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PZmomo · 2024年02月29日

有效久期

  1. CFA II
  2. Fixed Income

NO.PZ2018123101000104

问题如下：

Steele Ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, Inc.

A fall in interest rates would most likely result in:

选项：

A.

a decrease in the effective duration of Bond #3.

B.

Bond #3 having more upside potential than Bond #2.

C.

a change in the effective convexity of Bond #3 from positive to negative.

解释：

A fall in interest rates results in a rise in bond values. For a callable bond such as Bond #2, the upside potential is capped because the issuer is more likely to call the bond. In contrast, the upside potential for a putable bond such as Bond #3 is uncapped. Thus, a fall in interest rates would result in a putable bond having more upside potential than an otherwise identical callable bond. Note that A is incorrect because the effective duration of a putable bond increases, not decreases, with a fall in interest rates—the bond is less likely to be put and thus behaves more like an option-free bond. C is also incorrect because the effective convexity of a putable bond is always positive. It is the effective convexity of a callable bond that will change from positive to negative if interest rates fall and the call option is near the money.

这是二级的考点吗？一级学过忘记了…

老师请再讲解一下久期、修正久期和有效久期的概念

以及讲解一下为什么a选项是错的？

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1 个答案

吴昊_品职助教 · 2024年02月29日

嗨，爱思考的PZer你好：


1、这也是二级的考点，会考察到。

2、久期（Duration）是衡量利率风险的指标，反映了债券价格对利率变化的敏感性。利率变动带来的债券价格的变动程度。一般来说，久期越长，价格对利率变动的敏感性就越高。修正久期是麦考利久期/(1+r)得到的，有效久期用来衡量含权债券的利率风险。

3、回到本题：

债券2是callable bond，债券3是putable bond。现在利率下降，callable bond更容易行权，债券发行人会以提前约定好的call price将债券赎回。利率下降的时候，不含权债券或putable bond价格正常上涨，但是callable bond的价格涨不上去，会有一个上限，如下图显示。所以利率下降，债券3比债券2更有上升空间（upside potential），因此选项B正确。

选项A：Bond 3是一个putable bond，在利率上升的时候，债券持有人可以将债券提前卖还给发行人，由于提前结束现金流，此时平均还款期短，effective duration会下降。当利率下降的时候，putable bond就更像是一个不含权债券，债券持有人不会执行权利。和利率上升比，此时的effective duration更长。所以选项A说反了，故不正确。这道题A选项其实是比较putable bond在利率上升和利率下降两种情况下，债券duration的大小。

选项C：putable bond不会出现negative convexity。当利率下降的时候，convexity从正变为负，描述的是callable bond的特性而非putable bond，故选项C不正确。


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