Abstract
We investigate whether the distribution of share price follows a power law distribution at the regional level, using data from companies publicly listed worldwide. Based on ISO country codes, 7,796 companies are divided into four regions: America, Asia, Europe, and the rest of the world. We find that, at the regional level, the distributions of share price follow a power law distribution and that the power law exponents estimated by region are quite diverse. The power law exponent for Europe is close to that of the world and indicates a Zipf distribution. We also find that the theoretical share price and fundamentals estimated using a panel regression model hold to a power law at the regional level. A panel regression in which share price is the dependent variable and dividends per share, cash flow per share, and book value per share are explanatory variables identifies the two-way fixed effects model as the best model for all regions. The results of this research are consistent with our previous findings that a power law for share price holds at the world level based on panel data for the period 2004–2013 as well as cross-sectional data for these 10 years.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
America includes North America, South America, and Central America. Asia includes eastern Asia, southern Asia, central Asia, and the Middle East. The rest of the world includes Oceania and Africa.
- 2.
Total observations available in each region were as follows: America, 8935; Asia, 27,407; Europe, 8,791; rest of the world, 2028.
- 3.
The probability density function for the Pareto distribution is defined as \(f(x)=\frac{\alpha k^{\alpha }}{x^{\alpha +1}}, \quad x \ge k > 0 \).
- 4.
The graph fo the rest of the world is excluded. This is done throughout since the numbers of companies in this is only 5.2 % of the total.
- 5.
Details of the derivations are presented (Kaizoji and Miyano 2016c).
- 6.
- 7.
The two classes of measurement and computational details for this test are found in Čížek and Weron (2005, Chap. 13)
- 8.
The two-way random effects model cannot be used since we use unbalanced panel observations.
- 9.
Woodlridge (2010, p.299) proposes a method that uses residuals from pool OLS and checks the existence of serial correlations.
References
Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca & Frédéric Abergel (2011a) Econophysics review: I. Empirical facts, Quantitative Finance, Volume 11, Issue 7 991–1012.
Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca & Frédéric Abergel (2011b) Econophysics review: II. Agent-based models, Quantitative Finance, Volume 11, Issue 7 1013–1041.
Axtell R L. (2001) Zipf’s Distribution of U.S.Firm Sizes, Science, Vol. 293, 1818–1820.
Clauset A., Shalizi C.R., and Newman M. E. (2009) Power law distributions in empirical data, SIAM Review, Vol. 51, No.4, pp.661–703.
Čížek P. Härdlle, W. Weron, R. (2005) Statiscal tools for finance and insurance. Springer, Berlin.
D’Agostino, R. B. and Stephans, M.A. (1986) Goodness-of-Fit Techniques, Marcel Dekker New York.
Gabaix, X. (1999). Zipf’s Law for Cities: An Explanation. The Quarterly Journal of Economics, 739–767.
Kaizoji T. and Miyano M. (2016a) Why does power law for stock price hold? Journal of Chaos Soliton and Fractals. (press).
Kaizoji T. and Miyano M. (2016b) Stock Market Crash of 2008: an empirical study on the deviation of share prices from company fundamentals, mimeo, to be submitted.
Kaizoji T. and Miyano M. (2016c) Zipf’s law for company fundamentals and share price, mimeo, to be submitted.
Newman M. E.J. (2005) Power laws, Pareto distributions an Zipf’s law, Contemporary Physics, Volume 46, Issue 5, 323–351.
Woodlridge J. M. (2010) Econometric Analysis of Cross Section and Panel Data, MIT press.
Acknowledgements
This research was supported by JSPS KAKENHI Grant Number 2538404, 2628089.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Miyano, M., Kaizoji, T. (2017). Power Law Distributions for Share Price and Financial Indicators: Analysis at the Regional Level. In: Abergel, F., et al. Econophysics and Sociophysics: Recent Progress and Future Directions. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-319-47705-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-47705-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47704-6
Online ISBN: 978-3-319-47705-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)