How to Calculate Cross Rate

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The foreign exchange market, also known as Forex, allows traders to buy and sell currencies issued by various nations or regions. Many Forex markets use the U.S. dollar (USD) as the basis for determining currency exchange rates. When currency traders want to know the exchange rate between two currencies that do not have an explicitly-printed exchange rate, they can use a common currency, such as USD, to calculate the cross-currency exchange rate, also known as the cross rate.

How Cross Rates Work

Each currency exchange rate involves a currency pair. Some currency pairs, such as the euro and the British pound, have their exchange rates readily available through financial publications or websites. Other currency pairs, such as the British pound and the Japanese yen, require a cross rate to determine their exchange rates. Each currency pair in the cross rate calculation must have a currency in common. The common currency ensures that the comparison between the two exchange rates is mathematically valid.

How Currency Pairs Work

Currency pairs are quoted in terms of the base currency and the quote currency. The base currency is the currency to be converted, while the quote currency is the currency for which the base currency is exchanged. Each currency is denoted by a three-letter code. For instance, a currency pair to convert British pounds (GBP) to U.S. dollars (USD) has the pound as the base currency and the dollar as the quote currency. The currency pair is denoted as GBP/USD.

Cross Rate Formula

In cases where the currency exchange rate is not available, the trader can determine the cross rate if the two currencies share exchange rates with a third currency. For instance, if Currency A and Currency C are not published currency pairs, but each one shares a currency pair with Currency B, the formula to calculate the cross rate looks like this:

A/C = (A/B) x (B/C)

The "Currency B" factors cancel each other out, leaving a straightforward calculation for the A/C pair.

Cross Rate Example

A salesperson must travel from Paris to Tokyo for a presentation. He wants to know the exchange rate between the euro (EUR) and the yen (JPY). He uses the cross rate with the USD to determine the EUR/JPY exchange rate:

EUR/JPY = (EUR/USD) x (USD/JPY) = 1.128 x 123.466 = 139.253

He can exchange each euro for 139.253 yen.

Uses for Cross Rates

Forex traders use cross rates as a vital indicator for their currency trades. Cross rates act as signals to investors as to the value of the currencies being traded and their future performance in the Forex market. Since Forex traders make their income from analyzing currency fluctuations, cross rates provide highly useful information on the magnitude and direction of currency movements.

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