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Gabriela · 2024年09月07日

三个公式的理解

  1. CFA I
  2. Derivative

NO.PZ2018062007000072

问题如下：

Which of the following combinations replicates a long derivative position?

选项：

A.

A short derivative and a long asset

B.

A long asset and a short risk- free bond

C.

A short derivative and a short risk- free bond

解释：

B is correct. A long asset and a short risk- free asset (meaning to borrow at the risk- free rate) can be combined to produce a long derivative position.

A is incorrect because a short derivative and a long asset combine to produce a position equivalent to a long risk- free bond, not a long derivative.

C is incorrect because a short derivative and a short risk- free bond combine to produce a position equivalent to a short asset, not a long derivative.

中文解析：

本题考察的是合成一个long derivative头寸，如下图红线框出来的部分，选B 。


答案解析中出现的三个公式在基础班讲义的哪一页？李老师没讲啊？请问这三个公式分别如何理解，请老师详细解释。或者请李老师补充此部分的讲解视频！

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2 个答案

李坏_品职助教 · 2024年09月07日

嗨，爱思考的PZer你好：


如果是long一个risk free bond，那可以获得bond的无风险收益率，也就是获得risk free return。


如果是short一个risk free bond，那是要付出无风险收益率，也就是支付risk_free return，也就是负的risk_free return。

所以 - risk_free return = short risk_free bond

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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 · 2024年09月07日

嗨，从没放弃的小努力你好：


这道题是问你如何制造出一份衍生品多头的仓位。


答案解析里面的截图有点老了，现在已经从基础班讲义删除。新版的讲义是这样的（课程的Arbitrage and Replication这部分）：

这里写的是，long asset + short derivative = risk-free return，我们进行移项，那么-short derivative = long asset - risk_free return，

而-short 就像等于long，而 - risk_free return也就是short risk_free bond，所以也就是long derivative = long asset + short risk_free bond.


与这个公式相关的还有一道例题：

这个例题里面，Scenario 1就是short bond + long asset，而Scenario 2则是long derivative，最后可以看出Scenario1与Scenario 2是完全等价的，所以ong derivative = long asset + short risk_free bond.



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虽然现在很辛苦，但努力过的感觉真的很好，加油！

Gabriela · 2024年09月07日

为什么risk free return=short risk free bond?

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