# Forex Algebra

Okay, today we’re going to discuss forex algebra. Remember algebra from school, a + b = c ? I know there are some traders out there that don’t know this, and that’s fine. You can be a very successful trader without knowing this, but from my point of view I think it’ll make you look very amateur or ignorant. You want to look professional. Besides, this can come in handy sometimes and you always want to add to your knowledge. We’re going to get started right away.

### Long or Short

• If you buy USD/JPY, you are long USD and short JPY. You profit when the chart rises.
• If you sell USD/JPY, you are short USD and long JPY. You profit when the chart falls.

See the connection? If you buy you are always long the first currency (the base currency) in the currency pair and short the other. The other way around is also true. Now, how can this be useful?

Most of the time you just say you are long USD/JPY, it implies long USD and short JPY. The other way is also true.

### The Hedge

Say for example you decide to sell CAD/JPY, and at the same time you thought it was a good idea to buy EUR/JPY. What happens is this:

• JPY long
• EUR long
• JPY short

What really happens is this:

• JPY long
• EUR long
• JPY short

They cancel each other: you end up having bought EUR/CAD (long EUR, short CAD). Maybe you had a valid reason to do so, perhaps it was a part of your trading strategy and you viewed the two trades as two completely separate. However, it’s important to understand that, as for this moment, your exposure to JPY has been completely hedged*: whatever happens to JPY will not affect your NAV. Can we use this to our advantage?

### Synthetic Pairs

Creating a synthetic pair requires you to enter two orders simultaneously

For instance, you want to buy gold against your home currency SEK. Of course your broker is not offering you the XAU/SEK, you will have to create it for your own: long XAU/USD and long USD/SEK. Yes, do the calculation, see if it adds up (long XAU, short USD + long USD, short SEK).

*However, all of this is only true as long as the two positions completely cancel each other. In the example above, both the XAU/USD and the USD/SEK trade would have to be “worth” the same amount i.e. being of the same “trade value” at the time of execution. For example, a trade value of 10, 000 USD each (later the value will change according to the market).

Now, you could calculate the exact amount of units needed for each trade (search the internet if you don’t know how to do this, this is beyond the scope of this article). Although, most of the time I just use the order window on the platform, which has a field for the estimated trade value, and I get the numbers about right. Anyways, it’s impossible sometimes (e.g. if not both the base currencies are the same) to get the numbers exactly right as the market is constantly moving. I guess, if you’re really obsessed you could just buy or sell more of the pair you overshot with to get it exactly right. Although, it should be of such a small amount that it should not matter much.

### Quotation and Charting

How do we get the price for synthetic pairs and what about charting? Easy, since the expression is purely algebraic we just take (XAU/USD) / (USD/SEK) (USD was hedged out) -> (XAU/1) / (1/SEK), so to get the price of XAU/SEK just take XAU/USD * USD/SEK. Or in the original expression ((XAU/USD)/1) / (1/(USD/SEK)). The same goes for charting, just take the historical quotes and multiple them to get the data for your chart. However, for a more convenient way I sometimes rely on finance.yahoo.com. Just type in the currency pair you’re interested in in the quote box, like this “XAUSEK=X”, and you get some limited charting too.

### Final words

It's always good to keep track of your overall exposure

It’s not that often I trade synthetic pairs since I most do day trading, and as the higher costs, difficulties charting and the time required to enter and exit a trade it wouldn’t make sense anyways. However, I do use them sometimes for swing and position trading when I have a very clear picture of the position I want to take.

Another drawback of synthetic trading is the double margin requirement because you’re opening two positions. All retail forex brokers / market makers I know of are counting your margin based on open trades and not overall exposure, which however would seem like a more logical approach. I think there is more the brokers could do for us, besides better margin utilization, like synthetic charting and an easier way to open and close trades right on the platform. However, since we don’t trade synthetic pairs that often the demands are probably not high enough.

Even though you’re not going to use synthetic trading that much it’s always good as a trader to know how opening a position will affect your overall exposure and risk, and to be able to do some calculations if necessary. The possibilities are endless, to partial close a position—simply sell or buy back some units in the same pair, to partial hedge—open a position in a new pair. Construct synthetics from three pairs or more if you need to, for example TRY/JPY from (short EUR/TRY, long EUR/USD, long USD/JPY) and you would get the price from taking (EUR/USD / EUR/TRY) * USD/JPY (create TRY/USD first).

Last update: 2012-05-05 23:17

1 priyasekhar August 4, 2011 at 4:09 pm