Graphics Reference
In-Depth Information
Graphical data representation is an important model selection tool in bankruptcy
analysis, since this problem is highly nonlinear and its numerical representation is
not very transparent. In classical rating models, the convenient representation of the
ratings inaclosedformreducesthe need forgraphical tools.Incontrast tothis, more
accurate nonlinear nonparametric models oten rely on visualisation. We demon-
strate the utilisation of visualisation techniques at different stages of corporate de-
fault analysis, which is based on the application of support vector machines (SVM).
hese stages are the selection of variables (predictors), probability of default (PD)
estimation, and the representation of PDs for two- and higher dimensional models
with colour coding. he selection of a proper colour scheme becomes crucial to the
correct visualisation of PDs at this stage. he mapping of scores into PDs is done as
a nonparametric regression with monotonisation. he SVM learns a nonparametric
score function that is, in turn, nonparametrically transformed into PDs. Since PDs
cannotberepresentedinaclosedform,otherwaysofdisplayingthemmustbefound.
Graphical tools make this possible.
Company Rating Methodology
4.1
Statistical techniques were first applied to corporate bankruptcy in the
s due to
the advent of computers. he first technique introduced was discriminant analysis
(DA) for univariate (Beaver,
) and multivariate models (Altman,
). he logit
andprobitmodelswerethenintroducedin(Martin,
)and(Ohlson,
).hese
models are now widely used in practice - they are at the core of the rating solu-
tions used by most European central banks. he solution in the traditional frame-
work is a linear function (a hyperplane in a multidimensional feature space) that
separates successful and failing companies. A company score is computed as a value
of that function. In the probit and logit models, the score can be transformed di-
rectly into a probability of default (PD),which denotes the probability of a company
going bankrupt within a certain period. he major disadvantages of these popular
approaches is the linearity of the solution and, in the logit and probit models, the
prespecified form of the link function between the PDs and the linear combination
of predictors (Fig.
.
).
In Fig.
.
, successful and failing companies are denoted by black triangles and
whitequadrangles, respectively. Both classes contain the same number of companies
in the sample. According tothe DAand logit classification rules, whichgive virtually
the same results, we are more likely to find a failing company above and to the right
of the straight line.hismaylead tothe conclusion that companies with significantly
negative values of operating profit margin and equity ratio can be classified as being
successful. his, for example, means that companies with liabilities that far outweigh
their total assets can be classified as successful. Such a situation is avoided through
theuseofanonlinear classification method,suchassupportvectormachines(SVM),
which produces a nonlinear boundary.
