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FRM Part I · FRM Exam Part I · Measuring Credit Risk

Which statement about the Markov assumption in rating transition matrices is correct?

The Markov assumption means next-period transition probabilities depend only on the current rating, not on past rating history. Empirical findings such as rating momentum and business-cycle dependence contradict this, which is why the assumption is a recognised limitation of transition matrices.

  1. ANext-period rating probabilities depend only on the current rating, not on the earlier rating historyCorrect
  2. BNext-period rating probabilities depend on how long the firm has held its rating
  3. CTransition probabilities vary with the business cycle in a standard Markov matrix
  4. DDefault probabilities are always lower for recently upgraded firms than for firms with the same rating that were never upgraded

Explanation

A Markov chain assumes the future depends only on the present state. Empirically, ratings show momentum and cycle dependence, which violate this assumption, so options 1, 2 and 3 describe departures from it, not the assumption itself.

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