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yukijiang · 2021年04月29日

请问怎么求duration

NO.PZ2016031001000059

问题如下:

Which bond will most likely experience the smallest percent change in price if the market discount rates for all three bonds increase by 100 basis points?

选项:

A.

Bond A

B.

Bond B

C.

Bond C

解释:

B is correct.

Bond B will most likely experience the smallest percent change in price if market discount rates increase by 100 basis points. A higher-coupon bond has a smaller percentage price change than a lower-coupon bond when their market discount rates change by the same amount (the coupon effect). Also, a shorter-term bond generally has a smaller percentage price change than a longer-term bond when their market discount rates change by the same amount (the maturity effect). Bond B will experience a smaller percent change in price than Bond A because of the coupon effect. Bond B will also experience a smaller percent change in price than Bond C because of the coupon effect and the maturity effect.

请问这个题目怎么求duration呢?计算器可以吗?还是要现金流一笔笔算Macaulay duration,再➗(1➕ytm)得到modified duration?
2 个答案

吴昊_品职助教 · 2021年10月28日

嗨,努力学习的PZer你好:


欢欢,请看基础班讲义P137讲义原话。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

吴昊_品职助教 · 2021年04月29日

嗨,爱思考的PZer你好:


同学你好:

首先这道题不需要通过计算求duration的,通过计算方式强行做题,会增加了做题难度。下面提供两种分析问题的思路,可供同学参考。

思路1:

根据Maturity effect:在Coupon rate一样的情况下,当市场利率发生变动时,期限长的债券其价格变动幅度更大。所以对比A和C债券,A的变动幅度会更小。

根据Coupon effect:在time-to-maturity一样的情况下,当市场利率发生变动时,Coupon rate越小的债券,其价格变动幅度越大。对比A和B债券,A的Coupon rate更小,所以A的变动幅度更大,B更小。综上,债券B是价格变动幅度最小的债券。

思路2:

这道题也可以从duration的角度来定性分析,而不是定量分析。题目问的是当利率上涨100bp,哪一只债券价格改变最小。换句话说,是问哪一只债券的duration最小。首先排除债券C,因为其maturity最长。在A和B中,coupon rate越大的债券,期间现金流越大,还款时间更短,duration更小。因此,bond B的duration最小。选项B正确。

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努力的时光都是限量版,加油!

欢欢 · 2021年10月28日

“在time-to-maturity一样的情况下,当市场利率发生变动时,Coupon rate越小的债券,其价格变动幅度越大。”这句怎么理解呢,谢谢老师。

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2022-10-24 22:09 1 · 回答

B 和 C 的利率并不相等,如何比较 maturity?

2020-11-25 05:54 1 · 回答

这题140页的知识点老师视频当时说学过后面的回头讲的啊,这章学完了也没讲啊,不知道讲解是不是还在后面

2019-11-02 01:43 1 · 回答

老师这道题在讲义第几页啊

2019-09-28 10:28 1 · 回答