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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 (v) suggest that local financial markets are self-organized systems.

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Paper provided by BANCO DE LA REPÚBLICA in its series BORRADORES DE ECONOMIA with number 011144.

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Length: 18
Date of creation: 07 Mar 2014
Handle: RePEc:col:000094:011144
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Keywords: Scale-free; power-law; Zipf’s law; financial returns.;

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Find related papers by 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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  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 011104, BANCO DE LA REPÚBLICA.
  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. N. Lesca, 2011. "Introduction," Post-Print halshs-00640604, HAL.
  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 Herault & Carlos Eduardo León Rincón, 2008. "Índice representativo del mercado de deuda pública interna: IDXTES," BORRADORES DE ECONOMIA 004522, BANCO DE LA REPÚBLICA.
  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: 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, 2013. "The Interrupted Power Law and The Size of Shadow Banking," Discussion Papers 2013/166, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  10. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
  11. C. Dominguez-Pery, 2011. "Introduction," Post-Print halshs-00740570, HAL.
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