Let's assume you are based in France but you are a UK citizen. We can say you are mostly concerned about EUR (because you currently live and spend in Eurozone) and GBP (because you might at some point go back to UK to live there). So you are in a situation of uncertainty regarding which currency to see as your base currency. From a trading perspective I can see it makes a lot of sense to trade GBP/EUR (so that you can try at any time to keep your money invested in the currency you expect will be increasing in th next future).
But if you want to trade FX, how would you approach the trading of other currency pairs? So, assume I might want to trade USD/JPY and that I want to allocate to that activity 20,000 EUR. So the equivalent of 20,000 EUR will be dedicated to the trading of USD/JPY.
Even if I am always correct when trading this pair, I am ultimately concerned about its value in terms of EUR and GBP. In other words, I don't want the profits from that trading activity to go down only because the USD or JPY has depreciated against my two candidate base currencies.
What would be the best strategy to trade USD/JPY and still have some protection against depreciations in terms of base currencies?