Currency Exchanges

As trade expanded over wider regions, merchants from different sovereign regions began to interact. The importance of valuing currencies used by other sovereign entities emerged as an essential part of international trade. Mayer Amschel Rothschild took advantage of this kind of knowledge in the 18th Century to found one of the worlds most successful banking families. Today, exchange valuations are well understood and the market for currencies is one of the largest and most efficient on earth.
Currencies can be priced in two ways. You can specify how much of your currency is needed to buy one unit of a foreign currency. This approach is known as a price quote or a direct quote. For example, to an American a price quote for British pounds would be the number of dollars needed to buy one pound. Second, you can specify how many units of a foreign currency one unit of your own currency will buy. This approach is known as a volume quote or an indirect quote. For example, to an American an indirect quote for British pounds would be the number of pounds that one dollar would buy.
It should be obvious that a simple relationship exists between direct and indirect quotes. One is simply the inverse of the other. For example 1/direct quote = indirect quote.
Quotes given as either direct or indirect quotes are commonly called exchange rates.

Considering three currencies

Whenever more than two currencies are available and exchangeable for each other a necessary connection emerges. If exchange rates for two currencies are both known in a common currency, the necessary exchange rate between those two currencies known as the cross rate is also knowable. For example, if you know how many dollars are needed to buy one pound and you know how many dollars are needed to buy one euro, you can calculate the number of euros needed to buy one pound as follows:

(1)
\begin{align} \frac{euros}{pound}=\frac{\frac{dollars}{pound}}{\frac{dollars}{euro}} \end{align}

$\copyright$ Arlyn R. Rubash 2011

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