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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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File URL: http://arxiv.org/pdf/physics/0505142
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Paper provided by arXiv.org in its series Papers with number physics/0505142.

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Date of creation: May 2005
Date of revision: Jul 2006
Publication status: Published in Journal of Credit Risk 2(3), 2006, 33-55
Handle: RePEc:arx:papers:physics/0505142

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  1. Michael B. Gordy, 2002. "A risk-factor model foundation for ratings-based bank capital rules," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2002-55, Board of Governors of the Federal Reserve System (U.S.).
  2. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1519-1533, July.
  3. 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, Research Centre.
  4. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers, Financial Markets Group dp549, Financial Markets Group.
  5. Lucas, André & Klaassen, Pieter & Spreij, Peter, 1999. "An analytic approach to credit risk of large corporate bond and loan portfolios," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  6. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1317-1334, July.
  7. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
  8. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
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Citations

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Cited by:
  1. Baule, Rainer, 2014. "Allocation of risk capital on an internal market," European Journal of Operational Research, Elsevier, Elsevier, vol. 234(1), pages 186-196.
  2. Rosen, Dan & Saunders, David, 2010. "Risk factor contributions in portfolio credit risk models," Journal of Banking & Finance, Elsevier, Elsevier, vol. 34(2), pages 336-349, February.
  3. Cipollini, Andrea & Missaglia, Giuseppe, 2007. "Dynamic Factor analysis of industry sector default rates and implication for Portfolio Credit Risk Modelling," MPRA Paper 3582, University Library of Munich, Germany.
  4. Gürtler, Marc & Hibbeln, Martin & Vöhringer, Clemens, 2007. "Measuring concentration risk for regulatory purposes," Working Papers IF26V4, Technische Universität Braunschweig, Institute of Finance.
  5. 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, Elsevier, vol. 41(C), pages 69-92.
  6. Mager, Ferdinand & Schmieder, Christian, 2008. "Stress testing of real credit portfolios," Discussion Paper Series 2: Banking and Financial Studies 2008,17, Deutsche Bundesbank, Research Centre.
  7. Gourieroux, C. & Jasiak, J., 2012. "Granularity adjustment for default risk factor model with cohorts," Journal of Banking & Finance, Elsevier, Elsevier, vol. 36(5), pages 1464-1477.
  8. Siem Jan Koopman & Andr� Lucas & Bernd Schwaab, 2008. "Forecasting Cross-Sections of Frailty-Correlated Default," Tinbergen Institute Discussion Papers 08-029/4, Tinbergen Institute.

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