Cognitive processes and economic behaviour

1.1 Stock price of Royal Dutch relative to Shell 1.2 ENMD closing prices and trading volume 5.1 Payoff matrices for horse races 5.2 Evidence of non-best-response behavior 5.3 Games for t

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Cognitive Processes and

Economic Behaviour

There has been a marked increase in debate surrounding the issue of the cognitivefoundations of economic behaviour in recent years This debate seeks to explainthe determinants of a variety of activities such as forecasting economic variables,perception and decision under uncertainty and communication in interactivecontexts

This volume contains contributions from leading scholars in their respectivefields Themes covered range from behavioural finance to neuroscience

Under the impressive editorship of Dimitri, Basili and Gilboa, this book will be

of benefit to all those interested in the 'intersection between cognitive sciences andeconomics as well as economic theorists

Nicola Dimitriis Professor of Political Economy at the University of Siena, Italy.Marcello Basili is Associate Professor of Economics at the University ofSiena, Italy

Itzhak Gilboais Professor of Economics at Tel Aviv University, Israel, and Fellow

of the Cowles Foundation for Research in Economics, Yale University, US

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Routledge Siena Studies in Political Economy

The Siena Summer School hosts lectures by distinguished scholars on topics acterized by a lively research activity The lectures collected in this series offer

char-a clechar-ar char-account of the char-alternchar-ative resechar-arch pchar-aths thchar-at chchar-archar-acterize char-a certchar-ain field.Different publishers printed former workshops of the School They include:

Macroeconomics

A survey of research strategies

Edited by Alessandro Vercelli and Nicola Dimitri

Oxford University Press, 1992

Intemational Problems of Economic Interdependence

Edited by Massimo Di Matteo, Mario Baldassarri and Robert Mundell

Macmillan, 1994

Ethics, Rationality and Economic Behaviour

Edited by Francesco Farina, Frank Hahn and Stefano Vannucci

Clarendon Press, 1996

The Politics and Economics of Power

Edited by Samuel Bowles, Maurizio Franzini and Ugo Pagano

Routledge, 1998

The Evolution of Economic Diversity

Edited by Antonio Nicita and Ugo Pagano

Routledge, 2000

Cycles, Growth and Structural Change

Theories and empirical evidence

Edited by Lionello F Punzo

Routledge, 2001

General Equilibrium

Edited by Fabio Petri and Frank Hahn

Routledge, 2002

Cognitive Processes and Economic Behaviour

Edited by Nicola Dimitri, Marcello Basili and Itzhak Gilboa

Routledge, 2003

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Cognitive processes and economic behaviour / [edited by] Nicola Dimitri, Marcello Basili, and Itzhak Gilboa.

p cm - (Routledge Siena studies in political economy)

Includes bibliographical references and index.

1 Economics-Psychological aspects 2 Economic man 3 Cognition 4 Emotions and cognition 5 Decision making I Title: Cognitive processes and economic behaviour II Dimitri, Nicola III Basili, Marcello, 1959- IV Gilboa, Itzhak V Series.

To the memory of Michael Bacharach

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MARCELLO BASILI AND FULVIO FONTINI

3 On the existence of a "complete" possibility structure 30ADAM BRANDENBURGER

ITZHAK GILBOA AND DAVID SCHMEIDLER

9 Some elements of the study of language as a cognitive capacity 104LUIGI RIZZI

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viii Contents

PATRICK SUPPES

11 For a "cognitive program": explicit mental representations

forHomo Oeconomicus(the case of trust) 168CRISTIANO CASTELFRANCHI

12 The structured event complex and the human

JORDAN GRAFMAN

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1.1 Stock price of Royal Dutch relative to Shell

1.2 ENMD closing prices and trading volume

5.1 Payoff matrices for horse races

5.2 Evidence of non-best-response behavior

5.3 Games for testing reciprocity-based cooperation

6.4 The vase-faces illusion

11.1 The decision process

11.2 The different emotional impacts

12.1 Key components of an SEC mapped to PFC topography

5750545769186187220

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1.1 Returns, excess returns, trading volume, relative trading volume,

5.3 Parameter estimates of enhanced Rule Learning models 58

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Nicola Dimitri, Department of Political Economy, University of Siena,Siena, Italy

Fulvio Fontini, Department of Economic Sciences, University of Florence,Florence, Italy

Itzhak Gilboa, School of Economics, Tel Aviv University, Tel Aviv,Israel& Cowles Foundation, University of Yale, New Haven, USJordan Grafman, Cognitive Neuroscience Section, National Institute ofNeurological Disorders and Stroke National Institutes of Health,Bethesda, US

Gur Huberman, Columbia Business School, Columbia University,New York, US

Barton L Lipman, Department of Economics, Boston University,

Dale Stahl, Department of Economics, University of Texas, Austin, USPatrick Suppes, Department of Philosophy, Stanford University,

Stanford, US

Throughout most of the twentieth century, the official position of mainstreameconomics ignored cognition The revealed preferences paradigm held that eco-nomics could and should be based on observable choice behavior alone, and thatany other type of data would be at best irrelevant, if not meaningless and detrimental

to the progress of science

This position is perhaps best epitomized by Samuelson's (1937) canonical tribution But it had its roots in the preceding seven decades or so To understandthe popularity of the revealed preference paradigm, as well as its decline in thelate twentieth century, one might wish to distinguish among three types of expla-nations, relating to science, to the philosophy of science, and to the sociology ofscience

con-On the scientific, substantial level, the 1870s were crucial times At the ning of this decade, Marshall (1890), Menger (1871), and Walras (1873) suggestedthat marginal utility is key to understanding consumer demand Some two hun-dred years after the invention of the calculus, economists highlighted the role of

begin-the derivative of begin-the utility function, rabegin-ther than begin-the level of begin-the function itself, as a

determinant of demand This insight resolved Aristotle's diamond-water paradoxand paved the road to Marshall's theory of determination of price by both supplyand demand

Marginal utility is not a behavioral concept Indeed, the intuition behind theassumption of decreasing marginal utility has to do with cognition and affect.1However, when coupled with Walras's general equilibrium setup, the so-called

marginalism led to the realization that only ratios among derivatives, namely

marginal rates of substitution, mattered for the determination of demand It lowed that the utility function was only ordinal, and that direct measurement ofutility or of marginal utility was not related to behavior

fol-It was at the beginning of the twentieth century that Pareto (1916) suggested

a concept of efficiency that was to change the course of normative economics.Pareto pointed out that this concept did not resort to a cardinal utility function or

to interpersonal comparisons of utility This sufficed for economics to have a trivial normative question that, in principle, did not require data beyond revealedpreference It so happened that Pareto efficiency was also the most demandingnormative criterion about which the profession was in agreement The result was

non-Introduction xiiithat economics chose to focus on this criterion, and many economists view it asthe normative forefront of scientific research, arguing that the discipline shouldnot attempt to go beyond it.

Thus, by the time that neoclassical economics was taking center stage, itappeared that cognition does not matter Economists observed that, for descriptiveand normative purposes alike, they only had any use for behavior data

The philosophy of science also had an impact on the course of economics Therise of logical positivism at the end of the nineteenth century and the beginning ofthe twentieth, culminating in Carnap's (1923) formulation of the Received View,provided a template for scientific disciplines In particular, all theoretical conceptswere to be based on observable and measurable data Applying the Received View

to economics, one would have to ask how utility is measured before one could usethe concept It was probably rather natural to identify the notion of observabilitywith behavior, and to conclude that any economic theory that cannot be firmlybased on observed choice behavior was meaningless and therefore more likely tohinder scientific progress than to facilitate it

The sociology of science cannot be ignored as well Economics was traditionallyconsidered the branch of social science most closely related to the natural sciences

At the beginning of the twentieth century it found itself at a crossroad It couldchoose to associate with the "hard" sciences, relying on measurable data and onmathematical theories, or to be a "soft" science, closer to psychology and sociol-ogy As Loewenstein suggests, it is possible that the rise of psychoanalysis, fiercelyattacked for its unscientific nature (see Popper (1934)), made psychology a dubi-ous discipline to associate with, and pushed economics to the arms of the "hard"sciences It is also possible that the dual role of Marxism, as a socio-economictheory and as a political agenda, made sociology an uneasy partner for westerneconomists Finally, economists were probably also attracted by the sheer beautyand parsimony of the revealed preference paradigm, and by the modernist promise

of harnessing mathematical tools for the understanding of human behavior

In conclusion, it was a conjunction of purely scientific reasons with cal and sociological ones that made mainstream economics focus on behavior asthe sole legitimate and meaningful source of data, and use cognition as anythingbeyond a vague source of inspiration

philosophi-By the end of the twentieth century, however, the validity of the revealed erence approach was questioned on several fronts In fact, none of the- reasons forits rise to a status of a dominant paradigm could sustain it any longer in this role

pref-On the scientific level, various cracks began to appear in the revealed preferenceview of the world As a descriptive theory, economics has not proven capable ofproviding the type of precise predictions of individual agents' behavior, or ofmarket equilibrium Moreover, the most basic assumptions of rationality cameunder forceful attack by Kahneman and Tversky (see Kahneman and Tversky(1979, 1984), and Tversky and Kahneman (1981)) It became clear that economicscouldn't continue to ignore cognition based on the argument that it is successfulenough without it The dissatisfaction with economics as a descriptive scienceled economists to ask what went wrong and where more help could be found

an individual's relative standing in society, Foley (1967) suggested the concept ofenvy-free allocations, and so forth.

