Chapter 7. Cross-courses

Forex transactions are not only against the U.S. dollar, although so far we have intentionally not considered such transactions in order to simplify the presentation of the site. The rates of currencies that do not include the U.S. dollar are called cross rates. As a rule, only experienced traders work with cross rates on Forex, as for effective work with them you need in-depth knowledge of economic indicators and indicators of separate countries. As an example of cross-rate quotes we can quote the English pound sterling to Japanese Yen (GBP/JPY), the Euro to Japanese Yen (EUR/JPY), or the English pound sterling to Euro (GBP/EUR).

 

For the main (dollar) quotations currency positions are strictly defined. Positions of currencies in cross-currency quotes can vary depending on the party that gives the quote. For example, a bank in Canada can give a quote of Canadian dollar to Euro as CAD/EUR, and a bank in Europe can give such a quote as EUR/CAD. This nuance should be taken into account when making deals on cross rates in order not to make a false buy/sell decision. As an exception we can cite the English pound sterling, which in cross rates is always quoted as GBP/___, i.e. it is always the base currency.

Why are cross rates of interest in Forex? Let’s imagine a situation when you expect a big economic boom in Canada, caused by the development of new oil fields (Canada is one of the main oil exporters on the world stage). At the same time, the release of another economic indicator in Japan indicates a temporary decline in the Japanese economy. Since the state of the country’s economy is directly proportional to the value of its currency on the world currency market, it is obvious that it is worth buying Canadian dollars (CAD) and selling Japanese Yen (JPY). But if you perform such operations in relation to the U.S. dollar, you can get ambiguous results. The U.S. dollar can both rise in value and fall, as we may not have clear data on the state of the U.S. economy. Therefore, buying Canadian dollars for U.S. dollars (by USD/CAD quote) may not bring the expected profit, as well as selling Japanese Yen for U.S. dollars (by USD/JPY quote). If we perform these operations at the same time with the same transaction size, we as if exclude the U.S. dollar from the “equation”, and no longer depend on the economic state of the U.S. economy. We achieve this effect by working with cross rates on Forex – we as if exclude the influence of the U.S. economy on the change of direction of the rates of the currencies we are interested in.

The overwhelming majority of operations on Forex are operations on the main (dollar) quotations. The market of cross rates at Forex is much less liquid. Therefore, cross-courses quotes are not calculated relative to the supply and demand of currencies in relation to each other, as it is the case with the main quotes. Otherwise, the market of cross rates would turn out to be speculative, and some of its participants could fully control it. Thus, despite the fact that the U.S. dollar is not present in the quotations for cross rates, cross rates are calculated relative to the main quotations with the U.S. dollar.

So how are cross rates calculated? There are three possible ways of calculating cross rates, depending on whether the U.S. dollar is the base or quoted currency in the main quotations of the currencies of interest to us. In this case we will use simple rules of multiplication and division of fractions, known to us from the school course of mathematics. Of course, we should not take the writing of USD/JPY quote literally as a fraction. After all, if the record of Japanese Yen to US dollar quote would be represented by a real fraction, then the quote value 104.78 (the number of Japanese Yen for one US dollar) would correspond to writing the quote as JPY/USD. In practice, as we know, the reverse writing USD/JPY is used.

The first type of calculation is used for currencies with direct quotations against the U.S. dollar (the U.S. dollar is the base currency for both currencies). Consider the Japanese Yen (JPY) and the Swiss Franc (CHF). Having USD/JPY and USD/CHF quotes against the U.S. dollar, it is possible, using the properties of fractions, to derive the cross rate of the Swiss franc to the Japanese Yen:
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CHF/JPY = USD/JPY : USD/CHF,

that is, it is necessary to divide the dollar quotation of the Japanese Yen by the dollar quotation of the Swiss Franc. Having, for example, USD/JPY 104.78 and USD/CHF 1.0505, the cross rate of the Swiss Franc to the Japanese Yen will be (with rounding) equal to CHF/JPY 99.74.

