We provide new characterizations of the preference for additive and multiplicative risk apportionment when risk ordering relies on stochastic dominance. We then point out a simple property of risk apportionment with additive risks: Quite generally, an observed preference for additive risk apportionment in a specific risk environment is preserved when the decision-maker is confronted to other risk situations, so long as the total order of stochastic dominance relationships among risk couples remains the same. The main objective of this paper is to check whether this simple property also holds for multiplicative risks environments. We explain why this is not the case in general, and then provide a set of conditions under which this property holds. We also show that it holds – and even more strongly – in the case of CRRA utility functions due to a particular feature of this family of utility functions.