I assume some process will flip a fair coin to choose which of {A, B} will go up and which will go down.
In that case it seems to me that holding any combination of A and B is equally good. I don't see how this could be an example for principles intended to be used to choose an investment, given that there is no meaningful choice to be made here.
@robryk I think you're unusual, then, in that most people tend to think of how rich they are in terms of either the currency where they live, or maybe a major international currency.