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Entropy and Efficiency of the ETF Market

Author

Listed:
  • Lucio Maria Calcagnile

    (Scuola Normale Superiore
    LIST S.p.A.)

  • Fulvio Corsi

    (Università di Pisa
    City, University of London)

  • Stefano Marmi

    (Scuola Normale Superiore)

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-min and 5-min price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate residual 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.

Suggested Citation

  • Lucio Maria Calcagnile & Fulvio Corsi & Stefano Marmi, 2020. "Entropy and Efficiency of the ETF Market," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 143-184, January.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:1:d:10.1007_s10614-019-09885-z
    DOI: 10.1007/s10614-019-09885-z
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    References listed on IDEAS

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    9. Giglio, Ricardo & Matsushita, Raul & Figueiredo, Annibal & Gleria, Iram & Da Silva, Sergio, 2008. "Algorithmic complexity theory and the relative efficiency of financial markets - Updated," MPRA Paper 11150, University Library of Munich, Germany.
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    Cited by:

    1. Andrey Shternshis & Piero Mazzarisi & Stefano Marmi, 2022. "Efficiency of the Moscow Stock Exchange before 2022," Papers 2207.10476, arXiv.org, revised Jul 2022.
    2. Shternshis, Andrey & Mazzarisi, Piero & Marmi, Stefano, 2022. "Measuring market efficiency: The Shannon entropy of high-frequency financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Andrey Shternshis & Stefano Marmi, 2023. "Price predictability at ultra-high frequency: Entropy-based randomness test," Papers 2312.16637, arXiv.org, revised Dec 2023.
    4. Andrey Shternshis & Piero Mazzarisi, 2022. "Variance of entropy for testing time-varying regimes with an application to meme stocks," Papers 2211.05415, arXiv.org, revised Jun 2023.

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