vogel - financial market; bubbles and crashes (2010)

Jonathan Swift, the Irish-born English author of Gulliver’s Travels, wrote a poem in December 1720 that probably made the first reference to a ble” as being a stock price that far exceed

Financial Market Bubbles and Crashes

One would think that economists would by now have already developed a solidgrip on how financial bubbles form and how to measure and compare them This

is not the case Despite the thousands of articles in the professional literatureand the millions of times that the word “bubble” has been used in the businesspress, there still does not appear to be a cohesive theory or persuasive empiricalapproach with which to study bubble and crash conditions

This book presents what is meant to be a plausible and accessible descriptivetheory and empirical approach to the analysis of such financial market conditions

It advances this framework through application of standard econometric methods

to its central idea, which is that financial bubbles reflect urgent short side –rationed demand From this basic idea, an elasticity of variance concept isdeveloped The notion that easy credit provides fuel for bubbles is supported It

is further shown that a behavioral risk premium can probably be measured andrelated to the standard equity risk–premium models in a way that is consistentwith conventional theory

Harold L Vogel was ranked as top entertainment industry analyst for ten years

by Institutional Investor magazine and was the senior entertainment industry

analyst at Merrill Lynch for seventeen years

He is a chartered financial analyst (C.F.A.) and served on the New York StateGovernor’s Motion Picture and Television Advisory Board and as an adjunctprofessor at Columbia University’s Graduate School of Business He also taught

at the University of Southern California’s MFA (Peter Stark) film program and

at the Cass Business School in London He earned his Ph.D in economics fromthe University of London and currently heads an independent investment andconsulting firm in New York City

Mr Vogel is the author of the seven editions of Entertainment Industry nomics (eighth forthcoming) and Travel Industry Economics, all published by

Eco-Cambridge University Press

Reprinted with permission from Kevin KAL Kallaugher, www.Kaltoons.com

Financial Market Bubbles and

Crashes

Harold L Vogel

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Dubai, Tokyo

Cambridge University Press

32 Avenue of the Americas, New York, NY 10013-2473, USA

www.cambridge.org

Information on this title: www.cambridge.org/9780521199674

© Harold L Vogel 2010

This publication is in copyright Subject to statutory exception

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place without the written

permission of Cambridge University Press.

First published 2010

Printed in the United States of America

A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data

or will remain, accurate or appropriate.

TO MY DEAR PARENTS

–WHO WOULD HAVE GREATLY ENJOYED SEEING THIS

vii

viii Contents

Contents ix

Equilibrium concepts II – Walras, B´enassy,

Contents xi

Bubbles are wonders to behold They take your breath away and make yourpulse race They make fortunes and – just as fast or faster, in the inevitablestomach-churning crash aftermath – destroy them too But more broadly,bubbles create important distortions in the wealth (e.g., pensions), psychol-ogy, aspirations, policies, and strategies of society as a whole Bubbles, inother words, have significant social effects and aftereffects

One would think, given the importance of the subject, that economistswould by now have already developed a solid grip on how bubbles formand how to measure and compare them No way! Despite the thousands ofarticles in the professional literature and the millions of times that the word

“bubble” has been used in the business press, there still does not appear to

be a cohesive theory or persuasive empirical approach with which to studybubble and crash conditions

This book, adapted from my recent Ph.D dissertation at the University

of London, presents what is meant to be a plausible and accessible tive theory and empirical approach to the analysis of such financial marketconditions It surely will not be the last word on the subject of bubble

descrip-xiii

to what is needed And along these lines, the notion of a behavioral riskpremium is introduced.

Yet none of this gets to the heart of the matter: When it comes to asset pricebubbles and crashes, the most visibly striking and mathematically importantfeature is their exponentiality – a term that describes the idea that growthaccelerates over time

However, although exponentiality is the essence of any and all bubbles,

it is merely a manifestation of short-rationed quantities In plain English,this means that people make trading decisions based mainly on the amountthat, for whatever reasons – fundamental, psychological, or emotional – they

need to buy or sell now Considerations of current prices thus begin to take

a backseat to considerations of quantities: In bubbles you can never ownenough of the relevant asset classes, and in crashes you cannot own too little

As will, it is hoped, be convincingly shown, the market is never at, nor willever reach, this stage, because if it did, it would cease to exist; it woulddisappear, as there would be no further need for it

In extreme market events, as ever more investors stop denying and fightingthe tide and join the herd, the rising urgency to adjust quantities is reflected byvisible acceleration of trading volume and price changes noticeably biased to

one side or the other And this is where the magical constant e, which equals

2.718, enters as a way to describe the exponential price change trajectorythat distinguishes bubbles (and crashes)

What a number this e is It suggests steady growth upon growth, which

leads to acceleration Keep the pedal to the metal in your car or rocket shipand you go faster and faster with each additional moment of elapsed time

It is the mechanism of compound interest In the calculus, it is its ownderivative – no other function has this characteristic And, best of all, even anonmathematician such as I can figure it out using only basic arithmetic

A brief example suffices to demonstrate the power of compounding (i.e.,geometric progression) I sometimes ask MBA students in finance, whom

I occasionally have the privilege of addressing, “Quick, if I give you one

Prologue xv

penny today and double the resulting amount every day for the next 30days after, what will the total then be? Remember, we’re talking here aboutonly one single penny, one measly little hundredth of a dollar, and only amonths’ time Most guesses of even these bright students, helpless withouttheir pocket calculators and laptop computers, are, as most of ours would

be, far off the mark The correct answer is $10,737,417 That’s – startingfrom a penny – nearly $11 million in a short month! And that’s the ultimatebubble

This work should first of all be of interest to financial economists of allstripes Yet the potential audience ought to extend also to MBA- and Ph.D.-level students; central, commercial, and investment bank researchers; andinvestors and speculators In this pursuit I have aimed for comprehensibilityand comprehensiveness to appeal to as many types of readers as possible.Although not structured as a breezy popular book, with all academic andtechnical references tucked neatly out of the way in footnotes, this work forthe most part requires for assimilation only a background that might includecollege-level finance and economics courses A brief glossary of terms hasalso been appended to ease the journey for general readers

