A currency cross is any currency pair which does not involve the US Dollar (USD) directly. Since USD is the world’s reserve currency, it is involved in most currency exchange transactions as an intermediary, or “vehicle currency”. This is the basis for synthetic currency crosses.

There are times when we want to trade a particular cross and our broker doesn’t offer it in their tradeable instruments panel. We don’t want to miss the trade, so what can we do? We can try to open an account at another broker that does offer it, but this can be a time consuming, risky and ultimately futile exercise. If you are comfortable with your current broker and don’t want to risk your money in the unknown, or you want to take the trade now instead of waiting to open and fund a new account, or simply know that no one offers the same conditions as your current broker, then you are left with only one more choice, and that is to enter the exciting world of “Synthetic Crosses”.

A bit of advice first: Please make sure that your broker offers sufficiently small deal size increments – appropriate for your account size. Ideally, for maximum accuracy, single unit deals are recommended, but if you have a larger account you can get by with micro lots. In general though, the smaller, the better. You can look through my Broker Reviews section to find yourself a suitable one (link can be found at the bottom of this article).

The next thing to figure out is which USD components make up the currency cross you are trying to create synthetically. For example, if you want to trade CHF/JPY, then you would simultaneously open trades in USD/CHF and USD/JPY.

Once you know the components, you then need to figure out whether to go long or short on each one. Remember that currency pairs behave like fractions in mathematics, so we easily see that if you want CHF on top, you will have to “flip” USD/CHF, meaning you have to short it. You will also notice that JPY is already at the bottom where it should be, so you go long USD/JPY.

The next thing to figure out, naturally, is how much of each component pair do you buy or sell? In order to do that, we have to look a bit at the way the pairs are structured. For the most part, an arbitrary pair X/Y is the exact opposite of the pair Y/X. If you go long one, it is the same as shorting the other, with only one difference. The difference stems from the way brokers calculate lot sizes. If you are long 10,000 units (1 mini lot) of X/Y, you are buying 10,000 units of X by borrowing the appropriate amount of Y on margin. If you are short 10,000 units of X/Y, you are still using 10,000 of X, but this time borrowing it, and selling it for the appropriate amount of Y according the the current market rate. *The number of units always applies to the base currency*, regardless of whether you are going short or long – if you are long, you are buying 10,000 units of the base currency, and if you are short, you are selling 10,000 of the base currency. So the difference between X/Y and Y/X is due to the fact that when you are trading X/Y you are always dealing in units of X, but when trading Y/X you are dealing in units of Y. This is a very important distinction, and making it now will help us to calculate synthetic pairs.

There are 3 types of synthetic crosses that we can build. Let X/Y be our cross:

**Type1.** X/Y with components X/USD and Y/USD. An example of this type would be EUR/GBP, with X=EUR and Y=GBP. By looking at the components, we know we have to long one and short the other. If we want to go long X/Y, then we have to go long X/USD and short Y/USD. If you want to go short X/Y, you reverse that so go short X/USD and long Y/USD. Since we now know that position sizes always deal with the base currency, we know that the trade sizes for long and short positions will be the same even for the components. So let’s do the calculation:

Let S be the position size of the pair in parentheses, and P be the current market price of the pair in parentheses:

S(X/USD) = S(X/Y) –> The size of the X/USD component should be the same as the trade size you decided on for X/Y. This makes sense since in both instances we end up holding the same amount of X for longs, and selling the same amount of X for shorts.

S(Y/USD) = -P(X/Y) x S(X/Y) –> Simply take your desired position size for X/Y, multiply it by the current market price of X/Y and change its sign to indicate that the position is in the opposite direction of the X/USD component, that is, if one is long, the other is short.

**Type 2.** X/Y with components X/USD and USD/Y. An example of this type would be EUR/JPY, with X=EUR and Y=JPY. By looking at the components, we know that both trades will be in the same direction. If we want to go long X/Y, then we go long both X/USD and USD/Y.

Let S be the position size of the pair in parentheses, and P be the current market price of the pair in parentheses:

S(X/USD) = S(X/Y) –> Again, since we want to end up holding the currency X, we make sure that the amount of X/USD we buy is the same as the amount of X/Y we want to buy (for longs) or sell (for shorts) overall.

S(USD/Y) = P(X/USD) x S(X/Y) –> Our fact about long and shorts both being dealt in base currency sizes pays off again. The amount of USD/Y we deal is equal to the amount of X/Y we want to deal multiplied by the current market rate of X/USD. Please note that the sign remains the same as S(X/USD) since both trades will be in the same direction (either both long, or both short).

