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张大龙 · 2024年12月07日

为什么利率上升，有助于缩小gap

  1. FRM I
  2. Financial Markets And Products

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.

为什么利率上升，有助于缩小gap

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李坏_品职助教 · 2024年12月07日

嗨，努力学习的PZer你好：


由于本题是pension fund，所以资产和负债都可以看做类似债券，而债券的价值与利率是负相关的。

利率上升的时候，资产的价值会下降，负债的价值也会下降。


现在，资产的美元久期是33016，负债的美元久期是34125，美元久期反映了价值对利率变化的敏感度。这就说明，利率上升的时候，负债下降的幅度会更大。所以利率上升会缩小gap。

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张大龙 · 2024年12月07日

这个知识点在讲义里提过吗？

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