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七七 · 2024年07月21日

duration 辨析

  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.

effective duration衡量parallel shift

KRD衡量non-parallel shift

请问empirical duration可以衡量non-parallel shift吗？

spread duration衡量的是spread curve的parallel shift还是也可以衡量non-parallel shift？

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发亮_品职助教 · 2024年07月22日

请问empirical duration可以衡量non-parallel shift吗？


不行哈

Empirical duration和Effective duration是一组对标的duration，两个基本一致。

按照定义，Effective duration是指：当benchmark rate整条利率曲线平行移动时，债券价格的敏感度。

有2个要关注的，一个是，这里体现的是基准利率（benchmark rate）的改变，这是和modified duration最大的区别【modified duration是说当债券自身的YTM发生平行改变时，债券价格的敏感度】。第二个是，Effective duration衡量整条利率曲线的改变。


Empirical duration是指：当benchmark rate整条利率曲线平行移动时，利用债券实际价格的改变与benchmark rate改变算出来的回归值

所以Empirical duration和Effective duration最大的区别就是：effective duration是一个理论值，没有考虑benchmark rate被credit spread反向抵消的影响；

Empirical duration是一个实际值，考虑到了benchmark rate变动会被债券的credit spread反向抵消掉，所以导致债券对benchmark rate的实际价格敏感度没有那么大，empirical duration这个实际价格敏感度就比较小。所以同一个债券，其Empirical duration小于Effective duration。


剩下的Effective duration和Empirical duration都是完全一致的，没有任何区别。都是平行移动的指标。


spread duration衡量的是spread curve的parallel shift还是也可以衡量non-parallel shift？


不行哈，也是衡量spread curve平行移动带来的债券价格敏感度。


衡量非平行移动的指标只有一个，就是Key rate duration，剩下学到的其他duration都是平行移动的指标，包括convexity也是平行移动的指标。

七七 · 2024年07月23日

厉害了！很清楚，很明白！

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