Some of the material, specifically on bubble histories and on the randomwalk and related theories, has been around for a long time and has appeared

in much greater detail in many other books and articles Fast-trackers mightthus prefer to skim over those sections and to scan the extensive literaturereview in Chapter 4, the details of which are apt to be of greatest importanceonly to serious researchers in this area Also, readers initially unfamiliar withtechnical aspects of the subject should not be turned off by the somewhatchallenging start of the Preface Stick with it, as the ride should becomeincreasingly comfortable as you proceed through the text Indeed, I anticipatethat at a minimum most people will greatly enjoy the opening chapters.This project could never have been completed without the many greatworks that came before and the many kind people who provided encourage-ment, help, and good cheer during its production The following works standout for particular relevancy, clarity of exposition, and stimulative effects:

Asset Pricing, rev ed., by John H Cochran; Quantitative Financial nomics, 2nd ed., by Keith Cuthbertson and Dirk Nitzsche; Applied Econo- metric Time Series, 2nd ed., by Walter Enders; Options, Futures, and Other Derivatives, 5th ed., by John C Hull; Behavioural Finance: Insights into Irrational Minds and Markets, by James Montier; An Introduction to the Mathematics of Financial Derivatives, 2nd ed., by Salih Neftci; and Chaos Theory Tamed, by Garnett Williams.

Eco-I am fortunate to have met at Birkbeck, University of London, sor Zacharias Psaradakis, who encouraged my enrollment; Professor JohnDriffill, who supervised my academic endeavor there; Mr Nigel Foster, whoprovided timely clues in programming; and Mr Stephen Wright, who helped

Profes-to focus my thinking I’m also grateful Profes-to Professor Jerry Coakley of the versity of Essex, who provided valuable advice in review of an early draft

Bubbles and crashes have long been of immense interest not only totrained economists but also to the investing public at large Great stories

of massive wins and losses pertaining to bubbles and crashes have beenpublished over many years, and these tales still fascinate us It is my hopeand expectation that by the end of this book readers not only will have adeeper understanding of such dramatic events, but will see them also from

an entirely new perspective

October 2009

Jonathan Swift, the Irish-born English author of Gulliver’s Travels, wrote a

poem in December 1720 that probably made the first reference to a ble” as being a stock price that far exceeded its economic value.1 Sincethen asset price bubbles have been extensively reported and studied, withmany detailed accounts already extant on the presumed causes, settings, andgeneral characteristics of bubbles.2

“bub-A review of the literature nevertheless indicates that, although economistsconstantly talk about bubbles and have conducted numerous studies of them,there has thus far been little progress toward a commonly accepted (or stan-dardized) mathematical and statistical definition or method of categorizationand measurement that comes close to describing how investors actuallybehave in the midst of such extreme episodes

In fact, most studies outside of the behavioral finance literature take nality as a starting point and a given, even though this axiomatic assump-tion – itself an outgrowth of neoclassical economics – remains unproven anddebatable.3It is the intent of this study to conduct an exploration and analy-sis that might eventually lead to a robust, unified general theory applicable

ratio-to all types and sizes of financial-market, and, more broadly, asset-price

xvii

xviii Preface

bubbles (and also crashes) At a minimum, a comprehensive theory of price bubbles would appear to require that the descriptive elements be con-sistent with the ways in which people actually behave.4

asset-An understanding of bubbles is also enhanced through introduction offractal and exponential features Many natural phenomena, such as galacticspirals of stars and even snowflake patterns, are fractal (i.e., self-similaracross different time or distance scales) And these patterns are all intrinsi-cally governed by power law (i.e., exponential) distributions that also appear

in the markets for securities.5

These features were introduced into the stock market literature by delbrot (1964) and are discussed in greater detail in Chapter 4.6Mandelbrotshowed that stochastic processes describing financial time-series are muchbetter modeled by stable Paretian (also called L-stable, L´evy, or L´evy–Mandelbrot) distributions than by the normal (i.e., bell-shaped or Gaussian)distributions that had been used previously to describe asset price return prob-abilities Paretian distributions are of a discontinuous nature, contain a largenumber of abrupt changes, and suggest, in the words of Fama (1965, p 94),

Man-“that such a market is inherently more risky than a Gaussian market and

the probability of large losses is greater.”

Aside from their discontinuous nature, however, the most striking feature

of all stable distributions is infinite variance, which contrasts with the finitevariance of the Gaussian The infinite-variance aspect of stable distributions

is the one that best captures what happens to returns in the extreme eventsthat are informally known as bubbles and crashes These are the eventsthat generate the fat-tailed (leptokurtic) distribution characteristics seen inempirical data for most if not all financial markets But stability – meaningform-invariance under addition – is also important because it makes thedistribution self-similar (i.e., fractal).7

This empirically well-established background then leads readily to theidea that the theories of nonlinear dynamics (chaos) might also be applicable

to the study of bubbles and crashes In nonlinear dynamics, a variable appears

to be attracted to a time path or trajectory that may often look like randombehavior but that is described by a deterministic equation These types ofequations show how complex, chaotic behavior can arise from the simplest

of models, and also that there can be order behind disorder

From visual inspection alone it would appear that all bubbles (and crashes)are attracted to an exponential-like price-change trajectory.8If such an attrac-tor is indeed describable by a power law distribution, then the need to look

to chaos-theoretical approaches in analyzing bubbles is inescapable, eventhough it has not been established as yet that chaos theory has contributedmuch to understanding of how markets work.9

Chaos theory is also important for another reason: The basic marker

of nonlinear dynamic systems is what is known as sensitive dependence

on initial conditions (SDIC) The implication of SDIC is that it becomesimpossible to make long-range predictions This notion, however, conflicts

