Is there always a currency that goes up compared to all others?

Question

Suppose you go through every country's currencies and look at the change WRT all other currencies that day. Assuming there is a change in value that day, does it stand to reason that there will always be a certain currency that goes up WRT all others and one that goes down WRT to all others everyday?

Answer 1

This is true and the reason is that currency exchange rates are transitive. That means if you know the exchange rate between A and B, and the rate between B and C, the you can compute the exchange rate between A and C (we are assuming no conversion fees as is the case for published conversion rates).

This transitivity also implies that if for example A increased relative to B and B increased relative to C than A must have increased relative to C as well. Once you know that it is straightforward that there every day there must be one currency that increased relative to all others (assuming all exchange rates changed).