It is now well established that higher-order risk preferences play a crucial role in determining the risky choices of decision makers in a wide range of important areas such as economics, finance and health. While influential theories of risky choice in those fields can explain attitudes to second order risk, the implications of these models for higher order risk preferences is still to be developed. This paper addresses that gap for the Markowitz (J Political Econ, 60:151–58, 1952) (M) model of utility which embodies reference-dependent utility, loss aversion and was seemingly the first model to explain the fourfold attitude to risk. In this paper, we set out new properties of the M model for higher order preferences, such as higher-order risky choice reversals, that can help explain experimental evidence not readily reconcilable with other models of risky choice. A second contribution of the paper is to empirically examine the heterogeneity of preference functionals describing second as well as higher order risky choices using hierarchical Bayesian estimation methods. Our analysis of the risky choices revealed in three prominent studies provides support for the M model as a useful complement to other leading models of risky choice such as cumulative prospect theory (CPT). In addition, we set up a new experiment whose design is shown to have satisfactory discriminatory power between the M and CPT specifications, and our results based on the Bayes factor confirm the heterogeneity of preference functionals across decision makers, and that the CPT specification is more prevalent.