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Advances in multivariate back-testing for credit risk underestimation

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Listed:
  • Sauer, Stephan
  • Coppens, François
  • Mayer, Manuel
  • Millischer, Laurent
  • Resch, Florian
  • Schulze, Klaas

Abstract

When back-testing the calibration quality of rating systems two-sided statistical tests can detect over- and underestimation of credit risk. Some users though, such as risk-averse investors and regulators, are primarily interested in the underestimation of risk only, and thus require one-sided tests. The established one-sided tests are multiple tests, which assess each rating class of the rating system separately and then combine the results to an overall assessment. However, these multiple tests may fail to detect underperformance of the whole rating system. Aiming to improve the overall assessment of rating systems, this paper presents a set of one-sided tests, which assess the performance of all rating classes jointly. These joint tests build on the method of Sterne [1954] for ranking possible outcomes by probability, which allows to extend back-testing to a setting of multiple rating classes. The new joint tests are compared to the most established one-sided multiple test and are further shown to outperform this benchmark in terms of power and size of the acceptance region. JEL Classification: C12, C52, G21, G24

Suggested Citation

  • Sauer, Stephan & Coppens, François & Mayer, Manuel & Millischer, Laurent & Resch, Florian & Schulze, Klaas, 2016. "Advances in multivariate back-testing for credit risk underestimation," Working Paper Series 1885, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20161885
    Note: 362683
    as

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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp1885.en.pdf
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    References listed on IDEAS

    as
    1. Jankowitsch, Rainer & Pichler, Stefan & Schwaiger, Walter S.A., 2007. "Modelling the economic value of credit rating systems," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 181-198, January.
    2. François Coppens & Fernando Gonzáles & Gerhard Winkler, 2007. "The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary policy operations," Working Paper Research 118, National Bank of Belgium.
    3. González, Fernando & Coppens, François & Winkler, Gerhard, 2007. "The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary policy operations," Occasional Paper Series 65, European Central Bank.
    4. Reiczigel, Jeno & Abonyi-Tóth, Zsolt & Singer, Júlia, 2008. "An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5046-5053, July.
    5. Aussenegg, Wolfgang & Resch, Florian & Winkler, Gerhard, 2011. "Pitfalls and remedies in testing the calibration quality of rating systems," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 698-708, March.
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    Cited by:

    1. Patrick Kurth & Max Nendel & Jan Streicher, 2023. "A hypothesis test for the long-term calibration in rating systems with overlapping time windows," Papers 2312.14765, arXiv.org.
    2. António Antunes & Homero Gonçalves & Pedro Prego, 2017. "Firm default probabilities revisited," IFC Bulletins chapters, in: Bank for International Settlements (ed.), Uses of central balance sheet data offices' information, volume 45, Bank for International Settlements.
    3. Gianmarco Bet & Francesco Dainelli & Eugenio Fabrizi, 2023. "The financial health of a company and the risk of its default: Back to the future," Papers 2302.10140, arXiv.org.

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    More about this item

    Keywords

    back-testing; credit ratings; one-sided; probability of default;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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