Preface xix

with the extensive work that followed the Poterba and Summers (1988)article suggesting that markets have a tendency to revert to the mean, that is,

markets are somewhat predictable over the long run.10

These concepts will be tied together by the idea that in bubbles and crashesthe elasticity of stock price–change variance with respect to an equity riskpremium (ERP) measure tends to become infinite (as in a stable Paretiandistribution) The empirical objective will then be to develop a method that

finds instances in which this occurs It is thus the elasticity – not the

price-change (or returns) sequence itself – that is statistically fit to an exponentialexpression Measurement of this elasticity of price variance with respect to

ERP, εvt, has a conventional definition that allows the variance when theERP is 6% to be evaluated in the same way as when, say, the ERP is 2%.Although the elasticity of variance (EOV) concept is the main innovationand focus, it is supplemented (in Chapter 5) by the different perspectiveoffered through analysis of runs – sequences of up and down price changes.For instance, in extreme market events, it is proposed that high autoregres-siveness (i.e., gains begetting more gains) causes the number of runs in asample period (positive price-change sequences in bubbles and negative incrashes) to tend toward one and the variance of the length of a run to tendtoward zero But although such runs analysis has the potential to provide anew way to define bubbles and to understand their characteristics, it is ulti-mately highly arbitrary and dependent on Gaussian distribution assumptions,providing merely an interesting extension of the conventional approaches.The factors that motivate investors and speculators to behave in the waysthat they do are also explored with reference to theories of behavioral financeand of money and credit Behavioral finance was developed early on byKahneman and Tversky (1979, 2000) and then extended in works such asthose by Camerer (1989), De Bondt (2003), and Thaler (1992, 2005) Based

on these, a new concept of a “behavioral risk premium” is introduced

Changes in credit availability and interest rates might be expected, a priori,

to play a role in the development of bubbles and crashes And this projectprovides some evidence that this might be so The theory posited here isthat extension of credit facilities beyond what can be absorbed readily bythe real economy tends to spill over into asset price speculations that, ifnot early contained, restricted, or withdrawn, will inevitably evolve or meta-stasize into full-blown “bubbles.”11Yet the whole subject is fraught with dif-ficulties, beginning with frequent imprecision in usage of the term money –

an accepted medium of exchange (based on faith) and unit of account – and

the term credit, which is a transferable right to access money.12

Stiglitz and Greenwald (2003, pp 26–7) say, for example, that “[C]reditcan be created with almost no input of conventional factors, and can just aseasily be destroyed There is no easy way to represent the supply function

for credit The reason for this is simple: credit is based on information.”

And because information is asymmetrically derived, imperfect, and costly

to gather, “[I]nterest rates are not like conventional prices and the capital

to those of desired quantities – an aspect of trading that appears to beparticularly and acutely evident in bubbles and crashes.

Although the present project contains both deductive and inductive ments, wherever possible, the inductive approach is given preference andemphasis This contrasts with the primarily deductivist neoclassical meth-ods.14 Indeed, the previously cited works by Mandelbrot, Fama, and manyothers on the stable Paretian (and fractal) nature of the fat-tailed returns dis-tributions of stocks – and thus of the direct mathematical ties to power lawsand exponentiality – provide not only the inspiration but also the inductive,empirically determined starting point for the current project.15

ele-In financial economics, however, it is notable that the widely acceptedrandom walk, efficient market hypothesis (EMH), and capital asset pricingmodels (CAPM) all follow only from the presumption (or axiom) that peoplebehave rationally when it comes to money and investments, and that their

utility functions are independent of each other In the wake of an important

early Blanchard and Watson (1982) article, the resulting standard approachhas been to model bubbles as though they all intrinsically contained attheir core a rational valuation component, above which all else is bubblefroth

The trouble is, though, that with asymmetric, imperfect information being

an essential operating feature of all market exchanges, it is difficult to knoweven what such a rational valuation component is worth at any given point

in time Notable too is that with EMH/CAPM models, markets are assumed

to be nearly always at or close to “equilibrium” and, therefore, bubbles andcrashes are not possible

This project will instead attempt to show that such extreme events arereal manifestations of collective behaviors that do not at all conform to theneoclassical Walrasian models of equilibrium – that is, models that start byassuming a complete market system and no uncertainty, and are “concernedwith analyzing a dream world.”16Especially during extreme events, there is

no subtle matching of supply and demand of shares through a considered

Walrasian process of tˆattonnement.17 That is because, in approaching theextremes, price changes are often brutally discontinuous and liquidity –which refers to a condition wherein assets are easily convertible into otherassets or consumption without loss of value – is at a premium as there is, insuch stages, so relatively little of it.18

Figure P.1 Variance versus price change percentages: an example Gains (left) and losses

in percent, S&P 500 Index, 1960:01–2005:12, monthly rolling index percentage change measured over closing prices six months prior, with estimated variance in percent based on rolling last twelve months data.

In thus recognizing that the key assumptions – independence of each

indi-vidual’s utility function, availability of perfect (symmetrical) and instantlyassimilated information, rationality at all times, and the presence of immedi-ate arbitrage possibilities – are not realistic, the work ahead provides a clearbreak with previous methods and models.19

The theory presented here therefore does not at all depend on any suchassumptions It is, instead, inductively derived through the simple and empiri-cally demonstrable observation (Figure P.1) that the variance of price changeswill tend to rise along with the size of percentage changes in prices them-selves This is a pure function of the rules of arithmetic and of the statisticaldefinition of variance and has nothing to do with the rationality of humanbehavior, the existence of equilibrium, or any other such idealized notionsand constructs

Indeed, in the theory that evolves from this relational aspect of varianceand returns, it will later be seen that bubbles and crashes are formed by a

process in which time becomes of the essence, urgency becomes the driver,

and quantity held (instead of price paid or received) becomes the primary

concern.20

The goals are thus to establish a viable definition of a financial asset

“bubble,” to devise a method that allows consistent and convenient parisons of bubbles in the same or different asset classes (including foreignexchange), to understand why bubbles begin to inflate (and then often latercollapse into crashes), and to present and test a theoretical approach that is inharmony with the behavior of investors and with the basic time discountingand risk-adjustment principles of financial economics

com-In pursuit of these objectives, the four most important new theoreticalnotions to be introduced here for the first time are an elasticity-of-variancedefinition of bubbles, a concept of fractal microbubbles, derivation of behav-ioral risk premiums from transactions volume data, and development of

xxii Preface

bubble and crash strength indicators Characteristics of price-change runssequences in extreme market events are also explored And the underlyingtheoretical basis for why bubbles emerge (credit creation is in excess of what

is needed to finance non-GDP transactions) and why crashes occur (availablecash is insufficient to service debt obligations) is explained

