Understanding and Calculating Cross-Rates from Dollar Rates in Excel

Cross-rates are the exchange rates between two currencies that are not the official currency of the country where the rates are checked. For example, if you are in Indonesia and want to know how many Euros you can get for one British Pound, you need to use a cross-rate.

To calculate a cross-rate, you need to know the exchange rates of both currencies against a common third currency, usually the U.S. dollar. Then, you can use this simple formula:

Cross-rate = (Exchange rate of currency A / Exchange rate of common currency) * Exchange rate of currency B

For example, let’s say you want to calculate the cross-rate of EUR/GBP using the U.S. dollar as the common currency. You need to find the exchange rates of EUR/USD and GBP/USD first. According to this website, the exchange rates are:

EUR/USD = 1.2193 GBP/USD = 1.3549

Then, you can plug these values into the formula:

Cross-rate of EUR/GBP = (1.2193 / 1.3549) * 1 Cross-rate of EUR/GBP = 0.9001

This means that one Euro can be exchanged for 0.9001 British Pounds.

Basic Theory:

To calculate a cross-rate between two non-USD currencies (Currency A and Currency B), we typically use the following formula:

This formula essentially converts both currencies to USD and then calculates the ratio between them.

Procedures:

1. Collect Exchange Rates: Gather the exchange rates for each currency against the USD. For example, if you want to calculate the cross-rate between Euro (EUR) and Japanese Yen (JPY), you need the EUR/USD and JPY/USD exchange rates.
2. Apply the Formula: Use the formula mentioned above to calculate the cross-rate in Excel. You can use a dedicated cell for this calculation.
3. Format the Result: Format the result cell to display the cross-rate with the appropriate number of decimal places.

Comprehensive Explanation:

Let’s consider a scenario where we want to calculate the cross-rate between Euro (EUR) and Japanese Yen (JPY). Assume the following exchange rates:

Scenario Calculation:

Using the provided formula, the Excel formula in cell B4 for the cross-rate (EUR/JPY) would be:

Resulting in a cross-rate of approximately .

Other Approaches:

1. Direct Calculation: You can directly calculate the cross-rate without converting to USD by multiplying the two exchange rates:

      

2. Inverse Calculation: Alternatively, you can calculate the cross-rate by taking the inverse of one of the rates: