Death Of The Efficient Market Hypothesis

Min Deng*

Shenzhen Divine Vision Investment Planning Co., Ltd

* Email: dengmin@public.szptt.net.cn

To my friend

Mr. Chen Yuping

Without his generous one million RMB funding support, this research could never have been completed.

Acknowledgements

Copyright by the author. All rights reserved. No part of this publication may be reproduced, stored in a

retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or

otherwise, without the prior written permission of the author.

Death Of The Efficient Market Hypothesis

Min Deng

Shenzhen Divine Vision Investment Planning Co., Ltd

Abstract

This report summarizes the breakthroughs achieved by the present writer in

respect of the research on the investor behavior and stock price behavior as well as the

interrelationship between them.

On the basis of these achievements, the paper briefly analyzes the theory of

random walk, and point outs its main errors. The paper then dwells on details

identified with the errors and mistakes associated with the Efficient Market Theory.

The paper also provides an in-depth analysis into the basic elements constituting the

Efficient Market Theory (such as Rational Expectations and equilibrium) and

pinpoints the underlying non-scientific aspects in this regard, and provides a brief

judgment on the viewpoints advanced by Samuelson (1989), Fama (1998) and

Malkiel (2003), (2005).

Lastly, the paper concludes with the fact that Efficient Market Theory is far from

a reasonably close approximation to the stock market realities, and its scientific

content is close to zero.

Moreover, the paper provides brand-new interpretations on whether those

extraordinary investors who have succeeded in beating the market actually depended

on luck or not along with a number of other financial theoretical problems related to

the Efficient Market Theory.

KeywordsInvestor behavior; stock price behavior; theory of the random walk; Efficient Market Theory

JEL Classification: G14.

Table of Contents

1 Introduction ............................................................................... 1 2 The Investor Behavior and Stock Price Behavior................... 5

2.1 The investor behavior.......................................................................................................5 2.2 The stock price behavior ................................................................................................10 2.3 Inter-relationship between the investor behavior and stock price behavior ...................14

3 A Historical Perspective on EMT........................................... 16 3.1 Pre-history Stage Of EMT (19001965) ...................................................................16 3.2 Formation And Refinement Stage Of EMT (19651991) .........................................18 3.3 EMT At the Stage Of Decline ( 1991Present) .........................................................21

4 Analysis of Errors with The Theory of Random Walk......... 23 4.1 Mistakes with perception ...............................................................................................23 4.2 Erroneous research methodology...................................................................................25 4.3 Root cause analysis ........................................................................................................27

5 Analysis on Errors with EMT ................................................ 28 5.1 Absurdities with the efficient market definition.............................................................28 5.2 Unscientific theoretical models......................................................................................30 5.3 Assumptions and Theoretical Basis for EMT ................................................................34 5.4 Other mistakes................................................................................................................36

6 Analysis of Basic Elements Constituting EMT ..................... 37 6.1 Rational Expectations theory .........................................................................................38 6.2 Rational Investor ............................................................................................................46 6.3 Arbitrage ........................................................................................................................49 6.4 Equilibrium ....................................................................................................................51 6.5 Is EMT the reasonable approximation of the reality? ....................................................54

7 Commentaries on EMT Theorists Viewpoints ..................... 64 7.1 Viewpoints advanced in Samuelson (1989) paper .........................................................65 7.2 Fama (1998) ...................................................................................................................69 7.3 Malkiel (2003) and (2005) .............................................................................................71 7.4 Malkiel (2003)................................................................................................................74

8 Concluding Remarks............................................................... 82 8.1 Summary ........................................................................................................................82 8.2 Commentary...................................................................................................................83

Bibliography .................................................................................. 86

1 Introduction1

They (market inefficiency) exist because we do not root out their basic causes.

These causes are easy enough to identify, if one looks with enough dispassion and

rigor.2

------------Dean LeBaron

Efficient market theory3 (EMT) is generally regarded as the cornerstone of the

mainstream financial theories. Fama (1970, p. 383) provides a classical definition

on the efficient market:

A market in which prices always fully reflect available information is called

efficient.

Underlying this definition is the economists assumption that the stock market

investors are rational agents and that the stock price is determined by their

interaction.4 According to Frederic S. Mishkin, a more straightforward efficient

market definition can be provided as follows: in an efficient market, there is no

earning opportunity that has not been fully utilized.5 EMT advocates proclaim that

the real-life stock markets (such as the US stock markets) are consistent with the

above definition of efficient market.

In the 1970s, EMT had, for a certain period of time, been looked upon as a

scientific truth turning countless young economists and financial students into its

faithful disciples. With the emergence of the anomalies6 in the stock markets in

the 1980s and the 1987 stock market crash, EMT had aroused widespread suspicions 1In this paper, the present author has made extensive references to the contents of the works by such distinguished economists and finance professors as Paul A. Samuelson, Eguene F. Fama, Burton Malkiel, Stephen LeRoy and Frederic Mishkin. The present author acknowledges his sincere appreciation and regards to the foregoing scholars. 2LeBaron (1983). Quotation. 3Efficient market theory (EMT), in a broad sense, refers to efficient market hypothesis (EMH). In the context of this paper, both terms share the identical meaning. 4LeRoy (1989). See Page 1613. 5Mishkin, Frederic S., The Economics of Money, Baking, and Financial Markets, Chinese edition, China Renmin

University Press. See Page 660. Quotation. 6Anomaly refers to unexpected event, which could bring opportunities for investors to earn abnormal return, such as seasonal anomalies, etc.

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of the academic and investment management circles with regards to its scientific

nature. With the coming into fashion of Behavioral Finance in the academic circle

and the irrational exuberance in the US stock markets in the late 1990s, the

academic circle witnessed a major changeover in its attitude towards the EMT.

Some scholars believed that EMT should be abandoned, as in the case of Haugen

(1995) and Shiller (2000). Some other scholars took the view that EMT should still

play the role of a useful benchmark. A minority of scholars insisted that EMT

accurately recapture the realities as in the case of Malkiel (2003), (2005).

For the following three reasons, the academic circle has been unable to ascertain

whether EMT should be viewed as a scientific school of thought.

(i) Problems with EMT itself. First and foremost, the definition of efficient

market given by Fama (1970) was far too vague. According to Beaver (1981, p. 23):

The problem is not simply that concepts are difficult to test empirically, a

pervasive phenomenon not unique to the efficient Market literature, rather, the

problem is that, at a conceptual level, prior to empirical testing, it is unclear what is

meant by the term market efficiency.

Moreover, fully reflect in this particular context is not specified in any way, and it is

not possible to ascertain it.

Second, it had taken EMT more than 20 years from birth to final refinement.

During this period, Fama (1976) had strengthened the definition of efficient market.

And Fama (1991) carried out major revisions on the definition and description of

EMT.

(ii) Human factors. EMT may be described as the crystallization of years of

incisive research work conducted by scholars and pundits fully devoted to the study of

the behavior of stock price. As such scholar grouping enjoys high prestige in the

academic circle plus their religious faith in the accuracy of EMT, conclusions drawn

by those scholars opposed to the views of EMT have not received the same level of

attention. And research conclusions deviating from EMT viewpoints are invariably

questioned.

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(iii) Technical difficulty. With the Capital Asset Pricing Model becoming the

mainstream financial theory and the birth of the Rational Expectations Hypothesis,

theorists managed to integrate EMT with CAPM along with Rational Expectations

Hypothesis. And such integration made it extremely difficult to ascertain whether

EMT was a scientific theory. To confirm whether EMT is a scientific theory or not,

we must have in place a scientific stock pricing model to explain the stock price

behavior and investor behavior. As scholars entertaining a questioning attitude at

EMT have not been able to achieve any major breakthrough regarding the stock price

behavior and investor behavior, it was not very difficult for us to comprehend why the

research work conducted by a number of established economists and finance

professors, such as Shiller (1981), DeBondt and Thaler (1985), Lo and Mackinlay

(1988), Jegadeesh and Titman (1993), Shleifer and Vishny (1997), Haugen (1997) had

been unable to challenge the status of EMT as the cornerstone of the modern financial

investment theories.