The second type of calculation is used for currencies with forward and reverse quotes against the U.S. dollar (the U.S. dollar is the base quote currency for one currency and the quoted quote currency for the other). Consider the Japanese Yen (JPY) and the Australian dollar (AUD). Having USD/JPY and AUD/USD quotes against the U.S. dollar, it is possible, using the properties of fractions, to derive the cross rate of the Australian dollar to the Japanese Yen:

AUD/JPY = AUD/USD * USD/JPY,

i.e. it is necessary to multiply the dollar quotation of the Australian dollar by the dollar quotation of the Japanese Yen. Having, for example, USD/JPY 104.78 and AUD/USD 1.0564, the cross rate of the Australian dollar to the Japanese Yen will be (with rounding) equal to AUD/JPY 110.69.

The third type of calculation is used for currencies with inverse quotes against the U.S. dollar (the U.S. dollar is the quoted quote currency for both currencies). Consider the English pound sterling (GBP) and the Australian dollar (AUD). Having quotes against the U.S. dollar GBP/USD and AUD/USD it is possible, using the properties of fractions, to derive the cross rate of the English pound sterling to the Australian dollar:

GBP/AUD = GBP/USD : AUD/USD,

that is, it is necessary to divide the dollar quotation of the English pound sterling by the dollar quotation of the Australian dollar. Having, for example, GBP/USD 0.5028 and AUD/USD 1.0564, the cross rate of the English pound sterling to the Australian dollar will be (with rounding) equal to GBP/AUD 0.4760.

 

It should be noted that in order to simplify the calculation formulas, we have excluded the concept of bid and ask prices of currency quotations and used only current (spot) prices. But every basic (dollar) quote has two prices, and the calculated cross-currency quote also has two prices – so where to put the bid price and where to put the ask price in the formula? The answer to this question lies in understanding the logic of calculating cross rates. Let’s return to the example of the first type of calculation with the Swiss Franc (CHF) and Japanese Yen (JPY). We are interested in the CHF/JPY cross rate quote. To determine the rate of purchase of Swiss franc in such a quote (buy/sell rates, as we already know, always refer to the base currency of the quote), we need to reason as follows. We are interested in buying Swiss francs, so first we should buy dollars for Japanese Yen, and then sell them for Swiss francs. Thus, in the USD/JPY quote we are interested in the buying rate, and in the USD/CHF quote we are interested in the selling rate. So the rate of buying Swiss francs for Japanese Yen in the CHF/JPY cross rate quote is calculated by the formula:

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

Similarly, the formula for the rate of sale of the Swiss franc for the Japanese Yen in the CHF/JPY cross rate quote can be calculated:

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

For the examples for the second and third types of calculation, the formulas are calculated in the same way:

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 dealers practically do not use these formulas because of their cumbersomeness. There is a more convenient generally accepted way of calculating the buy and sell rates in cross rate quotes on Forex. This method is as follows. The average of the buy and sell rates for each of the dollar quotes is taken. Then, using formulas for current (spot) prices, the current value of the cross rate quote is calculated. Then this value is “moved” in opposite directions by a certain number of points (spread is set), and thus, the buy and sell rates for the cross-quote are obtained.

Let’s consider an example with Swiss franc (CHF) and Japanese yen (JPY). Suppose the buy/sell rates of these currencies against the U.S. dollar are as follows: USD/CHF 1.0502/08 and USD/JPY 104.74/82. The average rates are calculated:

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

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

which are then used in formulas for calculating cross rate quotes for current (spot) prices. The value of CHF/JPY(avg) 99.74 calculated in this way is then “extended”, say, by 5 points in both directions, forming buy and sell rates CHF/JPY 99.69/79.

It should be taken into account that there are pitfalls in such a simplified way of calculation. Since Forex money is earned on opposite (overlapping) trades, the value of the spread should be large enough to avoid losses in a reverse trade with another counterparty. This is especially true for low-liquidity markets of “exotic” cross-courses.

Summarizing the chapter, we can say that the analysis and forecasting of cross rates does not differ from the analysis and forecasting of the main rates against the U.S. dollar, i.e. the same tools are used, which will be discussed in the Forex School section of the Forex Arena information portal.