  Using one of the key property of copulas that they remain invariant under an
arbitrary monotonous change of variable, we investigate the null hypothesis
that the dependence between financial assets can be modeled by the Gaussian
copula. We find that most pairs of currencies and pairs of major stocks are
compatible with the Gaussian copula hypothesis, while this hypothesis can be
rejected for the dependence between pairs of commodities (metals).
Notwithstanding the apparent qualification of the Gaussian copula hypothesis
for most of the currencies and the stocks, a non-Gaussian copula, such as the
Student's copula, cannot be rejected if it has sufficiently many ``degrees of
freedom''. As a consequence, it may be very dangerous to embrace blindly the
Gaussian copula hypothesis, especially when the correlation coefficient between
the pair of asset is too high as the tail dependence neglected by the Gaussian
copula can be as large as 0.6, i.e., three out five extreme events which occur
in unison are missed.
