A foreign exchange market price made in two currencies (not involving the U.S. dollar) that are then both valued against a third currency A cross rate is a foreign exchange market quote between two currencies (not involving the U.S. dollar) that are then both valued against a third currency. If used as a base currency, the U.S. dollar is always seen to assume the value of one.  Below, we will show in extensive detail how the exchange market price made in two currencies differs vastly between each scenario. Understanding Cross Rate PairingsIn order to understand how to calculate cross rates, it is important to first be exposed to common cross rate pairings in order to develop comfortability with the concept. When two currencies are being valued against each other, they become a cross-rate pairing. The pairing is then compared to a base currency (e.g., U.S. dollar), creating a cross rate. Some of the more popular cross rates not involving USD include the following:
How are Cross Rates Calculated?As mentioned previously, a cross rate involves the exchange market price made in two currencies which are then valued to a third currency. During this process, two transactions are being computed. The first being the individual trading their one specific currency (EUR, JPY, GBP, etc.) for that same equivalent value in U.S. dollars. Once U.S. dollars have been received, an exchange occurs again when the U.S. dollars are traded for the second specific currency. Although it may seem complicated to grasp on paper, we will be using a comprehensive example in order to further illustrate the transaction. For the first example, we will be presenting the calculation of cross rates from two indirect quotations, while the second example will include a calculation with two direct quotations. 1. Indirect QuotationsAn indirect quotation is a currency quotation that is used to express how much base currency is needed to buy one unit of the quoted currency. It is used also for calculating cross rates. For example, let’s say the two foreign exchange pairs being used are USD/EUR and USD/JPY, and we want to calculate the cross rate of EUR/JPY. Firstly, we must find the bid/offer valuation of the two exchange pairs being used. In this case, the bid/offer for USD/EUR is about 1.2191-1.2193, while the bid/offer for USD/JPY is about 109.744-109.756. This means for every one USD, you can purchase 1.2191 EUR or 109.744 JPY. The bid/offer is an important concept. As mentioned, the USD is the base currency (monetary value of $1), while the non-domestic currency is considered the quoted currency. This concept varies when it comes to indirect and direct quotations, however. This is because a base currency is still needed for the calculation of two foreign currencies. In this example, we look to calculate EUR/JPY or Euro Yen, which would mean that the base currency in question is the Euro. In this case, the EUR is the base currency, so it must be on the denominator. If the client were to sell JPY and buy EUR (offer side), the equation would be as follows: But if the client were to buy JPY and sell EUR (bid side), the equation would differ slightly: Banks operate on the ideology of buying low and selling high. With consideration of this, the bank’s perspective of the EUR/JPY cross rate would be 90.01-90.03. 2. Direct QuotationsA direct quotation is a currency quotation that is used to express how much of the quoted currency is needed to buy one unit of the base currency. For example, similarly to the last example, we will need two foreign exchange pairs and their respective bid/offer valuation in order to conduct calculations. In this case, we will be using NZD/USD (0.7253-0.7256) and AUD/USD (0.7701-0.7719) in order to determine the cross rate of NZD/AUD. In this case, the NZD is the base currency, so it must be in the numerator. If the client were to buy AUD and sell NZD (bid side), the calculation would be as follows: But if the client were to sell AUD and buy NZD (offer side), the calculation would change to: With each in mind, the bank’s perspective of the NZD/AUD cross rate would be 0.94-0.97. Related ReadingsTo keep learning and developing your knowledge of financial analysis, we highly recommend the additional resources below: Anyone who has ever traveled to another country has probably had to deal with an exchange rate between two currencies. (I say “probably” because a person who travels from, say, Italy to Spain continues to use euros.) In a sense, exchange rates are very simple. However, despite their simplicity they never fail to generate confusion. To overcome that confusion this chapter begins by offering straightforward definitions and several rules of thumb that can help with these problems. The exchange rate (ER)Represents the number of units of one currency that exchanges for a unit of another. represents the number of units of one currency that exchanges for a unit of another. There are two ways to express an exchange rate between two currencies (e.g., between the U.S. dollar [$] and the British pound [£]). One can either write $/£ or £/$. These are reciprocals of each other. Thus if E is the $/£ exchange rate and V is the £/$ exchange rate, then E = 1/V. For example, on January 6, 2010, the following exchange rates prevailed:
It is important to note that the value of a currency is always given in terms of another currency. Thus the value of a U.S. dollar in terms of British pounds is the £/$ exchange rate. The value of the Japanese yen in terms of dollar is the $/¥ exchange rate. Note that we always express the value of all items in terms of something else. Thus the value of a quart of milk is given in dollars, not in quarts of milk. The value of car is also given in dollar terms, not in terms of cars. Similarly, the value of a dollar is given in terms of something else, usually another currency. Hence, the rupee/dollar exchange rate gives us the value of the dollar in terms of rupees. This definition is especially useful to remember when one is dealing with unfamiliar currencies. Thus the value of the euro (€) in terms of British pounds is given as the £/€ exchange rate. Similarly, the peso/euro exchange rate refers to the value of the euro in terms of pesos. Currency appreciationA currency appreciates with respect to another