NO.PZ2023090201000106
问题如下：
An analyst collects the following details about a bond portfolio. If each bond has a par value of £25 million, the modified duration of this bond portfolio is closest to:
选项：
A.5.8. B.6.1. C.6.2.解释：
A is correct.
Money duration is calculated as the annual modified duration times the full price (PVFull) of the bond, including accrued interest. Thus the modified durations of the bonds are 730/95 = 7.6842 and 515/120 = 4.29167, respectively. The modified duration of a bond portfolio is calculated as the weighted average of the statistics for the individual bonds. The shares of overall portfolio market value are the weights. Here, the market values of the bonds are £25 million * 95/100 = £23,750,000 and £25 million * 120/100 = £30,000,000. Thus the weight of the first bond in the portfolio is £23,750,000 / (£23,750,000 + £30,000,000) = 44.186% and the weight of the second bond in the portfolio is £30,000,000 / (£23,750,000 + £30,000,000) = 55.814%. The modified duration of the portfolio is therefore 44.186% * 7.6842 + 55.814% * 4.29167 = 3.3953 + 2.3953 = 5.7907, rounded to 5.8.
考点：portfolio duration
解析：组合久期是将组合中各资产的久期加权平均的结果，权重为各资产的市场价值占组合市场价值的比重。
1、首先先计算各资产的市场价值以及总市值。市场价值 = Price /100 × Par amount，两个债券的市场价值分别为 £23,750,000、£30,000,000，加总后总市值为 £53,750,000。
2、计算各资产的权重：W1= 0.4419、W2 = 0.5581
3、计算各债券的Modified duration：D1 = 7.6842、D2 = 4.2917
4、portfolio duration = 7.6842 × 0.4419 + 4.2917 × 0.5581 = 5.79，故选项A正确。
计算各债券的Modified duration：D1 = 7.6842、D2 = 4.2917
