expectations technological change

8/3/2019 Expectations Technological Change

1/26

Expectations, Technological Change, Information and the Theory of Financial

Markets

DavidN. Nawrocki

Villanova University

College of Commerce and Finance

Villanova, PA 19085 USA

610-519-4323 Office

610-519-6881 Fax

610-519-7520 Home Voice and Fax

[email protected] E-Mail

[email protected]

First Draft: May 1994

Second Draft: September 1994

Third Draft: September 1995

Fourth Draft: November 1995

Fifth Draft: January 1996


2/26

2

Expectations, Technological Change, Information and the Theory

of Financial Markets

Prologue

The Mathematician in Love

Let xdenote beauty, ymanners well-bred,

zFortune--this is essential--

Let L stand for love--our philosopher said.

Then L is a function ofx, y, and z.

Of the kind known as potential.

Now integrate L with respect to dt

(t, standing for time and persuasion);

Then between proper limits, tis easy to seeThe definite integral Marriagemust be:

(A very concise demonstration).

Said he: If the wandering course of the moon

By Algebra can be predicted,

The female affections must yield to it soon.

But the lady ran off with a dashing dragoon,

And left him amazed and afflicted.

Rankine(1870), reprinted in Georgescu-Roegen(1979)

Abstract

This paper concerns itself with understanding the operation of financial markets using realistic assumptions. The

expectations of economic agents generate prices in the marketplace. The generation of the expectations derives

from the information available in the marketplace and the perceived economic needs of the agents. The revision of

expectations occurs as new information is constantly entering the marketplace through the process of technological

change. In addition, the formulation of expectations has to derive from a realistic model of investor behavior such

as utility satisficing. This paper argues that an understanding of the financial marketplace requires a synthesis of

the study of economic change and the study of utility satisficing economic agents.

I. Introduction

This paper explores the role of two important theories in the operation of financial markets: expectations and

information theory. It is shown that a theory of participants behavior in capital markets is lacking in the current

financial economics literature, and that this issue was of concern in the 1950s and 1960s. Since finance became

financial economics, the study of the individuals behavior has been sidestepped. The academic world should


3/26

3

reflect on the fact that our knowledge is passed to us from our teachers. Periodically, we should repay our debt to

our teachers and their teachers by reexamining their original research. This paper will revisit theoretical work in

market theory over the past 120 years.

The theory of financial markets has reached a point in its development where researchers should seriously

reconsider the inclusion of, among many other assumptions, the fiction of equilibrium. Numerous empirical

studies have documented effects of small firms, large firms, January, weekend and the end of the year, calling them

anomalies. In fact, the anomalies are so numerous that they suggest the existence of a paradox; the paradox is then

the fact that if the theory is false, empirical evidence contrary to its prediction cannot be an anomaly but rather a

confirmation that the theory is false. Financial market theories themselves may be logically flawed in explaining

the operation of financial markets. This equilibrium asset pricing theory has been attacked by Roll(1977), Fama

and French(1992) and Frankfurter(1995). Phillips(1993) reaches the following conclusion:

There is a tendency in the literature to treat the inconsistencies that may arise in the theory

as unfortunate shortcomings that may somehow be compensated for by minor (sometimes ad

hoc) adjustment, rather than as a necessary consequence of wrong-minded assumptions and

systematic misconception.

The major problem with this equilibrium model are its assumptions which are not realistic and were never

intended to be. The equilibrium models have been detrimental to the study of finance since they have misdirected

research efforts toward mathematical models of equilibrium and have ignored the study of investor behavior and

disequilibrium in the markets.

Section II is a brief overview of the role of methodology in the social sciences. Section III is an exposition of

information theory and its objective in the formulation of expectations. Section IV is a derivative of an information

theory based equilibrium random walk model. Section V scrutinizes the concept of markets in equilibrium and

reviews attempts to study markets as disequilibrium processes. It also suggests that evolutionary economic theory

is the appropriate model of market operations since it integrates disequilibrium conditions with satisficing behavior

of economic agents. Section VI provides an information theory model of market disequilibrium that is consistent

with the evolutionary economic model and discusses empirical support for the model. The final section presents a

narrative example of market operation under this model.


4/26

4

II. The Study of Social Sciences

Because of the success in controlling our natural environment, there is the temptation to extend to fields like

economics, the methods of the natural sciences, in the hope of achieving a like measure of success. The major

emphasis of this effort is in the development of mathematical models of economic processes. Weiner(1948) points

out that we are successful with the natural sciences because there is a high degree of isolation of the phenomenon

from the observer. It is in the social sciences that separation between the observed phenomenon and the observer is

impossible. We can affect the phenomenon that we are studying. Weiner concludes,

In other words, in the social sciences we have to deal with short statistical runs, nor can we

be sure that a considerable part of what we observe is not an artifact of our own creation.

An investigation of the stock market is likely to upset the stock market. We are too much in

tune with the objects of our investigation to be good probes. In short, whether ourinvestigations in the social sciences be statistical or dynamic -- and they should participate

in the nature of both -- they can never be good to more than a very few decimal places, and

in short, can never furnish us with a quantity of verifiable, significant information which

begins to compare with that which we have learned to expect in the natural sciences. We

cannot afford to neglect them: neither should we build exaggerated expectations of their

possibilities. There is much which we must leave, whether we like it or not, to the un-

scientific, narrative method of the professional historian.

McGoun(1992) points out that the Black-Scholes option pricing model may well explain option pricing behavior

only because the model itself is the source of the pricing behavior. The publication of the model occurred shortly

after the opening of the first option exchanges and was very quickly implemented with statistical tables and with

programmable calculators. McGoun concludes,

that science feeds back on the external environment so that there is effectively no there out

there independent of the science.

