Counterparty Risk Allocation

39 Pages Posted: 20 Aug 2019

Date Written: August 16, 2019


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.

Keywords: conditional value-at-risk, credit portfolio, counterparty risk, expected shortfall, ill-posedness, spectral risk measures

JEL Classification: C44, D81, G11, G21

Suggested Citation

Baule, Rainer, Counterparty Risk Allocation (August 16, 2019). Available at SSRN: or

Rainer Baule (Contact Author)

University of Hagen ( email )

Universitaetsstrasse 41
Hagen, 58097

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