Single-name concentration risk measurements in credit portfolios

For assessing the effect of undiversifi ed idiosyncratic risk, Basel II has established that banks should measure and control their credit concentration risk. Concentration risk in credit portfolios comes into being through an uneven distribution of bank loans to individual borrowers (single-name concentration) or through an unbalanced allocation of loans in productive sectors and geographical regions (sectoral concentration). In this paper six properties that ensure a coherent measure of single-name concentration are identified. To evaluate single-name concentration risk in the literature, Herfi ndahl–Hirschman index has been used. This index represents a particular case of Hannah–Kay index proposed in monopoly theory. In this work the proof that Hannah–Kay index satisfi es all the six properties is given. Finally, the impact of the elasticity parameter in Hannah-Kay index on the single-name concentration measure is analysed by numerical applications.