W. K. Hardle, R. A. Moro, and D. Schafer
1 Company Rating Methodology
Application of statistical techniques to corporate bankruptcy started in the
60’s with the development of computers.1 The first technique introduced was
discriminant analysis (DA) for univariate [3] and multivariate models [1]. Af-
ter DA the logit and probit models were introduced in [14] and [16]. Nowadays
these models are widely used in practice, i.e. they are at the core of the rat-
ing solutions at most European central banks. The solution in the traditional
framework is a linear function (a hyperplane in a multidimensional feature
space) separating successful and failing companies. A company score is com-
puted as a value of that function. In the case of the probit and logit models the
score can be directly transformed into a probability of default (PD), which de-
notes the probability with which a company can go bankrupt within a certain
period. The ma jor disadvantages of these popular approaches is the linearity
of the solution and, in the case of logit and probit models, the prespecified
form of the link function between PDs and the linear combination of predictors
(Figure 1).
In Figure 1 successful and failing companies are denoted with black trian-
gles and white quadrangles respectively. There is an equal number of compa-
nies of both classes in the sample. Following the DA and logit classification
rule, which give virtually the same result, we are more likely to find a fail-
ing company above and to the right from the straight line. This may lead to
a conclusion that companies with significantly negative values of operating
profit margin and equity ratio can be classified as successful. This, for exam-
ple, allows for companies with liabilities much greater than total assets to be
classified as successful. Such a situation is avoided by using a non-linear clas-
sification method, such as the SVM, which produces a non-linear boundary.
Following a traditional approach we would expect a monotonic relationship
between predictors and PDs, like the falling relation for the interest coverage
ratio (Figure 2). However, in reality this dependence is often non-monotonic
as for such important indicators as the company size or net income change. In
the latter case companies that grow too fast or too slow have a higher prob-
ability of default. That is the reason for contemplating non-linear techniques
as alternatives. Two prominent examples are recursive partitioning [4] and
neural networks [17]. Despite the strength of the two approaches they have
visible drawbacks: orthogonal division of the data space in recursive parti-
tioning that is usually not justified and heuristic model specification in neural
networks.
1 The authors are grateful to the German Bundesbank for providing access to
the unique database of the financial statements of German companies. The data
analysis took place on the premises of the German Bundesbank in Frankfurt. The
work of R. A. Moro was financially supported by the German Academic Exchange
Service (DAAD) and German Bundesbank. This research was supported by the
Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk”.