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Zipf's law for share price and company fundamentals

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  • Taisei Kaizoji
  • Michiko Miyano

Abstract

We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of share price follows Zipf's law; that is, it can be approximated by a power law distribution with exponent equal to 1. An examination of the distributions of dividends per share, cash flow per share, and book value per share - three financial indicators that can be assumed to influence corporate value (i.e. share price) - shows that these distributions can also be approximated by a power law distribution with power-law exponent equal to 1. We estimate a panel regression model in which share price is the dependent variable and the three financial indicators are explanatory variables. The two-way fixed effects model that was selected as the best model has quite high power for explaining the actual data. From these results, we can surmise that the reason why share price follows Zipf's law is that corporate value, i.e. company fundamentals, follows Zipf's law.

Suggested Citation

  • Taisei Kaizoji & Michiko Miyano, 2017. "Zipf's law for share price and company fundamentals," Papers 1702.00144, arXiv.org.
    • Handle: RePEc:arx:papers:1702.00144
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    References listed on IDEAS

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    1. Taisei Kaizoji & Michiko Miyano, 2016. "Stock Market Market Crash of 2008: an empirical study of the deviation of share prices from company fundamentals," Papers 1607.03205, arXiv.org.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, December.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    4. Kaizoji, Taisei & Miyano, Michiko, 2016. "Why does the power law for stock price hold?," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 19-23.
    5. Urzua, Carlos M., 2000. "A simple and efficient test for Zipf's law," Economics Letters, Elsevier, vol. 66(3), pages 257-260, March.
    6. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Statistical theories of income and wealth distribution," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-31.
    7. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    8. William J. Reed, 2002. "On the Rank‐Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17, February.
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    Cited by:

    1. Da Silva, Sergio & Matsushita, Raul & Giglio, Ricardo & Massena, Gunther, 2018. "Granularity of the top 1,000 Brazilian companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 68-73.

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