Cumulative Prospect Theory Preferences Research Articles

A cumulative prospect theory explanation of gamblers cashing-out

Cash-out products offered by bookmakers allow a bettor to liquidate, for a small fee, an existing bet prior to “game end”. Previous research has found that bettors are likely to hold preferences consistent with cumulative prospect theory (CPT). We obtain analytic expressions for the ‘optimal’ proportion of the bet to cash-out for bettors with CPT preferences. Diminishing sensitivity or marginal utility leads bettors to prefer to cash-out likely winning bets, but not likely losing bets. Any preference to liquidate bets early is exacerbated by probability weighting and loss aversion. We demonstrate that partial liquidation (cashing-out a fraction of the bet) may be optimal under CPT in well-defined situations. Some potential solutions are presented for reducing the tendency for bettors to cash-out in the gain domain.

A CPT-based comparison of retirement products

We compare a variety of retirement products under cumulative prospect theory (CPT), including both well-known (variable) annuity products and some innovative, tontine-like retirement products, in which longevity risks are shared between insurers and policyholders. Following Hu and Scott (2007), an agent determines the overall CPT value by evaluating the total discounted payoffs over time compared to the initial investment made. Regarding the mortality-linked products, we find that tontines are widely preferred to annuities, tontines with guarantees and portfolios of annuities and tontines. Only in a few special cases, annuities deliver the highest CPT value. The reasons for the relative superiority of tontines is the presence of safety loadings or subjective mortality beliefs. Including financial market risk, variable annuities are found to be the most attractive source of retirement income under the majority of parameters considered. In some exceptional cases with safety loadings and some guarantee constraints, tontines with minimum guarantees can outperform variable annuities. Our results suggest that agents with CPT preferences prefer risk-carrying products with potentially higher returns to guaranteed annuities, providing alternatives to agents who are not fond of purchasing annuities.

Probability Dominance

The most commonly employed paradigms for decision making under risk are expected utility, prospect theory, and regret theory. We examine the simple heuristic of maximizing the probability of being ahead, which in some natural economic situations may be in contradiction to all three of the above fundamental paradigms. We test whether this heuristic, which we call probability dominance (PD), affects decisions under risk. We set up head-to-head situations where all preferences of a given class (expected utility, original or cumulative prospect theory, or regret theory) favor one alternative yet PD favors the other. Our experiments reveal that 49% of subjects' choices are aligned with PD in contradiction to any form of expected utility or prospect theory maximization; 73% are aligned with PD as opposed to preferences under risk aversion and under original and cumulative prospect theory preferences; and 68% to 76% are aligned with PD contradicting preferences under regret theory. We conclude that probability dominance substantially affects choices and should therefore be incorporated into decision-making models. We show that PD has significant economic consequences. The PD heuristic may have evolved through situations of winner-take-all competition.

Behavioral Investors in Conic Market Models

We treat a fairly broad class of financial models that includes markets with proportional transaction costs. We consider an investor with cumulative prospect theory preferences and a nonnegativity ...

On the Empirical Validity of Cumulative Prospect Theory: Experimental Evidence of Rank‐Independent Probability Weighting

Cumulative Prospect Theory (CPT), the leading behavioral account of decisionmaking under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by assuming that the probability weight applied to a given outcome depends on its ranking. We devise a simple and direct nonparametric method for measuring the change in relative probability weights resulting from a change in payoff ranks. We find no evidence that these weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences imply that the percentage change in probability weights should be an order of magnitude larger than we observe. It follows either that probability weighting is not rank‐dependent, or that the weighting function is nearly linear. Nonparametric measurement of the change in relative probability weights resulting from changes in probabilities rules out the second possibility. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well‐known certainty effect.

Optimal Exit Time from Casino Gambling: Strategies of Precommitted and Naive Gamblers

We consider a casino gambling model with an indefinite end date and gamblers endowed with cumulative prospect theory preferences. We study the optimal strategies of a precommitted gambler, who comm...

Direct Tests of Cumulative Prospect theory

Cumulative Prospect Theory (CPT), the leading behavioral account of decision making under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by assuming that the probability weight applied to a given outcome depends on its ranking. We devise a simple and direct non-parametric method for measuring the change in relative probability weights resulting from a change in payoff ranks. We find no evidence that these weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences imply that the percentage change in probability weights should be an order of magnitude larger than we observe. It follows either that probability weighting is not rank-dependent, or that the weighting function is nearly linear. Non-parametric measurement of the change in relative probability weights resulting from changes in probabilities rules out the second possibility. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well-known certainty effect.

Portfolio choice under cumulative prospect theory: sensitivity analysis and an empirical study

A sensitivity analysis of the impact of cumulative prospect theory (CPT) parameters on a Mean/Risk efficient frontier is performed through a simulation procedure, assuming a Multivariate Variance Gamma distribution for log-returns. The optimal investment problem for an agent with CPT preferences is then investigated empirically, by considering different parameters’ combinations for the CPT utility function. Three different portfolios, one hedge fund and two equity portfolios are considered in this study, where the Modified Herfindahl index is used as a measure of portfolio diversification, while the Omega ratio and the Information ratio are used as measures of performance.

Cumulative prospect theory preferences in rent-seeking contests

We investigate the equilibrium behavior for agents with cumulative prospect theory preferences in rent-seeking contests. Characterizing the equilibrium effort levels, we present results on the existence of equilibrium and total rent dissipation.

