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Ethan橙 · 2023年10月27日

还是不理解为什么是第二个scenario 能具体解释下么

  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.

还是不理解为什么是第二个scenario 能具体解释下么

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1 个答案

DD仔_品职助教 · 2023年10月28日

嗨，努力学习的PZer你好：


因为根据计算：

A=4billion，MDA=8.254，DDA=4000million*8.254=33016

L=5billion，MDL=6.825，DDL=5000million*6.825=34125

我们得出：

L的dollar duration大于A的dollar duration的。

第二个scenario是利率下降，利率和资产价格呈反比，所以利率下降，L会变得更多，我们要利用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

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