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

A bank's internal rating system maps each borrower to a grade using a transition matrix estimated from agency data. One-year transition probabilities for a BB borrower are: upgrade to BBB 6%, stay BB 84%, downgrade to B 7%, default 3%. The bank holds a BB loan and assumes migration follows a Markov process with this matrix. Which statement about using this matrix for multi-year analysis is most accurate?

Under the Markov assumption, the two-year transition matrix is the one-year matrix multiplied by itself, because next-period migration depends only on the current rating and not on past history. Simply doubling the default probability is wrong, since it ignores migration and survival effects.

  1. AThe two-year distribution is found by multiplying the matrix by itself, assuming rating changes are independent of past historyCorrect
  2. BThe two-year default probability is simply 2 × 3% = 6% under the Markov assumption
  3. CThe matrix implies ratings are momentum-driven, so downgrades make further downgrades less likely
  4. DThe two-year distribution equals the one-year distribution because transitions are stationary

Explanation

A Markov chain squares the one-year matrix for two years, assuming the next move depends only on the current rating. Doubling the default probability ignores migration to other grades and survival. Empirical evidence of momentum actually contradicts the Markov assumption, not supports it.

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