Calculating Currency Cross Rates When Given Two Spot Exchange Quotes Involving Three Currencies
A currency dealer located in a particular country will usually provide a set of exchange rate quotations between the country's currency and various foreign currencies. The cross-rate between two currencies not explicitly quoted is obtained by getting quotes for each currency in terms of the exchange rate with a third nation's currency. Suppose you are told that the exchange rate of the U.S. dollar per euro is 1.2440 and that the exchange rate for U.S. dollar per British pound is 1.8146. The euro-to-pound cross rate can be calculated as the euro-to-dollar rate multiplied by the dollar-to-pound rate, which is equal to (1/1.2440) × 1.8146 = 1.4587, or ¬1.4587 per British pound. Note that this result is an indirect quote from the viewpoint of a British entity, or a direct quote from the viewpoint of a business whose domestic currency is the euro.
In general, in calculating cross-rates, bid and ask prices will need to be dealt with.
This makes the calculation only slightly more difficult. The following equations should be kept in mind:
(FCa / FCb)ask = (FCa / DC)ask ×(DC/FCb)ask
(FCa / FCb)bid = (FCa / DC)bid ×(DC/FCb)bid
Where FCa and FCb are the two foreign currencies and DC is the domestic currency.
Similar equations are used when calculating FCb to FCa exchange rates.
Example: Currency Cross Rates and Ask Quotations
Verifications can be made by checking that (FCb/FCa)ask is equal to the reciprocal of (FCa/FCb)bid, and by checking that (FCb/FCa)bid is equal to the reciprocal of (FCa/FCb)ask.
Suppose you are given the following bid/ask quotations for two foreign currencies against the domestic currency, the U.S. dollar:
¬ / $ 0.9002 0.9023
¥ / $ 109.38 109.40
We want to calculate what the ¥ / ¬ bid and ask quotations will be.
The ¥ / ¬ bid price will be the number of yen the dealer is willing to pay in order to buy one euro. This transaction would be the equivalent of selling yen to purchase dollars (at the bid rate of 109.38), and simultaneously reselling the dollars to purchase euros (at the ask rate of 0.9023). The bid ¥ / ¬ would be calculated as 109.38/0.9023 = 121.22.
The ¥ / ¬ ask price would be the number of yen the dealer wants to receive in exchange for selling one euro. This transaction would be the equivalent of buying yen with dollars (at the 109.40 ask rate) and at the same time buying those dollars with euros, at the 0.9002 bid rate. The transaction could be expressed mathematically as:
Ask ¥ / ¬ = 109.40 / 0.9002 = 121.53
So the resulting dealer quotation would be:
¥ / ¬ = 121.22 - 121.53
You can count on getting questions like these on the exam, so make sure that you are comfortable with these types of questions.
Spot vs Forward Markets Within Foreign Exchange
There are two types of markets for setting currency exchange rates:
- The Spot Currency Exchange Market - This market involves trades of currencies for immediate delivery. Settlement usually occurs two days after the trade date. Participants in this market want to convert to the other currency relatively quickly. Transactions in the spot market are often used for investments, or to settle commercial purchases of goods.
- The Forward Currency Exchange Market - This market involves contracts for currency exchange in which settlement will take place more than two days after the trade date. While settlement dates are negotiable, standard foreign currency forward contracts usually settle 30, 90 or 180 days after the trade date. If a dealer quotes the 90-day ¥ / $ exchange rate at 109.80-109.83, that means the dealer is willing to commit today to buying dollars for 109.80 yen in 90 days, or to selling dollars at 109.83 yen per dollar 90 days from today.
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