I have a limited financial background but I'm trying to figure out the usefulness of buying size-n arbitrages (n > 3), and I wonder the kind of risks - if any - associated with such a strategy.
Say that I simultaneously detect :
- a triangular arbitrage with currencies A, B and C (one intermediate currency) ;
- a quadrangular arbitrage with currencies A, B, C and D (two intermediate currencies) ;
- a quintangular arbitrage with currencies A, B, C, D and E (three intermediate currencies) ;
Now suppose that I decide to buy all these arbitrage opportunities at the same time and buy, for each of them, the same amount of the first currency. If I get I right, I'll actually be buying 3 times the first size-3 arbitrage, 2 times the second one and 1 time the last one. Despite triangular arbitrage being theoretically risk-free, we know that we may encounter potential issues here when facing real market conditions, ie. latency, not to mentions transaction costs and finite (limited) margin.
Plus, buying the quadrangular arbitrage would also mean that we could possibly be buying up to 4 different triangular arbitrages opportunities instead (i.e. one, some or all of the following permutations : A, B, C / B, C, D / A, C, D / A, B, D).
The reasoning goes on for all size n arbitrages opportunity where I could potentially be simultaneously buying at least n - 2 arbitrage opportunities.
Both theoretically and practically speaking, would it be wise to filter out some (or all) of these size > 3 arbitrage opportunities, and if so, why ? Or, in the contrary, would a strategy actually benefit from simultaneously buying all these arbitrage opportunities ? The maths behind this puzzles me !