I have a set of loan performance data with a flag indicating whether the loan was good (1) or bad (defaulted) (2). The dataset also includes a custom model score based on customer credit attributes to predict bad. The range for the custom score is 61 to 545. I want to cut the custom score into 10 bands (pricing grades), each band corresponding to a target bad rate (# of bads / # of total loans). For example, band 1 needs to have a bad rate of 2.6%, band 2 needs a bad rate of 3.8%, and so on.
Determining cut points is often a function of the use to which they will be put. You haven't stated that.
If you want to validate the custom score, a discrimination tool often used in logistic regression is to use cut points based on the deciles of the data. Then you can plot the mean number of defaults against the mean score in the band as a way to look at the linearity of the prediction of default. The Hodges-Lemenshow test may be used to examine goodness of fit.
I figured I needn't state a use for the bands since I had indicated that I have pre-defined targets for the bands. I want to find the cuts that yield specified bad rates (means of my bad flag).
1st band would be 61 - x, where the mean of bad for this band = .026,
2nd band would be x - y, where the mean of bad for this band = .038,
and so on.
These bands will represent pricing tiers for consumer loans. The reason I need the bands to yield specific bad rates is so this new segmentation can be installed in place of an old one without the need to adjust pricing.