researchdirect.westernsydney.edu.auresearchdirect.westernsydney.edu.au/islandora/object/uws:3754... · Mazharul Kazi Ph.D Thesis ii CERTIFICATE OF ORIGINALITY 1. I certify that the

SYSTEMATIC RISK FACTORS IN AUSTRALIAN

SECURITY PRICING

A Thesis

Submitted in fulfilment of requirements for the Degree of

Doctor of Philosophy in Economics and Finance

BY

MAZHARUL HAQUE KAZI B.Sc. (Hons) Economics, M.Sc. Economics, M.Com (Hons) Economics and Finance

School of Economics & Finance

College of Law & Business

University of Western Sydney

New South Wales

Australia

JULY 2004

Mazharul Kazi Ph.D Thesis

ii

CERTIFICATE OF ORIGINALITY

1. I certify that the substance of this thesis has not already been submitted to any other degree

and this is an original work of the undersigned for the proposed degree.

2. I certify that the substance of this thesis is not currently being submitted for any other degree

except this one; and

3. I certify that any assistance received in writing this thesis, and sources used, have duly been

acknowledged.

Sd/

Mazharul Haque Kazi

University of Western Sydney


iii

DEDICATED TO

MY

PARENTS


iv

ABSTRACT

In the economic environment of the information age, the performance of the stock market is

considered an important indicator of the health of a nations economy. Typically, the

performance of any stock market is reflected through stock market prices. When the stock

market tumbles, investors and others become nervous about the weakness of the economy.

When the stock market is strong and steady, everyone senses economic prosperity. It would

not be over emphasizing to state that, now the stock market is shedding value, it is having a

tremendous influence in shaping the overall economies of most developed nations around

the globe.

Investors come from various segments of the population having in common the capacity

and willingness to invest in stocks. The success of investors depends on their knowledge

and effectiveness in decision making. Some are effective enough to make a profit from

investing in the stock market, while others lose. There are many theories and schools of

thought operating in the field of stock investment. An abundance of literature, training and

analytical tools is available to assist investors in making their investment decisions.

Investors need especially to understand the stock pricing mechanism. Despite the

availability of assistance, the whole process seems to be very difficult for most investors.

The common investor understands that stock market investment is not completely risk-free.

Investment risk is quite different from other types of gambling risk, because investment

decision making processes deal with risk management rather than just taking a blind risk.

Risks are usually to be understood as systematic assertions on which an investment decision


v

is based. In the relevant literature, the risks of investing in stocks are of two types. One type

of risk can be diversified away, while the other cannot. The risks that cannot be diversified

away are called systematic risks. The risk factors of the systematic risk category are

identified first in an investment decision making process. Usually, the systematic risk

factors vary from market to market and country to country. A review of the literature on

finance theory shows that only a few systematic risk factors affect the stock pricing

mechanism. If a systematic risk factor is responsive to any stock market price or industry

index, investors should closely watch the movement of that factor to manage their

investment risks effectively. A further consideration is that, under the prevailing worldwide

economic integration, stock markets around the globe are highly interrelated and are

strongly influenced by each other.

Against this backdrop, we have developed for empirical examination two research

questions from the perspective of the Australian stock market. The questions are: (i) what

systematic risk factors are influential for the Australian stock market returns in both the

long-and short-runs; and (ii) is the Australian stock market linked to developed stock

markets under the influence of globalization?

Through an extensive literature survey, we have identified a priori variables by considering

them as proxies for systematic risk factors in the stock market. We have also closely

investigated the methodological approaches suitable for empirical analyses to reveal the

precise characteristics of the long-run stock market pricing process. We have developed our

model for testing through employing econometrics software such as EViews4, SPSS 11,

Microfit 4.1 and SHAZAM 9. We have performed empirical tests to ascertain whether the


vi

Australian stock market is responsive to the a priori variables, and if so, which ones and to

what extent. We have applied cointegration techniques to help answer both our research

questions. To answer the second research question, we have performed an analysis that

examined six overseas developed stock markets and asked whether the Australian stock

market is cointegrated with those markets in the long-run. We have, in other words,

conducted two studies to find scientific answers of our research questions

The results of our first study show that only a few systematic risk factors are responsible for

Australian stock market price movements in the long-run while short-run dynamics are in

force. The results of our second study confirm that the Australian stock market is being

influenced by a small number of overseas markets and it is integrated with those markets

under the influence of globalization.


vii

ACKNOWLEDGEMENTS

I am grateful to Professor Tom Valentine and Dr Maria Varua for their help and support as

members of the panel supervising this PhD thesis. I am indebted to all staff members, colleagues

and friends of the School of Economics and Finance under the College of Law and Business,

University of Western Sydney (UWS), Australia, for their continued support.

I am also obliged to convey thanks to all staff members of the Post-Graduate Research Office,

Student Administration and the Libraries of UWS for their services. I acknowledge receiving help

in gathering data and other information materials from numerous sources, including SIRCA, ABS,

RBA, ASX, Morgan Stanley, HSBC, CNNFN, UNISON and Harcourt College Publishers.

I am thankful to all my friends and well-wishers both in Australia and abroad. Amongst others, in

random order, they are: Prof. Russel Cooper (UWS), Prof. Anis Chowdhury (UWS), Associate Prof.

Brian Pinkstone (UWS), Dr. Kevin Daly (UWS), Dr. Girija Mallik (UWS), Prof. Raja Junanker

(UWS), Associate Prof. Habibullah Khan (Singapore), Prof. Mustahidur Rahman (Jahangirnagar),

Prof. Kamal Ahmed (Dhaka), Prof. Abu Wahid (Tennessee), Associate Prof. Mohammed Quaddus

(Cartin), Associate Prof. Fazlur Rahman (UNSW), Associate Prof. Baker Ahmed (Illinois),

Associate Prof. Abul Shamsuddin (Newcastle), Associate Prof. Rafiqul Islam (Macquarie), Dr.

Kamran Ahmed (Latrobe), Dr Ziaul Haque (Melbourne), Dr. Akther Hossain (Newcastle), Dr.

Khoorshid Chowdhury (Woollongong), Associate Prof. Shahidur Rahman (Nanyang), Dr.

Shamsuzzaman Miah (UWS), Dr Shudhir Load (UWS), Dr. Masudul Haque(UWS) and Dr Abdul

Haque (Sydney).

I am very lucky to have received an abundance of divine love from both of my parents Mr. Harun-

al-Rashid Kazi and the late Mrs. Aklima Khatoon. I wish my father good health and long life. I pray

for the sanctity of my late mother. Also, I am grateful to each of my three brothers and four sisters

for their encouragement and patronage.

Finally, I owe gratitude to my family my wife Shaheen Akhter Banu, daughter Labeeba Nudrat

Kazi and son Atef Shadman Kazi, for their sacrifice, understanding and support, without which it

would not have been possible for me to complete this PhD thesis.

Mazharul Haque Kazi


viii

CONTENTS

Certificate of Originality ii

Dedication iii

Abstract iv-vi

Acknowledgement vii

CONTENTS viii-xi

PART I

RESEARCH OBJECTIVE

1

CHAPTER 1

INTRODUCTION

2

Research Aim 3

Research Domain 5

Empirical Approach 7

Research Progression 9

PART II

LITERATURE REVIEW

10

CHAPTER 2

THEORETICAL ASPECTS OF SECURITY PRICING

11

Remembrance 15

Security Pricing 17

-Portfolio Selection 17

-Capital Asset Pricing Model 20

-Arbitrage Pricing 22

-APT of Ross 26

-Roll and Ross APT 28

Attributes of APT 36


ix

Derived APT 47

-Factor Pricing Restrictions in APT 47

-Exact Pricing in a Noiseless APT 48

-Approximate Nonarbitrage Pricing Theory 49

-Compititive Equilibrium Derivations in APT 51

-Mean-Variance Efficiency and Exact Factor Pricing 52

-Dynamics in Asset Pricing 53

Summary 55

CHAPTER 3

EMPIRICAL FACADE OF ASSET PRICING THEORY

56

Empirical Episodes of APT 57

Akin Method 75

Summary 81

CHAPTER 4

FUNCTIONAL SECURITY PRICING FROM A MARKET VIEWPOINT

83

Summary 96

PART III

EMPIRICAL APPROACHES TO SECURITY MARKET PRICING

98

CHAPTER 5

METHODOLOGICAL OUTLINE

99

Empirical Methods in Asset Pricing 102

-General Linear Regression 102

-Maximum Likelihood 103

-Generalised Method of Moments 104


x

-Seemingly Unrelated Regression 104

Factor Analysis 105

-Strict Factor Model 108

-Approximate Factor Model 109

-Conditional Factor Model 110

-Multi-Factor Models 111

Time Series Analysis 113

Cointegration 113

-Applications of Cointegration Analysis 116

Summary 134

CHAPTER 6

MODELLING

136

Pool of a priori Variables 136

-Variables for Modelling 140

Modelling 142

Summary 149

PART IV

METHODOLOGY

151

CHAPTER 7

(EMPIRICAL ANALYSIS 1)

ANALYSIS OF SYSTEMATIC RISKS FOR THE AUSTRALIAN STOCK

MARKET

152

Data and Variables 153

Hypothesized Relationships of Variables 157

-Unit Root and Breakpoint Tests 161

-Lag Length Selection 164

Cointegration Analysis 165


xi

Caution 176

Summary 177

CHAPTER 8


INTERDEPENDANCE OF STOCK MARKETS UNDER GLOBALIZATION

178

Background 179

Data and Variables 182

Preliminary Tests 183

Analysis 1 184

-Cointegration Analysis 186

-Suplementary Tests 193

Analysis 2 194

-Structural Approach 195

-Autoregressive Approach 198

-Supplementary Tests 199

Summary 203

PART V

CONCLUSION

204

CHAPTER 9

CONCLUSION AND RECOMMENDATION

205

Outcomes 205

Recommendations 210

Future research 210

BIBLIOGRAPHY 211-226

ANNEXURE 1 227-232

Mazharul Kazi Ph.D Thesis 1

PART 1

RESEARCH OBJECTIVE

This part provides an entry into the thesis. It consists solely of one chapter, which

introduces the basic problem areas, objectives, scope, and processes of the overall

research program.


