问题如下图：
选项：
A. 
B. 
C. 
解释：
这道题是不是出的不够严谨？approximate modified duration=effective duration应该用于含权债券吧？还是说题目已经默认，该不含权债券的approximate MD=MD？
NO.PZ2016031001000132 问题如下 investor purchases annucoupon bonwith a 6% coupon rate anexactly 20 years remaining until maturity a priequto pvalue. The investor’s investment horizon is eight years. The approximate mofieration of the bonis 11.470 years. The ration gthe time of purchase is closest to: A.-7.842. B.3.470. C.4.158. C is correct.The ration gis closest to 4.158. The ration gis a bons Macaulration minus the investment horizon. The approximate Macaulration is the approximate mofieration times one plus the yielto-maturity. It is 12.158 (= 11.470 × 1.06). Given investment horizon of eight years, the ration gfor this bonpurchase is positive: 12.158 – 8 = 4.158. When the investment horizon is less ththe Macaulration of the bon the ration gis positive, anpririsk minates coupon reinvestment risk. 考点ration gap解析ration g= Macaculration - investment horizon = Mofieration × (1+y) - investment horizon = 11.470 × 1.06 - 8 = 4.1582，故C正确。 这提问的是ration gpurchase 不应该是ration - 20吗？（买的时候还有20年到期）
老师问下这里的1+y y为什么是coupon rate 这道题好像没说ytm哎 直接用coupon rate 不太对吧
这里的8是年限还是在投资收益？有点晕
这个6%是coupon rate不是YTM，怎么用6%直接算出了macaulration?