The philosophy of science has greatly changed since the 1930s The ReceivedView came under numerous attacks even when applied as a guideline for theprogress of the natural sciences (see Quine (1953), Hanson (1958)) It becameabundantly clear that it cannot serve as a template for economics In fact, in the lastquarter of the twentieth century economist theorists were increasingly promotingthe view that economics models were merely metaphors or illustrations that weredesigned to make a certain point rather than predict data precisely (see Gibbardand Varian (1978))

Finally, the sociology of science has also significantly evolved over the tieth century Psychological treatment is no longer dominated by psychoanalysis.Importantly, psychological research has become a very respectable and responsiblebranch of science, drawing very careful distinctions between theoretical conceptsand observable data and elevating issues of measurability to the level of a scientificdiscipline on its own Specifically, cognition is a realm of carefully documentedphenomena that offers relevant insights into the nature of economic activities.Past decades have also witnessed major developments in brain research Neuro-science has established itself as an interdisciplinary scientific field, holding apromise to provide better understanding of mental phenomena Admittedly, neuro-science has not yet produced any specific economic predictions or insights Yet,the very existence of the field and its potential applications convince economiststhat there are relevant observable data beyond choice behavior Moreover, the hall-marks of neuroscience, involving electrodes and tMRI images, project an image

twen-of a "hard" science As such, brain research constitutes a desirable scientific ally,which partly legitimizes cognitive data as well

As a result of the processes described above, the revealed preference paradigmhas become the target of numerous attacks In particular, a growing number ofeconomists voiced their dissatisfaction with a definition of rationality that is basedsolely on revealed choice The concept of procedural rationality, originally pro-posed by Simon (1986), became more popular in recent years (See Rubinstein1998) At present, economists begin to be interested in the cognitive and mentalprocesses that lead to behavior, and not just in behaviorper see Relatedly, eco-nomic theorists expand the scope of cognitive phenomena that they find relevant, orpotentially relevant, to the understanding of economic activity Thus, topics such

as emotions (Frank (1988), Rabin (1998), Elster (1998)) and language (Rubinstein(2000)) have become legitimate objects of study for economics

Introduction xvThe present volume includes several recent contributions to the study of cog-nitive processes and rationality in economic theory To a large extent, thesecontributions reflect the causes for and the highlights of the renewed interest

in cognition within economics The volume begins with descriptive economics,discussing new cognitive-based approaches to classical economic problems Itproceeds with normative issues Several chapters are devoted to less traditionaleconomic issues, and a final chapter surveys neurological evidence that mightprove relevant to economics in the long run

The first two chapters are devoted to financial markets While this is a classicaltopic of descriptive economics, there is a widespread sensation that classical eco-nomic theory fails to provide a perfectly accurate account of these markets Thechapter by Gur Huberman describes recent development in behavioral finance,2attempting to further our understanding of these markets It is followed by a chapter

by Marcello Basili and Fulvio Fontini, discussing financial markets with Knightianuncertainty The latter refers to situations in which uncertainty is not quantifiable

by a single probability measure Both chapters thus deal with models of behavior infinancial markets, inspired by intuition regarding cognitive processes that underlietrade choices

Chapters3-5deal with game theory Adam Brandenburger's contribution dealswith what people know, what they can know, and what they can conceive of

It presents an impossibility result regarding the scope of beliefs people mightpossibly entertain This chapter belongs to a tradition of epistemology in gametheory, starting with Aumann (1976) While this literature retains a formal linkage

to Savage's (1954) behavioral foundations of beliefs, most of the epistemologicaldiscussion is motivated by purely cognitive notions of knowledge and beliefs.The contribution by Nicola Dimitri, in Chapter 4, also belongs to the epis-temological tradition in game theory, with a stronger emphasis on economicapplications In particular, it studies the electronic mail game and explores the pos-sibility of risky coordination with noisy and correlated communication Finally, inChapter 5, Dale Stahl surveys rule learning in normal-form games Dealing withlearning in games, this chapter belongs to a long tradition in economic theory.However, it is distinguished from the bulk of the literature in that it deals withrule learning, and compares it to other types of learning methodologies All ofthese are motivated by hypothesized cognitive processes, rather than by axiomaticderivation based on behavioral data

The next five chapters deal with cognitive phenomena that are beyond the scope

of classical economics In Chapter 6, Michael Bacharach offers a model of framingeffects This phenomenon has been ignored by economic theory In fact, formalmodeling in economics has, almost with no exception, implicitly assumed that rep-resentation does not matter, and thus that framing effects do not exist Bacharach'schapter paves the way for an extension of the scope of formal modeling that wouldinclude framing effects in a way that may alter the directions of economic research.Barton Lipman, in Chapter 7, discusses language and economics This chaptersurveys the extension of economic formal modeling to the use of language Lan-guage is another realm of cognitive activity that has been largely ignored by

xvi Introduction

economists Yet, its importance in everyday economic decisions can hardly bedisputed This chapter also surveys the study of debates as strategic games, which

is a new topic of study to economists

Chapter 8, by Itzhak Gilboa and David· Schmeidler, discusses prediction.Whereas belief formation has always been implicit in economic behavior, thischapter takes the approach that prediction is an independent cognitive activity,which can be axiomatized based on cognitive data The goal of the axiomatization

is tochar~cterizeand generalize standard statistical techniques to situations thatare not readily formulated numerically

An analysis of language as a cognitive capacity is offered in Chapter 9 byLuigi Rizzi Taking as a starting point the Chomskian approach to the issue, theauthor stresses the view of linguistic knowledge as a computational capacity, alsodiscussing questions related to optimality and efficiency of such ability

Patrick Suppes has contributed Chapter 10, in which he discusses rationality andfreedom Freedom is an essential philosophical concept that is intuitively clear tohuman beings Yet, it serves no role in economic modeling Suppes highlights theimportance of this concept and relates it to the notion of uncertainty

Another recent addition to the topics that economics finds relevant is exemplified

in Chapter 11 In it, Cristiano Castelfranchi uses the case of trust to argue for acognitive program for economics This chapter discusses the notion of trust andargues that it cannot be reduced to other concepts, more familiar to economists.The volume concludes with a chapter by Jordan Grafman, describing theactivities recorded in the human prefrontal cortex Initiating economists into neuro-science, this chapter gives an inkling of the new directions in which economicsmay proceed

The present collection reflects a scientific discipline at the point of transition.After a century of domination of a behavioral, non-cognitive paradigm, eco-nomics opens up to other fields and to other ways of looking at the phenomena

of interest While it is too early to tell which directions will prove useful, one canhardly fail to be excited by the intellectual activity we are currently witnessing It

is the editors' hope that the reader would share this excitement while reading thefollowing chapters

The Editors

Notes

Affect is a psychological term encompassing phenomena such as emotion, mood, feeling,and so forth While these are distinct from cognition in the psychological literature, wewill henceforth not be too meticulous, and will use "cognition" to refer to the variousmental processes that are, in principle, open to introspection, but that are not directlyreduced to behavior

2 The terms "behavioral finance" and "behavioral economics" probably hark back to

"behavioral decision theory," which refers to the experimental study of decisions, ing, for the most part, the works of Kahneman and Tversky The epithet "behavioral" inthese titles means "how people actually behave" as opposed to "how economic the-ory assumes they behave." However, all these fields show much greater interest incognitive phenomena than does classical economics The latter, by adhering to therevealed preference paradigm, attempted to be "behavioral" in the sense that it restricted

follow-Introduction XVll

its attention to allegedly observable behavior Hence, somewhat ironically, ioral" finance/economics should perhaps be called "cognitive" or "cognitive-behavioral"finance/economics

"behav-References

Bazerman, M (1986), Judgment in Managerial Decision Making New York: John Wiley

and Sons

Brams, S (1997), "Game Theory and Emotions," Rationality and Society, 9: 91-124.

Camerer, C and M Weber (1992), "Recent Developments in Modeling Preferences:

Uncertainty and Ambiguity," Journal ofRisk and Uncertainty, 5: 325-370.

Carnap, R (1923), "Uber die Aufgabe der Physik und die Andwednung des Grundsatze der

Einfachstheit," Kant-Studien, 28: 90-107.

Damasio, A (1994), Descartes' Error New York: Putnam.

Duesenberry, J S (1949), Income, Saving, and the Theory of Consumer Behavior.

Cambridge, MA: Harvard University Press

Elster 1. (1998), "Emotions and Economic Theory," Journal of Economic Literature,

Forgas, J P and G H Bower (1987), "Mood Effects on Person Perception Judgments,"

Journal of Personality and Social Psychology, 53: 53-60.

Forgas, J P and G H Bower (1988), "Affect in Social Judgment," Australian Journal of

vol 1 Rationality and Well-being, pp 127-136, Oxford: Oxford University press.

Hanson, N R (1958), Patterns of Discovery Cambridge, England: Cambridge University

Press

Harless, D and C Camerer (1994), "The Utility of Generalized Expected Utility Theories,"

Econometrica, 62: 1251-1289.

