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nanaluo · 2021年10月16日

请解释下答案

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.

请解释一下答案及考点

2 个答案
已采纳答案

DD仔_品职助教 · 2021年10月16日

嗨,努力学习的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

选A

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

miao999 · 2022年02月12日

请问为什么利率和价格一定是反向变动关系,我们学的债券价格确实是和利率成反向变动关系,但是别的资产也是吗?

DD仔_品职助教 · 2022年02月12日

嗨,努力学习的PZer你好:


这个就是最基础的定价原理。

所有资产的合理价格等于这个资产未来可以带来的现金流的折现求和,用利率进行折现,利率是分母,变大,价格就变小。

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加油吧,让我们一起遇见更好的自己!

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