CHAPTER 1

INTRODUCTION

Since the start of human civilization, we have been trying to make our lives evenly

structured in every sphere of activity. However, civilization often fails to act in an

orderly fashion. Nature is not orderly. Institutions are created as a response to

disorderly nature to minimize uncertainty. Still, human created institutions are not

perfect. World economies and global capital markets also lack orderliness. The capital

market in particular is our own creation, operating in a controlled environment, but we

do not fully understand how it works. We have been trying to understand how capital

flows from one investor to another; what causes price movements; how capital markets

behave; and why they behave in this fashion. We often attempt to explain the lack of

market orderliness and try to make capital markets neater. We develop models and

theories based on simplifying assumptions under a controlled environment to help us

understand markets [Peters (1991)].

One may legitimately ask: why should we bother with theories and models? Why do

we not go to the real world and study it? Why do we not get the facts? To answer these

questions, Watson (1963) indicated two difficulties with facts. First, it is not always

easy to determine exactly what a fact is. Secondly, there are simply too many facts

about economic life. Clearly, it is impossible to get all of the facts. Therefore, we must

depend on theory, which is the systematic description of reality. Theory selects

essential features and shows the connections between them. It consists of

generalizations and pronouncements of causal relationships. All theories of economics


and finance consist of models. Models are sets of interconnected economic

relationships.

The models of any theory are clear and exact. Their foundations are carefully specified,

and so are the relationships among the variables. However, as simplifications of reality,

models have their limitations which theory recognizes. As there are always some

aspects of reality left out of the models, there must be caution in using them. Similarly,

theories may not completely explain the real world, yet they reveal some of the

structures of reality and guide us to understand the facts of our economic and financial

environment.

Research Aim

Both the national and international role of any security market is to provide a facility in

which investors and enterprises can come together with confidence to create prosperity

through sharing of risks and rewards. The security market helps facilitate the flow of

funds from investors to productive enterprises; this eventually stimulates economic

growth, creates national wealth, and generates employment and stability within society.

An effective security market is therefore a necessary condition for corporate vitality in

any national economy. It provides three principal opportunities: trading equities, debt

securities, and equity and index derivatives. Additionally, the security market is an

important conduit for the overseas flow of equity investments in any nation.


Capital markets around the globe have an impact on the performance of national

economies. Economic activities are interrelated with capital market movements. Capital

markets are very volatile. When the market is bullish, it is generally a sign of a strong

economy. On the other hand, a bearish market indicates a weak economy. The volatility

of security prices has become a real phenomenon. A capital market can crash and shake

the whole economy. Whether the market crash is a signal for necessary correction or

refers to a downturn in economic activities has been the subject of ongoing research in

every country. How are securities being priced? Should the pricing mechanism rely on

fundamental, technical or behavioural variables? Although there are a good number of

theories and models available to explain some of these problems, shortcomings are still

evident. We aim here to identify and assess factors that contribute to changes in

security market prices. We first attempt to understand the prevailing theories and

empirical approaches taken to investigate the long-term relationships among the

variables, including their dynamic co-movement in the adjustment process to long-term

equilibrium in the Australian stock market.

This research investigates two issues. First, we determine whether there exists, based

on finance theory and empirical evidence, any long-term relationship between

systematic risk factors and Australian stock market returns, and if so, which ones.

Secondly, we study selected cross-country stock market relationships to determine

whether the Australian stock market is cointegrated with other developed stock markets

under prevailing global economic and financial settings.

More specifically, our research questions are:


(i) Whether our a priori variables (derived from literature reviews,

intuition, and related checks and balances to proxy systematic risk

factors) influence the long-term return generating process in Australia,

and if so, whether these risk factors are being priced in the market.

(ii) Whether the Australian stock market is integrated to developed markets

(namely, the US, UK, Canada, Germany, France, and Japan) under the

influence of globalization, and if so, whether it is dynamic in nature.

Research Domain

There are many competing and complementary models and theories in asset pricing.

There are several models operating even within stock market pricing theory. Of the

prevailing models, arbitrage pricing theory (APT) is the most recent. APT has two

forms: the basic form of Ross, and an equilibrium form. APT can accommodate both

for latent factors and pre-specified factors in its empirical analyses, in line with its two

schools of thought. Additionally, linkages of APT to other models in financial theories

are inevitable. APT is an outcome of the empirical test on the capital asset pricing

model (CAPM) of Sharpe and Lintner (1960s) performed by Ross in the mid 1970s.

CAPM is often understood as a special case of APT. CAPM was also heavily

influenced by Markowitzs (1952) portfolio theory. Furthermore, there is evidence that

APT is linked with market equilibrium, efficient market hypothesis (EMH), market

microstructure, volatility, fundamental asset valuation theories, economic development,


growth, and so on. Technological innovation, globalization, international market

characteristics, financial liberalization and speculative bubbles are also, to some extent,

linked with the development of APT models. There is confusion about the implications

of a multi-factor APT and multi-beta CAPM [Shanken (1995b), and others]. Recent

works in the area of asset pricing have even attempted to explore its linkages to an

intertemporal, dynamic, nonlinear, and chaotic world environment.

APT has not been without controversy. Shanken (1992, 1995a) and others emphasized

that for individual securities, the approximation implied by Rosss APT has been so

imprecise that it makes it impossible to test whether the APT is true or false. Shanken

argued that as the expected return for any security or portfolio is related only

approximately to its factor sensitivities, to find an exact pricing relationship further

assumptions are required. He argued that researchers who attempted to test APT were

actually testing an equilibrium form of APT rather than Rosss APT. Hence, they

would have confronted the inherent difficulties in identifying appropriate risk-free

assets and market portfolio in one-factor modelling that arise when testing the CAPM.

Dybvig and Ross (1985) later responded to these criticisms of APT. However, it is

understood that, like the CAPM, there are fundamental limitations to any empirical

testing of APT, especially in explaining the priced risk factors in a security market.

APT is essentially a multi-factor or k-factor model of asset pricing, where the factors

are not explicitly described. This matter of non described, unidentified factors is

perhaps an advantage that enables researchers to accommodate currently influential

variables in their factor modelling. Hence, researchers have an opportunity to progress


with APTs inherent and ongoing and challenges for empirical testing. APT, like

CAPM, belongs to positive rather than normative theory. Thus, there exists an

opportunity in developing an APT model in such a way that represents positive as well

as normative theoretical views, or a positive approach that reflects normative

viewpoints. This amalgamation could be pursued in a market, which is not complete,

and in which equilibrium bubbles persist due to limited information or otherwise and

all investors are not equally informed. These are the incentives for pursuing research to

find out if the systematic or common risk factors are correctly priced in any stock

market.

Empirical Approach

The APT approach essentially seeks to measure the risk premia attached to various risk

factors and attempts to assess whether they are significant and priced into stock market

returns. There are quite a few approaches to studying security pricing behaviour,

namely, standard factor analysis, cross-sectional regression analysis, principal

component analysis, maximum likelihood analysis, multivariate analysis, and

generalized method of moments. Since APT analysis that considers factors as

inherently latent has shortcomings, the alternative approach that pre-specifies a set of

variables to act as common factors often performs well. This requires determining a

priori variables. These observable variables are pre-specified in the context of the

contemporary environment and economics and finance theory. The APT model

developed by Ross (1976) has been the most common framework in assessing the

influence of different factors.


An alternative approach is cointegration analysis. The cointegration approach is very

useful in examining the relationships between economic variables and stock markets

from an empirical viewpoint. Chen, et al. (1986) provided the basis for the view that a

long-term equilibrium relationship exists between stock prices and macroeconomic

variables, and Granger (1986) verified this notion through cointegration analysis. A

simple statement of the cointegration approach is that a set of time series variables is

said to be cointegrated if they are integrated of the same order and a linear combination

of them is stationary [Maysami and Koh (2000)]. Such linear combinations would then

point to the existence of a long-term relationship between the variables [Johansen and

Juselius (1990)]. The advantage of cointegration analysis is that through building an

error correction model, the dynamic co-movement among variables and the adjustment

process towards long-term equilibrium can be examined.

