Selecting Copulas for Risk Management

24 Pages Posted: 27 Jul 2006

See all articles by Kees C. G. Koedijk

Kees C. G. Koedijk

Tilburg University - Department of Finance

Marno Verbeek

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

Erik Kole

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

Multiple version iconThere are 3 versions of this paper

Date Written: April 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 favour 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: C12, C14, G11

Suggested Citation

Koedijk, Kees G. and Verbeek, Marno and Kole, Erik, Selecting Copulas for Risk Management (April 2006). CEPR Discussion Paper No. 5652, Available at SSRN: https://ssrn.com/abstract=920870

Kees G. Koedijk (Contact Author)

Tilburg University - Department of Finance ( email )

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

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

Erik Kole

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

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