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Altman's Z score for credit risk

Altman's Z is the most famous type of linear discriminant model: borrowers are classified into high or low default risk categories. It does not directly give a probability of default (PD), although we can map to the score to a credit rating and map the rating to a PD (so there is an indirect path from the score to the PD). Four drawbacks: 1. Not granular: only gives default/zone of ignorance/no default; 2. Constant factor weights (i.e., factor weights may be time varying); 3. Only considers five fundamental variables, ignores other variables; 4. No centralized database on defaulted business loans (not really an Altman's critique at all)
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