Rating Models and Validation - Oesterreichische Nationalbank

Rating Models and Validation
coefficients of the linear combinations of indicators. The relevant literature does
not indicate any binding guidelines for the maximum size of correlations
between indicators. As a rule of thumb, however, pairs of indicators which show
correlation coefficients greater than 0.3 should only be included in scoring
functions with great caution.
One tool which can be used to examine indicator correlations is hierarchical
cluster analysis. 55 Hierarchical cluster analysis involves creating groups (i.e. clusters)
of indicators which show high levels of correlation within the clusters but
only low levels of correlation between the various clusters. 56
Those indicators which return high Powerstat values are selected from the
clusters created. Indicators which have very similar definitions (e.g. various
types of return) but for which it is not possible to decide at the time of cluster
analysis which variant will be most suitable can be used in parallel in multivariate
analysis. For the sake of the modelÕs stability, however, it is advisable to avoid
including highly correlated variables in the final rating model.
5.2.2 Multivariate Analysis
Indicator preselection yields a shortlist of indicators, and the objective of multivariate
analysis is to develop a scoring function for these indicators. In this
section, we present a scoring function for quantitative data. The procedure
for developing scoring functions for qualitative information categories is analogous.
The catalogs of indicators/questions reduced in univariate analyses form
the basis for this development process.
In practice, banks generally develop multiple scoring functions in parallel
and then select the function which is most suitable for the overall rating model.
The following general requirements should be imposed on the development of
the scoring functions:
— Objective indicator selection based on the empirical procedure
— Attainment of high discriminatory power
For this purpose, as few indicators as possible should be used in order to
increase the stability of the scoring function and to ensure an efficient rating
procedure.
— Inclusion of as many different information categories as possible (e.g. assets
situation, financial situation, income situation)
— Explicit selection or explicit exclusion of certain indicators in order to
enhance or allow statements which are meaningful in business terms
On the basis of the shortlist of indicators, various scoring functions are
then determined with attention to the requirements listed above. Banks which
use discriminant analyses or regression models can estimate the indicatorsÕ
coefficients using optimization algorithms from statistics software programs.
The scoring functionÕs coefficients are always optimized using the data in the
analysis sample. The validation sample serves the exclusive purpose of testing
55 Cf. BACKHAUS ET AL., Multivariate Analysemethoden, chapter 6.
56 Rank order correlation (Spearman correlation) is an especially well suited measure of correlation in untransformed indicators.
In comparison to the more commonly used Pearson correlation, this method offers the advantage of performing calculations using
only the ranks of indicator values, not the indicator values themselves. Rank order correlation also delivers suitable results for
indicators which are not normally distributed and for small samples. For this reason, this method can be applied in particular to
indicators which are not uniformly scaled. Cf. SACHS, L., Angewandte Statistik, sections 5.2/5.3.
80 Guidelines on Credit Risk Management