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Chapter 7 Cross-rates

Cross rates

The trading operations on Forex are carried out not only against the U.S. dollar. We intentionally have not touched on this kind of operations until now to make the content more intelligible. The currency rates, which do not include the U.S. dollar, are called the “cross rates”. As a rule, only advanced traders work with the cross rates, as it is necessary to have a sound knowledge of economic indicators of specific countries to trade cross rates succesefully. GBP/JPY, EUR/JPY, and GBP/EUR can be cited as the examles of the cross rates.

The currency positions in the major (dollar) quotes are strictly determined. The positions of the currencies in the crosses could vary depending on the counterpart, which is quoted. For example, a bank in Canada can rate the Canadian dollar in EUR/CAD. This finer point should be kept in mind, when the cross rates transactions are made, unless to meet a bad trade decision. However, the British pound is an exception. It is always quoted as GBP/___, i.e. it is always the base currency.

Why are the cross rates so popular on Forex? Let us imagine a situation, when you are expecting a big economic upturn in Canada due, for instance, to the oil fields newly discovered (Canada is one of the main world oil suppliers). At the same time, in Japan the latest economic indicator gives a sign of a temporary breakdown in the economy. As the economic state of a country corresponds directly to the rate of its currency on the world foreign exchange, it is obvious, that one ought to buy the Canadian dollars and sell the Japanese yens. But if you make this deal with the U.S. dollars, the result could be pretty haphazard. The U.S. dollar can move up or drop down, because we might have no clear information about the U.S. economic climate. Therefore, the purchase of the Canadian dollars for the U.S. dollars (by the USD/CAD quote) may not bring an expected profit, as evenly the sale of the Japanese yens for the U.S. dollars (USD/JPY) could do the same. If we conduct these operations at once in an equal volume, as if we exclude dollar from the “equation”, and we cease to be depended on the situation with the American economy. We attain this effect, using the cross rates on Forex, and thus we omit the factor of the U.S. economy influencing the course of the currencies as to our example.

Most of Forex trades are performed on the major or dollar currenc pairs. The crosses are less liquid on Forex. As a consequence, the cross rates are not calculated in regard of asks and bids of the currencies relative to each other, as it is done with the major rates. Otherwise, the cross currency pairs market could become a speculative one, and any participants could take in under full control. Thus, in spite of absence of the dollar in the cross rate quotations, it is just those major rates with the U.S. dollar which are taken into account while cross rates quotations are formed.

How are the cross rates calculated? There are three possible variants of the cross rates calculation depending on whether the U.S. dollar is a base or quoted currency in the major quotes of currencies we are interested in. Thereby, we will apply simple arithmetic rules that are used for multiplication and division of the fractions. At the same time we should not take literally the USD/JPY pair as a fraction, of course. Thus, if represent the yen to the U.S. dollar as a real fraction, the value of the quote 104.78 (the quantity of the Japanese yens exchanged for one U.S. dollar) could be recorded as JPY/USD. From practical point of view, the currency pair is denoted as USD/JPY. The first type of calculation is used for the currencies with the direct quotations against the U.S. dollar (the U.S. dollar is the base currency in the pair for both currencies). Let us take the yen (JPY) and the Swiss franc, for instance. Having the quotes of USD/JPY and USD/CHF against the U.S. dollar on hand, we can deduce a cross rate of the Swiss franc against the yen using the fractions methods.


that means it is necessary to divide USD/JPY by USD/CHF. For instance, if USD/JPY costs 104.78 and USD/CHF is 1.0505, the cross rate of the Swiss franc against the yen will be equal to rounded CHF/JPY 99.74.

The second type of calculation is used for the currencies with direct and reverse quotations against the U.S. dollar (in this case the dollar is the base currency of the pair for one currency and quoted currency for another). Let us consider the yen (JPY) and the Australian dollar (AUD). Keeping in mind the quotes of USD/JPY and AUD/USD against the U.S. dollar, we can deduce by the fractions rules the cross rate of the Swiss franc against the yen.


