Abstract
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). 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, Herfindahl-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 satisfies 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.
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Notes
- 1.
The constant δ depends on the VaR confidence level and also on the variance of the systematic factor. Gordy and Lutkebohmert (2007) suggest a value of 5 as a meaningful and parsimonious number.
References
Banca d’Italia: New regulations for the prudential supervision of banks. Circular 263 (27 December 2006)
Basel Committee on Banking Supervision: The New Basel Capital Accord, Consultative document. Basel (January 2001)
Basel Committee on Banking Supervision: International Convergence of Capital Measurement and Capital Standards: A Revised Framework. BIS, Basel (June 2004)
Becker, S., Dullmann, K., Pisarek, V.: Measurement of concentration risk — A theoretical comparison of selected concentration indices. unpublished Working Paper, Deutsche Bundesbank. Social Sciences. John Wiley, New York (2004)
Dalton, H.: The measurement of the inequality of incomes. Economics Journal 30, 348–361 (1920)
Gordy, M.B.: A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation 12(3), 199–232 (2003)
Gordy, M.B., Lütkebohmert, E.: Granularity adjustment for Basel II. Deutsche Bundesbank Discussion Paper (series 2), n. 1. (2007)
Encaoua, D., Jaquemin, A.: Degree of monopoly, indices of concentration and threat of entry. International economic review 21 (1980)
Gini, C.: Measurement of Inequality of Incomes. Economic journal 31, 124–126 (1921)
Hannah L., Kay, J.A.: Concentration in modern industry. MacMillan Press, London (1977)
Herfindahl, O.: Concentration in the U.S. Steel Industry. Dissertion, Columbia University (1950)
Hirschmann, A.: National power and the structure of foreign trade. University of California Press, Berkeley (1945)
Hirschmann, A.: The paternity of an index. American Economic Review 54(5), 761 (1964)
Lorenz, M.O.: Methods of measuring the concentration of wealth. Publications of the American Statistical Association 9(70), 209–219 (1905)
Lütkebohmert, E.: Concentration risk in credit portfolios. Springer-Verlag (2009)
Pigou, A.C.: Wealth and Welfare. Macmillan Co., London (1912)
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Calabrese, R., Porro, F. (2014). Single-Name Concentration Risk Measurements in Credit Portfolios. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02499-8_8
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DOI: https://doi.org/10.1007/978-3-319-02499-8_8
Publisher Name: Springer, Cham
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