Zusammenfassung Zur Bewertung des Risikos von Tranchen eines Kreditportfolios existiert eine Vielzahl von Maßzahlen. Problematisch ist, dass sich für die einzelnen Konzepte meist noch keine einheitliche Bezeichnung herausgebildet hat. Auch stehen gleiche Bezeichnungen teilweise für unterschiedliche Maßzahlen. Ziel dieses Papieres ist es, die verwendeten Begriffe zu katalogisieren und eine einheitliche, unverwechselbare Bezeichnung für jede Maßzahl festzulegen. Des Weiteren werden für jede Maßzahl charakteristische Eigenschaften zusammengetragen. Es zeigt sich, dass im Prinzip zwei Maßzahlen zur Bewertung der Tranchen eines Portfolios genügen.Schlüsselwörter Risikomessung · Kreditportfolio · Tranche JEL Klassifikationen G32 · G24 · G13 Measures of risk for credit portfolio tranchesAbstract There is a multitude of measures to evaluate the tranches of a structured credit portfolio. One problem is that for each concept there exists a variety of different terms. Furthermore, some of these terms are used for different measures. For this reason, this paper aims to catalog the terms used and to define a term that is appropriate and unique. Additionally, characteristic properties for each measure are collected. It turns out that in principle two of the considered measures suffice to evaluate the tranches of a portfolio.

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Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m. In the literature, estimators for the three parameters of m, that is, the breakpoint θ and the levels a and b, are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y. The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.

In credit risk, debtors with different creditworthiness are divided into rating classes. One problem is to define the borders of the rating classes. A natural way to estimate these breakpoints from default observations comes out of the field of change point analysis. In order to account for dependency between the debtors, the literature proposes a combination of a breakpoint model with a one-factor model. One finds strongly consistent estimators for the threshold of the rating classes and the corresponding default probabilities, also called risk levels. But an investigation of the inherent model properties is as yet missing. For this reason we derive the default correlation and study its relationship to the model parameters, i.e., the breakpoint, the risk levels, and a new correlation term, named score correlation, appearing in a simulation study. Eventually, we check the magnitude of the score correlation used in the simulation study.

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