IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2104.07962.html
   My bibliography  Save this paper

Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity

Author

Listed:
  • Marcel Ausloos
  • Valerio Ficcadenti
  • Gurjeet Dhesi
  • Muhammad Shakeel

Abstract

The so-called Benford's laws are of frequent use in order to observe anomalies and regularities in data sets, in particular, in election results and financial statements. Yet, basic financial market indices have not been much studied, if studied at all, within such a perspective. This paper presents features in the distributions of S\&P500 daily closing values and the corresponding daily log returns over a long time interval, [03/01/1950 - 22/08/2014], amounting to 16265 data points. We address the frequencies of the first, second, and first two significant digits counts and explore the conformance to Benford's laws of these distributions at five different (equal size) levels of disaggregation. The log returns are studied for either positive or negative cases. The results for the S&P500 daily closing values are showing a huge lack of non-conformity, whatever the different levels of disaggregation. Some "first digits" and "first two digits" values are even missing. The causes of this non-conformity are discussed, pointing to the danger in taking Benford's laws for granted in huge databases, whence drawing "definite conclusions". The agreements with Benford's laws are much better for the log returns. Such a disparity in agreements finds an explanation in the data set itself: the inherent trend in the index. To further validate this, daily returns have been simulated calibrating the simulations with the observed data averages and tested against Benford's laws. One finds that not only the trend but also the standard deviation of the distributions are relevant parameters in concluding about conformity with Benford's laws.

Suggested Citation

  • Marcel Ausloos & Valerio Ficcadenti & Gurjeet Dhesi & Muhammad Shakeel, 2021. "Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity," Papers 2104.07962, arXiv.org.
  • Handle: RePEc:arx:papers:2104.07962
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2104.07962
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. M. Ryan Haley, 2017. "K-fold cross validation performance comparisons of six naive portfolio selection rules: how naive can you be and still have successful out-of-sample portfolio performance?," Annals of Finance, Springer, vol. 13(3), pages 341-353, August.
    2. Bernhard Rauch & Max Göttsche & Gernot Brähler & Stefan Engel, 2011. "Fact and Fiction in EU‐Governmental Economic Data," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 243-255, August.
    3. T. Mir, 2016. "The leading digit distribution of the worldwide illicit financial flows," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 271-281, January.
    4. Ausloos, M. & Bronlet, Ph., 2003. "Strategy for investments from Zipf law(s)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 30-37.
    5. Clippe, Paulette & Ausloos, Marcel, 2012. "Benford’s law and Theil transform of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6556-6567.
    6. Shi, Jing & Ausloos, Marcel & Zhu, Tingting, 2018. "Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 878-888.
    7. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    8. Fatima Alali & Silvia Romero, 2013. "Characteristics of failed U.S. commercial banks: an exploratory study," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 53(4), pages 1149-1174, December.
    9. Cerqueti, Roy & Ausloos, Marcel, 2015. "Evidence of economic regularities and disparities of Italian regions from aggregated tax income size data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 187-207.
    10. Uwe Hassler & Mehdi Hosseinkouchack, 2019. "Testing the Newcomb-Benford Law: experimental evidence," Applied Economics Letters, Taylor & Francis Journals, vol. 26(21), pages 1762-1769, December.
    11. Tariq Ahmad Mir & Marcel Ausloos, 2018. "Benford's law: A “sleeping beauty†sleeping in the dirty pages of logarithmic tables," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 69(3), pages 349-358, March.
    12. Steven J. Miller, 2015. "Benford's Law: Theory and Applications," Economics Books, Princeton University Press, edition 1, number 10527.
    13. M Lesperance & W J Reed & M A Stephens & C Tsao & B Wilton, 2016. "Assessing Conformance with Benford’s Law: Goodness-Of-Fit Tests and Simultaneous Confidence Intervals," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-20, March.
    14. Natasa Omerzu & Iztok Kolar, 2019. "Do the Financial Statements of Listed Companies on the Ljubljana Stock Exchange Pass the Benford’s Law Test?," International Business Research, Canadian Center of Science and Education, vol. 12(1), pages 54-64, January.
    15. Tariq Ahmad Mir & Marcel Ausloos & Roy Cerqueti, 2014. "Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions," Papers 1410.2890, arXiv.org.
    16. Ausloos, Marcel & Cerqueti, Roy & Mir, Tariq A., 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 238-256.
    17. Riccioni, Jessica & Cerqueti, Roy, 2018. "Regular paths in financial markets: Investigating the Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 186-194.
    18. Mebane, Walter R., 2011. "Comment on “Benford's Law and the Detection of Election Fraud”," Political Analysis, Cambridge University Press, vol. 19(3), pages 269-272, July.
    19. Jennifer L. Juergens & Laura Lindsey, 2009. "Getting Out Early: An Analysis of Market Making Activity at the Recommending Analyst's Firm," Journal of Finance, American Finance Association, vol. 64(5), pages 2327-2359, October.
    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. Herteliu, Claudiu & Jianu, Ionel & Dragan, Irina Maria & Apostu, Simona & Luchian, Iuliana, 2021. "Testing Benford’s Laws (non)conformity within disclosed companies’ financial statements among hospitality industry in Romania," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).

