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jessica喂喂喂 · 2023年02月13日

currency forward 的rebalance方法

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NO.PZ201601050100001502

问题如下:

Calculate the net cash flow (in euros) to maintain the desired hedge. Show your calculations.

选项:

解释:

When hedging one month ago, Delgado would have sold USD2,500,000 one month forward against the euro. Now, with the US dollar-denominated portfolio increasing in value to USD2,650,000, a mismatched FX swap is needed to settle the initial expiring forward contract and establish a new hedge given the higher market value of the US dollar-denominated portfolio.

To calculate the net cash flow (in euros) to maintain the desired hedge, the following steps are necessary:

1. Buy USD2,500,000 at the spot rate. Buying US dollars against the euro means selling euros, which is the base currency in the USD/EUR spot rate. Therefore, the bid side of the market must be used to calculate the outflow in euros.

USD2,500,000 × 0.8876 = EUR2,219,000.

2. Sell USD2,650,000 at the spot rate adjusted for the one-month forward points (all-in forward rate). Selling the US dollar against the euro means buying euros, which is the base currency in the USD/EUR spot rate. Therefore, the offer side of the market must be used to calculate the inflow in euros.

All-in forward rate = 0.8875 + (20/10,000) = 0.8895.

USD2,650,000 × 0.8895 = EUR2,357,175.

3. Therefore, the net cash flow is equal to EUR2,357,175 – EUR2,219,000, which is equal to EUR138,175.

中文解析:

首先呢我们是持有美元的外币资产,本币是欧元。因此在一个月前的头寸是short forward on EUR/USD,即锁定了一个月后卖美元买欧元的价格。

1. 现在到了一个月的时候,或者严格说是马上到了一个月的时候,因为在现实中我们不能真正在合约到期的当天进行平仓的,而是要提前个一两天,但是在做题的时候我们就忽略掉这个实务的问题处理哈。

此时我们的远期合约马上到期,如果到期我们就要按照合约约定的价格卖掉金额是2.5million的美元了,此时我们平仓的话是要在现货市场上买美元,注意这里我们需要保证的是买的美元的金额是2.5million,这一点是要保证的。但是使用的汇率却不是定下来的,是随行就市的。当前的汇率是0.8876才能买到美元,那么我们就只能使用这个汇率。因此我们买2.5million的美元需要花掉的欧元2.5million*0.8876=2.219million

2. 新签订的远期合约,注意此时的合约规模是2.65million,按照0.8895的汇率,因此在合约到期的时候我们会通过卖掉2.65million的美元收到2.357175million的欧元

3. 后者是收到前者是花掉二者作差就是所求

老师,forward的rebalance有两种,一种是买spot平仓再重新签一份,一种是仅针对变动部分补充签新的forward。那么怎么判断这题用的方法是先买spot平仓再重新签呢?题目中只是说Assume Rivera’s portfolio was perfectly hedged. 并没有说它原来签的是几个月的forward?这题可以直接针对增加的USD150,000补充签多一份150,000*(0.8875+20ps)=133425的forward吗?

1 个答案

lynn_品职助教 · 2023年02月14日

嗨,努力学习的PZer你好:


老师,forward的rebalance有两种,一种是买spot平仓再重新签一份,一种是仅针对变动部分补充签新的forward。那么怎么判断这题用的方法是先买spot平仓再重新签呢?题目中只是说Assume Rivera’s portfolio was perfectly hedged. 并没有说它原来签的是几个月的forward?这题可以直接针对增加的USD150,000补充签多一份150,000*(0.8875+20ps)=133425的forward吗?


其实是可以的。这道题是叫计算net cash flow,如果直接补签,其实就避免了现金流,也就不是协会想考察的点了。


这道题目其实经不起推敲的,因为新的一个月的合约发生的现金流应该是在新的1个月后,并不在此刻,而且退一万步讲即便是要计入在此刻,也应该有个折现的动作,但是本题做了简化处理,并没有做折现,就直接把新合约产生的现金流记在此刻了。


这是协会答案给到的处理方式,我们理解即可。

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2024-01-15 22:11 2 · 回答