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The Distribution Of Returns Of Stock Prices

Author

Listed:
  • LUÍS A. N. AMARAL

    (Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA)

  • VASILIKI PLEROU

    (Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA)

  • PARAMESWARAN GOPIKRISHNAN

    (Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA)

  • MARTIN MEYER

    (Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA)

  • H. EUGENE STANLEY

    (Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA)

Abstract

We perform a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets. We consider (i) the trades and quotes (TAQ) database, for which we analyze 40 million records for 1000 US companies for the 2-year period 1994–95, and (ii) the Center for Research and Security Prices (CRSP) database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-year period 1962–96. We study the probability distribution of returns over varying time scales — from 5 min up to 4 years. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponentα ≈ 3— well outside the stable Lévy regime0

Suggested Citation

  • Luís A. N. Amaral & Vasiliki Plerou & Parameswaran Gopikrishnan & Martin Meyer & H. Eugene Stanley, 2000. "The Distribution Of Returns Of Stock Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 365-369.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:03:n:s0219024900000218
    DOI: 10.1142/S0219024900000218
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    Citations

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    Cited by:

    1. Victor Olkhov, 2023. "Market-Based Probability of Stock Returns," Papers 2302.07935, arXiv.org, revised Feb 2024.
    2. Chen, Feier & Tian, Kang & Ding, Xiaoxu & Miao, Yuqi & Lu, Chunxia, 2016. "Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1058-1066.
    3. Lasko Basnarkov & Viktor Stojkoski & Zoran Utkovski & Ljupco Kocarev, 2019. "Option Pricing With Heavy-Tailed Distributions Of Logarithmic Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-35, November.
    4. Sudip Ratan Chandra & Diganta Mukherjee, 2016. "Barrier Option Under Lévy Model : A PIDE and Mellin Transform Approach," Mathematics, MDPI, vol. 4(1), pages 1-18, January.
    5. Olkhov, Victor, 2023. "The Market-Based Statistics of “Actual” Returns of Investors," MPRA Paper 116896, University Library of Munich, Germany.
    6. Yoshio Miyahara & Alexander Novikov, 2001. "Geometric Lévy Process Pricing Model," Research Paper Series 66, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 723-736.
    8. Wang, Lei & Liu, Lutao, 2020. "Long-range correlation and predictability of Chinese stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).

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