Rating Models and Validation - Oesterreichische Nationalbank

Rating Models and Validation
Chart 15: How Linear Discriminant Analysis Works
Linear multivariate discriminant analysis requires normal distribution (in
the strict mathematical sense of the term) in the indicators examined. Therefore,
the assumption of normal distribution has to be tested for the input indicators.
In cases where the indicators used in analysis are not normally distributed,
the MDA results may be compromised.
In particular, practitioners should bear this in mind when using qualitative
creditworthiness criteria, which generally come in the form of ordinal values
and are therefore not normally distributed. However, studies have shown that
rescaling the qualitative creditworthiness criteria in a suitable manner can also
fulfill the theoretical prerequisites of MDA. 22 For example, Lancaster scaling
can be used. 23
In addition to the assumption of normal distribution, linear discriminant
analysis also requires the same variance/covariance matrices for the groups
to be discriminated. In practice, however, this prerequisite is attributed less significance.
24
Applied example:
In practice, linear multivariate discriminant analysis is used quite frequently for
the purpose of credit assessment. One example is Bayerische Hypo- und Vereinsbank
AGÕs ÒCrebonÓ rating system, which applies linear multivariate discriminant
analysis to annual financial statements. A total of ten indicators are
processed in the discriminant function (see chart 16). The resulting discriminant
score is referred to as the MAJA value at Bayerische Hypo- und Vereinsbank.
MAJA is the German acronym for automated financial statement analysis
(MAschinelle Jahresabschlu§Analyse).
22 Cf. BLOCHWITZ, S./EIGERMANN, J., Unternehmensbeurteilung durch Diskriminanzanalyse mit qualitativen Merkmalen.
23 HARTUNG, J./ELPELT, B., Multivariate Statistik, p. 282ff.
24 Cf. BLOCHWITZ, S./EIGERMANN, J., Effiziente Kreditrisikobeurteilung durch Diskriminanzanalyse mit qualitativen Merkmalen,
p. 10.
42 Guidelines on Credit Risk Management