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Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle


  • Dirk Tasche


Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill this gap by presenting the theoretical background as well as practical aspects. In particular, we discuss how Euler risk contributions can be estimated for some important risk measures. We furthermore investigate the analysis of CDO tranche expected losses by means of Euler's theorem and suggest an approach to measure the impact of risk factors on non-linear portfolios.

Suggested Citation

  • Dirk Tasche, 2007. "Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle," Papers 0708.2542,, revised Jun 2008.
  • Handle: RePEc:arx:papers:0708.2542

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    References listed on IDEAS

    1. Hausmann, Ricardo & Hidalgo, Cesar A., 2010. "Country Diversification, Product Ubiquity, and Economic Divergence," Working Paper Series rwp10-045, Harvard University, John F. Kennedy School of Government.
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    Cited by:

    1. Puzanova, Natalia & Düllmann, Klaus, 2013. "Systemic risk contributions: A credit portfolio approach," Journal of Banking & Finance, Elsevier, vol. 37(4), pages 1243-1257.
    2. Eduard Kromer & Ludger Overbeck, 2013. "Suitability of Capital Allocations for Performance Measurement," Papers 1301.5497,, revised Jul 2014.
    3. Targino, Rodrigo S. & Peters, Gareth W. & Shevchenko, Pavel V., 2015. "Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 206-226.
    4. Drehmann, Mathias & Tarashev, Nikola, 2013. "Measuring the systemic importance of interconnected banks," Journal of Financial Intermediation, Elsevier, vol. 22(4), pages 586-607.
    5. Areski Cousin & Elena Di Bernardinoy, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
    6. Alejandro Ferrer Pérez & José Casals Carro & Sonia Sotoca López, 2014. "Linking the problems of estimating and allocating unconditional capital," Documentos de Trabajo del ICAE 2014-13, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    7. Buch, Arne & Dorfleitner, Gregor & Wimmer, Maximilian, 2011. "Risk capital allocation for RORAC optimization," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3001-3009, November.
    8. V'eronique Maume-Deschamps & Didier Rulli`ere & Khalil Said, 2015. "A risk management approach to capital allocation," Papers 1506.04125,
    9. Baule, Rainer, 2014. "Allocation of risk capital on an internal market," European Journal of Operational Research, Elsevier, vol. 234(1), pages 186-196.
    10. Mikhail Voropaev, 2011. "KISS approach to credit portfolio modeling," Papers 1107.2164,
    11. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    12. Laurent, Jean-Paul & Sestier, Michael & Thomas, Stéphane, 2016. "Trading book and credit risk: How fundamental is the Basel review?," Journal of Banking & Finance, Elsevier, vol. 73(C), pages 211-223.
    13. Kao, Lie-Jane, 2015. "A portfolio-invariant capital allocation scheme penalizing concentration risk," Economic Modelling, Elsevier, vol. 51(C), pages 560-570.
    14. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    15. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    16. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349,, revised Apr 2013.
    17. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Zhao, Shouqi, 2015. "On finite-time ruin probabilities in a generalized dual risk model with dependence," European Journal of Operational Research, Elsevier, vol. 242(1), pages 134-148.
    18. 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.
    19. Chris Kenyon & Andrew Green, 2014. "Efficient XVA Management: Pricing, Hedging, and Attribution using Trade-Level Regression and Global Conditioning," Papers 1412.5332,, revised Dec 2014.
    20. Csóka, Péter & Bátyi, Tamás László & Pintér, Miklós & Balog, Dóra, 2011. "Tőkeallokációs módszerek és tulajdonságaik a gyakorlatban
      [Methods of capital allocation and their characteristics in practice]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 619-632.
    21. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645,, revised Apr 2015.
    22. Bennani, T. & Després, M. & Dujardin, M. & Duprey, T. & Kelber, A., 2014. "Macroprudential framework:key questions applied to the French case," Occasional papers 9, Banque de France.
    23. Kretzschmar, Gavin & McNeil, Alexander J. & Kirchner, Axel, 2010. "Integrated models of capital adequacy - Why banks are undercapitalised," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 2838-2850, December.
    24. Nikolaus Rab & Richard Warnung, 2010. "Scaling portfolio volatility and calculating risk contributions in the presence of serial cross-correlations," Papers 1009.3638,, revised Nov 2011.
    25. McNeil, Alexander J. & Smith, Andrew D., 2012. "Multivariate stress scenarios and solvency," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 299-308.

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