Explanation

Let's analyze each statement:

Statement A: TRUE

• A perfect credit scoring model would correctly identify all defaults first, resulting in an accuracy ratio (AR) of 1.0, which is indeed the theoretical upper bound.

Statement B: FALSE (This is the incorrect statement)

• A purely random model that cannot differentiate between good and bad customers would generate an accuracy ratio (AR) of 0, not 0.40 to 0.60. The random model's CAP curve would be a straight diagonal line from (0,0) to (1,1), and the AR is calculated as the area between the actual model's curve and the random model's curve divided by the area between the perfect model's curve and the random model's curve. For a random model, this ratio is 0.

Statement C: TRUE

• The CAP curve is indeed monotonically increasing because as we include more customers (moving from highest risk to lowest risk), the cumulative percentage of defaults cannot decrease - it can only stay the same or increase.

Statement D: TRUE

• This correctly describes the construction of the CAP curve: the y-axis represents the cumulative fraction of defaulted customers, while the x-axis represents the cumulative fraction of the entire population sorted by risk score from highest risk (left) to lowest risk (right).

Therefore, statement B is the incorrect one and is the answer to the question "each of the following statements is true except which is not?"