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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A risk manager estimates a one-year transition matrix using the cohort method and compares it with the duration (hazard rate) method applied to the same data. Which statement is most accurate?

The hazard rate (duration) method uses timing of rating changes and time spent in each rating, so it can assign positive probabilities to rare transitions never seen in the sample, such as a top-rated issuer defaulting. The cohort method uses only start and end ratings and gives zeros.

  1. AThe cohort method uses the time spent in each rating, so it generally assigns non-zero probabilities to rare transitions that were never observed
  2. BThe two methods always give identical matrices because they use the same data
  3. CThe hazard rate method ignores the timing of rating changes within the year and uses only year-start and year-end ratings
  4. DThe hazard rate method uses the timing of migrations and time spent in each rating, so it can produce non-zero probabilities for rare transitions not observed in the cohort dataCorrect

Explanation

The cohort method uses only beginning and end-of-period ratings, so unobserved transitions get zero probability. The hazard rate method uses the full timing of changes and exposure time, and via the generator matrix exponential it can yield non-zero probabilities for such rare moves, such as a high-grade issuer defaulting through intermediate downgrades.

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