In the early 1990s, the special environment at the time of the birth of Chinas

stock market has provided a precious opportunity for people involved in studies on

the actual investor behavior and stock price behavior. The present writer has had the

luck to experience the entire process. Through unrelenting efforts over 14 years, the

present writer has finally achieved a breakthrough in respect of the research

associated with the investor behavior and stock price behavior. By relying on the

breakthroughs achieved on the investor behavior and stock price behavior, we are

already in a position to formulate a correct judgment on the puzzle of whether EMT is

scientific or not.

The specific method is as follows. First of all, the present writer set up a simple

analysis framework to analyze the actual investor behavior and stock price behavior.

Secondly, the present writer regard the foregoing research conclusions in the above

framework as the reference standards to perform comparative analysis on the

scientific connotations of the basic elements related to EMT as employed by the

economists (such as equilibrium, Rational Expectations Theory and rationality and so

forth). Lastly, the present writer perform a comparative analysis on the possible

outcomes arising from the integration between these essential elements constructing

the EMT by the economists versus the basic elements of our analysis frameworks in

terms of integration.

As EMT is but a simplified replica of the stock market realities, we are not in a

3

position to demand that it should be consistent with the actual stock market realities in

all aspects. As a scientific theory, EMT is only required to be the reasonable

approximation of the stock market realities. The crux of the matter lies in what

constitutes the criteria for the reasonable approximation? The present writer has

divided the stock market reasonable approximation criteria into the following 3

aspects: Whether EMT scientifically recaptures the investor behavior; whether EMT

scientifically describes the stock price behavior; whether EMT scientifically reflects

the interrelationship between the investor behavior and stock price behavior.

Based on the above criteria, this paper has carried out a full comparative analysis

on the EMT. The concluding part of the present report demonstrates that: EMT is by

no means the reasonable approximation of the stock market realities, and its scientific

content is close to zero. The reason is pure and simple: EMT absurdly describes the

investor behavior and mistakenly represents and explains the stock price behavior.

Furthermore, EMT wrongly captures the inter-relationship between the investor

behavior and stock price behavior.

This paper is primarily intended for the academic and investment management

circles. The present writer very much hope that his research achievements will be

conducive to the academic and investment management circles in correctly judging

whether EMT is scientific or not. And it is conducive to assisting others to obtain a

scientific understanding of the nature of the stock market as well as the actual stock

price behavior.

To better clarify the mistakes associated with EMT, the present writer has

divided EMT into three stages, viz. pre-history of EMT (1900--1965), EMT formation

and refinement (1965--1991) and EMT decline (1991--to date). This paper is

arranged in the following sequence: Section 2 briefly outlines the analysis framework

formulated on the basis of the present writers research results associated with the

investor behavior and stock price behavior. Section 3 takes a brief look at the

evolutionary history of EMT. Section 4 analyzes errors and inadequacies identified

with the theory of random walk which precedes EMT. Section 5 describes and

analyzes the errors with the EMT. Section 6 provides a comparative analysis on the

basic elements used by the economists to formulate EMT. Section 7 brings together

Samuelson (1989), Fama (1998), Malkiel (2003) and (2005) research conclusions for

judgment. Section 8 provides concluding remarks on the underlying causes relative

to the errors with EMT.

4

2 The Investor Behavior and Stock Price Behavior In order to provide a scientific description and forecast of the stock price

behavior in real life, we must obtain a scientific understanding of the

inter-relationship between the investor behavior and stock price behavior. To do

this, the prerequisite is that we must have in place a scientific description of the

investor behavior and stock price behavior.

2.1 The investor behavior

To have a scientific description of the stock price behavior, the most

fundamental condition is that we must provide a scientific description of the investor

behavior in the stock market. To scientifically describe the investor behavior, the

precondition is that we must have a scientific understanding of the investor behavior.

In respect of investor behavior, we are required to understand the human nature, the

limits of human brains, the investor ideal, investor expectations and investor

decision-making.

Human nature

The Wealth of Nations by Adam Smith is generally regarded as the Bible of

economics. In the foregoing book, Adam Smith laid emphasis on the self-seeking

nature of human beings. Another great book by Adam Smith entitled The Theory

of Moral Sentiments has not merited the same level of attention. In the book, Adam

Smith placed premium on the selflessness of human beings. Perception by Adam

Smith of human nature is comprehensive and profound: only by integrating

economical selfishness with moral selflessness can we hope to understand the

comprehensive true human nature.7 Unfortunately, human selflessness has not

become one basic assumption for economics in the same way as human selfishness.

Understanding the true and full human nature is of crucial importance to our

understanding of the stock price nature and actual stock price behavior. This is

because: if we only know that human beings are selfish without knowing their 7Smith, A., 1904, An Inquiry into the Nature and Causes of the Wealth of Nations, Chinese edition. See Introduction, p. 4--5. Quotation.

5

altruism, it would be very difficult for us to comprehend why people tend to unite

closely together to defend their common interests when individual selfish acts harm

others interests without bringing good benefits to themselves. Over 100 years ago,

the phoenix tree outside of the No. 68 of Wall Street showed such a spectacle. To

defend their common interests, over 20 stockbrokers joined hands to sign up the

famous Buttonwood Agreement to lead to the eventual birth of the New York

Stock Exchange. 8 If the investor is like the rational investor under EMT

assumptions, the stock market could not have come into being in the first place.

Limits of human brains

In 1956, the psychologist George Miller issued a famous paper the magic

number seven plus or minus two highlighting some limits on our capacity for

processing information. In the report, George Miller pointed out that the channel

capacity for processing information on the part of human brains appears to be limited.

The typical range is epitomized by the magic number seven plus or minus two.

Inspired by the research conclusions of George Miller, the present writer has carried

out substantial research on the channel capacity of the framework in terms of human

brains forming expectations of the future stock price.

The present writers research conclusions indicate that the channel capacity of

the framework for forming expectations of the future stock price on the part of the

human brains is very close to the conclusions drawn by George Millers research

work. Under specified time frame (yearly, monthly and daily), the human brains

channel capacity for containing stock price quantities stands at number seven plus or

minus two. That is to say, the human brains channel capacity for formation of stock

price expectations are limited to number seven plus or minus two. If the human

brains are compared to a forecasting machine, the human brains oriented stock price

quantity to the input and the expected conclusion to the output, the output will be far

less than the input quantity. That is to say, although the framework space within the

human brains for anticipation and forecasting is 72, When forecasting the stock price,

the human brains are only capable of having expectations of the stock price of any

statistical significance less than 7 unit time, In real-life environment, as the stock

market is full of mutually contradictory information, the investor can only have

8Gordon (1999), The Great Game: The emergence of Wall Street as a world power: 1653-2000, Chinese edition, Citic Publishing House. See Chapter 2. Quotation.

6

forecast of stock price within 1 to 3 unit time that is of any practical statistical value.

The investor ideal

All human creations are reflections of mankinds pursuit of determinism. Such

is the case with the civilized society, literature, music and fine arts. As one of the

greatest inventions of mankind, stock market clearly reflects investor aspirations.

In addition to the material home for the human being, there is a spiritual home.

And human ideal is to hold sway at the spiritual home. Apart from a visible world,

the investor also possesses an ideal world. Human ideal realm is one of determinism,

it is totally incompatible with the random realm of throwing dices as is the order of

the day in the gambling process.

