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卷帘门门主耳东大哥 · 2019年11月13日

问一道题：NO.PZ2016082404000023

  1. FRM I
  2. Financial Markets And Products

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.

还是没有理解这道题的意思？可否有一个更详细的解释呢？

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1 个答案

orange品职答疑助手 · 2019年11月14日

同学你好，这题的宗旨就是消除利率变化对财务赤字的不利影响（Asset-liability不能再扩大了）。用简单的假设利率变化1%，来产生以上变化的等式，计算上比较方便。

首先要看利率如何变化会使赤字变大，那就看利率增加或减少1%，A - L这个差会变大还是变小。那么直接假设利率减小1%，得出asset增加4000*8.254=33016million，liability增加5000*6.825=34125。这时候A -L会变大1109（不好）。反之利率增加1%是好的，也就是利率增加是不用有应对措施。

怕利率下降，要对冲利率下降带来的风险，所以他应该进入利率期货合约的多头。因为对于利率期货合约而言，当利率下降的时候，他是赚钱。

最后用公式算出合约数即可。


利率变化的情景只是提供了升降的情景，25bp这个数字没用。

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