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chiara9009 · 2023年08月14日

关于四年期债券在第二年提前卖出价格求解?

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\%

我的思路如下,想请问一下老师为何不对:

1.Total return=coupon +RI+CG,因为本题是假设zero-coupon bond,所以coupon=RI=0

=>Total return=CG


2.题干中未说yield curve是stable的,也就是无法确定riding the yied策略适用;


3.关于四年期债券在第二年提前卖出价格,未来CF(到期1元本金)折现(从第4年折现到第3年末用swap rate4,从第3年折现到第2年末用swap rate3)详情如下:


swap rate 3 swap rate 4

0__________1__________2__________3__________4

swap rate3=3.3%+4.5%=3.75

swap rate4=4.05%+0.7%=4.75%


假设到期本金为1,

P2=1/[(1+swap rate4)(1+swap rate3)]

=1/[(1+3.75%)*(1+4.75%)]

=0.92

2 个答案

pzqa31 · 2023年08月15日

嗨,爱思考的PZer你好:


他这里的公司债收益率其实就是YTM,相当于是spot rate的一个打包价。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

pzqa31 · 2023年08月15日

嗨,爱思考的PZer你好:


同学你这个算法不对,比如你去投一个三年期的债券,利率是3%,这是一个年化收益,那么你每年的收益都是3%,而不是第一年是1%,第二年是2%,第三年是3%这样每年都变,对吧?

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加油吧,让我们一起遇见更好的自己!

chiara9009 · 2023年08月15日

老师说的这个角度我能理解,但为什么在计算债券价格的时候,如果折现率是 spot rate的时候就是不同时段的CF对应不同spot rate,而不是采用YTM? 比如一个三年期债券:P=c/(1+s1)+c/(1+s2)^2+(c+par)/(1+s3)^3。

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