What is the Cross Rate in Forex?
A cross rate refers to a Forex transaction that values two currencies against a third one, involving two transactions. It usually refers to any currency pair that does not include the US Dollar. Historically if a trader wanted to trade a non-US Dollar currency, the first trade was exchanging the base currency for US Dollars and then purchasing the quote currency with the exchanged US Dollars.
The evolution of the Forex market with the introduction of the Euro has changed the cross-rate definition to include the exchange of two currencies for a third one that does not include the home currency. For example, for a US trader, the EUR/GBP pair represents a cross rate, but for a trader in the Eurozone, where the Euro, or the base currency in the EUR/GBP pair, is the domestic currency, it does not meet the definition. Rather than exchanging Euros for US Dollars and then buying British Pounds with US Dollars, a trader can directly exchange Euros for British Pounds.
The change and recalibration of cross-currency triangulation began in 1997 when the EU implemented Rule 1103/97. It provided a legal framework allowing the conversion of currencies to Euros and introduced pricing to six decimal places from the previous three.
FX Cross Rates Explained
Before 1997, FX cross rates were the primary means of calculating non-USD currency pairs like the EUR/JPY, the GBP/CHF, and the AUD/NZD. The introduction of the Euro and the broad-based evolution of the Forex market have resulted in significant positive changes. Today, most traders get the desired currency quotes for 100+ currency pairs without calculating cross rates from their Forex brokers, banks, or exchange offices.
Currency cross rates remain essential for calculating the exchange rates of two exotic currencies. For example, a trader looking for the MXN/ZAR rate cannot find this currency pair quote but can calculate it using the USD/MXN and the USD/ZAR exchange rates, which are readily available.
Each currency quote consists of two currencies, the base currency, the first one, and the quote currency, the second one. For example, in the EUR/USD, the Euro is the base currency, and the US Dollar is the quote currency.
Traders must understand the currency pairing hierarchy. The Euro is always the base currency, together with the British Pound, except for the EUR/GBP pair.
The currency pair hierarchy
- Euro (EUR)
- British Pound (GBP)
- Australian Dollar (AUD)
- New Zealand Dollar (NZD)
- US Dollar (USD)
- Canadian Dollar (CAD)
- Swiss Franc (CHF)
- Japanese Yen (JPY)
The cross-rate calculation formula consists of two transactions and must follow a specific order of currency quotes. For example, if the US Dollar is the base or the quote currency in both currency pairs, the trader must get the reciprocal rate, or inverse exchange rate, for one of the currency pairs to calculate the cross rate.
What Is the Purpose of a Cross Exchange Rate?
The cross-exchange rate allows for the calculation of currency pair quotes when they are not available directly or the identification of arbitrage trading opportunities.
Indirect quote example:
- Assume a trader wants the INR/CHF exchange rate, not quoted by the markets
- Using the USD/INR exchange rate and the USD/CHF reciprocal exchange rate allows for the INR/CHF cross rate calculation
Arbitrage quote example:
- The EUR/GBP is quoted by the markets
- Using the EUR/USD exchange rate and the GBP/USD exchange rate allows for the potential of a EUR/GBP arbitrage opportunity
How Do Currency Cross Rates Work?
Currency cross rates value two non-USD currencies against a third one, usually the home currency of the trader. Usually, the US Dollar remains the third currency, but since 1997 and the introduction of a Euro exchange framework, more cross-currency triangulation opportunities have become available. Using the reciprocal exchange rate, traders can calculate cross rates without limitations, but most include the US Dollar as a variable.
Cross Rate Exchange Types and Examples
The Forex market generally classifies currencies as major, minor, and exotic. Using currency cross rates allows for the calculation of any currency pair.
Major currency pairs and cross rates
This refers to any currency pair that includes the US Dollar as either a base or quote currency, for example, the EUR/USD and the USD/JPY.