    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. Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    2. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Ausloos, Marcel & Cerqueti, Roy & Mir, Tariq A., 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 238-256.
    4. Bogdan Vasile Ileanu & Marcel Ausloos & Claudiu Herteliu & Marian Pompiliu Cristescu, 2019. "Intriguing behavior when testing the impact of quotation marks usage in Google search results," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2507-2519, September.
    5. Ausloos, Marcel & Cerqueti, Roy & Bartolacci, Francesca & Castellano, Nicola G., 2018. "SME investment best strategies. Outliers for assessing how to optimize performance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 754-765.
    6. Arezzo, Maria Felice & Cerqueti, Roy, 2023. "A Benford’s Law view of inspections’ reasonability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    7. Herteliu, Claudiu & Jianu, Ionel & Dragan, Irina Maria & Apostu, Simona & Luchian, Iuliana, 2021. "Testing Benford’s Laws (non)conformity within disclosed companies’ financial statements among hospitality industry in Romania," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    8. Ausloos, Marcel & Castellano, Rosella & Cerqueti, Roy, 2016. "Regularities and discrepancies of credit default swaps: a data science approach through Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 8-17.
    9. Riccioni, Jessica & Cerqueti, Roy, 2018. "Regular paths in financial markets: Investigating the Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 186-194.
    10. Marcel Ausloos & Roy Cerqueti, 2016. "Studies on Regional Wealth Inequalities: the case of Italy," Papers 1602.05356, arXiv.org.
    11. Cunjak Mataković Ivana, 2019. "The empirical analysis of financial reports of companies in Croatia: Benford distribution curve as a benchmark for first digits," Croatian Review of Economic, Business and Social Statistics, Sciendo, vol. 5(2), pages 90-100, December.
    12. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    13. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    14. Ausloos, Marcel & Jovanovic, Franck & Schinckus, Christophe, 2016. "On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 7-14.
    15. Wang, Delu & Chen, Fan & Mao, Jinqi & Liu, Nannan & Rong, Fangyu, 2022. "Are the official national data credible? Empirical evidence from statistics quality evaluation of China's coal and its downstream industries," Energy Economics, Elsevier, vol. 114(C).
    16. Lee, Kang-Bok & Han, Sumin & Jeong, Yeasung, 2020. "COVID-19, flattening the curve, and Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    17. Shi, Jing & Ausloos, Marcel & Zhu, Tingting, 2018. "Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 878-888.
    18. Marcel Ausloos & Roy Cerqueti & Tariq A. Mir, 2018. "Data on the annual aggregated income taxes of the Italian municipalities over the quinquennium 2007-2011," Papers 1806.10935, arXiv.org.
    19. Natasa Omerzu & Iztok Kolar, 2019. "Do the Financial Statements of Listed Companies on the Ljubljana Stock Exchange Pass the Benford’s Law Test?," International Business Research, Canadian Center of Science and Education, vol. 12(1), pages 54-64, January.
    20. Roeland de Kok & Giulia Rotundo, 2022. "Benford Networks," Stats, MDPI, vol. 5(4), pages 1-14, September.

    More about this item

    JEL classification:

    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:2104.07962. 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.