It wasn't an arbitrage thing and I'm not sure there's anything fruitful in the comparison to saudi arabia.

The Spanish Empire was, more than anything else, a product of the reconquista. The major institutions of Spain were all directed towards the taking and holding of new lands. When granada finally surrendered in 1492, the monarchy turned towards conquering the canaries and then the new world to avoid the large scale structural changes needed to go from a militaristic, medieval nation to a peacetime state in the early modern. The systems of repartimiento and encomienda were more or less borrowed wholesale from the reconquista. The conquistadors and chroniclers all saw the Americas through the lens of the chivalric literature they loved. The name "California" was borrowed from one of those books, about a fictional island of Amazons who aided the moors.

Precious metals were a solution to the problems Spanish monarchs had in organizing Spanish society. It paid for soldiers in the monarchy's constant wars. It paid off loans to italian and dutch financiers, and it was something that could much more easily be controlled by a distant monarch than import duties or taxation (which nobility were largely exempt from). It also gave them some limited control over their inflation issues by devaluing and revaluing the coinage as financial pressures required. This eventually caused other problems, but the point is that Spain was never really an arbitrage play. They didn't have to be, since they controlled some 30% of the world's gold supply and >90% of its silver at points.