Journal of Risk

Risk.net

Counterparty risk allocation

Rainer Baule

  • Minimizing the expected shortfall (or other spectral risk measures) of a portfolio of exposures to a small number of defaultable counterparties may lead to economically odd results.
  • For discrete loss distributions, only a sparse finite set of solutions (including corner solutions) can be optimal; with two counterparties, the risk-minimizing allocation is either all-or-nothing or fifty-fifty.
  • In general, the risk-minimizing allocation does not depend monotonically on the input parameters, especially the confidence level used for calculating the expected shortfall.

We address the problem of minimizing the risk of an exposure to a small number of defaultable counterparties based on spectral risk measures, in particular expected shortfall. A typical application is the allocation of cash holdings to a few banks. The resulting risk-minimal allocation turns out to be economically odd or implausible in a number of ways. When the loss distribution is discrete, only a sparse finite set of solutions (including corner solutions) can be optimal. 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 confidence level used for calculating the expected shortfall. This nonmonotonicity also holds for continuous loss distributions. These results strengthen the doubts over the appropriateness of spectral risk measures in the target function for economic decision-making.

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