Cross Rate

A cross rate is a foreign exchange rate for transactions between two currencies valued against a third. The two currencies that make up the currency pair are mostly the home currencies of the parties involved in the transaction. The third one is usually a popular international currency like the US dollar.

These are used to facilitate cross-border payments with ease. It quotes the exchange price between two currencies relative to a third one. There are two types of quotations – direct and indirect – based on which the exchange and transactions are carried out.

• Cross rates refer to quoting the foreign exchange rates between two currencies against a third one. The third currency is likely to be an internationally used currency like the US dollar.
• While there is no standard formula, the currency pair is individually quoted against the third currency to arrive at the pair's exchange rate.
• There are two methods of calculation – direct and indirect quotes. The quote currency is estimated against the base currency in a direct quote. In the indirect quote, the converse is done.

Cross rate of exchange is a slightly tricky concept. However, there are a few prerequisites to understand before moving on to the topic. First, let us understand a currency pair. It refers to two currencies, with the value of one being quoted against the other. For example, EUR/ JPY is a currency pair. Here, EUR is the base currency, and JPY is the quote currency. Here, it is possible to compute the value of EUR against a JPY.

In currency cross rates, there is a third currency. It is usually a primary international currency like the US dollar. So, considering the example of EUR/JPY again, both these currencies are quoted against the US dollar to arrive at their exchange rate. This is what the mathematical expression looks like:

The significance of the concept of cross rates lies in the common occurrence of foreign exchange transactions in a globalized world. With numerous currencies and their fluctuating values, having a standardized measure is crucial. Quoting the value of these currencies against a single international currency simplifies transactions.

Consider a scenario where a buyer from Canada and a seller from Australia need to engage in a transaction. It is unlikely that both of them will have US dollars readily available. In such situations, the cross rate of exchange provides a practical solution for them to exchange value without requiring US dollars.

While there is no standardized cross rate formula, let us delve into the conversion process.

Consider the currency pair X and Y, with the base currency as P. Here's a step-by-step conversion:

Step 1: Determine the exchange rate of X against P. It tells you how much of X is equivalent to one unit of P. 

Step 2: Calculate the exchange rate of P against Y. This specifies how much of P is equal to one unit of Y.

These are the underlying logic of the concept, and there are two primary classifications:

#1 - Direct quote

A direct quote indicates how much of the quote currency is required to purchase one unit of the base currency. For example, let us consider EUR/JPY, where the base currency is EUR.

#2 - Indirect quote

An indirect quote specifies how much of the base currency is needed to acquire one unit of the quote currency. Using JPY/EUR as an example, where the base currency is JPY.

Let us discuss a few examples.

Example #1

Let us compare EUR/ JPY against USD data as of February 07, 2023.

EUR/ JPY = 140.61

EUR/ USD = 1.07

USD/ JPY = 131.05

EUR/ JPY = EUR/ USD x USD/ JPY

= 1.07 x 131.05

= 140.22

The difference of 0.39 is due to the bid-ask spreads in the forex market, which is yet to be considered here owing to the complexity of the calculations. That is why it is better to use cross rate calculators.

Example #2

The US dollar far outweighed most currencies in 2022. The dollar is considered a safe haven for investors during turbulent times and is a good investment option during inflation and recession. Adding to this, the Federal Reserve's move to hike the interest rates to combat inflation has resulted in attractive return on investment. 

While these developments favored American tourists and buyers, the rest of the world faced a different reality. The US dollar's strength relative to other major currencies like the euro, pound, Japanese yen, and Canadian dollar had significant implications for international transactions.

The impact on parties using different currencies in international trade largely hinged on the performance of their respective currencies against the U.S. dollar. Notably, the euro depreciated by approximately 8.8% against the dollar. It demonstrates how fluctuations in currency values can influence the competitive positions of various economies and the outcomes of cross-border transactions.

This has been a guide to what is Cross Rate. Here, we explain it in detail along with how to calculate it and its examples. You can learn more about it from the following articles –

• Fixed Exchange Rate
• Floating Exchange Rate
• Exchange Rate Mechanism