So one has to multiply AUD/USD by USD/JPY. For instance, if USD/JPY worth 104.78 and AUD/USD costs 1.0564, the cross rate of the Australian dollar to the Japanese yen is equal to rounded AUD/JPY 110.69.

The third type of calculation is used for the currencies with the reverse quotations against the U.S. dollar (dollar is the quoted currency for the both currencies). Let us consider the British pound and the Australian dollar. Having the GBP/USD and AUD/USD quotations against the dollar, we can deduce by the fractions rules the cross rate of British pound against the Australian dollar:


i.e. we have to divide GBP/USD by AUD/USD. For instance, if GBP/USD is 0.5028 and AUD/USD is 1.0564, the cross rate of the British pound for the Australian dollar is equal to rounded GBP/AUD 0.4760.

It should be noted, that we have excluded from our consideration the notion of bid and ask price of the currency rate to simplify the calculation formulas, and we have used only current (spot) prices until now. But each major (dollar) quotation has two prices, as well as the crosses. So where should we put the bid and ask prices? The answer to this query is in understanding of logics of the cross rates calculation. Let us return to our example of the first type calculation, which involves the Swiss franc (CHF) and the yen (JPY). We are interested in the cross rate quotation CHF/JPY. In order to define the bid price of the Swiss franc in this quote (the bid/ask rates, as we have just known, always refer to the base currency) we need to think the following way. As we are interested in buying the Swiss francs, we have to purchase the dollars for the Japanese yens first, and then sell them for the Swiss francs. Thus, the bid rate of the USD/CHF pair is important for us. we should also consider the ask price of the USD/CHF quote. Thus, the bid price of the Swiss franc to be exchanged for the Japanese yen in the cross pair CHF/JPY is calculated by the following formula:

CHF/JPY(bid) = USD/JPY(bid) : USD/CHF(ask)

In the same manner one can deduce a formula for the ask price of the Swiss franc vs the Japanese yen in the CHF/JPY cross pair quotation:

CHF/JPY(ask) = USD/JPY(ask) : USD/CHF(bid)

In the examples of the second and the third types of calculation we use the same formulas:

AUD/JPY(bid) = AUD/USD(bid) * USD/JPY(bid),

AUD/JPY(ask) = AUD/USD(ask) * USD/JPY(ask),

GBP/AUD(bid) = GBP/USD(bid) : AUD/USD(ask),

GBP/AUD(ask) = GBP/USD(ask) : AUD/USD(bid).

It should be noted, that the dealers do not use these formulas because of their awkwardness. There is a more convenient way to calculate the buying and selling cross rates on Forex. One takes the average of the bid and ask rates for each of the dollar quotes. Then, using the formulas for the current (spot) prices, we can calculate the current value of cross rate quotation. After that, this resulted value is quasi “drawn” apart for a certain number of points (the spread is settled up), and that is how we receive the buying and selling price for the cross rate quotation.

Let us consider an example of the Swiss franc (CHF) and the Japanese yen (JPY). Supposing, the selling/buying rates of these currencies are: USD/CHF - 1.0502/08 and USD/JPY - 104.74/82, so the average rates let be calculated:

USD/CHF(avg) = (1.0502 + 1.0508)/2 = 1.0505,

USD/JPY(avg) = (104.74 + 104.82)/2 = 104.78,

which are further used in the quotes calculation formulas with the cross rates for the current (spot) prices. The resulting value of the cross pair price CHF/JPY(avg) 99.74 undergoes then the drawing apart, for instance, by 5 points in both directions, forming the bid and ask price of the pair CHF/JPY 99.69/79.

Remember, that there are some underlying potential problems in this simplified way of calculation. As traders earn money on Forex just with the conversing (over crossing) transactions, the spread must be quite big to escape the losses at the reversing trade with another counterpart. It is particularly vital for the low liquid markets of the “exotic” cross rates. Summarizing the chapter we would say, that the analysis and forecasting for the cross rates do not differ from the testing and prospecting for the major pairs in regard to the U.S. dollar, i.e. there are the same tools in effect.