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TZXคิดถึง · 2023年02月27日

为什么不使用（1+S1）*（1+S2）....进行折现？而是直接使用（1+S4）^4，从题干中没读出它是YTM。

  1. CFA II
  2. Fixed Income

NO.PZ2018123101000027

问题如下：

Smith gathers information on spot rates for on-the-run annual-coupon government securities and swap spreads, as presented in Exhibit below.

Smith buys a four-year, zero-coupon corporate bond and then sell it after two years. Smith illustrates the returns from this strategy using the swap rate as a proxy for corporate yields. Smith should show a total return closest to:

选项：

A.

4.31%.

B.

5.42%.

C.

6.53%.

解释：

C is correct.

考点：考察Riding the yield curve策略

解析：由题干已知，Swap rate来代替公司债的收益率；四年期的Swap spread息差为0.70%，4年期的国债收益率Government spot rate 为4.05%，则4年期的swap rate = 4.05% + 0.70% = 4.75%。

因此，购买的4年期零息债券的价格为：

price=100(1+0.0475)4=83.058price=\frac{100}{{(1+0.0475)}^4}=83.058

两年期的公司债收益率为2年期的Swap rate, swap rate = 2.70% +0.30% = 3%,

4年期的零息债券持有2年后的卖出价格为：

price=100(1+0.0300)2=94.260price=\frac{100}{{(1+0.0300)}^2}=94.260

则这笔投资的年化总收益为：

94.26083.058−1=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%

为什么不使用（1+S1）*（1+S2）....进行折现？而是直接使用（1+S4）^4，从题干中没读出它是YTM。

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已采纳答案

pzqa015 · 2023年02月28日

嗨，爱思考的PZer你好：


4年期债用spot rate折现的公式如下：

由于是zero coupon bond，所以前面三期的coupon都是0，只用第四期的Par折现到期初。

没有讲过（1+S1）*（1+S2）这个公式，最多是（1+S1）*（1+f(1,1)）这样子，它是（1+s2)^2

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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