To address both of our research questions we have predominantly used the

cointegration approach as this is the most recent methodology trend in empirical

testing. In our analysis of how asset pricing in Australia responds to systematic risk

factors, the a priori variables to proxy for systematic risk factors in asset pricing were

determined from empirical evidence and the unique conditions of the Australian social,

economic and market environment or from simple intuition. We first considered 15 a

priori variables and conducted some basic tests on them, which allowed us to keep only

six for ultimate consideration. For our second analysis, we considered seven developed

national stock markets indices as proxies and essentially applied cointegration as our

method of analysis from the perspective of the Australian stock market.


Research Progression

We aim to pursue our study into empirical evidence for the Australian stock market

within the boundaries of asset pricing models and theories. In the following chapters

we have reviewed the existing literature in relation to security pricing theories and

empirical research. Chapter 2 reviews the literature from a theoretical perspective,

whereas Chapter 3 does the same from an empirical viewpoint. Chapter 4 surveys

various studies relevant to the security market pricing processes. Chapter 5 investigates

the empirical methodology appropriate to our study and Chapter 6 sets out our models

for the necessary analyses. Chapters 7 and 8 conduct the cointegration and related tests

and provide results. Chapter 9 concludes the thesis with its recommendations for future

research.


PART II

LITERATURE REVIEW

This part of the thesis reviews the literature on asset pricing from theoretical, empirical

and stock market perspectives. It contains three chapters that investigate the whole

gamut of prevailing theories, empirical aspects and intuitions relating to stock markets

and its pricing mechanisms. Chapter 2 reviews the literature on asset pricing and other

theories. Chapter 3 investigates security pricing theories from an empirical perspective.

Chapter 4 examines recent trends in empirical studies on security pricing phenomena.


CHAPTER 2

THEORETICAL ASPECTS OF SECURITY PRICING

Modern financial analyses are concerned with sources of common risk factors that

contribute to changes in security prices or values. By identifying such factors, investors

may be able to control their investment risks more efficiently and even improve their

investment returns [Kritzman (1995)]. Since risks and returns together play a vital role

in the process of security pricing, it is important to understand security market

behaviour.

There are many competing and conflicting theories of the determinants about the price

of a stock. These theories accord with their corresponding schools of thought

[Sivalingam (1990)]. There are a number of schools of thought in finance, including the

behavioural finance school. The behavioural or primeval school believes that the price

of a stock depends on what the next person in the market is willing to pay for it. In

other words, the value of a stock depends entirely on the psychology of investors in the

market. This school of thought considers that investors behave as a mob and tend to

build castles-in-the-air when stock prices move up. In other words, irrational investors

tend to push prices up because of optimistic expectations and tend to panic-sell when

they are pessimistic. An intelligent investor is advised by the advocates of this school to

read the mind of the crowd or the market and make buying or selling decisions just

before the crowd starts doing so. If the investor is able to outsmart the crowd, he/she

will be able to make abnormal or extraordinary profits out of such investment. Another

school, known as technical analysts or chartists, believes that there are repetitive


patterns in movements in stock prices. Accordingly, to some extent, chartists agree with

the castle-in-the-air paradigm that the past market pricing behaviour of a stock contains

useful information that can be used to predict future prices [Sivalingam (1990)].

Fundamental analysts disagree with the castle-in-the-air concept and the chartists. The

fundamentalists claim that the price of a stock is determined by its intrinsic value or

market fundamentals. Accordingly, if the stock is selling at a price lower than its

intrinsic value (discounted present value of future cash flow), investing in that stock

would generate extraordinary or abnormal profits for investors. In essence, the stocks

intrinsic value and the market price would determine the buying or selling decision for

investors. Thus, if the stock is under-valued, investors should buy and if the stock is

over-valued, investors should sell. Fundamental analysts claim that they have a

methodology for determining whether a security is currently over-valued or under-

valued [Sivalingam (1990)].

Neo-classical theorists do not agree with the castle-in-the-air paradigm, the chartists or

the fundamentalists. They argue that the information contained in the past price or

market behaviour of a stock is already reflected in todays price. The neo-classicists

believe that prices follow a random walk and are unpredictable. Accordingly, they do

not recommend that investors look for bargains in the stock market [Sivalingam

(1990)].

In other words, the neo-classical school argues that, because the market is efficient,

there are no under-priced securities; hence no opportunity for a bargain exists in the


market. Their advice for investors is to pick stocks based on the stocks risk and return

characteristics. This recommendation is based on their basic assumption that the return

on a stock is dependent on its risk class. The riskier the stock, the higher is its return

and vice versa. Modern portfolio theory, capital asset pricing theory, and arbitrage

pricing theory follow the neo-classical school of thought.

Finance theory is a branch of economics that customarily focuses on capital markets.

In the early life of the subject, emphasis was placed on describing the market

environment and valuing individual securities. In more recent years, modern financial

theories lay emphasis on broader aspects of the valuation of assets whose

characteristics extend across time, and which impose composite and complex risk on

investors. The development of asset pricing theory includes the valuation of a wide

range of financial assets and derivatives. One can present this development as a

coherent body of theory, rather than disjointed components. In particular, modern

financial theory is founded on three central assumptions, namely, markets are highly

efficient; investors exploit potential arbitrage opportunities; and investors are rational

[Dimson and Mussavian (1999)].

Within the neo-classical school, a common taxonomy usually divides modern financial

theories between normative and positive approaches. Normative theories are

prescriptive, and positive theories are descriptive. When a theory embraces some norms

or standards, mixing them with cause-effect analyses, it is normative or prescriptive

theory. When the theory confines itself to statements about cause-effect and the

fundamental relations that prevail, it is positive or descriptive theory [Watson (1963)].


Markowitzs path-breaking mean-variance portfolio theory falls into the former

category, dealing as it does with rules for optimal portfolio choice by an individual

investor. Asset pricing theory can be classified as belonging to the latter, since it is

concerned with the determination of the prices of capital assets in a competitive market

environment [Sharpe (1990)].

The domain of positive financial theory is often further divided into a set of models that

are described as utility-based and a complementary set that are described as arbitrage-

based. Models that fall in the latter category derive implications from the assumption

that capital asset prices will adjust until it is impossible to find a profitable strategy that

requires no initial investment. Models that fall in the former category typically conform

to the conditions required for the latter, but produce stronger implications due to added

assumptions about the utility functions that investors are assumed to maximize [Sharpe

(1990)].

According to Popper (1934), any scientific theory should lead to propositions that are

potentially verifiable or replicable by experimental or empirical observation. Asset

pricing theory is no exception. The large volume of capital investment using these

models around the globe has created further pressure to continue research into the

development of appropriate techniques for testing these theories empirically. The

literature on asset pricing is crucial to advance our understanding about the systematic

or common risk factors that affect investment decisions as well as to develop

appropriate models that explain the microstructure of financial markets.


Remembrance

Many issues addressed in modern finance are traced back to a remarkable paper

presented to the Imperial Academy of Sciences in St Petersburg by the Swiss

mathematician Bernoulli (1738). Bernoulli suggested that increases in wealth would

result in an increase in utility inversely related to the quantity of goods in an

individuals possession. This enabled him to demonstrate the trade-off between the

expected change in wealth and the risk associated with such an opportunity. Bernoullis

idea of decreasing marginal utility became central to economics by the late nineteenth

century, notably in price theory and the associated theoretical developments of the

notable late nineteenth century economists Walras (1834-1910) and Marshall (1842-

1924). In the literature of price theory, the concept of Bernoullis utility theory is

known as the St Petersburg Paradox [Watson (1963)]. Bernoulli also introduced the

concept of the maximization of expected utility. Despite endorsement by the scholar

Laplace, Bernoullis approach had little impact on the economics of decision making

under risk until the development of expected utility theory by Von Neumann and

Morgenstern during the mid 1940s and Savage in 1954 [Dimson and Mussavin (1999)].

In earlier ages, any economic problem was the topic of price theory that explained the

composition or allocation of total resources including capital. Price theory was the

centre of attention for economists during the eighteenth and nineteenth centuries, when

it was known as the theory of value. The theory of value played a leading role as one of

the intellectual foundations built after 1776. The theory of value was also at the heart of

the old controversies over capitalism and socialism. Karl Marxs critique of capitalism


was based upon his special version of the theory of the value of commodities. Price

theory or the theory of value, therefore, has for a long time been the most important

issue in economics and finance [Watson (1963)].

The concept of risk is now endorsed in economics, and especially in modern finance.

