Answer: 23.1%

The implied default correlation (ρ) for the credit portfolio for next year is calculated using the formula for two random variables X and Y, which in this case represent the probabilities of default for the two credit assets: \[ \rho_{XY} = \frac{P(X \cap Y) - P(X)P(Y)}{\sqrt{P(X)(1-P(X))P(Y)(1-P(Y))}} \] Given: - \( P(X) = 3.5\% \) (probability of default for the BBB rated credit) - \( P(Y) = 4.2\% \) (probability of default for the BB rated credit) - \( P(X \cap Y) = 1.0\% \) (joint default probability for both credits) Plugging these values into the formula: \[ \rho_{XY} = \frac{1.0\% - (3.5\% \times 4.2\%)}{\sqrt{3.5\% \times (100\% - 3.5\%) \times 4.2\% \times (100\% - 4.2\%)}} \] \[ \rho_{XY} = \frac{1.0\% - 0.147\%}{\sqrt{3.5\% \times 96.5\% \times 4.2\% \times 95.8\%}} \] \[ \rho_{XY} = \frac{0.853\%}{\sqrt{0.0015 \times 0.4032}} \] \[ \rho_{XY} = \frac{0.853\%}{0.01176} \] \[ \rho_{XY} \approx 0.23139 \text{ or } 23.14\% \] This calculation shows that the implied default correlation is approximately 23.14%, which corresponds to option C. The other options provided are incorrect as they do not follow the correct formula for calculating the default correlation. Option A simply adds the individual probabilities of default, option B adds the individual probabilities and the joint probability, and option D incorrectly uses a wrong numerator in the formula.

Author: LeetQuiz Editorial Team