An analytic approach to credit risk of large corporate bond and loan portfolios

Abstract

We consider portfolio credit loss distributions based on a factor model for individual exposures and establish an analytic characterization of the credit loss distribution if the number of exposures tends to infinity. Using this limiting distribution, we explain how skewness and leptokurtosis of credit loss distributions relate to the underlying factor model and the portfolio composition. A key role is played by the R2 of the factor model regression. Based on the limiting distribution and empirical data, it appears that the Basle 8% rule is not an unreasonable approximation for high confidence (99.9%) quantiles of credit losses of a typical portfolio of rated corporate bonds. The practical relevance of our results for credit risk management is investigated by checking the applicability of the limiting distribution to portfolios with a finite number of exposures. It appears that for relatively homogeneous portfolios a minimum of 300 exposures is enough, while for relatively heterogeneous portfolios a number of 800 exposures suffices to obtain an adequate approximation. Thus, our approach can be a fast and accurate alternative to the standard Monte-Carlo simulation approach adopted in much of the literature and in practice.

Business and default cycles for credit risk

“…Whereas the models of, e.g., Jarrow and Turnbull (1995) and Duffie and Singleton (1999) can in principle be used both for single-name and multi-name credit risky instruments, there is a crucial difference as to the type of risk that is important. Making the standard distinction between idiosyncratic and systematic risk, it is the systematic risk that is most important at a portfolio level, see for example Jarrow, Lando, and Yu (2000), Frey and McNeil (2001), Lucas, Klaassen, Spreij, and Straetmans (2001), and Giesecke and Weber (2003). The idiosyncratic risk can be largely diversified.…”

Justification of Per-Unit Risk Capital Allocation in Portfolio Credit Risk Models

“…This lemma is an extension of the law of large numbers and follows from the work of Lucas et al (2001).…”

Aggregating Credit and Market Risk: The Impact of Model Specification

“…Using the arguments in Lucas, Klaassen, Spreij, and Straetmans (2001), the total loss on this portfolio of n names as a percentage of the notional is given byL t+h,n = n −1 n i=1 L t+h,i , where L t+h,i is the loss on counter party i at time t+h. Considering the limiting case n → ∞ of an infinitely granular portfolio, we obtain under the recovery of treasury assumption that…”