Ebook Estimating Default and Downgrade Risk: Sector, Region and Structured Product estimates
Asset dependence in portfolio credit risk management is a topic of growing importance for practitioners and academics. Changes in the most common form of dependence (correlation) across assets transfers some of the risk from the mean toward the tail of the loss distribution. Any increase in correlation between the assets fattens the tail of the loss distribution and therefore requires a greater amount of capital set aside to cover unexpected losses. This makes asset correlation a very important parameter in the estimation of a bank’s capital requirement.
The Basel accord of 1988 was a first attempt to establish an international standard on a banks capital requirements. However a significant drawback, of this first attempt, was its crude approach in determining the risk weights assigned to different positions in a bank’s portfolio. An example of this situation is that a private firm with the best rating would receive a weight a hundred times higher than any type of sovereign debt, regardless of the rating of the former. The second Basel accord (2006) corrected the imbalance by accounting for the relative credit quality of the issuers. Under this accord, regulators given more leeway to institutions with the hope that they will be able to perform a more accurate measure of the risk heterogeneity within a bank’s portfolio. Hence bank managers will be able to calibrate in a more balanced manner the assigned risk weights. The Basel 2 accompanying document (2006) suggest a value for asset correlation parameter between 0.12 and 0.24. The literature proposes various estimates for these values in the ranges: (0.01, 0.1) Chernih et al. (2006), and (0.05, 0.21) Akhavein, Kocagil and Neugebauer (2005).
Clearly, the most popular approach to estimate asset correlation, using rating transition data, is the common risk factor model. This model is used extensible in the literature on dynamic modeling of default risk1. The model decomposes credit risk into systematic (macro related) and idiosyncratic (issuer specific) component. In this context McNeil and Wendin (2006) and Koopman, Lucas and Daniels (2005) develop methodologies, based on different concepts of heterogeneity, to explain the dynamics of default. The former explores heterogeneity among industry sectors and also across rating classes, whereas the later only explore heterogeneity across ratings. However both articles recognize two difficulties inherent to rating data and particularly default: 1) rating transitions are scarce events 2 and 2) defaults are extremely rare events. These two elements complicate the job of making statistical inference. Yet, rating transition data is a preferred source when accounting for changes in the creditworthiness of issuers, as it is more direct than using other sources such as equity or spread data. In some cases like for structured products or sovereigns the equity based correlation approaches are not feasible because there is no information on equity or debt available. Therefore, it is not possible to link equity and assets through the option-theoretic framework due to Merton(1974).
The aim of this article is to obtain estimates of asset and local factor correlation within and across different identifiable forms of grouping the firms. The rating information contains information on group affiliation of the firms such as sector, product or country in which they carry out their business. These results, based on the disaggregated rating data, will contribute to the existing literature on asset correlation because so far most of the available literature has focused on estimating these models on aggregate data. In particularly with respect to world region affiliation and structured products the results seem to be the first available. Furthermore, if accounting for heterogeneity in a bank’s portfolio is an important part of Basel 2, it does not make sense estimating models based on the aggregated data, although it is much easier because it makes events like default ”less” rare. By moving away from the aggregated data the few historical observation that are available on rating transitions (especially default) become even more sparse, therefore the methodologies encounter problems due to this sparsity of the data.
For the estimation we use a non-gaussian univariate or multivariate state space model developed by Koopman et al. (2005). The model considers the observed number of firms, that perform some migration (possibly to the default state) out of a total number of firms within a given group (say an economic sector or world region), as a realization of a binomial distribution conditional on the state of some unobserved systematic factor. The state space model build from this setup has a measurement equation that has the form of a binomial distribution (which makes the model non-gaussian and non-linear). From the model we are able to estimate both the unobserved factor and the loading parameter of this one factor model, used to decompose default or downgrade risk. Then we can map the loading to the asset correlation.
The results indicate significant differences in the estimated loading parameters across economic sector, world regions and structured products. This in turn means that there are significant differences in asset correlation within these groups. For most groups of data the asset correlation estimates are higher than values recommended in the Basel 2 accompanying document (2006). The results support the relevance of accounting for this type of heterogeneity when estimating asset correlation.
A downside of working with the disaggregated data is that it is not possible to obtain results for all groups. For example, out of a total of 23 economic sectors considered we obtained results for 15. This phenomenon is due to the sparsity of the rating data and it reflects itself in the data, used for estimation, as an excessive number of zeros (the number defaults or downgrades). Often this excess of zeros is called zero-inflation. The model and/or the estimation method ”as is” is not robust to the sparsity of the data encountered. This is a topic of continuing research.
The outline of the paper is as follows in: Section 2 presents the model of Koopman et al. (2005) to decompose default risk. Section 3 describes the data set and the results. Section ?? concludes.
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