A Beginner's Guide to Exchange Rates and the Foreign Exchange Market

Like most other rates in economics, the exchange rate is essentially a price and can be analyzed in the same way we would a price. Take a typical supermarket price, say lemons are selling at the price of 3 for a dollar or 33 cents each. Then we can think of the dollar-to-lemon exchange rate as being 3 lemons because if we give up one dollar, we can get three lemons in return. Similarly, the lemon-to-dollar exchange rate is 1/3 of a dollar or 33 cents, because if you sell a lemon, you will get 33 cents in return.
So when we speak of an X-to-Y exchange rate of Z, this means that if we give up 1 unit of X, we get Z units of Y in return. If we want to know the Y-to-X exchange rate, we calculate it using the simple exchange rate formula:

Y-to-X exchange rate = 1 / X-to-Y exchange rate

Of course, the exchange rates we read in the paper or hear on radio or TV are not prices for X and Y or for oranges and lemons. Instead they're relative prices for different currencies, but they work in the same fashion. On February 26, 2003 the U.S.-to-Japan exchange rate was 117 yen, so this means that you can purchase 117 Japanese yen in exchange for 1 U.S. dollar. To figure out how many U.S. dollars you can get for 1 Japanese yen, we can just use the formula:

Japan-to-U.S. exchange rate = 1 / U.S.-to-Japan exchange rate

Japan-to-U.S. exchange rate = 1 / 117 = .00854

So this tells us that one Japanese yen is worth .00854 U.S. dollars, which is less than a penny.

Similarly if the Canadian dollar is worth .67 U.S. dollars, we have a Canada-to-U.S exchange rate of .67. If we want to know how many Canadian dollars we can buy with 1 U.S. dollar, we use the formula:

U.S.-to-Canada exchange rate = 1/Canada-to-U.S. Exchange rate

U.S.-to-Canada exchange rate = 1/0.67 = 1.4925

So one U.S. dollar can get us $1.49 in Canadian funds.

To see why these relationships must hold, we'll look at the wonderful world of arbitrage.