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Klaas Schulze

18 February 2016
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 Code
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, Depository Institutions, Micro Finance Institutions, Mortgages
G24 : Financial Economics→Financial Institutions and Services→Investment Banking, Venture Capital, Brokerage, Ratings and Ratings Agencies