All of this is developed from a viewpoint that is consonant with the notions

of behavioral finance and nonlinearity and non-normal return distributions,and with the idea that bubbles and crashes are likely to be generated throughchanges in money and credit conditions Although the role of money andcredit in the fostering and support of bubbles is certainly not a new idea, it

is one that is here extended and explored in a nontraditional way

But, in addition, the basis for this whole approach is that – especially whilethey are caught up in extreme market events such as bubbles and crashes –behavior by both individuals and institutions is often not rational in the usual

sense of the word; emotions and mass psychology (i.e., zeitgeist) instead

become important concomitant factors.21

We humans, it seems from recent research in the emerging field of finance, are apparently not wired to do otherwise, that is, to be rational at alltimes For one, we tend to have a powerful and difficult-to-overcome urge

neuro-to join crowds and emulate whatever the crowd is doing As famed invesneuro-torWarren Buffett has recently said, “the markets have not gotten more rational

over the years when people panic, when fear takes over, or when greed

takes over, people react just as irrationally as they have in the past.”22

Related to this, also, is the basic flaw in the underlying and almost sally accepted assumption that supply and demand in the financial marketscan be modeled in the same way as in the markets for goods and services

univer-If, for example, the price of beef or steel or gasoline or haircuts rises, weconsumers tend to seek substitutes and demand fewer units of the affectedproducts or services

But if stocks or commodities or real estate prices rise, just the oppositeusually seems to occur, as we are drawn to invest in such financial assetvehicles and tend to demand more rather than less of them For whateverdeep-seated reasons, we respond differently to price changes in financialmarkets than to price changes in goods and services markets If so, and as aresult, the traditional financial economics approaches to modeling bubblesand crashes are inevitably destined to fail

The relevance of this research extends far beyond the usual intramuraldebates of academia or the direct interests of speculators and investors whowould gain advantage if they were able to identify bubbles in their earlieststages – that is, the points at which the risk of missing the impending upswing

or of experiencing a crash are the least.23

Keynes (1936, [1964], Ch 12, VI), for example, has written that

“[S]peculators may do no harm as bubbles on a steady stream of enterprise But the position

is serious when enterprise becomes the bubble on a whirlpool of speculation When the

Preface xxiii capital development of a country becomes a by-product of the activities of a casino, the job

is likely to be ill-done.” 24

And Shiller (2000 [2005]) says,

“If we exaggerate the present and future value of the stock market, then as a society we may invest too much in business startups and expansions, and too little in infrastructure, education, and other forms of human capital If we think the market is worth more than

it really is, we may become complacent in funding our pension plans, in maintaining our

savings rate and in providing other forms of social insurance” (p xii)

“The valuation of the stock market is an important national – indeed international – issue All of our plans for the future, as individuals and as a society, hinge on our perceived

wealth The tendency for speculative bubbles to grow and then contract can make for

very uneven distribution of wealth.” (p 204)

Still, notwithstanding such views, while they are inflating, bubbles are oftenseen by investors – both individual and institutional – as relatively benignand favorable events What’s not to like? Shares rise easily and participants

do not have to be especially skilled and selective when the tide tends to liftalmost all boats, often even those of the lowest quality and with the flimsiest

of finances

Both Wall Street (bankers, lawyers, accountants, analysts, corporate agements, etc.) and Main Street (car dealers, travel agents, brokers, jour-nalists, broadcast and cable networks, airlines, hotels, caterers, restaurants,retailers, limo drivers, dry cleaners, barbers, etc.) are beneficiaries Andsometimes, as perhaps in the 1990s (but not as for housing in the early2000s), the bubble makes it much cheaper and easier for new companiesdeveloping and promoting important productivity-enhancing technologies

man-to grow and prosper For the numerous constituencies served well by a ble’s inflation – for instance, investment bankers and tech entrepreneurs inthe 1990s and homebuilders, construction workers, mortgage servicers andpackagers, and owners in the early 2000s – the attitude will always be (andhas always been) dance while the music plays.25 “Laissez les bon temps

bub-rouler!” (Let the good times roll!)26

Moreover, how can anyone in the government agencies and branchesstrenuously object? Unless the bubble is immediately accompanied by highinflation on goods and services, which normally happens only in the laterstages, central banks do not have to focus too much on uncomfortable issuessuch as unemployment, falling exchange rates, capital account deficits, andmarket freeze-ups and bailouts of failing firms Treasury coffers are filledfrom higher capital gains tax realizations and employee payroll tax col-lections, whereas budget deficits, including those of states and municipali-ties, shrink And politicians everywhere will always welcome having moreincome to spend and having a richer platform on which to run for reelection

It is therefore likely that, at least in the beginning and into the middlephases, there is usually a broad coalition in the body politic that has nothing

xxiv Preface

particularly against – or that might even conceivably be tacitly in favor of –

the formation of bubbles It is only in the destructive aftermath that fingersare pointed, blame is affixed, retributions are sought, government institutionsflail and bail, and nastiness and distrust pervade

In sum, a financial asset bubble is perhaps best informally described as

a market condition in which the prices of asset classes increase to what – especially in retrospect – are seen as absurd or unsustainable levels that no

longer reflect purchasing power or utility of usage.27 It is hoped that thepresent project, based as it is on readily available data, will prove practical

in development of a more statistically rigorous approach to describing suchbubbles and the crashes that typically ensue

Balen (2003, p 91) indicates that reference to bubbles “was effectively the creation of the South Sea period, although in fact it had been used earlier Shakespeare, for example,

describes a ‘bubble reputation,’ and in Thomas Shadwell’s The Volunteers, written in

1692, men cheated or ‘bubbled’ each other for profit Certainly, the use of the word became commonplace in 1720 and contemporary illustrations suggest that it was understood

literally: like their counterparts in soap and air financial bubbles were perfectly formed,

and floated free of gravitational market forces But the implication, of course, was that there would be a day of reckoning, a time when they would grow too large to hold their shape, leaving them to implode with spectacular, and messy, consequences.”

