4. The Shadow Rating Approach: Experience from Banking Practice

This occurs e.g. when a new risk factor has been introduced or when a risk factor is relevant only for a small sub-sample of obligors.

There also might be other types of corporate relationships that can induce the support of one company for another one. For example, a company might try to bail out an important supplier which is in financial distress. However, since this issue is only a minor aspect of this article we will concentrate on the most common supporter-relationship in rating practice, i.e. corporate groups and sovereign support.

We will, however, also include a short proposal for the empirical estimation of corporate group influences/sovereign support (step 3).

In this article, the term “external data sets” or “external data” will always refer to a situation where – additional to internally rated companies – a typically much larger sample of not internally-rated companies is employed for rating development. This external data set will often come from an external data provider such as e.g. Bureau van Dijk but can also be the master sample of a data-pooling initiative. In such a situation, usually only quantitative risk factors will be available for both, the internal and the external data set while qualitative risk factors tend to be confined to the internal data set. In this situation, a number of specific problems arise that have to be taken into account. The problems we found most relevant will be dealt with in this article.

Long-term ratings because of the Basel II requirements that banks are expected to use a time horizon longer than one year in assigning ratings (BCBS (2004), § 414) and because almost all analyses of external ratings are conducted with long-term ratings. Local currency ratings are needed when a bank measures transfer risk separately from an obligor’s credit rating.

The Basel II default definition is given in (BCBS (2004), § 452). The rating agencies’ default definitions are described in their respective default reports (cf. Standard and Poor’s (2005), Moody’s (2005), and Fitch 2005).

This assessment draws on external agencies’ verbal definitions of those rating grades (cf. Standard and Poor’s (2002), Moody’s (2004), and Fitch 2006).

For example, for the comparison of external and internal defaults, the multinomial random variable would for each defaulted company indicate one of three potential outcomes: (1) External and internal default, (2) External default but no internal default, (3) Internal default but no external default. Moreover, due to the typically small amount of data, no large-sample approximation but the exact Chi-square distribution should be employed. Confidence limits can be estimated by applying the test statistic on a sufficiently fine grid for the parameters of the multinomial distribution.

See Standard and Poor’s (2005) and Moody’s (2005).

See agencies’ rating definitions: Standard and Poor’s (2002) and Moody’s (2004) respectively.

See Ammer and Packer (2000), Cantor and Falkenstein (2001), and Cantor (2004).

Ammer and Packer (2000) found default-rate differences between banks and non-banks. However, they pointed out that these differences are most likely attributable to a specific historic event, the US Savings and Loans crisis, and should therefore not be extrapolated to future default rates. Cantor and Falkenstein (2001), in contrast, found no differences in the default rates of banks and non-banks once one controls for macroeconomic effects.

For a discussion of LGD-estimation methods we refer to Chapter VIII of this book.

This method can be improved on by counting on a monthly or even finer base.

The matrix exponential applies the exponential series to matrices: exp (m) = I + m ¹ /1! + m ² /2! + …, where I is the identity matrix.

For an efficient derivation and implementation of exact confidence limits for the binomial distribution see Daly (1992).

The TTC-property of external ratings has been observed in the academic literature (cf. Löffler 2004) and has also been proved to be significant by our own empirical investigations. It must, however, be stressed that in practice rating systems will neither be completely TTC or PIT but somewhere in between.

See http://​www.​moodyskmv.​com/​.

For example, market-based measures such as Moody’s KMV’s EDF are only available for public companies.

External data are often employed for the development of SRA rating systems in order to increase the number of obligors and the number of points in time available for each obligor. See Sect. 4.1 for more details.

One category might for example include all balance sheet factors (triggered by the release of a company’s accounts). Another category will be qualitative factors as assessed by the bank’s loan manger. They are triggered by the internal rating event. A third category might be macroeconomic indicators.

Note that the external sample will typically also include some or almost all internal obligors. To construct two completely different sets, internal obligors would have to be excluded from the external data. However, if the external data set is much larger than the internal data set, such exclusion might not be judged necessary.

“Out-of-time” means that development and validation are based on disjoint time intervals.

