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依帆 · 2023年05月04日

YTM和risk-free rate的差

NO.PZ2020033002000034

问题如下:

Grapefruit Bank issued two semi-annual interest-bearing credit bonds, of which bond A matures after half a year, the coupon rate is 8.5%, the current price is $ 98, and the corresponding half-year T-bill interest rate is 4.5%. The bond B expires after one year, the coupon rate is 10%, the current price is $ 101, and the corresponding one-year T-bill rate is 5%. Assuming that their recovery rates are all 40%, and they will only default on the coupon payment date, which of the following statements is correct?

选项:

A.

The market implied risk-neutral default probability in the first half of the year is higher than that in the second half.

B.The market implied risk-neutral default probability in the first half of the year is lower than that in the second half.

C.The market implied risk-neutral default probability is equal in the first half and the second half.

D.

The market implied risk-neutral default probability in the first half and the second half cannot be compared.

解释:

A is correct.

考点:Spread Risk-DVCS and Credit Spread Curve

解析:对于bondA,通过金融计算器:PV=-98 FV=100 PMT=4.25 N=1 CPT I/Y=6.3776 年化YTM=12.76%spread=YTM-rf=12.76%-4.5%=8.255%债券B:PV=-101 FV=100 PMT=5 N=2 CPT I/Y=4.466% 年化YTM=8.93%spread=YTM-rf=8.93%-5%=3.93%根据题目已知RR=40%,那么spread=PD*RR,谁的spread大,PD肯定就大,A这个半年期bond的PD大于B这个一年期的bond,那么前半年的PD也就肯定大于后半年的PD

答案里面Bond A算出来一年的YTM是和半年的risk-free rate相减,但Bond B算出来一年的YTM是和一年的risk-free rate相减,请问YTM和risk-free rate相减求利差的时候不需要考虑时间的一致性吗?为什么不用Bond A半年的YTM和半年的risk-free rate相减,用Bond B一年的YTM和一年的risk-free rate相减,然后再拿两个债券的利差做比较呢?麻烦老师解答,谢谢!

2 个答案

pzqa27 · 2023年05月04日

嗨,从没放弃的小努力你好:


bond A算出来的是半年的YTM,解析做了一步年化的过程,半年的YTM年化和一年期的YTM是两个概念

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pzqa27 · 2023年05月04日

嗨,从没放弃的小努力你好:


请问YTM和risk-free rate相减求利差的时候不需要考虑时间的一致性吗?

解析考虑了呀

为什么不用Bond A半年的YTM和半年的risk-free rate相减,用Bond B一年的YTM和一年的risk-free rate相减,然后再拿两个债券的利差做比较呢

半年的YTM-半年的RIsk free rate得到的是半年的spread,一年的YTM-1年的risk free rate得到的是1年的spread,这期限不一样,没法比。所以解析就统一都年化了


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依帆 · 2023年05月04日

但Bond A是用1年的YTM减去半年的risk-free rate,得到的利差是半年的还是一年的呢?

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