However, this was not the case until 1921 when Knight made a distinction between risk

and uncertainty. According to Knight, when the randomness of an event can be

expressed in terms of numerical probabilities, the situation is said to involve risk. When

probabilities cannot be assigned to alternative outcomes, the situation is called

uncertainty. In a setting that embraces both risk and uncertainty, the model of general

equilibrium developed by Arrow and Debreu has been fundamental to economics and

finance since the early 1950s [Debreu (1959)]. Arrows theory of equilibrium operating

with incomplete asset markets is seminal. Arrow showed that by using the temporal

structure of the economy, equilibrium can be attained with a more limited number of

markets. He explained how markets that are almost complete through a series of

contingent claims resolve uncertainty. Arrows work has provided a conceptual

framework for the theory of asset pricing [Dimson and Mussavin (1999)].

Arrows concept of a complete market provided an opportunity to secure an individual

investor from any loss. In an economy where it is possible to insure against the range of

possible future outcomes, individuals are more likely to be willing to bear risk. It

provides encouragement to investors to hold diversified portfolios, rather than putting

all their eggs in one basket. Arrows framework set the direction for Markowitz (1952)

to take a more structured analysis of investors portfolio selection decisions.


Security Pricing

Portfolio Selection

With the seminal work of Markowitz (1952), finance as a discipline achieved its

creditable place in the modern era. Ever since the day of Bernoulli, it was clear that

individuals would prefer to increase their wealth, and also to minimize the risk

associated with any potential return. Markowitz rejected the previous idea that there

might be a portfolio which gives investors both maximum expected return and

minimum risk. He showed that the portfolio with maximum expected return is not

necessarily the one with minimum variance. There is a rate at which the investor can

gain expected return by taking on variance, or reduce variance by giving up expected

return [Reilly and Norton (1999)].

Markowitzs (1990) work on portfolio theory primarily considers how an optimizing

investor would behave in a market environment. Yet, portfolio theory differs in three

major ways from marketing theories, that is, from theory of the firm and theory of the

consumer behaviour. First, it is concerned with investors rather than consumers or

firms. Secondly, it is concerned with economic agents who act under uncertainty.

Finally, it is a theory that is supposed to direct prices rather than quantity of products

supplied in the market or economy.


The important contribution of Markowitz is his distinction between the variability of

returns from an individual security from a risky portfolio. He indicated that to make the

variance small it is not enough to invest in many securities. Rather, it is necessary to

avoid investing in securities with high covariances among themselves. Markowitz

demonstrated that one could identify a set of portfolios that provide the highest possible

expected return for a given level of risk or the lowest level of risk for each level of

expected return. These portfolios form an efficient frontier. He showed that the trade-

off between returns and risks would be economically efficient for the portfolios that fall

on this frontier. Markowitz (1959) also described a method of modelling the consumer

choice problem. If the set of portfolios that satisfy the mean-variance criterion is

identified and investors preferences can be modelled, then the investors chosen

portfolio would be the combination of risky assets that maximize expected utility

[Brailsford and Heaney (1998)].

The safety-first approach of Roy (1952) has many similarities to Markowitzs portfolio

selection framework. Roys model addressed the question of how an investor can

ensure a suitably small probability that wealth falls below some disaster level, which is

essentially the same problem that Markowitz addressed in a different fashion. Roys

approach was presented in a linear form that considered risk as an independent variable

and return as a dependent variable, and was adopted by finance professionals for quite

some time. Still, Markowitz is regarded as the pioneer of portfolio theory [Dimson and

Mussavin (1999)].


Tobin (1958) extended Markowitzs analysis by showing how to identify, out of a set

of efficient portfolios, which one should be held by an individual investor. He showed

how investors should divide their funds between safe liquid assets and risky assets and

proposed a framework for asset allocation that is intuitively appealing. Tobin suggested

breaking down the portfolio selection problem into stages at different levels of

aggregation-allocation, first among and then within, asset categories. The asset mix

should reflect the degree of risk tolerance of the investor. The optimal portfolio of risky

assets, however, should be independent of the risk preferences of the investor. This

proposition, known as the separation theorem, provides a basis for identifying the

efficient portfolio and clarifies the task of portfolio selection. Yet, Tobins theorem

requires the uses of Markowitzs full covariance model to embrace the analysis of

individual securities as well as individual investors. However, the data and

computational requirements of this approach are enormous unless the universe of

securities is limited to a manageable level. Sharpe (1963) addressed these difficulties

when he devised his simplified model for portfolio analysis [Dimson and Mussavin

(1999)].

Sharpe (1963) drew on an insight of Markowitz (1959) that stocks are likely to co-

move with the market. His model assumes that security returns linearly relate to

fluctuations in a market index with a known degree of sensitivity. Security-specific

returns are generated with a known mean-variance. With only three parameters per

security, the tasks of risk measurement and portfolio optimization are greatly

simplified. Markowitz (1990) pointed to the fact that his portfolio theory considers how

an optimizing investor would behave, whereas the Sharpe-Lintner capital asset pricing


model is concerned with economic equilibrium assuming all investors optimize in a

particular manner. However, Sharpes model has been extended to embrace more

complex issues concerning asset pricing in capital markets.

Capital Asset Pricing Model

Soon after the Markowitzs book on portfolio selection was published in 1959, Treynor

(1961) started to explore the possibility of developing a theory of asset pricing. Around

the same time, Sharpe set out to determine the relationship between the prices of assets

and their risk attributes. Sharpe aimed to use the theory of portfolio selection for

constructing a market equilibrium theory of asset prices under conditions of risk.

Sharpe noted that his model shed considerable light on the relationship between the

price of an asset and the various components of its overall risk [Dimson and Mussavin

(1999)].

In his Ph.D dissertation, Sharpe explored a number of aspects of Markowitzs portfolio

analysis. At that time, he called his approach the single-index model, which is now

known as the one-factor model. His key assumption was that security returns relate to

each other solely through responses to one common factor. In his dissertation he

addressed both normative and positive results. However, under the heading A Positive

Theory of Security Market Behaviour, his dissertation covered a result similar to the

capital asset pricing model (CAPM) [Sharpe (1990)].


Sharpe (1964) indicated that one of the problems which plagued him in attempting to

predict the behaviour of capital markets was the absence of a body of positive

microeconomic theory dealing with conditions of risk. The pervasive influence of risk

in financial markets forced him to adopt models of price behaviour, models which are

little more than assertions. In assessing the desirability of a particular investment,

Sharpe (1964) noted that an investor should make decisions based on only two

parameters: the expected return and the standard deviation of returns. In other words,

he considered the mean-variance approach under certain conditions in order to ascertain

the investors preference function. Sharpes paper was supplemented by contributions

from Lintner (1965) and Mossin (1966).

A number of researchers attempted to relax the strong assumptions that underpin the

original CAPM of Sharpe, Lintner and Mossin. The most frequently cited modification

was by Black (1972). Black showed that the model needed to be modified when

borrowing at a risk-free rate was not available. His version is known as the zero-beta

CAPM. Brennan (1970) found that when taxes were introduced into the equilibrium,

the structure of the original CAPM held. Mayer (1972) showed that when the market

portfolio included non traded assets, CAPM remained identical in structure to the

original version. Solnik (1974) and Black (1974) observed that CAPM was extendable

to encompass international investments. Williams (1977) noted that the theoretical

validity of the model was relatively robust if the assumption of homogenous return

expectations was relaxed. Treynor and Black (1973) showed how best to construct

managed portfolios (as a blend of a passive portfolio and an active portfolio) by linking

the CAPM with the index model of Sharpe (1963). Research aimed at extending the


classical one-period setting of CAPM to a continuous-time environment is generally

known as the intertemporal capital asset pricing model (ICAPM).

Until the early 1980s, CAPM was the standard and popular tool used to describe

common stock returns in an efficient market. A large number of empirical studies

published during the 1970s concluded that the CAPM was a good descriptor and

predictor of the behaviour of stock returns in the US, Europe and Japan [Hawawini

(1993)]. In the late 1970s, however, the validity of CAPM was seriously questioned, by

a number of researchers including Roll (1977), both on conceptual and empirical

grounds [Roll and Ross (1980)]. During the mid 1970s, Ross (1976) developed an

alternative pricing model called arbitrage pricing theory.

Arbitrage Pricing Theory

The core idea of Rosss arbitrage pricing theory (APT) is that only a small number of

systematic influences affect the long-term average returns on securities. Hence, APT is

a factor model. Unlike Sharpes (1963) single-index model, APT includes multiple

factors that represent the fundamental risks in asset returns and thus the prices of

securities. Multi-factor models allow an asset to have not just one, but many, measures

of systematic risk. Each measure captures the essential sensitivity of the asset to the

corresponding pervasive factor. Thus, APT is also a multi-factor equilibrium pricing

model that is more general than the CAPM. On both theoretical and empirical grounds,

APT is an attractive alternative to CAPM. It is argued that APT requires less stringent

and presumably more plausible assumptions and is more readily testable since it does


not require the measurement of market portfolios. Often, APT explains the anomalies

found in the application of CAPM to asset returns [Dhrymes, et al. (1984, 1985)].

