IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.16339.html

Financial Information Theory

Author

Listed:
  • Miquel Noguer i Alonso

Abstract

This paper introduces a comprehensive framework for Financial Information Theory by applying information-theoretic concepts such as entropy, Kullback-Leibler divergence, mutual information, normalized mutual information, and transfer entropy to financial time series. We systematically derive these measures with complete mathematical proofs, establish their theoretical properties, and propose practical algorithms for estimation. Using S&P 500 data from 2000 to 2025, we demonstrate empirical usefulness for regime detection, market efficiency testing, and portfolio construction. We show that normalized mutual information (NMI) behaves as a powerful, bounded, and interpretable measure of temporal dependence, highlighting periods of structural change such as the 2008 financial crisis and the COVID-19 shock. Our entropy-adjusted Value at Risk, information-theoretic diversification criterion, and NMI-based market efficiency test provide actionable tools for risk management and asset allocation. We interpret NMI as a quantitative diagnostic of the Efficient Market Hypothesis and demonstrate that information-theoretic methods offer superior regime detection compared to traditional autocorrelation- or volatility-based approaches. All theoretical results include rigorous proofs, and empirical findings are validated across multiple market regimes spanning 25 years of daily returns.

Suggested Citation

  • Miquel Noguer i Alonso, 2025. "Financial Information Theory," Papers 2511.16339, arXiv.org.
    • Handle: RePEc:arx:papers:2511.16339
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.16339
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    2. Shleifer, Andrei & Vishny, Robert W, 1997. "The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    3. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    4. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    5. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. John Cotter & Niall McGeever, 2018. "Are equity market anomalies disappearing? Evidence from the U.K," Working Papers 201804, Geary Institute, University College Dublin.
    2. Lu Zhang, 2017. "The Investment CAPM," European Financial Management, European Financial Management Association, vol. 23(4), pages 545-603, September.
    3. Adam Karp & Gary Van Vuuren, 2019. "Investment Implications Of The Fractal Market Hypothesis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-27, March.
    4. Daniel, Kent & Hirshleifer, David & Teoh, Siew Hong, 2002. "Investor psychology in capital markets: evidence and policy implications," Journal of Monetary Economics, Elsevier, vol. 49(1), pages 139-209, January.
    5. Godfrey, Keith R.L., 2017. "Toward a model-free measure of market efficiency," Pacific-Basin Finance Journal, Elsevier, vol. 44(C), pages 97-112.
    6. Chan, Wesley & Frankel, Richard & Kothari, S.P., 2002. "Testing Behavioral Finance Theories Using Trends and Sequences in Financial Performance," Working papers 4375-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Witte, Björn-Christopher, 2013. "Fundamental traders' ‘tragedy of the commons’: Information costs and other determinants for the survival of experts and noise traders in financial markets," Economic Modelling, Elsevier, vol. 32(C), pages 377-385.
    8. Fung, Scott & Obaid, Khaled & Tsai, Shih-Chuan, 2024. "Information acquisition and processing skills of institutions and retail investors around information shocks," Journal of Empirical Finance, Elsevier, vol. 77(C).
    9. Jiang, George J. & Zhu, Kevin X., 2017. "Information Shocks and Short-Term Market Underreaction," Journal of Financial Economics, Elsevier, vol. 124(1), pages 43-64.
    10. Schwert, G. William, 2003. "Anomalies and market efficiency," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 15, pages 939-974, Elsevier.
    11. Sandrine Jacob Leal, 2015. "Fundamentalists, chartists and asset pricing anomalies," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1837-1850, November.
    12. Bogousslavsky, Vincent, 2021. "The cross-section of intraday and overnight returns," Journal of Financial Economics, Elsevier, vol. 141(1), pages 172-194.
    13. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    14. Nobel Prize Committee, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    15. Friedrich-Carl Franz & Tobias Regele, 2016. "Beating the DAX, MDAX, and SDAX: investment strategies in Germany," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 30(2), pages 161-204, May.
    16. Sandrine Jacob Leal, 2015. "Fundamentalists, Chartists and Asset pricing anomalies," Post-Print hal-01508002, HAL.
    17. Glaser, Markus & Nöth, Markus & Weber, Martin, 2003. "Behavioral Finance," Sonderforschungsbereich 504 Publications 03-14, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    18. Dionysia Dionysiou, 2015. "Choosing Among Alternative Long-Run Event-Study Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 158-198, February.
    19. Stefanescu, Razvan & Dumitriu, Ramona, 2016. "Particularitǎţi ale evoluţiei variabilelor financiare [Some particularities of the financial variables evolution]," MPRA Paper 73481, University Library of Munich, Germany, revised 02 Sep 2016.
    20. Stephen A. Gorman & Frank J. Fabozzi, 2021. "The ABC’s of the alternative risk premium: academic roots," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 405-436, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2511.16339. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.