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

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  • 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.

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  • 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
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    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 Fraudâ€," 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.
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