Explanation:
To find the probability that a country with a rating of AA will have an AAA rating in two years, we calculate the 2-year transition probability. Using the transition matrix, we multiply the row vector for AA by the column vector for AAA (effectively applying the Chapman-Kolmogorov equations for a Markov chain).
Looking at the table, countries currently rated AA can only transition to AAA, AA, A, or B in one year.
Summing these probabilities: $0.04096 + 0.03878 = 0.07974$, or 7.97%. Statement D is correct.
Checking the others:
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Q.82 A risk manager in an investment bank was asked to forecast the sovereign rating of countries where the bank has significant holdings. The risk manager found sovereign transition rates across the Major Rating Categories 1995-2008 published by Fitch.
Annual Rating Transitions (% , Average Annual)
| AAA | AA | A | BBB | BB | B | CCC to C | D | Total | |
|---|---|---|---|---|---|---|---|---|---|
| AAA | 99.42 | 0.58 | – | – | – | – | – | – | 100.00 |
| AA | 4.12 | 94.12 | 1.18 | – | – | 0.59 | – | – | 100.00 |
| A | – | 3.55 | 92.91 | 3.55 | – | – | – | – | 100.00 |
| BBB | – | – | 8.11 | 87.84 | 3.38 | 0.68 | – | – | 100.00 |
| BB | – | – | – | 9.04 | 83.51 | 5.85 | – | 1.60 | 100.00 |
| B | – | – | – | – | 12.12 | 84.09 | 3.03 | 0.76 | 100.00 |
| CCC to C | – | – | – | – | – | 23.08 | 53.85 | 23.08 | 100.00 |
Given the table above, which of the below statements is correct?
A
A country has a 98.13% chance to have a rating of AA.
B
A country with a rating of BB has a 5.85% chance of a downgrade in one year.
C
AAA-rated countries will have the same rating in the future with a 99.12% probability.
D
There is a 7.97% probability that a country with a rating of AA will have an improved AAA rating in two years.
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