Free CFA Certification Practice Questions:


Exhibit 1 indicates a ratings transition matrix. constructed by Standard & Poor's. It indicates one-year ratings migration probabilities based upon bond rating data from the period 1981-2000.



A portfolio consists of 30 percent B and 70 percent CCC-rated bonds. If a randomly selected bond defaults in one year, what is the probability that it was a CCC-rated bond?

A) 9.38%

B) 90.62%

C) 16.95%

  • [Ans: B]






    • We can use Bayes rules as follows:

    P(CCC-rated Bond | Default) = P(Default | CCC-Rated Bond) * P(CCC-Rated Bond) / P (Default)


    P(Default | CCC-Rated Bond) = 21.94% (from the transition matrix)

    P(CCC-Rated Bond) = 70% (CCC-rated bond are 70% of portfolio)

    P(Default) = P(Default | B-rated) * P(B-rated) + P(Default | CCC-rated) * P(CCC-rated)

    = (5.30% * 30%) + (21.94% * 70%)

    = 16.95%


    P(CCC-rated Bond | Default) = P(Default | CCC-Rated Bond) * P(CCC-Rated Bond) / P (Default)

    = 21.94% * 70% / 16.95%

    = 90.62%






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