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andytsoi · 2020年09月29日

问一道题：NO.PZ2017121101000006 [ CFA III ]

  1. CFA III
  2. Derivative

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%).

老师，effective是年化，而2.7%是年化贷款利率，但0.75%应该是这半年做future的收益，为什么没有直接2.7-0.75，而不是2.7-（0.75*2）？
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xiaowan_品职助教 · 2020年09月30日

嗨，从没放弃的小努力你好：


同学你好，

这是一道原版书课后题，它所给的答案我感觉确实不太好，我下面做一下，你可以参考一下。

这道题使用的对冲工具利率期货，我们通常认为就是eurodollar futures，假设本金总额是N millions，那么要使用N份futures合约，且1bps对应25美元

  1. 正常3个月贷款的利息：2.7% * N millions * 90/360
  2. 通过hedge获得的收益：75 * 25 * N

最后年化的effective利率就是：（2.7% * N millions * 90/360 - 75 * 25 * N）* （360/90）/N millions = 1.95%

和这道题非常类似且解析写的很全的是基础班Interest rate forward and futures这部分的例题，我把截图放在下面同学可以参考。


-------------------------------
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NO.PZ2017121101000006 问题如下 The CIO of a Canaprivate equity company wants to loin the interest on a three-month “brie” lohis firm will take out in six months to complete Lal. He sells the relevant interest rate futures contracts 98.05. In six-months’ time, he initiates the lo2.70% anunwin the hee 97.30. The effective interest rate on the lois: A.0.75%. B.1.95%. C.2.70%. B is correct. The CIO sells the relevant interest rate future contracts 98.05, locking in a forwarrate of 1.95% (= 100 – 98.05). After six months, the CIO initiates the brie loa rate of 2.70%, but he unwin the hee the lower futures priof 97.30, thus gaining 75 bps (= 98.05 – 97.30). The effective interest rate on the lois 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 lo2.7%）,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。 1.“he initiates the lo2.7%”指他开展了一个借款，借款利率为2.7%；2.“unwin the hee 97.3”是指解除之前的借款，即现在将钱借出去，可以获得的利率为100-97.3=2.7，虽然都是2.7，但是概念不一样，对么？

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