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王平安 · 2021年06月20日

折现率疑问❓

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:

94.26083.0581=0.0653=6.53%\sqrt{\frac{94.260}{83.058}}-1=0.0653=6.53\%

题目中并未说yield curve在未来保持不变啊,那怎么能用现在0时刻的2年期折现率,去计算2年后的价格,不是应该用2年末的future spot rate去计算价格吗?
1 个答案

WallE_品职答疑助手 · 2021年06月20日

嗨,从没放弃的小努力你好:


折现是基于现在的即期利率,即期利率短到几个月,长到几十年,组成的一条利率曲线就是spot rate curve.


future spot rate是未来的即期利率,这些都是估计的,不是真实的利率,折现需要基于当下的利率来折现。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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