It is of paramount importance to understand the investor ideal vis--vis the

investor behavior and stock price behavior. The investor ideal constitutes the core

foundation for the birth and development of the stock market. The investor

aspiration constitutes the major driving force for the investor in terms of the purchase

of stocks. The stock price embodies the aspirations of the investor. As the stock

market embodies the aspirations of all the investors, all stock markets evolve towards

the orientation of the investors ideal stock market.

In the investors idealized stock market, due to all the investors holding fully

identical viewpoints on the history, present and near-term future of the market and

fully understand their own respective strengths and weaknesses, the market price will

only rise and never fall. The market price track is so clear-cut that prediction

becomes superfluous. Any new information, however good or bad, will not exert

any influence on the formation of the stock price. The reason is that, in an idealized

stock market, the investor is fully rational to such an extent that the market is strong

enough, this is very much like a healthy person (his own health being a source of

disease resistance or prevention) would not contract cough or catch cold in the wake

of sudden change in climate. In the idealized market, the stock price is equivalent to

its value, and the investor is completely rational. The investor does not need to

consider any specific investment strategy at all.

The idealized stock market is not a virtual market. Rather, it is the target that

all the current stock markets are striving for at this point in time. We can easily find

the shadow of the idealized stock market amongst the sways of the real-life stock

market tendencies, and feel the pulse of the real-life stock price in moving towards the

7

ideal stock market. For example, in the short term, any stock price index sequence

exhibits tendencies of more increase than decrease. In the long term, the stock price

indexes of the countries all over the world have been steadily on the increase, and

have not dropped below their respective initial starting points in the form of random

walk. The most obvious example is that, over the 100-odd years, the DJIA has shot

up from its initial 50 points to over 14000 points.

Investor expectations

The investor relies on his own innate patterns to form expectations on the future

movement of the stock price. In forming his expectations of the future stock price,

the investor invariably has three kinds of expected values. These are the intuitive

prospect value, the momentum prospect value and historical experience-based

prospect value. It is rather easy for us to observe the intuitive prospect value and the

momentum prospect value. But it is rather difficult to judge the historical

experience-based prospect value, as it is a kind of statistical expected value.

The intuitive prospect value epitomizes the expectation formed by the investor

on the past stock prices. It is consistent with human nature, and, as a result, each

and every investor can engage in the intuitive expected value.

The momentum prospect value takes shape on the basis of the intuitive expected

value. It is an expectation arising from the price differential between the investor

forecast price and the realized stock price.

The historical experience-based prospect value refers to the expectation arising from statistical conclusions drawn from the stock price patterns in recent

periods of time on the part of the investor in relation to the entire stock price historical

sequences showing similar patterns. Generally speaking, an investor needs a

minimum of 5 years of study of the market statistics to form the historical

experience-based prospect value. The historical experience-based prospect value

plays a pivotal role in the decision taken by the investor of a scientific nature.

Purely from the future expectancy standpoint, a veteran Wall Street pundit who has

spent over 3 decades in the area of financial analysis cannot said to be more accurate

than a newcomer to the Wall Street in terms of the forecast of tomorrows stock price

movement. However, from an investment decision point of view, a veteran Wall

Street pundit who has spent over 3 decades in the area of financial analysis will

certainly be able to arrive at a more reasonable investment decision than a green hand

8

at the Wall Street. This is because a newcomer can only rely on his intuitive

expected value and the momentum prospect value to reach an investment decision,

and he is simply unable to form precise historical experience-based prospect value.

The way that the investor anticipates the future stock price determines that the

investor can only predict the future stock price on the basis of the past and present

stock prices. The concept of discounting raised by the economist is not a basic

approach used by the investor to predict the future stock price in any way. It is only

an empirical methodology derived from the foregoing three approaches.

Discounting approach should not be used separately from the three basic modes of

investor expectation in the stock market.

It should be mentioned that, as the channel capacity of the framework for

forming the expectations of the future stock price on the part of human brains appears

to be limited, in forming expectation of the future stock price,

non-stock-price-information (such as interest rate increase by the US Federal Reserve

Bank and new products being unveiled by the listed companies etc.) cannot make its

way into the stock price expectation system on the part of the investor. Such

non-stock-price-information enters the expectation system that is independent of the

investors stock price expectation system. After going through the processing of the

investors expectation and cognition systems, what the investor eventually gets is no

longer the expected values of the non-stock-price-information, rather, it is qualitative

rather than quantitative assessment on the future stock price on the basis of the

expected values of the foregoing information. These assessments along with the

three expected values of the future stock price jointly make their way into the

decision-making system of the investor.

Investor decision-making

The investor decision-making system mainly comprises four parts, namely, the

investors 3 expected values, the investors assessments of the

non-stock-price--information, current earning/loss-making situation of the investor

and requirements imposed on his own behavior on the part of the investor. How the

investor takes his decision is dependent upon the outcome of the integration of the

foregoing four parts within the investors decision-making system. There are

thousands of investors in the stock market and the outcomes of the integration of the

foregoing four parts within the investors decision-making systems are miles apart, so

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there will be investors buy and sell stocks at any price point in any time interval in the

stock market. Success on any one of the stock transactions in the stock market is not

because of the same sort of expectations of the involved stock price on the part of the

investors in the market at the time, mainly because the outcomes of the integration of

the foregoing four parts within the investors decision-making systems of the buying

and selling investors are different.

2.2 The stock price behavior

Only on the basis of having obtained a scientific understanding of the above

investor behavior is it possible for us to really comprehend the stock price behavior.

To analyze stock price behavior, we must, first and foremost, understand the nature of

the stock price movement and the prospect values of the stock price sequence.

Secondly, we are required to understand the patterns of the movement of the stock

price and the rules governing the stock price movement. Finally, we must

understand the stock price behavior in the absence of external information

interference.

Nature of the stock price movement

From a macro point of view, the stock market is not a gambling outlet. Rather,

it is a place where the investor harbors their aspirations and ideals. The trend of

stock price movement reflects a delicate balance between aspirations and expectations

of the realities on the part of the investors. And the rising trend of the stock price

represents the direction of the investor aspirations. From a micro standpoint, as any

one stock price sequence embodies investor aspirations and prospect values, any one

stock price sequence should be considered as a source of generic information. Such

generic information differs, in substance, from the outside information (such as the

news released by the Federal Reserve Board and the Iraqi war etc). It constitutes the

core driving force associated with the stock price movement. Because of the reason

that any random time sequences or emulation stock price sequences cannot embody

the two elements of the investor prospect values and investor community collective

aspirations. Consequently, any random time sequences or emulation stock price

sequences arising from gambling table, throwing dices and random cards lottery are

incompatible with the real-life stock price sequences in terms of substance. The

allegation that stock price movement is the result of noise is a totally mistaken

10

representation of the root cause leading to the stock price movement. John Maynard

Keynes is also wrong in asserting that the stock price movement is motivated by

animal spirit.

The prospect values of the stock price sequence

The stock price at a unit time interval represents the basic unit of a stock price

sequence, it is composed of three elements, viz. direction of stock price movement,

magnitude of the stock price movement and stock price movement unit intervals.

The history sequence of the stock price is in fact, a sequence composed of these three

elements. As the stock price behavior is merely the result of the investor behavior,

any stock price sequence contains the aspirations and prospect values of the investor

community. In fact, stock price sequence constitutes the only basis for our

calculation of the stock price prospect values. Insofar as this is concerned, the use of

mathematical expectancy methodology by the standard financial theories to calculate

stock price expected values is totally unscientific.

Patterns of the stock price movement

Movement in stock price can be divided into three patterns. The first is the

pattern of continuity, which can be divided into upward continuous pattern and

downward continuous pattern. These two patterns can be sub-divided into certain

types. Any combination of two types of upward continuous pattern will result in a

brief stock price increase trend, Any combination of any type of upward continuous

pattern and downward continuous pattern will result in a brief stock price sequence

with variations in increase and decrease.