For an application of bootstrap methods in the context of rating validation see Appasamy et al. (2004). A good introduction to and overview over bootstrap methods can be found in Davison and Hinkley (1997).

Note that the time intervals of input factors and default indicator are shifted against each other by the length of the time horizon for which the rating system is developed. For example, if the horizon is 1 year and the default indicator is equal to zero from Jan 2003 to Dec 2004 then this value will be mapped to the risk-factor interval from Jan 2002 to Dec 2003.

See Erlenmaier (2001).

For an introduction to such models and further references see Greene (2003).

See Sect. 4.5.2. Throughout this article we will use the term “log external PD” to denote the natural logarithm of the PD of an obligor’s external rating grade. How PDs are derived for each external rating grade has been described in Sect. 4.2.

For an overview on measures of discriminatory power see Deutsche Bundesbank (2003) or Chap.​ 13.

A good discriminatory power of the internal rating system in terms of predicting external ratings and a good discriminatory power of the external ratings in terms of predicting future defaults will then establish a good discriminatory power of the internal rating system in terms of predicting future defaults.

Linear correlations are typically termed Pearson correlations while rank-order correlations are associated with Spearman. Linear correlations are important since they measure the degree of linear relationship which corresponds with the linear model employed for the multi-factor analysis. Rank-order correlations can be compared with linear correlations in order to identify potential scope for risk factor transformation.

This is often necessary for sensible visualization of the risk factor’s distribution.

An SRA-rating system will always face the problem that – due to the relative rareness of default data – it is difficult to validate it for obligors that are not externally rated. While some validation techniques are available (see Sect. 4.5.8), showing that the data for externally rated obligors is comparable with that of non-externally rated obligors will be one of the major steps to make sure that the derived rating system will not only perform well for the former but also for the latter.

Throughout this article Log denotes the natural logarithm with base e.

For reviews on formal model-selection methods see Hocking (1976) or Judge et al. (1980).

R² is the square of the linear correlation between the dependent variable (the log external PD) and the model prediction for this variable.

For a comprehensive overview on applied linear regression see Greene (2003).

Residuals (e) are the typical estimators for the (unobservable) theoretical error terms (ε). They are defined as the difference between the dependent variable and the model predictions of this variable.

BLUE stands for best linear unbiased estimator.

The term heteroscedasticity refers to cases where standard deviations of error terms are different as opposed to the assumption of identical standard deviations (homoscedasticity).

Indeed, a standard procedure for dealing with autocorrelated error terms in the way described above is implemented in most statistical software packages.

Note that this method is also suggested by standard regression outputs. The associated estimates are typically termed “standardized coefficients”. Moreover, if the risk factors have already been standardized to a common standard deviation – as described in Sect. 4.4 – they already have the same scale and coefficients only have to be mapped to [0,1] in order to add up to 1.

Additionally, the standard deviation tends to be a very unstable statistical measure that can be very sensitive to changes in the risk factor’s distribution. However, this problem should be reduced significantly by the truncation of the risk factors which reduces the influence of outliers.

With the SRA approach to rating development, there is the problem that the loan manager may use qualitative risk factors in order to make internal and external ratings match. If that is the case, the relative weight of qualitative factors as estimated by the statistical model will typically be too high compared to the weights of quantitative risk factors. The validation measures that are not linked to external ratings (see Sect. 4.5.8) and also expert judgement may then help to readjust those weights appropriately.

More formally, the implicit discriminatory power is defined as the expected value of the (explicit) discriminatory power – as measured by the Gini coefficient (cf. Chap.​ 13).

This can be derived from (4.7) and (4.8).

If X is normally distributed with mean μ and standard deviation σ, then E [exp (X)] = exp(μ + σ²/2), where E is the expectation operator (Limpert et al. 2001).

Note that for the sake of simplicity, the expression “supporter” is used for all entities that influence an obligor’s rating, be it in a positive or negative way.

The standalone and supporter PDs have of course been derived from the regression model of the previous sections, probably, after manual adjustments.

The typical modules of a SRA-rating system (statistical model, expert-guided adjustments, corporate-group influence/government support, override) have been discussed in Sect. 4.1.