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Sandy · 2021年04月21日

解析里最后一个算式没有理解,可以在纸上写一下吗？

  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.

像上课老师列的算式那样
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1 个答案

品职答疑小助手雍 · 2021年04月21日

嗨，爱思考的PZer你好：


前面算出来两个dollar duration分别是asset 33016million和liability 34125million。

现在害怕的是gap差的更大，而asset的dollar duration小于liability的，也就是利率下降时负债增加会比资产多，赤字会扩大。那就要买future增加资产端的duration来抵消这个扩大。

你要理解dollar duration的含义是利率变动1bp的金额变化，后面就可以理解最后一个式子的含义。

现在dollar duration相差了34125-33016million（分子），要使用future把它抵消就要使买的future的dollar duration也等于这个值。

现在一手future的dollar duration等于68336*2.1468（分母，如果要转化成带million的单位就要除以1,000,000），都转换成带million的数值方便上下消掉。那就得到了结果（34125-33016million）/（68336*2.1468/1000000 million）

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