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.