At a quick glance we can see that the islands are related by proximity. This is evident, for example, for the pairs that share a base currency: EURUSD, EURGBP... As a result, movement in one of the islands affect the movement of the adjacent: the move of EURSD affect to EURGBP, EURJPY...
This relationship is mathematically explicit by a simple equation:
EURUSD = x * EURGBP
Where x is something that explains the relationship between EURUSD and EURGBP; in this case x = GBPUSD
That is, the price of a pair can be deduced through the product of the proximate pairs. This algebraic equality can be expressed geometrically:
This equality is a constant that is deducted from the first axiom of the market: the no-arbitrage. Or, likewise: it’s impossible to obtain profitability without risk.
The above equality is what is known as a triangular position, but we can create all sorts of positions; for example, a square position:
EURJPY = EURGBP * GBPUSD * USDJPY
These algebraic equalities are much easier to see if we replace the name of the currency with a number:
EUR = 1
USD = 2
GBP = 3
JPY = 4
As a result of this replacement, the abo…