Combining risk measures to overcome their limitations - spectrum representation of the sub-additivity issue, distortion requirement and added-value of the Spatial VaR solution: An application to Regulatory Requirement for Financial Institutions.

Summary To measure the major risks experienced by financial institutions, for instance Market, Credit and Operational, regarding the risk measures, the distributions used to model them and the level of confidence, the regulation either offers a limited choice or demands the implementation of a particular approach. In this paper, we highlight and illustrate the paradoxes and issues observed when implementing an approach over another, the inconsistencies between the methodologies suggested and the problems related to their interpretation. Starting from the notion of coherence, we discuss their properties, we propose alternative solutions, new risk measures like spectrum and spatial approaches, and we provide practitioners and supervisor with some recommendations to assess, manage and control risks in a financial institution.