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Quantifying Stock Return Distributions in Financial Markets.

Federico Botta1, Helen Susannah Moat2, H Eugene Stanley3

  • 1Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, United Kingdom; Data Science Lab, Behavioural Science, Warwick Business School, University of Warwick, Coventry, CV4 7AL, United Kingdom.

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This study analyzed stock market price changes to understand financial crises. It found that price changes follow power law decays at shorter time scales and exponential decay at longer scales.

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Area of Science:

  • Quantitative finance
  • Market dynamics
  • Financial econometrics

Background:

  • Understanding stock market price fluctuations is vital for financial crisis analysis.
  • Price changes occur across diverse time scales, from minutes to longer periods.

Purpose of the Study:

  • To quantify the distribution of stock market price changes across various time scales.
  • To investigate the statistical properties of logarithmic returns for Dow Jones stocks.

Main Methods:

  • Analysis of second-by-second stock data for the Dow Jones Industrial Average (January 2008 - July 2010).
  • Statistical analysis of price change distributions at multiple time scales (300s to 3600s and beyond).

Main Results:

  • Logarithmic price returns exhibit power law decay tails for time scales between 300 and 3600 seconds.
  • For time scales exceeding 3600 seconds, the distribution tails shift to an exponential decay.

Conclusions:

  • The statistical behavior of stock market price changes varies significantly with the time scale analyzed.
  • Findings provide insights for developing more accurate financial market models across different temporal resolutions.