I've studied this so called, Triangular arbitrage and it's a misnomer. A misheld belief that a currency ring (ie. 3 currencies) has some kind of advantage over trading a single currency, but as I will explain.. it's a fallacy.
Take an example currency ring like:
by dividing AUDUSD / NZDUSD you get the AUDNZD price.
case in point. you would do the same to trade that 1 currency
and save yourself the cost of 2 spreads.
The other point is the other 2 pairs can converge or diverge
longer that you can hold onto a negative trade. They have
a term for this and it's called correlation drift.
I'd just like to save you guys, many hours and many dollars.
actually this is not the proper analysis. if you buy aud/nzd, sell aud/usd and buy nzd/usd, your exposure is nil except the spread, so how are you getting aud/nzd?
you are simply short .25 lots NZDUSD, but in a more convoluted way using 3 pairs instead of 1.buy aud/nzd, sell aud/usd and buy nzd/usd
I'm surprised you ask how to get AUDNZD and yet say it's not proper analysis?
AUDUSD / NZDUSD = AUDNZD you can use a calculator on current prices to verify this. The other 2 are always a product of the 3rd.
No your exposure is not nil...
This is how you calculate exposure in a currency ring, using the said pricing of the example 3 pairs, but it works for all currency rings.
AUDNZD 1.25 = buy 100000 AUD$ sell 125000 NZD$
AUDUSD 1.05 = sell 100000 AUD$ buy 105000 USD$
NZDUSD 0.84 = buy 100000 NZD$ sell 84000 USD$
now subtracting the like currencies exposure in USD$ is still long $21000 or .21 lots
and exposure in NZD$ is still short $25000 or .25 lots
so in your example:
you are simply short .25 lots NZDUSD, but in a more convoluted way using 3 pairs instead of 1.
So your exposure is niether nil nor is your risk reduced to less than those lots calculated. Anyway the important thing here is not so much the percieved nil exposure, but the view that you are trading anything more than a single currency when you have in fact purchased 3 at nothing but additional cost.