Isen, A M and B Means (1983), "The Influence of Positive Affect on Decision Making

Strategy," Social Cognition, 2: 18-31. •

Isen, A M and N Geva (1987), "The Influence of Positive Affect on Acceptable Level ofRisk and Thoughts about Losing: The Person with the Larger Canoe has a Large Worry,"

Organizational Behavior and Human Decision Processes, 39: 145-154.

Isen, A M., K A Daubman, and G P Nowicki (1987), "Positive Affect Facilitates

Creative Problem Solving," Journal of Personality and Social Psychology, 52:

1122-1131

Kahneman, D and A Tversky (1979), "Prospect Theory: An Analysis of Decision Under

Risk," Econometrica, 47: 263-291.

Kahneman D., P Slovic, and A Tversky (1982) (eds), Judgment under Uncertainty:

Heuristics and Biases Cambridge and New York: Cambridge University Press.

xviii Introduction

LeDoux, J E (1996),The Emotional Brain.New York: Simon and Schuster

Lewin, S (1996), "Economics andPsycholog~:Lessons For Our Own Day From the EarlyTwentieth Century,"Journal of Economic Literature,34: 1293-1323

Lewinsohn, S and H Mano (1993), "Multi-Attribute Choice and Affect: The ence of Naturally Occurring and Manipulated Moods on Choice Processes," Journal

Influ-of Behavioral Decision Making,6: 33-51

Loewenstein, G (1992), "The Fall and Rise of Psychological Explanation in the Economics

of Intertemporal Choice." In G Loewenstein and J Elster (eds), Choice over Time

(pp 3-34) New York: Russell Sage

Loewenstein, G (1996), "Out of Control: Visceral Influence on Behavior,"Organizational Behavior and Human Decision Processes,65: 272-292

Loomes G and R Sugden (1982), "Regret Theory: An Alternative Theory of RationalChoice under Uncertainty,"Economic Journal,92: 805-824

Mann, L (1992), "Stress, Affect, and Risk Taking." In Yates, J F (eds), Risk Taking Behavior(pp 202-230) Wiley Series in Human Performance and Cognition Chichester:John Wiley and Sons

Mano, H (1990), "Emotional States and Decision Making." In Goldberg, M., G Gorn, and

R Pollay (eds),Advances in Consumer Research,17: 577-584

Mano, H (1992), "Judgment under Distress: Assessing the Role of Unpleasantnessand Arousal in Judgment Formation," Organizational Behavior and Human Decision Processes,52: 216-245

Marshall, A (1890),Principles of Economics.9th edn (1961), London: Macmillan.Menger, C (1871),Principles of Economics.Reprinted (1951), Glencoe, Ill.: Free Press.Ortony, A., J L Clore, and Collins, A (1988),The Cognitive Structure of Emotions.NewYork: Cambridge University Press

Pareto, Vilfredo (1916),Trattato di Sociologia Generale.4 vols, Florence: Barbera lated into English and edited by Arthur Livingston asThe Mind and Society,New York:Harcourt Brace&Co., 1935

Trans-Piattelli-Palmarini (1994),Inevitable Illusions: How Mistakes of Reason Rule Our Minds.

New York: John Wiley and Sons

Popper, K R (1934),Logik der Forschung;English edition (1958),The Logic of Scientific Discovery.London: Hutchinson and Co Reprinted (1961), New York: Science Editions.Prelee, D and G Loewenstein (1998), "The Red and the Black: Mental Accounting ofSavings and Debt,"Marketing Science,17: 4-28

Quine, W V (1953), "Two Dogmas of Empiricism," inFrom a Logical Point ofV~ew.Cambridge, MA: Harvard University Press

Rabin, M (1993), "Incorporating Fairness into Game Theory and Economics,"American Economic Review,83: 1281-1302

Rabin, M (1998), "Psychology and Economics," Journal of Economic Literature, 36:

11-46

Rubinstein, A (1998),Modeling Bounded Rationality,Cambridge: MIT Press

Rubinstein, A (2000),Economics and Language,Cambridge: Cambridge University Press.Samuelson, P A (1937) "A Note on Measurement of Utility,"Review ofEconomic Studies,

1 Behavioral finance and markets*

Gur Huberman

1.1 Introduction

Economics is interested primarily in prices and aggregate quantities The study

of individual behavior is a building block to derive implications about socialoutcomes Until the behavioral approach became fashionable, individuals wereusually assumed to make choices so as to optimize a well-defined objective sub-ject to well-defined constraints This very simple idea is also very powerful, in that

it lends the analysis to aggregation, and thereby affords the study of markets andequilibrium

The main contribution of the behavioral approach has so far been to question thevalidity of modeling the individual decision maker as optimizing a simple objec-tive The earlier pioneers are Allais (1953) and Ellsberg (1961) More recently,the profuse work of Kahneman and Tversky (1979) (with various coauthors) has

had the strongest impact Their joint paper on Prospect Theory in Econometrica

(Kahneman and Tversky 1979) is reputed to be the most cited paper in that highlyesteemed journal

Once scholars acknowledged that the optimizing foundations were not as solid

as had been assumed, they ventured to modify them, and felt freer to discoveranomalies that would not have existed had economic agents (or at the least, theimportant agents, the marginal ones) been neoclassical optimizers

"Is the asset price right?" is the question at the heart of financial economics Toanswer it directly, one has to agree on what "right" means in this context An earlycommentator was Adam Smith

The value of a share in a joint stock is always the price which it will bring inthe market; and this may be either greater or less, in any proportion, than thesum which its owner stands credited for in the stock of the company

Adam Smith, The Wealth ofNations, 1776

The efficient market hypothesis that "the price is right" is difficult to studydirectly A circuitous, but profitable route, calls for the study of implications of

*This chapter is based on a lecture given at a workshop on Cognitive Processes and Rationality in

2 Gur Huberman

the "price is right" statement One of them is that price changes are unpredictable.This implication has stood up to empirical scrutiny very well There are no obviousand reliable ways to predict which way the prices of securities will go But pricechanges can seem unpredictable even if the price is not right, especially when itcomes to securities with open-ended payoffs such as common stocks

One problem for the "the price is right" school is not that price changes are

unpredictable; it is that ex post they are poorly explained.

A single dramatic day best illustrates how poorly stock price changes are stood On October 19, 1987, world stock markets crashed; in the United States,the S&P500 index lost 20.47 percent of its value TheNew York Times' "explana-tion" was "worry over dollar decline and trade deficit, fear of US not supporting

under-the dollar." Motivated by under-the 1987 crash, Cutler et ale (1989) list the top major

world news in 1941-87 and the stock market reaction to them, as well as the topfifty market moves, and theNew York Times,"explanations" to them Remarkably,although the major news produce some big price movements, they do not produceany of the top five and only seven of the top fifty price movements Thus, it seemsthat fundamentals move prices, but major price movements cannot be explained

as reaction to changes in major fundamentals

The Law of One Price states that two securities that represent identical claims

to cash flows should trade for the same price In financial economics the mostinteresting anomalies are violations of the Law of One Price They are importantbecause they constitute a direct assault on the efficient market hypothesis that themarket price is right, or at least approximately right

Examples ofviolations of the Law of One Price include closed-end mutual funds,Siamese twin stocks, and the case of EntreMed Together they allow the outlines

of a coherent story to emerge The story is about the influence of the demand side

of financial markets on asset prices The demand side may be affected by investorsentiment, whose fluctuations may be independent of fundamentals Shleifer andSummers (1990) summarize this approach

Prices are the main focus of financial economics Trading volume receives muchless attention In fact, the motives of security trading are poorly understood But

it is those who trade who also determine prices Therefore an acceptable model oftrading may herald a better understanding of security prices The neoclassicalapproach has not adequately explained the huge trading volume, but the behavioralapproach may offer some hope of doing just that

The balance of this chapter has two main sections The next section describesvarious violations of the Law of One Price The section that follows it considers arelated, but very differenta~dfundamental issue: Why do people trade?

1.2 Violations of the Law of One Price

1.2.1 Closed-end fu nds

Closed-end funds are investment companies that raise equity when they are formedand use it to acquire tradable securities After the inception period, the fund sells

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Behavioral finance and markets 3

and buys tradable securities and its shareholders are free to trade its shares Thefund does not redeem outstanding shares unless it liquidates or changes its status

to an open-end fund

The Law of One Price suggests that shares of closed-end funds should trade close

to net asset value (NAV) This is not the case, as a quick look at the appropriatetable on Monday'sWall Street Journal(Or Saturday'sNew York TimesorBarron's)

will attest

Lee et ale (1991) summarize the main empirical regularities associated withclosed-end funds as follows:

• Most of the time they trade at a discount relative to NAV

• The discounts fluctuate

• The discounts as well as changes in them across funds are positively correlated

• They are issued at a premium relative to NAV

• When liquidation or open-ending of a fund is announced, its price quicklyconverges to the NAV

Leeet ale(1991) also report that the discounts are negatively correlated with thereturns on small-company stocks Presumably, it is individual investors who tend

to hold and trade both closed-end funds and small stocks; correlation between thereturns on these very different sets of assets suggests that a common sentimentmoves their prices

These observations lead them to argue that noise traders affect the prices ofclosed-end funds, and, by extension, of securities in general

Closed-end country funds (often referred to as country funds) are an interestingsubset of closed-end funds because their assets trade in a foreign market A reasonfor the formation of country funds is the segmentation of international financialmarkets Country funds afford the study of the segmentation of investor sentimentinternationally and a novel approach to the speed-of-adjustment question: howquickly do prices react to news, and how dependent is the speed on the salience ofthe news?