The second type is non-continuous pattern. Such pattern takes the form of

continuous pattern being disrupted, and its quantity is simply too numerous to be

counted. The third type is the independent pattern, and can be divided into upward

independent pattern and downward independent pattern. Each independent pattern

can be further broken down into certain types of categories. The same type of the

same or different independent pattern occurs with great frequency. In stock price

sequence, we often see continuous skyrocketing or nose-diving, and these are

manifestations of the continuous occurrence of the same or different types

independent patterns.

Studies performed by the present author indicates that any stock price sequence

11

is comprised of the above three patterns of combinations of their constituents. The

three patterns and their types in identical or different combinations can yield

constantly changing combinations, and this is the root cause of why the movement in

stock price is so capricious. Although changes in stock price are evolving all the

time, the rules constituting the constraints of their movement are rather simple, and

the patterns and types of their movement are also limited. In the Dow Jones

Industrial Average daily closure figures spread over a period of 102 years (involving a

total of 28500 turnover figures), around 12000 days of turnover figures belong to the

continuous pattern, representing 42% of the total. Approximately 15000 days of

turnover figures belong to the non-continuous pattern representing 53% of the total.

About 1500 days of turnover figures belong to the independent pattern making up 5%

of the total.

Rules governing stock price movement

The stock price movement follows certain rules. Normally, a 5-year-long stock

price historical sequence with the transaction day as the time interval contains all the

patterns of the stock price movement. All the historical sequences of the stocks all

over the world are composed of the same kind of the patterns of the stock price

movement.

Movement in stock price boils down to the result of investor decisions. As

investor decision matches individual aspirations and logic, the patterns of stock price

movement certainly matches human aspirations and logic. As a result, patterns of

stock price movement must necessarily fit in with human aspirations and logic. As

human aspirations are knowable and human logic itself means the following of

prescribed rules, the stock price changes according to certain rules of the game.

However, only when we truly understand how investors make decisions is it possible

for us to understand the rules governing the stock price movement.

The rules governing stock price movement are different from the nature rules

such as the accurate automatic rotation of the earth within 24 hours for one round.

They are logical rules with multiple ways of expression. Through analysis of stock

price sequences, we are fully capable of analyzing logical rules governing stock price

movement, in the same way as the understanding of the meaning (logic) of a sentence

through its analysis.

To properly analyze the logic associated with the analysis of stock price

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movement is by no means an easy task. And to beat the market by utilizing the logic

linked with the analysis of stock price movement is even more difficult. The stock

price movement logic is expressed in multiple forms in the same way as we use

different sentences to express the same meaning (logic). For this reason, unless you

really understand the ways of expression of the logic associated with all stock price

movement, it is impossible for you to be sure to be able to beat the market.

The above discussion has, in fact, not taken into account the impact of

fundamental factors, which, if taken into consideration, would enable us to see that

the logic of stock price movement is invariably interrupted by the said fundamental

factors. Let us make a comparison, when someone is in the middle of talking, he is

abruptly interrupted, and so the logic of his flow of thoughts is put to a halt.

Consequently, to prevent the logic of your stock price movement from being affected

by fundamental factors, you must, beforehand, perform analysis on all possible

fundamental factors. This would mean that, unless you are both an expert at logical

analysis of the stock price movement plus an expert at the analysis of fundamental

factors, it is just impossible for you to be sure to be able to accurately understand the

stock price movement logic and ultimately beat the market.

Stock price behavior in the absence of external information interference

Due to the presence of thousands of investors in the stock market, the investor

behavior of pursuing profits has made the stock price fully covered with layers of

investor decision systems on any one timing point. Such a market does not entail

any lasting profitable opportunities at all. As the stock price is the most important

criterion determining the predilection of the investor and it consists of three elements,

viz. direction of stock price movement, magnitude of the stock price movement and

stock price movement unit intervals, change of any one of the foregoing three

elements could result in numerous investors experiencing change in their expectation

values. Change in the investor expectation values will give rise to change in the

investors decision. And change in the investors decision will in turn lead to new

change in the stock price. In this cycle of price change change in investor

expectation values change in investor decision new change in the stock price, in

the absence of influence exerted by the external information, the stock price will keep

on changing with the sole investors ideal is taken on board.

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2.3 Inter-relationship between the investor behavior and stock price

behavior

Only on the basis of having obtained a scientific understanding of the investor

behavior and stock price behavior is it possible for us to understand the

interrelationship between the investor behavior and stock price behavior. With

respect to the interrelationship between the investor behavior and stock price behavior,

the focus of our concern should be laid squarely on the way the investor interprets the

stock price sequences.

First of all, it is incumbent upon us to comprehend the way of the intrinsic

prospect values on the part of the investment communities conveyed and expressed by

the stock price sequences. Such prospect values are not expressed through one unit

time stock price from the stock price sequence, but through a group of the stock prices.

Although our vision system enables us to observe the stock price sequence over a

rather extended period of time on the surface, we cannot deduce the prospect values

embodied in the stock price historical sequences.

Second of all, to calculate the expected values of the stock price sequence, one of

the prerequisites is that we must obtain a scientific understanding of the relationship

between the stock price sequence, unit time stock price and the expected price (or

return).

The relationship between the real-life historical stock price sequence, unit time

stock price and the expected price (or return) is just like the relationship between a

sentence, word and the meaning of the sentence. The word is the basic element of a

sentence, and a sentence is normally composed of several or a dozen words. The

sequence of each word in a sentence is of crucial importance to a sentence. To

understand the complete meaning of a sentence, we must observe the meaning of each

and every single word. At the same time, we must observe the sequencing of the

words making up the sentence along with the involved internal logic. We cannot

decipher the meaning or the associated logic of the entire sentence from the meaning

of a single constituent word. If you change the sequencing of the words in the

sentence, the meaning of the sentence would be changed, because you have changed

the logic of the involved sentence.

When we embark on the analysis of the prospect values of a stock price sequence,

we must, concurrently, take the sequence order of the stock prices comprising the

14

stock price sequence and the basic elements of One unit time stock price, viz.

direction of stock price movement, magnitude of the stock price movement and stock

price movement unit intervals into consideration. This is because, if the sequencing

of the stock price experiences changes, the prospect values of this sequence change

accordingly; if we change any one element out of the foregoing three elements, the

prospect values associated with the stock price sequence experience change

accordingly. That is to say, change in the stock price sequencing or change in any

one of the three elements at a given time interval could lead to alteration in the stock

price sequence prospect values.

The stock price at a given unit time represents but one single reference point of

the prospect values of the stock price sequence, and, as such, does not possess any

independent logical connotations. In recognition of this, it is impossible for us to use

the stock price of a given time interval to fully reflect the prospect values contained

in a stock price sequence. In fact, it is merely impossible for us to derive the

prospect values of the stock price sequence involved from one unit time stock price.

Lastly, at the time of the formation of the future stock price expected value, the

investor has three kinds of different expectation values. As a result, we need a

sufficiently long stock price sequence instead of a single group of stock prices to form

accurate expectancy of the future of the stock price. On average, to scientifically

observe the movement of a certain stock over a certain transaction day, we must, at

least, examine the daily data for the involved stock over the past 5 years.

To integrate the above research conclusions regarding the investor behavior, the

stock price behavior, the interrelationship between the investor behavior and stock

price behavior along with a combination with the stock pricing formula drawn up by

the present author, we are in a position to pass brief judgment on whether Efficient

Market Theory is scientific or not. In the sections that follow, the present writer will

use the basic elements of this particular analysis framework as terms of reference to

carry out a detailed comparative analysis on the theoretical models of EMT and the

basic elements making up EMT.

