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Cooljas · 2024年04月18日

这个是什么意思啊?为啥要除以100

NO.PZ2023091701000041

问题如下:

A fixed-income portfolio manager currently holds a bullet 7-year US Treasuryp osition with USD 60 million face value.The manager would like to create a cost matching barbell portfolio by purchasing a combination of a 2-year Treasury and a 15-year Treasury that would have the same duration as the7-year US Treasury position.The data for the three US Treasuries are listed below:

Which of the following combinations correctly describes the weights of the two bonds that the manager will use to construct the barbell portfolio?

选项:

Weightof2-Year Treasury丨Weight of 15-Year Treasury A.

14.22%丨85.78%

B.44.46%丨55.54% C.55.54%丨44.46% D.85.78%丨14.22%

解释:

To construct a barbell portfolio with the same cost and same duration as the bullet:

Cost of bullet=(106.443/100)*USD60,000,000=USD63,865,800

If V2 and V15 are values (costs) of the 2-Year and 15-Year Treasuries, respectively, then,

V2+V15=USD63,865,800(1)

Therefore, to match duration:

Duration of bullet=weighted-average duration of 2-year and 15-yearTreasuries

6.272=(V2/63,865,800)*1.938+(V15/63,865,800)*11.687(2)

From Equation(1), V2=63, 865,800–V15. Then, Equation(2) becomes:

6.272=[(63,865,800–V15)/63,865,800)]*1.938+(V15/63,865,800)*11.687

400,566,297.6=123,771,920.4–1.938V15+11.687V15

276,794,377.2=9.749V15

And so,V15=USD28,392,078.90

And so,V2=63,865,800–V15=63,865,800–28,392,078.90=USD35,473,721.10

Giving weight of 2-Year Treasury=35,473,721.10/63,865,800=55.54%

And weight of 15-year Treasury=28,392,078.90/63,865,800=44.46%

A is incorrect. It incorrectly calculates the weights based on duration as: weight of 2-Year T=1.938/(1.938+11.687)=14.22%; and weight of 15-year T=1–0.1422=85.78%.

B is incorrect. It switches the weights derived in C above.

D is incorrect.It switches the weights explained in A above.



1 个答案

李坏_品职助教 · 2024年04月18日

嗨,从没放弃的小努力你好:


题目表格给出的国债报价,都是以100$为单位的,例如106.443表示:7年期的国债,每100$面值的报价为106.443$


我们的总面值是60million,也就是60,000,000美元,这么多美元一共有多少个100美元面值的债券?一共有60000000 / 100这么多100美元面值。

所以最后就是60000000 / 100 * 106.443

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努力的时光都是限量版,加油!

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