Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs...

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Tail -Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series

Transcript of Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs...

Page 1: Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series . 126 Reihe Ökonomie

Tail-Dependence in Stock-Return Pairs

Ines Fortin, Christoph Kuzmics

126

Reihe Ökonomie

Economics Series

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126

Reihe Ökonomie

Economics Series

Tail-Dependence in Stock-Return Pairs

Ines Fortin, Christoph Kuzmics

November 2002

Institut für Höhere Studien (IHS), Wien Institute for Advanced Studies, Vienna

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Contact: Ines Fortin Department of Economics and Finance Institute for Advanced Studies Stumpergasse 56, A-1060 Vienna, Austria (: +43/1/599 91-165 email: [email protected] Christoph Kuzmics Faculty of Economics and Politics University of Cambridge Sidgwick Avenue Cambridge CB3 9DD U.K. email: [email protected]

Founded in 1963 by two prominent Austrians living in exile – the sociologist Paul F. Lazarsfeld and the economist Oskar Morgenstern – with the financial support from the Ford Foundation, the Austrian Federal Ministry of Education and the City of Vienna, the Institute for Advanced Studies (IHS) is the first institution for postgraduate education and research in economics and the social sciences in Austria. The Economics Series presents research done at the Department of Economics and Finance and

aims to share “work in progress” in a timely way before formal publication. As usual, authors bear full responsibility for the content of their contributions. Das Institut für Höhere Studien (IHS) wurde im Jahr 1963 von zwei prominenten Exilösterreichern –dem Soziologen Paul F. Lazarsfeld und dem Ökonomen Oskar Morgenstern – mit Hilfe der Ford-Stiftung, des Österreichischen Bundesministeriums für Unterricht und der Stadt Wien gegründet und ist somit die erste nachuniversitäre Lehr- und Forschungsstätte für die Sozial- und Wirtschafts -

wissenschaften in Österreich. Die Reihe Ökonomie bietet Einblick in die Forschungsarbeit der Abteilung für Ökonomie und Finanzwirtschaft und verfolgt das Ziel, abteilungsinterne Diskussionsbeiträge einer breiteren fachinternen Öffentlichkeit zugänglich zu machen. Die inhaltliche Verantwortung für die veröffentlichten Beiträge liegt bei den Autoren und Autorinnen.

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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 is

such that it allows for the presence of lower tail-dependence and for asymmetric tail-

dependence, and that it encompasses the normal or t-copula. 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.

Keywords Value-at-Risk, copula, non-normal bivariate GARCH, asymmetric dependence, profile

likelihood-ratio test

JEL Classifications C12, C32, C52, C51, G15

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Comments The authors would like to thank Paul Embrechts, Andrew Harvey, Steve Satchell, three anonymous referees, and particularly Alessio Sancetta for helpful comments and suggestions.

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Contents

1 Introduction 1

2 Motivating Informal Evidence 4

3 Copula Choice 7

4 Model, Likelihood and Tests 12

5 Empirical Results 15

6 Conclusion 19

References 21

Tables 23

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Page 11: Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series . 126 Reihe Ökonomie

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Page 26: Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series . 126 Reihe Ökonomie

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Page 28: Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series . 126 Reihe Ökonomie

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Page 38: Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series . 126 Reihe Ökonomie

Authors: Ines Fortin, Christoph Kuzmics Title: Tail-Dependence in Stock-Return Pairs Reihe Ökonomie / Economics Series 126 Editor: Robert M. Kunst (Econometrics)

Associate Editors: Walter Fisher (Macroeconomics), Klaus Ritzberger (Microeconomics) ISSN: 1605-7996 © 2002 by the Department of Economics and Finance, Institute for Advanced Studies (IHS), Stumpergasse 56, A-1060 Vienna • ( +43 1 59991-0 • Fax +43 1 59991-555 • http://www.ihs.ac.at

Page 39: Tail-Dependence in Stock-Return Pairs · 2017. 3. 27. · Tail-Dependence in Stock-Return Pairs Ines Fortin, Christoph Kuzmics 126 Reihe Ökonomie Economics Series . 126 Reihe Ökonomie

ISSN: 1605-7996