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Question 21.3: Use the transition matrix in Table 21.1 to calculate a trans...

Use the transition matrix in Table 21.1 to calculate a transition matrix for two years. What is the probability of a company rated Aaa staying Aaa during the two years? What is the probability of it moving to Aa?

Table 21.1 One-Year Ratings Transition Matrix, 1970–2016, with Probabilities Expressed as Percentages and Adjustments for Transition to the WR (without rating) Category
Rating at Year-End Initial Rating
Defauly Ca-c Caa B Ba Baa A Aa Aaa
0 0 0 0 0.02 0.08 0.59 8.36 90.94 Aaa
0.02 0 0.02 0.04 0.07 0.45 8.84 89.68 0.87 Aa
0.06 0.01 0.04 0.12 0.51 5.67 90.9 2.64 0.06 A
0.18 0.02 0.17 0.75 4.09 90.16 4.44 0.16 0.01 Baa
0.99 0.12 0.78 7.9 93.03 6.66 0.47 0.05 0.01 Ba
3.79 0.61 7.39 82.18 5.32 0.51 0.16 0.03 0.01 B
9.75 3.3 78.52 7.82 0.46 0.11 0.03 0.01 0 Caa
33.24 51.28 11.41 3.19 0.8 0 0.07 0 0 Ca-C
100 0 0 0 0 0 0 0 0 Default
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The probability of an Aaa rating staying Aaa over two years is 82.77%. The probability of it moving to Aa is 15.12%.

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