when its value rises in terms of the other. means that a currency appreciates with respect to another when its value rises in terms of the other. The dollar appreciates with respect to the yen if the ¥/$ exchange rate rises. Currency depreciationA currency depreciates with respect to another when its value falls in terms of the other., on the other hand, means that a currency depreciates with respect to another when its value falls in terms of the other. The dollar depreciates with respect to the yen if the ¥/$ exchange rate falls. Note that if the ¥/$ rate rises, then its reciprocal, the $/¥ rate, falls. Since the $/¥ rate represents the value of the yen in terms of dollars, this means that when the dollar appreciates with respect to the yen, the yen must depreciate with respect to the dollar. The rate of appreciation (or depreciation) is the percentage change in the value of a currency over some period. Example 1: U.S. dollar (US$) to the Canadian dollar (C$) On January 6, 2010, EC$/US$ = 1.03. On January 6, 2009, EC$/US$ = 1.19.Use the percentage change formula, (new value − old value)/old value: (1.03−1.19)1.19=−0.161.19=−0.134.Multiply by 100 to write as a percentage to get −0.134 × 100 = −13.4%.Since we have calculated the change in the value of the U.S. dollar in terms of Canadian dollar, and since the percentage change is negative, this means that the dollar has depreciated by 13.4 percent with respect to the C$ during the previous year. Example 2: U.S. dollar ($) to the Pakistani rupee (R) On January 6, 2010, ER/$ = 84.7. On January 6, 2010, ER/$ = 79.1.Use the percentage change formula, (new value − old value)/old value: (84.7−79.1)79.1=+5.679.1=+0.071.Multiply by 100 to write as a percentage to get +0.071 × 100 = +7.1%.Since we have calculated the change in the value of the U.S. dollar, in terms of rupees, and since the percentage change is positive, this means that the dollar has appreciated by 7.1 percent with respect to the Pakistani rupee during the past year.
ArbitrageThe process of buying a product when its price is low and then reselling it after its price rises to make a profit. generally means buying a product when its price is low and then reselling it after its price rises in order to make a profit. Currency arbitrage means buying a currency in one market (e.g., New York) at a low price and reselling, moments later, in another market (e.g., London) at a higher price. The spot exchange rateThe exchange rate that prevails on the spot, that is, for trades to take place immediately. refers to the exchange rate that prevails on the spot, that is, for trades to take place immediately. (Technically, it is for trades that occur within two days.) The forward exchange rateThe rate that appears on a contract to exchange currencies either 30, 60, 90, or 180 days in the future. refers to the rate that appears on a contract to exchange currencies either 30, 60, 90, or 180 days in the future. For example, a corporation might sign a contract with a bank to buy euros for U.S. dollars sixty days from now at a predetermined ER. The predetermined rate is called the sixty-day forward rate. Forward contracts can be used to reduce exchange rate risk. For example, suppose an importer of BMWs is expecting a shipment in sixty days. Suppose that upon arrival the importer must pay €1,000,000 and the current spot ER is 1.20 $/€. Thus if the payment were made today it would cost $1,200,000. Suppose further that the importer is fearful of a U.S. dollar depreciation. He doesn’t currently have the $1,200,000 but expects to earn more than enough in sales over the next two months. If the U.S. dollar falls in value to, say, 1.30 $/€ within sixty days, how much would it cost the importer in dollars to purchase the BMW shipment? The shipment would still cost €1,000,000. To find out how much this is in dollars, multiply €1,000,000 by 1.30 $/€ to get $1,300,000. Note that this is $100,000 more for the cars simply because the U.S. dollar value changed. One way the importer could protect himself against this potential loss is to purchase a forward contract to buy euros for U.S. dollars in sixty days. The ER on the forward contract will likely be different from the current spot ER. In part, its value will reflect market expectations about the degree to which currency values will change in the next two months. Suppose the current sixty-day forward ER is 1.25 $/€, reflecting the expectation that the U.S. dollar value will fall. If the importer purchases a sixty-day contract to buy €1,000,000, it will cost him $1,250,000 (i.e., $1,000,000 × 1.25 $/€). Although this is higher than what it would cost if the exchange were made today, the importer does not have the cash available to make the trade today, and the forward contract would protect the importer from an even greater U.S. dollar depreciation. When the forward ER is such that a forward trade costs more than a spot trade today costs, there is said to be a forward premiumWhen the forward exchange rate is such that a forward trade costs more (or buys less foreign currency) than a trade on the spot market today.. If the reverse were true, such that the forward trade were cheaper than a spot trade, then there is a forward discountWhen the forward exchange rate is such that a forward trade costs less (or buys more foreign currency) than a trade on the spot market today.. A currency trader is hedgingThe process of protecting oneself from the riskiness of exchange rate movements; one method is by entering into a forward contract. if he or she enters into a forward contract to protect oneself from a downside loss. However, by hedging the trader also forfeits the potential for an upside gain. Suppose in the story above that the spot ER falls rather than rises. Suppose the ER fell to 1.10 $/€. In this case, had the importer waited, the €1,000,000 would only have cost $1,100,000 (i.e., $1,000,000 × 1.10 $/€). Thus hedging protects against loss but at the same time eliminates potential unexpected gain. Key Takeaways
Exercises
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What is called the exchange rate between the currencies expressed as the ratio of two foreign exchange rates that are both expressed in terms of a third currency?
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