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Chapter 7: Cross Rates
Trading on the Forex market involves not only transactions involving the US dollar. However, up until now, we intentionally focused on transactions involving the US dollar to simplify the presentation of the material on the website. Currency exchange rates that do not involve the US dollar are called cross rates. Cross rates are typically traded by experienced traders on the Forex market because effectively working with them requires in-depth knowledge of economic indicators and data specific to individual countries. Examples of cross rates include the British pound sterling to Japanese yen (GBP/JPY), the euro to Japanese yen (EUR/JPY), or the British pound sterling to euro (GBP/EUR) exchange rates.
For the major (dollar-based) currency quotes, the currency positions are strictly defined. However, in cross-rate quotes, the currency positions can vary depending on the party providing the quote. For example, a bank in Canada may quote the Canadian dollar to the Euro as CAD/EUR, while a bank in Europe may quote it as EUR/CAD. This nuance should be taken into account when trading cross rates to avoid making false buying/selling decisions. An exception to this is the British pound sterling, which is always quoted in cross rates as GBP/___, meaning it is always the base currency.
Cross-rates are of interest in Forex because they allow traders to bypass direct dependence on the US dollar and focus on specific factors and events related to individual countries and their economies. In the given example, using cross-rates allows the trader to concentrate on the economic boom in Canada and the temporary decline in Japan, bypassing the uncertainty regarding the US dollar.
By conducting operations based on cross-rates, traders exclude the intermediary currency (US dollar) and can have a more direct impact on the relationship between the currencies of their interest. This enables them to express their expectations more accurately regarding two specific currencies and potentially profit from their fluctuations without the additional uncertainty associated with the US dollar.
However, it should be noted that trading cross-rates requires a deeper understanding of the economic situation in each individual country and its currency, as well as consideration of other market factors. This is why trading cross-rates in Forex is typically associated with experienced traders who have a broader analytical toolkit and market knowledge.
The majority of Forex transactions involve major (dollar-based) currency pairs. The market for cross-rates, on the other hand, is much less liquid. Therefore, cross-rate quotes are not calculated based on the demand and supply of currencies relative to each other, as is the case with major currency pairs. Otherwise, the cross-rate market would become speculative, and individual participants could potentially control it completely. Thus, despite the absence of the US dollar in cross-rate quotes, cross-rates are calculated relative to major currency quotes involving the US dollar.
So, how are cross-rates calculated? There are three possible methods for calculating cross-rates, depending on whether the US dollar serves as the base or quote currency in the major currency pairs involving the currencies of interest. In these calculations, we use simple rules of multiplication and division of fractions, which are familiar to us from basic mathematics courses. However, it should be noted that the notation USD/JPY should not be interpreted literally as a fraction. If the quote for the Japanese yen against the US dollar were represented as an actual fraction, then the quote value of 104.78 (the amount of Japanese yen per US dollar) would correspond to the notation JPY/USD. In practice, however, the reverse notation of USD/JPY is used.
The first method of calculation is used for currencies with direct quotes against the US dollar (where the US dollar is the base currency for both currencies). Let's consider the Japanese Yen (JPY) and the Swiss Franc (CHF). By having quotes against the US dollar for USD/JPY and USD/CHF, we can use the properties of fractions to derive the cross-rate of the Swiss Franc against the Japanese Yen:
CHF/JPY = USD/JPY : USD/CHF,
meaning we need to divide the US dollar quote for the Japanese Yen by the US dollar quote for the Swiss Franc. For example, if we have USD/JPY at 104.78 and USD/CHF at 1.0505, the cross-rate of the Swiss Franc against the Japanese Yen would be (rounded) CHF/JPY 99.74.
