Given knowing exchange rates of one currency against all foreign currencies, can it be used to calculate the exchange rate of two foreign currencies?

Question

I have a small task to make a currency converter (not for practical use, just as an up-to-standards technical exercise).

The only source of data available (specific project requirements) is the exchange rates of EUR against different foreign currencies, AUD and GBP, for example.

Given that I have data on EUR -> AUD conversion and EUR -> GBP, can I get AUD -> GBP by using EUR such that AUD -> EUR -> GBP? In other words, convert AUD to EUR, then convert EUR to GBP.

Playing with some conversions on the back of an envelope somewhat checks out. I am fine with the implementation side of things, but not with exchange rates and the like, hence I would rather not make assumptions and double check how off this would be.

Answer 1

Given this is not for practical use, you should get sufficient accuracy 'triangulating' the exchange rate to a 3rd currency by going between 2 other known rates. Any 'slippage' between, say, CAD:USD, CAD:GBP, and GBP:USD would be infinitesimal, lasting only brief moments in time.

FX markets are incredibly liquid, which makes them incredibly efficient. Any discrepancy between your calculation and the 'true market rate' would represent an 'arbitrage opportunity', where someone could buy and sell the correct currencies to get the 'better' rate. Such opportunities in efficient markets are immediately captured by institutional trading algorithms that look for fraction-penny profits. So for sake of being 'close enough', this will very much meet your needs.