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SHAO · 2024年04月25日

老师，请问选项C怎么理解

  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.

老师，请问选项C怎么理解

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吴昊_品职助教 · 2024年04月26日

嗨，努力学习的PZer你好：


配合下图：callable bond在利率下降的时候，债券发行人以call price提前赎回债券，所以callable bond在利率下降的时候会有一个价格上限，由于价格涨不上去，会呈现出负凸的特性。即negative convexity。我们定义straight bond的图形是正凸性，callable bond的左侧部分是升不上去的，图像正好与straight bond 相反，所以是负凸。C选项如果针对的是callable bond就对了。

现在C选项的对象是putable bond，putable bond的convexity在任何时候都是正的，不会出现负的。



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