
Explanation:
Option B is the false statement. A purely random model generates a Cumulative Accuracy Profile (CAP) curve that is a straight diagonal line. The Accuracy Ratio (AR) is calculated as the ratio of the area between the model's CAP curve and the random model's CAP curve to the area between the perfect model's CAP curve and the random model's CAP curve. Therefore, for a purely random model, the AR is exactly zero (0.0), not 0.40 to 0.60. All other statements are true characteristics of CAP curves and AR.
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A
A perfect credit scoring model generates an accuracy ratio (AR) of 1.0, which is the upper bound on the AR
B
A purely random model that cannot differentiate between good and bad customers is likely to generate an accuracy ratio (AR) of 0.40 to 0.60; i.e., 50% +/- 10%
C
The CAP curve, which plots the actual rating model as a cumulative percentage of defaults, is monotonically increasing (aka, nondecreasing or weakly increasing)
D
The CAP curve plots the fraction of defaulted customers (y axis) against the fraction of entire customer population sorted by score from highest risk (left) to lowest risk (right)
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