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 Pairings
In 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:
AUD/NZD = Australian Dollar/New Zealand Dollar FX Cross Rate
EUR/SEK = Euro/Swedish Krona FX Cross Rate
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 Quotations
An 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 Quotations
A 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.
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