Behavioral Finance:

Prospect Theory Analysis

Introduction to Paper:

According to conventional financial theory, the world and its participants are, for the

most part, rational “wealth maximizers”. However, there are many instances where

emotion and psychology influence our decisions, causing us to behave in unpredictable or

irrational ways. It is a relatively new field that seeks to combine behavioral and cognitive

psychological theory with conventional economics and finance to provide explanations

for why people make irrational financial decisions.

In the present scenario, behavioral finance is becoming an integral part of the decision-

making process, because it heavily influences investors’ performance. They can improve

their performance by recognizing the biases and errors of judgment to which all of us are

prone. Understanding the behavioral finance will help the investors to select a better

investment instrument and they can avoid repeating the expensive errors in future.

The presence of anomalies in conventional economic theory was a big contributor to the

formation of behavioral finance. These so-called anomalies, and their continued

existence, directly violate modern financial and economic theories, which assume rational

and logical behavior.

Kahneman and Tversky developed the Prospect theory in 1979 which is an alternative

model to the Expected Utility Theory. This model contends that people value gains and

losses differently, and, as such, will base decisions on perceived gains rather than

perceived losses. Thus, if a person were given two equal choices, one expressed in terms

of possible gains and other in possible losses, people would choose the former – even

when they achieve the same economic end result.

In 1992, Kahneman and Tversky made further development and a variant of Prospect

Theory called as Cumulative Prospect Theory. The difference is that weighing is applied

to the Rank-Dependent Expected Utility Theory, rather than to the probabilities of

individual outcomes.

This paper provides an insight on the top two papers written in connection with Prospect

Theory.

Abstract of the top 2 papers in connection with Prospect Theory:

1. Kahneman and Tversky, 1979.

‘This paper presents a critique of expected utility theory as a descriptive model of

decision making under risk, and develops an alternative model, called prospect theory.

Choices among risky prospects exhibit several pervasive effects that are inconsistent

with the basic tenets of utility theory. In particular, people underweight outcomes that

are merely probable in comparison with outcomes that are obtained with certainty.

This is called the certainty effect, contributes to risk aversion in choices involving sure

gains and to risk seeking in choices involving sure losses. In addition, people generally

discard components that are shared by all prospects under consideration. This is called

the isolation effect, leads to inconsistent preferences when the same choice is

presented in different forms. An alternative theory of choice is developed, in which

value is assigned to gains and losses rather than to final assets and in which

probabilities are replaced by decision weights. The value function is normally concave

for gains, commonly convex for losses, and is generally steeper for losses than for

gains. Decision weights are generally lower than the corresponding probabilities,

except in the range of low probabilities. Overweighting of low probabilities may

contribute to the attractiveness of both insurance and gambling.’

2. Tversky and Kahneman, 1992.

‘We develop a new version of prospect theory that employs cumulative rather than

separable decision weights and extends the theory in several respects. This version,

called cumulative prospect theory, applies to uncertain as well as to risky prospects

with any number of outcomes, and it allows different weighting functions for gains

and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked

to explain the characteristic curvature of the value function and the weighting

functions. A review of the experimental evidence and the results of a new experiment

confirm a distinctive fourfold pattern of risk: risk aversion for gains and risk seeking

for losses of high probability; risk seeking for gains and risk aversion for losses of low

probability.’

Important people who contributed to the Prospect Theory concept in Behavioral

Finance:

Daniel Kahneman:

Born in 1934, Kahneman is an Israeli-American psychologist and Nobel laureate, notable

for his work on the psychology of judgment and decision-making, behavioral economics

and hedonic psychology. In 2002, Kahneman received the Nobel Memorial Prize in

Economics, despite being a research psychologist, for his work in Prospect theory in

collaboration with Amos Tversky. Currently he is a professor emeritus of psychology and

public affairs at Princeton University’s Woodrow Wilson School.

Amos Tversky:

Born in 1937, Tversky was a cognitive and mathematical psychologist, a pioneer of

cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the

discovery of systematic human cognitive bias and handling of risk. His early work with

Kahneman focused on the psychology of prediction and probability judgment. Amos

Tversky and Daniel Kahneman worked together to develop prospect theory, which aims

to explain irrational human economic choices and is considered one of the seminal works

of behavioral economics.