15

3 A Historical Perspective on EMT

3.1 Pre-history Stage Of EMT (19001965)

EMT can be traced back to the French mathematician Louis Bacheliers thesis

(1900) entitled Theory of Speculation. In the paper, Louis Bachelier, for the first

time ever, assumes that changes of the stock price from transaction to transaction are

independent, identically distributed random variables. He asserts that speculation

should be a fair game and the expected profits to the speculator should be zero.

Louis Bacheliers research means that the current stock price presented an unbiased

estimation of the future stock price. Unfortunately, Bacheliers research did not

arouse much attention at the time. Over 50 years later, his above-mentioned paper

caught the attention of the economists.

In the 1930s, research on stock and futures prices mainly include Cowles (1933),

Working (1934) and Cowles (1944). Through the study of the main financial

services companies and investment media of the time, Cowles finds that the best

financial institutions investment records and the best individual forecasting records

failed to demonstrate that they exhibited skill, and indicated that those records more

probably were results of chance. Cowles therefore conjectures that these financial

institutions relied on luck instead of competence or anticipating techniques to acquire

investment and anticipate results. At the same time, Security Analysis by Graham

and Dodd (1934) and Theory of Investment Value by Williams1938have influenced countless financial analysts and economists. The concepts of intrinsic

value, fundamental value, discounting outlined in these two books have played a

crucial role in shaping EMT.

The British statistician Kendall (1953) after examined the behavior of the weekly

changes in time sequences associated with the cotton, wheat futures price and stock

price indexes, declares in his paper that changes in the price sequences placed under

scrutiny are independent, the observed price changes in those time series seem to be

approximately normally distributed, there is no hope of being able to predict the

behavior of these price changes for a week ahead without extraneous information.

Roberts (1959) appeals that use should be made of Kendalls statistical approach in

studying the behavior of the stock price.

On the basis of Louis Bachelier, Osborne (1959) had carried out a major revision

16

on the research target: the percent change in the stock price is no longer the target of

research. In its place is the change in log price. For the first time ever, Osborne

specified that common stock prices can be regards as an ensemble of decisions in

statistical equilibrium, with properties quite analogous to ensemble of particles in

statistical mechanics. He declares that the investor evaluates the stock on the basis

of the expected return, and the expected return is the weighted average of the sum of

all possible rates of return. Research work carried out by Osborne represents a

major milestone in the development of EMT. Close on the heels of Osborne

research, Larson (1960), Working (1960), Houthakker (1961), Alexander (1961),

Cootner (1962), Moore (1962), Granger and Morgenstern (1963) in succession,

published their respective papers supporting the assumption that the stock price

follows a random walk.

The Random Character of Stock Market Price by Cootner (1964) is a

collection of a full batch of papers constituting the foundation of EMT. At the same

time, the theory of Portfolio Selection by Markowitz (1952) specifies why the

diversification of investments could reduce risk. The Capital Assets Pricing Model

by Sharpe (1964) proceeds on the basis of Markowitz to specify how investors would

go about their investment activities if they were rational.

The research paper by Fama (1965) concerning stock price behavior wrapped up

the research results of all of his predecessors concerning the random walk model, and

provides new theoretical evidence for the theory of random walk. That paper

highlights inconsistencies between the actually observed statistics of the behavior of

the stock price and the predictions of the theory of random walk. For instance, the

distribution of daily price changes in a speculative series is not approximately normal,

and changes in the stock price sequences are not fully independent etc. For the first

time ever, Fama (1965, p. 35) brings up the concept of efficient market and defines

that the independence assumption of the random walk model could be accepted as

long as the independence in the series of successive price changes is not above some

minimum acceptable level. More specifically,

The independence assumption is an adequate description of reality as long as

the actual degree of dependence in the series of price changes is not sufficient to allow

the past history of the series to be used to predict the future in a way which makes

expected profits greater than they would be under a nave buy-and-hold model.

Some findings of the same period also identify that the stock price movement is

17

inconsistent with the random walk model as in the cases of Houthakker (1957),(1961),

Osborne (1962), Larson (1960), Cootner (1962), Steiger (1964). But these findings

did not receive adequate attention from the academic circle. Alexande (1961) was

subjected to query. Cowles (1960, p. 914) discoveries that:

A positive first-order serial correlation in the first difference has been disclosed

for every stock price series analyzed in which the intervals between successive

observations are less than four years.

However, such important statistical analysis conclusions did not receive the level

of attention from the academic circle that they deserved due to suspicion that there

could be statistical anomaly and that there would be no economic return after

deduction of the involved transaction cost. Another noteworthy figure is Kendall

(1953, p. 20-21) who writes that:

We get greater serial correlation in the averages than in the constituent series,

which at first sight seems absurd and in any case is very misleadingWhatever the

reason, the existence of these serial correlation in average series is rather disturbing.

Fama (1965) also mentions the foregoing paragraph. However, such important

finding again did not merit adequate attention.

3.2 Formation And Refinement Stage Of EMT (19651991)

Mandelbrot (1966) gives Efficient Market Hypothesis, a rigorous probability

foundation and provides explanations on the stock price behavior from an economics

standpoint. To give a defined economic justification on the capricious stock price

behavior, Samuelson (1965) paper entitled proof that properly anticipated prices

fluctuate randomly provides the same sort of demonstration in his thesis in relation

to the Martingale models: in an information-efficient market, if the stock prices are

properly anticipated, their changes will certainly not be forecast. This particular

thesis by P. A. Samuelson concerning commodity futures price behavior is generally

regarded as a milestone for the formation of Efficient Market Hypothesis. From then

on, Martingale models have taken the place of the random walk model for economists

to describe the stock price behavior.

Roberts1967divides EMH into three categories, viz. weak form, semi-strong form and strong form.

Fama (1970) has brought together all the research results of his predecessors to

form the eventual Efficient Market Hypothesis. Fama (1970, p. 383-416) asserts:

18

We shall contend that there is no important evidence against the hypothesis in

the weak and semi-strong form testsand only limited evidence against the

hypothesis in the strong form testsin short, the evidence in support of the efficient

markets model is extensive, and (somewhat uniquely in economics) contradictory

evidence is sparse.

In the mean time, Markowitzs Portfolio Selection theory, Sharpes Capital Asset

Pricing Model, Rosss1976APT and Black-Scholes1973Option Pricing Model have jointly formed the theoretical framework of studying the capital markets. The

emergence of EMT has provided staunch theoretical support to the foregoing models.

As such expressions as fully reflect and all available information by Fama

(1970) are too vague, it is imperative to provide specification when actually applying

them to the practical stock market to ensure that they are operable. In addition,

Fama (1970) theoretical deduction process is somehow linked to intentional setting of

the logical framework. To accurately test the efficient market validity, especially the

feature of fully reflecting all available information, financial scholars have

conducted a large amount of research work in this regard.

A decade after Samuelsons (1965) landmark paper, many others extended his

framework to allow for risk-averse investors, yielding a neoclassical version of the

EMT (for example, LeRoy (1973), Rubinstein (1976) and Lucas (1978). Malkiel

1973best-seller A Random Walk Down Wall Street has made it possible for more people to accept the EMT.

Fama (1976a) serves to strengthen and reinforced the definition of EMT in Fama

(1970). Jensen (1978, p. 1) provides a succinct and practical definition of EMT and

asserts that:

I believe there is no other proposition in economics which has more solid

empirical evidence supporting it than the Efficient Market Hypothesis.

