0.5 ×AnnConvexity× (ΔYield)2 这个 0.5 从哪来的

问题如下：

A bond has an approximate modified duration of 10.3829 and an approximate modified convexity of 141.217. What is the estimated percentage price change for the bond if yield to maturity decreases by 50 bps?

选项：

A.–5.01% B.5.37% C.5.54%

解释：

B is correct.

The convexity-adjusted estimate of the percentage change in bond price is calculated as follows:

%Δ PV^Full ≈ ( −AnnModDur × ΔYield)+[ 0.5 ×AnnConvexity× (ΔYield)² ] ≈( −10.3829×−0.005 )+[ 0.5 ×141.217× (−0.005)²] =0.051915+0.001765 =0.05368

考点：Bond Convexity and Convexity Adjustment

解析：利率下降50 bps，即△Yield = -0.5% = -0.005（注意要代入负值）

%Δ PV^Full ≈ ( −AnnModDur × ΔYield)+[ 0.5 ×AnnConvexity× (ΔYield)²]

( −10.3829×−0.005 )+[ 0.5 ×141.217× (−0.005)²] =0.051915+0.001765 = 0.05368 = 5.37%，故选项B正确。