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yuqijeffery · 2021年03月13日

请问零息债券为什么会一年付息12次？

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000075

问题如下：

The annual yield-to-maturity, stated for with a periodicity of 12, for a 4-year, zero coupon bond priced at 75 per 100 of par value is closest to:

选项：

A.

6.25%.

B.

7.21%.

C.

7.46%.

解释：

B is correct.

The annual yield-to-maturity, stated for a periodicity of 12, is 7.21%. It is calculated as follows:

PV=FV(1+r)NPV=\frac{FV}{{(1+r)}^N}

75=(100(1+r)4×12)75={(\frac{100}{{(1+r)}^{4\times12}})}

10075=(1+r)48\frac{100}{75}=(1+r)^{48}

1.33333 =(1+r)48

[1.33333]1/48 = [(1+r)48]1/48

1.3333302083= (1 + r)

1.00601 = (1 + r)

1.00601−1 = r

0.00601 = r

r × 12 = 0.07212, or approximately 7.21%

请问零息债券为什么会一年付息12次？

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1 个答案

吴昊_品职助教 · 2021年03月13日

嗨，从没放弃的小努力你好：


同学你好：

零息债券期间不付息，不代表不计息。计息体现在债券的折价上。零息债券到期归还本金，一开始折价发行。比如两个面值为100，maturity为1，收益率为10%，一个零息债券一年计息一次，P=100/(1+10%)=90.91，另一个零息债券一年计息两次，P=100/(1+5%)^2=90.70.也就是说相同情况下，计息频率越高，一开始的折价就越低，即投资者的收益更大。

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NO.PZ2016031001000075 问题如下 The annuyielto-maturity, statefor with a periocity of 12, for a 4-year, zero coupon bonprice75 per 100 of pvalue is closest to: A.6.25%. B.7.21%. C.7.46%. B is correct.The annuyielto-maturity, statefor a periocity of 12, is 7.21%. It is calculatefollows:PV=FV(1+r)NPV=\frac{FV}{{(1+r)}^N}PV=(1+r)NFV​75=(100(1+r)4×12)75={(\frac{100}{{(1+r)}^{4\times12}})}75=((1+r)4×12100​)10075=(1+r)48\frac{100}{75}=(1+r)^{48}75100​=(1+r)481.33333 =(1+r)48[1.33333]1/48 = [(1+r)48]1/481.3333302083= (1 + r)1.00601 = (1 + r)1.00601−1 = r0.00601 = rr × 12 = 0.07212, or approximately 7.21%考点bonvaluation解析利用计算器PV= -75，FV=100，PMT=0，N=4×12=48，求得I/Y=0.601×12=7.21，故B正确。 计算求解过程明白了， 问两个表述是什么意思1. statefor a periocity of 12 的periocity 是什么含义， 分12期计息吗 2. 题干最后一句怎么看出是让求YTM的，75 of100是什么意思

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NO.PZ2016031001000075 问题如下 The annuyielto-maturity, statefor with a periocity of 12, for a 4-year, zero coupon bonprice75 per 100 of pvalue is closest to: A.6.25%. B.7.21%. C.7.46%. B is correct.The annuyielto-maturity, statefor a periocity of 12, is 7.21%. It is calculatefollows:PV=FV(1+r)NPV=\frac{FV}{{(1+r)}^N}PV=(1+r)NFV​75=(100(1+r)4×12)75={(\frac{100}{{(1+r)}^{4\times12}})}75=((1+r)4×12100​)10075=(1+r)48\frac{100}{75}=(1+r)^{48}75100​=(1+r)481.33333 =(1+r)48[1.33333]1/48 = [(1+r)48]1/481.3333302083= (1 + r)1.00601 = (1 + r)1.00601−1 = r0.00601 = rr × 12 = 0.07212, or approximately 7.21%考点bonvaluation解析利用计算器PV= -75，FV=100，PMT=0，N=4×12=48，求得I/Y=0.601×12=7.21，故B正确。 没看懂这道题讲啥，可以翻译一下吗

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