  We investigate a multi-factor extension of the asymptotic single risk factor
(ASRF) model that underlies the capital charges of the "Basel II Accord". In
this extended model, it is still possible to derive closed-form solutions for
the risk contributions to Value-at-Risk and Expected Shortfall. As an
application of the risk contribution formulae we introduce a new concept for a
diversification measure. The use of this new measure is illustrated by an
example calculated with a two-factor model. The results with this model
indicate that, thanks to dependence on not fully correlated systematic sectors,
there can be a substantial reduction of risk contributions by sectoral
diversification effects.
