How to Calculate a Cross Rate for Currency Exchange
Learn to calculate currency cross rates. Understand the methods for deriving exchange rates between any two currencies, empowering your financial insights.
A cross rate is an exchange rate between two currencies not official in the country providing the quote. For example, in the United States, the exchange rate between the Euro (EUR) and the Japanese Yen (JPY) is a cross rate. Understanding cross rates helps individuals with international activities like foreign travel or online purchases. It also offers insight into global financial news and currency strengths.
Understanding Exchange Rate Quotations
Currency exchange rates are expressed as a pair, such as EUR/USD. The first currency is the base currency, and the second is the quote currency. The exchange rate indicates how much of the quote currency is required to purchase one unit of the base currency. For example, if EUR/USD is 1.10, one Euro exchanges for 1.10 U.S. Dollars.
The way an exchange rate is presented can be direct or indirect, depending on the domestic currency’s perspective. From a U.S. perspective, a direct quotation shows the amount of U.S. Dollars needed to buy one unit of a foreign currency, such as USD/CAD 1.35. Conversely, an indirect quotation displays how many units of a foreign currency can be bought with one unit of the domestic currency, like EUR/USD 1.10. The U.S. Dollar is generally involved in most transactions.
Calculating Cross Rates with a Common Currency
Cross rates can be calculated when two currency pairs share a common currency, often the U.S. Dollar. This method uses existing quoted rates. The approach depends on whether the common currency is the base or quote currency in the initial pairs.
When both initial currency pairs have the same base currency, such as USD/EUR at 0.90 and USD/JPY at 150.00, calculate the EUR/JPY cross rate by dividing the quote currency values. To find EUR/JPY, divide the USD/JPY rate by the USD/EUR rate. For example, 150.00 (JPY per USD) divided by 0.90 (EUR per USD) equals approximately 166.67 JPY per EUR. This calculation cancels out the common U.S. Dollar, leaving the desired Euro to Japanese Yen rate.
If both initial currency pairs share the same quote currency, such as EUR/USD at 1.10 and GBP/USD at 1.25, use a different operation to find the cross rate, for instance, EUR/GBP. In this case, divide the EUR/USD rate by the GBP/USD rate. Specifically, 1.10 (USD per EUR) divided by 1.25 (USD per GBP) results in approximately 0.88 EUR per GBP. This method is common when the U.S. Dollar is the quote currency in both given pairs, allowing for a direct conversion between the two foreign currencies.
Calculating Cross Rates Using the Chain Method
The chain method is employed when there is no direct common currency between the two initial currency pairs. This approach uses a third, widely traded currency, typically the U.S. Dollar, as a bridge to determine the cross rate. The process involves two sequential conversions, effectively linking the two desired currencies through this intermediate currency.
To illustrate, consider calculating the AUD/GBP cross rate when you have AUD/USD at 0.65 and USD/GBP at 0.80. The first step involves converting the Australian Dollar (AUD) into the intermediate currency, the U.S. Dollar (USD). With AUD/USD at 0.65, one Australian Dollar is worth 0.65 U.S. Dollars.
The second step converts these U.S. Dollars into British Pounds (GBP) using the USD/GBP rate. Since USD/GBP is 0.80, one U.S. Dollar is equivalent to 0.80 British Pounds. To find the AUD/GBP cross rate, multiply the AUD/USD rate by the USD/GBP rate: 0.65 (USD per AUD) multiplied by 0.80 (GBP per USD) equals 0.52. Therefore, one Australian Dollar is worth 0.52 British Pounds. This multiplication mathematically cancels out the intermediate U.S. Dollar, providing the direct exchange rate between AUD and GBP.