Selecting Copulas for Risk Management
28 Pages Posted: 7 Mar 2005
Date Written: September 11, 2006
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.
Keywords: Financial dependence, copulas, distributional tests, tail dependence
JEL Classification: G11, C12, C14
Suggested Citation: Suggested Citation