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Clare · 2021年10月27日

这里的10%有用吗？All interest rates are 10%.

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2016082402000015

问题如下：

A bond portfolio has the following composition:

Portfolio A: price $90,000, modified duration 2.5, long position in 8 bonds

Portfolio B: price $110,000, modified duration 3, short position in 6 bonds

Portfolio C: price $120,000, modified duration 3.3, long position in 12 bonds

All interest rates are 10%. If the rates rise by 25 basis points, then the bond portfolio value will decrease by

选项：

A.

$11,430

B.

$21,330

C.

$12,573

D.

$23,463

解释：

ANSWER: A

The portfolio dollar duration is D∗P=∑xiDi∗Pi=+8×2.5×$90,000−6×3.0×$110,000D^\ast P=\sum x_iD_i^\ast P_i=+8\times2.5\times\$90,000-6\times3.0\times\$110,000 +12×3.3×$120,000=$4,572,000+12\times3.3\times\$120,000=\$4,572,000.The change in portfolio value is then −(D∗P)×△y-{(D^\ast P)}\times\bigtriangleup y=  −$4,572,000×0.0025=−$11,430=\;-\$4,572,000\times0.0025=-\$11,430

这里的10%有用吗？All interest rates are 10%. 

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DD仔_品职助教 · 2021年10月27日

嗨，从没放弃的小努力你好：


没啥用。。。如果题目给的是duration而不是MD，就要通过10%来求一下MD是多少了：MD=D/(1+r)。但这个题直接给的MD，所以就没用了。

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NO.PZ2016082402000015 问题如下 A bonportfolio hthe following composition: Portfolio pri$90,000, mofieration 2.5, long position in 8 bon Portfolio pri$110,000, mofieration 3, short position in 6 bon Portfolio pri$120,000, mofieration 3.3, long position in 12 bon All interest rates are 10%. If the rates rise 25 basis points, then the bonportfolio value will crease $11,430 $21,330 $12,573 $23,463 ANSWER: AThe portfolio llration is P=∑xi∗Pi=+8×2.5×$90,000−6×3.0×$110,000\ast P=\sum x_ii^\ast P_i=+8\times2.5\times\$90,000-6\times3.0\times\$110,000P=∑xi​∗​Pi​=+8×2.5×$90,000−6×3.0×$110,000 +12×3.3×$120,000=$4,572,000+12\times3.3\times\$120,000=\$4,572,000+12×3.3×$120,000=$4,572,000.The change in portfolio value is then −(P)×△y-{(\ast P)}\times\bigtriangleup y−(P)×△y=  −$4,572,000×0.0025=−$11,430=\;-\$4,572,000\times0.0025=-\$11,430=−$4,572,000×0.0025=−$11,430 解析组合A价格=90k，M2.5，long了8个债券组合B价格=110k，M3，short了6个债券组合C价格=120k，M3.3，long了12个债券所有的利率是10%，如果利率上升25bp，这个债券组合的价值会下降多少？组合的llarration=+8×2.5×$90k−6×3×$110k+12×3.3×$120k=$4,572k价值会下降=$4,572k*25bp= -11,430

2023-04-23 14:57 1 · 回答

NO.PZ2016082402000015问题如下 A bonportfolio hthe following composition: Portfolio pri$90,000, mofieration 2.5, long position in 8 bon Portfolio pri$110,000, mofieration 3, short position in 6 bon Portfolio pri$120,000, mofieration 3.3, long position in 12 bon All interest rates are 10%. If the rates rise 25 basis points, then the bonportfolio value will crease $11,430 $21,330 $12,573 $23,463 ANSWER: AThe portfolio llration is P=∑xi∗Pi=+8×2.5×$90,000−6×3.0×$110,000\ast P=\sum x_ii^\ast P_i=+8\times2.5\times\$90,000-6\times3.0\times\$110,000P=∑xi​∗​Pi​=+8×2.5×$90,000−6×3.0×$110,000 +12×3.3×$120,000=$4,572,000+12\times3.3\times\$120,000=\$4,572,000+12×3.3×$120,000=$4,572,000.The change in portfolio value is then −(P)×△y-{(\ast P)}\times\bigtriangleup y−(P)×△y=  −$4,572,000×0.0025=−$11,430=\;-\$4,572,000\times0.0025=-\$11,430=−$4,572,000×0.0025=−$11,430 Portfolio pri$90,000, mofieration 2.5, long position in 8 bonPortfolio pri$110,000, mofieration 3, short position in 6 bonPortfolio pri$120,000, mofieration 3.3, long position in 12 bon这道题为什么要乘以8、6、12呢？Portfolio A 不是一个含有8个bon的组合，Portfolio A 的价格是90,000吗？还是Portfolio 8个bon每个bon是90,000，合计720,000?

2022-04-08 14:32 1 · 回答

不是很懂为什么Portfolio B的ration要减去。0不是代表利率上升，价格会上升吗。还是只是因为头寸方向所以带负号？ 谢谢    

2019-10-06 22:23 1 · 回答

     我算的组合的3.025，组合价值2820000，算下来25个BP对应的变动是21330，为什么答案选A？

2018-04-15 19:09 2 · 回答