Altman's Z to PD

[Siamak]

Hi David,

here is your quote:
"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)"

do you have any hints which shows the way how to go from z score to PD

many thanks
siamaka

 

[David Harper CFA FRM]

Hi siamaka,

On the learning spreadsheet (Altman's z) @ http://www.bionicturtle.com/premium/spreadsheet/6.d.2_altmans_z/
..at row 23 I added a LOGIT transformation
(there are other resources on this I am sure, but mine on this is a book I think is terrific:
http://www.amazon.com/Active-Portfolio-Management-Practice-Finance/dp/0470080183/)

so I can't help you with calibration (I do not have a source on that...) but what i did is convert the Altman's Z to a linear score
with:
adjusted_Z = 1.6 - 2.6 (Z)
(I just made this up; a real calibration would be required, don't trust these for anything)...then the score is used in a LOGIT transform:

PD = 1 / (1+ EXP(-adjusted_Z))

maybe it's a start...David