Because of the importance of foreign exchange to trade and investment, businesspeople must understand how currencies are quoted in the foreign exchange market. Managers must know what financial instruments are available to help them protect the profits earned by their international business activities. They must also be aware of government restrictions that may be imposed on the convertibility of currencies and know how to work around these and other obstacles.
There are two components to every quoted exchange rate: the quoted currency and the base currency. If an exchange rate quotes the number of Japanese yen needed to buy one U.S. dollar (¥/$), the yen is the quoted currency and the dollar is the base currency. When you designate any exchange rate, the quoted currency is always the numerator and the base currency is the denominator. For example, if you were given a yen/dollar exchange rate quote of 110/1 (meaning that 110 yen are needed to buy one dollar), the numerator is 110 and the denominator is 1. We can also designate this rate as ¥ 110/$.
The numerator in a quoted exchange rate, or the currency with which another currency is to be purchased.
The denominator in a quoted exchange rate, or the currency that is to be purchased with another currency.
Direct and Indirect Rate Quotes
Table 9.1 lists exchange rates between the U.S. dollar and a number of other currencies as reported by the Wall Street Journal.5 There is one important note to make about this table. As we learned in Chapter 8, the currencies of nations participating in the single currency (euro) of the European Union are already out of circulation. To look up exchange rates for these nations, see the line reading “Euro area euro” in Table 9.1.
The second column of numbers in Table 9.1, under the heading “Currency per U.S. $,” tells us how many units of each listed currency can be purchased with one U.S. dollar. For example, find the row labeled “Japan (Yen).” The number 106.81 in the second column tells us that 106.81 Japanese yen can be bought with one U.S. dollar. We state this exchange rate as ¥ 106.81/$. Because the yen is the quoted currency, we say that this is a direct quote on the yen and an indirect quote on the dollar. This method of quoting exchange rates is called European terms because it is typically used outside the United States.
TABLE 9.1 Exchange Rates of Major Currencies
U.S. $ Equivalent
Currency per U.S. $
Czech Rep. (koruna)
Ecuador U.S. (dollar)
Euro area (euro)
Hong Kong (dollar)
New Zealand (dollar)
Peru (new sol)
Saudi Arabia (riyal)
Slovak Rep (koruna)
South Africa (rand)
South Korea (won)
Venezuela (b. fuerte)
Source: Wall Street Journal (www.wsj.com), July 9, 2008.
The first column of numbers in Table 9.1, under the heading “U.S. $ Equivalent,” tells us how many U.S. dollars it costs to buy one unit of each listed currency. The first column following the words “Japan (Yen),” tells us that it costs $0.009362 to purchase one yen (¥)—less than one U.S. cent. We state this exchange rate as $0.009362/¥. In this case, because the dollar is the quoted currency, we have a direct quote on the dollar and an indirect quote on the yen. The practice of quoting the U.S. dollar in direct terms is called U.S. terms because it is used mainly in the United States.
Whether we use a direct or an indirect quote, it is easy to find the other: simply divide the quote into the numeral 1. The following formula is used to derive a direct quote from an indirect quote: And for deriving an indirect quote from a direct quote:
And for deriving an indirect quote from a direct quote:
For example, suppose we are given an indirect quote on the U.S. dollar of ¥ 106.81/$. To find the direct quote, we simply divide ¥ 106.81 into $1:
$1 ÷ ¥ 106.81 = $0.009362/¥
Note that our solution matches the number in the first column of numbers in Table 9.1 following the words “Japan (Yen).” Conversely, to find the indirect quote, we divide the direct quote into 1. In our example, we divide $0.009362 into ¥ 1:
¥ 1 ÷ $0.009362 = ¥ 106.81/$
This solution matches the number in the second column of numbers in Table 9.1 following the words “Japan (Yen).”
Calculating Percent Change
Businesspeople and foreign exchange traders track currency values over time as measured by exchange rates because changes in currency values can benefit or harm current and future international transactions. Exchange-rate risk (foreign exchange risk) is the risk of adverse changes in exchange rates. Managers develop strategies to minimize this risk by tracking percent changes in exchange rates. For example, take PN as the exchange rate at the end of a period (the currency’s new price) and PO as the exchange rate at the beginning of that period (the currency’s old price). We now can calculate percent change in the value of a currency with the following formula:
exchange-rate risk (foreign exchange risk)
Risk of adverse changes in exchange rates.
