Cross rate calculation explained
One is generally aware about the foreign exchange rates in the currency markets. However, at times you might come across the term cross currency rates. The forex markets are comprised of the major currency pairs. A major currency pair is one where the USD is one of the currencies that is mentioned in the exchange rate.
The calculation for the cross currencies is however not as straightforward compared to other exchange rates. The term cross currency refers to currency pairs that does not involve the U.S. dollar.
A cross currency exchange rate therefore is where none of the two currencies are the official currencies of the country where the exchange rate is quoted.
In simple terms, when you see an exchange rate where there is no U.S. dollar, it refers to the cross currency rate.
An example of a cross currency rate is the EUR/GBP or the GBP/JPY.
In this article, we will give you details on how the cross rate calculation works. Most of the financial websites and charting platforms today automatically give you the cross currency exchange rates.
However, if you are speculating in the forex markets, then it is essential to understand how the cross rate calculation works and you can have a deeper understanding of what happens when you buy or sell a cross currency pair.
However, before we get into the details of the cross rates, it is important to lay the groundwork for the foreign exchange currency conventions.
It is essential to understand the conventions of the foreign exchange markets and thus gain an understanding of the cross currency rates as well. This is because, the same logic applies to other currency derivates such as FX forwards and non-deliverable forwards and options.
Foreign exchange currency convention and format
In the currency markets, the general convention is that you will find a currency pair. As a result, the exchange rate that you see is relative to one of the currencies.
A typical exchange rate is quoted as a currency pair.
The first currency is known as the base currency while the second currency is known as the quote currency.
For example, if you see something like EURUSD or USDJPY, this simply means that the euro is the base currency and the USD is the quote currency for the EURUSD. Similarly, the USD is the base currency and the JPY is the quote currency.
As the name implies, the rates you see in the foreign exchange markets belong to the quote currency.
Thus, when you see an exchange rate of EUR/USD = 1.1300, it means that 1 EURO of the base currency is equal to 1.13 of the U.S. dollars which is the quote currency.
The chart below shows a screengrab from the CNBC.com website. You can find that most financial news channels and websites will follow a similar convention.
Figure 1: Example of exchange rates quoted on CNBC.com
In figure 1, you can see that the USD/JPY rate quoted is 109.73. What this means is that 1 USD is equal to 109.73 Yen. You can see similar rates for other currencies. For example, the USD/SGD currency pair shows a rate of 1.3524. This means that 1 USD is equal to 1.3524 SGD.
How is FX rate calculated?
There are many types of exchange rates in the market today. Typically, the FX rates are classified into fixed, floating and pegged exchange rates. With the fixed exchange rates, the currency rates are either fixed to the U.S. dollar or any other currency.
Pegged exchange rates are where the currency is allowed to fluctuate within a certain band.
The floating exchange rate is of course the most widely used exchange rate especially in developing economies. The floating exchange rates are set by the market forces, set by the supply and demand forces.
With floating exchange rates, the currency exchange rates are influenced by the supply and demand factors and by the markets.
Economies that use the floating exchange rates have typical characteristics such as having a stable government, an advanced economy and hold large forex reserves. This allows such economies to withstand any fluctuations such as appreciation or depreciation of the exchange rates.
However, regardless of whether an exchange rate is fixed or floating, the respective economies can value their currencies. Thus, you can often see that some currencies are more valuable than the U.S. dollar while some currencies are kept artificially low.
At the end of the day, it is usually the market forces that set the exchange rates that you see. Most of the floating currencies also have good demand in the market and are widely in circulation. For example, the U.S. dollar enjoys the status of the world’s reserve currency.
The euro also comes in at a close second in popularity right after the U.S. dollar.
Investors set the exchange rate based on a number of factors such as the GDP, unemployment, the central bank’s interest rates and the balance of trade. When an exchange rate is floating it more or less reflects the fair value of the currency.
What are inverse rates and how to calculate them?
The general currency convention is that the USD can either be the base currency or the quote currency. The most common convention is that the USD is often the quote currency. Or in other words, for most exchange rates, the rate you see is quoted in U.S. dollars.
If you look back to figure 1, you can see that for currencies such as AUD and NZD, the quote currency is the USD. However, if you look at USDJPY or USDSGD, the USD is the base currency. Be that as it may, you can also calculate the inverse currency rate.
For example, using simple math, you can get the inverse rate.
If you want to get the inverse rate of AUDUSD, which is USDAUD, you simply divide the exchange rate by 1.
Therefore, if AUD/USD is quoted as 0.7163, then to get the USD/AUD exchange rate you can divide the rate by one.
Thus, 1/0.7163 = 1.3960. This rate is nothing but the USD quoted in Australian dollar. Thus USD/AUD rate is 1.3960, while the AUD/USD rate is 0.7163.
Understanding the inverse rates is important when you are calculating the cross rates.
