Higher-order Risk Preferences Research Articles

Higher-order risk preferences and livelihood choices of farmers from West Bengal, India

Higher-order risk preferences and livelihood choices of farmers from West Bengal, India

Higher order risk preferences and economic decisions

Higher order risk preferences and economic decisions

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

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

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.

The Reflection Effect for Higher-Order Risk Preferences

Abstract Higher-order risk preferences are important determinants of economic behavior. We apply insights from behavioral economics: we measure higher-order risk preferences for pure gains and losses. We find a reflection effect not only for second-order risk preferences, as did Kahneman and Tversky (1979), but also for higher-order risk preferences: we find risk aversion, prudence and intemperance for gains and much more risk-loving preferences, imprudence and temperance for losses. These findings are at odds with a universal preference for combining good with bad or good with good, which previous results suggest may underlie higher-order risk preferences.

Framing effects on the strength of higher-order risk preferences

This study provides the first experimental evidence on whether framing affects elicited intensity of prudence. The framing effect is not significant at the aggregate level, but a closer look shows that more than 70% of subjects are influenced by framing.

Multivariate risk preferences in the quality-adjusted life year model.

The interest in multivariate and higher‐order risk preferences has increased. A growing body of literature has demonstrated the relevance and impact of these preferences, but for health the evidence is lacking. We measure multivariate and higher‐order risk preferences for quality of life (QoL) and longevity, the two attributes of the Quality‐Adjusted Life Year (QALY) model. We observe preferences for a positive correlation between these attributes and for pooling together a fixed loss in one of the attributes and a mean‐zero risk in the other, and for pooling together mean‐zero risks in QoL and longevity. The findings indicate that higher‐order risk preferences are stronger for health than for money. Furthermore, we test if preferences for a risky treatment for a disease affecting only QoL, depend on life expectancy. We find no such a relation, but there is a positive relation between riskiness of a comorbidity affecting life expectancy and risk aversion for a QoL treatment. We therefore observe no definitive deviation from the QALY model, although the model is more robust when expected longevity is high. Our findings suggest that the current practice of cost‐effectiveness analysis should be generalized to account for risk aversion in QoL and longevity, and higher‐order preferences.

Higher Order Risk Preferences in the Koszegi-Rabin

Higher Order Risk Preferences in the Koszegi-Rabin

Higher Order Risk Preferences in the Koszegi-Rabin

Higher Order Risk Preferences in the Koszegi-Rabin

Risk aversion, prudence and temperance: It is a matter of gap between moments

Higher order risk preferences are important determinants of choices under uncertainty. We build a questionnaire different from usually adopted ones: our questionnaire is simpler in order to reduce the number of random choices, and it includes questions with largely diversified stake sizes to observe different gaps between moments. Moreover, we collect results from a large and heterogeneous population to provide more general and unbiased results. Our results confirm the preference of the majority of the respondents for higher odd and lower even moments of the expected return distribution. However, we highlight three features: (i) the importance of the gap between the values of the corresponding moments of the two choices, (ii) the behavioral change in presence of a positive/zero/negative expected value, (iii) the huge heterogeneity in behaviors, also due to the complexity of the choice as an important driver of the propensity to switch from choosing on the basis of preferences to choosing randomly. We also find that age and geographical location are important determinants of risk propensity.

Higher Order Risk Preferences: New Experimental Measures, Determinants and Field Behavior

We use a novel method to elicit and measure higher order risk preferences (prudence and temperance) in an experiment with 658 adolescents. In line with theoretical predictions, we find that higher order risk preferences - particularly prudence - are strongly related to adolescents' field behavior, including their financial decision making, eco-friendly behavior, and health status, including addictive behavior. Most importantly, we show that dropping prudence and temperance from the analysis of students' field behavior would yield largely misleading conclusions about the relation of risk aversion to these domains of field behavior. Thus our paper puts previous work that ignored higher order risk preferences into an encompassing perspective and clarifies which orders of risk preferences can help understand field behavior of adolescents.

Higher Order Risk Preferences: New Experimental Measures, Determinants and Field Behavior

We use a novel method to elicit and measure higher order risk preferences (prudence and temperance) in an experiment with 658 adolescents. In line with theoretical predictions, we find that higher order risk preferences particularly prudence are strongly related to adolescents' field behavior, including their financial decision making, eco-friendly behavior, and health status, including addictive behavior. Most importantly, we show that dropping prudence and temperance from the analysis of students' field behavior would yield largely misleading conclusions about the relation of risk aversion to these domains of field behavior. Thus our paper puts previous work that ignored higher order risk preferences into an encompassing perspective and clarifies which orders of risk preferences can help understand field behavior of adolescents.

