The point of statistical arbitrage is to make markets consistent. For example, if
- GBP trades against USD at 2:1, and
- USD trades against JPY at 10 000:1, then
- GBP had better be trading against JPY at 20 000:1 !!
! Anything else wouldn’t make sense. Wouldn’t be fair either. The Japanese shouldn’t get a better or worse deal vis-à-vis the British than anybody else.
So stat arbs look for inconsistencies across markets — across currencies, products, different issues of the same stock — and trade against them.