Reconsidering the logit: the risk of individual names

In this paper I examine whether the probability of default (PD) of an obligor estimated by a logit model can really be considered a good estimate of the true PD. The general answer seems to be no, although in this paper I don’t carry out a large scale (simulation) analysis. With a simple set-up I show that the logit has a high potential of ‘mixing’ probabilities, that is, as signing similar scores to obligors with quite different PDs. I demonstrate how this situation is reflected in the convexity that can often be observed in empirical ROC curves. I think that the results have important implications in the pricing of individual exposures and raise the question of the stability of estimated PDs when the value-combinations of the risk factors underlying the portfolio change. This latter issue also relates to capital calculation, model building and validation as required by the new Basel capital rules. For example, because of the concavity of the risk weight formula a bank may want to avoid PD mixing thereby reducing its capital requirement.