Quotes:

1. ‘Kahneman and Tversky’s (1979) “Prospect theory: An analysis of decision under

risk” is the second most cited paper in economics during the period, 1975 – 2000

(Coupe, in press; Laibson & Zeckhauser, 1998).’ – Wu, Zhang and Gonzalez (2004)

2. ‘Prospect Theory was developed by Kahneman and Tversky (1979). In its original

form, it is concerned with behaviour of decision makers who face a choice between

two alternatives. The definition in the original context is: “Decision making under

risk can be viewed as a choice between prospects and gambles.” Decisions subject to

risk are deemed to signify a choice between alternative actions, which are associated

with particular probabilities (prospects) or gambles. The model was later elaborated

and modified.’ – Goldberg and Von Nitzsch (2000)

3. ‘Prospect theory, which was developed by Kahneman and Tversky (1979), is one of

the most quoted and best-documented phenomena in economic psychology. The

theory states that we have an irrational tendency to be less willing to gamble with

profits than with losses.’ – Tvede (1999)

4. ‘Not very long after expected utility theory was formulated by Von Neumann and

Morgenstern (1944) questions were raised about its value as a descriptive model

(Allais, 1953). Recently Kahneman and Tversky (1979) have proposed an alternative

descriptive model of economic behaviour that they call prospect theory.’ – Thaler

(1980)

5. ‘If Richard Thaler’s concept of mental accounting is one of two pillars upon which

the whole of behavioral economics rests, then prospect theory is the other.’ – Belsky

and Gilovich (1999)

6. ‘In a nutshell, prospect theory assumes that investors’ utility functions depend on

changes in the value of their portfolios rather than the value of the portfolio. Put

another way, utility comes from returns, not from the value of assets.’ – Cornell

(1999)

Definition of Concepts:

Behavioral Finance: A field of finance that proposes psychology-based theories to

explain stock market anomalies. Within behavioral finance, it is assumed that the

information structure and the characteristics of market participants systematically

influence individuals’ investment decision as well as market outcomes.

Cognitive Psychology: It is the branch of psychology that studies mental processes

including how people think, perceive, remember and learn.

Heuristic: It is an adjective for experience-based technique that helps in problem

solving, learning and discovery. Heuristics stand for strategies using readily accessible,

though loosely applicable, information to control problem solving in human beings.

Expected Utility Hypothesis: It is a theory of utility in which betting preferences with

regard to uncertain outcomes (gambles) are represented by a function of payouts (whether

in money or other goods), the probabilities of occurrence, risk aversion, and the different

utility of the same payout to people with different assets or personal preferences.

Loss Aversion: It is an important psychological concept which receives increasing

attention in economic analysis. The investor is a risk-seeker when faced with prospect of

losses, but is risk-averse when faced with the prospects of enjoying gains. The

phenomenon is called loss aversion.

Equity Premium Puzzle: It is based on the observation that in order to reconcile the

much higher return on equity stock compared to government bonds, individuals must

have implausibly high risk aversion according to standard economics models.

Endowment Effect: It is a hypothesis that people value a good or service more once

their property right to it has been established.

Mental Accounting: It attempts to describe a process whereby by people code,

categorize and evaluate economic outcomes.

Allais Paradox: It is a choice problem designed by Maurice Allais to show an

inconsistency of actual observed choices with the predictions of Expected Utility Theory.

The Rank-Dependent Expected Utility Model: It is a generalized expected utility

model of choice under uncertainty, designed to explain the behaviour observed in the

Allais Paradox, as well as for the observation that many people both purchase lottery

tickets (implying risk-loving preferences) and insure against losses (implying risk

aversion).

Disposition Effect: It is an anomaly discovered in behavioral finance. It relates to the

tendency of investors to sell shares whose price has increased, while keeping assets that

have dropped in value. Investors are less willing to recognize losses (which they would

be forced to do if they sold assets which had fallen in value), but are more willing to

recognize gains.

Pseudocertainity Effect: It is a concept from prospect theory. It refers to people’s

tendency to make risk averse (avoiding risk) choices if the expected outcome is positive,

but make risk-seeking choices to avoid negative outcomes. Their choices can be affected

by simply reframing the descriptions of the outcome without changing the actual utility.

Stochastic Dominance: It is a form of stochastic ordering (quantifying the concept of

one random variable being “bigger” than another). The term in used in decision theory

and decision analysis to refer to situations where one gamble can be ranked as superior to

another gamble.

Cognitive Bias: It is the human tendency to make systematic errors in certain

circumstances based on cognitive factors rather than evidence. Such biases can result

from information-processing shortcuts called heuristics.

The Framing Effect: It is one of the cognitive biases. It describes that presenting the

same option in different formats can alter people’s decisions. Specifically, individuals

have a tendency to select inconsistent choices, depending on whether the question is

framed to concentrate on losses or gains.

Prospect Theory: A theory that people value gains and losses differently and, as such, will base decisions on perceived gains rather than perceived losses. Thus, if a person were given two equal choices, one expressed in terms of possible gains and the other in possible losses, people would choose the former.

Prospect Theory: Kahneman and Tversky, 1979

This theory was developed by Daniel Kahneman, professor at Princeton University’s

Department of Psychology, and Amos Tversky in 1979 as a psychologically realistic

alternative to Expected Utility Theory. It allows one to describe how people make

choices in situations where they have to decide between alternatives that involve risk,

e.g., in financial decisions. Starting from empirical evidence, the theory describes how

individuals evaluate potential losses and gains. In the original formulation the term

prospect refers to lottery.

