If you’ve spent any time perusing the foreign exchange market, you’ve likely already encountered the concepts of cross rates and currency pairs. The foreign exchange market (also known as the forex or FX market) is essentially a place where different national currencies are exchanged for one another. But what establishes the value of one currency relative to another?
The answer to this question generally involves the U.S. dollar (USD), which serves as a common reference point against which other currencies are priced. The most popular and most traded currency pairs in the forex marketplace involve USD as either the base currency (the first currency in the quotation) or the quote currency (the second currency in the quotation). The U.S. Congressional Research Service estimates that the U.S. dollar is involved in nearly 90% of all transactions in foreign exchange markets.
But this is not always the case. In some cases, you may need to find an exchange rate between two currencies, neither of which is USD. This is generally referred to as the cross rate between two currencies.
In this article, we’ll review the concepts of cross rates, currency pairs, and currency triangulation. We’ll also review how to calculate the cross rate between two currencies using exchange rates based on the USD.
What is a cross rate?
A cross rate is generally defined as the exchange rate between two currencies in which neither of the currencies is the U.S. dollar. For example, the exchange rate between the Australian dollar (AUD) and the Swiss franc (CHF) would be considered a cross rate.
Currency cross rates such as the example above are actually a bit unusual, and only a few important currency pairs in the forex marketplace do not involve the USD. The EUR/GBP exchange rate, which pairs the euro and the British pound, is one example that’s significant due to the geographic and economic links between Europe and the U.K. Another commonly referenced cross rate is the exchange rate between the euro and the Japanese yen (JPY).
We should make one important distinction before moving on. While cross rates are almost always considered to be an exchange of currencies in which neither is the U.S. dollar, one could also define cross rate more broadly. So long as neither of the two currencies being exchanged is the official national currency of the country where the exchange quote is given, the exchange can be considered a cross rate.
Why do cross rates matter?
To understand the significance of cross rates, a historical perspective is helpful.
Years ago, if you wanted to convert one non-USD currency to another non-USD currency, you first had to convert it into USD. Then, you had to convert your USDs into the third currency. Cross rates allow traders to streamline this process and easily derive an exchange rate between two currencies using the USD as a reference point. Essentially, you can go straight from the currency you have to the currency you want to exchange it for—without an intermediary transaction in USD.
Cross rates aren’t just a way of making it easier to calculate the exchange rate between currencies. Understanding how cross rates work and the process of cross-currency triangulation (i.e. converting one currency to another via a third currency) can allow some traders and investors exploit arbitrage opportunities that arise when small discrepancies arise across different cross-currency pairs.
We’ll discuss cross-currency triangulation a bit more later in this article. For now, let’s take a deeper look at how currency pairs work and how to calculate a cross rate between two currencies.
Breaking down currency pairs
In foreign exchange, a currency pair is a price quote that includes two different national currencies. Currency pairs exist so that the value of one currency can be quoted against another. There are two components to a currency pair—the base currency and the quote currency:
- The base currency is the first currency listed in the currency pair. It typically represents a single unit of currency (e.g. 1 USD or 1 EUR).
- The quote currency is the second currency listed in the currency pair. It represents how much of the second currency is needed to purchase a single unit of the base currency.
How currency pairs are written
Currency pairs are typically written in a simple format that includes a slash between the base currency and the quote currency. For example: the EUR/USD currency pair tells us how many U.S. dollars are required to purchase one euro. If we were to write EUR/USD = 1.25, this would mean that 1.25 USD is needed to purchase 1 EUR.
In the above example, EUR is the base currency and USD is the quote currency. While EUR/USD is among the most heavily traded forex pairs in the world, it’s worth noting that it is atypical, as the USD is typically the base currency in its currency pairs.
Bid prices, ask prices, and the bid-ask spread
There is always a buyer and a seller in currency pairs. Because of this, a currency pair quote is based on a bid price and ask price. To understand how to calculate the cross rate between two currencies—and why this rate may differ from the actual exchange rate—it’s helpful to first know these concepts:
- The bid price is the highest price at which a potential buyer (e.g. a foreign exchange broker) is willing to buy a currency
- The ask price is the lowest price at which a potential seller (e.g. a foreign exchange broker) is willing to sell a currency
- The bid-ask spread is the difference between the bid price and the ask price
With these concepts in mind, let’s now put it all together and look at how to calculate the cross rate between two currencies.
How to calculate the cross rate between two currencies
To calculate the cross rate between two different currencies, you’ll need to know the bid prices for both of the currencies involved when paired with the USD. It’s easiest when these bid prices are listed in the order of your desired transaction.
Say you want to know the cross rate for the EUR/AUD currency pair. In order to calculate this, you would follow a three-step process:
- Find the bid price for the EUR/USD currency pair.
- Multiply this by the bid price for the USD/AUD currency pair.
- Arrive at the cross rate for EUR/AUD.
Let’s say the bid price for EUR/USD is 1.25 USD and the bid price for USD/AUD is 1.1 AUD. Following the process outlined above, we could calculate the cross rate for EUR/AUD by multiplying 1.25 x 1.1. In this case, the cross rate for EUR/AUD would be 1.375.
Another way to think about the cross rate is that it is the ratio between the two currency pairs when USD is used as the quote currency. For example, the EUR/AUD cross rate should be equal to EUR/USD divided by AUD/USD. We’ll use the above example to illustrate this:
- EUR/USD = 1.25
- AUD/USD = 0.909 (1 USD divided by 1.1 AUD)
- 1.25 divided by 0.909 = 1.375
The above example uses what we might call a “non-symmetrical pairing,” because USD is the quote currency in both currency pairs.
Cross-currency triangulation and arbitrage opportunities
If you perform the above calculation and find that the actual exchange rate differs from the cross rate you arrive at, there may be a couple of reasons for this. One reason is that some small transaction cost may be included in the exchange rate. But an exchange rate may also differ from the cross rate you calculate due to discrepancies in the bid-ask spreads across different currency pairs.
Some traders and investors use cross-currency triangulation to profit from these discrepancies. In other words, they sniff out mispriced exchange rates and use these as opportunities to buy the currency that’s priced too low and sell the currency that’s priced too high. These transactions should ultimately eliminate the discrepancies by pushing the low price higher and the high price lower—but not before the traders are able to benefit from the arbitrage opportunity.
If you’re interested in learning more on exchange rates and how they’re calculated using the bid-ask spread for a particular currency, check out our article on the mid-market exchange rate (otherwise known as the interbank rate).
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Understanding exchange rates and how they work can make a huge difference for an international business that works across borders and currencies. Knowing the basics of how exchange rates—including cross rates—are calculated can save you from falling victim to unfavorable exchange rates.
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