Cross Rates: Meaning, Calculation, Importance and Challenges

In the preceding chapters, we learned about exchange rates and various other aspects of currency markets. We will now touch upon another important aspect, i.e. cross rates. No mention of international finance is complete without a reference to the foreign exchange market, which assumes a prime spot. Currencies are exchanged here, and exchange rates, i.e. the relative values of these currencies against each other, are determined. Apart from being the largest in terms of trading volume, the forex market is also crucial for enabling global trade, investment, and economics. 

Within this market, benchmark currencies exist, such as the US dollar, which serves as the primary reserve currency globally. It is often used as a baseline to price goods in international trade. Additionally, it is also used to benchmark other currencies, and as the go-to currency in times of economic uncertainty.

The dominance of the US dollar simplifies many transactions. However, there are situations when the dollar itself is not directly involved in a trade. This introduces a layer of dependency and potential inefficiency.

Enter cross rates – a vital financial tool that we will try to understand through this chapter.

Definition of Cross Rates

A cross rate is defined as the exchange rate between two currencies that is calculated independently of the domestic currency of the country where the rate is published. This calculation is typically performed by referencing each currency's exchange rate against a common third currency, which is usually a major global currency like the US dollar or the euro. The primary purpose of a cross rate is to enable direct currency conversion between two foreign currencies without converting them into a local currency first.

To illustrate the concept of cross rates, consider the following examples:

Euro to Japanese Yen in the United States: Suppose a trader in the U.S. wants to convert euros to Japanese yen. Instead of converting euros to U.S. dollars and then from U.S. dollars to yen, the cross rate directly relates euros to yen. If the exchange rate is 1 euro = 1.10 U.S. dollars and 1 U.S. dollar = 110 yen, the cross-rate calculation would show that 1 euro equals 121 yen (1.10 x 110).

British Pound to Canadian Dollar in Australia: An Australian business needs to convert British pounds to Canadian dollars. Using the cross rate, they avoid using the Australian dollar as a bridge. If the current rates are 1 British pound = 1.75 Australian dollars and 1 Canadian dollar = 1.10 Australian dollars, the cross rate would imply that 1 British pound is equivalent to approximately 1.59 Canadian dollars (1.75 / 1.10).

These examples demonstrate how cross rates simplify transactions by eliminating unnecessary steps and potential costs associated with converting through an intermediary currency. This helps enhance efficiency in international financial operations.

Calculating Cross Rates

The below steps can be followed to calculate cross rates between two currencies using their exchange rates against a common third currency:

Identify the Exchange Rates: Determine the current exchange rates of the two currencies (Currency A and Currency B) against a common third currency (Currency C).

Select the Base and Quote Currencies: Decide which currency you want as the base (the one-unit representation) and which as the quote (the equivalent value in another currency).

Calculation Formula: Use the formula: Cross Rate = (Rate of Currency A against Currency C) / (Rate of Currency B against Currency C).

Perform the Calculation: Apply the formula to find the direct exchange rate between Currency A and Currency B.

Let us understand this with an example

Suppose you want to convert euros (EUR) to Japanese yen (JPY) using their exchange rates against the U.S. dollar (USD). If the exchange rate for EUR/USD is 1.13 (1 euro = 1.13 USD) and the exchange rate for USD/JPY is 110 (1 USD = 110 yen), the cross rate would be calculated as follows:

Cross Rate Calculation: (EUR/USD) / (USD/JPY) = 1.13 / (1/110) = 1.13 * 110 = 124.3

This means that 1 euro is equivalent to approximately 124.3 Japanese yen, according to the cross rate calculated using the U.S. dollar as the intermediary.

Significance of Cross Rates

Cross rates are regarded as significant in currency markets. Here’s why:

Importance in global trade: Cross rates play a crucial role in smoothing international transactions by facilitating direct currency conversions. This avoids the need for double conversions and associated costs when two trading partners do not use the same currency nor involve a major intermediary like the USD. For example, a European company can directly pay a Japanese supplier in yen using euros, streamlining transactions and potentially securing better exchange rates.

Application in financial markets: Cross rates are essential for forex trading and international investing. They enable traders and investors to speculate on currency movements and hedge against currency risk without involving a third currency. This can reduce transaction costs and improve the efficiency of trading operations, making markets more liquid and pricing more competitive.

Business operations: For businesses operating across multiple countries, cross rates reduce the layers of currency conversion, minimising transaction fees and currency exchange risks. This is particularly beneficial for multinational corporations managing cash flows and capital allocation between different subsidiaries. It simplifies accounting and financial management by allowing companies to operate more fluidly across diverse currency environments, thereby enhancing operational efficiency and reducing financial overhead.

Challenges in Cross-Rate Calculations

Just like all other aspects of finance, cross rates are not without challenges. Below are some of them:

Market Volatility: Fluctuations in the forex market can significantly impact the stability and accuracy of cross rates. Because these rates are derived from the exchange rates of two currencies against a common third currency, any volatility in these base rates directly affects the cross rate. For instance, sudden economic events or changes in monetary policy can cause rapid shifts in currency values, making the previously calculated cross rates obsolete or inaccurate within a short period. This volatility can pose a challenge for businesses and traders who rely on stable exchange rates for budgeting, pricing, and hedging against risks.

Lack of Uniformity: Different financial institutions may offer varying exchange rates for the same currency pairs based on their own supply, demand, and operational strategies. This discrepancy can lead to a lack of uniformity in cross rates and complicate transactions that involve large sums or require precise calculations. For example, two banks in the same country might quote slightly different cross rates for the EUR/JPY pair, leading to inconsistencies that can affect pricing, trading, and arbitrage opportunities in the market.

Regulatory and Operational Challenges: The use of cross rates is further complicated by the diverse regulatory environments and operational limitations in different countries. Regulations regarding currency conversions, fund transfers, and foreign exchange trades can vary widely, affecting how cross rates are calculated and used. Additionally, operational challenges such as differing time zones, transaction cut-off times, and local banking practices can delay or disrupt the efficient use of cross rates, particularly for real-time or near-real-time financial activities.

Wrapping Up

Cross rates are essential in global finance as they simplify transactions in international trade, enhance financial market efficiency, and reduce currency conversion costs for multinational businesses. However, the calculation and use of cross rates can be influenced by certain limitations.

Looking ahead, the role and utility of cross rates are likely to evolve with global economic trends and technological advancements. Innovations in financial technology, such as blockchain and real-time processing systems, could improve the accuracy and immediacy of cross-rate calculations and make them more reliable and widely accessible. As global markets become increasingly interconnected and digital platforms dominate financial transactions, the strategic importance of cross rates is set to grow. This is because it can facilitate international currency flows and offer both opportunities and challenges to all market participants.

This brings us to the end of this module about currency markets.