Minor currency pairs and cross rates
This includes any currency pair from the primary eight currencies, excluding the US Dollar, for example, the EUR/JPY and the GBP/CHF.
Exotic currency pairs and cross rates
This includes any currency pair outside the primary eight currencies plus any non-symmetrical pairings, for example, the MXN/ZAR and the USD/EUR.
The Cross Rate Formula and How to Calculate the Cross Rate of Exchange
Knowing the cross-rate formula allows traders to calculate exchange rates for exotic currency pairs or derive an arbitrage trading strategy.
The cross-rate formula
Cross Rate Currency (Currency A / Currency B) = (Currency A / USD) x (USD / Currency B)
Here is a cross-rate calculation example for AUD/CHF:
- The AUD/USD exchange rate is 0.69235
- The USD/CHF exchange rate is 0.96106
Therefore:
0.69235 (AUD/USD) x 0.96106 (USD/CHF) = 0.66539
Please note: The AUD/CHF exchange rate from the same source quotes it as 0.66551, providing a potential arbitrage trading opportunity
Cross Rate with Bid/Ask Spread Calculation
Assume a trader needs the MXN/ZAR exchange rate. It consists of two exotic currencies that most Forex brokers do not quote.
An example of a cross-rate calculation
- The USD/MXN bid/ask is 20.5370/20.5561
- The USD/ZAR bid/ask is 16.8223/16.8511
- The USD is the base currency in both, and a trader requires the reciprocal exchange rate for one currency pair (in this example, the USD/ZAR)
The reciprocal exchange rate for USD/ZAR is:
1 / 16.8223 = 0.0594 (bid)
1 / 16.8511 = 0.0596 (ask)
Therefore:
The ZAR/USD quote is: 0.0594/0.0596
Calculating the MXN/ZAR bid:
20.5370 (USD/MXN bid) x 0.0594 (USD/ZAR bid) = 1.2199
Calculating the MXN/ZAR ask:
20.5561 (USD/MXN ask) x 0.0596 (USD/ZAR ask) = 1.2251
Therefore:
The MXN/ZAR quote is: 1.2199/1.2251
Conclusion
Currency cross rates allow traders to calculate exchange rates for exotic and non-symmetrical pairings. They also allow for arbitrage opportunities. A cross rate references two currencies against each other, quoted by a third one, usually the home currency of a trader. Given Forex hierarchies, the reciprocal exchange rate becomes necessary.
FAQs
How is the cross rate calculated?
The cross rate requires three currencies, the base currency, and the quote currency of the desired currency pair, and a third one, usually the US Dollar, to determine the value of the other two. For example, the cross-rate formula for the EUR/GBP is the EUR/USD exchange rate divided by the GBP/USD. Another example is the GBP/CHF, calculated by multiplying the GBP/USD by the USD/CHF exchange rate.
What is the reciprocal rate?
A reciprocal exchange rate is the inverse of the quoted exchange rate. For example, if a trader needs the USD/GBP exchange rate for a cross-rate calculation, a reciprocal exchange rate is necessary, as the USD/GBP does not exist in Forex, where the quote is GBP/USD. The formula for the reciprocal exchange rate is 1.0000 divided by the exchange rate. Therefore, if the GBP/USD is 1.2015, the inverse rate is 0.8323.
What is the cross rate?
A cross rate is the exchange rate of two non-USD currencies valued against a third currency. It applies to currencies not involving the home currency of the trader. For example, the GBP/JPY is a cross rate for an Australian trader but not for a UK trader.
What are cross rates and arbitrage?
A cross rate relies on three currencies, and most Forex brokers, banks, and exchange offices readily quote desired currency pairs. Arbitrage involves exploiting temporary price discrepancies to profit from the spread. Traders can use the cross rate with bid/ask spread calculations to identify discrepancies and potential profit opportunities. The price discrepancies usually last a few seconds or less and require sophisticated software and algorithms to create a long-term profitable arbitrage strategy using cross rating.