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水瓶公主 · 2023年07月11日

无风险收益率是半年的还是一年的

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

4.5%与5%两个量纲不一样,一个是半年的一个是一年的,用8.93%—5%没有意见,但是12.755%—4.5%,因为4.5%是半年的rf,是否需要4.5%*2?

1 个答案

品职答疑小助手雍 · 2023年07月11日

同学你好,这种描述下他俩量纲是一样的,都是指年化利率,所以解析里是拿年化的YTM和他们直接相减的。

考试通常也都是默认描述为年化利率的。

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