2 Well-known incidents include the tulip and South Sea bubbles in the 1600s and 1700s,

respectively, and the “roaring” 1920s experience The Japanese stock market/real estate episode that ended in 1989 and the global technology/Internet stock mania of the late 1990s were notable for their persistence and strength And more recently, price movements

in housing and oil have often been referred to as “bubbles,” although these situations are, for many complex reasons, not entirely comparable to those that occur in securities markets.

3 An axiom is an assumption that no reasonable person could reject.

4 Descriptive is how the world is, as opposed to normative, how it ought to be.

5 An early example of this was shown in the early 1900s by the Italian economist Vilfredo

Pareto (1982), who found that in certain societies the number of individuals with an income

larger than some value x 0 scaled as x 0 −µ Taleb (2007, p 280) illustrates how the Gaussian

is not self-similar.

6 See Mantegna and Stanley (2000), Voit (2002, pp 95–115), and Mandelbrot and Hudson

(2004) See also Vaga (1994, pp 16–22), who emphasizes that it is during bubbles and crashes that the departure from a normal to a Paretian distribution occurs.

7 Campbell et al (1997, pp 19–21) show evidence of “extremely high sample excess

leptokurtosis a clear sign of fat tails.” To fit the financial data better, the distributions are

Notes xxv usually modified (e.g., truncated) because, in the extreme tails, financial asset returns decay faster than suggested by the unmodified Paretian See also a related article on catastrophe insurance risk pricing by Lewis (2007).

8 Baumol and Benhabib (1989) describe an attractor as “a set of points toward which

complicated paths starting off in its neighborhood are attracted.”

9 Scheinkman and LeBaron (1989), for example, found evidence of nonlinear dependence

on weekly returns for the value-weighted index of the Center for Research in Security Prices (CRSP), but as noted in Brooks (2002 [2008]) and in Alexander (2001), the issue is far from resolved See also Vaga (1994, pp 2–3) and Laing (1991).

10 A proposed resolution of these two opposing aspects, presented in Ch 10, is that in

bubbles (and crashes too) there is an exponential attractor and that SDIC is operative.

In such extreme episodes, it is proposed that there is no long-term predictability But in normal-trending markets the nonlinear dynamic aspects may be either faint or nonexistent,

so that mean-reversion and long-run predictability are then possible.

11 Thus, the word “bubble” describes as much a process as a thing.

12 Hartcher (2006, p vii) observes, “It is no coincidence that the word ‘credit’ stems from

the Latin credere – to believe.” A further important distinction is that self-liquidating credit,

with loans repaid from sales of produced goods and services, adds value to an economy, whereas non-self-liquidating credit used for non-GDP transactions such as financial asset speculations generally does not.

13 In the post-1992 experience of Japan, Werner (2005, p 62) observes that “high powered

money, M1 + M2 + CD growth increased sharply However, these increases in the money supply failed to be associated with commensurate increases in economic activity.” Nor, it seems, did this increase in money lead to anything resembling a bubble It was quite the contrary Between September 1992 and December 1994, the Nikkei 225 index essentially traded sideways, in a range from approximately 17,000 to 21,000, but by June of 1995 it had fallen to just above 14,000, close to where it had been three years earlier The two most recent lows were 7,607.88 on 28 April 2003 and 7,162.90 on 27 October 2008.

14 Werner (2005, p 17) writes, “the neoclassical school of thought is based on the

deductive approach This methodology argues that knowledge is brought about by starting with axioms that are not derived from empirical evidence, to which theoretical assumptions are added.” In contrast, the inductive approach “examines reality, identifies important facts and patterns, and then attempts to explain them, using logic, in the form of theories These theories are then tested and modified as needed, in order to be most consistent with the facts of reality.” Taleb (2007, 2005), however, provides coverage of problems of induction See also Bezemer (2009, pp 29–30).

15 The philosophical differences between the deductivist and inductivist approaches to

economics are discussed in Keuzenkamp (2000, Ch 1) And George (2007) observes that

“Orthodox economics is increasingly dominated by sterile formalism, which refers only to itself.”

16 The quotation is from Evans et al (2007) As Kamarck (2001, pp 5–7) has noted:

“Walras, in trying to construct an economic theory on the analogy of Newtonian physics, confronted the problem of how there could be any regularity when manias have the richness

of emotions, motives, expectations and uncertainties which affect all of us Walras solved

his problem by limiting human beings to a single drive, infinite selfishness A remarkable aspect of the fundamental assumption is that it lacks substantiation There is no a priori guarantee that this assumption is true The rationality-optimization assumption depends

on the belief that the individual’s choices are his own: that preferences are not influenced

by what others do If people change their choices following on others’ actions the demand

xxvi Preface

curves dance around and become indeterminate Beliefs and emotions drive actions as much

as self-interest.”

17 The present work nevertheless suggests that although securities markets are never in

equilibrium in the classical sense, it is possible (in Ch 6) to devise a practical statistical description of such an idyllic (absolute or perfect, as it is later called) equilibrium, were it ever to be attained.

18 Allen and Gale (2007, p 52) define liquidity as a condition wherein assets “can be

easily converted into consumption without loss of value.” And Smick (2008, p 22) writes,

“[i]t may be that liquidity, when all is said and done, is not much more than confidence.”

