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Answer: c) If the coupon decreases, then (ceteris paribus) then the convexity decreases
The false statement is **(C)**. - **Convexity generally increases when coupon decreases**, holding maturity and yield constant. A lower-coupon bond has more of its value concentrated in later cash flows, which raises convexity. - In the extreme, a **zero-coupon bond** has the greatest convexity for a given maturity. Therefore, statement **(C)** is false because it says convexity decreases when coupon decreases. The other statements are true: - **(A)** Lower yield raises the present value of distant cash flows more, which typically increases convexity. - **(B)** Lower yield generally increases duration because later cash flows receive relatively more weight in present value terms. - **(D)** The convexity adjustment for a 50 bps shock is approximately 0.010, consistent with the given convexity measure.
Author: Manit Arora
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Q-714.3. Consider a three-year $100.00 face value bond that pays a 14.0% semi-annual coupon and offers a yield of 9.0% per annum with continuous compounding. The bond's cash flows and its duration and convexity are illustrated below. Please note the discount factors assume the yield's continuous compounding; for example, df(1.5) = exp(-0.090*1.5) = 0.87372 ≈ 0.874.
| Face value | $100.00 |
|---|---|
| Semi-annual coupon | 14.0% |
| Yield (continuously comp, CC) | 9.0% |
| Semi-Annual Period (t) | d.f. | Cash flow | Time * Weight | Time^2 * Weight | |
|---|---|---|---|---|---|
| FV | PV | Weight (W) | (t*W) | ||
| 0.5 | 0.956 | $7.00 | $6.69 | 0.060 | 0.030 |
| 1.0 | 0.914 | $7.00 | $6.40 | 0.057 | 0.057 |
| 1.5 | 0.874 | $7.00 | $6.12 | 0.054 | 0.082 |
| 2.0 | 0.835 | $7.00 | $5.85 | 0.052 | 0.104 |
| 2.5 | 0.799 | $7.00 | $5.59 | 0.050 | 0.124 |
| 3.0 | 0.763 | $107.00 | $81.68 | 0.727 | 2.182 |
$142.00 | $112.324 | 1.000 | 2.5785 |
About this bond, each of the following statements is true EXCEPT which is false?
A
a) If the yield decreases, then (ceteris paribus) the convexity increases
B
b) If the yield decreases, then (ceteris paribus) then duration increases
C
c) If the coupon decreases, then (ceteris paribus) then the convexity decreases
D
d) If the yield shock is 50 basis points (0.50%), the convexity adjustment is about $0.010
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