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How to Calculate Cross Rates

The idea of cross rates implies two exchange rates with a common currency, which enables you to calculate the exchange rate between the remaining two currencies.

Financial media provide information only about the most frequently used exchange rates. Therefore, you may not have all the exchange rate information you need. No worries — the concept of cross rates helps you here. You can deduce information about other exchange rates based on the given exchange rates.

For example, you can easily find, say, the euro–dollar or the yen–dollar exchange rates in financial media. However, the euro–yen exchange rate may not be listed. Because the dollar is the common currency in this example, you can calculate the euro–yen (and also the yen–euro) exchange rate.

Section C4 of the WSJ of Monday, September 10, 2012, listed the yen–dollar and euro–dollar rates as ¥78.56 and €0.7802, respectively. Suppose you want to know the euro–yen exchange rate. In this case,

image0.jpg

and

image1.jpg

and you want to know what the following is:

image2.jpg

Because the dollar is the common currency here, cancel it. Think in terms of the currencies involved: When you divide the euro–dollar exchange rate by the yen–dollar exchange rate, the dollars cancel and you get the euro–yen exchange rate:

image3.jpg

Therefore, if you divide the euro–dollar exchange rate by the yen–dollar exchange rate,

image4.jpg

the euro–yen exchange rate turns out to be €0.0099.

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