19 McCauley (2004, p xi), indeed, explains: “There is no empirical evidence for stable

equilibrium Standard economic theory and standard finance theory have entirely

differ-ent origins and show very little, if any, theoretical overlap The former, with no empirical

basis for its postulates, is based on the idea of equilibrium ”

20 “In all investment,” as Mehrling (2005, p 290) writes, “the biggest source of risk is

time.” In bubbles you don’t want to delay lest you miss some of the anticipated gains (and thereby perhaps fail to match your peer group’s performance), and in crashes you don’t want to be the last to hold onto a rapidly vanishing asset.

21 Furnham and Argyle (1998, p 5) write, “the psychological literature again and again

shows people to act in ways quite different from the dispassionate, logical, utility and profit-maximisation model so long held by economists.”

22 Burnham (2008) provides a popular treatment of the “new science” of irrationality and

writes (p 47) that “our lizard brains tend to make us greedy when we ought to be fearful, and fearful when we ought to be greedy.” Burnham’s behavioralist approach (p 33) is that

“irrationality is a fundamental part of human nature.” See also Varchaver (2008).

23 Hunter et al (2005 [2005], p xiii) refer to bubbles as “costly, destabilizing episodes.”

De Bondt (2003, p 207) observes that “Financial earthquakes undermine the public’s trust

in the integrity of the market system.” Voth (2000) believes that “Higher volatility in asset

prices can lead to instability in the rest of the economy.” Cecchetti (2008) says that bubbles contort “economic activity – not to mention the balance sheets of commercial

banks.” And Werner (2005, p 229) adds, “Instances of asset inflation are not welfare optimal.”

24 A similar view encompassing both the tech and housing bubbles appears in Laperriere

(2008).

25 This paraphrases the now-famous quote by Chuck Prince, former CEO of Citigroup,

who said (in the Financial Times, 9 July 2007) with regard to subprime lending and the

private equity buyout boom, “[W]hen the music stops, in terms of liquidity, things will be complicated But as long as the music is playing, you’ve got to get up and dance We’re still dancing.”

26 The expression was a New Orleans slogan that prevailed prior to the devastation of

Hurricane Katrina in 2005.

27 Janszen (2008, note 1) writes that the familiar term “bubble” “confuses cause with

effect A better, if ungainly, descriptor would be ‘asset-price hyperinflation’ – the huge spike in asset prices that results from a perverse self-reinforcing belief system, a fog that clouds the judgment of all but the most aware participants in the market.” He begins by saying that “A financial bubble is a market aberration manufactured by government, finance, and industry, a shared speculative hallucination and then a crash, followed by depression.”

Part I

Background for analysis

This segment reviews the historical events and theories that have been oped for the purpose of explaining and describing bubbles and crashes Assuch, it necessarily touches on a wide variety of subjects, from a review ofthe random-walk and efficient market hypotheses, to rational expectations,behavioral finance, technical analysis of transaction volumes, entropy, ele-ments of chaos theory, credit and money, and even psychology and money.All of this is needed to establish a baseline of knowledge of what has alreadybeen tried and what already exists in this field It is then possible, in Part

devel-II, to more readily present the new approaches developed here and comparethem to those that have come before

1

Circumstantial and anecdotal evidence of speculation, some of which issketched below, goes back as far as ancient Rome and Greece and Babylon(Mesopotamia).2 It is important to recognize, however, that as the term

is loosely understood today, a “bubble” cannot occur without speculation,but there can be speculation without a “bubble.”3 The presence of merespeculation alone, which was clearly an aspect of trade in the ancient world,

is not sufficient to make an asset price “bubble.”

Bubbles are instead characterized by a frenzy of speculation that, as

will later be demonstrated, is apparently fueled by a ready availability ofmoney and credit that collectively invites, stimulates, and enables broad andextreme participation by the public at large The major bubbles of the last

3

4 1 INTRODUCTION

400 years – Dutch tulip bulbs in the 1600s and the South Sea and MississippiBubbles in the 1700s, the 1929 U.S stock market, Japanese real estate andequities in the 1980s, and the Internet stock boom of the 1990s – all hadthese features in common

In classical Athens of the years 479-323 BCE, for instance, the earliest

banks, the trapeza, named after the trapezoidal shapes of their dealing tables,

were active retail financiers and suppliers of consumer credit and other ing services According to Cohen (1992, p 15), trapeza were involved with

bank-the perfume business, a major Abank-thens obsession heavily dependent on bank-theavailability of credit Evidently, elementary functions including recordkeep-ing and credit extension – and thus in all likelihood speculative trading –were already known in those times.4

In the days of the Roman Empire, moreover, a period roughly ing the years 27 BCE to 476 CE, a review by Garnsey and Saller (1987,

cover-p 47) suggests that “individual aristocrats (and emperors) were proprietors

of large warehouses, brickyards and pottery works, or the source of loancapital invested by third parties in, among other things, shipping.” Realestate and moneylending were also important, as were taxes collected by theRoman authorities Here too, as Rostovtzeff (1941) makes clear, speculation

on price movements and asset valuation undoubtedly occurred:

“The evil effects of the existence of various types of coins were lessened by the establishment

of definite rates of exchange Gold and silver coinage, on the other hand, was monopolized

by the state Though the amount of currency was not sufficient even in these metals, the evils were lessened by the activities of the banks As agents or concessionaires of the cities, the banks also took an active part in the issue and distribution of local currency, which often led to speculation and profiteering and provoked acute crises.” (p 171)

“The depreciation of money was closely connected with the rise in the prices of products of

prime necessity It is not surprising that under such conditions speculation of the wildest

kind was one of the marked features of economic life, especially speculation connected with exchange.” (pp 419–20)

Roman bankers, called argentarii, were private businessmen and, as

the famed historian Durant (1944, p 331) recounts, “[T]hey served

as money-changers, accepted checking accounts and interest bearing

deposits managed, bought and sold realty (land and buildings), placed

investments and collected debts, and lent money to individuals and nerships.” And, within this environment, episodes of money scarcity andcredit contractions – deflationary crashes of sorts – are also known to haveoccurred.5

part-For both Greece and Rome, an inherent and inevitable component of thespeculations that occurred was a subtext of familiarity with, and a penchantfor, gambling; the nexus between gambling and speculation is strong Games

using astragali, which were small stones (or bones and early versions of

dice), were played by both Greek children and adults, and other wagers on theoutcomes of events were also common All of these elements were expanded

1.1 Overview 5

upon by the Romans As Schwartz (2006, p 25) writes, “[f]atalistic Romansgambled incessantly Gambling was more than a pastime for the Romans – itwas a metaphor for life itself.” If so, then the presence of such environmental

features raises the question: How could there not have been any bubbles?

