Concentration measures in risk management

Abstract

Following the increasing use of external and internal credit ratings made by the Bank regulation, credit risk concentration has become one of the leading topics in modern finance. In order to measure separately single-name and sectoral concentration risk, the literature proposes specific concentration indexes and models, which we review in this paper. Following the guideline proposed by Basel 2 on risk integration, we believe that standard approaches could be improved by studying a new measure of risk that integrates single-name and sectoral credit risk concentration in a coherent way. The main objective of this paper is to propose a novel index useful to measure credit risk concentration integrating single-name and sectoral components. From a theoretical point of view, our measure of risk shows interesting mathematical properties; empirical evidences are given on the basis of a data set. Finally, we have compared the results achieved following our proposal with respect to the common procedures proposed in the literature.

Keywords:

• risk
• concentration index
• inequalities measures
• single-name credit risk
• sectoral credit risk

Notes

1 We underline that different risk measures (ie Value at Risk, Variance and so on) can be employed as r_i, but in real financial application focused on small and medium enterprises (as in our case) it turns out difficult to compute classical risk measures based on returns distributions in the times series analysis framework.

2 We have renamed I_V as I_sn to underline the single0name risk component in the decomposition context.