Prospect Theory Preferences Research Articles

Probability weighting, stop-loss and the disposition effect

In this paper we study a continuous-time, optimal stopping model of an asset sale with prospect theory preferences under pre-commitment. We show for a wide range of value and probability weighting functions, including those of Tversky and Kahneman (1992), that the optimal prospect takes the form of a stop-loss threshold and a distribution over gains. It is skewed with a long right tail. This is consistent with both the widespread use of stop-loss strategies in financial markets, and recent experimental evidence. Moreover, our model with probability weighting in tandem with the S-shaped value function makes predictions for the disposition effect which match in magnitude that calculated by Odean (1998).

Expected Utility Preferences versus Prospect Theory Preferences in Bargaining

Are individuals always better off when their preferences can be represented by expected utility? I study this question in a bargaining game where individuals bargain over a pie of fixed size, and I contrast the share received in the long-run by expected utility maximisers with the share they would receive if their preferences were described by prospect theory preferences instead when, in either case, they bargain with expected utility maximisers. I present a necessary and sufficient condition for individuals to obtain a higher share of the pie if their preferences obey prospect theory rather than expected utility. I decompose the effect that the three features that characterise prospect theory preferences - reference point dependence, loss-aversion and probability weighting - have on the bargaining outcome, and show that loss-aversion does not have any effect on the outcome of the bargaining process, reference-point dependent preference confers an unambiguous advantage and probability weighting is unambiguously disadvantageous. This ties in with the main result outlined earlier: if the upward pull of reference point dependence is relatively stronger than the downward push of probability weighting, then individuals are better off with prospect theory preferences than with expected utility preferences, and vice-versa.

An Alternative Behavioral Explanation for the MAX Effect

Stocks with high maximum daily returns (MAX) yield low future returns. We thoroughly examine the underlying behavioral mechanism based on stock market and individual trading data. We argue that the anomaly is driven by investor overreaction rather than cumulative prospect theory (CPT) preferences. First, we show empirically that high-MAX stocks are not comparably more attractive for CPT-investors. Second, we observe immediate price reversals and no preference-induced price pressure following the MAX return. Third, in line with theories on information-dependent over- and underreaction, the MAX effect reverses if MAX is caused by earnings announcements. Fourth, the MAX effect only exists for stocks far away from an anchoring point as overreaction is mitigated by anchors. Further, discount brokerage data shows that retail investors' speculative buying pressure for lottery-like stocks is not able to explain the specific return patterns associated with the MAX effect.

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.

A Prospect Theory Approach Explaining the Low Demand for Index-Based Insurance

In a neoclassical framework risk averse agents ask for full insurance coverage if the premium is actuarially fair. Recent empirical observations of the demand for index-based weather insurance in developing countries reveal the opposite: the more risk averse farmers are, the less they buy insurance. In this work, we investigate if the same holds for loss averse farmers, i.e., if loss aversion might explain low take-up rates of index insurance. Therefore, we set up a stochastic model using prospect theory preferences. We distinguish two different groups of farmers: sophisticated farmers who understand the insurance product and naive farmers. Naive farmers neglect insurance coverage even if the premium is highly subsidized. Further, higher loss aversion implies a lower take-up rate. Sophisticated farmers buy more insurance the more loss averse they are. Finally, insurance demand might increase with a more frequent payout and a deferred premium payment.

On the Impossibility of Protecting Risk‐takers

Risk-neutral sellers can extract high profits from risk-loving buyers by oering them lotteries. To limit risk-taking, gambling is heavily regulated in most countries. I show that protecting risk-loving buyers is essentially impossible. Even if buyers are risk-loving only asymptotically, the seller can construct a nonrandom winner-pays auction that ensures unbounded profits. Buyers are asymptotically risk-loving, for example, when their preferences satisfy Savage’s axioms or they have prospect theory preferences. The profits are unbounded even if the seller cannot use any mechanism that resembles a lottery.

