NO.PZ2023052301000046
问题如下：
Consider a bond that has three years remaining to maturity, a coupon of 4% paid semiannually, and a yield-to-maturity of 4.60%. Assuming it is 12 days into the first coupon period and a 30/360 basis, the bond’s annualized Macaulay duration is closest to:
选项：
A.1.8764 years.
2.8386 years.
2.8553 years.
解释：
B is correct.
第一笔现金流：
PVCF1 = PMT /【（1+I/Y）^(n- t/T)】= 4/ （1+4.6%）^(1-12/360)=3.829
P0= 100✖️[1+PMT coupon^( t/T) ] = 100✖️（1+4.6%）^(12/360)=100.15
t= n- t/T = 1- 12/360
W1= PVCF1 / P0 ✖️ t = 3.829 / 100.15 ✖️（1-12/360）=0.0369
第二笔现金流：
PVCF1 = PMT /【（1+I/Y）^(n- t/T)】= 4/ （1+4.6%）^(2-12/360)= 3.66
P0= 100✖️[1+ I/Y ^( t/T) ] = 100✖️（1+4.6%）^(12/360)=100.15
t= n- t/T = 2- 12/360 =1.966
W2= PVCF1 / P0 ✖️ t = 3.66 / 100.15 ✖️（2-12/360）=0.0718
第三笔现金流：
PVCF1 =（PMT +FV）/【（1+I/Y）^(n- t/T)】= （100+4）/（1+4.6%）^(3-12/360)= 91.01
P0= 100✖️[1+ I/Y ^( t/T) ] = 100✖️（1+4.6%）^(12/360)=100.15
t= n- t/T = 3- 12/360 =2.9667
W3= PVCF1 / P0 ✖️ t = 91.01 / 100.15 ✖️2.9667=2.69
0.0369+0.0718+ 2.69 = ？不对
