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hyi725 · 2024年08月06日

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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.

rate下降 PV liability会上升更多

所以long 更多的futures对吗?

但是asset不受rate上升的影响

1 个答案

发亮_品职助教 · 2024年08月07日

本题是需要long更多的futures,futures的作用主要是用来增加或者降低asset BPV的,Long futures就是增加资产的BPV,short futures就是降低资产的BPV


是增加资产的BPV,还是降低资产的BPV,以及使用更多、更少,还是刚合适的futures份数,这个要根据利率的预期来判断,每个题都不一样。

总之目标就是,使用futures之后,使得资产相对于负债有更多的受益。


本题预期利率下降,asset和liability都会受到利率下降的影响,因为Asset与liability都存在duration(BPV)。


然后这块的逻辑是这样,背景是要multiple liability duration-matching,即,要达到:

资产的BPV = 负债的BPV


这样就保证了在利率改变时,资产与负债的Value改变是一致的,即,利率对资产与负债的影响是一致的,又由于期初资产已经足够cover负债了,利率改变对两者的影响还是一致的,说明利率改变之后,资产依然cover负债,这就是做duration-matching的意义,保证哪怕利率会改变,资产也能足够cover负债、偿还地起负债。


下面这段的题干说:

让资产与负债的interest rate sensitivty match住了(即达到了duration-matching)。但是如果基金经理对未来利率的改变方向有足够的信心,且资产的value有10%的surplus时,基金经理可以暂时退出duration-matching策略,来做一个主动策略,使用衍生品主动调节资产的duration,让资产来享受利率的改变,从而使得资产的surplus扩大


Puhuyesva’s approach matches the interest rate sensitivity of the asset portfolio to that of the liabilities. 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.


本题已知,资产的BPV=243,376,负债的BPV = 299,860


资产的BPV过小,不满足duration-matching的条件,所以现在使用衍生品long futures来增加资产端的BPV,使得:

资产BPV + 衍生品BPV = 负债BPV

这样就可以达到duration-matching。


我们可以先算一下,使用多少份futures可以彻底消除资产与负债之间的duration差距(close duration gap):

243376 + 102.30× 份数 = 299860

份数=552份


所以,如果想要彻底达到duration-matching,应该long 552份futures。但现在题干说,基金经理可以基于对未来利率的预期,调节资产端的BPV,使得资产可以享受利率改变的好处。

已知预期是利率下降,所以,我们利用futures要额外增加资产端的BPV,使得:

资产BPV + Futures BPV > 负债BPV

因为利率下降,债券的价格上升,当资产一侧的BPV更大时,资产的价格上升更多,这会进一步扩大surplus。


如果long 552份futures,可以使得资产BPV + Futures BPV = 负债BPV

那如果long的份数超过552份,就可以使得资产BPV + Futures BPV > 负债BPV,在利率下降时,资产端的价格上升更多,扩大surplus。

所以,基于本题利率下降的预期,应该选B long 614份

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