This paper examines the predictions of expectations-based reference-dependent models for risk-apportionment tasks that elicit higher-order risk attitudes. We consider some of the most commonly used specifications of Kőszegi and Rabin (2006, 2007) and disappointment aversion models. Our analysis reveals that higher order risky choices exhibited by decision makers defined by those model specifications depend on whether risks to be apportioned in these tasks are symmetric or asymmetric, whether they include small probability outcomes, and on the level of loss aversion. We highlight that some of the predicted choice behaviour in the risk-apportionment tasks differs from the ones in alternative models of decision under risk. We employ experimental data to examine whether choice patterns in the risk apportionment tasks are in line with the predictions of the model specifications described here. We find that only a small proportion of them are consistent with those predictions.