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苏·Xu · 2022年10月21日

问

  1. CFA I
  2. Fixed Income

NO.PZ2018062006000081

问题如下：

There is a two-year FRN with quoted margin at 50 basis points and the reference rate is 6-month Libor. The current 6-month Libor is 1.2% which is supposed to be constant for the following 2 years and the floater is priced at 95 per 100 of par value. Please calculate the discount margin for the floater assuming a 30/360 day-count convention and evenly spaced periods.

选项：

A.

298 bps

B.

314 bps

C.

217 bps

解释：

B is correct.

First we need to calculate the interest payment each period:

{(6-month Libor+QM) × FV}/m={(0.012+0.005) × 100}/2=0.85

then calculate the discount rate per period :

95=0.851+r+0.85(1+r)2+0.85(1+r)3+0.85+100(1+r)495=\frac{0.85}{1+r}+\frac{0.85}{(1+r)^2}+\frac{0.85}{(1+r)^3}+\frac{0.85+100}{(1+r)^4}

r=2.168%

Now, solve for DM:

1.2%+DM2=2.168%\frac{1.2\%+DM}2=2.168\%

DM = 3.14%

考点：浮动利率债券

解析：知道浮动利率债券当前的债券价格和分子的Coupon rate，先反求出折现率，利用计算器：PV= -95，FV=100，PMT=0.85，N=4，得到I/Y=2.168

再利用折现率反求出discount margin：2.168%=(1.2%+DM)/2，求得DM=3.14%，故选项B正确。

题目只是给了6个月的libor, 哪里可以看出半年付息一次？

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1 个答案

吴昊_品职助教 · 2022年10月21日

嗨，爱思考的PZer你好：


给了6-month XXX，就说明债券是半年付息一次。倘若换一下条件，变成了3-month XXX，就说明债券是三个月付息一次的。

考试中所有利率默认都是年化的，题目中给出的所有利率也都是年化的形式。Quoted margin=50bp、Libor=1.2%，这两个利率都是年化的形式。做题时需要去年化，除以2得到一期的利率。

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2023-08-16 21:03 1 · 回答

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