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Cherry · 2021年10月03日

这题我通过计算 (-D*delta y)能选出正确答案,还是需要通过delta P/P这个思路才对?

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NO.PZ201512181000007205

问题如下:

Based only on Exhibits 2 and 3, it is most likely that under:

选项:

A.

Scenario 1, Bond 2 outperforms Bond 1

B.

Scenario 2, Bond 1 underperforms Bond 3.

C.

Scenario 3, Bond 3 is the best performing security

解释:

C is correct. The change in value of a bond is inversely related to a change in yield. Given a bond priced at B with duration D and yield change of Δy, the rate of return or percentage price change for the bond is approximately given as follows: ΔB/B ≈ -DΔy/(1 + y). Under Scenario 3, interest rates decrease by 20 bps. In an environment of decreasing interest rates, the bond with the highest duration will have the greatest positive return. Bond 3 has a duration of 10.2, which is greater than that of both Bond 1 (duration = 1.3) and Bond 2 (duration = 3.7).

这题我通过计算 (-D*delta y)能选出正确答案,还是需要通过delta P/P这个思路才对?

1 个答案

星星_品职助教 · 2021年10月03日

同学你好,

这道题并不需要用到公式。从定义出发即可。(modified)duration衡量的是利率变化1%,价格反向变化百分之几。当利率变化都相同的时候,duration大的债券价格变化的多。(由于利率变化是相同的,此时macaulay duration和modified duration一致,不需要区分)

所以在scenario 1中,利率上升价格下降,此时duration更大的bond 2表现差;scenario 2中,利率上升价格下降,此时duration更大的bond 3表现差;所以A,B对应的scenario里的描述都反了。

只有在scenario 3里,利率下降,价格上升,此时duration大的bond 3表现最好,描述正确。

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