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Answer: At low yields, a callable bond exhibits negative convexity and therefore negative duration
The false statement is **D**. - **A** is true: both Macaulay duration and modified duration are expressed in time units, commonly years. - **B** is true: duration/convexity approximations are still based on a single-factor, parallel shift assumption. - **C** is true for a plain vanilla fixed-rate bond: convexity generally rises with maturity and falls as coupon rate or yield rises. - **D** is false: a callable bond can exhibit **negative convexity** at low yields, but that does **not** mean duration is negative. Duration is usually still positive, though it may become very low or behave nonlinearly. Therefore, the exception is **D**.
Author: Manit Arora
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Question 161.4. Each of the following is TRUE with respect to duration and convexity EXCEPT:
A
Both modified and Macaulay duration are denoted in units of “years”
B
To estimate bond price change with both duration and convexity, per two-term Taylor series, is still to employ a single-factor measure of sensitivity that assumes a parallel shift in the yield curve
C
With respect to a plain vanilla bond (without embedded options), bond convexity increases with maturity, decreases with coupon rate and decreases with yield
D
At low yields, a callable bond exhibits negative convexity and therefore negative duration
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