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Jwang · 2024年07月20日

如题

  1. CFA III
  2. Fixed Income

NO.PZ2023032703000048

问题如下：

Camille Blanc is a fixed income manager who recently started the Optima mutual fund. The fund is invested in a diversified portfolio of government and corporate bonds. The fund’s mandate requires the effective duration of its portfolio to match that of its benchmark. Blanc’s objective is to outperform a fixed-income benchmark by using an enhanced-indexing strategy.

Blanc evaluates the price sensitivities of Optima relative to its benchmark for changes in the yield curve using scenario analysis:

Scenario 1: She simulates an immediate 10 basis point (bps) parallel shift in the yield curve and finds no difference in the price sensitivities between Optima and its benchmark.

Scenario 2: She simulates an immediate 30 bps change in the 5-year spot rate and holds all other rates constant. She finds a 19 bps difference in the price sensitivities between Optima and its benchmark.

A. Determine whether Optima most likely violates its mandate under each of the following:

i. Scenario 1

ii. Scenario 2

Justify your response for each scenario. (2015 Q3)

Note: Consider each scenario independently.

选项：

解释：

Effective duration measures the sensitivity of a portfolio’s price to a small parallel shift in the yield curve (interest rate risk). For a larger parallel shift, a convexity adjustment is used to improve the accuracy of the estimated price change. Key rate duration captures non-parallel shifts (yield curve risk) such as a steepening in slope or a twist in the yield curve. It measures the effect of changes at key points along the yield curve.

i. Optima does not violate its mandate in Scenario 1. Optima and its benchmark exhibit the same price sensitivity to a small parallel shift in the yield curve because Optima is matched on effective duration.

ii. Optima does not violate its mandate in Scenario 2. Optima and its benchmark exhibit different price sensitivities to a non-parallel shift in the yield curve, indicating that Optima is not matched on key rate duration at the 5-year spot rate. However, its mandate does not require that it be matched on key rate duration.

老师好，effective duration是等于key rate duration之和吧？场景2暗示的应该是其中一个key rate duration变化了，但是没有给其他key point的情况，应该无法严谨的判断出场景2没有违反effective duration match的mandate？

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发亮_品职助教 · 2024年07月21日

effective duration是等于key rate duration之和吧？


是的。Effective duration等于各个期限的key rate duration之和。


这道题的Mandate是让组合的Effective duration match index的Effective duration。

需要注意的是，effective duration是一个整体指标。就是两个组合的Effective duration相等，并不能保证两者的Key rate duration也match。

因为Effective duration相等只能保证组合整体的Duration数据一致，至于组合内部各个期限的Key rate duration如何分配，2个组合可能会有很大的差异。


比如，组合和index的Effective duration都是10，但是KRD的分配可能有巨大差异：

组合：1-year key rate duration=2; 5-year KRD=3; 10-year KRD=5

index：1-year KRD=1; 5-year KRD=4.5; 10-year KRD=4.5



场景2暗示的应该是其中一个key rate duration变化了，但是没有给其他key point的情况，应该无法严谨的判断出场景2没有违反effective duration match的mandate？


场景2确实是非平行移动，只有1个点的利率改变了，其他点的利率没变。但是场景2的发生不能证明组合违反了mandate。


因为让组合的effective duration match index effective duration，只能保证在平行移动时，两者的表现同步。

场景2是用非平行移动的改变去验证effective duration是否match。这个没办法验证哈。


因为就算组合的effetive duration匹配上index的ED了，此时，发生非平行移动时，2个组合的表现依然会不同。因为Effective duration是平行移动的指标，不是非平行移动的指标。


反过来，如果发生5-year的利率非平行移动，此时组合和index的表现一致，这只能说明组合和index在这个5-year的KRD一样，但没办法保证整体指标Effective duration也一样。因为不知道其他期限的KRD如何。


这道题，就算出现了场景2的情况，也不能证明：组合违反了Mandate（match effective duration）


如果真的要检验是否违反了Mandate（是否match Effective duration），只能用利率平行移动来验证，因为Effective duration是平行移动的指标。当平行移动发生时，如果组合与index的表现不一致，则说明组合违反了mandate。

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