R56 练习: 利率风险与回报
考纲范围
Calculate and interpret the sources of return from investing in a fixed-rate bond.
Describe the relationships among a bond’s holding period return, its Macaulay duration, and the investment horizon.
Define, calculate, and interpret Macaulay duration.
Q1.
Which of the following statements about the capital gains on the sale of bonds is most accurate?
A. Capital gains arise when the selling price is higher than the carrying value.
B. Capital gains arise when the selling price is higher than the original purchase price.
C. Capital gains arise when the selling price is lower than the original purchase price.
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答案：A
解析：债券的资本利得(capital gain/loss)是以账面价值(carrying value)为基础计算的，而非原始购买价格。Capital gain = Selling price - Carrying value。若卖出价高于carrying value则为资本利得。
选项 判断 解析 A ✓ capital gain = selling price - carrying value，正确 B ✗ 应以carrying value而非original purchase price为基础 C ✗ 卖价低于成本是资本损失，且应以carrying value为基础 关联：R56: 利率风险与回报
Q2.
Suppose an investor bought a 10-year bond priced at 98.15 five years ago. Now the carrying value of this bond is 99.02 and the market price of this bond is 98.96. If the investor sells the bond now, what is the capital gain or loss for this bond?
A. 0.06
B. -0.06
C. 0.08
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答案：B
解析：Capital gain/loss = Selling price - Carrying value = 98.96 - 99.02 = -0.06。注意是以carrying value(99.02)为基础，而非原始购买价格(98.15)。
选项 判断 解析 A ✗ 符号错误 B ✓ 98.96 - 99.02 = -0.06，为资本损失 C ✗ 这是以原始购买价格计算的结果(98.96 - 98.15)，方法错误 关联：R56: 利率风险与回报
Q3.
Assuming all payments are made as promised, an investor intends to hold the bond until maturity. Which of the following risks is the investor most likely exposed to?
A. Market price risk
B. Reinvestment risk.
C. Default risk.
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答案：B
解析：持有至到期的投资者不面临市场价格风险（不需要中途卖出），题目假设所有支付按约定执行（无违约风险），但票息收入需要再投资，因此面临再投资风险(reinvestment risk)。
选项 判断 解析 A ✗ 持有至到期不需卖出，不面临market price risk B ✓ 票息需要再投资，面临reinvestment risk C ✗ 题目假设所有支付按约定执行，排除了default risk 关联：R56: 利率风险与回报
Q4.
In a fixed-rate bond investment, given that reinvestment risk dominates for investor A and market price risk dominates for Investor B, which of the following statements is most accurate?
A. Investor A is at risk of higher interest rates.
B. Investor A is at risk of lower interest rates.
C. Investor B is at risk of lower interest rates.
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答案：B
解析：再投资风险主导意味着投资期限 > Macaulay duration（duration gap为负），投资者担心利率下降导致票息再投资收益降低。市场价格风险主导意味着投资期限 < Macaulay duration（duration gap为正），投资者担心利率上升导致债券价格下跌。
选项 判断 解析 A ✗ reinvestment risk主导时，担心利率下降而非上升 B ✓ reinvestment risk主导，investor A担心利率下降减少再投资收益 C ✗ market price risk主导时，investor B担心利率上升而非下降 关联：R56: 利率风险与回报
Q5.
A positive duration gap indicates that:
A. the investment horizon is greater than the bond’s Macaulay duration.
B. the investor is at risk of higher interest rates.
C. coupon reinvestment risk dominates market price risk.
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答案：B
解析：Duration gap = Macaulay duration - Investment horizon。正的duration gap意味着Macaulay duration > investment horizon，即市场价格风险主导。此时投资者面临利率上升的风险（利率上升导致债券价格下跌，且持有期短于久期，价格效应占主导）。
选项 判断 解析 A ✗ 正的duration gap意味着Macaulay duration > investment horizon B ✓ market price risk主导，投资者面临利率上升风险 C ✗ 正的duration gap时market price risk主导，而非reinvestment risk 关联：R56: 利率风险与回报
Q6.
A 6% semiannual coupon payment bond has a yield-to-maturity of 8%. Its modified duration is 5.21. The bond’s Macaulay duration is closest to:
A. 5.42
B. 5.52
C. 5.63
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答案：A
解析：Macaulay duration与modified duration的关系（注意r为期间利率）：
选项 判断 解析 A ✓ MacDur = 5.21 × 1.04 = 5.42 B ✗ 可能使用了年化YTM而非期间利率 C ✗ 计算有误 关联：R56: 利率风险与回报
Q7.
A 2-year 5% annual-pay corporate bond has a yield of 6%, its Macaulay duration is closet to:
A. 1.83
B. 1.9
C. 1.95
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答案：C
解析：计算Macaulay duration需要对每笔现金流的加权平均时间进行计算。先求债券价格，再求加权平均。
选项 判断 解析 A ✗ 计算有误 B ✗ 计算有误 C ✓ 加权平均计算MacDur ≈ 1.95 关联：R56: 利率风险与回报
Q8.
A 2-year 5% annual-pay corporate bond has a yield of 6%, which of the following statements is most likely correct?
A. If an investor holds the bond for 1.98 years, the market price risk will offset the coupon reinvestment risk.
B. If an investor holds the bond for 1.98 years, the market price risk will dominate the coupon reinvestment risk.
C. If an investor holds the bond for 1.95 years, the market price risk will offset the coupon reinvestment risk.
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答案：C
解析：当投资期限等于Macaulay duration时，市场价格风险和再投资风险相互抵消。该债券的Macaulay duration ≈ 1.95年，因此持有1.95年时两种风险相互抵消(duration gap = 0)。
选项 判断 解析 A ✗ 1.98 ≠ MacDur(1.95)，两种风险不会完全抵消 B ✗ 持有1.98年 > MacDur(1.95)，reinvestment risk主导 C ✓ 持有期 = MacDur = 1.95年，两种风险完全抵消 关联：R56: 利率风险与回报