APT conventionally assumes that the returns on securities are linearly related to a small

number, k, of common or systematic factors rather than a single factor, β. The model

applies to any set of securities as long as their number, n, is much larger than the

number k of common factors [Hawawini (1993)]. APT does not specify what the k-

factors are; rather it has kept this open for consideration by researchers [Brailsford and

Heaney (1998), Reilly and Norton (1999)]. Moreover, the model does not require that

investors hold all outstanding securities; hence the market, which is central to CAPM,

plays no role in APT [Dimson and Mussavian (1999)].

To understand the basic formulations of both APT and CAPM, let us consider three

common factors that influence the stock market. According to APT, with Rf being the

risk-free return the expected return on asset i is

E(Ri) = Rf + λ1 b1i + λ2 b2i + λ3 b3i (2.01)

where λ1, λ2 and λ3 are three risk-premia corresponding to the three sensitivity

coefficients of asset i, that is, b1i, b2i and b3i. These sensitivity coefficients are similar to

the β coefficient in CAPM.

E(Ri) = Rf + [E(Rm)−Rf] βI (2.02)


where the β of a stock is a measure of the sensitivity of that stocks returns to the return

of the market as a whole. Likewise, b1i is a measure of the sensitivity of the returns of

stock i to the returns of the first common factor, and so on. There is a structural

similarity between the APT model and CAPM. Assuming there is only one common or

systematic factor affecting all outstanding securities and that this factor is the return on

the market as a whole, then the APT pricing relationship collapses to the CAPM pricing

relationship. In this case the sensitivity coefficient to the unique market factor is the

beta (β) coefficient and the risk premium of APT (λ1) is the CAPM risk premium

[E(Rm)−Rf].

APT may appear to be similar to the multiple betas in the intertemporal capital asset

pricing model (ICAPM) of Metro (1973), but this is not the case. Although the CAPM

of Sharpe (1964) and Lintner (1965) identifies the factor as the return on the market

portfolio, Roll (1977) provides convincing arguments for the unobservability of market

returns. APT essentially is an arbitrage-based model, while CAPM is utility-based.

Again, Ross viewed APT as an arbitrage relation rather than an equilibrium condition

[Dimson and Mussavian (1999)].

APT has two basic forms: the first is the nonarbitrage theorem, derived by Ross (1976);

the second is an equilibrium model [Brailsford and Heaney (1998)]. Factor pricing

theories, such as the APT of Ross and the equilibrium APT, occupy a central place in

the theory of asset pricing. The APT of Ross and the equilibrium APT extend the basic

intuition of CAPM to large diversified asset markets without imposing strong


assumptions on the nature of investors preferences and asset return distributions

[Nawalkha (1997)].

Given perfectly competitive and frictionless capital markets where investors believe in

a k-factor return generating model, APT assumes that random returns for n assets,

denoted by R(i), for i= 1, 2, n, equal the expected return for each asset E(i), plus k

risk premiums B(i,k)D(i). Each risk premium is determined by the k market risk

components D(i), and the sensitivity of the asset to that risk component B(i), plus an

unexplained residual term e(i), as follows:

R(i) = E(i) + k∑ B(i, k) D(i) + e(i) (2.03)

The arbitrage portfolio has a proportion of wealth x(i) invested in each asset and has

returns equal to x(i)R(i, k):

x(i)R(i,k) =x(i)E(i) + x(i)B(i,1)D(1) +

+ x(i)B(i,k)D(k) + x(i)e(i) (2.04)

Purchases of new assets will exactly equal the proceeds of short sales of other assets, so

that the portfolio has no net effect on investment. The x(i) are chosen in such a way that

the sum of the x(i)B(i,k) equals zero. This implies that the portfolio has no systematic

risk. As the number of securities in the portfolio increases, the unsystematic risk

approaches zero:


i

∑ x(i) e(i) = 0

Thus, an arbitrage portfolio has no net investment and no risk (either systematic or

unsystematic) and earns no return. For other portfolios, with both risk and investment,

returns on assets are a linear combination of a risk-free rate λ(0), plus a risk premium

for each risk component to which the asset is sensitive, x(i)B(i, k)λ(k):

E(i) = λ(0) + k

∑ x(i) B(i,k) λ(k) (2.05)

A risk-free or zero beta portfolio, for which all B(i,k) = 0, would yield the risk-free rate

of return [McGowan and Francis (1991)]: E(i) = λ(0) = E(0).

APT of Ross

Ross (1976) started with the following return generating process for securities to

construct his form of the APT model for testing purposes:

rt = Et + ft B + ut (2.06)

where rt is an m-element row vector containing the observed rates of return at time t for

the m securities. Et is an m-element row vector containing the expected (mean) returns,

while ft is a k-element vector of common (but unobservable) factors affecting security

returns, both at time t. B is a k×m matrix of parameters indicating the sensitivity of


securities to the common factors, and ut is the idiosyncratic component of the error

term. Ross showed that if the number of securities, m, is sufficiently large, there exists

a (k+1)-element row vector ct such that

Et = ct B*, t = 1, 2, T (2.07)

where B*′ = [e:B′] and e is an m-element column of ones. The empirical tests of the

APT model, therefore, are based upon a two-stage factor analytic approach [Dhrymes,

et al. (1985)].

Not all studies supported APT. However, most studies reported positive relationships

between the APT factors and asset cross-sectional mean returns. In the early 1980s, at

least three studies directly addressed the problem of factor identification for testing

APT. Fogler, et al. (1981) attempted to define the relationship between estimated

factors and a market index, the US Treasury bond rate, and AA (Double A

class/quality) utility bond rates. They indicated that there was a significant relationship

between security returns and these three independent variables. Anckonie (1983)

employed a more systematic approach to factor identification. He used principal

component analysis to decompose the variation of quarterly returns for two industries:

large commercial banks and regulated utilities. Seven significant factors were found

through this study. These seven factors were then regressed against 13 macroeconomic

variables. Significant relationships were found for each APT factor. Anckonies results

also indicated that industrial production, inflation, and interest rates are the three most

important macroeconomic factors. Chen, et al. (1983) found a statistically significant


relationship between factors using security returns and unanticipated inflation, long-

term interest rates, industrial production, and risk premium. Chen, et al. (1983) did not

find statistically significant relationships with a market index, consumption, or oil

prices. Their results were similar to those of Anckonie (1983).

Later, Leudecke (1984) and Trzcinka (1986) both explored the Chamberlain and

Rothschild (1983) concept of an approximate factor structure using US data. Leudecke

(1984) examined a sample of 392 assets and found that the first eigenvalue is dominant.

Even for his large sample, the approximate size of the k-factors was not obvious, as his

analysis did not decisively distinguish between the approximate one-factor structure

and the many-factor structure. Trzcinka (1986) conducted another analysis on 865 firms

over 1,069 weeks. He found one large factor and no obvious way to choose more than

one. He also suggested that the number was very unlikely to be zero, which supported

the crucially fundamental APT assumption of the existence of an underlying factor

structure.

Roll and Ross APT

Most APT tests employed the methodology suggested by Roll and Ross (1980),

commonly known as the RR method [Hawawini (1993)]. Roll and Ross (1980)

followed a two step procedure in their empirical tests of APT. In the first step, they

estimated the expected returns and the factor coefficients on individual asset returns

from time series data. In the second step, they used the estimates from the first step to

test the basic cross-sectional pricing conclusion of APT.


Roll and Ross (1980) used daily return data, from July 1962 to December 1972, for a

sample of 1,260 NYSE and AMEX listed companies. They divided their sample of

stocks into 42 groups of 30 securities each. From the return data they established each

groups variance-covariance matrix. Due to the lack of high-powered computing

facilities at that time, they analyzed each group separately. By applying maximum

likelihood factor analysis, they determined simultaneously the number of common

factors, Fj, and their corresponding sensitivity coefficient, bij, called the factor loading.

Finally, they performed a cross-sectional test of the APT model by running a linear

regression in which the average stock return, E(Ri), was the dependent variable and the

set of factor loadings, bij, were the independent variables. Their model allows them to

estimate the risk premium associated with each factor and determine the number of

factors that are priced according to APT. Roll and Ross (1980) found that for 75% of

the groups, there is a 50% chance that five factors are significant; and that three to four

factors explain the cross-sectional variation in average stock returns. They concluded

that the APT model performs well in empirical tests on securities.

During the mid 1980s, the RR method was applied to European data by Dumontier

(1986), Winkelmann (1984) and Beenstock and Chan (1983, 1984) for France,

Germany and the UK respectively. The European evidence indicated that equity pricing

was generally consistent with the RR model. However, the number of significant

common factors from the French, German and UK data varied. In the case of France,

seven common factors were significant in explaining the variance of common stock

returns. For the German data, the number of factors retained was dependent on the


criterion employed to select those that are significant. The smallest number of factors

identified was one, while the largest number was 43. The British study suggested 15 to

20 relevant factors.

