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Mercury. · 2024年07月07日

为什么是最后减去美元的成本而不是直接除

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NO.PZ201512020800000103

问题如下:

3. Based on Exhibit 3, the potential all-in USD return on the carry trade is closest to:

选项:

A.

1.04%.

B.

1.40%.

C.

1.84%.

解释:

A is correct.

The carry trade involves borrowing in a lower yielding currency to invest in a higher yielding one and netting any profit after allowing for borrowing costs and exchange rate movements. The relevant trade is to borrow USD and lend in Euros. To calculate the all-in USD return from a one-year EUR Libor deposit, first determine the current and one-year later USD/EUR exchange rates. Because one USD buys CAD 1.0055 today, and one CAD buys EUR 0.7218 today, today’s EUR/USD rate is the product of these two numbers:

1.0055 × 0.7218 = 0.7258. The projected rate one year later is: 1.0006 × 0.7279 = 0.7283. Accordingly, measured in dollars, the investment return for the unhedged EUR Libor deposit is equal to:

(1.0055 × 0.7218) × (1 + 0.022) × [1/(1.0006 × 0.7279)] –1

= 0.7258 × (1.022)(1/0.7283) –1 = 1.0184 – 1 = 1.84%

However, the borrowing costs must be charged against this gross return to fund the carry trade investment (one-year USD Libor was 0.80%). The net return on the carry trade is thereby closest to: 1.84% – 0.80% = 1.04%.

考点Carry trade 是二级经济必考的一个知识点

解析:整体的逻辑就是从利率低的国家借钱投资到利率高的国家,这道题从表格可以看出美国的利率最低,而欧洲的利率最高,因此我们要从美国借钱投资到欧洲,然后再换回美元,再减去美元的资金成本,可以得到all-in return

第一步,我们需要确定即期以及一年之后USD/EUR的汇率报价,根据表3,利用交叉汇率可得 EUR/USD=CAD/USD*EUR/CAD:

即期汇率:1.0055 × 0.7218 = 0.7258

一年后的汇率:1.0006 × 0.7279 = 0.7283

接着我们套用 carry trade 的公式,计算得到借美元,投欧元的投资收益:

(1.0055 × 0.7218) × (1 + 0.022) × [1/(1.0006 × 0.7279)] –1

= 0.7258 × (1.022)(1/0.7283) –1 = 1.0184 – 1 = 1.84%

注意到,借美元本身也有成本,那就是美元的利息,所以在计算all-in return时需要把这部分利息扣去这部分成本,最终得到:

1.84% – 0.80% = 1.04%.

为什么不可以(0.7258*1.022)/(0.7283*1.008)-1=1.04% 而且结果居然也是对的

1 个答案
已采纳答案

笛子_品职助教 · 2024年07月08日

嗨,从没放弃的小努力你好:


为什么不可以(0.7258*1.022)/(0.7283*1.008)-1=1.04% 而且结果居然也是对的

Hello,亲爱的同学~

这里也可以用同学的方法来计算。

都可以算出正确答案。

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加油吧,让我们一起遇见更好的自己!

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