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Ausilio · 2024年05月26日

关于这个3.99的算法

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NO.PZ202209060200004602

问题如下:

According to the information in Exhibit 1 and assuming Berendsen retires in four years, the fixed-income portfolio most likely:

选项:

A.should have a shorter duration. B.needs a higher cash flow yield. C.has currently achieved zero replication.

解释:

Solution

C is correct. The portfolio’s Macaulay duration of approximately 4.0 matches the time horizon of the liability and can be calculated as follows:

[(Portfolio weightBond 1 × DurationBond 1) + (Portfolio weightBond 2 × DurationBond 2) + (Portfolio weightBond 3 × DurationBond 3)] ÷ 3 = 3.99.

When compared with the single liability due in four years, the portfolio has the same return and duration characteristics of a single zero-coupon bond maturing in four years. The interest rate risk has been immunized, which is known as zero replication.

A is incorrect because the portfolio’s current duration matches the duration of the liability, or retirement date.

B is incorrect because the cash flow yield matches the required investment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the required rate of return.

老师好,大案里这个:

[(Portfolio weightBond 1 × DurationBond 1) + (Portfolio weightBond 2 × DurationBond 2) + (Portfolio weightBond 3 × DurationBond 3)] ÷ 3 = 3.99.

具体是怎么算出来的啊?我用allocation那三个百分比配合macauly duration算,算得应该是4.0143,是我哪里用的有问题吗

1 个答案

发亮_品职助教 · 2024年05月27日

嗨,爱思考的PZer你好:


答案的算法是错的,你用的计算方法正确。算下来差不多就是4.0几,也是基本接近负债的期限4-years的


正确的算法应该是:

Bond 1权重×Bond 1 MD久期 + Bond 2权重×Bond 2 MD久期 + Bond 3权重×Bond 3 MD久期

用权重给Macaulay duration久期加权,这里面已经是平均数了,无需再除以3.


答案的计算是先乘了权重算了加权平均,又除以3相当于是想算算数平均,算了2次平均,这个是错的。


债券1的权重:732412/(732412+930720+986100)=732412/2649232=27.65%

债券2的权重:930720/(732412+930720+986100)=35.13%

债券3的权重:1-27.65%-35.13%=0.3722=37.22%

上面用题目表格给的权重也OK。


加权Macaulay duration:

1.49×27.65% + 3.48×35.13% × 6.43×37.22% = 0.4120+1.2225+2.3932=4.0277

----------------------------------------------
努力的时光都是限量版,加油!

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