IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1812.02371.html
   My bibliography  Save this paper

Quantification of market efficiency based on informational-entropy

Author

Listed:
  • Roland Rothenstein

Abstract

Since the 1960s, the question whether markets are efficient or not is controversially discussed. One reason for the difficulty to overcome the controversy is the lack of a universal, but also precise, quantitative definition of efficiency that is able to graduate between different states of efficiency. The main purpose of this article is to fill this gap by developing a measure for the efficiency of markets that fulfill all the stated requirements. It is shown that the new definition of efficiency, based on informational-entropy, is equivalent to the two most used definitions of efficiency from Fama and Jensen. The new measure therefore enables steps to settle the dispute over the state of efficiency in markets. Moreover, it is shown that inefficiency in a market can either arise from the possibility to use information to predict an event with higher than chance level, or can emerge from wrong pricing/ quotes that do not reflect the right probabilities of possible events. Finally, the calculation of efficiency is demonstrated on a simple game (of coin tossing), to show how one could exactly quantify the efficiency in any market-like system, if all probabilities are known.

Suggested Citation

  • Roland Rothenstein, 2018. "Quantification of market efficiency based on informational-entropy," Papers 1812.02371, arXiv.org.
    • Handle: RePEc:arx:papers:1812.02371
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1812.02371
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    3. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, May.
    4. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    5. Timmermann, Allan & Granger, Clive W. J., 2004. "Efficient market hypothesis and forecasting," International Journal of Forecasting, Elsevier, vol. 20(1), pages 15-27.
    6. Shleifer, Andrei & Summers, Lawrence H, 1990. "The Noise Trader Approach to Finance," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 19-33, Spring.
    7. De Bondt, Werner F M & Thaler, Richard, 1985. "Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    8. repec:pri:cepsud:91malkiel is not listed on IDEAS
    9. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    10. Challet, Damien & Zhang, Yi-Cheng, 1998. "On the minority game: Analytical and numerical studies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 514-532.
    11. Ball, R & Brown, P, 1968. "Empirical Evaluation Of Accounting Income Numbers," Journal of Accounting Research, Wiley Blackwell, vol. 6(2), pages 159-178.
    12. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    13. Ariel, Robert A., 1987. "A monthly effect in stock returns," Journal of Financial Economics, Elsevier, vol. 18(1), pages 161-174, March.
    14. Allen, Helen & Taylor, Mark P, 1990. "Charts, Noise and Fundamentals in the London Foreign Exchange Market," Economic Journal, Royal Economic Society, vol. 100(400), pages 49-59, Supplemen.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Robert J. Shiller, 2014. "Speculative Asset Prices," American Economic Review, American Economic Association, vol. 104(6), pages 1486-1517, June.
    17. Rothenstein, Roland & Pawelzik, Klaus, 2005. "Limited profit in predictable stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 419-427.
    18. Meredith Beechey & David Gruen & James Vickery, 2000. "The Efficient Market Hypothesis: A Survey," RBA Research Discussion Papers rdp2000-01, Reserve Bank of Australia.
    19. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    20. Chan, K C & Chen, Nai-Fu, 1991. "Structural and Return Characteristics of Small and Large Firms," Journal of Finance, American Finance Association, vol. 46(4), pages 1467-1484, September.
    21. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    22. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    23. Robert J. Shiller, 2003. "From Efficient Markets Theory to Behavioral Finance," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 83-104, Winter.
    24. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    25. Fama, Eugene F., 2013. "Two Pillars of Asset Pricing," Nobel Prize in Economics documents 2013-8, Nobel Prize Committee.
    26. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
    27. Fama, Eugene F, et al, 1969. "The Adjustment of Stock Prices to New Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(1), pages 1-21, February.
    28. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    29. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-574, May.
    30. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    31. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    32. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ioan Roxana, 2020. "Capital Market Correlations Structure During The Covid-19 Crisis," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 6, pages 67-79, December.

    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. Ashok Chanabasangouda Patil & Shailesh Rastogi, 2019. "Time-Varying Price–Volume Relationship and Adaptive Market Efficiency: A Survey of the Empirical Literature," JRFM, MDPI, vol. 12(2), pages 1-18, June.
    2. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    3. Kin-Boon Tang & Shao-Jye Wong & Shih-Kuei Lin & Szu-Lang Liao, 2020. "Excess volatility and market efficiency in government bond markets: the ASEAN-5 context," Journal of Asset Management, Palgrave Macmillan, vol. 21(2), pages 154-165, March.
    4. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    5. Pernagallo, Giuseppe & Torrisi, Benedetto, 2020. "Blindfolded monkeys or financial analysts: Who is worth your money? New evidence on informational inefficiencies in the U.S. stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    6. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    7. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    8. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    9. 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.
    10. Taufiq Choudhry & Ranadeva Jayasekera, 2015. "Level of efficiency in the UK equity market: empirical study of the effects of the global financial crisis," Review of Quantitative Finance and Accounting, Springer, vol. 44(2), pages 213-242, February.
    11. Bernard Njindan Iyke, 2019. "A Test Of The Efficiency Of The Foreign Exchange Market In Indonesia," Bulletin of Monetary Economics and Banking, Bank Indonesia, vol. 0(12th BMEB), pages 1-26, January.
    12. Mikio Ito & Akihiko Noda & Tatsuma Wada, 2016. "The evolution of stock market efficiency in the US: a non-Bayesian time-varying model approach," Applied Economics, Taylor & Francis Journals, vol. 48(7), pages 621-635, February.
    13. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    14. Thomas Delcey & Francesco Sergi, 2019. "The Efficient Market Hypothesis and Rational Expectations. How Did They Meet and Live (Happily?) Ever After," Working Papers hal-02187362, HAL.
    15. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    16. Thomas Delcey & Francesco Sergi, 2019. "The Efficient Market Hypothesis and Rational Expectations. How Did They Meet and Live (Happily?) Ever After," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02187362, HAL.
    17. Thomas Delcey, 2019. "Samuelson vs Fama on the Efficient Market Hypothesis: The Point of View of Expertise [Samuelson vs Fama sur l’efficience informationnelle des marchés financiers : le point de vue de l’expertise]," Post-Print hal-01618347, HAL.
    18. Alexander S. Sangare, 2005. "Efficience des marchés : un siècle après Bachelier," Revue d'Économie Financière, Programme National Persée, vol. 81(4), pages 107-132.
    19. Meredith Beechey & David Gruen & James Vickery, 2000. "The Efficient Market Hypothesis: A Survey," RBA Research Discussion Papers rdp2000-01, Reserve Bank of Australia.
    20. Ziliotto, Arianna & Serati, Massimiliano, 2015. "The semi-strong efficiency debate: In search of a new testing framework," Research in International Business and Finance, Elsevier, vol. 34(C), pages 412-438.

    More about this item

    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:1812.02371. 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.