Can financial innovation succeed by catering to behavioral preferences? Evidence from a callable options market

We examine the notion that financial products which cater to investors’ behavioral biases can yield high trading activity and thus be profitable for issuers. Our setting considers options with a callback feature, namely, callable bull/bear contracts (CBBCs). Such contracts have high skewness when close to callback and thus appeal to cumulative prospect theory preferences. CBBCs with high skewness earn negative average returns, and issuers’ gross profits vary positively with CBBC skewness. Over the 2009–2014 period, issuers earn gross profits of about $1.67 billion by trading CBBCs on the Hang Seng Index. These findings highlight the role of behavioral finance in financial innovation.

Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model

We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a precommitting gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) [Barberis N (2012) A model of casino gambling. Management Sci. 58(1): 35–51.] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.

Skorohod's Representation Theorem and Optimal Strategies for Markets with Frictions

We prove the existence of optimal strategies for agents with cumulative prospect theory preferences who trade in a continuous-time illiquid market, transcending known results which previously pertained only to risk-averse utility maximizers. The arguments exploit an extension of Skorohod's representation theorem for tight sequences of probability measures. This method is applicable in a number of similar optimization problems.

Climate risk and state-contingent technology adoption: shocks, drought tolerance and preferences

Climate risk represents an increasing threat to poor and vulnerable farmers in drought-prone areas of Africa. This study assesses the maize adoption responses of food insecure farmers in Malawi, where drought-tolerant (DT) maize was recently introduced. A field experiment, eliciting relative risk aversion, loss aversion and subjective probability weighting parameters of farmers, is combined with a detailed farm household survey. A state-contingent production model with cumulative prospect theory preferences is estimated. More risk-averse households were more likely to have adopted DT maize, less likely to have adopted other improved maize varieties and less likely to have dis-adopted traditional local maize (LM). Exposure to past drought shocks stimulated adoption of DT maize and dis-adoption of LM.

Equilibrium Notions for Agents with Cumulative Prospect Theory Preferences

Relying on the experimental findings that actual choice behavior often violates the axioms of expected utility theory (EUT), we study non-EUT preferences in a noncooperative game-theoretic framework. In particular, agents’ preferences are represented by the pair of functions suggested in cumulative prospect theory (CPT). Accordingly, three key aspects of CPT are incorporated: subjective probability weighting, loss aversion, and reference dependence. We introduce a correlated equilibrium and two mixed strategy equilibria for agents with CPT preferences. We prove the existence of equilibria for finite normal form games and investigate the sets of equilibria in some examples.

Mixed Strategy Equilibrium for Agents with Cumulative Prospect Theory Preferences

Relying on the experimental findings that actual choice behavior often violates the axioms of expected utility theory (EUT), we study non-EUT preferences in a non-cooperative game-theoretic framework. In particular, agents' preferences are represented by the pair of functions suggested in cumulative prospect theory (CPT). Accordingly, three key aspects of CPT are incorporated: subjective probability weighting, loss aversion, and reference dependence. We present two types of mixed strategy equilibrium for agents with CPT preferences and prove the existence of these equilibria for finite normal form games.

Correlated Equilibrium for Agents with Cumulative Prospect Theory Preferences

We study correlated equilibrium for finite normal form games in which agents’ preferences are represented by the pair of functions suggested in cumulative prospect theory (CPT). Accordingly, three key aspects of CPT are incorporated: subjective probability weighting, loss aversion, and reference dependence. We show the existence of equilibrium and investigate the set of equilibria under CPT preferences. JEL Classification: C72, D81

Optimal Investment with Nonconcave Utilities in Discrete-Time Markets

We consider an arbitrage-free, discrete-time and frictionless market. We prove that an investor maximizing the expected utility of his or her terminal wealth can always find an optimal investment strategy provided that his or her dissatisfaction of infinite losses is infinite and his or her utility function is nondecreasing, continuous, and bounded above. The same result is shown for cumulative prospect theory preferences, under additional assumptions.

Optimal Casino Betting: Why Lucky Coin and Good Memory are Important

We consider the dynamic casino gambling model initially proposed by Barberis [Manage. Sci., 2012, 58, 35-51] and study the optimal stopping strategy of a pre-committing gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis [2012] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.

Investor Behavior and Financial Innovation: A Case Study on Callable Bull/Bear Contracts

We examine the notion that financial products which cater to investors' behavioral biases can attain popularity and yield substantial profits for issuers. Our setting considers options with a callback feature, namely, callable bull/bear contracts (CBBCs). These contracts have high skewness when close to callback and thus appeal to cumulative prospect theory preferences. CBBCs with high skewness earn negative average returns, and issuer profits vary positively with CBBC skewness. Over the 2009-2014 period, issuers earn (investors lose) the equivalent of $1.66 billion by trading CBBCs on the Hang Seng index. These findings highlight the role of behavioral finance in financial innovation.

A note on the existence of CAPM equilibria with homogeneous cumulative prospect theory preferences

This note identifies and fixes a minor gap in Proposition 1 in Barberis and Huang (Am Econ Rev 98(5):2066–2100, 2008). Assuming homogeneous cumulative prospect theory decision makers, we show that CAPM is a necessary (though not sufficient) condition that must hold in equilibrium. We support our results with numerical examples where security prices become negative.