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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40960.

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Date of creation: 28 Aug 2012
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Handle: RePEc:pra:mprapa:40960

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

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  1. 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.
  2. Bertola, Giuseppe & Caballero, Ricardo, 1990. "Target Zones and Realignments," CEPR Discussion Papers 398, C.E.P.R. Discussion Papers.
  3. Dorfleitner, Gregor & Klein, Christian, 2009. "Psychological barriers in European stock markets: Where are they?," Global Finance Journal, Elsevier, vol. 19(3), pages 268-285.
  4. Harris, Lawrence, 1991. "Stock Price Clustering and Discreteness," Review of Financial Studies, Society for Financial Studies, vol. 4(3), pages 389-415.
  5. Koedijk, Kees G. & Stork, Philip A., 1994. "Should we care? psychological barriers in stock markets," Economics Letters, Elsevier, vol. 44(4), pages 427-432, April.
  6. Schindler, Robert M & Kirby, Patrick N, 1997. " Patterns of Rightmost Digits Used in Advertised Prices: Implications for Nine-Ending Effects," Journal of Consumer Research, University of Chicago Press, vol. 24(2), pages 192-201, September.
  7. 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.
  8. 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.
  9. 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).
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