Hardouveliset ale(1994) have done an exhaustive study of the sources of ral variation in country fund discounts The article's main finding is in its table 8.8where it estimates a linear regression of the relation between weekly changes inthe premiums and the discount itself (positive), the return on the foreign market(negative), the dollar return on the exchange rate (negative), the dollar return onthe world stock market index (positive), the return on large US stocks (positive),and the difference in return on small and large US stocks (positive) The direction

tempo-of all these relations is consistent with the investor sentiment hypothesis: ment in the United States is mean-reverting (hence the negative relation betweenchanges in the discount and the discount itself), not sensitive to pricing of for-eign stocks (hence a negative relation with the foreign market), related to US(or world) sentiment about the foreign market (hence the negative relation withthe changes in the exchange rate), related to world and US stock returns (hencethe positive relations with these two variables) and is primarily correlated with

country fund Hardouvelis et ale (1994) study a cross-country potential difference

in investor sentiment Klibanoff et al (1998) study cross-country difference in

the impact of news on asset prices

Klibanoff et ale (1998) examine how fast share prices of country funds adjust

to news about the relevant foreign markets They show that in normal weeks,typically, a country fund's return lags significantly by a few weeks behind thereturn on its underlying assets, which are traded on the foreign market Then theyconsider weeks with salient news about the foreign country, which are weeks inwhich news about the foreign country appear on the front page of theNew York

Times. In these weeks the prices of country-funds shares (which trade on theNew York Stock Exchange) react more robustly to changes in the prices of thefunds' underlying assets (which trade on the foreign markets)

1.2.2 Siamese twin stocks

Siamese twin stocks afford a similar trading and sentiment structure These are twoclasses of shares of the same firm Their relative property rights are well specified,and the bulk of the trading of each class of shares takes place in different stockmarkets The contractual specification of the relative property rights implies thatthe shares should trade at the same relative prices On the other hand, if they trade

on different markets which are subject to different sentiments, relative prices maydiverge, and the divergence should be correlated with the relative movements inthe respective markets

Following the early work of Rosenthal and Young (1990), Froot and Dabora(1999) revisit the Siamese twin stocks These companies are: Royal Dutch andShell, Unilever NV and Unilever pIc, and SmithKline Beecham class A and class Eshares All three are large international publicly held firms whose stocks trade atvarious markets But in each case, the two stock classes trade primarily on differentmarkets Calculation of the theoretical relative values of the two types of equityare straightforward, and derived directly from the original agreement which gaverise to the two stock classes in each case Nonetheless, hardly ever do the two stockclasses trade at the theoretically correct relative prices Figure 1.1 demonstratesthe disparity for Royal Dutch and Shell

Froot and Dabora (1999) go further, and estimate the relation between relativeprices in the stock markets in which the two stocks trade and the relative prices ofthe stocks themselves It turns out that indeed, when the London Stock Exchange(where Shell trades) rallies relative to the Amsterdam or New York Stock Exchange

Behavioral finance and markets 5

vio-1.2.3 EntreMed

Can stories that appear in the New York Times cause stock price movements even

when they don't report any new information?

Huberman and Regev (2001) narrowly focus on implications of the Law ofOne Price for a biotech firm, EntreMed (ENMD), and related firms Their work

is prompted by a front page story in the Sunday, May 3, 1998, edition of the

New York Timeswhich reported on a recent breakthrough in cancer research, andmentioned ENMD, a company with licensing rights to the breakthrough Thestory's impact on the stock prices was immediate, huge, and to a large extentpermanent

The new-news content of the Times story was nil, though: the substance of the story had been published as a scientific piece in Nature and in the popular press (including the Times itself) more than five months earlier, in November 1997 The cover of the November 27, 1997, issue of Nature prominently features

the lead headline, "Resistance-free cancer therapy" as well as a related image

In that issue, Boehm et ale (1997) report on a breakthrough in cancer research

achieved by a team led by Dr Judah Folkman, a well-known Harvard scientist

6 Gur Huberman

In a "News and Views" piece in the same issue, Kerbel (1997) explains and

comments on the findings, suggesting that, "[T]he results of Boehm et ale are

unprecedented and could herald a new era of cancer treatment But that era could

be years away." Reports on the discovery of Dr Folkman's team appeared also in

the popular press, such as the Times and Newsday on November 27, 1997 as well

as in the electronic media, such as CNN's MoneyLine and CNBC's Street Signs

It seems that an effort was made to bring the news to the attention of circles widerthan the scientific community

The November 27 Times article appeared on page A28 It, as well as CNN and

CNBC, mentioned ENMD On November 28, ENMD itself issued a press releasethat covered the news and the company's licensing rights to the proteins developed

by the team of Dr Folkman The closing price of ENMD was 11.875 on November

26, and on November 28 it was 15.25; thus, the news caused a price appreciation

of 28.4 percent, an observation made in the Business Section of the November

29 edition of the Times The unusually high trading volume on November 28 and

December 1 indicates that the market paid attention to the news On the whole, anadherent of the efficient market hypothesis would argue that the market digestedthe news in a timely and robust fashion

In the months between November 27, 1997 and May 3, 1998, ENMD's stocktraded between 9.875 and 15.25

Kolata's Times article of Sunday, May 3, 1998, presented virtually the same

information that the newspaper had reported in November, but much more nently; namely, the article appeared in the upper left comer of the front page,accompanied by the label "A special report." The article featured comments fromvarious experts, some very hopeful and others quite restrained (of the "this is inter-esting, but let's wait and see" variety) The article's most enthusiastic paragraphwas " 'Judah is going to cure cancer in two years,' said Dr James D Watson,

promi-a Nobel Lpromi-aurepromi-ate Dr Wpromi-atson spromi-aid Dr Folkmpromi-an would be remembered promi-alongwith scientists like Charles Darwin as someone who permanently altered civiliza-

tion." (Watson, of The Double Helix fame, was later reported to have denied the

quotes.) ENMD's stock, which had closed at 12.063 on the Friday before the articleappeared, opened at 85 and closed at 51.81 on Monday, May 4 The Friday-close-to-Monday-close return of 330 percent was truly exceptional: bigger than all buttwo of the over 28 million daily returns of stocks priced at $3 or more between

January 1, 1963 and December 31, 1997 Not surprisingly, the Times story, and

ENMD, received tremendous attention in the national media (print and electronic)

in subsequent weeks

In the May 10 issue of the Times, Abelson (1998) essentially acknowledged

that its May 3 article contained no new-news, noting that "[p]rofessional investorshave long been familiar with [ENMD's] cancer-therapy research and had reflected

it in the pre-runup price of about $12 a share." (The Times did not question its own

editorial choice of essentially re-reporting the November 27 article, by a differentreporter, with the label, "A special report," on the upper left comer of the front

page Gawande (1998) did that in the New Yorker's May 18 issue, which hit the

newsstands on May 11.)

Behavioral finance and markets 7

.Q C;;

Q)

1,000 ~ en

Figure 1.2 ENMD closing prices and trading volume 10/1/97-12/30/98.

Source: Huberman and Regev (2001).

Figure 1.2 gives the distinct impression that while some of the May 4 pricerun-up was temporary, a substantial portion of it was permanent ENMD's stockprice fell in the days following May 4, to close the week at 33.25 - still, almostthree times higher than its price a week earlier Moreover, ENMD's closing pricedid not fall below 20 until late August 1998, and by late fall it had not closed below16.94, which was 40 percent higher than its May 1 price (Between mid-July andlate August 1998, the S&P500 lost almost 20 percent and the NASDAQ CombinedBiotechnology Index lost almost 24 percent of its value.)

By early November 1998 ENMD was trading at the upper 20s and lower 30s

On November 12, 1998, another piece of new-news came to light: on· its front

page, the Wall Street Journal reported that other laboratories failed to replicate the results described earlier in the Times ENMD stock price fell from 32.625 on

November 11 to close at 24.875 on November 12 - still more than twice ENMDprice on May I!

Contagion: Can old news reported in the New York Times cause prices of related

stocks to increase?

