We address the problem of minimizing the risk of an exposure (e.g., cash holdings) to a small number of defaultable counterparties based on spectral risk measures, in particular the expected shortfall. The resulting risk-minimal allocation turns out to be economically implausible in a number of ways: When the loss distribution is discrete, only corner solutions can be optimal, and the optimization problem is ill-posed, as the risk-minimal allocation does not depend continuously on the input parameters. With two counterparties, only a total allocation to one counterparty or a fifty-fifty solution can be optimal. In general, the risk-minimal allocation is not monotonic in the quantile used for calculating the expected shortfall. This non-monotonicity also holds for continuous loss distributions. These results strengthen the doubts on the appropriateness of spectral risk measures in the target function for economic decision making.