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Measuring Portfolio Risk Under Partial Dependence Information

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  • Carole Bernard
  • Michel Denuit
  • Steven Vanduffel

Abstract

The bounds for risk measures of a portfolio when its components have known marginal distributions but the dependence among the risks is unknown are often too wide to be useful in practice. Moreover, availability of additional dependence information, such as knowledge of some higher‐order moments, makes the problem significantly more difficult. We show that replacing knowledge of the marginal distributions with knowledge of the mean of the portfolio does not result in significant loss of information when estimating bounds on value‐at‐risk. These results are used to assess the margin by which total capital can be underestimated when using the Solvency II or RBC capital aggregation formulas.

Suggested Citation

  • Carole Bernard & Michel Denuit & Steven Vanduffel, 2018. "Measuring Portfolio Risk Under Partial Dependence Information," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(3), pages 843-863, September.
    • Handle: RePEc:bla:jrinsu:v:85:y:2018:i:3:p:843-863
    DOI: 10.1111/jori.12165
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    Cited by:

    1. Natalia Nehrebecka, 2019. "Credit risk measurement: Evidence of concentration risk in Polish banks’ credit exposures," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 37(2), pages 681-712.
    2. Cornilly, Dries & Vanduffel, Steven, 2019. "Equivalent distortion risk measures on moment spaces," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 187-192.
    3. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    4. Rüschendorf, L., 2019. "Analysis of risk bounds in partially specified additive factor models," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 115-121.
    5. Asimit, Alexandru V. & Gerrard, Russell, 2016. "On the worst and least possible asymptotic dependence," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 218-234.
    6. Marius Hofert, 2020. "Implementing the Rearrangement Algorithm: An Example from Computational Risk Management," Risks, MDPI, vol. 8(2), pages 1-28, May.
    7. Xu, Chi & Zheng, Chunling & Wang, Donghua & Ji, Jingru & Wang, Nuan, 2019. "Double correlation model for operational risk: Evidence from Chinese commercial banks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 327-339.
    8. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    9. Paulusch, Joachim & Schlütter, Sebastian, 2021. "Sensitivity-implied tail-correlation matrices," ICIR Working Paper Series 33/19, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR), revised 2021.
    10. Lambert, Philippe, 2023. "Nonparametric density estimation and risk quantification from tabulated sample moments," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 177-189.
    11. Bernard, Carole & Kazzi, Rodrigue & Vanduffel, Steven, 2020. "Range Value-at-Risk bounds for unimodal distributions under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 9-24.
    12. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.

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