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Selecting Copulas for Risk Management


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

September 11, 2006


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 \studt copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the \studt 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.

Number of Pages in PDF File: 28

Keywords: Financial dependence, copulas, distributional tests, tail dependence

JEL Classification: G11, C12, C14

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Date posted: March 7, 2005  

Suggested Citation

Kole, Erik and Verbeek, Marno and Koedijk, Kees C. G., Selecting Copulas for Risk Management (September 11, 2006). Available at SSRN: http://ssrn.com/abstract=676966 or http://dx.doi.org/10.2139/ssrn.676966

Contact Information

Erik Kole (Contact Author)
Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute ( email )
P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 12 58 (Phone)
HOME PAGE: http://people.few.eur.nl/kole
ERIM
P.O. Box 1738
3000 DR Rotterdam
Netherlands
Tinbergen Institute ( email )
Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands
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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