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Quantifying Stock Return Distributions in Financial Markets

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  • Federico Botta
  • Helen Susannah Moat
  • H Eugene Stanley
  • Tobias Preis

Abstract

Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.

Suggested Citation

  • Federico Botta & Helen Susannah Moat & H Eugene Stanley & Tobias Preis, 2015. "Quantifying Stock Return Distributions in Financial Markets," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-10, September.
    • Handle: RePEc:plo:pone00:0135600
    DOI: 10.1371/journal.pone.0135600
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    References listed on IDEAS

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    1. Yan, C. & Zhang, J.W. & Zhang, Y. & Tang, Y.N., 2005. "Power–law properties of Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 425-432.
    2. Alexander M. Petersen & Fengzhong Wang & Shlomo Havlin & H. Eugene Stanley, 2010. "Market dynamics immediately before and after financial shocks: quantifying the Omori, productivity and Bath laws," Papers 1006.1882, arXiv.org, revised Oct 2010.
    3. Daniele Barchiesi & Helen Susannah Moat & Christian Alis & Steven Bishop & Tobias Preis, 2015. "Quantifying International Travel Flows Using Flickr," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-8, July.
    4. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    5. Frédéric Abergel & Anirban Chakraborti & B.K. Chakrabarti & M. Mitra, 2011. "Econophysics of order-driven markets," Post-Print hal-00872396, HAL.
    6. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical distributions of Chinese stock returns at different microscopic timescales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 495-502.
    7. Zhang, J.W. & Zhang, Y. & Kleinert, H., 2007. "Power tails of index distributions in chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 166-172.
    8. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    9. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    10. Farmer, J. Doyne & Joshi, Shareen, 2002. "The price dynamics of common trading strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 149-171, October.
    11. Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2005. "On fitting the Pareto–Levy distribution to stock market index data: Selecting a suitable cutoff value," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 437-449.
    12. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    13. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    14. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    15. Bertram, William K, 2004. "An empirical investigation of Australian Stock Exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 533-546.
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    Cited by:

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    4. Wu, Ting & Wang, Yue & Li, Ming-Xia, 2017. "Post-hit dynamics of price limit hits in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 464-471.
    5. Abeer ElBahrawy & Laura Alessandretti & Anne Kandler & Romualdo Pastor-Satorras & Andrea Baronchelli, 2017. "Evolutionary dynamics of the cryptocurrency market," Papers 1705.05334, arXiv.org, revised Nov 2017.
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    8. Benjamin M Blau & Ryan J Whitby, 2017. "Range-based volatility, expected stock returns, and the low volatility anomaly," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-19, November.
    9. Jaroonchokanan, Nawee & Termsaithong, Teerasit & Suwanna, Sujin, 2022. "Dynamics of hierarchical clustering in stocks market during financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
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    11. Fernandes, Leonardo H.S. & de Araujo, Fernando H.A. & Tabak, Benjamin M., 2021. "Insights from the (in)efficiency of Chinese sectoral indices during COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    12. Oldham, Matthew, 2020. "Quantifying the concerns of Dimon and Buffett with data and computation," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    13. Fonseca, Carla L.G. & de Resende, Charlene C. & Fernandes, Danilo H.C. & Cardoso, Rodrigo T.N. & de Magalhães, A.R. Bosco, 2021. "Is the choice of the candlestick dimension relevant in econophysics?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    14. Fjærvik, Thomas, 2023. "Crash risk in the Nordic Stock Market - a cross-sectional analysis," Discussion Papers 2023/5, Norwegian School of Economics, Department of Business and Management Science.
    15. L. L. B. Miranda & L. S. Lima, 2024. "Singular Stochastic Differential Equations for Time Evolution of Stocks Within Non-white Noise Approach," Computational Economics, Springer;Society for Computational Economics, vol. 64(5), pages 2685-2694, November.

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