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小一一 · 2021年11月14日

请老师解释一下为什么是buy futures,有点没想明白。感谢老师

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.

请问从哪个方面分析会比较容易,,,

1 个答案

李坏_品职助教 · 2021年11月14日

嗨,爱思考的PZer你好:


题干里给出的信息,资产的PV是4 billion, 负债PV是5 billion。先计算一下资产和负债的dollar duration,资产的dollar duration = 4,000×8.254=33,016(单位是million),负债的dollar duration = 5,000×6.825=34,125(单位是Million)。因为资产的dollar duration小于负债,所以 如果利率上涨,那么负债跌的比资产跌的多,这是好事,不用做什么。


如果利率下跌,负债涨的比资产多,这样就不好了。我们需要买入一些interest rate futures来增加资产的久期。需要买的futures数量=(负债的dollar duration - 资产的dollar duration) / (期货价格*期货久期/1000000),这里的1000000是一张期货的面值。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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