Selecting Copulas for Risk Management

Posted: 22 Jun 2007

See all articles by Erik Kole

Erik Kole

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute; ERIM; Tinbergen Institute

Marno Verbeek

Erasmus University - Rotterdam School of Management; Erasmus Research Institute of Management (ERIM); Netspar

Kees C. G. Koedijk

Tilburg University - Department of Finance

Multiple version iconThere are 3 versions of this paper

Abstract

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper, we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student's t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.

Keywords: Financial dependence, Risk management, Copulas, Distributional tests, Tail dependence

JEL Classification: G11, C12, C14

Suggested Citation

Kole, Erik and Verbeek, Marno and Koedijk, Kees G., Selecting Copulas for Risk Management. Journal of Banking and Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=993293

Erik Kole (Contact Author)

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
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HOME PAGE: http://people.few.eur.nl/kole

ERIM

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3000 DR Rotterdam
Netherlands

Tinbergen Institute ( email )

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Rotterdam, 3062 PA
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HOME PAGE: http://people.few.eur.nl/kole

Marno Verbeek

Erasmus University - Rotterdam School of Management ( email )

P.O. Box 1738
Room T09-53
3000 DR Rotterdam
Netherlands
+31 10 408 2790 (Phone)

HOME PAGE: http://www.rsm.nl/mverbeek

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Netspar

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Kees G. Koedijk

Tilburg University - Department of Finance ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4663048 (Phone)
+31 13 4662052 (Fax)

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