A look at the stock prices of other biotechnology stocks magnifies the puzzle

On average, the number of members of the NASDAQ Biotechnology CombinedIndex, excluding ENMD, went up by 7.5 percent on Monday, May 4, 1998 Thereturns of seven of the stocks in the index (other than ENMD) exceeded 25 percent

on a trading volume that was fifty times the average daily volume

That news about a breakthrough in cancer research affects not only the stock

of a firm that has direct commercialization rights to the development is not

8 Gur Huberman

surprising; the market may recognize potential spillover effects and surmise thatother firms may benefit from the innovation Moreover, the market may interpretthe news as good for other firms because it may suggest that the research and devel-opment conducted by these other firms is closer to commercial fruition However,the news did not break on May 4, 1998, but on November 27, 1997 And the peoplewith the expertise to evaluate the spillover effects closely follow the news withinthe scientific community, probably readNature, and pay attention to the coverage

of biotechnology in theTimes even when the relevant material appears well inside

the newspaper

On November 28, 1997, the average return of the seven firms was a respectable,but not extraordinary 4.89 percent The trading volume of these stocks on thatday was below the average daily volume, perhaps because it was the Friday afterThanksgiving The returns and trading volume in the following days were quiteordinary Thus, it seems that in the week or two after the November 27 news broke,prices of the seven stocks did not react strongly to the news

The motivation and identity of the people who traded the seven stocks so sively on May 4 is puzzling If they are experts on the fundamental aspects ofbiotechnology, they could, and should have traded five months earlier If they arestock market experts, with no special understanding of biotechnology, it is unclearhow they picked these particular seven stocks Perhaps they speculated on noisetrader behavior, but why with these stocks? And it is difficult to imagine peoplewho can competently follow highly technical news on biotechnology research and

aggres-be good at guessing, and speculating on the contagion effect of the no-new-newsarticle in theTimes.

It is possible, however, that those who knew were not necessarily those whotraded Brokers could have had theories on the relation between ENMD's future andthat of other biotechnology firms, and the May 3Times article and the tremendous

interest in ENMD may have created an opportunity for them to encourage tradingbased on those theories Under this interpretation the information contained inthese theories was not impounded in stock prices when the hard information aboutENMD came out in late November, but in early May, when the brokers perceivedthe publicity surrounding ENMD as an opportunity to profit from these theories.And the clients traded on the brokers' suggestions

An adherent of the efficient markets hypothesis would have expected a severeprice drop for the seven biotechnology stocks on November 11, 1998, when the

Wall Street Journal reported on the failures to replicate Dr Folkman's results.

Nonetheless, their average return was -0.81 percent-quite an ordinary return, onquite an ordinary volume A reasonable explanation is that the brokers who tookadvantage of the unusual, and unusually favorable publicity surrounding ENMD

on May 4, fell silent when the news turned bad for ENMD

1.2.4 What happened to Bristol-Myers Squibb?

Both the November 27, 1997 and the May 3, 1998, Times articles mention

Bristol-Myers Squibb (BMY), a major pharmaceutical firm with a market

Behavioral finance and markets 9

capitalization of over $100 billion in early May 1998, as working with ENMD

to develop Angiostatin, one of the proteins at the core of the scientific through According to ENMD's press release of November 28,1997, it and BMYhad forged a strategic partnership in December 1995 Therefore BMY was a likelybeneficiary of ENMD's success if it materializes

break-BMY is a large and widely followed company, and the behavior of its stockprice is more important than that of a small and fairly obscure firm But, sinceBMY is involved in numerous businesses, its stock price is subject to numerousinfluences, which renders deviations from the Law of One Price difficult to detect.Its movements can be rationalized more easily than those of a small firm with anarrowly defined business Nonetheless, the evidence suggests that even BMY'sstock price moved on theTimes' May 3, 1998 article.

Table 1.1 focuses on four important days, and reports BMY's returns, excessreturns, trading volume, relative trading volume, and the frequency of observingsuch numbers or larger in 1996 and 1997 February 10, 1999, is included because

on the previous evening both ENMD and BMY announced a modification (i.e.something close to a breakup) of the research agreement between the two com-panies regarding Angiostatin, and on that day ENMD's stock price dropped from24.5 to 12.875

Table 1.1 suggests that only May 4 was unusual for BMY's stock Its tradingvolume soared, and its return was 3.12 percent, much higher than the NYSE's0.14 percent return on that day While that return is marginally unusual comparedwith BMY's daily excess returns in 1996-97, it amounts to a $3.3 billion appre-ciation in the company's market capitalization - more than four times the dollarappreciation in ENMD and the seven biotech stocks with the highest return onthat day combined A search in the ABI Inform database suggests the absence of

Table1.1 Returns, excess returns, trading volume, relative trading volume, and

correspond-ing p-values for BMY

Date Return Excess Fraction of Volume (BMY Fraction of

(%) return a(%) 1996-'97 (thousands volume)/ 1996-'97

excess ofshares) (NYSE volume

11/28/97 0.40 0.04 0.774 1,607 0.85 0.50205/04/98 3.12 2.98 0.044 8,671 1.57 0.02411/12/98 -1.29 -1.14 0.367 1,805 0.27 1.00002/10/99 -0.20 -0.55 0.680 5,825 0.81 0.559

Source: Huberman and Regev (2001).

Notes

a BMY return in excess of that of the NYSE.

b The fraction of the 507 1996-97 daily excess returns that were higher than BMY on that day.

c The fraction of the 507 1996-97 daily (BMY volume)/(NYSE volume) ratio that was higher than the similar ratio on that day.

10 Gur Huberman

other significant news directly relevant to BMY on May 2, 3, or 4 Therefore one

could attribute at least part of BMY's price rise on May 4 to the Times article of

the previous day On the whole, then, we can rule out BMY's price reaction ondays when new-news about ENMD came out - November 28, 1997, November

12, 1998, and February 10, 1999 - and argue that both the high return and high

volume of May 4 suggest some stock market reaction to the Times' no new-news

article While BMY's return on that day is miniscule compared with that ofENMDand a few other biotech stocks, it translates to an increase in market capitalization.that dwarfs that of the biotech stocks

The big difference between ENMD stock price in the months before May 3(between 12 and 15) and the months following May 3 (around 30) must puzzlebelievers in the efficient markets orthodoxy An interpretation charitable to theefficient market hypothesis is that the May 3 article was good news relevant to

the pricing of ENMD, in that it demonstrated the Times' and James Watson's

stamp of approval of Dr Folkman's scientific discovery Perhaps these are valuable

to the valuation of ENMD Yet, the magnitude of ENMD's price appreci~tion,

especially in comparison with the reaction to the initial publication of the news

in the previous November, seems to exceed what the efficient market hypothesiswould suggest is acceptable

The market delivered two very different prices when the available informationwas virtually the same Thus, both prices cannot be "based on correct evaluation ofall information available at that time." Which price is correct is unclear In fact, it

is unclear what a "correct price" is It seems that ENMD's stock price underreacted

to the November 27 news, and overreacted to the May 3 publicity The early Maycontagion to other biotechnology stocks can also be interpreted as late reaction tothe November 27 news, and their subsequent price decline may well be evidence

of overreaction

The cleanliness of the circumstances exploited here is rare But the evidence

is suggestive for the general understanding of the determinants of security prices.Prices probably move on no new-news, and the movements may be concentrated

in stocks that have some things in common, but these need not be economicfundamentals The serious investor in search of excess returns will be wise to lookfor such seemingly extraneous price-moving factors

The possible arbitrariness of stock prices implies that capital markets may cate funds in a somewhat arbitrary fashion For instance, ENMD would have raised

allo-Behavioral finance and markets 11

money on very different terms before and after the publication of theTimes article

of May 3, 1998

The skeptical reader should reflect on the following hypothetical question: whatwould have been the price of ENMD in late May 1998 if the editor of theTimes

had chosen to kill the May 3 story?

1.2.6 Discussion of violations ofthe Law of One Price

Violations of the Law of One Price imply that stock prices need not reflectfundamentals Moreover, various correlation patterns seem consistent with thenoise trading approach; they are broadly consistent with the presence of marketparticipants whose trades are at times motivated by stimuli which are inconsistentwith fundamental information Moreover, these trades are sufficiently similar tomove prices away from their fundamental values This speculation about specula-tive prices seems attractive but has to be examined empirically Indeed, Lakonishok

et ale (1992) do exactly that, and come up virtually empty-handed: they find scant

evidence that members of a large group of money managers buy (or sell) the samestocks at the same time Remarkably, in his book titledInefficient Markets, Shleifer

(2000) fails to cite this paper

1.3 Why do people trade?

Economic theory provides two reasons for trading risky securities One, savingsand dissavings, and two, risk sharing A portion of one's savings should go tothe stock market, but toward the purchase of a portfolio, not individual stocks.Similarly, when the time comes to liquidate some of the savings, whole portfoliosshould be sold, not individual stocks Risk sharing refers to the recommendation totilt one's stock portfolio away from other systematic risks in one's life, especiallythose associated with labor income Thus, a person who takes up employment

in the technology sector should reduce his stock portfolio's exposure to that sector

If anything, the opposite behavior is observed: overinvestment in the employer'sstock and in familiar stocks in general (Huberman 2001)

Much stock trading is of the form: a person (or an institution) funds the purchase

of stock A with the proceeds of the sale of stock B Such a double transactionsuggests that the trader believes that stock A will appreciate more than B On whatbasis?

The standard answer is that people who have superior information trade ably on it But then, who is on the other side of the trade? Moreover, how can one

profit-be certain that his information is superior to that of the counterparty?

