The prospect theory is an economics theory developed by Daniel Kahneman and Amos Tversky in 1979. It challenges the expected utility theory, developed by John von Neumann and Oskar Morgenstern in 1944, and earned Daniel Kahneman the Nobel Memorial Prize in Economics in 2002. It is the founding theory of behavioral economics and of behavioral finance, and constitutes one of the first economic theories built using experimental methods.
Based on results from controlled studies, it describes how individuals assess in an asymmetric manner their loss and gain perspectives. For example, for some individuals, the pain from losing $1,000 could only be compensated by the pleasure of earning $2,000. Thus, contrary to the expected utility theory, which models the decision that perfectly rational agents would make, the prospect theory aims to describe the actual behavior of people.
In the original formulation of the theory, the term prospect referred to the predictable results of a lottery. However, the prospect theory can also be applied to the prediction of other forms of behaviors and decisions.
The prospect theory starts with the concept of loss aversion, an asymmetric form of risk aversion, from the observation that people react differently between potential losses and potential gains. Thus, people make decisions based on the potential gain or losses relative to their specific situation (the reference point) rather than in absolute terms; this is referred to as reference dependence.
- Faced with a risky choice leading to gains, individuals are risk-averse, preferring solutions that lead to a lower expected utility but with a higher certainty (concave value function).
- Faced with a risky choice leading to losses, individuals are risk-seeking, preferring solutions that lead to a lower expected utility as long as it has the potential to avoid losses (convex value function).
These two examples are thus in contradiction with the expected utility theory, which only considers choices with the maximum utility.
The theory continues with a second concept, based on the observation that people attribute excessive weight to events with low probabilities and insufficient weight to events with high probability. For example, individuals may unconsciously treat an outcome with a probability of 99% as if its probability was 95%, and an outcome with probability of 1% as if it had a probability of 5%. Under- and over-weighting of probabilities is importantly distinct from under- and over-estimating probabilities, a different type of cognitive bias observed for example in the overconfidence effect.
The theory describes the decision processes in two stages:
- During an initial phase termed editing, outcomes of a decision are ordered according to a certain heuristic. In particular, people decide which outcomes they consider equivalent, set a reference point and then consider lesser outcomes as losses and greater ones as gains. The editing phase aims to alleviate any framing effects.It also aims to resolve isolation effects stemming from individuals’ propensity to often isolate consecutive probabilities instead of treating them together. The editing process can be viewed as composed of coding, combination, segregation, cancellation, simplification and detection of dominance.
- In the subsequent evaluationphase, people behave as if they would compute a value (utility), based on the potential outcomes and their respective probabilities, and then choose the alternative having a higher utility.
|High probability (certainty effect)||95% chance to win $10,000 or 100% chance to obtain $9,499. So, 95% × $10,000 = $9,500 > $9,499. Fear of disappointment. Risk averse. Accept unfavorable settlement of 100% chance to obtain $9,499||95% chance to lose $10,000 or 100% chance to lose $9,499. So, 95% × −$10,000 = −$9,500 < −$9,499. Hope to avoid loss. Risk seeking. Rejects favorable settlement, chooses 95% chance to lose $10,000|
|Low probability (possibility effect)||5% chance to win $10,000 or 100% chance to obtain $501. So, 5% × $10,000 = $500 < $501. Hope of large gain. Risk seeking. Rejects favorable settlement, chooses 5% chance to win $10,000||5% chance to lose $10,000 or 100% chance to lose $501. So, 5% × −$10,000 = −$500 > −$501. Fear of large loss. Risk averse. Accept unfavorable settlement of 100% chance to lose $501|
Probability distortion is that people generally do not look at the value of probability uniformly between 0 and 1. Lower probability is said to be over-weighted (that is a person is over concerned with the outcome of the probability) while medium to high probability is under-weighted (that is a person is not concerned enough with the outcome of the probability). The exact point in which probability goes from over-weighted to under-weighted is arbitrary, however a good point to consider is probability = 0.33. A person values probability = 0.01 much more than the value of probability = 0 (probability = 0.01 is said to be over-weighted). However, a person has about the same value for probability = 0.4 and probability = 0.5. Also, the value of probability = 0.99 is much less than the value of probability = 1, a sure thing (probability = 0.99 is under-weighted). A little more in depth when looking at probability distortion is that π(p) + π(1 − p) < 1 (where π(p) is probability in prospect theory).
Some behaviors observed in economics, like the disposition effect or the reversing of risk aversion/risk seeking in case of gains or losses (termed the reflection effect), can also be explained by referring to the prospect theory.
The pseudocertainty effect is the observation that people may be risk-averse or risk-acceptant depending on the amounts involved and on whether the gamble relates to becoming better off or worse off. This is a possible explanation for why the same person may buy both an insurance policy and a lottery ticket.
An important implication of prospect theory is that the way economic agents subjectively frame an outcome or transaction in their mind affects the utility they expect or receive. Narrow framing is a derivative result which has been documented in experimental settings by Tversky and Kahneman, whereby people evaluate new gambles in isolation, ignoring other relevant risks. This phenomenon can be seen in practice in the reaction of people to stock market fluctuations in comparison with other aspects of their overall wealth; people are more sensitive to spikes in the stock market as opposed to their labor income or the housing market. It has also been shown that narrow framing causes loss aversion among stock market investors. This aspect has also been widely used in behavioral economics and mental accounting.
The digital age has brought the implementation of prospect theory in software. Framing and prospect theory has been applied to a diverse range of situations which appear inconsistent with standard economic rationality: the equity premium puzzle, the excess returns puzzle and long swings/PPP puzzle of exchange rates through the endogenous prospect theory of Imperfect Knowledge Economics, the status quo bias, various gambling and betting puzzles, intertemporal consumption, and the endowment effect. It has also been argued that prospect theory can explain several empirical regularities observed in the context of auctions (such as secret reserve prices) which are difficult to reconcile with standard economic theory.
Limits and extensions
The original version of prospect theory gave rise to violations of first-order stochastic dominance. That is, prospect A might be preferred to prospect B even if the probability of receiving a value x or greater is at least as high under prospect B as it is under prospect A for all values of x, and is greater for some value of x. Later theoretical improvements overcame this problem, but at the cost of introducing intransitivity in preferences. A revised version, called cumulative prospect theory overcame this problem by using a probability weighting function derived from rank-dependent expected utility theory. Cumulative prospect theory can also be used for infinitely many or even continuous outcomes (for example, if the outcome can be any real number). An alternative solution to overcome these problems within the framework of (classical) prospect theory has been suggested as well.
Critics from the field of psychology argued that even if Prospect Theory arose as a descriptive model, it offers no psychological explanations for the processes stated in it. Furthermore, factors that are equally important to decision making processes have not been included in the model, such as emotion.
A relatively simple ad hoc decision strategy, the priority heuristic, has been suggested as an alternative model. While it can predict the majority choice in all (one-stage) gambles in Kahneman and Tversky (1979), and predicts the majority choice better across four different data sets with a total of 260 problems than cumulative prospect theory did, this heuristic, however, fails to predict many simple decision situations that are typically not tested in experiments and also does not explain heterogeneity between subjects.
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Ofer Abarbanel is a 25 year securities lending broker and expert who has advised many Israeli regulators, among them the Israel Tax Authority, with respect to stock loans, repurchase agreements and credit derivatives. Founder of TBIL.co STATX Fund.