How to Calculate Cross Rates between Currencies
Cross rates are simply the exchange rates between two currencies. Their purpose serves multiple functions in the financial markets with such uses as hedging currency risk, pricing foreign securities, arbitrage, investment and trade, and pricing commodities. Their most well-known function is to define the exchange rate for travelers around the world.
Let’s say, you bought a good from a Japanese firm with your home currency, Mexican Pesos. You paid 20 pesos and want to know how much Japanese Yen the firm will receive in exchange. Using the U.S. dollar as a benchmark to find the Yen/Peso cross rate, you notice the spot rate between the peso and the dollar is 18.7939 pesos for $1, and the spot between the yen and the dollar is 130.18 yen for $1.
To calculate the Yen/Peso cross rate, you would divide the yen/dollar spot rate by the peso/dollar spot rate.
¥130.18/$1 ÷ Mex$18.7939/$1 = ¥6.9267/Mex$
Therefore, the exchange rate between the Yen and the Peso can be determined using the U.S. dollar as a benchmark. The reason why the peso/dollar spot rate is divided by the yen/dollar spot rate is due to the fact that you are trying to find the relative value of the Yen to the Peso. This calculation gives you the amount of yen it takes to buy one peso. So, if you paid 20 Pesos and want to know the total amount of yen the firm received, you would multiply the 20 Pesos by the exchange rate between the Yen and Peso.
Mex$20 × ¥6.9267/Mex$ = ¥138.53
Therefore, by paying 20 Pesos and knowing that 6.9267 yen equals one peso, you would multiply those two numbers to obtain the amount of yen that equals 20 pesos.
Let’s use a travel example now, where a Brazilian citizen wants to visit his friend in Guatemala. He has R$4,500 Brazilian Reals and needs to convert it to Guatemalan Quetzals. This time, however, we will be using the GTG/Euro spot rate and the Euro/Real spot rate.
Spot rate on GTQ/€: GTQ 8.5239/€1
Spot rate on €/R$: €0.1768/R$1
Using these two different spot rates, we can compute the R$/GTQ cross rate:
GTQ 8.5239/€ × €0.1768/R$ = GTQ 1.5070/R$
Therefore, 1.5070 Quetzals equals one Brazilian Real. This method is called the triangulation method and can be used when you don’t have direct information on the exchange rate between two currencies and have to use a third currency as a benchmark. By multiplying the spot rate on GTQ to Euros by the spot rate on Euros to Reals, you are essentially taking the Euro as a benchmark and finding out how many Quetzals equal one Real. Now that you have the exchange rate, you can find out how many Guatemalan Quetzals you’ll receive for your Brazilian Reals.
R$4,500 × GTQ 1.5070/R$ = GTQ 6781.50
The triangulation method can also be calculated by inversing the benchmark currency. Let’s say you live in Germany and want to travel to Russia. You have 16,000 Euros and need to exchange them for Russian Rubles.
Spot rate on $/Euro: $1.09/€1
Spot rate on ₽/$: ₽69.45/$1
Using the triangulation method inversely with the U.S. dollar as the benchmark currency, you can calculate the cross rate of Rubles to Euros:
$1.09/€ × ₽69.45/$ = ₽75.70/€
Now knowing the exchange rate between Russian Rubles to the Euro, you can compute how many Russian Rubles you’ll get for your 16,000 Euros.
€16,000 × ₽75.70/€ = ₽1,211,200