The seminal paper of Milgrom and Stokey (1982) argues that no speculativetrade will take place if all market participants are rational and rationality is commonknowledge But of course lots of security trading takes place and financial marketsare characterized by a high degree of liquidity, that is, by the ease of trading in them

In fact, liquidity is considered socially desirable, and its drying up is associatedwith financial crises

12 Gur Huberman

The study of trading is important not only because trading itself is an importantand puzzling empirical regularity, but also because traders determine asset prices,which in tum affect resource allocation

Neoclassical economics has not provided much guidance regarding why there is

so much speculative trading, so it seems that the question is ripe for the behavioralapproach to make a constructive and important contribution But it will not be easy

In fact, two related behavioral results, the status quo bias and the endowmenteffect both suggest under-, not overtrading The status quo bias refers to the lethargy

of decision makers whose preferred course of action is inaction Examples includestaying with a medical insurance plan chosen years earlier and not re-balancingone's portfolio of defined contribution pension plan (Samuelson and Zeckhauser1988; Ameriks and Zeldes 2001) The endowment effect refers to subjects' ten-dency to demand a higher price for an object which they had just been given thanother subjects' willingness to pay for the same object (Thaler 1980)

The status quo bias then predicts that market participants are inactive, and donot chum their portfolios The endowment effect predicts that even if a potentialseller and a buyer meet in the market place, they will fail to transact because theformer will demand a higher price than the latter is willing to pay

But the status quo bias and endowment effect do not apply to all people allthe time And trading is done by some people some of the time Enough peopleand money are involved in financial markets to render them very liquid most ofthe time

Trading entails strategic and tactical choices The strategic decision is whether

to be a market participant at all Most people do not trade, either professionally orfor their personal accounts A minority makes the exceptional choice to becomemarket participants, and these people are responsible for the vast amount of trad-ing observed Actual trading entails tactical decisions in response to fast-movinginformation market participants buy and sell

Although there is a lot of trading, it is done by very few individuals who are in themarket to make money for themselves, and stay there as long as they think that theyare doing so successfully It will help to characterize them and understand theirmotives But characterizing a small subset of individuals is somewhat outside thebehavioral tradition which focuses on studying the typical person, and shies awayfrom studying individual differences

A very important group of market participants work for institutions Theirmotives are quite different from those of individuals who trade for their ownaccounts Institutional traders make money by marketing their ostensible money-making skills within the organization and by letting their organizations marketthese skills to outside clients Thus their motives and probably trading behaviordiffer from those of individual market participants

In fact, even an exit decision is different for an individual and institutionaltraders If the individual realizes that he loses money in trading, it is in hisself-interest to quit Moreover, he is probably employed in another business towhich he can devote his full energy Not so the institutional trader Even theacknowledgement that he is bad at trading will be harder for him to make, because

Behavioralfinance and markets 13

he had chosen trading as his profession Furthermore, even if he acknowledges tohimself that he is a bad trader, he is likely to hide this insight from his employer,because its implications are quite grim for him

Behavioral finance covers many more issues than are covered in this chapter, and itmeans different things to different people The focus here is on the strongest embar-rassments to the efficient market hypothesis - violations of the Law of One Price -and on a question that has been mostly unexplored, namely why do people trade.Violations of the Law of One Price are difficult to document They are unlikely

to arise when market participants can safely exploit them, because then they would

be profitably exploited and thereby disappear So, to be documented, a deviationfrom the Law of One Price must be of a special kind, that is observable on the onehand, but difficult to exploit on the other The first part of this chapter reports onsome of these

Once the researcher entertains the possibility that the "price is right" may be afalse statement, perhaps even most of the time, the question is where to look for analternative theory of prices Within this pursuit it seems natural to try to address aquestion that has been mostly ignored by economists, namely why the volume offinancial markets transaction is so big

References

Abelson, Reed, "Reality Punctures Entremed's Bubble,"New York Times,May 10 (1998).Allais, Murice, "Le Comportement De L'homme Rationnel Devant Le Risque: Critique DeL'ecole Amercaine,"Econometrica,Vol 21 (1953): 503-546

Ameriks, John and Stephen P Zeldes, "How do household portfolio shares vary with age?,"working paper 12/3/2001

Boehm, Thomas, Judah Folkman, Timothy Browder, and Michael S O'Reilly, genic therapy of experimental cancer does not induce acquired drug resistance,"Nature,

Fama, Eugene F., "Efficient capital markets: a review of theory and empirical work,"Journal

of Finance,Vol 25, No.2 (1970): 383-417

Froot, Kenneth A and Emil Dabora, "How are stock prices affected by the location of thetrade?,"Journal of Financial Economics,Vol 53, No.2 (1999): 182-216

Gawande, Atul, "Mouse Hunt,"New Yorker,May 18 (1998): 5-6

Hardouvelis, Gikas, Rafael La Porta, and Thierry A Wizman, "What moves the discount

on country equity funds?" In Jeffrey A Frankel (ed.)The Internationalization of Equity Markets,Chicago: University of Chicago Press, 1994

Huberman, Gur, "Familiarity breeds investment," Review of Financial Studies, Vol 14,No.3 (2001): 659-680

14 Our Huberman

Huberman, Gur and Tomer Regev, "Contagious speculation and a cure for cancer: a

non-event that made stock prices soar," Journal of Finance, Vol 56, No.1 (2001): 387-396.

Kahneman, Daniel and Amos Tversky, "Prospect theory: an analysis of decision under

risk," Econometrica, Vol 47, No.2 (1979): 263-292.

Kerbel, Robert S., "A cancer therapy resistant to resistance," Nature, Vol 390 (1997):

335-336

Lakonishok, Joseph, Andrei Shleifer, and Robert W Vishny, "The impact of institutional

trading on stock prices," Journal of Financial Economics, Vol 32, No.1 (1992): 23-43.

Lee, Charles M.C., Andrei Shleifer, and Robert W Thaler, "Investor sentiment and the

closed-end fund puzzle," Journal of Finance, Vol 46, No.1 (1991): 75-109.

Milgrom, Paul and Nancy Stokey, "Information, trade and common knowledge," Journal

of Economic Theory,Vol 26, No 1 (1982): 17-27

Rosenthal, Leonard and Colin Young, "The seemingly anomalous price behavior of Royal

Dutch Shell and Unilever nv/plc," Journal of Financial Economics, Vol 26 (1990):

123-141

Samuelson, William and Richard Zeckhauser, "Status quo bias in decision making," Journal

ofRisk and Uncertainty,Vol 1 (1988): 7-59

Shleifer, Andrei, Inefficient Markets: An Introduction to Behavioral Finance, Oxford

University Press, 2000

Shleifer, Andrei and Lawrence Summers, "The noise trader approach to finance," Journal

of Economic Perspectives,Vol 4, No.2 (1990): 19-33

Thaler, Richard, "Toward a positive theory of consumer choice," Journal of Economic

Behavior and Organization,Vol 1 (1980): 39-60

as the formation cost of a replicating portfolio of marketed assets Thus financialmarket failures, such as price booms and crashes, excess volatility of asset prices,portfolio rigidity, bid and ask spreads and violation of call and put parity cannot

be explained unless "market imperfections," such as transaction costs, restrictedshort-sales, asymmetric information and market incompleteness are assumed.Recent developments in decision theory have recalled the concept of Knigh-tian uncertainty1 (Knight 1921) as an additional source of financial marketfailures Knight's distinction between risk and uncertainty refers to the con-cept of the vagueness or ambiguity of probability: risk is a situation in whichthe relative odds of events are known; uncertainty is a condition in whichprobabilities of events are unknown and no unique assignment of them can beobtained Consider the famous test of Savage's decision theory as illustrated

by Ellsberg (1961) An urn contains 90 balls, 30 of which are red and theother 60 either blue or white Agents are allowed to extract one ball only Let

Zj = [a ifr,f3ifb,Xifw] be a bet (or act), such that givesa if a red ball isdrawn, f3 if it is blue and X if it is white There are four possible bets (j =

1,2,3,4), that is Zl = [100 if r, 0 if b,0 ifw]; Z2 = [0 if r, 100 if b,0 ifw];

Z3 =[100 ifr,0 ifb,100 ifw]; Z4 =[0 ifr, 100 ifb,100 ifw].Agents are asked

to choose between two pairs of lotteries, Zl andZ2, thenZ3 andZ4. Most (morethan 70 percent) have the following strict preferencesZl >-Z2andZ4 >-Z3.Thisobserved behavior leads to a contradiction since:Zl >-Z2 implies Pr > Ph, while Z4 >- Z3 implies Ph +Pw > Pr +Pw or Pr < Ph, where Pi, i =b, r, w denotes

the probability of the event "a ball of color i is drawn."