Grossman and Stiglitz (1980) advance a paradox. Grossman and Stiglitz (1980,

p. 404-405) argue that perfect informational efficient market is impossible. In view

of the paradox presented by Grossman and Stiglitz (1980), especially some research

conclusions showing enormous amounts of transactions in the stock market and the

observation of the irrational behavior of investors, it is hard to see proper coordination

with the EMT. Black provides an answer: Noise causes markets to be somewhat

inefficient. Black (1986, p. 533) also supplies a definition of EMT as follows:

We might define an efficient market as one in which price is within a factor of 2

19

of values, i.e., the price is more than half of value and less than twice value.

From the development history of EMT over this period of time, we can see that

the research work carried out by some scholars has possibly changed the fate of EMT.

For example, Niederhoffer and Osborne (1966, p. 897) identifies that:

The accurate record of stock market ticker prices displays striking properties of

dependenceafter two prices changes in the same directions, the odds in favor of a

continuation in that direction are almost twice as great as after two changes in

opposite directions.

Although their findings aroused some attention, they did not exert any impact on

the formation of EMT. As far as Fama is concerned, the type of dependence

uncovered does not imply market inefficiency.

Shiller (1981) research conclusion dealing with stock price volatility poses a

challenge of historic significance on EMT. DeBondt and Thaler (1985) took issue

with the correctness of EMT. The real heavy blow to EMT is the stock market crash

of 1987. From October 13 through October 19 of 1987, DJIA falls from 2508 to

1739 with the stock price index witnessing a drop of nearly 31% within 4 full trading

days, which represent about 1 thousand billion US$ loss of all the US stocks.

Economists commented that there did not exist any tangible factor leading to 30%

fluctuations on the stock price.9 Confronted with the above crude reality, EMT

theorists have had no alternative but maintain silence.

For some investors such as Warren Buffet, John Templeton, John Neff, Paul

Tudor Jones, beating the market over the long-term is clearly contradictory with the EMT. Samuelson (1989, p. 4-5) argues:

Those lucky money managers who happen in any period to beat the

comprehensive averages in total return seem primarily to have been merely

luckybroadly speaking, the case for efficient markets is a bit stronger in 1989 than

it was in 1974

However, for the first timehe admits that: On the whole, I side with Shiller and Modigliani and am prepared to doubt

Macro Market Efficiency.

Confronted with a large amount of evidence contradictory to EMT stemming

from theoretical study and empirical research, Fama (1991) makes major revisions on

9Samuelson, Paul A. and Nordhaus, W., 1998, Economics, Chinese edition, Hua Xia Publishing House. See p. 395, comment by the Nobel laureate economist James Tobin of Yale University: to the effect that there does not exist any tangible factors could cause stock value to change by 30%.

20

the definition of EMT and the descriptions of the three forms of the EMT. In view

of the paradox of Grossman and Stiglitz (1980), Fama (1991) lists a number of

prerequisites in support of the establishment of EMT.

He further incorporates Jensen (1978) definition into EMT. At the same time,

Fama (1991) revamps the weak-form test under Fama (1970) to tests for return

predictabilityand changes semi-strong test into event studies, and strong-form test into test for private information. Fama (1991, p. 1577) writes:

The empirical literature on efficiency and assert-pricing models passes the acid

test of scientific usefulness. It has changed our views about the behavior of returns,

across securities and time...the empirical work on market efficiency and assert-pricing

models has also changed the views and practices of market professionals.

To this point, revisions and refinement of EMT drew to a conclusion.

3.3 EMT At the Stage Of Decline ( 1991Present)

With the emergence of a large number of Anomalies in the 1980s stock

market, CAPM could no longer provide rational explanations on them. Fama (1992),

(1993), (1996) abandoned his support for CAPM which he had adhered to for over

two decades. By that point, when mentioning market efficiency, economists no

longer referred to fundamental value efficiency and informational efficiency together.

They were, in fact, making references to informational efficiency.

In the 1990s, Behavioral Finance began to emerge in the financial academic

circle. Important research papers of this period include the following: Jegadeesh and

Titman (1993), Lakonishok, Shleifer, and Vishny (1994), Shleifer and Vishny (1997)Barberis, Shleifer, and Wishny (1998), Hirshleifer, and Subramanyam (1998).

Lo and Mackinlay (1999) argue that the random walk hypothesis can be rejected.

Shiller (2000) gives a detailed analysis the behavior factors that lead to investment

bubbles. He argues that stock prices are to some extent predictable and that efficient

market hypothesis should be rejected.

In the face of the wave-like challenges to the EMT, Fama (1998, p. 284) writes:

It is time, however, to ask whether this literature, viewed as a whole, suggests

that efficiency should be discarded, my answer is a solid no.

He reiterates yet again:

Like all models, market efficiency (the hypothesis that prices fully reflect

available information) is a faulty description of price formation. But following the

21

standard scientific rule, market efficiency can only be replaced by a better specific

model of price formation, itself potentially rejected by empirical tests.

He further warns his opponents:

Any alternative model has a daunting task. It must specify biases in formation

processing that causes the same investors to under-react to some types of events and

over-react to others. The alternative must also explain the range of observed results

better than the simple market efficiency story.

The real lethal blow to EMT came when the irrational exuberance and the

Internet Stock Price Bubble emerged in the United States stock markets in the late

1990s. To make matters worse, one of the main proponents of EMT, Paul A.

Samuelson issued a statement through his personal correspondence to the effect that

the stock market is Micro Efficient but Macro Inefficiency. According to Jung

and Shiller (2002, p. 3), Samuelson argues:

Modern markets show considerable micro efficiency (for the reason that the

minority who spot aberrations from micro efficiency can make money form those

occurrences and, in doing so, they tend to wipe out any persistent inefficiency). In

no contradiction to the previous sentence, I had hypothesized considerable macro

inefficiency, in the sense of long waves in the time series of aggregation indexes of

security prices below and above various definitions of fundamental values.

Over the past 5 years, reports which continue to defend the EMT include

Rubinstein (2001), Schwert (2003), Malkiel (2003) and (2005). Although CAPM is

no longer held in high esteem, EMT has also somehow reached a dead end.

However, it should be noted that the hot Behavioral Finance also contains its own

inherent drawbacks, and cannot replace EMT as the new core of financial theories.

Currently, some scholars have already embarked on the coordination of EMT with

Behavioral Finance, such as Lo (2004) and (2005). Some scholars have proposed

New Finance as in the case of Haugen (1995) and (2003), Stout (2005). In addition,

some scholars are relatively pessimistic, such as Barberis and Thaler (2003, p. 61)

concludes:

We have two predictions about the outcome of direct tests of the assumptions of

economic models. First, we will find that most of our current theories, both rational

and behavioral, are wrong. Second, substantially better theories will emerge.

22

4 Analysis of Errors with The Theory of Random Walk It can be clearly seen from the history of development of EMT that the theory of

random walk essentially represents the pioneering empirical study of EMT. From

this perspective, EMT is the theory of random walk duly tempered and rationalized by

the principles of economics. Although EMT does not necessarily mean that stock

price changes follow a random walk, if the stock price movement follows a random

walk, it follows that the market is efficient. According to Fama (1965, p. 34-35), the

random walk theory can be recaptured as follows:

The theory of random walk says the future path of the price level of a security is

no more predictable than the path of a series of cumulated random numbers. In

statistical terms the theory says that successive price changes are independent,

identically distributed random variables. Most simply this implies that the series of

price changes has no memory, that is, the past cannot be used to predict the future in

any meaningful wayThe theory of random walks in stock prices actually involves

two separate hypothesis: (1) successive price changes are independent, and (2) the

price changes confirm to some probability distribution

Fama (1965, p. 90-98) conclusion concerning the random walk theory:

The independence assumption of the random-walk model seems to be an

adequate description of realityit seems safe to say that this paper has presented

strong and voluminous evidence in favor of the random-walk hypothesis

Research performed by the present author indicates that Fama (1965) research

conclusions are entirely wrong. Errors with the random walk theory also include

cognitive errors and mistaken research methodology.

