Risk Measurement in the Presence of Background Risk

27 Pages Posted: 12 Aug 2007 Last revised: 3 Jan 2014

See all articles by Andreas Tsanakas

Andreas Tsanakas

Bayes Business School (formerly Cass), City, University of London

Abstract

A distortion-type risk measure is constructed, which evaluates the risk of any uncertain position in the context of a portfolio that contains that position and a fixed background risk. The risk measure can also be used to assess the performance of individual risks within a portfolio, allowing for the portfolio's re-balancing, an area where standard capital allocation methods fail. It is shown that the properties of the risk measure depart from those of coherent distortion measures. In particular, it is shown that the presence of background risk makes risk measurement sensitive to the scale and aggregation of risk. The case of risks following elliptical distributions is examined in more detail and precise characterisations of the risk measure's aggregation properties are obtained.

Keywords: Risk measures, Background risk, Capital allocation, Portfolio management, Elliptical distributions

Suggested Citation

Tsanakas, Andreas, Risk Measurement in the Presence of Background Risk. The final version of this article appeared as: Tsanakas A (2008), 'Risk measurement in the presence of background risk', Insurance: Mathematics and Economics, 42(2), p.520-528., Available at SSRN: https://ssrn.com/abstract=1006634

Andreas Tsanakas (Contact Author)

Bayes Business School (formerly Cass), City, University of London ( email )

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