Stochastic Dominance Analysis Without the Independence Axiom

We characterize the consistency of a large class of nonexpected utility preferences (including mean-variance preferences and prospect theory preferences) with stochastic orders (for example, stochastic dominances of different degrees). Our characterization rests on a novel decision theoretic result that provides a behavioral interpretation of the set of all derivatives of the functional representing the decision maker’s preferences. As an illustration, we consider in some detail prospect theory and choice-acclimating preferences, two popular models of reference dependence under risk, and we show the incompatibility of loss aversion with prudence. This paper was accepted by James Smith, decision analysis.

The consumption–investment decision of a prospect theory household: A two-period model

This study extends the literature on portfolio choice under prospect theory preferences by introducing a two-period life cycle model, where the sufficiently loss averse household decides on optimal consumption and investment in a portfolio with one risk-free and one risky asset. The optimal solution depends primarily on whether the household’s present value of the consumption reference levels is below, equal to, or above the present value of its endowment income. Reference levels below the endowment income are associated with the self-enhancement motive. In this case, the household avoids relative losses in consumption in any present or future state of nature (good or bad). As a result the degree of loss aversion does not directly affect optimal consumption and risk taking activity. Reference levels equal to the endowment income are associated with the belonging motive. An example would be a household comparing to others that belong to the same social class. In this case the household’s optimal consumption is the reference consumption and the household will not invest in the risky asset. Finally, reference levels above the endowment income are associated with the self-improvement motive (or high aspirations). For such high reference levels, households cannot avoid experiencing a relative loss in consumption, either now or in the future. As a result, loss aversion directly affects consumption and risky investment.

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.

When Prospect Theory Preference Meets Mean-Reverting Asset Returns: A Dynamic Asset Allocation Model

We examine how the evidence of mean-reversion in stock returns affects dynamic trading behavior for investors with prospect-theory preferences. Particular attention is paid to the trading incentives created by the interaction between prospect-theory preferences and mean-reverting return dynamics. Under general assumptions for the continuous-time financial market, we develop the semi-analytical portfolio policy by inverse Fourier Transformation method. By the revealed policy, we find that a small degree of mean reversion can be sufficient to reverse the direction of the investors' trading patterns. Further simulation results demonstrate that the combination of prospect theory and mean reversion can generate the disposition effect close to the data at the reasonable values of the underlying parameters. The results suggest that trading behavior patterns can be seriously misleading if the prospect theory allocation framework ignores time-variation in expected returns such as mean reversion.

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.

Behavioral mechanism design

Incentives are more likely to elicit desired outcomes when they are based on accurate models of agent behavior. A growing literature---from behavioral economics, as well as online user studies---suggests, however, that people do not quite behave like standard economic agents in a variety of environments, both online and offline. What consequences might such differences have for the optimal design of these environments? In this note, we summarize our results from Easley and Ghosh [2015] which explores this question of behavioral design---how departures from standard economic models of agent behavior affect mechanism design---via the problem of the optimal choice of contract structure in crowdsourcing markets where workers make decisions according to prospect theory preferences [Kahneman and Tversky 1979] rather than classical expected utility theory: we show that a principal might indeed choose a fundamentally different kind of mechanism---an output-contingent contest versus a 'safe', output-independent, fixed-payment scheme---and do better as a result, if he accounts for deviations from the standard economic models of decision-making that are typically used in theoretical design.

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.

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 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.

Capital gains and trading

This paper verifies that prospect theory preferences and speculative motives are drivers of trading in relation to capital gains at the stock level. Initially, investors are less likely to sell a stock as capital gains or losses become larger, consistent with the prospect theory. When capital gains exceed some threshold, investors are more likely to initiate selling as profits increase, in line with speculative motives. The trading-gains relation is more prominent for stocks with a larger proportion of irrational shareholders. The findings are robust to various subgroup analyses.