Such behavior, known as the Ellsberg Paradox, is incompatible with anyprobability-based decision-making model, such as the Savage model, (whichassumes a unique well-defined additive probability distribution, that represents

beliefs of an individual) or the theory of the probabilistic sophisticated agent of

Machina and Schmeidler (1992) In order to explain the paradox, two closely

16 Marcello Basili and Fulvio Fontini

related decision theories under uncertainty have been formalized: the multiplepriors approach and the related setup with nonadditive probability measures orcapacities (Schmeidler 1982, 1986, 1989; Gilboa 1987; Gilboa and Schmeidler1989), that have been introduced in "standard" (i.e probability-based) financialmodels to explain anomalies that occur in financial markets without any apparentchange in fundamentals or frictions By taking uncertainty and uncertainty attitudeinto account rich new insights can be gained into the behavior of financial marketsfrom the standpoint of advances in theory and from the positive point of view ofshedding new light on certain financial market puzzles

In the next section we introduce the concept of Knightian uncertainty InSection 2.3 we show how uncertainty can be embodied in financial models and wesurvey models that deal with optimal choices in financial markets where agentsare assumed to face uncertainty Technical details are grouped in the Appendix

2.2 Decision making under uncertainty

Decision theory under uncertainty describes how an individual makes and/orshould make a decision between a set of alternatives, when the consequences

of each action are tied to events, about which the individual is uncertain, that is,she does not know what will occur The decision-maker formalizes the problemsetting alternatives (technically, acts), states of the world and consequences Theindividual acts on the basis of a well-defined utility function, which representsher preferences, and evaluates consequences and their likelihood The rationaldecision-maker's goal is to maximize expected utility in the case in which proba-bilities are given in advance (von Neumann and Morgenstern 1944) or derived frompreferences (Savage 1954) Both theories and their mixed version (Anscombe andAumann 1963) weigh consequences with a single probability measure, objectiveand subjective respectively, of the set of states of the world, deriving a linear pref-erence functional As a consequence, expected utility can be represented as themathematical expectation of a real function on the set of consequences with respect

to a single probability distribution and acts are ranked with respect to their expectedutility Nevertheless, a consistent body of literature2 has highlighted systematicdiscrepancies between theoretically correct behavior and effective ones in cases

in which information is perceived as "scanty, unreliable, ambiguous" (Ellsberg

1961, p 661), and thus the decision-maker cannot rely on a single probabilisticjudgment Consider a decision problem in which the states of the world included

in the model are not exhaustive The decision-maker apprehends an "unfamiliar"world, in the sense that she is aware she does not have a full description of itsstates.3She can represent her beliefs by a non-necessarily-additive measure or by

a set of additive probability distributions on the set of events

Two closely related models4have been proposed to bring uncertainty and tainty attitude into an "expected" utility framework Schmeidler (1989) and Gilboa(1987), in the Anscombe-Aumann and Savage approaches, respectively, axiom-atize a generalization of expected utility, which provides a derivation of utilityand non-necessarily-additive probability by the Choquet integral (Choquet 1954)

uncer-A non-expected glance at markets 17

Gilboa and Schmeidler (1989) extend standard expected utility, representing erences with a utility function and a set of additive probabilities, instead of a singleprobability, on the set of events

pref-LetQ = {WI, ,w n }be a nonempty finite set of states of the world A function

v: 2Q -+ ffi+ is a non-necessarily-additive probability measure or a capacity if itassigns a value 0 to the impossible event0 and value 1 to the universal eventQ,

that is, the measure is normalized, and for allA, B E2Q such thatA :J B, v(A) :::: v(B),that is, the measure is monotone A capacity is convex (concave) if for allA,

if for allA, B E2Qsuch thatv(AnB)= 0, v(A U B) :::: (~)v(A)+v(B).Noticethat a capacity v is superadditive if and only if it is convex, and is subadditive ifand only if it is concave Moreover, if a capacity is both concave and convex,

v(A U B) = v(A)+v(B), that is, it is an additive probability measure However,sillcevis in general a nonadditive measure, integration of a real-valued function

f :Q -+ fH with respect tovis impossible in the Lebesgue sense and the properintegral for a capacity is the Choquet integral:

version of the Choquet integral:

where outcomes are ranked as f(Wt) :::: :::: f(w n )andv(wo)= 0 is assumed

In the Choquet integral, less favorable states are overweighed (under-weighed)with respect to the weight that each outcome receives in the expected utility func-tional, provided that the capacity is convex (concave) Therefore convex (concave)capacities can be seen as representing agents' pessimism (optimism)

Uncertainty may be represented by a set of possible priors instead of a uniqueone in the underlying state space, that is "each subject does not know enough aboutthe problem to rule out a number of possible distributions" (Ellsberg 1961, p 657)

In this case the agent attaches a set of multiple additive probability measures~on

Q = {wI, ,w n } and her preferences are compatible with either themaxmin or

themaxmax expected utility decision rules Gilboa and Schmeidler (1989) proved

that if the agent is uncertainty-averse, she maximizes the minimal expected utilitywith respect to each probability in the prior set, thusIQ f d~ =min J f dp.

18 Marcello Basili and Fulvio Fontini

On the contrary, if she is uncertainty-loving, she maximizes the maximal expectedutility with respect to the setp,thusJfdp = maxpEpJf dp.5

Interestingly enough, the representation of uncertainty by means of the Choquet

integral (or by the closely related maxmin or maxmax models) make it possible

to distinguish uncertainty attitude from marginal utility movements (i.e maker's risk attitude in standard models).6

decision-2.3 Financial models with uncertainty

In a competitive market with no frictions, if the number of linearly independentsecurities equals all possible states of the world (there is a sufficiently rich array ofsecurities), security markets are complete and portfolios of securities can replicateany pattern of returns across states

Let a security a :Q -+ ffi Qbe defined by its vector of returns in different states

of the world, such that aj = 1 ifw = j and aj = 0 otherwise, and let q E ~~

be the price vector of securities Any marketable portfolio\II : Q -+ mQcan beconstructed and its payoff is equal to a linear combination of marketed securitypayoffs,? and with no frictions the cost of the portfolioC(\II)= :E?=la jqj.Thisportfolio can be considered equivalent to an asset fJ that yields an equal amount

in each state The no-arbitrage principle implies that two portfolios\II and<I>withthe same payoff have the same cost, that is,C(\II) = C(<I»

Under conditions of no arbitrage and no frictions, the market value of an asset

is the expectation of the discounted value of future dividends The main ture of this argument is that the price at which an asset is traded is given by theformation costs of portfolios replicating it As a consequence, the pricing func-tional of the economy is unique, positive and linear.8 In Arrow (1953), securityprices can be normalized so that they add up to one and security prices may

fea-be interpreted as a probability distribution in the space of states Note that thederived probability distribution is not a probability distribution (subjective or objec-tive) of the agents on the set of states of the world, but simply "a weighting

of the states made by prices which express an aggregation of agents'

behav-iors towards uncertainty" (Chateauneuf et al 1993) From a theoretical point

of view, all valuation models in finance, the most famous of which is the Blackand Scholes (1973) model, can be considered a generalization of the completeArrow model Given no frictions, no arbitrage conditions and an asset price thatfollows a log-normal diffusion process, in the Black and Scholes model there

is a unique probability distribution on the measurable space (Q,S) such thatthe market value of an asset is the expectation of its discounted payments Theunique additive probability distribution is "the analogue of Arrow's probabilities

of the states defined by the (Arrow) security price that probability is revealed

by market prices and has nothing to do with agents' subjective beliefs" (Ami

etal.1991).

Some recent articles have shown that the valuation of an asset is not a linearpricing rule (Lebesgue integral of the asset payments) but is obtained by Choquetintegral of the asset payments (nonlinear pricing rule), if an agent faces Knightian

A non-expected glance at markets 19

uncertainty By a nonlinear pricing rule, there may be portfolio inertia, that is

an interval of prices in which each agent neither buys nor sells the asset short(Simonsen and Werlang 1991; Dow and Werlang 1992a; Billotet ale2000; Basiliand Fontini 2001, 2002) The Choquet integral of asset payments, on the otherhand, is consistent with price puzzles, such as bid and ask spread or call and putparity9(Chateauneufet ale 1996).

Consider the "standard" theory of portfolio selection: a risk-neutral agent whohas to allocate her wealth between a riskless asset and a risky asset would calculatethe discounted expected value of the risky asset and would behave accordingly,buying the risky asset if its current price were less than its discounted expectedvalue and selling it if it were greater (assuming no frictions).10

Introducing uncertainty, the individual cannot rely on an additive probabilitydistribution on states of the world (future asset prices) but she attaches a non-necessarily-additive probability measure (or conceives a whole set of possibleadditive distribution) onQ.Simonsen and Werlang (1991) and Dow and Werlang(1992a) postulate a pessimistic agent (i.e an individual who holds a convex capac-ity) and show how uncertainty might lead to portfolio inertia: an investor may notadjust her portfolio to small variations in asset prices As a consequence, thereexists a whole set of prices for which she either holds positive quantities of allassets without selling them or she does not hold any risky assets and is not willing

to buy them

Simonsen and Werlang (1991) introduce inertia in a portfolio with risky assets,assuming that the investor is pessimistic about future asset prices The risk-neutraland non-satiable investor has to allocate her initial wealth between two risky assets

x and y, with a priceqx andqy, and maximize her expected utility Both assetsare traded without transaction costs, but short sales are restricted Simonsen andWerlang consider two possible scenarios (states of the world), namely the expectedprice ofx is greater than the expected price of y,and the converse, with respectivemeasuresVIandV2,such thatVI C·)+V2C,) < 1 By superadditivity of the capacity,the agent's indifference curve has a kink, and there exists a corner equilibrium in theinitial position Until the asset price ratio(qx/qy)is in the interval defined by theasset price ratio obtained in the two scenarios, the individual optimal portfolio willnot change and there will be inertia.I I There exists an interval of asset prices inwhich pessimistic agents do not trade in the markets and this only depends on theagent's beliefs and uncertainty aversion