The disparity in the number of significant common factors reported might have been

due to differences in: (a) the size of groups analyzed; (b) the statistical technique

employed to extract the factors from the data; and (c) the type of criterion adopted to

select those factors. On the other hand, the cross-sectional evidence provided three to

five factors that seemed to explain the cross-sectional variation of the average returns

on the French stocks. The number was eight for the German stocks and one to eight for

the UK stocks.

A major weakness of these tests was their inability to identify the nature of common

factors since they treated them as inherently latent. An alternative approach that pre-

specifies a set of economic (or financial) variables to act as common factors was likely

to perform well. Upon determination of a priori variables, this approach of testing APT

examines whether the sensitivity coefficients of stock returns to these factors explain

the cross-sectional variation of average stock returns. Chen, et al. (1986) and Hamao

(1986) applied this approach to US and Japanese stocks respectively.

Chen, et al. (1986) tested whether innovations in macroeconomic variables are risks

and warrant reward in the stock market. They pre-specified their variables in

accordance with the theory that a few macroeconomic variables should systematically

affect stock market returns. These variables were: (i) the spread between long and short


interest rates; (ii) expected and unexpected inflation; (iii) industrial production; and (iv)

the spread between high and low grade bonds. They found these sources of risk were

significantly priced in the US stock market.

Chen, et al. (1986) considered the common belief that asset prices are sensitive to

external forces. Consistent with the ability of investors to diversify unsystematic

influences, pervasive or systematic external influences are the likely sources of

investment risk. They understood that an additional component of long-run returns was

required whenever a particular asset was influenced by systematic economic news and

no extra reward for bearing diversifiable risk. Since APT has been silent about which

events are likely to influence all assets, a gap exists between the theoretically exclusive

importance of systematic state variables and complete ignorance about their identity.

The co-movements of asset prices suggest the presence of underlying exogenous

influences, yet it is difficult to determine the responsible variables. As an example,

Chen, et al. (1986) argued that a variable should be one that has no direct influence on

current cash flows but does describe the changing investment opportunity set.

Accordingly, stock prices of Chen et al. (1986) were determined by expected

discounted dividends:

( )E c

pk

= (2.08)

where c is the dividend stream and k is the discount rate. This implies that actual

returns in any period are:


[ ]p

c

k

dk

cE

cEd

p

c

p

dp +−=+)(

)(

(2.09)

At least trivially, it follows that the systematic forces that influence returns are those

that change discount factors, k, and expected cash flows, E(c).

On the other hand, Hamao (1986) selected a set of eight economic variables as likely

common factors that would affect the returns of Japanese stocks. His pre-determined

variables were: (i) the monthly growth rate in an index of industrial production; (ii)

changes in expected inflation; (iii) unexpected inflation; (iv) unexpected changes in the

risk premium with the risk premium defined as the spread between government and

corporate bonds; (v) unexpected changes in the slope of the term structure of interest

rates with the slope defined as the spread between the rate on long-term government

bonds and the short-term risk-free rate; (vi) unexpected changes in the forward yen-

dollar exchange; (vii) the growth rate in oil prices; and (viii) the return of a market

index of TSE stocks. Only three factors were found to be significant for the Japanese

common stock returns. These were: (a) changes in expected inflation; (b) unexpected

change in the risk premium; and (c) unexpected changes in the slope of the term

structure of interest rates.

McGowan and Francis (1991) studied asset pricing using a multivariate statistical

analysis technique. Like factor analysis and principal component analysis, the ability of

the multivariate technique to discern interesting empirical insights depends upon the

size and heterogeneity of the sample and the way data are analyzed. Their approach had


three stages. In stage one principal component analysis was used to calculate factor

scores for 86 different industry indices. They extracted 10 orthogonal principal

components of stock price volatility. In stage two principal component analysis was

again used to calculate factor scores for 95 macroeconomic time series from the data

set. It detected nine principal components of economic activity. In stage three each of

10 principal component scores (derived from stage one) was regressed one-at-a-time on

all nine macroeconomic variables (identified from stage two) to test statistically

significant relationships between the APT factors and macroeconomic factors. They

observed that at least one principal component of economic activity had a statistically

significant impact on each of the 10 principal components of stock price variation.

Thus, the results of McGowan and Francis (1991) verified the relationships between

stock price movements and the real sector of the economy that are suggested by

economic theory.

The seminal work of Fama and French (1993) to ascertain common risk factors in the

returns on stocks and bonds based on pre-specified financial variables has been widely

discussed. Fama and French (1993) identified five common risk factors. Out of the five,

three were significant stock market factors and two bond market factors. The stock

market factors were factors related to the size and book-to-market equity, and an

overall market factor. Bond market factors were related to maturity and default risks.

Fama and French (1993) extended their earlier asset-pricing tests [Fama and French

(1992a)] in three ways. These were: (i) the extension of the set of asset returns to be

explained; (ii) the expansion of the set of variables used to explain returns; and (iii) a


different approach from those of Fama and French (1992a) and Fama and MacBeth

(1973) in testing asset pricing models.

Fama and French (1993) used the time series regression approach of Black, Jensen and

Scholes (1972). Monthly returns on stocks and bonds were regressed against the returns

on a market portfolio of stocks and mimicking portfolios for the size, book-to-market

equity (BE/ME), and term structure risk factors in returns. The time series regression

slopes were treated as factor loadings that, unlike size or BE/ME, had a clear

interpretation as risk factor sensitivities for the securities. Time series regressions were

used to study two additional issues of asset pricing. The first was whether variables

related to average returns (for example, size and book-to-market equity) act as proxies

for sensitivity to common risk factors in returns for rationally priced assets. The time

series regressions gave direct evidence on this issue. Their regression slopes and R2

values showed that mimicking portfolios for risk factors related to size and BE/ME

captured shared variation in stock and bond returns not explained by other factors. To

study the second issue, Fama and French (1993) used returns (monthly stock/bond

returns minus the one-month Treasury bill rate) as dependent variables in their time

series regressions, and excess returns or returns on zero-investment portfolios as

explanatory variables. In such regressions, their well-specified asset-pricing model

produced intercepts that were indistinguishable from zero [Merton (1973), Fama and

French (1993)].

Fama and French (1993) also checked the robustness of their inference in the following

manner. First, they used the residuals from the five-factor time series regressions to


check that the regressions captured the variation through time in the cross-section of

expected returns. Secondly, they examined whether their five risk factors captured the

January seasonal in stock and bond returns. Thirdly, they contemplated split-sample

regressions that used one set of stocks in the explanatory returns and another disjoint

set in the dependent returns. Finally, they examined whether the stock-market factors

that captured the average returns on portfolios were informative enough.

In observing the predictability of the regression residuals, Fama and French (1993)

used (i) excess returns or returns on zero-investment portfolios; (ii) dividend yields

(D/P); (iii) spreads of low-grade over high-grade bond yields (that is, default spreads or

DFS); (iv) spreads of long-term over short-term bond yields (that is, term spreads or

TS), and (v) short-term interest rates (that is, one-month bill rate or RF). They

hypothesized that if these five factors captured the cross-section of expected returns,

the predictability of stock and bond returns should be embodied in the explanatory

returns in the regressions. To test their hypothesis, they estimated 32 time series

regressions:

ep (t+1) = k0 + k1( )

( )

D t

P t+ k2DFS(t) + k3TS(t) + k4RF(t) + ηp(t+1) (2.10)

The ep (t+1) were the time series of residuals for 25 stock and seven bond portfolios

from the regressions. Their estimates did not produce any evidence that the residuals

from the five-factor time series regressions were predictable. In 32 regressions, 15

produced negative values of 2

R . Only four R2 exceeded 0.1; the largest was 0.3. Fama


and French (1996) concluded that, in various cases, average returns on common stocks

are related to firm-characteristics and, except for the continuation of short-term returns,

the anomalies largely disappear in a three-factor model. Their results were in harmony

with the rationales of both capital asset pricing model and APT.

Attributes of APT

Most applications of security pricing aimed to find factors that explain security returns

and the associated risk premiums using multi-factor models. Multi-factor models of

security returns are normally divided into three types: macroeconomic, fundamental,

and statistical factor models [Connor (1995)]. Macroeconomic factor models use

observable economic time series, such as inflation and interest rates, as measures of the

pervasive shocks to security returns. Fundamental factor models use the returns to

portfolios associated with observed security attributes such as dividend yields, the

book-to-market ratio, and industry identifiers. Statistical factor models derive their

pervasive factors from factor analysis of the panel data set of security returns.

Connor (1995) investigated the explanatory power of the three types of factor models

for security returns in the US capital market. He observed that statistical and

fundamental factor models substantially outperformed the macroeconomic factor

model. The fundamental factor model slightly outperformed the statistical factor model.

From the point of view of theoretical consistency and intuitive appeal, macroeconomic

factor models performed better. Although interesting and useful, his results did not


allow him to make final recommendations about selecting a specific model out of the

three.

