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Brocolli · 2024年06月11日

什么时候会选option free bond?

  1. CFA III
  2. Fixed Income

NO.PZ2021120102000004

问题如下：

An investment manager is considering decreasing portfolio duration versus a benchmark index given her expectations of an upward parallel shift in the yield curve.

If she has a choice between a callable, putable, or option-free bond with otherwise comparable characteristics, the most profitable position would be to:

选项：

A.

own the callable bond.

B.

own the putable bond.

C.

own the option-free bond.

解释：

B is correct. The value of a bond with an embedded option is equal to the sum of the value of an option-free bond plus the value to the embedded option.

With a putable bond, the embedded put option is owned by the bond investor, who can exercise the option if yields-to-maturity increase, as in this scenario.

Under A, the embedded call option is owned by the bond issuer, who is more likely to exercise if yields-to-maturity decrease (that is, the bond investor is short the call option).

As for C, the option-free bond underperforms the putable bond given the rise in value of the embedded put option.

老师讲过option free bond的duration比callable和putable bond都大。同时，基础班讲义51页的例题问most profitable，老师说也就是选duration最大的。请问这道题为什么不是选duration的思路？以及这两道题结合在一起，什么时候根据duration最大、什么时候选含权债？

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发亮_品职助教 · 2024年06月11日

option free bond的duration比callable和putable bond都大


是的。因为callable和Putable都存在期权option，要么发行人以行权价赎回债券，要么投资者以行权价卖还债券，总之，债券的价格涨跌有一个限制——就是行权价。


对于callable bond，债券的价格不可能涨过行权价，因为如果涨过行权价，发行人就有动力以行权价提前把价值更高的债券买回来，所以其价格上限就是行权价。

对于putable bond，债券的价格不可能低于行权价，因为如果低于行权价，投资者就会行使权利，以行权价把市场价值更低的债券卖还给发行人，所以其价格下限就是行权价。


于是callable bond存在价格上限，putable bond存在价格下限，价格涨跌受限，这两个债券不能像option-free bond一样自由涨跌。即，callable bond与putable bond的duration小于option-free bond的duration


我在讲义第51页没有找到对应的题。我猜测可能是下面这个题

针对下面这个题，大前提是利率平行下降，如下图红框。在利率下降的情况下，我们应该找duration最大的债券，因为可以享受最多的价格上升。

所以下面这道题直接选A，long option-free bond，因为option free bond的duration大于其他两个债券。


这道题如果要再细致地分析的话是这样，利率下降，债券的价格上升，选项A的option-free bond享受债券的正常价格上升

选项C的long callable bond，利率下降时，发行人很可能把债券赎回，所以投资者能享受到的就是债券价格最多上涨至行权价，显然long callable bond的价格上升不如选项A的option-free大，所以本题利率下降时，long callable不如long option-free盈利

选项B的short putable bond，注意这是short债券头寸，在利率下降——债券价格上升时，short债券头寸是亏损的。所以这道题肯定不选B



回到题库这道题，大的利率背景是利率上升（upward parallel shift）。如果要通过Duration选择的话，应该选择duration最小的，因为duration越小，债券的价格下跌幅度越小。

三个债券里面，应该排除选项C的option-free bond，然后在剩下的两个债券putable和callable bond里面，其实两者的duration都相对更小，所以通过duration其实已经很难选出来了。


这时候就要结合债券的特点分析了。对于callable bond，当利率上升时，债券价格正常下跌，就像option-free bond一样正常下跌。而对于Putable bond，当利率上升时，债券价格虽然也会下跌，但是可能会触发投资者行权，投资者会以行权价提前把债券卖还给发行人，所以债券的价格最多下跌至行权价。于是putable bond不会下跌地太狠，下跌幅度要小于Callable bond和option-free bond。


这道题另外一个解题思路就是三级固收给的分析体系：

putable bond = option-free bond + put option on bond

callable bond = option-free bond - call option on bond

以及option-free bond这三个债券


三个债券是可比的，即option-free bond部分完全一致。当利率上升时，option-free bond的部分下跌完全一致。

但对于putable bond，当利率上升时，option-free部分的债券价格下跌，同时，债券的看跌期权put option的价值上升。所以put option的盈利可以抵消一部分option-free bond的价格下跌。最终净的效果时，putable bond的价格下跌幅度最小，而callable和option-free的价格下跌相对更大。本题选表现最佳的应该就是putable bond。


建议到了3级这块，尽量按照我上面最后回复的这个思路体系分析哈，这是这个知识模块原版书给的标准分析方法，其实何老师在讲这道题时候最开始也用的是这个方法。通过duration大小判断的话可能有时候不能得到最终答案。

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