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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

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    3. 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.
    4. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
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    8. 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.
    9. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    10. 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..
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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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