R53 练习: Yield and Yield Spread Measures for Fixed-Rate Bonds

R53 练习: 固定利率债券的收益率和利差度量

考纲范围

Calculate annual yield on a bond for varying compounding periods in a year.

Compare, calculate, and interpret yield and yield spread measures for fixed-rate bonds.

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Q1.

There is a semiannual bond with a YTM of 4%. If we want to convert its compounding frequency to a periodicity of 4, the YTM is:

A. 3.98%

B. 4%

C. 3.86%

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答案：A

解析：将半年复利(periodicity=2)转换为季度复利(periodicity=4)，需保持”本息和一致”：

$(1+\frac{4\%}{2}{)}^2=(1+\frac{r}{4}{)}^4$

$(1.02{)}^2=(1+\frac{r}{4}{)}^4$

$(1.02{)}^{1/2}=1+\frac{r}{4}$

$r=4\times [(1.02{)}^{0.5}-1]=4\times 0.00995=3.98\%$

选项	判断	解析
A	✓	正确转换：periodicity越高，名义利率越低
B	✗	仅当复利频率不变时YTM才不变
C	✗	计算有误

关联：R53: 固定利率债券的收益率和利差度量

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Q2.

Which of the following statements is least likely to be accurate?

A. True yield is never lower than street convention yield.

B. Current yield is equal to the annual coupon payments divided by the flat price.

C. Street convention yield assumes payments are made on scheduled dates.

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答案：A

解析：True yield考虑了实际支付日期（可能因节假日延后），如果付款延迟，投资者实际收到现金流的时间更晚，因此true yield不会高于street convention yield，可能更低。选项A说”never lower”是错误的，应该是”never higher”。Current yield = 年票息/flat price是正确的。Street convention yield确实假设按计划日期支付。

选项	判断	解析
A	✓	true yield可能低于street convention yield（因延迟付款），说法最不准确
B	✗	current yield = annual coupon / flat price，定义正确
C	✗	street convention yield确实假设按计划日期付款

关联：R53: 固定利率债券的收益率和利差度量

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Q3.

A 6% annual coupon bond with 5 years remaining until maturity is currently trading for 101. The bond is first callable in 3 years at price 103 and second callable in 4 years at price 102. The bond’s annual yield-to-first-call is closest to:

A. 5.76%.

B. 6.17%.

C. 6.56%.

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答案：A

解析：计算yield-to-first-call时，N为到第一次可赎回日的年数，FV为第一次赎回价格：

$N=3,PV=-101,PMT=6,FV=103$

求解 I/Y ≈ 5.76%

选项	判断	解析
A	✓	N=3, PV=-101, PMT=6, FV=103, 求得I/Y≈5.76%
B	✗	可能使用了第二次call的参数
C	✗	可能使用了到期参数

关联：R53: 固定利率债券的收益率和利差度量

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Q4.

John buys a 5-year, 6% annual coupon payment callable bond with a two-year call protection period at a price of USD 103 per USD 100 of par value. After two years, the bond is callable on each coupon date. The call schedule for this bond is as follows:

	Call price
First Call	102.1064
Second Call	101.6238
Third Call	100.6777

The yield-to-worst of the bond is closest to:

A. 5.2989%.

B. 5.3045%.

C. 5.3013%.

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答案：C

解析：Yield-to-worst是所有可能收益率（各call date的YTC和YTM）中最低的。需分别计算每个call date的YTC和YTM，取最小值。

• YTC (First Call): N=3, PV=-103, PMT=6, FV=102.1064
• YTC (Second Call): N=4, PV=-103, PMT=6, FV=101.6238
• YTC (Third Call): N=5, PV=-103, PMT=6, FV=100.6777 (同YTM)

计算后取最低值 ≈ 5.3013%

选项	判断	解析
A	✗	非最低收益率
B	✗	非最低收益率
C	✓	yield-to-worst取所有收益率中的最低值 ≈ 5.3013%

关联：R53: 固定利率债券的收益率和利差度量

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Q5.

Option-adjusted spread (OAS) is the yield spread that eliminates the impact of embedded option from Zero volatility spread (Z-spread). Which of the followings about OAS is most accurate?

A. For a callable bond, OAS is larger than Z-spread.

B. For a callable bond, OAS is smaller than Z-spread.

C. For a putable bond, OAS is smaller than Z-spread.

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答案：B

解析：Z-spread = OAS + Option value。对于callable bond，call option对发行人有价值(option value > 0)，因此OAS < Z-spread。对于putable bond，put option对投资者有价值，option value为负，因此OAS > Z-spread。

选项	判断	解析
A	✗	callable bond的OAS < Z-spread，因为option value > 0
B	✓	Z-spread = OAS + option value(正), 所以OAS < Z-spread
C	✗	putable bond的OAS > Z-spread，因为option value为负

关联：R53: 固定利率债券的收益率和利差度量

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Q6.

Lily has just learned the relevant knowledge about the yield spreads, and made the following notes:

Note 1: Z-spread can be calculated by subtracting the government bond yield from the yield of a specific bond.

Note 2: Government spot curve is used as benchmark yield curve to calculate G-spread.

Note 3: OAS is the difference between G-spread and option value.

The number of correct notes made by Lily is:

A. 0.

B. 1.

C. 2.

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答案：A

解析：三个笔记都有错误：Note 1描述的是G-spread而非Z-spread（Z-spread是加在每个即期利率上的固定利差）；Note 2描述错误，G-spread使用的是政府债券到期收益率而非即期利率曲线；Note 3中OAS = Z-spread - option value，不是G-spread - option value。

选项	判断	解析
A	✓	三个笔记都不正确
B	✗	没有任何笔记是正确的
C	✗	没有任何笔记是正确的

关联：R53: 固定利率债券的收益率和利差度量

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Q7.

Which of the following statements about the term structure of credit spreads is correct?

A. The relationship between the credit spreads and the benchmark rate of different maturities is called term structure of the credit spreads.

B. The term structure of credit spreads reflects how credit spreads change with times-to-maturity.

C. The term structure of I-spreads reflect how yield spreads over government bonds change with times-to-maturity.

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答案：B

解析：信用利差期限结构(term structure of credit spreads)反映的是信用利差如何随到期期限变化。选项A的描述不准确，信用利差期限结构是信用利差与期限的关系，而非信用利差与基准利率的关系。选项C错误，I-spread是相对于互换利率(swap rate)的利差，不是相对于政府债券。

选项	判断	解析
A	✗	描述不准确，混淆了概念
B	✓	正确描述了信用利差期限结构：信用利差随期限的变化关系
C	✗	I-spread是相对于swap rate的利差，不是government bonds

关联：R53: 固定利率债券的收益率和利差度量