IDEAS home Printed from https://ideas.repec.org/p/col/000094/011144.html
   My bibliography  Save this paper

Scale-free tails in Colombian financial indexes: a primer

Author

Listed:
  • 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.

Suggested Citation

  • Carlos León, 2014. "Scale-free tails in Colombian financial indexes: a primer," Borradores de Economia 11144, Banco de la Republica.
    • Handle: RePEc:col:000094:011144
    as

    Download full text from publisher

    File URL: http://www.banrep.gov.co/sites/default/files/publicaciones/archivos/be_812.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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 Herault & Carlos Eduardo León Rincón, 2008. "Índice representativo del mercado de deuda pública interna: IDXTES," Borradores de Economia 4522, Banco de la Republica.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexander Eastman & Brian Lucey, 2008. "Skewness and asymmetry in futures returns and volumes," Applied Financial Economics, Taylor & Francis Journals, vol. 18(10), pages 777-800.
    2. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    3. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    4. 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.
    5. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    6. López Martín, María del Mar & García, Catalina García & García Pérez, José, 2012. "Treatment of kurtosis in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2032-2045.
    7. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "VaR performance during the subprime and sovereign debt crises: An application to emerging markets," Emerging Markets Review, Elsevier, vol. 20(C), pages 23-41.
    8. Stephen Morris & Muhamet Yildiz, 2019. "Crises: Equilibrium Shifts and Large Shocks," American Economic Review, American Economic Association, vol. 109(8), pages 2823-2854, August.
    9. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    10. Jaramillo-López, Oscar Andrés & Forero-Laverde, Germán & Venegas-Martínez, Francisco, 2020. "Evolución del supuesto de normalidad en finanzas: un análisis epistemológico del tipo Popper-Kuhn ¿Por qué la normalidad no cae en desuso? [Evolution of the assumption of normality in finance: a ep," MPRA Paper 101938, University Library of Munich, Germany.
    11. Paulo Ferreira & Luís Carlos Loures, 2020. "An Econophysics Study of the S&P Global Clean Energy Index," Sustainability, MDPI, vol. 12(2), pages 1-9, January.
    12. Omid M. Ardakani, 2022. "Option pricing with maximum entropy densities: The inclusion of higher‐order moments," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1821-1836, October.
    13. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    14. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    15. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    16. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    17. Hayley Jang & Young Hoon Lee & Rodney Fort, 2019. "Winning In Professional Team Sports: Historical Moments," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 103-120, January.
    18. Scheffknecht, Lukas & Geiger, Felix, 2011. "A behavioral macroeconomic model with endogenous boom-bust cycles and leverage dynamcis," FZID Discussion Papers 37-2011, University of Hohenheim, Center for Research on Innovation and Services (FZID).
    19. V. Alfi & L. Pietronero & A. Zaccaria, 2008. "Minimal Agent Based Model For The Origin And Self-Organization Of Stylized Facts In Financial Markets," Papers 0807.1888, arXiv.org.
    20. Vincenzo Candila, 2013. "A Comparison of the Forecasting Performances of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:col:000094:011144. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Clorith Angelica Bahos Olivera (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.