The application of the methodology of natural science to the social sciences focuses on two issues: assumptions

and modeling. Assumptions are required in order to make the preliminary mathematical work tractable.

Assumptions allow a problem to be broken into smaller problems and then be solved sequentially. Alchian(1950)

argues that,

Analytic models in all sciences postulate models abstracting from some realities in the belief

that derived predictions will still be relevant. Simplifications are necessary, but continued

attempts should be made to introduce more realistic assumptions into a workable model with

an increase in generality and detail.

Friedman(1953) provides the alternative point of view,


5/26

5

The relevant question to ask about the assumptions of theory is not whether they are

descriptively realistic, for they never are, but whether they are sufficiently good

approximations for the purpose at hand. . . . .Truly important and significant hypotheses

will be found to have assumptions that are wildly inaccurate descriptive representations of

reality.

Friedman and Savage(1948) argue that it is not necessary for the theory to be realistic. A pool player does not

solve a complex set of geometric relationships before making a shot. However, the mathematical theory is useful if

the pool player behaves asi fthe mathematical relationships are in use. Unfortunately, mathematical models are

rarely grounded in reality. The use of mathematical models requires the simplifying assumptions to be useful.

Hawking(1988) notes,

Even if we do discover a complete (grand) unified theory, it would not mean that we would be

able to predict events in general, . . . . .We would not solve the equations of the theory

exactly except in very simple situations. (We cannot even solve exactly for the motion of

three bodies in Newtons theory of gravity, and the difficulty increases with the number of

bodies and the complexity of the theory.)

This polemic over the value of mathematical models in economics has been around for some time. Georgescu-

Roegen(1979) acknowledges the contribution of mathematical models to economics, provided that the theory is

not separated completely from fact. He concludes that there is an absolute necessity for historical and institutional

studies in social sciences, economics inclusive. The simplification of the mathematical model results in the

exclusion of structural effects from the model. We give up knowledge of how the system works.

The argument thus becomes that mathematical models are useful if they derive from a realistic set of

assumptions. Are mathematical models the proper approach to studying economics? The mathematical model is

valid only if its predictions hold in repeatable experiments under controlled conditions (a closed system).

Unfortunately, Godels Incompleteness Theorem states that such an effort is doomed to failure. Godels theorem

states that a mathematical algorithm cannot prove its own validity. In other words, there can never be a final best

system of mathematics. Every mathematical system will eventually run into certain simple problems that it cannot

solve. Kafatos and Nadeau(1990) state that,

The Incompleteness Theorem simply reveals that the language of mathematical physics, no

matter what progress is made in the effort to better coordinate experience with physical

reality, cannot in principle completely disclose this reality . . . . that reality-in-itself can

never be fully disclosed or defined. If no mathematical system, no matter how formal, can

reach closure, then it follows no physical theory built, as all physical theories must be, on

mathematical systems, can reach closure. . . . . . . . .problems of order, organization and


6/26

6

wholeness are not comprehensible in the closed system mechanistic approach. . . . Systems

theory regards living systems as wholes in terms of dynamic processes that combine

energy and information in reciprocal relationships. Since living systems are always open

and interactive with other systems, they cannot be described in classical linear chains of

cause and effect.

Reducing these systems to a system of mathematical equations simply will not work. Lacking a mathematical

theory that is not separated from fact implies that academics have to rely more on historical and institutional

studies. Kafatos and Nadeau(1990) argue that the correct approach to this problem is systems theory. The basis of

systems theory is non-Euclidean mathematics, psychology, anthropology, biology, information theory, cybernetics

and quantum physics. By maintaining an open interactive systems approach to understanding economic processes,

the resulting models must be well grounded in reality. Finance will have to become more statistical and descriptive

rather than mathematical and precise.

Even so, mathematical models are not to be abandoned. Given an ingenious setting of the boundary conditions

required to achieve closure in a mathematical model, theories explaining interactions in a localized area of the

market could prove useful. Such partial theories can go a long way towards understanding the financial markets.

However, a group of partial mathematical theories will not aggregate into a grand unified theory [GUT,

subsequently]. So do not derive some GUT of how open system financial markets operate using a closed form

mathematical model. Godels theorem states that a GUT of financial market operations is not possible using

mathematics with some type of boundary conditions (closure). This is the major weakness of the CAPM and APT

attempts to derive a GUT.

Finally, even in the natural sciences, there is room for imagination and hints. The natural sciences are not

necessarily a formal set of mathematical equations that follow logically from beginning to end. Richard Feynman

et al. (1966) presents this interesting view on studying physics.

Experiment is the sole judge of scientific truth.. But what is the source of knowledge?

Where do the laws that are to be tested come from? Experiment, itself, helps to produce theselaws, in the sense that it gives us hints. But also needed is the imagination to create from

these hints the great generalizations -- to guess at the wonderful, simple, but very strange

patterns beneath them all, and then to experiment to check again whether we have made the

right guess.

To conclude, our experiments to test various theories have to generate realistic results deriving from realistic

assumptions.


7/26

7

III. Information and Formation of Expectations

In developing a model of market operation, the first need is a model of the derivation of future expectations

from the information flow in the market. Weiner(1954) best expresses the concept of information:

Information is a name for the context of what is exchanged with the outer world as we adjust

to it, and make our adjustment felt on it. The process of receiving and of using information is

the process of our adjusting to the contingencies of the outer environment, and of our living

effectively with that environment.

Although the idea of devising a measure of information occurred first to Fisher(1925) and Hartley(1928) and

later to Kolmogorov(1941), it was Shannon(1948) and Weiner(1948) who formalized the logarithmic concept of

information. The formal definition of information content is the surprise in a message. Theil(1966) provides the

following example.

