Cross rates are a function of the
prices of the underlying USD pairs. Depending how the dollar pairs are quoted
(that is, whether the USD is the primary or the secondary currency), the cross
rate is going to be either the product of multiplying the rates of two dollar
pairs or the quotient of dividing the rates of two dollar pairs. But each currency
quote has two sides: the bid and the offer.
To calculate the cross rate,
EUR/JPY for example, look at each bid/offer of each dollar pair and ask
yourself what it means. If EUR/USD is quoted as 1.3110/13, from the
market-maker’s perspective the price of 1.3110 is where EUR are bought and USD
are sold. The price of 1.3113 is where EUR are sold and USD are bought. If
USD/JPY is quoted at 117.50/54, the price of 117.50 is where USD are bought and
JPY are sold, and the price of 117.54 is where USD are sold and JPY are bought.
To calculate the bid in EUR/JPY, you need to come up with the price that
matches where EUR are bought and JPY are sold, which corresponds to a 1.3110
bid in EUR/USD (where EUR are bought) and a 117.50 bid in USD/JPY (where JPY
are sold), resulting in a EUR/JPY bid rate of 154.0425 (1.3110 X 117.50). To
calculate the offer of EUR/JPY, you’d use the offer side of both USD rates, in
this case 1.3113 and 117.54, giving you a EUR,/JPY offer rate of 154.1302.
Putting the two together and rounding a bit, you’d have a EUR/JPY quote of
154.04/13. But that’s a very wide spread, and the conventional market quote
would be only 3 to 4 pips wide. In this case, an online trading platform would
likely show a EUR/JPY price of 154.06/10 or 07/10. As you can see, you can get
a tighter spread by dealing directly in the cross pair than you could ever get
by going through the dollar pairs (or components
or legs, as they‘re typically
called).
The reality for online traders is
that you don’t really need to know how cross rates are calculated, because the
online trading platforms are doing it for you and narrowing the spread to boot.
Different cross pairs have different
spreads depending on the spreads of the underlying USD pairs, with less-liquid
and more-volatile pairs resulting in wider cross spreads. For instance, GBP/JPY
is going to have a wider spread than EUR/JPY because of the lower liquidity and
higher volatility of GBP/USD relative to EUR/USD. But because the components of
wider-spread crosses are more volatile, the cross rates themselves will also be
more volatile, allowing the spread to be recouped, typically in relatively
short order.