Note: This equation yields the percent change in the base currency, not in the quoted currency.
Let’s illustrate the usefulness of this calculation with a simple example. Suppose that on February 1 of the current year, the exchange rate between the Norwegian krone (NOK) and the U.S. dollar was NOK 5/$. On March 1 of the current year, suppose the exchange rate stood at NOK 4/$. What is the change in the value of the base currency, the dollar? If we plug these numbers into our formula, we arrive at the following change in the value of the dollar:
Thus the value of the dollar has fallen 20 percent. In other words, one U.S. dollar buys 20 percent fewer Norwegian kroner on March 1 than it did on February 1.
To calculate the change in the value of the Norwegian krone, we must first calculate the indirect exchange rate on the krone. This step is necessary because we want to make the krone our base currency. Using the formula presented earlier, we obtain an exchange rate of $.20/NOK (1 ÷ NOK 5) on February 1 and an exchange rate of $.25/NOK (1 ÷ NOK 4) on March 1. Plugging these rates into our percent-change formula, we get:
Thus the value of the Norwegian krone has risen 25 percent. One Norwegian krone buys 25 percent more U.S. dollars on March 1 than it did on February 1.
How important is this difference to businesspeople and exchange traders? Consider that the typical trading unit in the foreign exchange market (called a round lot) is $5 million. Therefore, a $5 million purchase of kroner on February 1 would yield NOK 25 million. But because the dollar has lost 20 percent of its buying power by March 1, a $5 million purchase would fetch only NOK 20 million—5 million fewer kroner than a month earlier.
International transactions between two currencies other than the U.S. dollar often use the dollar as a vehicle currency. For example, a retail buyer of merchandise in the Netherlands might convert its euros (recall that the Netherlands uses the European Union currency) to U.S. dollars and then pay its Japanese supplier in U.S. dollars. The Japanese supplier may then take those U.S. dollars and convert them to Japanese yen. This process was more common years ago, when fewer currencies were freely convertible and when the United States greatly dominated world trade. Today, a Japanese supplier may want payment in euros. In this case, both the Japanese and the Dutch companies need to know the exchange rate between their respective currencies. To find this rate using their respective exchange rates with the U.S. dollar, we calculate what is called a cross rate—an exchange rate calculated using two other exchange rates.
Exchange rate calculated using two other exchange rates.
Cross rates between two currencies can be calculated using either currency’s indirect or direct exchange rates with another currency. For example, suppose we want to know the cross rate between the currencies of the Netherlands and Japan. Looking at Table 9.1 again, we see that the direct quote on the euro is € 0.6354/$. The direct quote on the Japanese yen is ¥ 106.81/$. To find the cross rate between the euro and the yen, with the yen as the base currency, we simply divide € 0.6354/$ by ¥ 106.81/$:
€ 0.6354/$ ÷ ¥ 106.81/$ = € 0.0059/¥
Thus it costs 0.0059 euros to buy 1 yen.
We can also calculate the cross rate between the euro and the yen by using the indirect quotes for each currency against the U.S. dollar. Again, we see in Table 9.1 that the indirect quote on the euro to the dollar is $1.5737/€. The indirect quote on the yen to the dollar is $0.009362/¥. To find the cross rate between the euro and the yen, again with the yen as the base currency, we divide $1.5737/€ by $0.009362/¥:
$1.5737/€ ÷ $0.009362/¥ = € 168.09/¥
We must then perform an additional step to arrive at the same answer as we did earlier. Because indirect quotes were used in our calculation, we must divide our answer into 1:
1 ÷ € 168.09/¥ = € 0.0059/¥
Again (as in our earlier solution), we see that it costs 0.0059 euros to buy 1 yen.
Table 9.2 shows the cross rates for major world currencies. When finding cross rates using direct quotes, currencies down the left-hand side represent quoted currencies; those across the top represent base currencies. Conversely, when finding cross rates using indirect quotes, currencies down the left side represent base currencies; those across the top represent quoted currencies. Look at the intersection of the “Euro” row (the quoted currency in our example) and the “Yen” column (our base currency).