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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

A risk analyst at a bank reviews a one-year rating transition matrix built from agency data. The row for BBB-rated obligors shows 90% remain BBB, 4% upgrade, 5% downgrade to non-default grades, and 1% default. Which statement about the matrix is correct?

Each row sums to 100%, because a row shows all possible end-of-period states, including default, for obligors starting in one rating. Columns need not sum to 100%, the default state is absorbing, and diagonal entries are normally the largest probabilities.

  1. AEach row must sum to 100% because it lists all possible end-of-period states for obligors starting in that ratingCorrect
  2. BEach column must sum to 100% because it lists all possible starting ratings for a given end rating
  3. CThe default row typically shows a probability of upgrading since defaulted firms can recover
  4. DThe diagonal entries of the matrix are generally the smallest values in each row

Explanation

A transition matrix gives probabilities of moving from a starting rating (row) to each ending rating (column), including default. Row probabilities must sum to 100%: 90+4+5+1=100. Columns have no such constraint, and the default state is absorbing in standard matrices. Diagonal entries are usually the largest.

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