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Olivia.W🌸 · 2024年01月07日

为什么buy unit要对应buy put？而不是buy call？

  1. CFA I
  2. Derivative

NO.PZ2021061002000071

问题如下：

Suppose the current price (S0) of a non-dividend-paying stock is $50, and a put option on the stock has an exercise price (X) of $54 with six months left to maturity. Now an investor believes that the stock’s price in six months’ time will be either 10% higher or 10% lower.

Which of the following is true about constructing a perfectly hedged portfolio using put options and their underlying stocks?

选项：

A.

Buy one put option and buy 0.9 units of the underlying asset.

B.

Buy one put option and sell 0.9 units of the underlying asset.

C.

Sell one put option and buy 0.9 units of the underlying asset.

解释：

解析：

S1u = 50 * (1+10%) = 55, p1u=Max(0, 54 -55)= 0

S1d = 50 * (1-10%) = 45, p1d=Max(0, 54 -45)= 9

h = p1u - p1d / S1u - S1d = (0-9) / (55-45) = -0.9

注意计算的h是每份期权对应的标的资产的份数。Long stock与long put构成对冲组合，因此A对。

为什么buy unit要对应buy put？而不是buy call？或者sell put之类的

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2 个答案

李坏_品职助教 · 2024年01月09日

嗨，爱思考的PZer你好：


short stock的意思是做空股票，相当于你现在从券商手里借来100股的股票然后立刻卖出去，等过几天股票价格跌了再低价把股票买回来还给券商，这样才可以赚钱。


如果价格不幸涨起来，那你只能按照高价买回股票还给券商，那就是“低卖、高买”的赔钱操作了。

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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01月07日

嗨，从没放弃的小努力你好：


题目最后问的是"a perfectly hedged portfolio using put options and their underlying stocks", 这里要求你用put options了。


所以这道题的意思是，让你使用put option和一些股票构造一个完美对冲（perfectly hedged）的投资组合。


对于long stock来说，股价下跌会亏钱，那么就需要long put进行对冲（因为long put可以在股价下跌时赚钱）。所以应该是long stock + long put。如果是short stock的话，那么可以是sell put，但很显然ABC三个选项都没有short stock。


注意，选项里面的 buy 0.9 units of the underlying asset，意思是买入0.9份股票（股票就是基础资产）。A选项的意思是买入一份put的同时再买入0.9份股票。



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加油吧，让我们一起遇见更好的自己！

Olivia.W🌸 · 2024年01月08日

short stock不是股票跌了亏钱吗？那不是应该long put？买一个跌了赚钱的。

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