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Pina · 2022年07月05日

years

NO.PZ2018113001000027

问题如下:

A portfolio manager has a $200 million bond portfolio, he wants to reduce the duration from 5 to 4 by using a swap. There are two swaps, a one-year swap with an average modified duration of -0.625,and a two-year swap with an average modified duration of –1.25。

1.Should the manager enter into a payer swap or receiver swap?

2. Which swap the manager would prefer and determine its notional principal.

选项:

A.

Payer swap and NP=160 million

B.

receiver swap and NP=160 million

C.

Payer swap and NP=320 million

解释:

A is correct.

考点:Interest Rate Swap: Adjust the Duration

解析:

现在希望降低duration,所以应该进入一个duration为负数的swap,即payer swap

我们需要判断应该prefer哪个swap?判断的依据是为了达到目标的duration,哪个swap需要名义本金越少,我们就应该更prefer哪个swap。根据公式:

NS=MVP(MDURTMDURPMDURswap)N_S=MV_P{(\frac{MDUR_T-MDUR_P}{MDUR_{swap}})}

Swap的duration越大,需要的NP就越少,因此我们需要选择一个duration绝对值更大的一个swap

第二个swap的duration绝对值更大,因此应该选第二个swap,它的NP计算如下:

NS=MVP(MDURTMDURPMDURswap)=$200,000,000(4.05.01.25)=$160,000,000N_S=MV_P{(\frac{MDUR_T-MDUR_P}{MDUR_{swap}})}=\$200,000,000{(\frac{4.0-5.0}{-1.25})}=\$160,000,000

老师好 这题是因为要降低成本所以选用2 year swap. 原来的想法是从5 years 到4 years就降低1year, 所以就用了 one-year swap with an average modified duration of -0.625, 这样的想法, 哪错了?谢谢。

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Hertz_品职助教 · 2022年07月05日

嗨,从没放弃的小努力你好:


同学你好

思考角度是错的。

对于互换来说降低成本是需要找名义本金要小的互换。

为什么呢?

我们知道互换中交换的现金流是基于名义本金的,比如一个支付固定5%,收到浮动利率,单纯的利率没有办法换,不能说你给我5%, 我给你libor, 应该乘以一个名义本金转换成多少钱才可以,所以名义本金越小,互换时需要准备的现金越少,对流动性的要求低,因此更好,所以要选名义本金小的。

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努力的时光都是限量版,加油!

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