Use the transition matrix in Table 19.1 to calculate a transition matrix for two years. What is the probability of a company rated AAA being AAA at the end of two years? What is the probability of it moving to AA? 

Table 19.1

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Initial Rating AAA AA A BBB BB B CCC/C D AAA AA 89.85 9.35 0.50 90.76 0.10 Rating at Year-end A 0.03 1.67 92.61 0.00 0.00 0.55 0.05 8.08 0.49 0.00 3.45 0.01 0.03 0.12 BBB BB 0.11 0.00 0.02 0.08 0.12 5.03 0.17 0.20 0.00 0.00 0.00 0.00 B CCC/C 0.03 0.05 0.05 0.06 0.27 0.12 5.23 91.93 3.78 0.46 0.11 0.02 0.00 0.02 86.00 7.51 5.18 85.09 5.66 0.00 0.65 14.72 50.90 0.61 D 0.00 0.02 0.05 0.17 0.70 3.81 33.42 0.00 100.00