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张大龙 · 2024年12月07日

关于正负号

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。

我看有的教材写的公式是一PxD。其实是不是完全不用管这个负号,完全用P×D+N×D×Vf=0 然后只看结果正负相应long和short就可以?

1 个答案

李坏_品职助教 · 2024年12月07日

嗨,爱思考的PZer你好:


可以的。我平时也是建议学生不用管正负号,完全用P×D+N×D×Vf=0,结果的正负即对应long和short。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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