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FRM Part II · FRM Exam Part II · Credit Scoring and Rating

A bank's rating model validation team finds that, for grade 6, the average estimated PD was 1.5% each year over five years, while the realized annual default rates were 0.8%, 0.9%, 1.0%, 4.1%, and 0.7%. The defaults are strongly correlated across obligors, driven by a common economic shock in year four. Which conclusion about backtesting is most appropriate?

A binomial test assuming independent defaults would overstate evidence of underestimation, because default correlation widens the spread of annual default rates. The year-four spike should be interpreted allowing for correlation; the five-year average of about 1.5% matches the assigned PD, so ignoring the year or using the maximum is wrong.

  1. AA binomial test assuming independent defaults would overstate evidence of underestimation; default correlation should be considered when interpreting the year-four exceedanceCorrect
  2. BThe binomial test with independence is preferred because it is conservative for correlated defaults
  3. CYear four should be excluded because correlated years cannot be used in validation
  4. DThe PD should be raised to 4.1% because the maximum observed rate is the correct estimate

Explanation

With positive default correlation, the dispersion of annual default rates is wider than under independence, so a test assuming independence rejects too often. The year-four spike must be interpreted with correlation in mind. The five-year average is about 1.5%, consistent with the PD, so mechanically using the maximum or dropping the year is wrong.

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