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Capital adequacy tests and limited liability of financial institutions

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  • Koch-Medina, Pablo
  • Moreno-Bromberg, Santiago
  • Munari, Cosimo

Abstract

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate the class of surplus-invariant acceptance sets. We argue that surplus invariance is a reasonable requirement from a regulatory perspective, since the corresponding capital adequacy tests do not depend on the surplus of a financial institution, which benefits exclusively its shareholders, but only on the default profile, which affects its liability holders. We provide a detailed analysis of surplus-invariant acceptance sets and their associated risk measures and we discuss the link with loss-based and excess-invariant risk measures, recently studied by Cont et al. (2013) and by Staum (2013), respectively.

Suggested Citation

  • Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Munari, Cosimo, 2015. "Capital adequacy tests and limited liability of financial institutions," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 93-102.
    • Handle: RePEc:eee:jbfina:v:51:y:2015:i:c:p:93-102
    DOI: 10.1016/j.jbankfin.2014.11.002
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    References listed on IDEAS

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    1. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Capital requirements with defaultable securities," Papers 1203.4610, arXiv.org, revised Jan 2014.
    2. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2013. "Measuring risk with multiple eligible assets," Papers 1308.3331, arXiv.org, revised Mar 2014.
    3. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    4. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    6. Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142, April.
    7. Artzner, Philippe & Delbaen, Freddy & Koch-Medina, Pablo, 2009. "Risk Measures and Efficient use of Capital 1," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 101-116, May.
    8. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 58-67.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. repec:dau:papers:123456789/342 is not listed on IDEAS
    11. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
    12. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    13. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
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    Citations

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    Cited by:

    1. Chen, Ouxiang & Hu, Taizhong, 2019. "Extreme-aggregation measures in the RDEU model," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 155-163.
    2. Niushan Gao & Cosimo Munari, 2017. "Surplus-invariant risk measures," Papers 1707.04949, arXiv.org, revised May 2018.
    3. Maria Arduca & Cosimo Munari, 2020. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Papers 2012.08351, arXiv.org, revised Apr 2022.
    4. Koch-Medina, Pablo & Munari, Cosimo, 2016. "Unexpected shortfalls of Expected Shortfall: Extreme default profiles and regulatory arbitrage," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 141-151.
    5. Niushan Gao & Cosimo Munari, 2020. "Surplus-Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1342-1370, November.
    6. Valeria Bignozzi & Matteo Burzoni & Cosimo Munari, 2020. "Risk Measures Based on Benchmark Loss Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(2), pages 437-475, June.
    7. Maria Arduca & Cosimo Munari, 2023. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Finance and Stochastics, Springer, vol. 27(3), pages 831-862, July.
    8. Samuel Solgon Santos & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2022. "The limitations of comonotonic additive risk measures: a literature review," Papers 2212.13864, arXiv.org, revised Jan 2024.
    9. Xue Dong He & Xianhua Peng, 2017. "Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk," Papers 1707.05596, arXiv.org, revised Jan 2018.

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    More about this item

    Keywords

    Surplus invariance; Capital adequacy; Limited liability; Risk measures;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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