Relation between currency crosses

Question

Suppose we have 3 crosses that are related.

USD/EUR, CNY/EUR and CNY/USD.

If two develop in some way, over say a month? Must the three develop in a certain one?

Say if USD/EUR up and CNY/EUR down by same amount must CNY/USD be flat?

Answer 1

If USD:EUR does not correlate precisely with the movements in EUR:CNY and CNY:USD, then there would be an 'arbitrage' opportunity. This means you could profit, at no risk to yourself, by quickly buying, say, CNY, converting to USD, and then converting to EUR, which you would again use to buy a larger amount of CNY, which you would then use to buy USD, then buy EUR, then buy a little more CNY again...

Consider this from first principles: in any efficient, liquid market [ie: publicly available information is acted on quickly by many parties, creating a constant 'true value' based on that information of tradeable securities], you should assume that such arbitrage opportunities do not exist. Major currencies are traded with incredible speed and efficiency, so much so that in order to take advantage of things like central bank interest rate announcements, large trading firms will benefit even by placing their computer physically closer to exchange centres, to trade milliseconds faster than the other guy, because any possible arbitrage opportunity, even a small one, will vanish (nearly) immediately.

There is simply no way for any retail investor to profit in any way whatsoever by taking advantage of theoretical pricing differences in currency crosses, as in your example. On a long-term basis, it is even more true that a currency cross should provide for exactly equivalent rates, no matter the 'direction' you travel to get there. This is before even considering transactional 'friction' on rate differentials available to a retail investor, or anything like broker commissions.