Understanding the principal components of portfolio credit risk and their interaction is of considerable importance. Investment banks use risk-adjusted capital ratios such as risk-adjusted return on capital (RAROC) to allocate economic capital and measure performance of business units and trading desks. The current attempt by the Basel Committee for Banking Supervision in its Basel II proposals to develop an appropriate framework for a global financial regulation system emphasizes the need for an accurate understanding of credit risk; see BIS (2001). Thus bankers, regulators and academics have put considerable effort into attempts to study and model the contribution of various ingredients of credit risk to overall credit portfolio risk. A key development has been the introduction of credit portfolio models to obtain portfolio loss distributions either analytically or by simulation. These models can roughly be classified as based on credit rating systems, on Merton's contingent claim approach or on actuarial techniques; see Crouhy et al. (2001) for exact description and discussion of the various models.
However, each model contains parameters that effect the risk measures
produced, but which, because of a lack of suitable data, must be
set on a judgemental basis. There are several
empirical studies investigating these effects:
Gordy (2000) and Koyluoglu and Hickmann (1998) show that parametrisation
of various models can be harmonized, but use only default-driven
versions (a related study with more emphasis on the mathematical side of the models
is Frey and McNeil (2001)).
Crouhy et al. (2000) compare models on benchmark
portfolio and find that the highest VaR estimate is per cent larger than the
lowest. Finally, Nickell et al. (1998) find that models yield too many
exceptions by analyzing VaRs for portfolios over rolling twelve-month periods.
Despite these shortcomings credit risk portfolio models are regarded as valuable tools to measure the relative riskiness of credit risky portfolios - not least since measures such as e.g. the spread over default-free interest rate or default probabilities calculated from long runs of historical data suffer from other intrinsic drawbacks - and are established as benchmark tools in measuring credit risk.
The calculation of risk capital based on the internal rating approach, currently favored by the Basel Supervisors Committee, can be subsumed within the class of ratings-based models. To implement such an approach an accurate understanding of various relevant portfolio characteristics within such a model is required and, in particular, the sensitivity of the risk measures to changes in input parameters needs to be evaluated. However, few studies have attempted to investigate aspects of portfolio risk based on rating-based credit risk models thoroughly. In Carey (1998) the default experience and loss distribution for privately placed US bonds is discussed. VaRs for portfolios of public bonds, using a bootstrap-like approach, are calculated in Carey (2000). While these two papers utilize a "default-mode" (abstracting from changes in portfolio value due to changes in credit standing), Kiesel et al. (1999) employ a "mark-to-market" model and stress the importance of stochastic changes in credit spreads associated with market values - an aspect also highlighted in Hirtle et al. (2001).
The aim of this chapter is to contribute to the understanding of the performance of rating-based credit portfolio models. Our emphasis is on comparing the effect of the different approaches to modelling the dependence structure of the individual obligors within a credit-risky portfolio. We use a default-mode model (which can easily be extended) to investigate the effect of changing dependence structure within the portfolio. We start in Section 5.2 by reviewing the construction of a rating-based credit portfolio risk model. In Section 5.3 we discuss approaches to modelling dependence within the portfolio. In Section 5.4 we comment on the implementation in XploRe and present results from our simulations.