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Spectral Capital Allocation

by Ludger Overbeck of the Institute of Mathematics, University of Giessen & HypoVereinbank

July 27, 2004

Abstract: In the paper the theory of spectral risk measures is applied to the question of capital allocation. Spectral risk measures enables the financial institution to associated with each loss level a risk aversion weight. If higher losses have higher risk aversion this leads to a coherent risk measure. Consistently with this coherent risk measure a capital allocation scheme is proposed which is basically a sensitivity measure - a differential - of the portfolio with respect to subportfolios or single transactions. Additionally the proposed allocation rule supports diversification, in contrast to many other allocation rules based on Value-at-Risk and volatility contributions.

Keywords: Capital allocation, spectral risk measures, risk aversion, economic capital.

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