Answer-first summary for fast verification
Answer: 1.425
## Explanation Effective duration measures the sensitivity of a bond's price to changes in interest rates. The formula for effective duration is: \[\text{Effective Duration} = \frac{V_- - V_+}{2 \times V_0 \times \Delta y}\] Where: - \(V_-\) = price when yields decrease - \(V_+\) = price when yields increase - \(V_0\) = current price - \(\Delta y\) = change in yield (in decimal) For the callable bond: - \(V_0 = 99.63\) - \(V_- = 100.35\) (50 bps down) - \(V_+ = 98.93\) (50 bps up) - \(\Delta y = 0.005\) \[\text{Effective Duration} = \frac{100.35 - 98.93}{2 \times 99.63 \times 0.005} = \frac{1.42}{0.9963} = 1.425\] Therefore, the effective duration of the callable bond is 1.425, which corresponds to option B.
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
An analyst gathers the following prices for a 2-year, 4% annual coupon bond and an otherwise identical bond callable in one year at par:
| Straight Bond | Callable Bond | |
|---|---|---|
| Current price | 100.00 | 99.63 |
| Price with a 50 bps shift down in the benchmark yield curve | 100.95 | 100.35 |
| Price with a 50 bps shift up in the benchmark yield curve | 99.06 | 98.93 |
The effective duration of the callable bond is closest to:
A
1.074
B
1.425
C
1.890
No comments yet.