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

Which of the following is a well-documented limitation of using a historical rating transition matrix to forecast future credit migration with a time-homogeneous Markov assumption?

Historical transition matrices assume a time-homogeneous Markov process, but actual migrations show momentum, where downgrades tend to follow downgrades, and vary across the business cycle. These features violate the memoryless, constant-probability assumption and limit the reliability of the forecasts.

  1. AMigration probabilities are known to be independent of the business cycle, so no adjustment is ever needed
  2. BThe matrix cannot be estimated for investment-grade issuers because they never migrate
  3. CRatings exhibit momentum (downgrades tend to be followed by further downgrades) and probabilities vary with the economic cycle, violating the Markov assumptionCorrect
  4. DThe matrix always overstates default rates for speculative-grade issuers because withdrawn ratings are treated as defaults

Explanation

Empirically, transition probabilities depend on the cycle and show rating momentum, so the next move depends on past moves, contradicting the memoryless Markov property. Other options are false statements.

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