What is a Cross Rate?

Let’s assume USD is your main currency, and you get FX rates for USD with other currencies, e.g. USD>EUR, USD>CAD, USD>AUD

Cross Rates are defined as FX rates which don’t include USD, e.g. EUR>CAD, AUD>EUR, CAD>AUD


How are Cross Rates obtained?

If your rates source provides FX rates for all combinations of currency pairs you have two options for obtaining Cross Rates:

  1. Direct from the source – simply use the EUR>CAD rate provided by your source.
  2. Triangulation – take the USD>EUR and USD>CAD rates provided by your source and then divide one by the other to get EUR>CAD.


Surely both these methods get the same results?

Rates obtained using the 2 methods described above will be very close, but they are not always the same.

Let’s have a look at some rates published by OANDA on 04-Aug-20:

USD>EUR        0.849271

USD>AUD        1.400425

EUR>AUD        1.648972

And now compare with the EUR>AUD rate obtained by triangulation:

1.400425 / 0.849271 = 1.648973

The reason for the difference is that the direct rate reflects the market between EUR and AUD, whereas the triangulated rate is using USD market rates.


What if my rates source does not provide all combinations?

If your rates source does not publish all currency combinations, then you have no choice other than triangulation to obtain cross rates.

This is usually the situation if your source is a Central Bank e.g. European Central Bank or Bank of Canada, as banks tend to publish rates from one currency only.


Which method is best?

Both the above methods are valid, and are acceptable to auditors. However, there are some points to consider before deciding on your method of obtaining cross rates:

  • Rates obtained directly from the source are easier to “tie back” to the source at a later date.
  • Triangulation will use less “hits” from your source, i.e. you will only have to pull rates for your main currency from the source – all other combinations are calculated. This may be relevant if you need a large number of rates and your rates subscription has a limit to the number of rates you can obtain.
  • If you are using Bid or Ask rates then the difference between direct and triangulated rates is greater, so this may have a bearing on your decision. The example earlier was using Mid rates and gave a difference only at the 6th decimal. Here’s the same example using Bid rates:

USD>EUR        0.849213

USD>AUD        1.400267

EUR>AUD        1.648810

And now compare with the EUR>AUD rate obtained by triangulation:

1.400267 / 0.849213 = 1.648900

The difference is now at the 4th decimal.


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