If we know that event A will take place with a probability of 0.99, then when we are told that event A has taken

place, we are not surprised. Suppose event B has a probability of 0.01, then a reliable message that event B has

occurred will greatly surprise us. The message, B has taken place," has a great deal of information content while

the message, A has taken place," does not. Information content is defined as a function of the probability that the

event will take place before themessageisreceived. Informationisadecreasingfunctionoftheprobability. The

more unlikely the event, the greater the information content whenever the event occurs. Ifp is the probability of

the event before the message is received then the information content of the message is:

I = l og( 1/ p) ( 1)

This relationship extends to a number of different outcomes (n) through the use of the entropy measure (H):

n

H = - pi l oge pi ( 2)

i =1

Shackle(1952) integrates surprise into his theory of economic expectations. If an expectation is formulated

based on the probabilityp, then the weight of the outcome is apotentialsurprise. The surprise is only potential

because we do not experience any surprise when we contemplate the outcome. We experience the surprise only if

the outcome occurs. If there are different weights of outcomes (potential surprise), then there will be apotential


8/26

8

surprisefunction. Therefore, the function summarizes the relation between the monetary pay-offs from possible

outcomes and the degrees of potential surprise attached to them. Thepotentialsurprisefunction of Shackle(1952)

is analogous to the weighted entropy measure derived by Guiasu(1977) and used by Nawrocki and Harding(1986)

as a measure of portfolio risk.

n

Hw = - Xi pi l oge pi ( 3)

i =1

where Hw is the weighted entropy, Xi is the monetary payoff or return, n is the number of outcomes, and pi is the

a priori probability of the outcome I.

Shackle continues the analysis and defines corresponding degrees of potential surprise: focus gain and focus

loss. They are points on the potential surprise (weighted entropy) function that reflect the participants

expectations of gain or loss. Note that a focus loss can occur if the return does not exceed the minimum

expectation of the participant. The minimum expectation can be the opportunity cost to the participant or the

riskless rate of return. Shackles work integrates information theory into the formulation of economic expectations

by providing a formal model of how expectations are derived from the information content or surprise of a

stream of messages available in the marketplace.

IV. Information and Market Equilibrium Theory

This section will derive an equilibrium random walk model using information theory. This derivation is

important since it demonstrates that the information theory/systems theory approach is compatible with

equilibrium models. Walras(1877,1954) provides the first mathematical model of market equilibrium. His

assumptions include:

(1) economic agents maximize their cardinal utility,(2) price competition is strong and widespread,


9/26

9

(3) all economic phenomena are interrelated,(4) entrepreneurs by buying factors of production and selling finished goods in different markets make these

markets interdependent,

(5) the impetus of economic growth is saving and investment,(6) the anticipation of profits by entrepreneurs determines the allocation of resources within the economy,(7) consumer sovereignty in a capitalist system determines the pattern of production of consumer goods within the

economy, and

(8) a capitalistic competitive market economy tends to generate a maximum of well-being for its participants.Given these assumptions, Walras describes the mechanism by which markets achieved equilibrium as a process

of tatonnement or groping (Walker, 1989). The market gropes its way towards equilibrium through the

announcement of bid and ask prices in the marketplace.

In modern times, Gale(1986) notes that the Walrasian equilibrium is utilized whenever a description of the

outcome of trade in competitive markets is required. Implicit in competitive markets are the following

assumptions:

(1) There are a large number of individually insignificant economic agents so that no one agent has market powerto set prices,

(2) there are no transaction costs,(3) there are no information costs,(4) there are no informational asymmetries, and

(5) rational agents maximize their ordinal utility. 1

When these assumptions hold, the market is said to be frictionless i.e., it is in continuous equilibrium.

Although Walras does not explicitly make these assumptions, Walrasian markets meet these conditions and, thus,

are frictionless. In the context of bargaining theory, Gale(1986) concludes that when there are no transaction

costs, every equilibrium is a Walrasian equilibrium.


10/26

10

In a Walrasian market, as information enters the market and disseminates through announcements by an

auctioneer, the price reflects all currently available information. This result can be also shown through:

Rt = f ( I t ) (4)

where Rt = ( Pt - Pt - 1) / Pt - 1 and It is the information set in period t. Pt is the price during period t. Equation

(4) implies that the information set determines the pricing in the market. According to Mandelbrot(1971), if

successive causes of the price changes are independent, then there will be a no arbitrage random walk. If the

successive causes of the price changes are dependent, then the frictionless arbitrage process of the market will

provide a random return process. However, from information theory, it is known that because information is

measured as the amount of surprise in a message, therefore, the information process has to be independent by

definition, as in equation (5).

I t +1 f ( I t ) (5)

Any knowledge that extrapolates from past or present information sets is already assimilated in the current

price. Consequently, the arrival of new information is an independent event. Given that prices reflect all available

information (equation 4) and the independence of the information process (equation 5), returns have to follow a

random walk derived from a Walrasian frictionless market (Cozzolino and Zahner, 1973) as in:

Rt +1 f ( Rt ) (6 )

Equation (6) is an economic random walk a market that is always in equilibrium, akin to the pure statistical

random walk models of the early 1960s (See Cootner, 1962). Equation (6) is also the classic static equilibrium

model based on the principles of Newtonian mechanics.

