Cross currency rates

What Are Cross Currency Rates?

Cross currency rates represent the exchange rate between two currencies that are not typically quoted directly against each other in the foreign exchange market. Instead, their value is derived indirectly through a common third currency, most often the U.S. dollar (USD). This derivation is essential within the broader foreign exchange market, which is the global decentralized market for the trading of currencies. While major currencies like the Euro (EUR) and Japanese Yen (JPY) have direct quotes against the USD, obtaining an EUR/JPY rate often involves using the USD as an intermediary.⁴⁷, ⁴⁸, ⁴⁹, ⁵⁰ Cross currency rates facilitate international transactions and investments where a direct exchange pair might be less liquid or nonexistent.⁴⁵, ⁴⁶

History and Origin

The evolution of modern currency exchange, and by extension, cross currency rates, is deeply intertwined with shifts in global monetary systems. For much of the mid-20th century, the Bretton Woods system, established in 1944, pegged member countries' currencies to the U.S. dollar, which was in turn convertible to gold.⁴², ⁴³, ⁴⁴ This system aimed to ensure stability in international currency transactions following World War II.⁴⁰, ⁴¹ Under such a fixed exchange rate regime, the concept of independently floating cross currency rates as we know them today was less prevalent, as all rates were effectively linked through the dollar's gold parity.

The system began to face pressure in the late 1960s and early 1970s, with the U.S. dollar experiencing significant strain.³⁹ The eventual abandonment of the gold standard and the collapse of the Bretton Woods system in the early 1970s led to the widespread adoption of floating exchange rates.³⁷, ³⁸ This transition meant that currency values were increasingly determined by market forces rather than fixed pegs. In this new environment, the need to calculate the value of one currency against another without a direct quote became paramount, solidifying the importance of cross currency rates derived via a highly liquid third currency like the USD.

Key Takeaways

Cross currency rates are exchange rates between two currencies calculated indirectly through a common third currency, usually the U.S. dollar.³³, ³⁴, ³⁵, ³⁶
They are crucial for international trade and investment involving currency pairs that lack a direct, highly liquid market.
The calculation involves multiplying or dividing two separate exchange rates that share a common base currency or quote currency.³¹, ³²
Cross currency rates enable market participants to execute conversions efficiently and identify potential arbitrage opportunities.³⁰
Their significance grew with the shift from fixed to floating exchange rate systems in the 1970s.

Formula and Calculation

The calculation of cross currency rates depends on how the individual currency pairs are quoted. Generally, it involves using a common intermediary currency, typically the U.S. dollar.²⁸, ²⁹

There are two primary scenarios for calculating cross currency rates:

Scenario 1: Both currencies are quoted against the common third currency with the third currency as the base currency.
If you have EUR/USD (Euro per U.S. dollar) and JPY/USD (Japanese Yen per U.S. dollar) and you want to find EUR/JPY:

\text{EUR/JPY} = \frac{\text{JPY/USD}}{\text{EUR/USD}}

Alternatively, if you want JPY/EUR:

\text{JPY/EUR} = \frac{\text{EUR/USD}}{\text{JPY/USD}}

(\text{EUR/USD}): Represents how many U.S. dollars one Euro can buy (e.g., 1 EUR = 1.10 USD).
(\text{JPY/USD}): Represents how many U.S. dollars one Japanese Yen can buy (e.g., 1 JPY = 0.009 USD).

Scenario 2: One currency is the base currency against the third currency, and the other is the quote currency against the third currency.
If you have EUR/USD (Euro per U.S. dollar) and USD/JPY (U.S. dollar per Japanese Yen) and you want to find EUR/JPY:

\text{EUR/JPY} = \text{EUR/USD} \times \text{USD/JPY}

(\text{EUR/USD}): Defines the value of the Euro in terms of the U.S. dollar.
(\text{USD/JPY}): Defines the value of the U.S. dollar in terms of the Japanese Yen.²⁵, ²⁶, ²⁷

This method effectively converts the first currency into the common third currency, and then that third currency into the second target currency.²⁴

Interpreting the Cross Currency Rates

Interpreting cross currency rates involves understanding the relative strength of two non-USD currencies against each other. For example, a rising EUR/JPY cross rate indicates that the Euro is strengthening relative to the Japanese Yen, or conversely, the Japanese Yen is weakening relative to the Euro. This movement can be a result of economic factors influencing either the Euro's relationship with the U.S. dollar or the Japanese Yen's relationship with the U.S. dollar, or both.

Traders and investors use these rates to gauge market sentiment for specific [currency pair]s, even if they don't involve the U.S. dollar directly. An increase in a cross rate means that the [base currency] of that pair is gaining value against the [quote currency]. Such shifts can signal potential opportunities for profit or risk, influencing decisions related to [global trade] and international investment.

Hypothetical Example

Suppose an investor in Europe wants to convert Euros (EUR) to Australian Dollars (AUD) for an investment opportunity, but the direct EUR/AUD exchange rate is not readily available or is less liquid than quotes against the U.S. dollar.

