In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments, implying the potential for penalizing portfolio diversification. For this purpose we introduce the notion of extreme-aggregation risk measures. The extreme-aggregation measure characterizes the most superadditive behavior of a risk measure by yielding the worst-possible diversification ratio across dependence structures. One of the main contributions is demonstrating that, for a wide range of risk measures, the extreme-aggregation measure corresponds to the smallest dominating coherent risk measure. In our main result, it is shown that the extreme-aggregation measure induced by a distortion risk measure is a coherent distortion risk measure. In the case of convex risk measures, a general robust representation of coherent extreme-aggregation measures is provided. In particular, the extreme-aggregation measure induced by a convex shortfall risk measure is a coherent expectile. These results show that, in the presence of dependence uncertainty, quantification of a coherent risk measure is often necessary, an observation that lends further support to the use of coherent risk measures in portfolio risk management.

Wang, R., Bignozzi, V., & Tsanakas, A. (2015). How superadditive can a risk measure be?. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 6(1), 776-803 [10.1137/140981046].

How superadditive can a risk measure be?

BIGNOZZI, VALERIA
;
2015

Abstract

In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments, implying the potential for penalizing portfolio diversification. For this purpose we introduce the notion of extreme-aggregation risk measures. The extreme-aggregation measure characterizes the most superadditive behavior of a risk measure by yielding the worst-possible diversification ratio across dependence structures. One of the main contributions is demonstrating that, for a wide range of risk measures, the extreme-aggregation measure corresponds to the smallest dominating coherent risk measure. In our main result, it is shown that the extreme-aggregation measure induced by a distortion risk measure is a coherent distortion risk measure. In the case of convex risk measures, a general robust representation of coherent extreme-aggregation measures is provided. In particular, the extreme-aggregation measure induced by a convex shortfall risk measure is a coherent expectile. These results show that, in the presence of dependence uncertainty, quantification of a coherent risk measure is often necessary, an observation that lends further support to the use of coherent risk measures in portfolio risk management.
Articolo in rivista - Articolo scientifico
Dependence uncertainty; Distortion risk measures; Diversification; Expectiles; Risk aggregation; Shortfall risk measures; Numerical Analysis; Finance; Applied Mathematics
English
776
803
28
Wang, R., Bignozzi, V., & Tsanakas, A. (2015). How superadditive can a risk measure be?. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 6(1), 776-803 [10.1137/140981046].
Wang, R; Bignozzi, V; Tsanakas, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/143464
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