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Measuring sectoral diversification in an asymptotic multi-factor framework

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  • Dirk Tasche

Abstract

We investigate a multi-factor extension of the asymptotic single risk factor (ASRF) model that underlies the capital charges of the "Basel II Accord". In this extended model, it is still possible to derive closed-form solutions for the risk contributions to Value-at-Risk and Expected Shortfall. As an application of the risk contribution formulae we introduce a new concept for a diversification measure. The use of this new measure is illustrated by an example calculated with a two-factor model. The results with this model indicate that, thanks to dependence on not fully correlated systematic sectors, there can be a substantial reduction of risk contributions by sectoral diversification effects.

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  • Dirk Tasche, 2005. "Measuring sectoral diversification in an asymptotic multi-factor framework," Papers physics/0505142, arXiv.org, revised Jul 2006.
  • Handle: RePEc:arx:papers:physics/0505142
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    References listed on IDEAS

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    1. Danielsson, Jon & Jorgensen, Bjørn N. & Mandira, Sarma & Samorodnitsky, Gennady & Vries, C. G. de, 2005. "Subadditivity re–examined: the case for value-at-risk," LSE Research Online Documents on Economics 24668, London School of Economics and Political Science, LSE Library.
    2. Lucas, Andre & Klaassen, Pieter & Spreij, Peter & Straetmans, Stefan, 2001. "An analytic approach to credit risk of large corporate bond and loan portfolios," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1635-1664, September.
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    6. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    7. Memmel, Christoph & Wehn, Carsten, 2005. "The supervisor's portfolio: the market price risk of German banks from 2001 to 2003 - Analysis and models for risk aggregation," Discussion Paper Series 2: Banking and Financial Studies 2005,02, Deutsche Bundesbank.
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    9. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
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    Cited by:

    1. Mager, Ferdinand & Schmieder, Christian, 2008. "Stress testing of real credit portfolios," Discussion Paper Series 2: Banking and Financial Studies 2008,17, Deutsche Bundesbank.
    2. Lee, Yongwoong & Poon, Ser-Huang, 2014. "Forecasting and decomposition of portfolio credit risk using macroeconomic and frailty factors," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 69-92.
    3. Gourieroux, C. & Jasiak, J., 2012. "Granularity adjustment for default risk factor model with cohorts," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1464-1477.
    4. Baule, Rainer, 2014. "Allocation of risk capital on an internal market," European Journal of Operational Research, Elsevier, vol. 234(1), pages 186-196.
    5. Karl-Theodor Eisele & Philippe Artzner, 2013. "Multiperiod Banking Supervision," Working Papers of LaRGE Research Center 2013-05, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    6. Andrea Cipollini & Giuseppe Missaglia, 2007. "Dynamic Factor analysis of industry sector default rates and implication for Portfolio Credit Risk Modelling," Center for Economic Research (RECent) 007, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    7. Kao, Lie-Jane, 2015. "A portfolio-invariant capital allocation scheme penalizing concentration risk," Economic Modelling, Elsevier, vol. 51(C), pages 560-570.
    8. Bernardi, Enrico & Falangi, Federico & Romagnoli, Silvia, 2015. "A hierarchical copula-based world-wide valuation of sovereign risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 155-169.
    9. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    10. M. Dietsch & C. Welter-Nicol, 2014. "Do LTV and DSTI caps make banks more resilient?," Débats économiques et financiers 13, Banque de France.
    11. Rosen, Dan & Saunders, David, 2010. "Risk factor contributions in portfolio credit risk models," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 336-349, February.
    12. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.
    13. Bernardi Enrico & Romagnoli Silvia, 2015. "A copula-based hierarchical hybrid loss distribution," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 73-87, April.
    14. Gürtler, Marc & Hibbeln, Martin & Vöhringer, Clemens, 2007. "Measuring concentration risk for regulatory purposes," Working Papers IF26V4, Technische Universität Braunschweig, Institute of Finance.

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