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Enjoy · 2024年05月10日

麻烦解释一下这道题目

  1. CFA I
  2. Fixed Income

NO.PZ2023052301000020

问题如下：

A non-callable, fixed-coupon bond has a price of 106.0625 and a YTM of 2.8%. If the YTM were to increase instantaneously by 80 bps, the price of the bond would decrease by 11%. If the YTM were to decrease instantaneously by 80 bps, the price of the bond would increase by:

选项：

A.

less than 11%.

B.

exactly 11%.

C.

more than 11%.

解释：

C is correct. The absolute amount of the price increase would be more than the absolute amount of the price decrease for the same absolute change in YTM because of the convex relationship between bond price and yield.

A is incorrect because of the positive convex relationship between bond price and yield. For a given level of yield change, the price rise for that given amount of yield decrease will be larger than the price decline for that amount of yield increase.

B is incorrect because the relationship between bond price and yield is not linear.

不是涨多跌少吗？这道题怎么理解？

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1 个答案

吴昊_品职助教 · 2024年05月10日

嗨，从没放弃的小努力你好：


1、以何老师基础班上的图形为例，如果考虑了二阶导的因素，利率上升带来的价格下降幅度＜利率下降带来的价格上升幅度。所谓涨多跌少，针对的是债券价格上涨的更多，下跌的更少。也就是说利率变动相同幅度，债券价格涨幅更多，跌幅更少。

2、回到本题： If the YTM were to increase instantaneously by 80 bps, the price of the bond would decrease by 11%. 现在利率上升80bp，带来价格下跌了11%，价格的跌幅更小。小于利率下降80bp带来的价格涨幅，所以价格涨幅应该大于11%，选C。

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NO.PZ2023052301000020 问题如下 A non-callable, fixecoupon bonha priof 106.0625 ana YTM of 2.8%. If the YTM were to increase instantaneously 80 bps, the priof the bonwoulcrease 11%. If the YTM were to crease instantaneously 80 bps, the priof the bonwoulincrease by: A.less th11%. B.exactly 11%. C.more th11%. C is correct. The absolute amount of the priincrease woulmore ththe absolute amount of the pricrease for the same absolute change in YTM because of the convex relationship between bonprianyielA is incorrebecause of the positive convex relationship between bonprianyiel For a given level of yielchange, the pririse for thgiven amount of yielcrease will larger ththe pricline for thamount of yielincrease.B is incorrebecause the relationship between bonprianyielis not linear. 回到本题 If the YTM were to increase instantaneously 80 bps, the priof the bonwoulcrease 11%. 现在利率上升80bp，带来价格下跌了11%，价格的跌幅更小。小于利率下降80bp带来的价格涨幅，所以价格涨幅应该大于11%，选C。----以上是助教老师在其他问题下的回复，我的问题如下涨多跌少也不是一个量纲，怎么比较的呢。 一个涨了用basis point衡量 一个是跌了11% ，看绝对值是价格的变动幅度更大，为什么老师解答说价格跌幅更小。按照老师的逻辑， 是怎么从“价格跌幅小于80bp带来的价格涨幅”推到“价格涨幅应该大于11%”的结论

2024-09-08 12:22 1 · 回答

NO.PZ2023052301000020 问题如下 A non-callable, fixecoupon bonha priof 106.0625 ana YTM of 2.8%. If the YTM were to increase instantaneously 80 bps, the priof the bonwoulcrease 11%. If the YTM were to crease instantaneously 80 bps, the priof the bonwoulincrease by: A.less th11%. B.exactly 11%. C.more th11%. C is correct. The absolute amount of the priincrease woulmore ththe absolute amount of the pricrease for the same absolute change in YTM because of the convex relationship between bonprianyielA is incorrebecause of the positive convex relationship between bonprianyiel For a given level of yielchange, the pririse for thgiven amount of yielcrease will larger ththe pricline for thamount of yielincrease.B is incorrebecause the relationship between bonprianyielis not linear. 难道不是涨多跌少吗？到底怎么理解？

2024-06-14 22:17 1 · 回答