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Tail‐dependence in stock‐return pairs

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  • Ines Fortin
  • Christoph Kuzmics

Abstract

The empirical joint distribution of return pairs on stock indices displays high tail‐dependence in the lower tail and low tail‐dependence in the upper tail. The presence of tail‐dependence is not compatible with the assumption of (conditional) joint normality. The presence of asymmetric tail‐dependence is not compatible with the assumption of a joint student‐t distribution. A general test for one dependence structure versus another via the profile likelihood is described and employed in a bivariate GARCH model, where the joint distribution of the disturbances is split into its marginals and its copula. The copula used in the paper is such that it allows for the existence of lower tail‐dependence and for asymmetric tail‐dependence, and is such that it encompasses the normal or t‐copula, depending on the benchmark tested. The model is estimated using bivariate data on a set of European stock indices. We find that the assumption of normal or student‐t dependence is easily rejected in favour of an asymmetrically tail‐dependent distribution. Copyright © 2002 John Wiley & Sons, Ltd.

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  • Ines Fortin & Christoph Kuzmics, 2002. "Tail‐dependence in stock‐return pairs," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 89-107, April.
    • Handle: RePEc:wly:isacfm:v:11:y:2002:i:2:p:89-107
    DOI: 10.1002/isaf.216
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    Cited by:

    1. Giovanni De Luca & Giorgia Rivieccio, 2009. "Archimedean copulae for risk measurement," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 907-924.
    2. Dobrić, Jadran & Frahm, Gabriel & Schmid, Friedrich, 2007. "Dependence of stock returns in bull and bear markets," Discussion Papers in Econometrics and Statistics 9/07, University of Cologne, Institute of Econometrics and Statistics.
    3. Janani Sri S. & Parthajit Kayal & G. Balasubramanian, 2022. "Can Equity be Safe-haven for Investment?," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 21(1), pages 32-63, March.
    4. Su, Jianxi & Hua, Lei, 2017. "A general approach to full-range tail dependence copulas," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 49-64.
    5. Pourkhanali, Armin & Kim, Jong-Min & Tafakori, Laleh & Fard, Farzad Alavi, 2016. "Measuring systemic risk using vine-copula," Economic Modelling, Elsevier, vol. 53(C), pages 63-74.
    6. YiHao Lai, 2008. "Does Asymmetric Dependence Structure Matter? A Value-at-Risk View," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 7(3), pages 249-268, December.
    7. Krämer, Walter & van Kampen, Maarten, 2011. "A simple nonparametric test for structural change in joint tail probabilities," Economics Letters, Elsevier, vol. 110(3), pages 245-247, March.
    8. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    9. Magnolia Sosa Castro & Christian Bucio Pacheco & Héctor Eduardo Díaz Rodríguez, 2021. "Extreme Volatility Dependence in Exchange Rate," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, vol. 40(82), pages 25-55, February.
    10. Fischer, Matthias J., 2003. "Tailoring copula-based multivariate generalized hyperbolic secant distributions to financial return data: an empirical investigation," Discussion Papers 47/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    11. Lai, YiHao & Tseng, Jen-Ching, 2010. "The role of Chinese stock market in global stock markets: A safe haven or a hedge?," International Review of Economics & Finance, Elsevier, vol. 19(2), pages 211-218, April.
    12. Knyazev, Alexander & Lepekhin, Oleg & Shemyakin, Arkady, 2016. "Joint distribution of stock indices: Methodological aspects of construction and selection of copula models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 30-53.
    13. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    14. Thomas Fung & Eugene Seneta, 2010. "Modelling and Estimation for Bivariate Financial Returns," International Statistical Review, International Statistical Institute, vol. 78(1), pages 117-133, April.
    15. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    16. Dias, Alexandra & Embrechts, Paul, 2010. "Modeling exchange rate dependence dynamics at different time horizons," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1687-1705, December.
    17. Xiao, Qin & Yan, Meilan & Zhang, Dalu, 2023. "Commodity market financialization, herding and signals: An asymmetric GARCH R-vine copula approach," International Review of Financial Analysis, Elsevier, vol. 89(C).
    18. Giovanni De Luca & Paola Zuccolotto, 2011. "A tail dependence-based dissimilarity measure for financial time series clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 323-340, December.
    19. Abberger, Klaus, 2004. "A simple graphical method to explore tail-dependence in stock-return pairs," CoFE Discussion Papers 04/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    20. Filip Žikeš, 2007. "Dependence Structure and Portfolio Diversification on Central European Stock Markets," Working Papers IES 2007/02, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jan 2007.
    21. Marco Valerio Geraci & Tomas Garbaravicius & David Veredas, 2016. "Short Selling in the Tails," Working Papers ECARES ECARES 2016-30, ULB -- Universite Libre de Bruxelles.
    22. Dobric Jadran & Frahm Gabriel & Schmid Friedrich, 2013. "Dependence of Stock Returns in Bull and Bear Markets," Dependence Modeling, De Gruyter, vol. 1, pages 94-110, December.
    23. Geraci, Marco Valerio & Garbaravičius, Tomas & Veredas, David, 2018. "Short selling in extreme events," Journal of Financial Stability, Elsevier, vol. 39(C), pages 90-103.
    24. Stübinger, Johannes & Mangold, Benedikt & Krauss, Christopher, 2016. "Statistical arbitrage with vine copulas," FAU Discussion Papers in Economics 11/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    25. Arno Onken & Steffen Grünewälder & Matthias H J Munk & Klaus Obermayer, 2009. "Analyzing Short-Term Noise Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation," PLOS Computational Biology, Public Library of Science, vol. 5(11), pages 1-13, November.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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