rid of regularities that make prices more predictable, but do not imply any profitable strategies. The methodology of filtering regularities was introduced in [9]. However, such a filtering has not usually been applied in other research works (see e.g.…”

Comparative analysis of the stock quotes dynamics for IT-sector and the entertainment industry companies based on the characteristics of memory depth

“…Along with the Hurst exponent for the study of financial markets and, in particular, stock markets, the following indicators are used: Lyapunov exponent (indicator of nonlinear dynamics) to diagnose the crash of stock mar-kets [7], Shannon information entropy [8,9], Renyi entropy [9], the Hurst-Holder exponent [10], local Whittle estimator [11]. The presence of fractal properties in the dynamics of financial markets is also investigated by calculating the Hausdorff dimension and applying the Mittag-Leffler functions [12].…”