The theory describes such decision processes as consisting of two stages, editing and

evaluation. In the first, possible outcomes of the decision are ordered following some

heuristic. In particular, people decide which outcomes they see as basically identical and

they set a reference point and consider lower outcomes as losses and larger as gains. The

formula that Kahneman and Tversky observe in the evaluation phase is given by:

 where   are the potential

outcomes and   their respective probabilities. v is a so-called value function

that assigns a value to an outcome. The value function (sketched in the Figure) which

passes through the reference point is s-shaped and, as its asymmetry implies, given the

same variation in absolute value, there is a bigger impact of losses than of gains (loss

aversion). In contrast to Expected Utility Theory, it measures losses and gains, but not

absolute wealth. The function w is called a probability weighting function and expresses

that people tend to overreact to small probability events, but under react to medium and

large probabilities.

Applications:

1. Certain behaviors in economics such as the Disposition Effect can be explained using

the Prospect Theory. The Disposition Effect can be avoided by changing our mental

approach on how we perceive the new information we get.

2. The Pseudocertainity Effect provides an explanation as to why the same investor will

invest in an insurance company and also buy a lottery ticket.

3. 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

accept or receive.

4. The portfolios of prospect theory investors are sensitive to the location of reference

point. For low reference points, prospect theory investors choose traditional portfolios.

Higher reference points induce risk-seeking behavior, or the reluctance to engage in

trade.

5. Prospect theory has been used to explain the profitability of value strategy and the

predictability of past returns.

6. Prospect Theory has played a vital role in explaining the under-pricing and over-

pricing of Initial Public Offerings.

Prospect Theory: Kahneman and Tversky, 1992

Perhaps the most important change to the original prospect theory is that of Tversky and

Kahneman (1992) about how probabilities are transformed. The original specification in

Kahneman and Tversky (1979) applies only to binomial gambles, and violates the first-

order stochastic dominance property. The essence of change in Tversky and Kahneman

(1992) is that the transformation is first applied to the cumulative density function rather

than directly to the probabilities. Thus, the Tversky and Kahneman (1992) version is

usually called the cumulative prospect theory. It applies to the most general gambles and

is also consistent with first- order stochastic dominance.

The main observation of Cumulative Prospect Theory is that people tend to think of

possible outcomes usually relative to a certain reference point rather than to a final status,

a phenomenon which is called the framing effect. Moreover they have different risk

attitudes towards gains and losses and care generally more about potential losses and

potential gains. Finally, people tend to overweigh extreme, but unlikely events, but

underweight ‘average’ events.

Therefore, in Cumulative Prospect Theory weighing is applied to the cumulative

probability distribution function, as in rank-dependent expected utility theory, rather than

to the probabilities of individual outcomes. Cumulative prospect theory has been applied

in various situations which appear inconsistent with standard economic rationality, in

particular with equity premium puzzle, various gambling and betting puzzles,

endowment effect, etc.

Conclusion:

Prospect theory refers to an idea created by Drs. Kahneman and Tversky that essentially

determined that people do not encode equal levels of joy and pain to the same effect. The

average individuals tend to be more loss sensitive (in the sense, he/she will feel more

pain in receiving a loss compared to the amount of joy felt from receiving an equal

amount of gain).

Prospect theory is a descriptive model of decision making under uncertainty. Under

prospect theory, people evaluate risk using a value function that is defined over gains and

losses, is concave over gains and convex over losses, and is kinked at the origin; and

using transformed rather than objective probabilities by applying a weighting function.

Though the various examples given under Prospect Theory are widely observed, one

must note that all the investors will not suffer from the same illusion simultaneously. The

susceptibility of an investor to a particular illusion is likely to be a function of several

variables. For example, there is suggestive evidence that the experience of the investor

has an explanatory role in his regard with less experienced investors being prone to

representativeness while more experienced investors commit gamblers fallacy. Similarly,

behavioral factors play a vital role in the decision making process of the investors. Hence

the investors have to take necessary steps to minimize or avoid illusions for influencing

in their decision making process, investment decisions in particular.

Bibliography:

1. Kahneman, Daniel, and Amos Tversky, 1979. Prospect Theory: An Analysis of

Decision under Risk. Econometrica, 47(2), 263-292.

2. Barberis, Nicholas, Ming Huang, and Tano Santos, 2001. Prospect Theory and Asset

Prices. The Quarterly Journal of Economics, 116(1), 1-53.

3. Thayer Watkins, San Jose State University, Economics Department. Kahneman and

Tversky’s Prospect Theory.

4. Albert Phung, University of Alberta. Behavioral Finance: Key Concepts – Prospect

Theory.

5. Kannadhasan, M., Faculty, BIM, Trichy. Role of Behavioral Finance in Investment

Decisions.

6. Barberis, Nicholas and Richard Thaler, University of Chicago. A Survey of Behavioral

Finance.

7. Han, Bing and Jason Hsu, 2004. Prospect Theory and Its Applications in Finance.

Research Affiliates, LLC.