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xyrg+ · 2023年04月21日

答案中分子的乘100,000如何理解?

NO.PZ2019052801000041

问题如下:

It's June 2nd and a fund manager with USD 10 million invested in government bonds is concerned that interest rates will be highly volatile over the next three months. The manager decides to use the September treasury bond futures contract to hedge the value of the portfolio. The current futures price is USD 95.0625, each contract is for the delivery of USD 100,000 face value of the bonds. The duration of the manager's bond portfolio in three months will be 7.8 years, the cheapest to deliver bonds in the treasury bond futures contract is expected to have a duration of 8.4 years at maturity of the contract. At the maturity of the treasury bond futures contract, the duration of the underlying benchmark treasury bond is 9 years. What position should fund manager undertake to mitigate his interest rate risk exposure?

选项:

A.

Long 95 contracts.

B.

Short 95 contracts.

C.

Long 98 contracts.

D.

Short 98 contracts.

解释:

D is correct.

考点:Duration Based Hedge

解析:

N=($10,000,000×7.8)($100,000×8.4×95.0625%)=98N=-\frac{(\$10,000,000\times7.8)}{(\$100,000\times8.4\times95.0625\%)}=-98

基金经理应该short 98份合约来进行对冲。

8.4是久期,95.0625*N是future的总金额,还要100,000干啥呢?这个点一直不理解啊,每次做到hedge这个点都在错,希望老师讲解

1 个答案
已采纳答案

李坏_品职助教 · 2023年04月21日

嗨,从没放弃的小努力你好:


这个10万是对应的题目里的信息:each contract is for the delivery of USD 100,000 face value of the bonds.,就是每一张国债期货合约的面值是10万。


投资组合的总价值是1000万,一张期货的面值是10万,所以应该是分子乘以投资组合的总价值,分母乘以期货的面值。

假设一个简单情况,期货的久期和投资组合的久期都一样,假设期货价格是USD 100,那么我们需要N = 1000万/10万 = 100张合约来对冲。


本题计算如下:


----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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