V. Disequilibrium in Markets

Boulding(1981) considers Walras work to be a major catastrophe to modern economic thought. While Walras

work was an important achievement in explaining how markets reach equilibrium, it placed unwarranted


11/26

11

importance on equilibrium conditions. As a result, economics took the wrong fork in the road a century ago

following the path of classical Newtonian mechanics. This was also unfortunate as Walras himself, did not believe

that markets operated in equilibrium. Walras(1877) conceived of an economy which is always in change, always

in dynamic motion, and always in disequilibrium because of changes in market parameters caused by the arrival of

new information. The market, according to Walras, is always drifting toward equilibrium without ever arriving

there because it cannot move along a path towards equilibrium except by tatonnements (groping). Before the

tatonnements finish they have to begin again, following new routes, since all the parameters of the problem have

changed with the arrival of new information (Walker, 1989). Walras emphasized that the goal of economic

science is to explain disequilibrium. In disequilibrium, individuals will strive in a variety of ways to maneuver

themselves into a position of maximum utility.

Shackle(1965) notes that the equilibrium market pays a high price for its incisive elegant simplicity.

To reconcile ourselves to this price, we have three alternatives. We can suppose that

economic agents will resign themselves to a total ignorance of the future and disregard it.

We can suppose that economic agents are wholly engrossed in living hand to mouth so that

their actions and choices are concerned purely with securing food and fuel for immediate

use. Finally, we can assume a constant environment of choice, just as the onset of the winter

season governs the buying of clothes despite our knowing nothing of each future days

weather.

In essence, this means that economic agents cannot formulate future expectations in a market equilibrium.

Shackle sees the market as a place for information exchange. Markets and prices are a means to information,

providing economic agents with a basis of judgment as to what best to do. Shackle argues that Marshalls concept

of an equilibrium is a fiction:

Equilibrium is a state of adjustment to circumstances (new information), but it is a fiction, for

it is an adjustment that would be obtained if the very endeavour to reach it did not reveal

fresh possibilities, give fresh command of resources, and prepare the way for inevitable,

natural, organic further change.

In a disequilibrium market, expectations are important. Ozga(1965) concludes that the introduction of

expectations into economic theory gives it a teleological (a purpose in nature) form and make its hypotheses

intuitively more appealing. In some cases, expectations help account for specific facts like gambling or insurance.

However, the more scientifically expectations are formulated, the less they seem to explain. The scientific view, of

course, is the equilibrium model.


12/26

12

Ozga(1965) discusses expectation models used for decision making under conditions of uncertainty. These

models include Shackles focus gain and loss, the maximin and maximax criteria, the Hurwicz optimism criterion,

Roys safety first, Fellners hypothesis, the Savage regret criterion and the Laplace Insufficient-Reason Criterion.

Philippatos(1973) reviews these criteria and applies them to a problem of selecting between two alternatives. Five

of the criteria provide three distinctly different answers that leads to some doubts about the scientific validity of

these methods.

Ozga argues that if we have limited information (disequilibrium) about the pay-offs, then our choices cannot be

the result of a process of maximization of pay-offs. What exists rather is a situation where one can classify

alternatives as satisfactory or not satisfactory. As one searches for alternatives, and comes across an alternative

that one regards as satisfactory, one accepts it and does not consider other alternatives. This is the theory of

choice, based on satisfiers rather than optimizers, developed by Simon(1955). If the rational economic agent

assumption is relaxed, the process is satisficing rather than maximizing.

Bringing behavioral theory into economics is not a new concept. Simon(1979) notes that Marshall(1920)

proclaims economics to be a psychological science.

Economics is a study of mankind in the ordinary business of life; it examines that part of

individual and social action which is most closely connected with the attainment and with the

use of the material requisites of well-being. Thus it is on the one side a study of wealth;

and the other, and more important side, a part of the study of man. For mans character has

been moulded by his every-day work, and the material resources which he thereby procures,

more than by any other influence unless it be that of his religious ideals.

Simon is not alone in the view that economics is the study of human behavior. In fact, Weiner(1948) is a fore-

runner of Simon:

The stock market is a game subject to the theory of games developed by von Neumann and

Morgenstern(1944). If the game is played by a large number of rational maximizers, even

with the formation of coalitions, there is a large reward for breaking the coalition agreement

and betraying their companions. There is no homeostasis whatever, with the result beingbusiness cycles of boom and failure. Since von Neumanns completely rational and ruthless

game player is rare in the marketplace, people will form close knit communities in order to

obtain a homeostasis. These groups will tend to cooperate and satisfy the economic wants of

the community.

Later, Simon(1979) demonstrates that individuals often fail the test of economic rationality even when faced

with very simple decision scenarios. Arrow(1982) observes that individuals cannot calculate expected utilities


13/26

13

exactly and therefore, may not be precise expected-utility maximizers. More recently, Bear and Maldonado-

Bear(1994) discuss whether a moral/ethical system needs to be integrated into economics. They conclude that the

homoeconomicus is the product of treating economics as a natural science and stress that economics deals with

social processes. Therefore, a legal/ethical system is needed to protect societys welfare from the rational behavior

of the utility maximizerhomoeconomicus. These results lead to the conclusion that the pricing of risky assets in

the stock market is affected by behavior that is not necessarily consistent with the von Neumann and

Morgenstern(1944) postulates. In essence, there is a need to combine behavioral theory with disequilibrium

economics.

The combination of behavioral theory with disequilibrium is the purpose of evolutionary economics (Nelson and

Winter, 1982). Evolutionary economics derives from three sources. Veblen(1935) emphasizes the role of culture

in economics. The dynamic nature of culture is subject to evolutionary development that in turn motivates

economic progress. Economic progress is the product of technological advances.2

This first school of thought derives from the institutional school which originally was the study of the

interaction of institutions in the economy. It is empirical and descriptive as opposed to the classical static

economics which is theoretical since it is based on the mathematics of Newtonian mechanics. Embodied in

institutional theory, however, is a Darwinian concept of cumulative and constant evolution in which change is

developmental, not mechanical. The emphasis is on change rather than a static process.

