  We provide a necessary and sufficient condition for the ratio of two jointly
alpha-Frechet random variables to be regularly varying. This condition is based
on the spectral representation of the joint distribution and is easy to check
in practice. Our result motivates the notion of the ratio tail index, which
quantifies dependence features that are not characterized by the tail
dependence index. As an application, we derive the asymptotic behavior of the
quotient correlation coefficient proposed in Zhang (2008) in the dependent
case. Our result also serves as an example of a new type of regular variation
of products, different from the ones investigated by Maulik et al. (2002).
