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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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    3. Fa-Bin Shi & Xiao-Qian Sun & Jin-Hua Gao & Li Xu & Hua-Wei Shen & Xue-Qi Cheng, 2019. "Anomaly detection in Bitcoin market via price return analysis," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-11, June.
    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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    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).
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