This paper was prepared for John B. Taylor and Michael Woodford, Editors

3

human behavior.  The examples below of application of theories from other social sciences

to understanding anomalies in financial markets will illustrate.

Each section below, until the conclusion, refers to a theory taken from the literature in

psychology, sociology or anthropology.  The only order of these sections is that I have

placed first theories that seem to have the more concrete applications in finance, leaving

some more impressionistic applications to the end.  In the conclusion I attempt to put these

theories into perspective, and to recall that there are also important strengths in conventional

economic theory and in the efficient markets hypothesis itself.  

Prospect Theory

Prospect theory (Kahneman and Tversky, 1979; Tversky and Kahneman, 1992) has probably

had more impact than any other behavioral theory on economic research.  Prospect theory

is very influential despite the fact that it is still viewed by much of the economics profession

at large as of far less importance than expected utility theory.  Among economists, prospect

theory has a distinct, though still prominent, second place to expected utility theory for most

research.

I should say something first about the expected utility theory that still retains the

position of highest honor in the pantheon of economic tools.  It has dominated much

economic theory so long because the theory offers a parsimonious representation of truly

rational behavior under uncertainty.  The axioms (Savage, 1954) from which expected utility

theory is derived are undeniably sensible representations of basic requirements of ration-

ality.  For many purposes, it serves well to base an economic theory on such assumptions

of strictly rational behavior, especially if the assumptions of the model are based on simple,

robust realities, if the model concerns well-considered decisions of informed people, and if

the phenomenon to be explained is one of stable behavior over many repetitions, where

learning about subtle issues has a good chance of occurring.

Still, despite the obvious attractiveness of expected utility theory, it has long been

known that the theory has systematically mispredicted human behavior, at least in certain

circumstances.  Allais (1953) reported examples showing that in choosing between certain

lotteries, people systematically violate the theory.  Kahneman and Tversky (1979) give the

following experimental evidence to illustrate one of Allais’ examples.  When their subjects

were asked to choose between a lottery offering a 25% chance of winning 3,000 and a

lottery offering a 20% chance of winning 4,000, 65% of their subjects chose the latter, while

when subjects were asked to choose between a 100% chance of winning 3,000 and an 80%

chance of winning 4,000, 80% chose the former.  Expected utility theory predicts that they

should not choose differently in these two cases, since the second choice is the same as the

first except that all probabilities are multiplied by the same constant.  Their preference for

the first choice in the lottery when it is certain in this example illustrates what is called the

“certainty effect,” a preference for certain outcomes.

Prospect theory is a mathematically-formulated alternative to the theory of expected

utility maximization, an alternative that is supposed to capture the results of such

experimental research.  (A prospect is the Kahneman–Tversky name for a lottery as in the

---

4

Allais example above.)  Prospect theory actually resembles expected utility theory in that

individuals are represented as maximizing a weighted sum of “utilities,” although the

weights are not the same as probabilities and the “utilities” are determined by what they call

a “value function” rather than a utility function.

The weights are, according to Kahneman and Tversky (1979) determined by a function

of true probabilities which gives zero weight to extremely low probabilities and a weight of

one to extremely high probabilities.  That is, people behave as if they regard extremely

improbable events as impossible and extremely probable events as certain.  However, events

that are just very improbable (not extremely improbable) are given too much weight; people

behave as if they exaggerate the probability.  Events that are very probable (not extremely

probable) are given too little weight; people behave as if they underestimate the probability.

What constitutes an extremely low (rather than very low) probability or an extremely high

(rather than very high) probability is determined by individuals’ subjective impression and

prospect theory is not precise about this.  Between the very low and very high probabilities,

the weighting function (weights as a function of true probabilities) has a slope of less than

one.

This shape for the weighting function allows prospect theory to explain the Allais

certainty effect noted just above.  Since the 20% and 25% probabilities are in the range of

the weighting function where its slope is less than one, the weights people attach to the two

outcomes are more nearly equal than are the probabilities, and people tend just to choose the

lottery that pays more if it wins.  In contrast, in the second lottery choice the 80%

probability is reduced by the weighting function while the 100% probability is not; the

weights people attach to the two outcomes are more unequal than are the probabilities, and

people tend just to choose the outcome that is certain.

If we modify expected utility function only by substituting the Kahneman and Tversky

weights for the probabilities in expected utility theory, we might help explain a number of

puzzling phenomena in observed human behavior toward risk.  For a familiar example, such

a modification could explain the apparent public enthusiasm for high-prize lotteries, even

though the probability of winning is so low that expected payout of the lottery is not high.

It could also explain such phenomenon as the observed tendency for overpaying for airline

flight insurance (life insurance policies that one purchases before an airline flight, that has

coverage only during that flight), Eisner and Strotz (1961).

The Kahneman–Tversky weighting function may explain observed overpricing of out-

of-the-money and in-the-money options.  Much empirical work on stock options pricing has

uncovered a phenomenon called the “options smile” (see Mayhew, 1995, for a review.).

This means that both deep out-of-the-money and deep in-the-money options have relatively

high prices, when compared with their theoretical prices using Black–Scholes formulae,

while near-the-money options are more nearly correctly priced.  Options theorists,

accustomed to describing the implied volatility of the stock implicit in options prices, like

to state this phenomenon not in terms of option prices but in terms of these implied

volatilities.  When the implied volatility for options of various strike prices at a point in time

derived using the Black–Scholes (1973) formula are plotted, on the vertical axis, against the

strike price on the horizontal axis, the curve often resembles a smile.  The curve is higher

both for low strike price (out-of-the-money) options and for high strike price (in-the-money)

---