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The Joint Distribution Of Stock Returns Is Not Elliptical

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  • RÉMY CHICHEPORTICHE

    ()
    (Capital Fund Management, 6–8 Boulevard Haussmann, Paris, 75009, France)

  • JEAN-PHILIPPE BOUCHAUD

    ()
    (Capital Fund Management, 6–8 Boulevard Haussmann, Paris, 75009, France)

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    Abstract

    Using a large set of daily US and Japanese stock returns, we test in detail the relevance of Student models, and of more general elliptical models, for describing the joint distribution of returns. We find that while Student copulas provide a good approximation for strongly correlated pairs of stocks, systematic discrepancies appear as the linear correlation between stocks decreases, that rule out all elliptical models. Intuitively, the failure of elliptical models can be traced to the inadequacy of the assumption of a single volatility mode for all stocks. We suggest several ideas of methodological interest to efficiently visualise and compare different copulas. We identify the rescaled difference with the Gaussian copula and the central value of the copula as strongly discriminating observables. We insist on the need to shun away from formal choices of copulas with no financial interpretation.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 15 (2012)
    Issue (Month): 03 ()
    Pages: 1250019-1-1250019-23

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    Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:03:p:1250019-1-1250019-23

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    Related research

    Keywords: Copulas; stock returns; multivariate distribution; linear correlation; Non-linear dependences; Student distribution; elliptical distributions;

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    Cited by:
    1. R\'emy Chicheportiche & Jean-Philippe Bouchaud, 2013. "A nested factor model for non-linear dependences in stock returns," Science & Finance (CFM) working paper archive 1309.3102, Science & Finance, Capital Fund Management.

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