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lion · 2023年03月02日

求解释。。。。。

NO.PZ2016082404000023

问题如下:

Albert Henri is the fixed income manager of a large Canadian pension fund. The present value of the pension fund’s portfolio of assets is CAD 4 billion while the expected present value of the fund5s liabilities is CAD 5 billion. The respective modified durations are 8.254 and 6.825 years. The fund currently has an actuarial deficit (assets < liabilities) and Albert must avoid widening this gap. There are currently two scenarios for the yield curve: The first scenario is an upward shift of 25bp, with the second scenario a downward shift of 25bp. The most liquid interest rate futures contract has a present value of CAD 68,336 and a duration of 2.1468 years. Analyzing both scenarios separately, what should Albert Henri do to avoid widening the pension fund gap? Choose the best option.

选项:

First Scenario       
Second Scenario

A.

Do nothing
Buy 7,559 contracts

B.

Do nothing
Sell 7,559 contracts.

C.

Buy 7,559 contracts
Do nothing.

D.

Do nothing
Do nothing.

解释:

ANSWER: A

We first have to compute the dollar duration of assets and liabilities, which gives, in millions,4,000×8.254=33,016   and  5,000×6.825=34,125, respectively. Because the DD of liabilities exceeds that of assets, a decrease in rates will increase the liabilities more than the assets, leading to a worsening deficit. Albert needs to buy interest rate futures as an offset. The number of contracts is (34,125-33,016)/(68,336×2.1468/1,000,000) =7,559.

请问是哪的知识点。。。

2 个答案

pzqa27 · 2024年05月08日

嗨,从没放弃的小努力你好:


long futures 相当于long bond,会增加原有头寸的duration。

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pzqa27 · 2023年03月03日

嗨,爱思考的PZer你好:


同学你好~

考点是duration gap以及duration based hedge。

首先分别计算A和L的dollar duration

A=4billion,MDA=8.254,DDA=4000million*8.254=33016

L=5billion,MDL=6.825,DDL=5000million*6.825=34125

那么我们很容易看出来,L的dollar duration大于A的dollar duration的。

我们担心的事情是这个差距gap会越来越大,也就是害怕L增加的比A多,在利率下降的时候,会发生这种情况,因为利率和价格是成反向变动关系的,所以第一个scenario是利率上升,我们啥都不干。第二个scenario是利率下降,我们要采取措施了。

具体的措施是利用futures作为对冲工具。

已知 这个futures的价格是68336,duration是2.1468.

A和L的dollar duration相差了34125-33016=1109million。

我们要用futures这个工具来消除这个dollar duration,因为是A的dollar duration小,所以我们要买这个futures。

一个futures合同的dollar duration=68336*2.1468=146703.7

一共要买1109million/146703.7=7559个futures才能达到目的

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

MiaZh · 2024年05月08日

为什么A的dollar duration小就要买futures?

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