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lyphardsun · 2025年03月26日

关于sell futures和unwind the hedge

  1. CFA III
  2. Derivative

NO.PZ2017121101000006

问题如下：

The CIO of a Canadian private equity company wants to lock in the interest on a three-month “bridge” loan his firm will take out in six months to complete an LBO deal. He sells the relevant interest rate futures contracts at 98.05. In six-months’ time, he initiates the loan at 2.70% and unwinds the hedge at 97.30. The effective interest rate on the loan is:

选项：

A.

0.75%.

B.

1.95%.

C.

2.70%.

解释：

B is correct.

The CIO sells the relevant interest rate future contracts at 98.05, locking in a forward rate of 1.95% (= 100 – 98.05). After six months, the CIO initiates the bridge loan at a rate of 2.70%, but he unwinds the hedge at the lower futures price of 97.30, thus gaining 75 bps (= 98.05 – 97.30). The effective interest rate on the loan is 1.95% (= 2.70% – 0.75%).

中文解析：一个CIO一开始签订了一个期货合约，锁定了借款利率是1.95%（100-98.05），后来他又通过签订另一个期货合约锁定了自己将钱借出去时的利率是2.7%（100-97.3），于是在这一对期货合约上，他收益是2.7%-1.95%=75bps.到了六个月的时候，这个人是在市场上以2.7%的利率借的钱（he initiates the loan at 2.7%）,所以期货头寸赚了75bps,借钱付出2.7%，等效借款利率就是1.95%了。

为什么sell futures是借入，而unwind the hedge是借出，以及initiate the loan是借入

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1 个答案

李坏_品职助教 · 2025年03月26日

嗨，从没放弃的小努力你好：


这个题目其实有个简单的解法。


任何的期货，都是满足下面的规律：

  1. Long futures是在futures price上升时候赚钱。
  2. short futures是在futures price下跌时候赚钱。

现在期货价格是从98.05降低到97.30，差值是0.75，由于这个人是sell futures，那就是Short，所以这个人在利率期货上赚了0.75. 这个反映在利率上就是0.75%的利润。


原来的loan利率是2.7%，那么扣掉这个利润之后，真实的贷款利率 = 2.7 %- 0.75% = 1.95%.



这个人是一开始去贷款了，我去找银行贷款，那我就是借入资金，所以loan = 借入资金。


而short futures是在期货价格下跌时赚钱，期货价格与利率反向变动，那也就是在利率上升时赚钱。假如我一开始以固定利率借入资金，即便未来利率上升，我依然按照一开始较低的利率还钱，那我就是占便宜了。所以short futures与借入资金都会在利率上升时候赚钱，所以short futures = 借入资金。


unwind the hedge意思是把前面的short futures平仓了结，那就需要long futures来结束这个交易。既然short = 借入，那么long就是反过来，是借出资金。



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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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