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:
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:
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.
Ultimate access to all questions.
An analyst estimates the following partial 1-year transition matrix:
| From/To | AAA | AA | A |
|---|---|---|---|
| AAA (%) | 90.00 | 7.00 | 2.00 |
| AA (%) | 1.00 | 92.00 | 6.00 |
| A (%) | 0.10 | 1.50 | 87.00 |
Credit spread (%)
The expected price change for an AAA rated bond with a duration of 3.7, when downgraded to an A rating, is closest to:
A
–6.48%.
B
–3.70%.
C
–0.07%.
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