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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

A bank builds a retail credit scorecard using logistic regression to predict default within 12 months. A risk analyst notes that the model output for each applicant lies between 0 and 1 and is interpreted as a probability. Which feature of the logistic model best explains why it is preferred over a linear probability model for this purpose?

The logistic model applies a sigmoid transformation to a linear combination of predictors, so fitted default probabilities always stay between 0 and 1. A linear probability model can give values below 0 or above 1, which makes it unsuitable for estimating default probability.

  1. AIt transforms a linear combination of predictors through a sigmoid function, keeping fitted probabilities within 0 and 1Correct
  2. BIt guarantees that all predictor variables are normally distributed
  3. CIt eliminates the need to test the model on out-of-sample data
  4. DIt ensures that the residuals have constant variance across all applicants

Explanation

Logistic regression passes a linear score through the logistic (sigmoid) function, so predicted default probabilities always lie between 0 and 1. A linear probability model can produce values outside this range. It does not remove the need for out-of-sample validation or assume normal predictors.

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