The second source of evolutionary economics derives from Schumpeter(1942) who argues that disequilibrium in

the marketplace is necessary. Economic development depends on structural changes and adjustments. These

changes, which include innovation, higher quality, new supply sources, or new industry, become known as

creative destruction." Schumpeter argues that creative destruction is the force that propels economic change in a

capitalistic market system. Evolutionary change describes and explains such phenomena as economic growth,

competition through innovations, and adjustment of firms to altered market conditions. Boulding(1981) notes that

unfortunately, Schumpeters insights were admired and then laid to the side for 30 years.


14/26

14

Evolutionary economics according to Nelson and Winter(1982) builds on two cornerstones. First, there is the

Schumpeterian concept of creative destruction and second, the Simon(1955), March and Simon(1958), and Cyert

and March(1963) behavioral theory of the firm. This is an important synthesis. These authors construct a theory

of firm and industry behavior in an uncertain and unpredictable economy. The behavioral theory of the firm deals

with the observable process of decision making in large firms which consists of following simple rules and the

application of established methods to adjust to changes in the environment due to creative destruction.

The third source of evolutionary economics builds directly from the theory of evolution and systems theory and

is based on work by Alchian(1950), Georgescu-Roegen(1971), and Boulding(1981). These authors build their

theories on the general systems theory developed in the 1930s and 1940s by von Bertalanffy(1963). These models

place economic systems into a biological model of evolution. The same argument that physics has to derive its

models from systems theory is made by Kafatos and Nadeau(1990).

The modern evolutionary economics (or energy economics) derives from the integration of the entropy

processes into the energy and information systems of the economy by Georgescu-Roegen(1971). Boulding(1981)

completes the theory by stating that there are two factors of production: energy and information. (Space and time

act as constraints to economic activity.) Energy provides raw materials and converts them into products and

services. Information provides the blueprint (technology) to design and build the product or service. Energy and

information systems maintain stability or homeostasis by balancing long-term supply and demand. In the short

term, energy and information markets are disequilibrium processes because of changes in energy sources and

changes in technology.

In summary, there are two postulates of disequilibrium markets. First, there is constant change due to

technological change. Second, the behavior of market participants follows the theory of satisficing economic utility

instead of the maximization of expected utility.

VI. Towards a Theory of Market Disequilibrium

Consider the simple random walk return model in equation (7):

_R( t ) = R + e( t ) ( 7)

_


15/26

15

where Ris the mean of the process;

and with e distributed randomly over time t. This is a simple stationary equilibrium model of security

returns. This random walk model consists of stationary mean and stationary error processes. It is very likely that

returns follow a more complex process. Groth(1979) starts by describing the return process as a two step process:

First, there is the information market that generates the arrival of information flows and second is the pricing

mechanism that disseminates information in order to determine the appropriate price.

However, if the information arrival process operates according to information theory (Shannon & Weaver,

1963), then when new information ("surprise") arrives, the mean return has to change reflecting the new

information. While Groth(1979) does not use the formal information theory model, he does agree with it by

drawing a distinction between data and information. Data affecting price when processed by the pricing

mechanism are considered as information and data received at the pricing mechanism not affecting price are not

defined as information.

Because information arrives in discrete batches at discrete points in time, the resulting process is a mean-jump

process.3

The mean-jump process has received empirical support from Oldfield, Rogalski, and Jarrow(1977),

Ball and Torous(1983), Jorion(1988), Tucker(1992), and Vlaar and Palm(1993). In addition, Akgiray and

Booth(1988) and Lau, Lau and Wingender(1990) provide evidence that stock market returns cannot be described

using stable probability distributions with stationary means.

The pricing mechanism disseminates and assimilates information and can be modeled as an adaptive-reactive

control process. Murphy(1965) and Copeland(1976) both model the pricing mechanism as a process that reacts to

the sequential information dissemination process. Information arrives sequentially due to frictions in the

marketplace. Groth(1979) argues that all markets do not have the same ability to assimilate information because of

information costs. Larger markets can afford more security analysts, etc. than smaller markets. Therefore, smaller

markets will be informationally less efficient.

Morse(1980) argues that the amount of information is important as well. The arrival of new information has

to be sufficiently large enough to trigger additional analyses and trades. The speed of information dissemination

will be finite and will vary with the amount of new information. With large amounts of new information, the

markets will not react as quickly as with small amounts of information. For support, Morse(1980) shows


16/26

16

significant serial dependence in price changes during periods of increased trading volume. Nawrocki(1984) argues

that a market under these conditions will exhibit an error process with a nonstationary autocovariance function

because of the varying information assimilation efficiency. Chan(1993) provides empirical evidence supportive of

this argument by showing positive cross-autocorrelation between pairs of stock price series due to nonsynchronous

trading. Trading in large stocks (where Groth(1979) feels that information will be more efficiently assimilated)

will lead to trading in smaller stocks where the information is inefficiently assimilated. In addition, the cross-

autocorrelations of the error process vary with the size of market movements indicating a nonstationary

autocovariance function. Thus, the return process can be modeled in equation (8) as in Nawrocki(1984):

_R( t ) = R[ I ( t ) , t ] + E[ I ( t ) , t ] ( 8)

_where R[I(t),t] is a mean jump process (nonstationary mean);

and E[I(t),t] is a nonstationary autocovariance matrix that is dependent on the arrival of new information over

time. The nonstationary mean and nonstationary autocovariance processes vary over time in direct response to the

amount of new information arriving into the market and to the varying finite speed of information dissemination.

