Cross Rate Essay

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A cross  rate  reflects  the  exchange  rate  between  a foreign currency and another foreign currency. It shows the relationship  between two foreign currencies with neither  currency  being the domestic  currency. If the  exchange  rate  between  U.S. currency and country X’s currency is known, and the exchange rate between U.S. currency and currency of county Y is also known, it is possible to determine  the implied exchange rate between the currencies of countries X and Y. The implied exchange rate is what is referred to as a cross rate.

Foreign exchange rates can be quoted in two ways: direct  quote  and  indirect  quote.  A direct  quote  is stated  in  the  form  of  domestic  currency  per  foreign currency. An indirect  quote is expressed as the number  of foreign currency units needed to acquire one unit of domestic currency. A direct quote is also referred to as a normal quote, while an indirect quote is called a reciprocal  quote. An example of a direct quote between the U.S. dollar (USD) and the British pound  (GBP) is USD/GBP = 1.90. This means  that $1.90 of U.S. currency  is needed  to purchase  a unit (₤1) of British currency. The direct quote can be converted into an indirect quote of the form, GBP/USD = 0.53. Again, this means that ₤0.53 British currency is needed to purchase a unit ($1.00) of U.S. currency.

The cross rate is usually calculated from two other foreign exchange rates. Let the exchange rate between U.S. dollar (USD) and South African rand (ZAR) be stated as USD/ZAR = 7.5. Again, let the exchange rate between U.S. dollar (USD) and Mexican peso (MXP) be stated as USD/MXP = 10.5. From these two quotes, it is easy to determine  the implied cross rate between ZAR and MXP. The cross rate is MXP/ZAR = 0.71 (calculated as 7.5/10.5).

In order to understand the rationale for its use, it is important to examine the concept  of vehicle currencies. Vehicle currencies are currencies that are actively traded  in the foreign exchange market.  Examples of vehicle currencies  are U.S. dollar (USD), euro (EUR), Japanese yen (JPY), and the British pound (GBP). International transactions are conducted in a few vehicle currencies. The logic for using a few currencies for international transactions  is to promote  efficiency. If the number of currencies used in international transactions is denoted as N, then there are N(N-1)/2 possible exchange rates. The larger the value of N, the larger is the number of exchange rates to be determined. Therefore, it makes sense to use a few currencies  for international  transactions  and  then  infer  the  cross  rates from existing relationships  among trading currencies of the world. The Wall Street Journal publishes a table of cross rates daily.

The foreign exchange market is an integrated market that  is made up of a network  of large commercial banks in the major financial centers of the world. The existence of modern communication technology means that information  is quickly transmitted in the market. Thus, all the markets are linked together. This is the reason why quoted  exchange rates are consistent. For example, the USD/GBP rate quoted in New York is not significantly different from the USD/GBP rate quoted by a London bank.


  1. Ball and W. McCulloch,  International Business (Irwin McGraw-Hill, 1999);
  2. Bekaert and R. J. Hodrick, International Financial Management (Pearson Prentice-Hall, 2009);
  3. Livingston, Money and  Capital Markets (Kolb, 1993);
  4. Melvin, International Money & Finance (Pearson  Addison-Wesley,  2004);
  5. J. O’Brien, International Financial Economics (Oxford, 2005).

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