4.1 Mistakes with perception

First of all, the theorists of random walk wrongly judge the nature of the stock

price behavior.

The only similarity between a real-life stock price sequence and a random time

sequence is that they change with the passage of time.

In the random time sequences of turning gear, throwing dice and random card

dealing along with particle movement in the micro world, past, present and future do

not have any particular meaning. As any one of the historical sequences of the stock

price embodies human aspirations, it enables the historical sequences of the stock

23

price to contain the time arrow aimed at the future.

In addition, the stock price movement sequences also contain the prospect values

of the investment community. Such intrinsic prospect values are not expressed

through one unit time stock price from the stock price sequence, but through a group

of the stock prices. Consequently, the random walk model assumes that successive

changes of the stock price are mutually independent is simply not fit for describing

the stock price sequences.

Because of the reason that any random time sequences or emulation stock price

sequences cannot embody the two elements of the investor prospect values and

investor community collective aspirations. Consequently, any random time

sequences or emulation stock price sequences is not fit for describing or

approximating the stock price historical sequences. This means that any models

describing the random time sequences or emulation stock price sequences are not fit

for describing the real-life stock price sequences. But in the eyes of the scholars of

the time, the historical price sequence behavior on the part of a particular stock is no

different from that of the random time sequence of throwing dices and dealing cards

or molecular particles movement in the micro world.

Second of all, the theorists of random walk wrongly judge the very nature of the

stock market.

On the surface, the stock price behavior appears to be determined by the

capricious psyche of the market. To the mind of the random walk theorists, stock

price movement is very much like the footprints left behind by a drunkard with no

logic to speak of. In other words, stock price movement is comparable to the digits

of the gambling table with no memory capacity at all. In recognition of this, stock

price movement follows no defined rules. Stock market is akin to a gambling house.

But, in actual fact, stock market is not a gambling house. Rather, it is the venue

where investors harbor their dreams and aspirations. The rising trend in the stock

market price points to the same ideal direction of the investors. It goes without

saying that the stock market is not a balanced static market. Rather, it is a dynamic

market that is constantly evolving towards the direction of hope and aspirations for

the investors. The ideal market is not an assumed or virtual one. It is the ultimate

objective of present stock market.

24

4.2 Erroneous research methodology

The theorists of random walk have chosen the wrong research direction and

inappropriate research target analysis of the stock price behavior from probability

distribution angle boils down to statistical behavior of the stock price. Percent

changes of the stock price or changes in log price of the stocks become the research

object.

Irrespective of Bachiler, Osborne or Fama, they are all engaged only in studying

the statistical behavior of the stock price to the total neglect of the three principal

elements, viz. direction of the stock price movement (rise and fall), the magnitude of

the stock price movement and the unit time of the stock price movement. This has

not come about abruptly, and should be attributed to the fact that, irrespective of

Bachiler or the contemporary scholars, they all hope to be able to formulate a full set

of mathematical statistical models to accurately capture the speculative price

behavior.

And standard statistical techniques are the tools with which to make the

foregoing dreams come true. However, in order to apply the standard statistical

techniques to the analysis of the behavior of the time sequence of the stock price,

people must assume that the behavior of the time sequence of the stock price has the

same statistical nature as the behavior of a random time sequence. That is because

the target of such standard statistical techniques must be independent and identically

distributed variables. If the successive price changes are independent, and

identically distributed variables, then when the amount of the stock price sequence is

big enough, the Central-Limit theory will leads us to expect that price changes will

have normal distributions.

Substantial studies carried out in the 1960s demonstrate that stock price

statistical behavior is inconsistent with the scholars assumptions. Such studies

demonstrate that price changes do not conform to normal distributions. If the stock

rate of return is not normally distributed or approximation to normal distribution,

standard statistical analysis tools, such as serial correlation analysis, will give

misleading answers. Scholars assume that the stock price follows a random walk,

25

and such assertion is very much in doubt.

Since two reasons have created the situation whereby the statistical behavior of

the stock price and the stock rate of return are not fit for the research direction and

target.

First, The overwhelming majority of the people (with the notable exception of a

very small minority who have received very good professional training) are not used

to conduct their thinking on the basis of probabilistic distribution. The human brains

are not used to calculation on the basis of percentile figures. The overwhelming

majority of the people will have the mistaken impressions, viz. stock price movement

sequences are of the same statistical nature as the gambler games in terms of random

time sequence.

Second, Each and every investor only focuses his attention on the stock price

point. And the stock market is concerned about the price zone of the entire stock

market. From an analysis technique point of view, we can use stock price point and

stock price zone as a combination for calculating the expected stock price. But it is

very hard, if not impossible, for us to set a sort of reasonable zone for the rate of

return of the stock price, and then integrate it into the calculation of the expected

return. Even if we preset a reasonable zone for the stock rate of return, that would

result in misguided conclusions of the standard statistical tests of the data.

Based on the above conclusions, we can say with certainty that, in analyzing the

stock price statistical behavior, by using the standard statistical analysis tools, we will

be able to arrive at the misguided conclusions. For instance, when we use run

tests10 to test dependence of the stock rate of return, the results would be major

deviations or totally misguided conclusions. In actual reality, Fama (1965), (1966)

mentions such run tests maybe resulting in mistaken conclusions on two occasions.

Specifically, Fama (1965, p. 80) writes:

There are situations in which they do not provide an adequate test of either

practical or statistical dependencethe run tests are much too rigid in their approach

to determining the duration of an upward and downward movements in prices. In

particular, a run is terminated whenever there is a change in sign in the sequence of

prices changes, regardless of the size of the price changes that causes the change of

the signit is possible, however, that price changes are dependent only in special

conditions.

10According to Fama (1965): A run is defined as a sequence of price changes of the same sign.

26

4.3 Root cause analysis

The main reason contributing to errors with the random walk theory is that the

theorists simply lacked systematic study of the actual investor behavior.

For instance, According to Campbell, Lo and Mackinlay (1997), the simplest

random walk model can be written as the following equation:

ttt PP ++= 1 , , (1) ),0(~ 2 IIDt

(Where is the expected price changes or drift, and denotes that ),0(~ 2 IIDtt is independently and identically distributed with mean 0 and variance .) 2

Based on the research conclusions of the present author in Section 2 of the

present paper: First of all, the stock price sequences contain the ideal of the investor and

prospect values of the investment community. Such prospect values are not

expressed through one unit time stock price of the stock price sequence, but through a

group of the stock prices.

Second of all, The stock price at a given unit time represents but one single

reference point of the prospect values of the stock price sequence, and, as such, does

not possess any independent logical connotations. In recognition of this, it is

impossible for us to use the stock price of a given time interval to fully reflect the

prospect values contained in a stock price sequence. In fact, it is merely impossible

for us to derive the prospect values of the stock price sequence involved from one unit

time interval stock price.

Based on a comparative study of the foregoing two points and the random walk

model, we can easily make our judgment on whether the random walk model can be

used to describe the stock price behavior. The conclusion is crystal clear: the

random walk model is simply unfit for use in describing the stock price behavior.

The reason is that: the random walk model simply cannot scientifically reflect the

investor aspirations and prospect values as embodied in the stock price sequences (the

investor simply cannot rely on the random walk model to correctly calculate the

expected value of the stock price sequence). The random walk model simply cannot

reflect the rules governing the stock price movement. It cannot scientifically

recapture the inter-relationship between the investor behavior and stock price behavior.

27

In actual fact, to use the random walk model to describe the real-life stock price

behavior is akin to asking an illiterate to read poetry, which is certainly absurd to the

extreme.

