NO.PZ2018062006000113
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 10bps:
V（-）: N=6，FV=100，PMT=8，I/Y=5.9, PV=110.36
The price of the bond, if the yield increases by 10bps:
V（+）: 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
这个公式不是effective-duration的公式吗？这道题问的是modified-duration啊！！还有这个modified-duration到底有好多个变身？我知道的有：（三角形p/p）/三角形y=md～～～～～～还有Mac-du/1+y=md～～～～～～就这两个变身～～～～怎么又变成了effective-duration？？？？？？
