BASEL II: PROBLEMS AND USAGE

(thin line), the more accurately the model can distinguish between defaulters
and non-defaulters. A AUC value of 0,5 (dotted line) corresponds
to a model without discriminative power while a AUC value of one characterizes
a perfect model. Within the ROC framework, it is important that
debtors with weak creditworthiness receive worse ratings than those with
strong creditworthiness.
5.2.2. Cumulative Accuracy Profile
Another popular validation technique is the cumulative accuracy profile.
In order to obtain the CAP curve, borrowers are ordered by their credit
score, from the riskiest to the safest. Subsequently, the fraction of debtors
with the worst ratings (WR) is plotted against the hit rates. By repeating
this procedure for every rating category s, the CAP curve is constructed,
which is depicted in figure 11.
HR s
1
Perfect rating
function
Random rating function
WR s
DR
1
Figure 11. Cumulative Accuracy Profile
The straight dotted line below the CAP curve in figure 11 represents a
rating system with random assignment of credit scores whereas the CAP
curve of a rating system with perfect predicting power (thin line) is determined
by the default rate (DR) of the portfolio. Actual rating functions will
typically lie between these two extreme cases.
The predictive power of a rating system is summarized by the accuracy
ratio (AR). This ratio is determined as the ratio of the area between the
CAP curve of the rating function under validation and the random CAP
curve to the area between the perfect and the random CAP curves. 30 The
closer the AR value to one, the better is the rating model.
30 See Sobehart/Keenan/Stein (2003) and Engelmann/Hayden/Tasche (2003).
32