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

A bank builds a retail scorecard using logistic regression, where the dependent variable equals 1 if the borrower defaults within 12 months and 0 otherwise. A risk analyst notes that a linear probability model was rejected in favor of the logistic model. What is the principal reason for this choice?

The logistic model is preferred because its S-shaped function constrains fitted default probabilities to lie between 0 and 1, unlike a linear probability model, which can produce impossible values. Its coefficients are log-odds effects, and out-of-sample validation is still necessary.

  1. AThe logistic model guarantees fitted probabilities between 0 and 1Correct
  2. BThe logistic model removes the need for out-of-sample validation
  3. CThe logistic model assumes borrower characteristics are normally distributed
  4. DThe logistic model produces coefficients that directly equal changes in default probability

Explanation

The logistic function maps a linear score into the interval (0,1), so fitted values are valid probabilities. A linear probability model can produce values below 0 or above 1. Logistic coefficients are changes in log-odds, not direct probability changes, and validation is still required.

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