The second method of calculation is used for currencies with direct and indirect quotes against the US dollar (where the US dollar is the base currency for one currency and the quote currency for the other). Let's consider the Japanese Yen (JPY) and the Australian Dollar (AUD). By having quotes against the US dollar for USD/JPY and AUD/USD, we can use the properties of fractions to derive the cross-rate of the Australian Dollar against the Japanese Yen:
AUD/JPY = AUD/USD * USD/JPY,
meaning we need to multiply the US dollar quote for the Australian Dollar by the US dollar quote for the Japanese Yen. For example, if we have USD/JPY at 104.78 and AUD/USD at 1.0564, the cross-rate of the Australian Dollar against the Japanese Yen would be (rounded) AUD/JPY 110.69.
Similarly, for the cross-rate of the British Pound against the Australian Dollar:
GBP/AUD = GBP/USD : AUD/USD,
meaning we need to divide the US dollar quote for the British Pound by the US dollar quote for the Australian Dollar. For example, if we have GBP/USD at 0.5028 and AUD/USD at 1.0564, the cross-rate of the British Pound against the Australian Dollar would be (rounded) GBP/AUD 0.4760.
It is worth noting that to simplify the calculation formulas, we have excluded the concepts of bid and ask prices of currency quotes and have so far only used the current spot prices. However, each major (dollar-based) quote has two prices, and the calculated cross-rate quote also has two prices. So where do we plug in the bid price and the ask price in the formula? The answer lies in understanding the logic of calculating cross-rates.
Let's revisit the example of the first calculation method with the Swiss Franc (CHF) and the Japanese Yen (JPY). We are interested in the cross-rate quote CHF/JPY. To determine the bid price of the Swiss Franc in this quote (bid/ask prices, as we already know, always relate to the base currency of the quote), we need to reason as follows: We are interested in buying Swiss Francs, which means we first need to buy US dollars with Japanese Yen and then sell them for Swiss Francs. Therefore, in the USD/JPY quote, we are interested in the bid price, and in the USD/CHF quote, we are interested in the ask price. Hence, the bid price of the Swiss Franc for the Japanese Yen in the cross-rate quote CHF/JPY is calculated using the formula:
CHF/JPY(bid) = USD/JPY(bid) : USD/CHF(ask)
Similarly, we can calculate the formula for the ask price of the Swiss Franc for the Japanese Yen in the cross-rate quote CHF/JPY:
CHF/JPY(ask) = USD/JPY(ask) : USD/CHF(bid)
For the examples in the second and third calculation methods, the formulas are computed similarly:
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 is worth noting that dealers rarely use these formulas due to their complexity. There is a more convenient commonly accepted method for calculating the bid and ask rates in cross-rate quotes on Forex. This method is as follows: Take the average value of the bid and ask rates for each of the dollar-based quotes. Then, using the formulas for spot prices, calculate the current value of the cross-rate quote. This value is then "spread" in opposite directions by a certain number of pips (the spread is set), thus obtaining the bid and ask rates for the cross-rate quote.
Let's consider an example with the Swiss Franc (CHF) and the Japanese Yen (JPY). Suppose the buying/selling rates for these currencies against the US Dollar are as follows: USD/CHF 1.0502/08 and USD/JPY 104.74/82. We calculate the average rates:
USD/CHF(avg) = (1.0502 + 1.0508) / 2 = 1.0505,
USD/JPY(avg) = (104.74 + 104.82) / 2 = 104.78.
These average rates are then used in the formulas to calculate the cross-rate quotes for spot prices. The calculated value of CHF/JPY(avg) as 99.74 is then "spread" by, let's say, 5 pips in both directions, resulting in the bid and ask rates of CHF/JPY as 99.69/79.
It should be noted that in this simplified calculation method, there are some pitfalls. Since profits are made in Forex through opposing (offsetting) transactions, the spread should be large enough to avoid losses when closing the position with another counterparty. This is especially important for low-liquidity markets of "exotic" cross-rate quotes.
In conclusion, the analysis and forecasting of cross-rate quotes do not differ from the analysis and forecasting of major currency rates against the US Dollar. The same tools and techniques are used, which will be discussed in the "Forex School" section of the Forex Arena information portal.