  We propose a novel strategy for multivariate extreme value index estimation.
In applications such as finance, volatility and risk present in the components
of a multivariate time series are often driven by the same underlying factors,
such as the subprime crisis in the US. To estimate the latent risk, we apply a
two-stage procedure. First, a set of independent latent series is estimated
using a method of latent variable analysis. Then, univariate risk measures are
estimated individually for the latent series to assess their contribution to
the overall risk. As our main theoretical contribution, we derive conditions
under which the effect of the first step to the asymptotic behavior of the risk
estimators is negligible. Simulations demonstrate the theory under both i.i.d.
and dependent data, and an application into financial data illustrates the
usefulness of the method in extracting joint sources of risk in practice.
