Cross rate: When is it used?

Definition

A cross rate refers to the exchange rate between two currencies, neither of which is the official currency of the country in which the quote is provided.

What is cross rate?

The cross rate is the exchange rate between two currencies, calculated from their respective exchange rates with a third currency, often known as the base currency. These rates are used in situations where the currencies being exchanged are not commonly traded directly against each other in the foreign exchange market. Instead, their exchange rate is calculated indirectly through a common intermediary currency.

Cross rates are calculated using the exchange rates of the currencies involved and the base currency. The process involves multiplying or dividing the exchange rates to calculate the cross rate. For example, if you want to find the cross rate between Currency A and Currency B, you would first convert both currencies to a common base currency, such as the US dollar, and then calculate the exchange rate between Currency A and Currency B based on their respective rates against the base currency.

Cross rates are crucial for businesses and investors engaged in international trade or investment, especially when dealing with currencies that are not widely traded. They allow parties to calculate exchange rates for currency pairs that may not have direct liquidity in the foreign exchange market.

The efficiency of the foreign exchange market ensures that cross rates remain consistent with direct exchange rates after accounting for transaction costs and other factors. Any significant changes from this consistency could signal market inefficiencies or trading opportunities.

Example of cross rate

A company in the United States needs to find the exchange rate between the Japanese yen (JPY) and the British pound (GBP). Direct quotes aren’t available, but they have the rates USD/JPY = 110 and USD/GBP = 0.75.

They calculate the cross rate by multiplying the inverse of USD/JPY (1/110) by USD/GBP:

1/110 x 0.75 ≈ 0.0068175 JPY/GBP

So, the cross rate for JPY/GBP is approximately 0.0068175, allowing the company to trade indirectly between these currencies.