Spectral Risk Measures for Credit Portfolios

by Claudio Albanese of the University of Toronto, and
Stephan Lawi of the University of Toronto and the National University of Singapore

April 15, 2003

Abstract: In this article, we experiment with several different risk measures such as standard deviation, value-at-risk, expected shortfall and power-law spectral measures. We consider several families of test-portfolios, one with a typical market risk profit-and-loss profile, and the others containing defaultable bonds of various credit ratings and various degree of diversification. We find that the risk measures are roughly equivalent on the market risk portfolios but differ significantly on the credit ones. In fact, value-at-risk as well as some coherent risk measures including expected shortfall have counter-intuitive features as a function of the degree of diversification for return distributions deviating substantially from the normal. Certain spectral risk measures possess the most intuitive properties regarding diversification.

JEL Classification: C13, D81, G11, G12.

Keywords: value-at-risk, expected shortfall, spectral risk measure, coherence, credit risk, diversification risk.

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