For a price process that has an equivalent risk neutral measure, we investigate if the same property holds when the numraire is changed. We give necessary and sufficient conditions under which the price process of a particular asset-which should be thought of as a different currency can be chosen as new numraire, I he result is related to the characterization of attainable claims that can be hedged. Roughly speaking: the asset representing the new currency is a reasonable investment (in terms of the old currency) if and only if the market does not permit arbitrage opportunities in terms of the new currency as numraire. This rough but economically meaningful idea is given a precise content in this paper. The main ingredients are a duality relation as well as a result on maximal elements. The paper also generalizes results previously obtained by Jacka, Ansel-Strieker and the authors