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Scale-free tails in Colombian financial indexes: A primer

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  • Carlos León

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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.

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Bibliographic Info

Paper provided by Banco de la Republica de Colombia in its series Borradores de Economia with number 812.

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Length: 18
Date of creation: Mar 2014
Date of revision:
Handle: RePEc:bdr:borrec:812

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Keywords: Scale-free; Power-law; Zipf’s law; Financial returns. Classification JEL: C46; C58; G32;

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  1. Alejandro Reveiz & Carlos Eduardo León Rincón, . "Índice representativo del mercado de deuda pública interna: IDXTES," Borradores de Economia 488, Banco de la Republica de Colombia.
  2. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  3. X. Freixas & B. Parigi & J-C. Rochet, 2000. "Systemic Risk, Interbank Relations and Liquidity Provision by theCentral Bank," DNB Staff Reports (discontinued) 47, Netherlands Central Bank.
  4. Marsili, Matteo, 2003. "Scale invariance and criticality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 17-24.
  5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  6. 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.
  7. Davide Fiaschi & Imre Kondor & Matteo Marsili & Valerio Volpati, 2013. "The Interrupted Power Law and The Size of Shadow Banking," Papers 1309.2130, arXiv.org, revised Apr 2014.
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