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Answer: Increase of 29 bps
Using the modified duration approximation: \[ \%\Delta P \approx -D_{mod} \times \Delta y \] So, \[ \Delta y \approx -\frac{\%\Delta P}{D_{mod}} = -\frac{85.65/87.20 - 1}{4.52} \approx 0.00393257 = 39.33\text{ bps} \] If the benchmark yield rose by 10 bps, then the credit spread must have widened by approximately: \[ 39.33 - 10.00 \approx 29.33\text{ bps} \] So the nearest answer is **A. Increase of 29 bps**.
Author: Manit Arora
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Question 507.1. On a single day the price of a corporate bond with a modified duration of 4.52 years drops from $87.20 to $85.65. If the benchmark yield increases by 10 basis points during the day, which is nearest to the approximate change in the bond's credit spread?
A
Increase of 29 bps
B
Increase of 19 bps
C
Approximately unchanged
D
Decrease of 15 bps
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