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李庚熹 · 2020年11月27日

问一道题：NO.PZ2018123101000027 [ CFA II ]

  1. CFA II
  2. Fixed Income

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\%

为什么要用swap rate折现呢？
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WallE_品职答疑助手 · 2020年11月27日

同学您好，

因为题目里面明确的说了using the swap rate as a proxy for corporate yields，现在要求公司债的价格所以自然是要用公司债的yield折现，而swap rate现在是他的替代折现率，所以用swap rate

李庚熹 · 2020年11月28日

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