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Scale-free tails in Colombian financial indexes: A primer

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  • Carlos León

Abstract

A maximum likelihood method for estimating the power-law exponent verifies that the positive and negative tails of the Colombian stock market index (IGBC) and the Colombian peso exchange rate (TRM) approximate a scale-free distribution, whereas none of the heavy tails of a local sovereign securities index (IDXTES) are a plausible case for such distribution. Results also (i) support critiques regarding the flaws of ordinary least squares estimation methods for scale-free distributions; (ii) question the validity of Zipf’s law; (iii) suggest that IGBC and TRM display the scale-free nature documented as a stylized fact of financial returns, and that they may be following a gradually truncated Lévy flight; and (iv) suggest that local financial markets are self-organized systems.

Suggested Citation

  • Carlos León, 2014. "Scale-free tails in Colombian financial indexes: A primer," Borradores de Economia 812, Banco de la Republica de Colombia.
    • Handle: RePEc:bdr:borrec:812
    DOI: 10.32468/be.812
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    References listed on IDEAS

    as
    1. Carlos León & Ron J. Berndsen, 2013. "Modular scale-free architecture of Colombian financial networks: Evidence and challenges with financial stability in view," Borradores de Economia 11104, Banco de la Republica.
    2. Freixas, Xavier & Parigi, Bruno M & Rochet, Jean-Charles, 2000. "Systemic Risk, Interbank Relations, and Liquidity Provision by the Central Bank," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(3), pages 611-638, August.
    3. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    4. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    5. Marsili, Matteo, 2003. "Scale invariance and criticality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 17-24.
    6. Alejandro Reveiz & Carlos Eduardo León Rincón, 2008. "Índice representativo del mercado de deuda pública interna: IDXTES," Borradores de Economia 488, Banco de la Republica de Colombia.
    7. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, H.Eugene, 2003. "Understanding the cubic and half-cubic laws of financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 1-5.
    8. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    9. Davide Fiaschi & Imre Kondor & Matteo Marsili & Valerio Volpati, 2014. "The Interrupted Power Law and the Size of Shadow Banking," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
    10. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
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    Cited by:

    1. León, Carlos & Machado, Clara & Sarmiento, Miguel, 2018. "Identifying central bank liquidity super-spreaders in interbank funds networks," Journal of Financial Stability, Elsevier, vol. 35(C), pages 75-92.
    2. León, C., 2015. "Financial stability from a network perspective," Other publications TiSEM bb2e4e44-e842-45c6-a946-4, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    Scale-free; Power-law; Zipf’s law; Financial returns.;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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