R54 练习: Yield and Yield Spread Measures for Floating-Rate Instruments

R54 练习: 浮动利率工具的收益率和利差度量

考纲范围

Calculate and interpret yield spread measures for floating-rate instruments.

Calculate and interpret yield measures for money market instruments.

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Q1.

The quoted margin for a FRN is 100bps and the required margin is 110bps. On its next reset date, the price of this FRN will ___ and it means the credit of the company is ___.

A. Equal to par; unchanged.

B. Less than par; downgrade.

C. Less than par; upgrade.

查看答案与解析

答案：B

解析：当required margin(110bps) > quoted margin(100bps)时，说明市场要求的回报高于债券提供的票面利差，意味着公司信用质量下降(downgrade)。在重置日，由于quoted margin不足以补偿信用风险，FRN价格将低于面值(less than par)。

选项	判断	解析
A	✗	仅当required margin = quoted margin时价格等于面值
B	✓	required margin > quoted margin，信用恶化，价格低于面值
C	✗	价格低于面值是对的，但信用是downgrade而非upgrade

关联：R54: 浮动利率工具的收益率和利差度量

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Q2.

Use the following information:

Item	Detail
Coupon rate	Libor+2%
Face value	1,000
Coupon frequency	Twice a year
Time to maturity	Three years
6-month Libor rate	2.2%
Current price	1,020

What is the required margin of this bond?

A. 3.5%.

B. 0.45%.

C. 1.3%.

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答案：C

解析：本质是知四求一的过程，将利率拆成参考利率和利差。已知：N = 3×2 = 6，PMT = (2.2%+2%)/2 × 1000 = 21，FV = 1000，PV = -1020。

求解半年期收益率 I/Y，再乘以2得到年化收益率。年化收益率 = Libor + required margin。

$I/Y\approx 1.75\%,\text{年化}=3.5\%$ $\text{Required margin}=3.5\%-2.2\%=1.3\%$

选项	判断	解析
A	✗	3.5%是总的年化收益率，不是required margin
B	✗	计算有误
C	✓	required margin = 年化YTM - Libor = 3.5% - 2.2% = 1.3%

关联：R54: 浮动利率工具的收益率和利差度量

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Q3.

For a 90-day commercial paper (face value 1000), it is quoted at add-on basis (365-day) and the rate is 3.5%. What is the bond equivalent yield of this bond?

A. 3.5%

B. 3.58%

C. 3.55%

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答案：A

解析：Bond equivalent yield (BEY)是365天的add-on rate。该商业票据已经以365天add-on basis报价，rate为3.5%，因此BEY就是3.5%，无需转换。

选项	判断	解析
A	✓	BEY就是365天的add-on rate，已经是该基准，不需转换
B	✗	无需进行额外转换
C	✗	无需进行额外转换

关联：R54: 浮动利率工具的收益率和利差度量

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Q4.

A 270-day commercial paper is quoted at 4.33%, on a discount rate basis, assuming 360 days in a year. The bond equivalent yield is closest to:

A. 4.48%

B. 4.54%

C. 4.57%

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答案：B

解析：先求价格，再转换为BEY(365天add-on rate)。

$PV=FV\times (1-DR\times \frac{Days}{360})=100\times (1-0.0433\times \frac{270}{360})=100\times (1-0.032475)=96.7525$

$BEY=\frac{FV-PV}{PV}\times \frac{365}{Days}=\frac{100-96.7525}{96.7525}\times \frac{365}{270}=\frac{3.2475}{96.7525}\times 1.3519\approx 4.54\%$

选项	判断	解析
A	✗	计算有误
B	✓	正确从discount rate转换为365天add-on rate
C	✗	计算有误

关联：R54: 浮动利率工具的收益率和利差度量

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Q5.

A bond analyst is considering two money market instruments, which are a 270-day commercial paper with a quoted discount rate of 4.35%, assuming a 30/360 day-count convention and a 180-day T-bill quoted at 4.5% on an add-on rate basis and actual/actual day-count convention is assumed. Which instruments offers higher rate of return?

A. The 270-day commercial paper.

B. The 180-day T-bill.

C. The two money market instruments offer the same rate of return.

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答案：A

解析：需要将两者都转换为相同基准(BEY = 365天add-on rate)进行比较。

270天CP：先求价格 PV = 100 × (1 - 4.35% × 270/360) = 96.7375，BEY = (3.2625/96.7375) × (365/270) ≈ 4.56%

180天T-bill：已经是add-on rate但基于actual/actual。BEY = 4.5% × (365/365) = 4.5%（若已是365天基准则直接比较）

4.56% > 4.5%，因此270天CP回报率更高。

选项	判断	解析
A	✓	转换为统一基准后，CP的BEY ≈ 4.56% > T-bill的4.5%
B	✗	T-bill的回报率较低
C	✗	两者回报率不同

关联：R54: 浮动利率工具的收益率和利差度量