On the predictions of cumulative prospect theory for third and fourth order risk preferences

Abstract

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.

Higher order risk attitudes: new model insights and heterogeneity of preferences

“…The M model of utility can accommodate those possibilities under any of the three reference points employed in the estimations as shown in the previous section. In that regard, the CPT model is more limited given that, for instance, under either status quo or MaxMin reference points, decision makers only exhibit prudent and temperate choices in the gains domain [see Paya et al (2022)]. It is therefore probably not surprising that the CPT specification more successfully explains the experimental results in NTK relative to those in DS10 and DS14.…”

“…In addition to this empirical analysis, we set up a new experiment to further investigate heterogeneity of risky choices of different orders across subjects, and to discriminate between M and CPT specifications. The new insights about the M model we provide in this paper, together with existing analysis about higher order risk preferences in the CPT model (Bleichrodt & van Bruggen, 2022;Paya et al, 2022), reveal different predictions between the two models under the status quo reference point that are exploited in the design and analysis of the experiment to discriminate between the two models. A comprehensive simulation exercise shows that the experimental design has satisfactory discriminatory power between M and CPT specifications that can be considered as 'representative' of those models.…”

“…Brunette and Jacob (2019) report, for lotteries in the gains domain, an average of 47.6% imprudent choices and 31.6% intemperate choices. 10 The result demonstrated in Paya et al (2022) that, from the status quo reference point, experimental subjects with the representative CPT preferences will make the prudent lottery choice over both the gains domain and the losses domain is important since CPT does not therefore accommodate a reflection effect. Bleichrodt and van Bruggen (2022) corroborate their result employing the CPT parameters of Tversky and Kahneman (1992).…”

“…However, from the average-payoff reference point, the lottery choice is temperate for ∈ [2, 3.37] and intemperate for parameter values of the expo-power exponent outside that interval. Paya et al (2022) find that the representative CPT subject will choose the prudent and temperate lottery choices from the MaxMin reference point. That result contrasts with the one for the M model and could be used to discriminate alternative preference functionals in future experimental research which can, by experimental design, implement the MaxMin reference point.…”

“…Alternatively, Deck and Schlesinger (2010) and Ebert and Wiesen (2014) assumed that the reference point was the expected value of the lottery. One of the early attempts to address the gap in the literature about reference dependence and higher order risk preferences can be found in Paya et al (2022). They examine the behaviour with regard to third and fourth order risky choices of a DM using a cumulative prospect theory (CPT) specification under three alternative reference points.…”