5 Analysis on Errors with EMT Kendall (1953) conclusions mean that the stock market is predisposed by

unstable market psyche without following any set rules. However, the financial

economists could not accept the irrationality characterization implied in Kendalls

conclusions. Through consistent efforts over more than a decade, economists and

financial scholars at long last succeeded in creating EMT. EMT provides a

brand-new footnote to Kendalls conclusions. EMT states: stock price random

change does not mean the irrationality of the stock market itself, on the contrary, that

is the natural outcome of the numerous rational investors vying with one another in

making use of the information to gain profits from the stock market. EMT attributes

the stock price behavior looking like a random walk to the competition of countless

rational investors in the stock market.

Unfortunately, the stock price movement resembles a random walk is only

spurious. That is to say, Kendall and the random walk theorists conclusions are

mistaken. EMT theorists have never expected Kendall and the random walk

theorists conclusions could be mistaken. Moreover, it has not occurred to the EMT

theorists that, due to lack of systematic and scientific study of the actual investor

behavior on the part of the economists, some general concepts and principles

applicable to economics are simply not fit for use in analyzing the stock price

behavior. In actual factEMT theorists engage themselves in giving a defined economic justification on the mistaken research conclusions of the random walk

theorists with the improper economic equilibrium framework. Precisely for this

reason, EMT and the random walk theory are both mistaken.

5.1 Absurdities with the efficient market definition

According to Fama (1970, p. 383), the efficient market is defined as follows:

28

That security prices at any time fully reflect all available information. A

market in which prices always fully reflect available information is called

efficient.

The definition of efficient market in succinct terms as that the stock price, at any

given unit time, fully reflects all available information. In Section 2, the present

paper has already stated that,

Firstly, as any one stock price sequence contains investor aspirations and investor

prospect values, any one stock price sequence should be seen as a source of generic

information, the stock price at any one given unit time is a part of this sort of

information in its own right.

Secondly, the stock price at a given unit time represents but one single reference

point of the prospect values of the stock price sequence, and, as such, does not possess

any independent logical connotations. In recognition of this, it is impossible for us

to use the stock price of a given time interval to fully reflect the prospect values

contained in one stock price sequence.

Lastly, at the time of the formation of the future stock price expected value, the

investor has three kinds of different expectation values as mentioned in Section 2 of

the present paper. But EMH assumes that the investor relies on mathematical

expectation to form expectations of the future stock price.

Integration of the above three points and comparing it with the definition of

efficient market by Fama (1970), we can clearly ascertain that the definition of

efficient market is rather absurd.

The root reasons account for the absurdities of the efficient market definition are

that: EMT theorists simply lack scientific understanding of the inter-relationship

between the investor behavior and stock price behavior. (i) From the development history of EMT, we can see that EMT theorists have

simply carried forward the majority of the mistaken beliefs and perceptions of the

random walk theory concerning the stock price behavior. Irrespective of the random

walk theorists or EMT theorists, stock price is but a random variant with no special

connotations. In the stock market depicted by EMT, the relationship between the

historical stock price sequence and the information acts like that represented in the

best-selling Investing Money11 by N. Danbar, as follows: as the investors absorb

information like armies of ants devour the black bear in the woods, and the stock price 11Dunbar, N., 2002, The story of Long-term Capital Management and the Legends behind it, (First edition of Chinese version), Shanghai, Peoples Press. P. R. of China. See p. 22. Quotation.

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is very much like the skeleton consumed to the extreme. Consequently, the history

sequence of the stock price is of no use to predict the future path of the stock price.

(ii) On the key question of the investor behavior, EMT theorists have been

unable to conduct any systematic and scientific study on the actual investor behavior.

What they have done has been to pick a hypothetical rational investor from the

framework of economics analysis, and then use the assumed rational investor to

replace the real-life investor. The consequence of such unscientific practice is that

EMT theorists simply cannot scientifically acknowledge and explain the

inter-relationship between the investor behavior and stock price behavior.

Unfortunately, the key to this question lies in that, to scientifically describe the

relationship between the stock price behavior and external information, the

precondition is that we could scientifically explain the interrelationship between the

investor behavior and stock price behavior. From the background information, we

can see that it has already taken theorists over 30 years to look for the right sort of

stock price behavior to ascertain the matching of efficient market definition with

actual stock price movement. They have not succeeded to date, however.

5.2 Unscientific theoretical models

As a result of the creative studies performed by Samuelson (1965) and (1973),

Mandelbrot (1966) and Fama (1970), Martingale models have replaced the random

walk model to become the approximate model adopted by economists to describe the

stock price behavior. Consequently, the EMT theorists closely combined the EMT

with the Martingale models. In actual application, validations of the Martingale

models are tantamount to validation of the EMT. Because of the theoretical studies

of LeRoy (1973), Lucas (1978) and empirical studies of Shiller (1979), (1981b) and

LeRoy (1981) on EMTit dawned on the financial theorists that there is no inherent linkage between martingale models and market efficiency, and that it is just a

convenient but imprecise way to say that market efficiency means that stock price

follows the Martingales.12

In this section, the present writer will scrutinize the EMT models listed by Fama

12The Martingale model means that the actual volatility in the stock price should not be excessive; the stock price itself, without the cumulative dividends added in, does not follow the Martingale model. In addition, we need to assume such factors as the investor being risk-neutral etc. So it is difficult to reconcile EMT with the Martingale model. For details, please refer to LeRoy (1989).

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1970along with a model which economists used to test Efficient Market Theory. In addition, the present writer will carry out a simple analysis on the assumptions

constituting the basis for the foregoing models.

Fair Game model

[ ] jtttjttj prEpE )~(1)~( 1,1, += ++ (2) First of all, the stock price at a given unit time represents but one single reference

point of the prospect values of the stock price sequence, and, as such, does not possess

any independent logical connotations. In recognition of this, it is impossible for us

to use the stock price of a given unit time interval to fully reflect the prospect values

contained in one stock price sequence. In fact, it is merely impossible for us to

derive the prospect values of the stock price sequence involved from one unit time

interval stock price.

Second of all, in forming his expectations of the future stock price, the investor

invariably has three kinds of expected values. In real-life situations, the real

individual investor does not rely on mathematical expectation at all to calculate the

stock price index expected return or individual stock expected return.

Lastly, please note that, in the Fair Game model, the information set stands

for all available information (including all the information concerning the historical

stock prices). As a result, we can see that, if Fair Game model can perfectly

recapture the stock price behavior, or act as a good approximation of the stock price

behavior, we simply cannot integrate with the information set .

t

)( 1, +tjPE t

From the above cause analysis, we can clearly see that the left side of the

formula )~( 1, ttjpE + is obviously absurd. The right side of the formula [ )]~( 1, ttjrE + is also absurd for the same reason. Consequently, the Fair Game

model

[ ] jtttjttj prEpE )~(1)~( 1,1, += ++

is not fit for describing the stock price behavior. Nor is it fit for describing the

interrelationship between the investor behavior and stock price behavior.

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The Martingale models

jtttj ppE =+ )~( 1, and jtttj ppE >+ )~( 1,

(3)

Due to the same reasons as illustrated above, the Martingale and Sub-Martingale

Models are also not suited to be used to describe the stock price behavior.

In light of the brief history of EMT, we can see that, because of Samuelson

(1965), Martingale models have replaced the random walk model as the theoretical

models of EMT. Additionally, because of Samuelson (1973), Martingale models are

regarded as equivalent to the expected present-value model. Regrettably, due to the

following three reasons, irrespective of Samuelson (1965) or Samuelson (1973), the

conclusions are, without exception, unscientific.

(i) To construct a stock price behavior model, we have to describe the investor

behavior. The reason is that the stock price behavior is but the outcome of the

investor behavior. Should we fail to scie