Although experts on the history of these eras have not been able to

specifi-cally identify bubbles per se, that may be because monetary systems were not

yet sufficiently developed and/or because price records of transactions neverexisted, were not comprehensive, or were never found.6 However, giventhat banking-type money-creating merchants and goldsmiths are known toalso have operated in ancient Babylon, Egypt, tenth-century China (the SongDynasty from 960 to 1279), and the Mongol Empire of Genghis Khan (1206–1368), it would seem quite likely that speculation and perhaps “bubble-like”conditions might have sometimes appeared in those societies too

Intense mercantile activity throughout these times, for instance, alsoinvolved trade in spices such as cinnamon, cardamom, ginger, pepper, andturmeric that originated on the Indian subcontinent Such trading in spicesand aromatics, and eventually also in silk, ebony, and fine textiles, firstextended to the Middle East, especially Egypt, and then later to Europe.Both the early Greeks and Romans participated, and speculation must havebeen a common feature, as spice traders were normally quite secretive abouttheir sources.7

China’s Song (sometimes spelled Sung) Dynasty, in particular, was knownfor the development of trade, maritime commerce, paper money, and a unifiedtax system And with such features in place, some sort of speculative activitywould also have been likely Gascoigne (2003, p 124), for example, describesthe passion for art and observes with respect to such items that “even if theirextreme age was not fully appreciated they stimulated a craze for collectionand study of antiquities.”

Gernet (1982, pp 323–5) goes on to say that “principal wealth in the Sung

age came from commerce and craftsmanship Ceramics, silks, iron and

other metals, salt, tea, alcohol, and printed books were the objects of intense

commercial activity One of the prerequisites for the economic upsurge of

the eleventh to thirteenth centuries was a very considerable increase in the

means of payment and the spread of the monetary economy The cates of deposit issued in favour of merchants in the ninth century were the precursors of banknotes This institution gave powerful assistance

certifi-to expansion of both the private and state economy during the Sungperiod.”

Kruger (2004, p 249) notes that “[S]ilver coins as well as iron and copperwere in circulation, and variations in rates between them gave rise to muchspeculation which was fuelled by the state’s issue of deposit certificates,opening the way to the use of paper money, first printed in 1024 Commercealso brought in negotiable instruments in the form of cheques, promissory

notes, and bills of exchange China’s economy had become a monetary

one and the circulation of so much money resulted in inflation.”

6 1 INTRODUCTION

Speculation was also present in Italy’s Medici era of the fifteenth century.Parks (2005, p 39) writes, “Like all major banks at the time, the Mediciwere merchants as well as bankers They would procure goods abroad for

rich clients: tapestries chandeliers, manuscript books, silverware, jewels, slaves They would speculate There was risk involved Demand and

prices swung alarmingly, depending on how many merchants had sensed aparticular gap in the market.”

By the 1600s, though, money and credit-extension mechanisms hadevolved considerably further, and the Netherlands had by then alreadybecome quite sophisticated in applying them As recalled by Davies (2002,

pp 550–51), “the Amsterdam stock exchange quoted a list of prices as

early as 1585 the Dutch East India Company of 1602 and the West

India Company of 1621, provided the financial backing for Dutch political

and economic competition with England the public Bank of Amsterdam

(Wisselbank) was established in 1609.”

It is fair to say that such a rapid pace of financial innovation provided thebanking and transactions processing structure that was essential to the devel-opment of the first documentable bubble episodes – tulips, the MississippiCompany, and the South Sea Company – which soon followed (and whichare described in greater detail in Chapter 2)

Yet although the bursting of all such bubbles is undoubtedly a distinctlyunpleasant experience for the speculators directly involved, the historicalrecord suggests that not all bubble endings are necessarily followed byperiods of severely depressed economic conditions Neither the tulip manianor the South Sea episode resulted in extended disruption of overall economicactivities, whereas the recent Japanese episode was indeed followed bydecade-long deflation.8

Despite the widespread attention that financial bubbles attract, their ioral characteristics have not been well described or understood from anoperational and statistical standpoint How is a bubble formally defined?What properties do bubbles all have in common? Does the rate of advancehave any relationship to the rate of decline? Are there any constant rela-tionships? Is the behavior fractal – that is, do big (macro) and small (micro)episodes, like a coastline, have jaggedness and self-similarity on all orders ofmagnitude? As will be demonstrated from the introductory survey, relativelylittle work has been done on answering such questions

behav-The current project will first briefly survey the existing literature on thissubject and then, as an extension, attempt to provide through empiricaltesting the statistical foundation on which all asset price bubbles can bedefined, identified, described, and compared

Such an understanding ought to be of great importance in real-worldapplications Central bankers, for example, might be able to better steereconomic policies if they could know whether and when their actions werelikely to be creating a bubble And speculators too might benefit by being

1.2 On the nature of humans and bubbles 7

able to better position themselves if it were possible to determine early onthe potential strength and the stage of a bubble’s development

