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A simple graphical method to explore tail-dependence in stock-return pairs

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Klaus Abberger () (IFO Munich)

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Abstract

For a bivariate data set the dependence structure can not only be measured globally, for example with the Bravais-Pearson correlation coefficient, but the dependence structure can also be analyzed locally. In this article the exploration of dependencies in the tails of the bivariate distribution is discussed. For this a graphical method which is called chi-plot and which was introduced by Fisher and Switzer (1985, 2001) is used. Examples with simulated data sets illustrate that the chi-plot is suitable for the exploration of dependencies. This graphical method is then used to examine stock-return pairs. The kind of tail-dependence between returns has consequences, for example, for the calculation of the Value at Risk and should be modelled carefully. The application of the chi-plot to various daily stock-return pairs shows that different dependence structures can be found. This graph can therefore be an interesting aid for the modelling of returns.

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Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 04-03.

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Length: 16 pages
Date of creation: Feb 2004
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Handle: RePEc:knz:cofedp:0403

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Keywords: Association; bivariate distribution; chi-plot; copula; correlation; local dependence; tail-dependence;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04. [Downloadable!] (restricted)
  2. Fisher N. I. & Switzer P., 2001. "Graphical Assessment of Dependence: Is a Picture Worth 100 Tests?," The American Statistician, American Statistical Association, vol. 55, pages 233-239, August. [Downloadable!] (restricted)
  3. Tim Bollerslev & Robert F. Engle & Daniel B. Nelson, 1993. "ARCH Models," University of California at San Diego, Economics Working Paper Series 93-49, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
    • Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier. [Downloadable!] (restricted)
  4. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies. [Downloadable!]
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