It is also conventional to divide factor models into two schools of thought [Zhou

(1999)]. The first school of thought takes the stand that the factors are inherently latent

and unobservable directly from market data. Rosss (1976) basic APT provides

theoretical justification for the use of latent factors. The second school of thought takes

a more pragmatic stand. Rather than identifying either observable or unobservable

factors by using any asset pricing theory, this school treats factors as pre-specified

economic or financial variables that seem related to asset returns by simple reasoning

or plain intuition.

Consistent with the latent factor school, there are two notable methods that can be used

to extract factors from asset return data. These are Connor and Korajczyks (1986)

asymptotic principal components approach, and the standard factor analysis approach

[Seber (1984)]. There are two weaknesses with these approaches. First, they rely on

information on security returns alone, making it difficult to link the estimated factors to

economic fundamentals. Secondly, there is an error-in-variables problem when the

estimated factors are used to test APT. Although the one-step procedures, namely, the

maximum likelihood and Bayesian approaches, will not be subject to an error-in-

variables problem as suggested by Geweke and Zhou (1996), they will not be as robust

as the approaches proposed by Zhou (1999).


The advantage of approaches consistent with the pre-specified factor school of thought

is their flexibility in including useful economic, financial or perhaps any other form of

variables in the analysis. Examples of such studies include Chen, et al. (1986) and

Fama and French (1993). Yet, one may run into the danger of including too many

variables that are highly correlated with one another and hence redundant, resulting in

an overstatement of the number of factors and inaccurate estimation of parameters.

Conversely, the exclusion of important variables from consideration might also give

estimation problems. Furthermore, as highly correlated variables are included, say, in a

linear regression system, it is often difficult to interpret the associated factor risk

premiums, as they might simply reflect the same source of economic risk factor [Zhou

(1999)]. To solve the problems associated with the testing of APT, Zhou (1999)

suggested a new framework that applies to both the latent and pre-specified factor

schools.

For the latent factor school, which treats the risk factor as unobservable, Zhou (1999)

modelled the latent factors explicitly as a linear function of economic variables plus a

noise. Then he proposed to use those linear combinations of the economic variables that

best forecast the latent factors. There are three interesting aspects of this new approach.

First, it estimates the latent factors by using the best forecasts from the economic

variables, naturally linking the latent factors to economic fundamentals. Secondly, the

estimation of the factors is carried out jointly with the estimation of the factor load

parameters or sensitivity of variables. Thus, the previous error-in-variables problem is

no longer found in the test of APT. Finally, the new approach has the flexibility of


using many economic variables to analyze a factor model with only a few factors,

which is in contrast to Chen, Roll and Ross (1986).

For the pre-specified factor school, for the purposes of estimating the minimum number

of factors needed to explain asset returns, Zhous (1999) procedure based on the

generalized method of moments of Hansen (1982) is proposed. This minimum number

is not necessarily the number of pre-specified variables. The procedure also yields the

best linear combinations (that is, minimum number) of pre-specified economic

variables to serve the non redundant factors. An interesting feature of this method is

that the factors so obtained are orthogonal to one another. Consequently, it allows the

use of potentially many pre-specified economic or other form of variables to generate a

few orthogonal factors.

The APT of Ross (1976) hypothesized that the cross-sectional distribution of expected

returns of financial assets can be approximately measured by their sensitivities, called

factor loadings or κ, to k unknown economic factors. Chamberlain and Rothschild

(1983) extended the APT of Ross (1976) and Ross (1977) which postulated that with a

factor structure the mean returns are approximately linear functions of the factor

loadings, and provided a unique approach often known as principal components

analysis. This extended approach indicates that when κ eigenvalues (the weights in the

principal components) of the population covariance matrix increase without bound as

the number of securities in the population increases, elements of the corresponding κ

eigenvectors of the covariance matrix can be treated as the factor sensitivities.


Connor and Korajczyk (1988) have shown that Chamberlain and Rothschilds (1983)

findings hold good even for the sample covariance matrix. They have shown that the

eigenvectors can be used instead of statistical factor loadings in the return generating

model for a large (infinitely many assets) economy. This does not necessarily imply

that the eigenvectors can be used in a cross-sectional model of security pricing in a

small (finitely fewer assets) economy.

Beggs (1986) provided an insight into APT operating in a finite economy by using

quadratic preferences and standard regression analysis. He observed that the standard

APT result of a linear relationship between expected returns and the covariances of

returns is approximately true, although it does not hold exactly in a finite economy. He

provided an expression for the error of the approximation and suggested some

computational procedures to keep the error small. However, principal component

analysis is found to be equivalent to factor analysis only when the idiosyncratic risks of

all firms are equal; otherwise the use of factor analysis is less complicated [Shukla and

Trzcinka (1990)].

It is customary to contemplate two approaches that identify factors: factor analysis and

cross-sectional regression analysis. The factor analysis approach isolates factors by

observing common variables in the returns of different securities. These factors are

statistical constructions that represent some underlying sources of risk; that source may

or may not be observable. Cross-sectional regression analysis, on the other hand,

requires that we define a set of security attributes that measure exposure to an


underlying factor and determine whether differences across security returns correspond

to differences in these security attributes [Kritzman (1995)].

As a common guide, factor analysis is used as a method of analyzing APT that begins

by calculating the daily returns of a representative sample of stocks during some period

and then isolates the factors that underpin stock market performance. To isolate the

factors, it computes the correlations between the (daily) returns of each stock and the

returns on every other stock. Then it seeks to identify groups consisting of stocks that

are highly correlated with each other but not with the stocks outside the group.

Similarly, it proceeds to isolate other groups of stocks whose returns are highly

correlated with each other within their own group, until it isolates all the groups that

seem to respond to a common source of risk. Then the factor analysis pursues the task

of identifying the underlying sources of risk for each group. Initially, it relies on

intuition to identify the factor that underlies the common variation in returns among

stocks. Then it tests the intuition. In doing so, this approach defines a variable that

serves as a proxy for the unanticipated change in the factor value [Kritzman (1995)].

Factor analysis looks at covariation in returns and attempts to identify the sources of

this covariation, whereas cross-sectional regression analysis requires specification of

the sources of return covariation and attempts to affirm that these sources do indeed

correspond to differences in return. Based upon intuition and prior research, researchers

infer attributes, rather than factors, that correspond to differences in stock returns. Once

a set of attributes is specified, a measure of sensitivity to the common sources of risk

can be determined. The process regresses the returns across a large sample of stocks


during a given period, say a month, on the attribute values for each stock as of the

beginning of the month. Then it repeats this regression over many different periods. If

the coefficients of the attribute values are not zero and are significant in a sufficiently

high number of regressions, this approach concludes that differences in returns across

the stocks relate to differences in their attribute values [Kritzman (1995)]. According to

this approach, a securitys return in a particular period equals:

Ri = α + λ1 bi1 + λ2 bi2 + ……… + λn bin + εI (2.11)

where Ri is the return of security i; α is a constant; λ1, λ2, . λn are marginal returns to

attributes 1, 2, .n respectively; bi1 is the attribute 1 of security i; bi2 is the attribute 2

of security i,; bin is the attribute n of security i; and εi is the unexplained component

of security is return. It is not necessary for the coefficients in the above formula to be

significantly positive or negative on average over all regressions. In some periods, there

may be positive returns associated with an attribute, and in some other period there may

be negative returns associated with an attribute. Consequently, the average value for a

coefficient over many regressions may be zero. Nonetheless, the attribute would still be

important if the coefficient were not zero in a large number of regressions. One can

measure the extent to which a coefficient is significant in a particular regression by its

t-statistic.

Kim and Lee (1995) presented the APT with the assumption that k-linear factor models

generate random returns on any set of assets:


Rit = Ei + 1

k

k=∑ bik fkt + εit, i = 1,N, t = 1,T (2.12)

where Ei is the expected return on the ith

asset; bik is the sensitivity of the return on asset

i to factor fkt; fkt is a mean zero common factor to the return of all assets under

consideration; and εit is the nonsystematic idiosyncratic error to the ith

asset with

E(ε1tƒ1t,…ƒkt) = 0, Cov (ε1t, ƒkt) = 0 (2.13)

and

Ψ = Cov (ε1t,…εkt )′ = diag ( )1

2 2,.....

Nε εσ σ (2.14)

In vector notation,

Rt = E + Bft + εt (2.15)

where Rt = (R1t,RNt)′; E = (E1,EN)′; ft = (f1t,fkt)′; εt = (ε1t, εNt)′; B = (b1,bk);

and bk = (b1k,bNk)′. The idiosyncratic error terms are assumed to all equal zero (that

is, nonexistent) in the principal component analysis, whereas they exist in the factor

analysis [Kim and Lee (1995)].

More recently, Zhou (1999) has suggested models, in line with both the latent and pre-

specified factor schools, for consideration when using the generalized method of


moments for testing APT. When factors are pre-specified variables, he assumed M pre-

specified observable factors X1, X2, XM and allowed returns to be generated by

factors in the following linear form:

rit = αi + βi1 Χ1t + … + βiM ΧMt + εit i = 1,…N (2.16)

where εit is the model disturbance with a zero mean conditional on available

information. It can have conditional heteroskedasticity as shown by Hansen (1982).

