Answer: 23.1%

The implied default correlation for the credit portfolio for the next year is calculated using the formula for the correlation of defaults between two credit assets. The formula is derived from the relationship between the individual probabilities of default (π1 and π2) and the joint probability of default (π12). The formula to calculate the implied default correlation (ρ) is: \[ \rho = \frac{\pi_{12} - \pi_1 \pi_2}{\sqrt{(\pi_1 (1 - \pi_1)) \times (\pi_2 (1 - \pi_2))}} \] Given the probabilities: - π1 (probability of default for the BBB-rated credit) = 3.5% - π2 (probability of default for the BB-rated credit) = 4.2% - π12 (joint probability of default for both credits) = 1.0% Plugging these values into the formula gives: \[ \rho = \frac{1\% - (3.5\% \times 4.2\%)}{\sqrt{(3.5\% \times (100\% - 3.5\%)) \times (4.2\% \times (100\% - 4.2\%))}} \] \[ \rho = \frac{1\% - 0.147\%}{\sqrt{(0.035 \times 99.65) \times (0.042 \times 95.8)}} \] \[ \rho \approx 23.14\% \] This calculation shows that the implied default correlation is approximately 23.14%, which corresponds to option C. The other options (A, B, and D) are incorrect as they do not follow the proper formula for calculating the default correlation between the two assets.

Author: LeetQuiz Editorial Team