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Asker · 2020年11月06日

问一道题：NO.PZ2016031001000076

问题如下：

A 5-year, 5% semiannual coupon payment corporate bond is priced at 104.967 per 100 of par value. The bond’s yield-to-maturity, quoted on a semiannual bond basis, is 3.897%. An analyst has been asked to convert to a monthly periodicity. Under this conversion, the yield-to-maturity is closest to:

选项：

A.

3.87%.

B.

4.95%.

C.

7.67%.

解释：

A is correct.

The yield-to-maturity, stated for a periodicity of 12 (monthly periodicity), is 3.87%.The formula to convert an annual percentage rate (annual yield-to-maturity) from one periodicity to another is as follows:

${(1+\frac{APRm}m)}^m={(1+\frac{APRn}n)}^n$

${(1+\frac{0.03897}2)}^2={(1+\frac{APR12}{12})}^{12}$

${(1.01949)}^2={(1+\frac{APR12}{12})}^{12}$

$1.03935={(1+\frac{APR12}{12})}^{12}$

${(1.03935)}^{1/12}={\lbrack{(1+\frac{APR12}{12})}^{12}\rbrack}^{1/12}$

$1.00322={(1+\frac{APR12}{12})}$

$1.00322-1={(\frac{APR12}{12})}$

APR₁₂ = 0.00322 × 12 = 0.03865, or approximately 3.87%.

我用计算器这么按的：

N=5*12=60

PV= -104.967

PMT= 100*5%/12=0.4167

FV=100

算出来 IY=0.3254这个应该是月化，我再乘以 12 得到对应的年化是 3.9，为什么这样是不对的呢？

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吴昊_品职助教 · 2020年11月07日

同学你好：

首先这个债券是半年付息一次的，不是一个月付息一次的。你就不可以直接拿着coupon rate除以12，也不能把年份乘以12。如果一定要按计算器，也只能是N=5×2=10，PMT=5÷2=2.5，PV=-104.967，FV=100，求得I/Y=1.949，再乘以2得到 3.897%（这个数据其实题干中也给出了）。但是这是一年计息两次的年化收益率，即APR2，所以还需要通过APR2转换到APR12，按照题目解析中给出的公式计算即可。

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2023-04-27 05:08 1 · 回答

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2022-06-24 01:19 1 · 回答