The information process, I(t), is presumed to be sequential, following a sporadic jump process. The information

jump process is the source of nonstationarity that drives the mean jump process. Market frictions and rigidities

prevent the immediate dissemination of information, resulting in the nonstationary autocovariance process (e.g.

Chan, 1993).

Equation (8) represents a mixture of distributions model as originally suggested by Clark(1973). There are,

however, other explanations for the nonstationary autocovariance process. One explanation is the competence-

difficulty gap hypothesized by Heiner(1983) and supported by Kaen and Rosenman(1986). The gap is created by

the phenomenon that greater spreads between the information analysis competence of investors and the complexity

of the information, creates greater market dependence.

Guth and Philippatos(1989) suggest a concept that they call the lack of common knowledge beliefs by

investors for causing increased volatility when new information arrives. Also, Peters(1991,1994) suggests that

new information affects investors interpretation of their respective investment horizons. Different horizons will

create different expectations because the market is an amalgam of many investors with many different investment


17/26

17

horizons. In that way, if a piece of information that causes a severe drop in price at the short investment horizon,

the longer term investors will step in to buy, because they do not value the information as important as it is to the

short term investor. In contrast, when all investors have the same investment horizon, then the market becomes

unstable due to the lack of liquidity. Market stability is based on the diversification of investment horizons of the

participants. The market is stable because the different horizons value the information flow differently.

Accordingly, a crash or a stampede occurs rarely, because different investment horizons assure liquidity.

As a result of the previous discussion, the market model might look as follows:

I nf or mat i on I nf or mat i onAr r i val Pr ocess ----> Di ssemi nat i on and

Assi mi l at i on Pr ocess_X = f ( I nf or mati on) e = f ( I nf ormat i on Di ssemi nat i on

and Assi mi l at i on Process)

The error term, e, is the result of the market trying to find the homeostatic mean return, X, that arrives with the

new information set. This leads to the conclusion that the mean return or even the expected return is not a

function of risk. This conclusion is at variance with the static equilibrium asset pricing theory.

VII. One Possible Narrative of a Behavioral Disequilibrium Market

Alchian(1950) provides the starting point of the narrative by suggesting that more realistic assumptions be

introduced into a standard model (such as the CAPM). The CAPM is based on the perfect capital market

assumptions: no market power, no transaction costs, no information costs, unlimited borrowing, symmetric

information systems, and homoeconomicus resulting in the capital market line A (CML) as in Figure 1.

Because of finite borrowing, the borrowing line will become nonlinear since it will represent a margined

efficient frontier derived from the Markowitz portfolio theory.4

This model is represented as line B. As

transaction costs enter into the model, the error range CML of Francis and Archer(1979, pp.166-167) appears as

lines C1, C2, and C3. If information costs, asymmetric information systems, and utility satisficing exist, then one

obtains the preferred habitat or segmented markets model shown as Line D. Line D is de facto the normative

portfolio theory of Markowitz(1991).


18/26

18

Next, following the discussion in Section V of this paper, models of investor behavior and technological change

can be used to arrive at the same result as Figure 1, starting with a realistic model of investor behavior.

Consequently, investors are not one-period expected utility maximizers (who have knowledge of security mean

returns, variances and covariances nor do they act asi fthey have this information). Rather, investors are described

by the Weiner(1948) and Simon(1955) models. Faced with a complex problem, investors will break the problem

into subproblems and sequentially solving each. These subproblems are solved using local rationality, because

each one has its own subgoal. The local rationality is limited to satisficing, because investors will engage in

localized search and will expand the area of search only if there is no satisfactory solution. Upon reaching a

satisfactory solution, the search will end. Rarely will the search be an optimal search.

Instead of investors aggregating their localized utility functions into one grand unified utility function (GUUF)

(See Friedman and Savage, 1948), they will compartmentalize their utility. They will break investment decisions

into different compartments and have a separate satisficing utility function for each compartment. An investor

may have different compartments for saving, for retirement, for childrens education, or for a down payment on a


19/26

19

car or a house. There would also be a compartment for entertainment including going to the movies, ballgames, or

to gambling casinos, among other things.. The individual compartments contain different time horizons.5

The

different time horizon argument is the basis for the liquidity that helps markets to maintain homeostasis.

The markets will segment according to the different time horizons because of information costs, analysis costs

and unequal access to information. Because of information costs, investors will be either informed investors or

uninformed investors (Grossman and Stiglitz, 1980). Also because of information costs, the cost of analysis and

unequal access to information, some stocks will have information rich markets and some stocks will have

information poor markets (Groth, 1979). The characteristics of the two types of investors can be described in the

following manner:

1. Informed investorsa. Satisficing utility based on initial wealth and investment horizon (Simon, 1955; Peters, 1994).

b. Investors in information poor markets will make decisions based on information from information rich

markets (Groth, 1979).

2. Uninformed investors

a. Satisficing utility based on initial wealth and investment horizon (Simon, 1955; Peters, 1994).

b. Uninformed investors will try to deduce information from actions of informed investors (Grossman and

Stiglitz, 1980).

c. Uninformed investors will join cooperatives which employ informed investors to manage investments

for the cooperative. The cooperative will deliver satisfactory performance (Weiner, 1948). This

forms the theoretical basis for financial institutions such as pension funds, savings and loans, credit

unions, banks, insurance companies and mutual funds.

Markowitz portfolio theory is still the appropriate normative model under these conditions. The mathematical

technique is appropriate with the local rationality conditions stated above. Each compartment of investor utility

will have a unique efficient frontier with the optimal portfolio determined by a unique utility function.

