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Carina9999 · 2022年04月28日

为什么The sum of the key rate durations equals the effective portfolio duration.

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202112010200000701

问题如下：

Which of the following statements is true if yield levels increase by 50 bps?

选项：

A.

The active portfolio will outperform the index portfolio by approximately 61 bps.

B.

The index portfolio will outperform the active portfolio by approximately 61 bps.

C.

The index portfolio will outperform the active portfolio by approximately 21 bps.

解释：

A is correct.

The sum of the key rate durations equals the effective portfolio duration.

The approximate (first-order) change in portfolio value may be estimated from the first (modified) term, namely (-EffDur × ΔYield).

Solving for this using the -1.22 effective duration difference multiplied by 0.005 equals 0.0061%, or 61 bps.

  1. 为什么The sum of the key rate durations equals the effective portfolio duration.
  2. 麻烦老师解析一下这道题考点和答案吧。


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1 个答案

pzqa015 · 2022年04月30日

嗨，从没放弃的小努力你好：


假定Portfolio中全是零息债，KRD是每一个关键时间点（债券到期时间）利率变动，其他期限利率不变，对Portfolio value的影响。KDR=wi*Di，wi为i时刻到期债占portfolio value的权重，Di为i期限债的久期，因为是0息债，所以每一个时间点的现金流都是本金。Portfolio中有几个关键时间点，就有几个KRD。只考虑某个时间点利率变动，它对portfolio value的影响就是-KRD*△y。如果收益率曲线平行移动，即各个关键时间点的利率变动一致，那么portfolio value的变化（△P/P）=-（∑KRDi）*△y，由于portfolio value的变化还等于-portfolio duration*△y，所以，portfolio duration=-∑KRD，这个等式有个前提，就是收益率曲线平行移动。


这道题考察的就是（△P/P）=-（∑KRDi）*△y这个公式的应用

active portfolio的∑KRDi为6.115，index的∑KRDi为7.335，在收益率曲线向上平移50Bp时（一般提到level，就是平行移动），

active portfolio的△P/P=-3.0575%，index的△P/P=-3.6675%，所以，active 的表现比index要好，收益率少下降61bp。


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