Prospect theory is a theory that describes
decisions between alternatives that involve
risk, i.e. alternatives with uncertain outcomes, where
the probabilities are known. The model is
descriptive: it tries to model real-life
choices, rather than optimal decisions.
Model
Prospect 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
gain. In the original formulation the term
prospect referred to a
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. In
the following evaluation phase, 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.
The formula that Kahneman and Tversky assume for the evaluation
phase is (in its simplest form) given
byU=w(p_1)v(x_1)+w(p_2)v(x_2)+\dots,where x_1,x_2,\dots are the
potential outcomes and p_1,p_2,\dots 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 underreact to medium and large probabilities.
To see how Prospect Theory (PT) can be applied in an example,
consider a decision about buying an insurance policy. Let us assume
the probability of the insured risk is 1%, the potential loss is
$1000 and the premium is $15. If we apply PT, we first need to set
a reference point. This could be, e.g., the current wealth, or the
worst case (losing $1000). If we set the frame to the current
wealth, the decision would be to either pay $15 for sure (which
gives the PT-utility of v(-15)) or a lottery with outcomes $0
(probability 99%) or $-1000 (probability 1%) which yields the
PT-utility of w(0.01) \times v(-1000)+w(0.99) \times v(0)=w(0.01)
\times v(-1000). These expressions can be computed numerically. For
typical value and weighting functions, the former expression could
be larger due to the convexity of v in losses, and hence the
insurance looks unattractive. If we set the frame to $-1000, both
alternatives are set in gains. The concavity of the value function
in gains can then lead to a preference for buying the
insurance.
We see in this example that a strong overweighting of small
probabilities can also undo the effect of the convexity of v in
losses: the potential outcome of losing $1000 is
overweighted.
The interplay of overweighting of small probabilities and
concavity-convexity of the value function leads to the so-called
four-fold pattern of risk attitudes: risk-averse behavior
in gains involving moderate probabilities and of small probability
losses; risk-seeking behavior in losses involving moderate
probabilities and of small probability gains. This is an
explanation for the fact that people simultaneously buy lottery
tickets and insurances, but still invest money
conservatively.
Applications
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 orworse 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. This aspect has
been widely used in
behavioral
economics and
mental
accounting. 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
status quo
bias, various gambling and betting puzzles,
intertemporal consumption and the
endowment effect.
Another possible implication for economics is that
utility might be reference based, in contrast with
additive utility functions underlying much of
neo-classical economics. This means
people consider not only the value they receive, but also the value
received by others. This hypothesis is consistent with
psychological research into
happiness, which finds subjective measures of
wellbeing are relatively stable over time, even in the face of
large increases in the standard of living (Easterlin, 1974; Frank,
1997).
Military historian John A. Lynn argues that prospect theory
provides an intriguing if not completely verifiable framework of
analysis for understanding
Louis XIV's
foreign policy nearer to the end of
his reign (Lynn, pp. 43-44).
Limits and extensions
The original version of prospect theory gave rise to violations of
first-order
stochastic
dominance. That is, one prospect might be preferred to another
even if it yielded a worse outcome with probability one. The
editing phase 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 (e.g. if the outcome
can be any
real number).
Sources
- Easterlin, Richard A. (1974)
"Does Economic Growth Improve the Human Lot?" in Paul A. David and
Melvin W. Reder, eds., Nations and Households in Economic
Growth: Essays in Honor of Moses Abramovitz, New York:
Academic Press, Inc.
- Frank, Robert H. (1997) "The Frame of Reference as a Public
Good", The Economic Journal 107 (November),
1832-1847.
- Kahneman, Daniel, and Amos Tversky (1979) "Prospect Theory: An
Analysis of Decision under Risk", Econometrica, XLVII
(1979), 263-291.
- Lynn, John A. (1999) The Wars of Louis XIV 1667-1714.
United Kingdom: Pearson Education Ltd.
- McDermott, Rose, James H.
Fowler, and Oleg Smirnov. "On the
Evolutionary Origin of Prospect Theory Preferences." Journal of
Politics, forthcoming (April 2008) Paper Available at SSRN:
http://www.ssrn.com/abstract=1008034
- Post, Thierry, Van den Assem, Martijn J., Baltussen, Guido and
Thaler, Richard H., "Deal or No Deal? Decision Making Under Risk in
a Large-Payoff Game Show" (April 2006). EFA 2006 Zurich Meetings
Paper Available at SSRN: http://www.ssrn.com/abstract=636508
- http://prospect-theory.behaviouralfinance.net/
External links
See also