Multivariate risk preferences in the QALY model

In recent years the interest in multivariate and higher-order risk preferences has increased noticeably. A growing body of literature has demonstrated both the relevance and the impact of these preferences in several domains, although for health the empirical evidence is lacking. In this study we empirically measure multivariate and higher-order risk preferences for quality of life and longevity, the two elements of the Quality-Adjusted Life Year (QALY) model. We observe overwhelming support for correlation seeking between these two attributes as well as significant evidence of cross-imprudence and cross-intemperance. These findings indicate that higher-order risk preferences appear to deviate more from neutrality for health than for money. Furthermore, we test if preferences for a risky treatment for a disease affecting only quality of life, depend on life expectancy. Our results show no systematic evidence of such a relation, although there is a marginally significant positive relation between riskiness of the comorbidity affecting life expectancy and risk aversion for a treatment affecting quality of life. We therefore observe no definitive deviation from the QALY model, although the model appears to be more robust when expected longevity is high.

Higher Order Risk Preferences: New Experimental Measures, Determinants and Field Behavior

Higher Order Risk Preferences: New Experimental Measures, Determinants and Field Behavior

Portfolio choice with skewness preference and wealth-dependent risk aversion

This paper studies a dynamic portfolio choice problem for an investor with both wealth-dependent risk aversion and wealth-dependent skewness preferences. In a general economic setting, the solution is characterized in terms of a system of extended Hamilton-Jacobi-Bellman (EHJB) equations and the solution is given in closed form in some special cases. We demonstrate the effects of higher order risk preferences and state-dependent risk aversion on the optimal asset allocation decisions. We find that wealth-dependent risk aversion facilitates risk taking and the skewness preference leads to a more positively skewed portfolio in certain circumstances.

Risk Aversion, Prudence and Temperance: It Is a Matter of Gap Between Moments

Abstract Higher order risk preferences are important determinants of choices under uncertainty. We build a questionnaire different from usually adopted ones: our questionnaire is simpler in order to reduce the number of random choices, and it includes questions with largely diversified stake sizes to observe different gaps between moments. Moreover, we collect results from a large and heterogeneous population to provide more general and unbiased results. Our results confirm the preference of the majority of the respondents for higher odd and lower even moments of the expected return distribution. However, we highlight three features: (i) the importance of the gap between the values of the corresponding moments of the two choices, (ii) the behavioral change in presence of a positive/zero/negative expected value, (iii) the huge heterogeneity in behaviors, also due to the complexity of the choice as an important driver of the propensity to switch from choosing on the basis of preferences to choosing randomly. We also find that age and geographical location are important determinants of risk propensity.

Higher-order risk preferences in social settings

We study prudence and temperance (next to risk aversion) in social settings. Previous experimental studies have shown that these higher-order risk preferences affect the choices of individuals deciding privately on lotteries that only affect their own payoff. Yet, many risky and financially relevant decisions are made in the social settings of households or organizations. We elicit higher-order risk preferences of individuals and systematically vary how an individual’s decision is made (alone or while communicating with a partner) and who is affected by the decision (only the individual or the partner as well). In doing so, we can isolate the effects of other-regarding concerns and communication on choices. Our results reveal that the majority of choices are risk averse, prudent, and temperate across social settings. We also observe that individuals are influenced significantly by the preferences of a partner when they are able to communicate and choices are payoff-relevant for both of them.

Higher-degree stochastic dominance optimality and efficiency

We characterize a range of Stochastic Dominance (SD) relations by means of finite systems of convex inequalities. For ‘SD optimality’ of degree 1 to 4 and ‘SD efficiency’ of degree 2 to 5, we obtain exact systems that can be implemented using Linear Programming or Convex Quadratic Programming. For SD optimality of degree five and higher, and SD efficiency of degree six and higher, we obtain necessary conditions. We use separate model variables for the values of the derivatives of all relevant orders at all relevant outcome levels, which allows for preference restrictions beyond the standard sign restrictions. Our systems of inequalities can be interpreted in terms of piecewise polynomial utility functions with a number of pieces that increases with the number of outcomes and the degree of SD. An empirical study analyzes the relevance of higher-order risk preferences for comparing a passive stock market index with actively managed stock portfolios in standard data sets from the empirical asset pricing literature.

Skewed background risks and higher-order risk preferences: prudent versus temperate behavior

ABSTRACTIn recent economic experiments, lotteries with left-skewed background risks elicit more prudent choices than lotteries with right-skewed background risks. In this letter, we use an expected utility framework to show that a skewed zero-mean background risk may induce not only prudent but also temperate behaviour. We suggest that the experimental findings could also be due to temperance, rather than merely to prudence.

Greater Mutual Aggravation

A large strand of research has identified when (i) a single risk is undesirable and (ii) two independent risks aggravate each other. We extend this line of inquiry by establishing when (iii) mutual aggravation is greater for greater risks. This natural property of greater mutual aggravation explains recent experimental findings on higher-order risk preferences, and can guide managerial behavior when risks in the decision environment become more severe. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2746 . This paper was accepted by Han Bleichrodt, decision analysis.