Use the transition matrix in Table 19.1 and software on the author's website to calculate a transition matrix for six months. What is the probability of a company rated Aaa staying Aaa during the six months? What is the probability of it moving to Aa?

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Table 19.1 Initial Rating AAA AA A B CCC/C D AAA AA A 89.85 9.35 0.50 90.76 Rating at Year-end 0.10 0.55 0.05 0.03 1.67 92.61 8.08 0.49 0.00 0.00 0.00 3.45 0.01 0.03 0.12 0.00 0.02 0.08 0.12 0.20 B CCC/C D 0.05 0.11 0.03 0.00 0.00 0.00 0.00 0.05 0.06 5.23 91.93 3.78 0.46 0.27 0.12 0.02 86.00 7.51 0.61 5.03 0.17 5.18 85.09 5.66 0.02 0.00 0.11 0.00 0.00 0.02 0.05 0.17 0.70 0.65 14.72 50.90 33.42 3.81 0.00 100.00