**Type 3.** X/Y with components USD/X and USD/Y. An example of this type of cross would be CHF/JPY with X=CHF and Y=JPY. By looking at the components, we know that we have to long one and short the other. This is the easiest type of synthetic cross to construct because, as you will see below, the trade sizes for both components are identical to one another (albeit in opposite directions).

Let S be the position size of the pair in parentheses, and P be the current market price of the pair in parentheses:

S(USD/X) = -S(X/Y) / P(USD/X) –> Since we have to invert this pair to get X on top, we short this one when we want to go long X/Y, and we long this one when we want to go short X/Y. The trade size is just your intended trade size for X/Y divided by the current marketk rate of USD/X

S(USD/Y) = S(X/Y) / P(USD/X) –> Both pairs have USD as the base currency, so the trade sizes will be the same – only the direction will be different. As a result, please note the absence of a negative sign in this equation.

Just to make sure this is not all too abstract, here is an example for each type of synthetic cross:

1. Long 10,000 units of EUR/GBP at price 0.8000 by using USD components EUR/USD and GBP/USD:

S(EUR/USD) = S(EUR/GBP) = **10,000 units**

S(GBP/USD) = -P(EUR/GBP) x S(EUR/GBP) = -0.8000 x 10,000 = **-8,000 units** (negative means that a short position is taken in this pair)

2. Short 10,000 units (-10,000 units) of GBP/JPY at a market rate of 200.00 by using USD components GBP/USD and USD/JPY. This is a type 2 synthetic pair, so in this example we also need to know the price of GBP/USD at the time we enter the trade, so let’s say it is 2.0000:

S(GBP/USD) = S(GBP/JPY) = **-10,000 units** (negative means short)

S(USD/JPY) = P(GBP/USD) x S(GBP/JPY) = 2.0000 x (-10,000) = **-20,000 units **(negative means short)

3. Long 10,000 units CHF/JPY at a market rate of 90.00 by using USD components USD/CHF and USD/JPY. This is a type 3 synthetic pair, so in this example we also need to know the price of USD/CHF at the time we enter the market so let’s make it 1.1000:

S(USD/CHF) = -S(CHF/JPY) / P(USD/CHF) = -10,000 / 1.1000 = **-9,090 units **(negative means short)

S(USD/JPY) = S(CHF/JPY) / P(USD/CHF) = 10,000 / 1.1000 = **9,090 units** (we already saw earlier that type for type 3 synthetic crosses -S(X/USD) = S(Y/USD) which checks out fine here)

I would like to add that for types 2 and 3, in theory, as soon as price moves away from your entry, the trade sizes should be recalculated and you should add to the positions which become misaligned, since the unit sizes depend on price. In practice, however, this is normally both unnecessary and impractical. In fact, even your broker doesn’t do it when you trade their “natural crosses”. This only becomes an issue for trades spanning thousands of pips, and can usually be done every 500 pips or so, depending on the pair.

**Spreads**

It should also be noted that spreads were not taken into account in this article. It is assumed that traders understand the idea of bid and ask prices. In any case, spreads are normally insignificant in longer term trading and I generally don’t recommend trading crosses (synthetic or otherwise) in the short term. If you plan to do this, you would be well advised to check how much you are paying in spread for each USD component, taking into account the trade sizes you calculated using the above methods, and see if the spread is comparable to the spread other brokers charge for this cross.

**Swap**

Because brokers each have their own way of calculating swap, or overnight interest, also check how the swap you are receiving on your synthetic pairs compares to the swap other brokers pay for that same cross. This is important in carry trade strategies, many of which are best served by cross pairs.

**Used Margin**

The USD components of your synthetic cross actually cancel each other out – if you check, you will notice that you are always both short USD and long USD by the same amount, giving you no net exposure to USD. Most broker platforms are not smart enough to figure that out, so as a result, your “used margin” will in many cases be higher when trading synthetic crosses than when trading their natural counterparts. This should not make a difference to most traders, unless they are over-leveraged.

**Arbitrage**

It is possible at times to see a difference between the price offered on a natural cross and the price you could get by trading the same cross in synthetic form, opening up the possibility of arbitrage, particularly if the price feeds come from two different market makers. The situation is rare, the lucky trader who spots it must be quick (or better yet, use an automated system), and the opportunity must be big enough to cover the large spread on crosses. Needless to say, viable opportunities don’t arise often. On top of that, if your broker finds out, they probably won’t be too happy with you either. In any case, opportunities like this can be found from time to time, and they are worth a second look. Free, riskless pips will always put a smile on your face.

Source by Eric Mills