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miao999 · 2022年02月11日

你好 场景2的意思是利率下降吗，如果是的话，不应该short contract来对冲吗

  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.

你好 场景2的意思是利率下降吗，如果是的话，不应该short contract来对冲吗

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5 个答案

李坏_品职助教 · 2022年03月17日

嗨，努力学习的PZer你好：


avoid widening gap，这里的gap指的是liabilities超过assets的部分，所以利率下降，那么liabilitie价值上升的部分会超过assets上升的部分，所以我们需要long futures来对冲风险。


之前的答案是笔误了， Long futures可以使得我们在利率下降的时候获利。这里most liquid assets不一定是eurodollar，也可能是CAD的bond futures



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李坏_品职助教 · 2022年02月16日

嗨，从没放弃的小努力你好：


你理解的没问题，对于利率（债券）期货来说，影响最大的就是利率的变动，这个变动和价格是反向的，是主导作用。


欧洲美元期货也是反向的关系。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

李坏_品职助教 · 2022年02月15日

嗨，爱思考的PZer你好：


利率期货，最典型就是treasury bond futures，这种期货的标的物是美国短期国债，所以利率期货就是债券期货。利率下降会导致债券 / 债券期货价格下跌，这个是金融市场的通识。你写的F(0)的公式是商品期货价格公式，在这里不适用。



另外"4等评分"是属于差评了，同学如果觉得我的答疑没有问题的话，还请修改一下，谢谢！

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

miao999 · 2022年02月16日

你好，我的理解是：对于长期国债期货，利率下降根据求债券价格的公式，就相当于折现率变小，债券价格变高，所以债券期货的现货价格变高，所以期货价格变高。我之前只考虑到求QFP的公式里，价格随利率下降而下降，没考虑到现货价格其实也发生了变化，而大部分时候利率变化对现货价格影响更大。对于欧洲美元期货，100-libor，利率下降，期货价格上升，long赚钱。不知道是否正确。 另外我不知道怎么改，如果你告诉我怎么改，我不介意改。

he123456 · 2022年03月17日

利率下降会导致债券 / 债券期货价格下跌？利率下降不是导致债券价格上升吗？我不太明白为什么是long futures to avoid widening the pension fund gap。题目中说的the most liquid interest rate futures contract是指Eurodollar futures吗？因为ED futures是会随着利率下降而报价上升的，所以long futures赚钱

李坏_品职助教 · 2022年02月12日

嗨，爱思考的PZer你好：


请问这位同学为什么要给4级评分呢？我说的有问题吗？

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

miao999 · 2022年02月15日

你好，我不知道四级评分是什么，但是看了一下我们的问答记录，我问的问题是为什么利率下降了，买利率期货可以赚钱，我觉得应该short来对冲啊，F0（T）=S0*(1+rf)^n如果rf下降，比如说就会F1(T)<F0(T)，那long position的收益F1(T)-F0(T)就要小于0，所以不应该short吗，但你给的回答没有解答我的疑惑，解答了我之前就明白的地方。你能再讲讲吗？

李坏_品职助教 · 2022年02月11日

嗨，努力学习的PZer你好：


场景2 是利率下降25个基点，也就是下降0.25%.


因为liabilities的美元久期超过了assets，所以如果利率下降，那么liabilites上升的幅度会超过assets上升的幅度，也就是负债与资产之间的gap会恶化（liability- assets差额变大）。


所以需要买入利率期货，当利率下降的时候，利率期货会涨价，以此来对冲上面说的gap恶化的风险。

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加油吧，让我们一起遇见更好的自己！

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