FX Basics - Cross Rates

Previously in FX basics we talked about the difference between direct (USDCAD) and indirect (AUDUSD) rates and introduced the notion of calculating cross rates from various combinations of direct and indirect rates. Remember, the US dollar (USD) is the currency against which all other currencies are priced and any exchange rate (AUDCAD for instance) not involving the USD is considered a cross rate.

The example used to illustrate the first rule was how to cross a direct rate (USDCAD) with an indirect rate (GBPUSD) to get a GBPCAD cross rate. The direct/indirect rule is to multiply on the same side of the market – USDCAD bid with GBPUSD bid to get the GBPCAD bid rate, and USDCAD offer with the GBPCAD offer to calculate the GBPCAD offer.

The second rule we looked at was crossing two direct currencies – in our example, USDJPY and USDCAD. The rule when crossing two direct currencies is to divide the terms currency by the base currency on the opposite side of the market. So to calculate the JPYCAD bid, divide the USDCAD bid by the USDJPY offer. And to get the JPYCAD offer, divide the USDCAD offer by the USDJPY bid. If you missed the WMU’s where these rules were explained in detail with examples and you want to see the material, please let us know and we’ll get it to you.

The third and final cross rate rule that we’ll cover involves crossing two indirect rates. We’ll use the common example of deriving GBPEUR and EURGBP rates from the conventional GBPUSD and EURUSD quotes.

The rule to remember when crossing two indirect currencies is:

Divide the base currency by the terms currency on opposite sides of the spread.



Given the following market rates:

Bid Ask

GBPUSD 1.9850 1.9950 GBP is base, USD is terms

EURUSD 1.3460 1.3520 EUR is base, USD is terms



The British look at the EUR exchange rate in the form GBPEUR – how many EUR do they get or pay for one GBP. In this format GBP is the base currency and EUR is the terms currency. So apply the rule:

GBPEUR Bid: divide the base currency bid by the terms currency offer

GBPEUR Bid = 1.9850 / 1.3520 = 1.4682

The market maker buys GBP and sells EUR at 1.4682 EUR per GBP.

To calculate the GBPEUR Offer: divide the base currency (GBP) offer by the terms currency (EUR) bid.

GBPEUR Offer = 1.9950 / 1.3460 = 1.4821

The market maker sells GBP and buys EUR at 1.4821 EUR per GBP.

On the continent (and in Ireland) they look at the GBP rate from the perspective EURGBP where the euro is the base currency. So applying the rule we get:

EURGBP Bid = 1.3460 / 1.9950 = .6747.

The market maker buys EUR and sells GBP at .6747 GBP per EUR

EURGBP Offer = 1.3520 / 1.9850 = .6811.

The market maker sells EUR and buys GBP at .6811 GBP per EUR.



Now you have the three cross rate rules and you should be able to double check the accuracy of any fx rate you’re quoted. Although the cross rates are largely calculated by computers these days, traders are still required to work out less common crosses manually. And it still amazes me how often even bank traders miscalculate cross rates when they have to do the calculation themselves. With computerization, calculating crosses accurately and quickly is certainly becoming a lost art.