Cross currency rates
Now that we have an understanding of how exchange rates are set and the general convention used in quoting the forex exchange rates, let’s take a deeper look into the cross currency rates and how the exchange rate is set for a cross currency.
As a general rule of thumb, a cross currency is where the U.S. dollar is neither the base or the quote currency.
For example, EUR/JPY is a cross currency rate and so is the EUR/GBP. This is because as you can see there is no U.S. dollar mentioned in the cross currency rates.
Another definition of the cross currency rate is when the currencies being mentioned do not belong to the domicile. Therefore, a finance journalist in Japan will refer to EUR/GBP as the cross currency rate. This is because neither the euro or the British pound are the official currencies in Japan.
However, the widely accepted convention is that when there is a currency pair that does not include the USD, it is called a cross currency rate.
Within the cross currency rates, there are some widely traded and popular cross currency rates.
Some examples of cross currencies include:
How to calculate cross currency rates?
The calculation for the cross currency rates requires a slightly different approach. Although the USD is not used as the cross currency rate, it is still essential when calculating such rates.
Let’s take an example
If you want to calculate the cross currency rate for EUR/GBP, then this means that you need to take two exchange rates.
EUR/USD and GBP/USD
However, because both the quote currencies are in USD, one of the exchange rate needs to be inversed.
Let’s take a look at the following quotes.
Figure 2: Calculating cross currency rates
In figure 2, we have the EUR/USD, GBP/USD and the EUR/GBP rates. You can see that the EUR/GBP is the cross currency rate.
However, let’s explain how this cross currency rate is derived.
Firstly, take the EUR/USD and the GBP/USD rates. But you can see that the exchange rates for these two currency pairs shows the USD as the quote currency.
Therefore, one of these currencies need to be inversed.
We will inverse the GBP/USD currency rate. The current GBP/USD rate is 1.295. So, the inverse of GBP/USD, which is USD/GBP is 1/1.295 = 0.7722.
Thus, we now have EUR/USD which is 1.1394 and USD/GBP which is 0.7722
Now you simply multiply both the rates. EUR/USD x USD/GBP = 1.1394x 0.7722 = 0.8799 (rounded).
Using the above method, you can also derive other cross currency rates. The table below gives a quick overview on how the cross currency rates are calculated.
Figure 3: Cross currency rate calculation
From the above chart, you can see how the EUR/JPY and the GBP/JPY rates have been calculated. Here, the calculation is straightforward. We simply take the EUR/USD rate and multiply it by the USD/JPY rate to get the EUR/JPY rate.
Likewise, to get the GBP/JPY rate, we take the GBP/USD rate and multiply it with the USD/JPY rate.
Notice that for EUR/JPY and GBP/JPY we did not use any inverse rates. This is because in the EUR/USD or GBP/USD, the USD is the quote currency. But with USD/JPY the USD is the base currency. Thus, we did not have to use inverse rates.
But in the case of EUR/GBP, we had to use the inverse rate of GBP/USD because the USD was the quote currency in both the currency pairs.
Most trading platforms now a days automatically display the cross currency rates for you.
You do not have to manually do the calculation. However, it is still important that you understand how the cross currency rates are calculated.
When you are multiplying two exchange rates or inverting one of the exchange rates, you are basically buying and selling the currency pairs
Going back to the example of EUR/JPY, you get this rate when you buy EUR/USD and buy USD/JPY. If you closely observe, when you buy EUR/USD, you are buying euros and selling the USD. Likewise, when you are buying USD/JPY, you are buying USD and selling JPY.
The USD, as you can observe in both the currency pairs are negated.
EUR/USD * USD/JPY = EUR/JPY
EUR/USD * USD/GBP = EUR/GBP where USD/GBP = 1/(GBP/USD)
GBP/USD * USD/EUR = GBP/EUR where USD/EUR = 1/(EUR/USD)
GBP/EUR = 1/(EUR/GBP)
Cross currency rates – Conclusion
To summarize, the cross currency rates are exchange rates where the USD is neither the base currency nor the quote currency. Typically, a cross currency rate is calculated by multiplying two exchange rates, where the USD is the quote currency in the first currency pair and the USD is the base currency in the second currency pair.
When you have to calculate the cross currency rate wherein the USD is the quote currency in both the currency pairs, you can simple invert the second currency pair to get the correct cross currency rate.
In general terms, cross currency rates also imply quoting of exchange rates that are not the official currencies of the country. Therefore, a EUR/GBP would be a cross currency rate if it was quoted by someone in the United States. At the same time, the EUR/GBP would not be a cross currency if it was quoted from the United Kingdom or in the Eurozone.
Now a days, with the advent of electronic trading platforms, the calculations for the cross currency rates are done automatically. Traders do not have to spend too much time in having to calculate the cross currency rates manually.
However, it does help to understand how the cross currency rates are derived so that whether you are a trader or merely exchanging cross currencies, you can understand how the rates are derived.
Cross currency rate calculations are widely used in the FX derivatives markets.