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Infinite · 2020年02月24日

问一道题: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.

老师您好,这个是之前同学提出的问题,老师的解答“利率下跌,国债期货就会赚钱,来弥补这个赤字的扩大。”这句话的意思,我理解不就是利率下降会缩小赤字吗?那就不就是资产会增加,负债会减少吗? 为什么答案说 利率下降, liability反而会大于asset呢? 这地方能用经济学的思路来想吗?利率下降不就是为减少deficit?利率下降,债券价格上升,这不是利好的吗?

1 个答案

orange品职答疑助手 · 2020年02月25日

同学你好,因为这边题目还给了久期啊,因为资产和负债都是债券,不能单纯只看asset和liability的金额,还要看久期的,因为我们更关心利率的变动对我账户盈亏的影响,而久期是对它有影响的。这边考点就是用带久期的价格变动公式去考虑。考虑久期的情况下,我更担心利率下降,所以要签一个新合约,使得当利率下降时能赚钱。所以买国债期货。

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