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王昕彤 · 2024年01月14日

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NO.PZ202208100100000403

问题如下:

Using Exhibit 1, if the Spanish shares had been sold after three months, the cash outflow (in US dollars) required to close out the forward contract would have been closest to:

选项:

A.489,182.00 B.489,850.00 C.491,400.00

解释:

B is correct.

The initial foreign asset position was EUR18 million: 200,000 shares × EUR90/share. The six-month forward contract would have been sold using the bid of the base currency (euro) at an all-in forward rate of 1.3935 – 19/10,000 = 1.3916 USD/EUR.

If the position had been closed in three months, a three-month forward contract would have to be purchased at the offer of the base currency at an all-in forward rate of 1.4210 – 21/10,000 = 1.4189 USD/EUR.

The cash outflow at settlement would have been EUR18 million × (1.4189 – 1.3916) USD/EUR = USD491,400. This amount needs to be discounted by three months at the US dollar Libor rate: 491,400/(1 + 0.01266 × 90/360) = USD489,850.

A is incorrect. The euro Libor rate is used to discount the settlement cash flow: 491,400/(1 + 0.01814 × 90/360) = USD489,182.

中文解析:

初始的外币资产头寸是18million的欧元(0.2million股*90欧元/股)。

因此一开始需要short forward on 欧元,期限是6个月,对应的远期汇率是1.3935 – 19/10,000 = 1.3916 USD/EUR。(此合约在到期的时候是卖欧元,收到美元)

那现在3个月的时候股票被卖掉了,所以原来的6个月期限的合约用不到了,需要平仓平掉。签反向对冲合约:long forward on欧元,期限是3个月,对应的远期汇率是1.4210 – 21/10,000 = 1.4189 USD/EUR。(此合约到期的时候是买欧元,支付美元)

那么在到期的时候(也就是再过3个月后),对应的cash outflow就是EUR18 million×(1.41891.3916)USD/EUR = USD491,400。

但现在是站在3时刻,因此需要在到期时候的金额USD491,400向前折现3个月,即:491,400/(1 + 0.01266 × 90/360) = USD489,850。

C is incorrect. It uses the settlement cash flow, ignoring any discounting: USD491,400.Solution

老师,为什么三个月以后平仓用的是ask-price 的价格,按照乘小除大的原则,要把EUR销掉,不是都应该用乘法吗,也就是乘以小的,每次一到这个点就犯迷糊,请老师详细讲解一下

1 个答案

pzqa31 · 2024年01月15日

嗨,从没放弃的小努力你好:


因为这里不适合乘小除大原则哈,总结一下:


乘小除大的规则

1)判断乘法还是除法:

DC/FC的汇率表达:

想要DC则为乘法(short FC对应long DC,这里想要可以理解为做多)

想要FC则为除法(short DC对应long FC,这里想要可以理解为做多)

如果是卖出分母币种,那么就是需要消掉汇率表达形式(DC/FC)中的分母适用乘小除大

如果是买进分母币种,那就不是要消掉分母,此时就不适用乘小除大。


2)乘小除大:乘法就乘以Bid-ask中小的,也就是bid。除法就是除bid -ask中大的,也就是ask。

原理是,最终得出的数,都是小的。乘以小的,最终结果小。除以大的,最终结果也小。



举例

CAD/USD:1.2597~1.2598

(1)如果是卖1million的美元,问会收到多少加拿大元,则是1,million乘以1.2597(适用乘小除大)

(2)如果是买1million的美元,问需要花掉多少加拿大元,则是1million乘以1.2598(本题的情景)


ps:如果同学觉得乘小除大过于复杂的话,可以直接就用bid-ask来判断,这里要买欧元,用ask,消分母直接用乘法,这样判断不是更简单么,学习方法应该是为咱们所用的哈。

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