Cross-rates are the exchange rates between two currencies that are not the official currency of the country where the quote is given. For example, if you are in Indonesia and you want to know how many euros you can get for one Japanese yen, you need to use a cross-rate.
To calculate a cross-rate, you need to know the exchange rates of both currencies against a third currency, usually the U.S. dollar. For example, let’s say the USD/EUR rate is 1.2191 and the USD/JPY rate is 109.744. This means that one U.S. dollar can buy 1.2191 euros or 109.744 Japanese yen. To find the EUR/JPY rate, you need to divide the USD/EUR rate by the USD/JPY rate. This gives you 0.0111, which means that one euro can buy 0.0111 Japanese yen.
Cross-rates are useful for traders and investors who want to compare the value of different currencies or make transactions in foreign markets. Cross-rates can also reflect the economic and political conditions of the countries involved. For example, if the EUR/JPY rate increases, it means that the euro is strengthening against the yen, or that the yen is weakening against the euro. This could be due to factors such as interest rates, inflation, trade balance, or geopolitical events.
Basic Theory
Traditionally, exchange rates are quoted in terms of a base currency against a quote currency (e.g., EUR/USD, where EUR is the base currency). Cross-rates, however, involve two non-U.S. Dollar currencies, and their calculation is derived from the exchange rates of both currencies against a common third currency (usually the U.S. Dollar).
The formula for cross-rates is:
![\[ Cross\_Rate = \frac{Exchange\_Rate\_Base\_Currency}{Exchange\_Rate\_Quote\_Currency} \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-57c6040059f85b380f9698f5b43befee_l3.svg "Rendered by QuickLaTeX.com")
Procedures
Let’s break down the steps to calculate cross-rates in Excel:
- Collect Exchange Rates: Gather the exchange rates for each currency against a common third currency. For example, if you want to find the cross-rate between EUR and GBP, obtain the exchange rates for EUR/USD and GBP/USD.
- Set Up Excel Table: Create a table in Excel with columns for the currencies involved, their respective exchange rates against the common currency, and the calculated cross-rate.
- Use Excel Formula: In the cell where you want the cross-rate, use the formula:
=Exchange_Rate_Base_Currency / Exchange_Rate_Quote_Currency
Substitute the cell references with the actual cells containing the exchange rates.
- Format Cells: Format the cells to display the cross-rate with the desired number of decimal places.
Comprehensive Example
Let’s consider a scenario with the following exchange rates:
- EUR/USD = 1.20
- GBP/USD = 1.40
We want to find the cross-rate between EUR and GBP.
-
- Set Up Excel Table:
| Currency | Exchange Rate |
|---|---|
| EUR/USD | 1.20 |
| GBP/USD | 1.40 |
| Cross-Rate EUR/GBP | Formula Here |
- Use Excel Formula: In the cell for Cross-Rate EUR/GBP, use the formula:
=B2/B3
Assuming B2 contains the EUR/USD rate, and B3 contains the GBP/USD rate.
- Calculate Result:
. Therefore, the cross-rate between EUR and GBP is approximately 0.8571.
Other Approaches
While the basic formula is straightforward, more complex scenarios may involve multiple currencies. In such cases, you can use additional intermediate currencies to calculate cross-rates indirectly.
For example, if you have direct rates for EUR/USD, GBP/USD, and EUR/GBP, you can calculate the cross-rate between GBP and JPY by first finding the cross-rate between EUR and JPY using the intermediate EUR/USD and EUR/GBP rates.
In Excel, this would involve nested formulas and multiple steps, but the fundamental principle remains the same.
