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Capital allocation and RORAC optimization under solvency 2 standard formula

Author

Listed:
  • Fabio Baione

    (Sapienza University of Rome)

  • Paolo Angelis

    (Sapienza University of Rome)

  • Ivan Granito

    (Sapienza University of Rome)

Abstract

Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called “Standard Formula” or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator allows for a capital reduction due to the diversification effect, according to the typical subadditivity property of risk measures. However, once the overall capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall Solvency Capital Requirement. The aim of this paper is twofold. First, we provide a closed formula for capital allocation fully compliant with the Solvency II Capital Requirement assessed by means of the Standard Formula. The solution enables a top-down approach to assess the allocated Solvency Capital Requirement among the risks considered in the Solvency II multilevel aggregation scheme; we demonstrate that the allocation formula adopted is consistent with the Euler allocation principle. Second, a solution is found as a result of an optimum capital allocation problem based on a Return On Risk Adjusted Capital measure; we establish the equivalence between the Return On Risk Adjusted Capital optimization, when the risk adjusted capital is calculated according to the Standard Formula, and the Markowitz mean-variance optimization.

Suggested Citation

  • Fabio Baione & Paolo Angelis & Ivan Granito, 2021. "Capital allocation and RORAC optimization under solvency 2 standard formula," Annals of Operations Research, Springer, vol. 299(1), pages 747-763, April.
    • Handle: RePEc:spr:annopr:v:299:y:2021:i:1:d:10.1007_s10479-020-03543-6
    DOI: 10.1007/s10479-020-03543-6
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    References listed on IDEAS

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    1. 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.
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    4. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
    5. Buch, A. & Dorfleitner, G., 2008. "Coherent risk measures, coherent capital allocations and the gradient allocation principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 235-242, February.
    6. Filipović, Damir, 2009. "Multi-Level Risk Aggregation," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 565-575, November.
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    Cited by:

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    3. Li, Jinzhu, 2022. "Asymptotic results on marginal expected shortfalls for dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 146-168.
    4. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.

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