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Answer: BB loans have a 75.73% chance of staying at BB for one year.
## Explanation Looking at the transition matrix: - **Option A**: BBB loans have a 4.08% chance of being upgraded in one year. - From the BBB row, upgrades would be to AA (0.02%), A (0.21%), or AA (0.02%) - total upgrade probability is only about 0.23%, not 4.08%. - **Option B**: BB loans have a 75.73% chance of staying at BB for one year. - ✓ CORRECT: In the BB row, the diagonal element is 75.73%, which represents the probability of staying at the same rating. - **Option C**: BBB loans have an 88.21% chance of being upgraded in one year. - This is incorrect as the total upgrade probability for BBB is only about 0.23%. - **Option D**: BB loans have a 5.72% chance of being upgraded in one year. - From the BB row, upgrades would be to BBB (5.27%) and higher ratings - total upgrade probability is about 5.35%, close but not exactly 5.72%. The matrix shows transition probabilities where the diagonal elements represent the probability of staying at the same rating class. For BB-rated loans, the value 75.73% in the BB column represents the probability that a BB-rated loan will still be BB-rated after one year.
Author: LeetQuiz .
Based on the transition matrix provided, which statement is correct?
A
BBB loans have a 4.08% chance of being upgraded in one year.
B
BB loans have a 75.73% chance of staying at BB for one year.
C
BBB loans have an 88.21% chance of being upgraded in one year.
D
BB loans have a 5.72% chance of being upgraded in one year.
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