  The stability of the financial system is associated with systemic risk
factors such as the concurrent default of numerous small obligors. Hence it is
of utmost importance to study the mutual dependence of losses for different
creditors in the case of large, overlapping credit portfolios. We analytically
calculate the multivariate joint loss distribution of several credit portfolios
on a non-stationary market. To take fluctuating asset correlations into account
we use an random matrix approach which preserves, as a much appreciated side
effect, analytical tractability and drastically reduces the number of
parameters. We show that for two disjoint credit portfolios diversification
does not work in a correlated market. Additionally we find large concurrent
portfolio losses to be rather likely. We show that significant correlations of
the losses emerge not only for large portfolios with thousands of credit
contracts but also for small portfolios consisting of a few credit contracts
only. Furthermore we include subordination levels, which were established in
collateralized debt obligations to protect the more senior tranches from high
losses. We analytically corroborate the observation that an extreme loss of the
subordinated creditor is likely to also yield a large loss of the senior
creditor.