Dow and Werlang (1992a) consider the portfolio decision of a risk-neutral agentwho is a pessimist, that is, who holds a superadditive capacityV. More formally,they suppose that an asset can only take two values with respect to the initialwealthW: "low"(1)or "high"(h);a superadditivevimplies thatvel)+v(h) < 1.Denote vel) asVI and v(h) as Vh. Consider the case of the agent who wishes to

buy an asset f3 at a price qIJ. She evaluates the expected return according to theChoquet integral by ranking them and underestimating the best case with respect

to the weights she would have attached if she had been uncertainty-neutral, that

is, the probability of each state When she is buying, the worst return is the lowone, that is,(I - q(3) net of price, while the high one(h - qIJ) is the best Thus,

20 Marcello Basili and Fulvio Fontini

the Choquet integral becomes:

She would buy the asset if and only if the price were less than the expected value

E(fJ) =1+v(h - I). Similarly, suppose she has to sell the asset short The bestoutcome is(q/3 -I),the worst one(q/3 - h).The Choquet integral is:

Thus, she would sell it if and only if the price were higher than the expected value

-E(-fJ) = h - vh(h -I).It follows that-E(-fJ) > E(fJ)sinceVI+Vh < 1.Therefore, there exists an interval of prices [E (fJ), - E (-fJ)] for which agentswould face inertia Dow and Werlang also introduce a measure of uncertainty based

on the "distance" of the capacity from the additivity:p(v, A) = -v(A) - v(A C

),

where A E 2°, which is aimed at capturing theamountof uncertainty aversionand showing that the difference-E(-fJ) - E(fJ)is increasing inp(., ),meaningthat the greater the uncertainty aversion, the greater the inertia interval

Chateauneufet al. (1996) consider an economy characterized by a dealer whobuys and sells an asset fJ to agents, aiming to gain a profit The buying price

is q (fJ), the selling one is-q (fJ) (given that selling fJ is equal to buying short

-fJ). The profit she can score by trading fJ is q(fJ) +q( -fJ) ~ O Prices areassumed to fulfill a set of axioms that replicates standard no-arbitrage ones12

and subadditivity of asset prices is also assumed: q(fJl +fJ2) ~ q(fJl) +q(fJ2),

where equality holds if131 andfJ2 are co-monotone This assumption is meant toexpress a sort ofpreferencefor hedging.Risk is reduced when portfolio(fJl+fJ2)

is sold together instead offit orfi2 alone, provided that fi1 andfi2 are not monotone, since non co-monotone assets vary in the opposite direction and make

co-it possible to reduce the overall risk of the portfolio The dealer is thus induced

to sell the portfolio (fJl +fJ2) at a discount with respect to the price offJl and

fJ2alone(co-monotonicity premium).In this framework the authors show that thevalue of the assetfJequals the Choquet integral of the asset calculated with respect

to a concave capacity v o , that is, q (fJ) = fQfJdv o , and this can be applied toasset pricing models in order to explain certain financial paradoxes Consider theproblem of the prime-score premium: it is well known that under no-arbitrageassumptions, the price of a security at timet,call itqt, should equal the price of

the prime (i.e the termination value k of an option in the money) at time t,call it

rt,plus the score (the excess of the price over the prime) at timet,call itSt,since

S/ =max{qt - k,O},rt = min{qt, k}and clearlyqt =rt+St.This is contradicted

by market evidence, for whichqt < rt+St,that is, the components of the securitycan sell at a premium with respect to the price of the underlying security On theother hand, this is fully explained by the Choquet pricing of the security and itscomponents, since the observed inequality is replicated by the Choquet integral ofthe prime, the score and the underlying security Similarly, consider the violation

of call put parity:q(c) +q(-s) +k i= q(f),wheref is the put, c the call with

strike price k and is the security It can be encompassed in the model since the

A non-expected glance at markets 21

value of the replicating portfolio of a put obtained by the Choquet pricing rule

observed inequality

Kelsey and Milne ( 1995) consider several conditions under which the ArbitragePrice Theorem holds under uncertainty, according to different agents' patterns ofpreferences and risk attitude In particular they show that ArbitragePri~eTheo-rem holds not only for von Neumann-Morgenstern utility maximizers but alsofor risk-averse agents who hold either Gateaux-differentiablel3 preferences orstate-dependent ones, non-additive beliefs about asset returns and (at least) onecommon prior

This result depends crucially on assumptions about preferences (included inthe utility function) and beliefs (capacity and common prior assumptions) Ensu-ing research has fully exploited the Choquet integral's property of distinguishingpreferences and uncertainty by focusing on the relationship between uncertaintyattitude, belief structure and allocations or portfolio consequences, dropping anyrestrictive utility assumption

In a general equilibrium framework, Billotet ale (2000) analyze the relationship

between "betting possibilities" (i.e trading of an uncertain asset) and optimality in a two-period pure-exchange economy under uncertainty The latter

Pareto-is modeled by means of the multiple prior model, in which agents are supposed tohold whole sets of distributions in state space(SJi),and to be uncertainty averse.This assumption leads tomaxmin behavior, according to the Gilboa-Schmeidler

theorem:14agents consider expected utility for all additive probabilities in the set

SJi,and select those acts for which the minimal expected utility is maximized mally, agents maximize the overall utility function Vi (Xi) =minpESJi En Vi (Xi),

For-whereVi is the underlying utility function Vi : 9t+ -+ 9t, Xi is an allocation and

En is the expected value operator with respect to an additive distributionp E 6Ji.

They showl5 that, for a given vector of endowmentW = (WI, , W n ),the set

of Pareto-optimal allocations is either identical to the set of "full-insurance" ones(no-bet or no-trade allocations) or disjoint, and that they are identical if and only

if agents share at least one prior distribution in eachSJi. For uncertainty-averseagents sharing at least one prior, this is a necessary and sufficient condition toprevent them from trading among each other, and leads to Pareto-optimality.Basili and Fontini (2001, 2002)16 bridge the two approaches of Billotet ale

(2000) and Dow and Werlang (1992a) by formalizing a portfolio choice model with

"pessimistic" (uncertainty averse) and "optimistic" (uncertainty loving) agentswho are Choquet expected utility maximizers holding ambiguous beliefs on theunderlying asset payment They suppose that the market can be described by tworepresentative agents The pessimist player holds a pessimistic belief represented

by the convex capacityv,with Choquet integral10.fJdv.Similarly,V ois the cave capacity which represents the optimistic player's belief and10.fJdV ois hisChoquet integral Each agent follows a well-defined behavioral rule: for the opti-mist, it is assumed that he sells the asset if and only if its price is higher thanthe maximum possible expected value of the replicating portfolio, which is eval-uated by means of the maximum additive distribution in thecorel? of his concave

con-22 Marcello Basili and Fulvio Fontini

capacity V o. For the dual problem, namely buying, it is assumed that he buysthe asset if and only if its price is lower than the minimum possible expectedvalue calculated with respect to the dual capacityvg(A) = 1 - vo(A C

) VA C 2°.The pessimist will consider the worst case, that is, the expected value associ-

ated with the worst distribution in the core of her (convex) capacity v Thus, it

is assumed that she buys the asset if and only if its price is lower than this tainty equivalent On the contrary, she sells the asset (dual problem) if and only

cer-if its price is higher than the expected return associated with the maximum

dis-tribution in the core of her dual capacity vd(A) = 1 - v(A C

)VA c 2° Finally,

agents share common expectations onf3 if there is at least one price in common

for which both classes of agents face inertia, which is defined as the set of beliefs

for which each of them will neither buy nor sell the asset Basili and Fontini18assess this behavioral rule showing that there will be no trade if and only if agentsshare at least a common belief on the asset f3, thus generalizing the result of

Billot et ale (2000) to portfolio selection in financial markets with heterogeneous

agents

Interestingly enough, their analysis can be used to compute agents' inertiainterval after a trading price has been observed in the market Consider thefollowing numerical example (from Basili (1999» Suppose that an asset f3 istraded at a price p f3 = ~, and that there are three possible states of the world,

namely Q = {WI,W2, W3}. Assume that the buying agent has an upper boundary

of buying price that equals ~ +8 (and set 8 ~ 0 for simplicity of

calcula-tion) Such a price can be represented by the Choquet integral with respect to

a capacity v (.) whose structure replicates the observed price For instance, thefollowing is a convex capacity coherent with the observed price (its concav-ity denotes agents' pessimism): v(0) = 0, V(Wl) = V(W2) = V(W3) = i,

V(WI U(2) =V(WI U(3) =V(W2U(3) = i,v(Q) =1 The capacity is obtained

by settingv(w;) = i and solving the simple determined system in two unknowns:

(~-i)(l) =~+t and 1-~ =~, where ~ =v(w; UWj)and~=I-v(w;UWj).

It is possible to evaluate the upper boundary of the inertia interval, that is, the est boundary of the price at which she would sell the asset by computing the dualcapacityofv(·) (denote it asvd(.» :vd(0) =0,Vd(WI)=Vd(W2) =Vd(W3) = i,

following Choquet integral (lowest selling price):

E~d = (G)(2) + (~-;\)(1)+ (1 - ~)(-1) = :n

The buying agent's inertia interval is therefore [~,H-].

Similarly for the selling agent, we assume her lowest selling price is ~ - 8.The following concave capacity v o (·) replicates the observed price: v o (0) = 0,

respect to the dual capacityvg(.) : vg(0) =0, vg(WI) =vg(W2) =vg(W3) =