What Is a Cross Rate? Definition and Examples

Cross rates are widely used in international trade, investing, and finance to help people understand the value of one currency compared to another when neither is their own country’s currency.

Understanding the Concept of a Cross Rate

A cross rate is the exchange rate between two currencies, neither of which is the domestic currency of the country where the rate is quoted. Unlike direct currency exchange rates, which involve converting a foreign currency directly to the home currency, cross rates are derived by using a common third currency as a reference point. Typically, this third currency is a major global currency like the U.S. dollar or the Euro. This method allows for determining the relative value between two foreign currencies, which is especially useful in foreign currency exchange online and international financial transactions.

How Cross Rates Are Calculated

Calculating a cross rate involves using two known currency pairs that share a common currency, usually a major currency like the U.S. dollar, and then deriving the exchange rate between the two other currencies. The process helps find the exchange rate between two foreign currencies without converting directly through the home currency.

Step-by-step Calculation:

Here is how you ought to carry out the calculation:

1. Identify the two currency pairs that involve a common base or quote currency. For example, if you want to find the EUR/JPY cross rate, you can use the USD/EUR and USD/JPY rates, where USD is the common currency.
   
2. Use the formula to calculate the cross rate. If the two pairs are quoted as:
   

• USD/EUR = A (meaning 1 USD equals A EUR),
• USD/JPY = B (meaning 1 USD equals B JPY),

then the cross rate for EUR/JPY can be calculated as:

EUR/JPY=USD/EURUSD/JPY​=AB​

This formula works because it expresses how many Japanese yen equal one euro by comparing each to the U.S. dollar.

Example:

Suppose:

• USD/EUR = 0.85 (1 USD = 0.85 EUR)
• USD/JPY = 110 (1 USD = 110 JPY)

Then,

EUR/JPY=0.85110​≈129.41

So, 1 euro is approximately equal to 129.41 Japanese yen.

When it comes to understanding indirect vs. direct quote perspectives, things are as follows:

• A direct quote shows how much domestic currency is needed to buy one unit of foreign currency (e.g., USD/JPY: how many yen per USD).
• An indirect quote shows how much foreign currency you get for one unit of domestic currency (e.g., EUR/USD: how many USD per euro).
  

Depending on which perspective is used, you may need to invert the rates before calculating the cross rate to ensure consistency. Understanding these calculations is important, especially in peer to peer currency exchange, where accurate cross rates determine fair value when exchanging currencies without involving a bank or official intermediary.

Why Cross Rates Matter in Global Finance

Cross rates play an important role in global finance by enabling traders, multinational companies, and financial institutions to compare two foreign currencies directly, without involving their home currency. This aids in making better trading and investment decisions. Additionally, cross rates can highlight pricing differences between currency pairs, creating opportunities for arbitrage. Understanding what is currency hedging also relies on recognizing these cross rate movements to manage risk effectively.

Examples of Common Cross Rate Pairs

Common cross rate pairs include EUR/JPY, GBP/CHF, and AUD/JPY. These pairs are popular because they involve major economies with strong trade relationships. Regional trading flows heavily influence which pairs are frequently used, as countries with close economic ties tend to have higher currency exchange volumes, making these cross rates important for traders and businesses operating in those areas.

Cross Rates in Practice: Real-World Applications

Cross rates play a key role in international trade contracts by helping businesses agree on prices between two foreign currencies without involving their own. In global investment portfolios, cross rates allow investors to assess the value of assets held in different currencies. They are also essential in currency hedging strategies to manage risk from exchange rate fluctuations. Additionally, cross rates help price multi-currency products or services accurately for international customers.

Benefits and Drawbacks of Using Cross Rates

Cross rates offer unique advantages and challenges that traders and businesses should carefully consider when dealing with foreign currencies.

Benefits:
Cross rates offer greater flexibility by allowing currency conversions without relying on the U.S. dollar. They enable trading directly between two foreign currencies and help identify arbitrage opportunities, which can lead to profits in the forex market.

Drawbacks:
Using cross rates requires understanding multiple exchange rates, which can be complex. They may involve higher spreads or fees, and their value can be affected by volatility in the common third-party currency used for calculation.

Cross Rates vs. Spot and Forward Rates

Spot rates are the current exchange rates used for immediate currency exchange, while forward rates are agreed-upon rates for exchanging currencies at a future date. Cross rates differ because they show the exchange rate between two foreign currencies without involving the domestic currency. Cross rates are preferred when direct spot rates are unavailable or when trading between two currencies that don’t have a widely quoted direct rate.

What Is a Cross Currency Interest Rate Swap?

In the end, it would be practical to know that a cross currency interest rate swap is a financial agreement where two parties exchange principal and interest payments in different currencies. It is related to cross rates because the swap’s value depends on the exchange rate between the two currencies involved. For example, a company borrowing in euros but earning revenue in dollars might use this swap to hedge against interest rate changes and currency risk, exchanging euro payments for dollar payments to stabilize costs.

FAQs

What is a cross rate?

It’s the exchange rate between two currencies that do not involve the domestic currency of the quoting country.

Why are cross rates useful?

They allow for currency conversions without using the domestic currency and are useful for international investors and traders.

How do you calculate a cross rate?

By using two exchange rates that share a common currency, you divide or multiply to find the cross rate between the other two.

What’s the difference between a cross rate and a spot rate?

A spot rate is the current direct exchange rate between two currencies, while a cross rate uses a third currency as a reference.

What is a cross currency interest rate swap?

It’s a financial contract where two parties exchange interest payments and principal in different currencies, often involving cross rates.

References

Convera: What is a cross rate & how to derive one

https://convera.com/blog/foreign-exchange/what-is-a-cross-rate-how-to-derive-one

Corporate Finance Institute: Cross Rates

https://corporatefinanceinstitute.com/resources/foreign-exchange/cross-rates

Investopedia: What Is a Cross Rate? Definition and Examples of Major Cross Rates

https://www.investopedia.com/terms/c/crossrate.asp