In the world of FX, a cross rate is the exchange rate between two currencies that aren’t domestic to the country where the quote is being provided. For example, if you’re in the USA and want to know the exchange rate between the euro (EUR) and Japanese yen (JPY), the rate you get would be a cross rate. Whether you’re a business looking into an international investment or an international student paying fees abroad, understanding the concept of cross rates can help you make informed decisions.
Why derive a cross rate?
Due to its status as the world’s primary reserve currency, the United States dollar (USD) is used as a benchmark currency in the foreign exchange market. Several currency pairs are regularly quoted against the USD, such as the EUR/USD and GBP/USD.
However, at times valuing a currency against the USD may not be the best approach. Businesses engaged in international trade might find that deriving a cross rate facilitates smoother international transactions and a more accurate insight into the rate of exchange, which can help with the development of currency risk management strategies.
Similarly, international students may find themselves juggling multiple currencies when paying fees and other expenses, which makes cross rates an important factor in budgeting and planning.
Direct and indirect quotes
Before you calculate a cross rate, it’s important to understand the difference between a direct quote and an indirect quote. A direct quote indicates the domestic currency per unit of foreign currency, and an indirect quote determines the foreign currency per unit of domestic currency. For example:
Direct quote: If 1 US dollar (USD) equals 0.85 euro (EUR), then the direct quote for USD/EUR is 0.85
Indirect quote: If 1 EUR equals 1.18 USD the indirect quote for EUR/USD would be 1.18
Major and minor cross rates
Industry professionals will often refer to major or minor cross rates. A major cross rate involves currencies that are widely traded in the fx market such as EUR/GBP or USD/JPY. Major cross rates typically involve currencies from developed economies and tend to have higher liquidity.
Minor cross rates feature currencies from smaller or emerging economies. Common minor cross rates include AUD/NZD and CAD/JPY. Despite having lower liquidity than major cross rates, these pairs still have a significant role to play in international trade.
How to calculate a cross rate
If you are trying to derive the rate at which you would change your base currency and it does not involve USD, you may need to find the cross rate.
To do this, you must identify two currency pairs: one that contains your home currency and the other containing the foreign currency that you want to exchange it with. Next, determine what type of quote each of your two selected currency pairs is and apply a cross currency formula to determine the rate.
Direct quote: 1 foreign currency unit = x home currency units
Indirect quote: 1 home currency unit = x foreign currency units
Derive a cross rate for an indirect quote & indirect quote:
Rule: divide the base currency by the terms currency on opposite sides of the spread.
In this example we are deriving the rate for GBPEUR
| Currency Pair | Bid | Ask | Details |
|---|---|---|---|
| GBPUSD | 1.9850 | 1.9950 | GBP is base, USD is terms |
| EURUSD | 1.3460 | 1.3520 | EUR is base, USD is terms |
| The GBPEUR Bid rate | = divide the base currency bid by the terms currency ask |
| = 1.9850 / 1.3520 = 1.4682 | |
| *this is the rate at which the market buys GBP and sells EUR at 1.4682 EUR per GB |
| The GBPEUR Ask rate | = divide the base currency ask by the terms currency bid |
| = 1.9950 / 1.3460 = 1.4821 | |
| *this is the rate at which the market sells GBP and buys EUR at 1.4821 EUR per GBP |
Derive a cross rate from a direct quote & indirect quote:
Rule: multiply on the same side
In this example we are deriving the rate for EURAUD
| Currency Pair | Bid | Ask |
|---|---|---|
| EURUSD | 1.3798 | 1.3858 |
| USDAUD | 1.0432 | 1.0502 |
| The EURAUD Bid rate | = Multiply the term currency bid by the base currency ask |
| = 1.3798 x 1.0432 = 1.4394 | |
| *this is the rate at which the market buys EUR and sells AUD |
| The EURAUD Ask rate | = Multiply the term currency ask by the base currency bid |
| = 1.3858 x 1.0502 = 1.4553 | |
| *this is the rate at which the market sells EUR and buys AUD |
Derive a cross rate for an indirect quote & indirect quote:
Rule: divide the base currency by the terms currency on opposite sides of the spread.
Derive the rate for GBPEUR
| Currency Pair | Bid | Ask | Details |
|---|---|---|---|
| GBPUSD | 1.9850 | 1.9950 | GBP is base, USD is terms |
| EURUSD | 1.3460 | 1.3520 | EUR is base, USD is terms |
| The GBPEUR Bid rate | = divide the base currency bid by the terms currency ask |
| = 1.9850 / 1.3520 = 1.4682 | |
| *this is the rate at which the market buys GBP and sells EUR at 1.4682 EUR per GB |
| The GBPEUR Ask rate | = divide the base currency ask by the terms currency bid |
| = 1.9950 / 1.3460 = 1.4821 | |
| *this is the rate at which the market sells GBP and buys EUR at 1.4821 EUR per GBP |
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