The second model required by this narrative is a model of technological change. One such model that

introduces technological change into the market process is product life cycles. Consider the firm to be a portfolio

of product life cycles. Then each investment exists in terms of where it maps in the aggregate life cycle. In Figure

2, the four stages of product life cycle are shown: start-ups, stars, cash cows and dogs. Investors will find their

preferred habitat and specialize in investing in certain types of financial instruments. Some investors will take a

long term view and invest in new ventures. Even though they currently do not provide any income, the investor is

betting on a market success generating satisfactory future cash flows.


20/26

20

Other investors will invest in stars, hoping that they will continue their growth. More risk averse investors will

invest in cash cows preferring current income to future projected cash flows. Finally, the speculators in the

markets will pick over the dead and dying looking for value that can be liquidated and reallocated. These investors

all exhibit different investment horizons and specialize in different satisficing behavior. In the preferred habitat

model, investors will stay within their preferred investment horizon because of the information costs associated

with switching between different investment horizons. Individual investors might participate in different areas of

the product life cycle because of different compartments in their personal investment planning.

Because the risk-return chart represents a short term horizon, investors may invest away from the efficient

frontier simply because they have longer investment horizons. New venture investors are hoping that their new

venture will eventually turn into a star in the long run. Stars in various stages are long run expected growth or

they are short run accomplished growth. Cash cows are short term liquid cash generators for short term horizons

while the dogs are being liquidated for reallocation into start-ups and stars. These possibilities are portrayed in

Figure 3. Clearly the intersections of cash cows, stars, and startups are similar to Markowitzs feasible region.


21/26

21

VIII. Conclusions

Economic processes are social process, a fact that we cannot continue to ignore. Thus, when Feynman et

al.(1966) ask the question, Have we made the right guess? given the anomalies of the equilibrium market model,

the resounding answer is no. Accordingly, models of market mechanisms must reflect reality. Reality is a mix

of constant technological change and reaction of participants, who are utility satisficers.

Weiner(1948) states, whether we like it or not, there is much we must leave to the un 'scientific' narrative

method of the historian. Weiners maxim, if followed will not make finance less scholarly. Finance simply has

to drop the absurd notion that it is a natural science that can be modeled using Newtonian mechanics, a antiquated

notion even in the study of physics. Time has come for finance also to abandon the neo-classical dogma and take

its place as a social science interested in studying dynamic and changing markets. Financial economics must

mature to the point of understanding Godels theorem of incompleteness. The theories described in this paper as a

narrative following these theories, although not new, deserve a chance to help the understanding of the financial


22/26

22

marketplace, something which has been systematically neglected since the 1960s. Therefore, financial research

must become more descriptive.

ACKNOWLEDGMENTS

The author wishes to acknowledge the correspondence on the issues and comments offered by George

Frankfurter, George Philippatos, and Herbert Phillips. The views expressed in the paper and all errors are the

responsibility of the author.

NOTES

1. Walras cardinal utility is a primitive utility measure. Ordinal utility is the modern method.2. It is ironic that Veblen(1898) is known for his essay, Why Economics is not an Evolutionary Science.

Boulding(1981) points out that evolutionary science was not well developed and that it is his later work that

inspired evolutionary economics.

3.

Poisson and Bernoulli jump processes are the most commonly suggested processes.

4. Relaxing the assumption of unlimited borrowing provides a model with a finite margin limit such as thecurrent 50 percent margin requirement on stock purchases.

5. Peters(1991,1994) argument that different investors will have different investment horizons will also apply tothis model.

References

Akgiray, Vedat & Booth G. Geoffrey. (1988). The stable-law model of stock returns.JournalofBusiness

EconomicsandStatistics, 6, 51-58.

Alchian, Armen A. (1950). Uncertainty, evolution, and economic theory.JournalofPoliticalEconomy, 58, 211-

221.

Arrow, Kenneth J. (1982). Risk perception in psychology and economics.EconomicInquiry, 20, 1-9.

Ball, Clifford A. & Torous, Walter N. (1983). A simplified jump process for common stock returns.Journalof

FinancialandQuantitativeAnalysis, 18, 53-65.

Bear, Larry A. & Maldonado-Bear, Rita. (1994).Freemarkets,finance, ethics, andlaw. Englewood Cliffs, NJ,

Prentice Hall.

Boulding, Kenneth E. (1981).Evolutionaryeconomics, Sage Publications, Beverly Hills, CA.

Clark, Peter K. (1973). A subordinated stochastic process model with finite variance for speculative prices.

Econometrica , 41, 135-155.

References (Continued)


23/26


24/26

24

Guth, Michael A. & Philippatos George C. (1989). A reexamination of arbitrage pricing theory (APT) under

common knowledge beliefs. RevistaInternazionalediScienzeeCommerciali, 36, 729-746.

Hawking, Stephen. (1988).Abriefhistoryoftime:Fromthebigbangtoblackholes. New York: Bantom Books,

Paperback edition.

Hartley, R.V.L. (1928). Transmission of information.BellSystemTechnicalJournal, 7, 535-563.

Heiner, Ronald A. (1983). The origin of predictable behavior. TheAmericanEconomicReview, 76, 560-595.

Jorion, Philippe. (1988). On jump processes in the foreign exchange and stock markets. TheReviewofFinancial

Studies, 1, 427-445.

Kaen, Fred R. & Rosenman, Robert E. (1986). Predictable behavior in financial markets: Some evidence in

support of Heiner's hypothesis. TheAmericanEconomicReview, 76, 212-220.

Kafatos, Menas & Nadeau, Robert. (1990). Theconsciousuniverse. New York: Springer-Verlag.

Kolmogorov, Andrei N. (1941). Interpolation und extrapolation von stationaren zufalligen folgen. inBulletinAcademyScienceUSSRSec.Math, 5, 3-14.

