问

问题如下：

A client purchases a 6-year bond at 109.83, and the coupon rate is 8%. The coupon is paid annually. The yield-to-maturity is 6% now. If the yield changes 10bps, calculate the approximate modified duration of the bond.

选项：

A.

4.78.

B.

4.06.

C.

4.02.

解释：

A is correct.

The price of the bond, if the yield decreases by 10 bps:

PV-: N=6，FV=100，PMT=8，I/Y=5.9，PV- = 110.36

The price of the bond, if the yield increases by 10 bps:

PV+: N=6，FV=100，PMT=8，I/Y=6.1，PV+ = 109.31

ApproxModDur = [PV(-) - PV(+)] / [2×(△Yield)×(PV₀ )] = (110.36-109.31)/[2×0.001×109.83] = 4.78

考点：approximate modified duration

解析：分别算出利率上升10 bps后的PV+(109.31)和利率下降10 bps后的PV-(110.36)，代入approximate modified duration公式即可，故选项A正确。