In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status quo and the lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence.