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Exchange Rates

What to Use as the Base?

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[Q:] I want to be able to read exchange rate charts. I read "A Beginner's Guide to Exchange Rates and the Foreign Exchange Market" and I understand the lemons and oranges, but I am missing the base.

If I look at a chart produced by someone in the United States and the index number next to US$ is 1.69 and the index value of the Euro is 1.89, am I saying that 1.89 Euros has the same value as 1.69 US$?

Or is there a base value that says $1.00 of X is equal to 1.69 US$ and 1.89 Euros?

I am in an economics class, and I cannot seem to get this concept down to satisfy my instructor.

[A:] Thanks for your question!

By charts, I'm guessing you mean an exchange rate chart like the one in my article "The Canadian Exchange Rate". Foreign exchange charts typically look like the one produced by the Pacific Exchange Rate Service. You can get today's current exchange rate chart at http://pacific.commerce.ubc.ca/xr/today.html. I've recreated the first five entries of the exchange rate chart for September 10, 2003 on the bottom of this article.

The first two columns of the chart contain the country code, country, and country name for five currencies. The third column has the title Units/USD and compares each of the five currencies to the US Dollar. The base of comparison for these exchange rates is the U.S. Dollar. The base is normally the currency given after the "/". According to this chart, 1 U.S. Dollar is worth 1.5205 Australian Dollars and similarly 1 U.S. Dollar is worth 2.9149 Brazilian Real.

The fourth column has the column USD/Units. Under this category each currency listed in column 1 is used as the base. So the figure "0.3396" has the Argentinean Peso as the base and indicates that 1 Argentinean Peso is worth a little less than 34 U.S. cents. The Canadian Dollar is worth 73 U.S. cents as indicated by the figure "0.7321".

We saw in "A Beginner's Guide to Exchange Rates" that exchange rates must have the following property:

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

The American-to-Canadian exchange rate is 1.3659 as 1 U.S. Dollar can be exchanged for $1.3659 Canadian (so here the base is the U.S. Dollar). Our relationship implies that 1 Canadian Dollar must be worth (1 / 1.3659) U.S. Dollars. Using our calcuator we find that (1/1.3659) = 0.7321, so the Canadian-to-American exchange rate is 0.7321 which is the same as the value in our chart. So the relationship does indeed hold.

Columns 5 and 6 are the same as columns 3 and 4, except now column 5 uses the Canadian Dollar as a base, and column 6 indicates how many Canadian Dollars you would get for 1 unit of each currency. We should not be surprised to see that 1 Canadian Dollar is worth 1 Canadian Dollar, as shown by the number "1.0000" on the bottom right corner of the chart.

From this chart, we can also see if there are any opportunities for arbitrage. If we exchange 1 American Dollar we can get 1.3659 Canadian. From the Units/CAD column, we see that we can exchange 1 Canadian dollar for 2.1561 Argentinean Real. Instead we'll exchange our 1.3659 Canadian for Argentinean currency and receive 2.9450 Argentinean Real (1.3659*2.1561 = 2.9450). If we then turn around and exchange our 2.9450 Argentinean Real for U.S. Dollars at the rate of .3396, we will receive 1 U.S. Dollar in return (2.9450*0.3396 = 1). Since we started with 1 U.S. Dollar, we have not made any money from this currency cycle so there are no arbitrage profits.

Regarding your last question, the base of comparison is generally dictated by whatever country you are in, so Americans use the U.S. Dollar as a base, and Canadians generally use the Canadian Dollar. There are several currencies which are more valuable than the U.S. Dollar, including the Euro, the Bahamian Dinar, the Latvian Lat, and the British Pound. I hope this answers your questions on exchange rates.

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Today's Exchange Rates

CodeCountryUnits/USDUSD/UnitUnits/CADCAD/Unit
ARP Argentina (Peso) 2.9450 0.3396 2.1561 0.4638
AUD Australia (Dollar) 1.5205 0.6577 1.1132 0.8983
BSD Bahamas (Dollar) 1.0000 1.0000 0.7321 1.3659
BRL Brazil (Real) 2.9149 0.3431 2.1340 0.4686
CAD Canada (Dollar) 1.3659 0.7321 1.0000 1.0000

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