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A. FOGLIA^S. IANNOTTI^P. MARULLO REEDTZ Ã An internal risk rating system can be de®ned as the process used to classify bank borrowers into categories of different credit riskiness. Most of the related literature has investigated various aspects of this process, but the problem of de®ning the categories and the distribution of borrowers into the different classes or grades has received rather less attention, other than noting that the number of grades and their dispersion should achieve a meaningful differentiation of risk. An appropriate de®nition of the grading scale is of primary importance because the probability of default associated to each grade is the key inputs of capital allocation systems at many best-practice banks and is the core of the January 2001's new proposal of the Basel Committee for the calculation of capital requirements. Statistical techniques such as cluster analysis can help in identifying distinct subgroups of borrowers possessing the same creditworthiness. We use a logit model to estimate individual default probabilities for four categories of borrowers and apply cluster analysis to assign borrowers to each grade. However, since cluster analysis is not a purely mechanical process, but requires examination of the nature of observations and of the objective of clustering, the ultimate choice of the most appropriate grading scale for a given portfolio relies on empirical grounds. A suf®cient granularity and an appropriate quanti®cation of risk must be balanced.(

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