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A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford’s Law

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  • Kalaichelvan, Mohandass
  • Lim Kai Jie, Shawn

Abstract

In this study, we test the hypothesis that psychological barriers exist in 5 European Equity Market indices [ATX, CAC, DAX, FTSE, SMI]. We employ both a traditional methodology that assumes a uniform distribution of M-Values and a modified approach that accounts for the fact that the digits of stock prices may be distributed in accordance with Benford’s law. In addition, we test the validity of the various assumptions employed in these tests using a Monte Carlo Simulation and Kuiper’s Modified Kolmogorov-Smirnov Goodness of Fit Test. We find evidence for barriers in 1 index [SMI] at the 1000 level under the assumption of uniformity but no significant evidence of barriers at the 100 level or at the 1000 level in the remaining indices. We also find evidence that substantiates the criticism of the use of the uniformity assumption for tests at the 1000 level in favour of a distribution consistent with Benford’s Law. However, we do not reach a different conclusion on the presence of psychological barriers when tests are performed without the implicit use of that uniformity assumption. In addition, we find possible evidence of price clustering around round numbers at the 1000 level in 2 indices [CAC, DAX] even after adjusting for the expected concentration within the region due to Benford-specific effects.

Suggested Citation

  • Kalaichelvan, Mohandass & Lim Kai Jie, Shawn, 2012. "A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford’s Law," MPRA Paper 40960, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:40960
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    References listed on IDEAS

    as
    1. Sonnemans, Joep, 2006. "Price clustering and natural resistance points in the Dutch stock market: A natural experiment," European Economic Review, Elsevier, vol. 50(8), pages 1937-1950, November.
    2. David Giles, 2007. "Benford's law and naturally occurring prices in certain ebaY auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 157-161.
    3. Bertola, Giuseppe & Caballero, Ricardo J, 1992. "Target Zones and Realignments," American Economic Review, American Economic Association, vol. 82(3), pages 520-536, June.
    4. Harris, Lawrence, 1991. "Stock Price Clustering and Discreteness," Review of Financial Studies, Society for Financial Studies, vol. 4(3), pages 389-415.
    5. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
    6. Morrow, John, 2014. "Benford's Law, families of distributions and a test basis," LSE Research Online Documents on Economics 60364, London School of Economics and Political Science, LSE Library.
    7. Dorfleitner, Gregor & Klein, Christian, 2009. "Psychological barriers in European stock markets: Where are they?," Global Finance Journal, Elsevier, vol. 19(3), pages 268-285.
    8. Donaldson, R. Glen & Kim, Harold Y., 1993. "Price Barriers in the Dow Jones Industrial Average," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(03), pages 313-330, September.
    9. Schindler, Robert M & Kirby, Patrick N, 1997. " Patterns of Rightmost Digits Used in Advertised Prices: Implications for Nine-Ending Effects," Journal of Consumer Research, Oxford University Press, vol. 24(2), pages 192-201, September.
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    More about this item

    Keywords

    Benford’s Law; psychological barriers in stock prices; significance of round numbers in stock prices;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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