Answer: –6.48%.

## Explanation To calculate the expected price change when an AAA rated bond is downgraded to an A rating, we need to consider the change in credit spread and the bond's duration. **Step 1: Calculate the credit spread change** Current credit spread for AAA bonds: 0.75% New credit spread for A bonds: 1.75% Change in credit spread = 1.75% - 0.75% = 1.00% **Step 2: Calculate the price change** Price change ≈ -Duration × Change in credit spread = -3.7 × 1.00% = -3.70% However, this is not the correct answer. Let me reconsider the approach. **Step 3: Consider the probability-weighted approach** From the transition matrix for AAA bonds: - Probability of staying AAA: 90.00% - Probability of downgrading to AA: 7.00% - Probability of downgrading to A: 2.00% We need to calculate the expected price change specifically for the scenario where the bond is downgraded to A rating. When downgraded from AAA to A: - Credit spread increases from 0.75% to 1.75% - Change in credit spread = 1.00% Price change = -Duration × Change in credit spread = -3.7 × 1.00% = -3.70% But the correct answer is -6.48%, which suggests we need to consider the full impact including the probability of the downgrade. Expected price change = Probability of downgrade × Price change due to downgrade = 2.00% × (-3.70%) = -0.074% This doesn't match either. Let me reconsider the calculation: Price change = -Duration × ΔSpread = -3.7 × (1.75% - 0.75%) = -3.7 × 1.00% = -3.70% However, the correct answer is -6.48%, which suggests the duration might be applied to a larger spread change or there might be additional factors.

Author: LeetQuiz Editorial Team