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Ausilio · 2024年05月24日

关于这道题对应的知识点

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NO.PZ202209060200004002

问题如下:

The most appropriate action given Puhuyesva’s views on interest rates and the information in Exhibit 1 would be to buy:

选项:

A.492 contracts. B.614 contracts. C.552 contracts.

解释:

Solution

B is correct.

The number of futures contracts needed to fully remove the duration gap between the asset and liability portfolios is given by

(BPV liability - BPV asset) / Futures BPV

where BPV is basis point value (of the liability portfolio, asset portfolio, and futures contract, respectively).

In this case, Nf = (299,860243,376) / 102.30 =+552.1, where the plus sign indicates a long position in or buying 552 futures contracts.

Because the value of assets is more than 2% greater than the value of liabilities (217.3/206.8 – 1 = 5.1%) and Puhuyesva believes interest rates will fall, the duration of assets should be greater than the duration of liabilities so that the surplus will rise if interest rates do fall. Therefore, more than 552 contracts should be bought.

A is incorrect because buying 492 contracts would leave the duration of assets lower than the duration of liabilities and the surplus would decrease if interest rates fall.

C is incorrect because buying 552 contracts would fully immunize the surplus and it would neither increase nor decrease if interest rates fall.

老师好,我想问一下这道题对应的是基础班的那一个考点或者哪句话呢?之前完全没有意识到要增大duration所以要多买futures的这个情况。

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已采纳答案

发亮_品职助教 · 2024年05月24日

这道题对应Learning module 2【讲义107页】里面的Derivatives overlay的知识点。

后面配了一道例题也是类似于这道题的,可以再回顾下例题。



Overview一下这里的思路:

Long futures和long bonds是一样的,因为这里的Futures底层资产就是债券,Futures获得的头寸归根到底就是债券的头寸,所以Long futures获得正的Duration,可以增加组合的Duration;Short futures可以获得负的Duration,可以起到降低组合Duration的作用。


然后一般情况下,直接买卖债券的话流动性太差,有时候就用衍生品来调节组合的Duration头寸了。


一般我们是利用long/short futures来使得Asset-liability之间的BPV相等,实现Duration-matching。使用Futures来增加or降低资产端的BPV,使之BPV与负债端一致。

所以本题Asset的BPV是243376,Liability的BPV事299860,一份Futures的BPV是102.30


资产负债BPV的缺口是:负债299860-资产243376 = 56484

所以需要Futures的份数是:56484/102.30=552.14(份)

需要Long 552份Futures增加资产端的BPV,使得达到Fully hedge。


但注意,本题没有问fully hedge应该用多少futures。本题问的是基于利率预期,应该用多少份futures。


如果题目问,要彻底Fully hedge duration-gap,要彻底抹平资产负债间的Duration缺口,使得Asset BPV + Futures BPV = Liability BPV,实现Duration-matching我们需要Long 552份Futures。


但注意,有时候题干对未来利率有预期,要故意留一个Duration缺口,利用这个利率预期实现盈亏,其实就是Contingent immunization。


比如,本题题干的利率预期是:利率会下降。

那基于这样的预期,我们可以多Long一些Futures,使得Asset BPV + Futures BPV > Liability BPV,这样的话,当利率下降时,由于资产端的BPV更大,所以价值上升幅度大于负债的价值上升幅度,这会扩大我们的Surplus。所以可知,本题使用的futures份数应该大于552


注意,这道题下面这句说明了是要基于利率预期做策略,并不是要使用futures fully hedge:


当他对未来的利率改变有信心时,并且资产的Surplus超过10%的Asset时【本题数据满足】,可以基于利率预期来做对应的策略,试图扩大surplus:

If she has reasonably strong beliefs about how interest rates will change in the near future and the surplus exceeds her threshold of 10% of assets, she will adjust the interest rate sensitivity of the asset portfolio to attempt to increase the surplus.

这句其实告诉我们,这道题可以做contingent immunization。


这道题的题干也在问基于这样的利率预期应该如何做策略,并没有问达到duration-matching时需要用多少futures,所以本题不能选552

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