为什么计算美元/欧元，而不是欧元/美元？

问题如下：

Ed Smith is a new trainee in the foreign exchange (FX) services department of a major global bank. Smith’s focus is to assist senior FX trader, Feliz Mehmet, CFA. Mehmet mentions that an Indian corporate client exporting to the United Kingdom wants to estimate the potential hedging cost for a sale closing in one year. Smith is to determine the premium/discount for an annual (360 day) forward contract using the exchange rate data presented in Exhibit 1.

Exhibit 1. Select Currency Data for GBP and INR

Mehmet is also looking at two possible trades to determine their profit potential. The first trade involves a possible triangular arbitrage trade using the Swiss, US and Brazilian currencies, to be executed based on a dealer’s bid/offer rate quote of 0.5161/0.5163 in CHF/BRL and the interbank spot rate quotes presented in Exhibit 2.

Exhibit 2. Interbank Market Quotes

Mehmet is also considering a carry trade involving the USD and the Euro. He anticipates it will generate a higher return than buying a one-year domestic note at the current market quote due to low US interest rates and his predictions of exchange rates in one year. To help Mehmet assess the carry trade, Mehmet provides Smith with selected current market data and his one year forecasts in Exhibit 3.

Exhibit 3. Spot Rates and Interest Rates for Proposed Carry Trade

Finally, Mehmet asks Smith to assist with a trade involving a US multinational customer operating in Europe and Japan. The customer is a very cost conscious industrial company with a AA credit rating and strives to execute its currency trades at the most favorable bid/offer spread. Because its Japanese subsidiary is about to close on a major European acquisition in three business days, the client wants to lock in a trade involving the Japanese yen and the Euro as early as possible the next morning, preferably by 8:05 AM New York time.

At lunch, Smith and other FX trainees discuss how best to analyze currency market volatility from ongoing financial crises. The group agrees that a theoretical explanation of exchange rate movements, such as the framework of the international parity conditions, should be applicable across all trading environments. They note such analysis should enable traders to anticipate future spot exchange rates. But they disagree on which parity condition best predicts exchange rates, voicing several different assessments. Smith concludes the discussion on parity conditions by stating to the trainees:

“I believe that in the current environment both covered and uncovered interest rate parity conditions are in effect.”

The conversation next shifts to exchange rate assessment tools, specifically the techniques of the IMF Consultative Group on Exchange Rate Issues (CGER). CGER uses a three-part approach including the Macroeconomic Balance Approach, the External Sustainability Approach, and a Reduced Form Econometric Model. Smith asks Trainee #1 to describe the three approaches. In response, Trainee #1 makes the following statements to the other trainees and Smith:

Statement 1 Macroeconomic Balance focuses on the stocks of outstanding assets and liabilities.

Statement 2 Reduced Form has a weakness in underestimating future appreciation of undervalued currencies.

Statement 3 External Sustainability centers on adjustments leading to long-term equilibrium in the capital account.

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%.