R59 练习: 基于曲线的风险度量
考纲范围
Explain why effective duration and effective convexity are the most appropriate measures of interest rate risk for bonds with embedded options.
Calculate the percentage price change of a bond for a specified change in benchmark yield, given the bond’s effective duration and convexity.
Define key rate duration and describe its use to measure price sensitivity of fixed-income instruments to benchmark yield curve changes.
Describe the difference between empirical duration and analytical duration.
Q1.
Which of the following statements with respect to the duration is/are most accurate?
Statement 1: Effective duration is applicable to the valuation of a bond with an embedded option.
Statement 2: Modified duration is not applicable to the valuation of a bond with an embedded option.
A. Statement 1.
B. Statement 2.
C. Both Statement 1 and Statement 2.
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答案：C
解析：有效久期(effective duration)基于基准收益率曲线的变化来衡量价格敏感性，适用于含权债券，因为含权债的现金流会随利率变化而变化。修正久期(modified duration)假设现金流不变，不适用于含权债券。
选项 判断 解析 A ✗ 两个说法都正确 B ✗ 两个说法都正确 C ✓ effective duration适用于含权债，modified duration不适用于含权债
Q2.
Which of the following statements is correct?
Statement 1: Both callable bonds and putable bonds have lower effective durations compared to otherwise identical option-free bonds, especially when interest rates are falling.
Statement 2: Callable bonds often have higher positive convexity, while putable bonds often have negative convexity.
A. statement 1.
B. statement 2.
C. None of the statements are correct.
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答案：C
解析：Statement 1部分错误：callable bond在利率下降时有效久期更小（因为可能被赎回），putable bond在利率上升时有效久期更小（因为可能被回售），而非两者都在利率下降时。Statement 2完全反了：callable bond在利率低时具有负凸性，putable bond永远是正凸性。
选项 判断 解析 A ✗ putable bond在利率上升时久期更小，不是利率下降时 B ✗ callable bond有负凸性，putable bond有正凸性，说反了 C ✓ 两个说法都不正确
Q3.
A callable bond has an effective duration of 6.37 and an effective convexity of 27.62. The yield curve will move upward by 50 basis points parallelly. The bond’s percentage price change is closest to:
A. -3.185%.
B. 3.185%.
C. -3.150%.
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答案：C
解析：
选项 判断 解析 A ✗ 仅考虑了久期效应，未加凸性调整 B ✗ 方向错误，利率上升价格应下降 C ✓ 久期效应 + 凸性调整 = -3.185% + 0.035% = -3.150%
Q4.
Which of the following statements regarding duration is most accurate?
A. Effective duration can be used to measure bond prices’ sensitivity to shaping risk.
B. Partial duration can be used to measure bond prices’ sensitivity to shaping risk.
C. For a bond with a positive yield to maturity, its Macaulay duration is less than its modified duration.
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答案：B
解析：Partial duration(部分久期/关键利率久期)衡量的是收益率曲线某一特定期限变动对债券价格的影响，可以衡量shaping risk（收益率曲线非平行移动的风险）。Effective duration衡量的是平行移动的风险。MacDur > ModDur（因为MacDur = ModDur × (1+r)，r>0时）。
选项 判断 解析 A ✗ effective duration衡量平行移动风险，不能衡量shaping risk B ✓ partial/key rate duration可衡量非平行移动的shaping risk C ✗ 当YTM>0时，MacDur > ModDur，而非小于
Q5.
An analyst observes that short-term interest rates are falling and long-term interest rates are rising in the market. Which duration should the analyst use to measure interest rate risk?
A. modified duration.
B. effective duration.
C. key rate duration
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答案：C
解析：短期利率下降而长期利率上升，说明收益率曲线发生非平行移动（变陡）。关键利率久期(key rate duration)可以衡量收益率曲线特定期限点变动对价格的影响，最适合衡量这种shaping risk。
选项 判断 解析 A ✗ modified duration假设收益率曲线平行移动 B ✗ effective duration也假设平行移动 C ✓ key rate duration衡量非平行移动（steepen/flatten）的风险
Q6.
Which of the following statements about empirical duration and analytical duration is least likely accurate?
A. Under stressed market, empirical duration is a better risk measure for high-yield bonds than analytical duration.
B. Analytical duration is calculated by using statistical methods and historical data.
C. Empirical duration and analytical duration are similar for government bonds with little or no credit risk.
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答案：B
解析：经验久期(empirical duration)使用统计方法和历史数据计算，分析久期(analytical duration)基于数学公式和假设计算。选项B将两者混淆了。在压力市场下，高收益债的经验久期确实比分析久期更好。对于政府债券（信用风险低），两者相似。
选项 判断 解析 A ✗ 压力市场下empirical duration对高收益债更好，正确 B ✓ 混淆了：empirical使用统计方法，analytical使用数学公式，最不准确 C ✗ 政府债券的两种久期确实相似，正确
Q7.
During extremely stressed market conditions, analytical duration may be an inferior risk measure to empirical duration if a portfolio contains a large quantity of:
A. sovereign bonds issued by the United States.
B. high-yield bonds issued by manufacturing issuers.
C. highly rated bonds issued by publicly traded companies.
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答案：B
解析：在极端压力市场条件下，高收益债券的实际价格行为可能与分析模型预测不同（如出现flight to quality），经验久期（基于历史数据）比分析久期更准确。政府债券和高评级公司债因信用风险低，两种久期差异不大。
选项 判断 解析 A ✗ 美国国债信用风险极低，两种久期差异小 B ✓ 高收益债在压力市场下analytical duration不够准确 C ✗ 高评级公司债风险较低，两种久期差异不大