Single-name concentration risk in credit portfolios: a comparison of concentration indices

For assessing the effect of undiversified 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). To evaluate single-name concentration risk in the literature concentration indices proposed in welfare (Gini Index) and monopoly theory (Herfindahl- Hirschman index, Theil entropy index, Hannah-Kay index, Hall-Tidemann index) have been used. In this paper such concentration indices are compared by using as benchmark six properties that ensure a consistent measurement of single-name concentration. Finally, the indices are compared on some portfolios of loans.