1.2 On the nature of humans and bubbles

Macro aspects

No two bubbles or manias follow a path that is exactly the same, but as

is later illustrated in Figures 5.4 and 5.5, for example, bubbles exhibit tures that are similar and readily identifiable by visual inspection And on amacro scale, all bubbles create financing, production, and service capacitiesthat, once the bubble bursts, will no longer be needed Consolidation andcontraction then follow naturally, as formerly misallocated capital flows areredirected

fea-But news itself does not (as some studies, e.g., Cutler et al 1989, haveshown) move the markets; news is only the catalyst What happens in markets

depends on how traders react to specific news events Announcements and

developments seen as being favorable – whether of a political, technological,

or monetary nature – typically provide the fertile soil in which bubbles areable to sprout and grow large.9For the larger, longer-lived bubbles perceivedgood news, leading to bouts of intense speculation, usually comes in theform of productivity-enhancing innovations, with some of the historicallymost important ones being the introduction of canals, railways, automobiles,radios, airplanes, computers, and the Internet.Table 1.1shows that bubblesand crashes related to such innovations have regularly appeared in the last 200years in both the United States and the United Kingdom.Figure 1.1provides

a visual overview of real asset class returns for 1900–2008

Indeed, the manic market reaction to technological innovation in the 1990swas not unique and unprecedented, as many of the most fervid participantsthen believed Something of the same sort, writes Sylla (2001), had alreadyhappened 150 years before: “Britain in the 1840s was in much the position of

the United States today It also had several years of irrational exuberance

related to a new network technology, in this case, the railways.”10

Schumpeter (1939, pp 689–91) also wrote extensively on the role inthe business cycle played by innovation and described the linkages betweenspeculation, credit, and central banking In regard to stock market speculation

he first notes (p 683) that it is “availability rather than cost of credit that

we should look to.” He then observes (pp 689–91) that “ speculation in stocks does not, or not to a significant extent, ‘absorb credit’ the stock exchange is not a sponge but a channel Since stock speculation does not

absorb funds, it must be extremely difficult to stop or to restrain by any ofthe ordinary tools of central banking.”11

However, once a bubble has burst, scapegoats are sought and tive and political inquiries and policy initiatives are typically begun with a

1.2 On the nature of humans and bubbles 11

widespread sense of outrage and a desire that perpetrators be punished Thelarger the bubble, of course, the more intense is the urge for retribution.12None of this ought to be surprising in that over the centuries humannature does not appear to have changed much if at all, and that episodes ofspeculative euphoria are always led and fed by, among other things, avarice,envy, emulation of neighbors, and crowd psychology.13In fact, many of theinvestment concepts and vehicles for speculation were devised or inventedlong ago Osaka’s Dojima Rice Exchange established in 1697, for instance,offered forward contracts as early as the eighteenth century.14

Says Chancellor (1999, p 57),

“ there is really very little in our financial understanding that is actually new Already in

the seventeenth century, both in Amsterdam and in London, we find financial derivatives being used for both risk control and speculation We also find sophisticated notions of value, together with the idea of discounted cash flows and present values Wagering and probability theory provided contemporaries with an understanding that the risk-reward ratio could, in certain circumstances, be calculated.”

Lord Keynes also recognized the nature of speculative bubbles:

“It might have been supposed that competition between expert professionals, possessing judgment and knowledge beyond that of the average private investor, would correct the vagaries of the ignorant individual left to himself.” (Keynes ( 1936 , [1964], p 154))

And even former Fed Chairman Alan Greenspan recognized that bubbles arenothing new

“Whether tulip bulbs or Russian equities the market price patterns remain much the same.” Greenspan ( 1999 ) and in Haacke ( 2004 , p 3)

The random-walk and the affiliated efficient market hypothesis (EMH)approaches that emerged from academia in the 1960s (e.g., Samuelson

1965), however, did provide fresh and stimulative insights that ultimatelyled, through extensive empirical analysis, to a much deeper understand-ing of stock price behavior and portfolio risks and rewards In effect, theseapproaches posited that stock movements are unpredictable (a random walk)because the most recent share prices already presumably reflected all infor-mation relevant to their value and that markets are efficient because they areable to assimilate and react to the randomly timed arrival of new informationrather rapidly

Social and utility theory aspects

The random walk/EMH framework has been studied and debated to tion by academics and practitioners In the early years, the random-walkersappeared to marshal virtually incontrovertible statistical evidence for thereliability and viability of their models Yet despite the spirited defense

exhaus-in Malkiel (1999 [2003, 2007]), other academic work, for example, by

12 1 INTRODUCTION Utility

of

wealth, U(V)

Utility of wealth, U(V)

non-bubble

risk aversion

bubble greed

Figure 1.2 Idealized collective market utility functions, non-bubble risk averse, left, and nonrational bubble greed, right The right panel conceptually illustrates the attitudinal conversion (or flip) of market participants from risk aversion to the obliviousness to risk that characterizes bubbles It essentially portrays an accelerating attitude of, “the richer I become, the more I want,” monetarily, emotionally, and psychologically 19

Lo and MacKinlay (1999) and Poterba and Summers (1988), gives weight

to alternative arguments

The Long-Term Capital Management (LTCM) debacle of 1998 – the

single-day loss was $553 million on 21 August (CFA Magazine, March–April

2006) – has also cast doubts on the practical usefulness of such theories andmodels.15Moreover, the EMH in particular plays a peculiar counterpoint inthat it is totally incompatible with any notion of stock market bubbles: If theEMH is correct, there can never be any bubbles However, history suggests,

in hindsight and in most interpretations (as discussed below), that many suchevents have occurred – including but not limited to the tulip mania of the1600s, the South Sea episode of the 1700s, and the Internet craze of the1990s

In this regard, the key underlying assumption for many neoclassically

trained economists is that investors are at all times rational in

indepen-dently ordering their preferences and in maximizing expected utility, which

is economists’ vague jargon for the amount of pleasure (perhaps monetarygain) that is expected to be derived from the outcome of events or fromdoing something (e.g., buying, selling, owning).16The standard presentation

of such risk-averse rationality, which results in a concave and increasingutility function, is seen in the left-hand panel ofFigure 1.2

With a utility function of this type, equal movements to either side from the

average level of wealth, V0, will result in unequal changes in utility.17ing to conventional explanations and interpretations, this is considered thenormal state of affairs.18

Accord-In many spheres of life, though, it in fact appears from recent researchinto human behavior that people are influenced by economically irrelevantinfluences and will often make decisions in context and in relation to whatothers are doing.20And nowhere in economic relationships is this seen moreprominently than under extreme market conditions Investors, it seems, rarelymake decisions in isolation