Lau, Amy Hing-Ling, Lau, Hon-Shiang & Wingender, John R. (1990). The distribution of stock returns: New

evidence against the stable model.JournalofBusinessEconomicsandStatistics, 8, 217-224.

Mandelbrot, Benoit B. (1971). When can price be arbitraged efficiently? A limit to the validity of the random

walk and martingale models.ReviewofEconomicsandStatistics, 53, 225-236.

March, James G. & Simon, Herbert A. (1958). Organizations. John Wiley and Sons, New York.

Markowitz, Harry M. (1991).Portfolioselection:Efficientdiversificationofinvestment. Second Edition,

Cambridge, MA, Basil Blackwell.

Marshall, Alfred. (1920).PrinciplesofEconomics. Eighth Edition, New York.

McGoun, Elton G. (1992). On knowledge in finance.InternationalReviewofFinancialAnalysis, 1, 161-177.

Morse, Dale. (1980). Asymmetrical information in securities markets and trading volume.JournalofFinancial

andQuantitativeAnalysis, 15, 1129-1148.

Murphy, Roy E. (1965).Adaptiveprocessesineconomicsystems. Academic Press.

Nawrocki, David N. (1984). Entropy, bifurcation and dynamic market disequilibrium. TheFinancialReview, 19,

266-284.

Nawrocki, David N. & Harding, William H. (1986). State-value weighted entropy as a measure of investment

risk.AppliedEconomics, 18, 411-419.

Nelson, Richard R. & Winter, Sidney G. (1982).Anevolutionarytheoryofeconomicchange. Cambridge, MA,

Harvard University Press.



25/26

25

Oldfield, George S., Jr., Rogalski, Richard J., & Jarrow, Robert A. (1977). An autoregressive jump process for

common stock returns.JournalofFinancialEconomics, 5, 389-418.

Ozga, S. Andrew (1965).Expectationsineconomictheory. Aldine Publishing, Chicago.

Peters, Edgar E. (1991). Chaosandorderinthecapitalmarkets. John Wiley and Sons, New York.

_______. (1994).Fractalmarketanalysis. John Wiley and Sons, New York.

Philippatos, George C. (1973).Financialmanagement: Theoryandtechniques. Holden Day, San Francisco.

Phillips, Herbert E. (1993). Objectivist misinterpretations of bayesian nuances in portfolio theory and the models.

InternationalReviewofFinancialAnalysis, 2, 69-76.

Rankine, William J.M. (1870). Songsandfables. Glasgow: James Mackelhouse.

Roll, Richard. (1977). A critique of the asset pricing theorys tests, part 1: On past and potential testability of

theory.JournalofFinancialEconomics, 4, 129-176.

Schumpeter, Joseph A. (1942). Capitalism,socialismanddemocracy. New York, McGraw-Hill.

Shackle, G.L.S. (1952).Expectationsineconomics. Cambridge University Press, 1949 ; Second Edition, 1952.

______. (1961).Decision, orderandtimeinhumanaffairs. Cambridge University Press.

______. (1965).Aschemeofeconomictheory. Cambridge University Press.

Shannon, C.E. (1948). A mathematical theory of communications.BellSystemTechnologyJournal, 27, 379-423.

Shannon, C.E. & Weaver W. (1963). Themathematicaltheoryofcommunication. Urbana, University of Illinois,

Second Edition, 1963, First Edition, 1949.

Simon, Herbert A. (1955). A behavioral model of rational choice. QuarterlyJournalofEconomics, 69, 99-118.

_______. (1979). Rational decision making in business organizations.AmericanEconomicReview, 69, 493-513.

Theil, Henri. (1966).Appliedeconomicforecasting. Rand McNally & Co., Chicago.

Tucker, Alan L. (1992). A reexamination of finite- and infinite-variance distributions as models of daily stock

returns.JournalofBusinessEconomicsandStatistics, 10, 83-92.

Veblen, Thorstein. (1898). Why is economics not an evolutionary science. QuarterlyJournalofEconomics, 2,

56-81.

_______. (1935). Thetheoryofbusinessenterprise. New York, Scribner.

Vlaar, Peter J. G. & Palm, Franz C. (1993). The message in weekly exchange rates in the european monetary

system: Mean, reversion, conditional heteroscedasticity, and jumps.JournalofBusinessEconomicsandStatistics,

11, 351-360.



26/26

von Bertalanffy, Ludwig. (1963). Generalsystemstheory:Foundations, development, applications. New York:

Braziller.

von Neumann, John. & Morgenstern, Oskar. (1944). Theoryofgamesandeconomicbehavior. Princeton

University Press, Princeton, NJ.

Walker, Donald A. (1989). A primer on Walrasian theories of economic behavior. HistoryofEconomics

SocietyBulletin, 11, 1-23. Reprinted inLeonWalras(1834-1910). edited by Mark Blaug, Cambridge University

Press, 1992.

Walras, Leon. (1877).Elementsd'economiepolitiquepureoutheoriedelarichessesociale. First Edition,

Second Part, Lausanne, Imprimerie L. Corbaz et Cie; Paris, Guillaumin et Cie Bale. H. Georg.

________. (1954).Elementsofpureeconomicsorthetheoryofsocialwealth. translated from 1926 edition by

William Jaffe. Richard D. Irwin, Homewood, IL.

Weiner, Norbert. (1948). Cybernetics. The Technology Press of M.I.T. and John Wiley and Sons, New York,

1948. Second Edition, M.I.T. Press, Cambridge, MA, 1961.

________. (1954). Thehumanuseofhumanbeings. Houghton Mifflin Company, Boston, 1950, Second Edition,

1954, Paperback edition, Doubleday, New York, 1954.

expectations technological change

Documents