提问

问题如下：

A bond has an annual modified duration of 7.140 and annual convexity of 66.200. The bond’s yield-to-maturity is expected to increase by 50 basis points. The expected percentage price change is closest to:

选项：

–3.40%.

–3.49%.

–3.57%.

解释：

B is correct.

The expected percentage price change is closest to −3.49%. The convexity adjusted percentage price change for a bond given a change in the yield-to-maturity is estimated by:

%ΔPVFull≈[−AnnModDur×ΔYield]+0.5×AnnConverxity×(ΔYield)^2

%ΔPVFull≈[−7.14×0.005]+0.5×66.2×(0.005)^2

= -0.034873 or -3.49%

考点：duration & convexity

解析：这道题考察的是综合考虑duration和convexity对债券价格的影响。题干中利率上升50bps，即△yield = 0.5% = 0.005，duration=7.14，Convexity=66.2。

△P/P= -duration × △y+0.5 × convexity × (△y)2

= -7.14 × 0.5%+0.5 × 66.2 × (0.5%)2

= -3.49%

故选项B正确。