Assume the following real-time exchange rates:

EUR/USD = 1.0850 (meaning 1 Euro buys 1.0850 U.S. dollars)
AUD/USD = 0.6650 (meaning 1 Australian Dollar buys 0.6650 U.S. dollars)

To calculate the EUR/AUD cross currency rate:

Find the inverse of AUD/USD to get USD/AUD:
USD/AUD = 1 / AUD/USD = 1 / 0.6650 ≈ 1.5037
(This means 1 U.S. dollar buys approximately 1.5037 Australian Dollars.)
Multiply EUR/USD by USD/AUD to get EUR/AUD:
EUR/AUD = EUR/USD × USD/AUD
EUR/AUD = 1.0850 × 1.5037
EUR/AUD ≈ 1.6316

Therefore, the cross currency rate for EUR/AUD is approximately 1.6316. This means 1 Euro can buy about 1.6316 Australian Dollars. This allows the investor to understand the true value of their conversion without needing a direct market for that [currency pair].

Practical Applications

Cross currency rates are fundamental to various aspects of the global financial system and play a significant role in the [foreign exchange market].

International Trade and Business: Businesses engaged in [global trade] often deal with multiple currencies. Cross currency rates enable them to price goods, manage payments, and calculate profits and losses accurately, even when direct conversion pairs are not commonly traded. This facilitates smoother cross-border transactions and financial planning.
²², ²³Investment and Portfolio Management: Investors diversifying their portfolios across different international markets may need to convert funds between non-USD currencies. Cross currency rates provide the necessary valuation tools for assessing investment returns and managing currency exposure in markets like the [spot market] or those involving [derivatives].
Arbitrage Opportunities: Experienced traders constantly monitor cross currency rates for discrepancies that could lead to [arbitrage] opportunities. If the calculated cross rate differs from a direct quote (if one exists), or if triangular arbitrage is possible through three separate currency pairs, traders can profit from these temporary inefficiencies.
²¹Central Bank and Financial Institution Operations: Central banks and large financial institutions utilize cross currency rates for managing foreign reserves and conducting operations in the [interbank market]. The Bank for International Settlements (BIS) conducts triennial surveys providing comprehensive insights into the structure and size of the global foreign exchange market, including turnover of various currency pairs. The I¹⁸, ¹⁹, ²⁰nternational Monetary Fund (IMF) also plays a role in fostering international monetary cooperation and promoting exchange rate stability, which influences the environment in which cross currency rates operate.

L¹³, ¹⁴, ¹⁵, ¹⁶, ¹⁷imitations and Criticisms

While essential, cross currency rates are not without their limitations and potential complexities. One primary concern is the [liquidity] of the underlying currency pairs used in their calculation. If one or both of the constituent pairs (e.g., EUR/USD or USD/JPY) have wide [bid-ask spread]s or low trading volumes, the derived cross rate may not accurately reflect the true market value or may be subject to significant slippage during execution.

Moreover, market [volatility] can introduce rapid fluctuations in the base rates, potentially leading to quick changes in cross currency rates. Economic or political events, such as changes in central bank policies or geopolitical tensions, can trigger sharp movements in exchange rates, impacting cross rates. This ⁸, ⁹, ¹⁰, ¹¹, ¹²volatility can increase the risk for entities that rely heavily on these derived rates for large transactions or [hedging] strategies. Market participants must remain vigilant to these shifts and consider the risks associated with rapid price changes in the underlying currency pairs.

Cross Currency Rates vs. Spot Exchange Rate

Cross currency rates and [spot exchange rate]s both pertain to currency conversions but differ in their directness and derivation.

A spot exchange rate is the current price at which one currency can be exchanged for another for immediate delivery. These are direct quotes, reflecting the real-time market value between a specific [currency pair]. For instance, EUR/USD or USD/JPY are common spot exchange rates, where the values are determined by supply and demand in the direct market for that pair.

Cross currency rates, on the other hand, are derived exchange rates. They are calculated indirectly using a common third currency, typically the U.S. dollar, as an intermediary. While a spot rate provides a direct quotation for a currency pair, a cross rate calculates the implied exchange rate between two currencies that might not have a widely traded direct spot market. The existence of a robust spot market for major currency pairs facilitates the efficient calculation of cross currency rates for less frequently traded pairs.

FAQs

Q: Why are most cross currency rates calculated using the U.S. dollar?
A: The U.S. dollar is the world's most traded [currency pair] and acts as a common denominator due to its high [liquidity] and widespread acceptance in international transactions. Most ⁵, ⁶, ⁷major currencies have direct and highly liquid spot exchange rates against the USD, making it the most convenient and efficient intermediary for deriving other currency pairs.

Q: Are cross currency rates only for exotic currency pairs?
A: No. While they are crucial for determining rates for less liquid or "exotic" [currency pair]s, cross currency rates are also frequently calculated for major non-USD pairs like EUR/JPY or GBP/CHF, which are often derived from their respective U.S. dollar rates.

Q:⁴ Can cross currency rates be different from direct quotes for the same pair?
A: In highly efficient markets, direct quotes and calculated cross rates for the same [currency pair] should be very close. Any significant difference would present an [arbitrage] opportunity that market participants would quickly exploit, thereby eliminating the discrepancy. Small variances may occur due to bid-ask spreads or temporary market inefficiencies.

Q: How do central banks influence cross currency rates?
A: Central banks influence all [exchange rate]s, including those used to calculate cross currency rates, through monetary policy decisions such as interest rate adjustments, quantitative easing, or direct intervention in the [foreign exchange market]. Their actions can strengthen or weaken a country's currency relative to others, thereby impacting the values used in cross rate calculations.¹, ², ³