Since the factor selection procedure may include more variables than necessary, some

of the variables could be correlated and hence redundant.

Obtaining the minimum number of orthogonal factors that are necessary depends on the

rank of the regression coefficient matrix B = (βij), N × M formed by the betas. If rank

B=(βij) = K< M, there exists an N×K rank matrix A and K×M matrix C such that B is their

product. This means H0: B = AC; A: N × K; and C: K × M and

rit = αi + Ai1 ƒ1t + … + AiK ƒKt + εit i = 1,…N (2.17)

where ƒ1t ƒKt are new factors linear combinations of the pre-specified ones:

ƒkt = Ck1 X1t + … + CkM XMt, k = 1, … K (2.18)


Thus, the K-factors are orthogonal and out of the M individual factors, K-linear

combinations are sufficient to explain returns.

In the case of a model where factors are inherently latent, Zhou (1999) begins with a

one-factor model, which is extendable to multi-factor or K-factor models.

Rit = αi + βi ƒt + εit, i = 1, … N (2.19)

where Rit is the return of asset i in excess of the risk-free rate, ƒt is the latent factor and

εit is the model residual with zero mean. Without a loss of generality, ƒt is assumed to

have zero mean and unit variance. Its realizations are unobservable directly from

market data. As the factor is unknown, it may be extracted through the applications of

Connor and Korajczyks (1986) asymptotic principal component approach and the

standard factor analysis see, for example, Seber (1984). It is usually difficult to

relate the estimated factor to X1,XM (a set of M given observable economic or

financial variables) which have zero expected values. To overcome this, Zhou (1999)

projected ƒt onto X1, XM to obtain

ƒt = C1 X1t + … + CM XMt + υt (2.20)

where υt is the projection error which is uncorrelated with X1, XM, that is, Ε[Χm εit] =

0. This is not restrictive because εit measures the idiosyncratic risk, whereas both ƒt and

the observable factors are pervasive risks that are common to all assets. The advantage

of the above projection formula is that latent factors are modelled explicitly as a linear


function of observable factors plus white noise. By estimating the parameters, C1CM,

the contributions of the known variables to the latent factor can be estimated.

Combining the two equations, we get:

Rit = αi + βi (C1 X1t + … + CM XMt) + uit, where uit = βi υt + εit (2.21)

This can be written in vector form as:

Rt = α + BXt + ut (2.22)

where Rt is an N-vector of the returns; α , Xt and ut are defined similarly; and B is an

N×M matrix of regression coefficients, B = βC′ with β = (β1,…βN)′, N×1; and C =

(C1,…CM)′, M×1.

When applying this method to analyze APT, Zhou (1999) assumes that the returns on a

vector of N assets relate to K latent factors by a K-factor model. Thus, the equation for

APT becomes:

rit = Ε[rit] + βi1 ƒ1t + … + βiK ƒKt + εit i = 1,…N, t=1,T (2.23)

where rit is the return on asset i at time t; ƒKt the kth

factor at time t; εit the idiosyncratic

factor of asset i at time t; βiK the factor loading of the kth

factor for asset i; N the number

of assets; and T the time periods. This equation is equivalent to the following:


rt = Ε[ rt ] + βƒt + εt (2.24)

where rt is an N×1 vector of returns, Ε[rt] is the expected returns conditional on ƒt; and

β, N×K, ƒt and εt are defined accordingly. The standard assumptions for the factor

model are: Ε[ƒt] = 0, Ε[ƒt ƒ′] = Ι, Ε[εt|ƒt] = 0, Ε[εt ε′ t|ƒt] = Σ.

With the factor model, the classic APT is derived under the assumption that the residual

covariance matrix Σ is diagonal [Shanken (1992)], although this assumption has been

relaxed in the study of Zhou (1999) by a much weaker one where Σ does not need to be

a diagonal matrix as long as the matrix is positive definite.

Derived APT

Factor Pricing Restrictions in APT

The APT pricing process is often derived from the factor models of equity returns as

under:

λλι Β+≈ 0][ nrE (2.25)

where λ0 is a constant; λ is a k-vector of factor risk premia; and ιn is an n-vector of

ones. The approximate equality sign ≈ reflects the fact that APT holds only

approximately. For APT to become an accurate pricing model, on average, it requires

that the economy possess a large number of traded assets [Connor and Korajczyk,


(1995)]. The derivation of APT follows various approaches, namely, exact pricing in a

noiseless factor model; approximate nonarbitrage, competitive equilibrium derivation;

mean-variance efficiency and exact factor pricing; and pricing dynamics.

Exact Pricing in a Noiseless APT

A noiseless factor model is one with no idiosyncratic risk, where [ ]r E r f= + Β . This is

of course a strong restriction on asset returns. Yet it is useful for the intuition that APT

provides. Here, an exact arbitrage argument is sufficient. It does not require a large

number of assets, and there is no approximation error in the APT pricing restriction to

satisfy Ross (1977). To derive APT, simply project E[r] on ιn and B to obtain

projection coefficients λ0 and λ, and a projection residual vector η:

ηλιλ +Β+= nrE 0][ (2.26)

The projection residual properties provide 0η ′Β = and 0nη ι′ = . Viewing the n-vector,

η, as a portfolio of asset purchases and sales, the portfolio will have zero cost structure.

If this portfolio possessed positive expected returns, it would represent an arbitrage

opportunity. This condition is inconsistent with even the weakest type of pricing

equilibrium. The expected payoff of the portfolio here is [ ]E rη η η′ ′= and this can be

zero if η = 0. Thus, the pricing model of Ross, 0[ ] nE r t λ λ≈ +Β , holds with equality in

the absence of arbitrage opportunities.


Connor and Korajczyk (1995) combined the noiseless factor model, [ ]r E r f= +Β , with

the Ross pricing result, 0[ ] nE r ι λ λ= +Β , to show that

)(0 λλι +Β+= fr n

(2.27)

where a unit-cost portfolio is any collection of assets such that 1=′ nιω . The payoff to

a unit-cost portfolio is a portfolio return. A unit-cost portfolio with 0=Β′ω (that is, no

factor risk) has a risk-free return equal to λ0. As long as the (k+1)×n matrix [ι n, B] has

the rank k+1, one can construct such a portfolio, and identify λ0 as the risk-free return.

A unit-cost portfolio with a unit sensitivity to factor j and zero sensitivity to the other

factors will have expected returns λ0+λ j. Hence, the k-vector λ measures the risk

premium per beta-unit of each factor risk. This risk premium depends on factor

rotation, which affects the scales of the betas [Connor and Korajczyk (1995)].

Approximate Nonarbitrage Pricing Theory

The argument of the noiseless APT is extended to a strict or approximate factor model

case, where the pricing relationship holds approximately in an economy with many

assets. Connor and Korajczyk (1995) combined the original formulation of Rosss

(1976) APT with some refinements of Huberman (1982) and considered the orthogonal

price, η, as in the noiseless model above. Accordingly, the nth

portfolio consists of

holdings of the first n assets in proportion to their price deviations, scaled by the sum of

squares of these deviations, as under:


( )

nn

n n

ηωη η

= ′

(2.28)

Using the same steps as in the noiseless case, one can show that the cost of each of

these portfolios is zero, the expected payoff of each is one, and the variance is

2( )n n n n nVη η η η−′ ′ . Using the property of maximum eigenvalues, we can have

( )n n n n n nV Vη η η η′ ′≤ , where n

V denotes the maximum eigenvalue of V n. Thus, the

portfolio variance is less than or equal to 1( )

n n nVη η −′ . This is the case in an economy

with a large, but finite, number of assets.

For an economy with an infinite number of assets, Chamberlain (1983) extended the

model by way of expanding the space of portfolio returns to include infinite-

dimensional linear combinations of asset returns, as under:

nn

nrr′

=→∝

ωω lim (2.29)

where rn denotes the n-vector of the first n of the infinite set of assets, and rw defines a

limit portfolio return as the limit of the returns to n-asset portfolios as n tends to

infinity. The limit takes the second-moment norm 2[ ]r E rω ω= . The simple form of

convergent sequence of portfolios is (1/ ,1/ ,...1/ )n n n nω = . This sequence of portfolio

weights converges to a zero vector. Yet, the limit portfolio of this sequence is a well-

defined non zero return in some cases. However, limit portfolio returns can be perfectly


diversified, that is, they have idiosyncratic variance of exactly zero [Connor and

Korajczyk (1995)].

Ross (1978b) and Kreps (1981) developed an exact nonarbitrage pricing theory, which

is not same as APT. Their approach suggested that in the absence of exact arbitrage

opportunities there must exist a positive, linear pricing operator over state-contingent

payoffs. Chamberlain and Rothschild (1983) showed that in an infinite-asset model the

approximate APT is an extension of Ross-Krepss exact nonarbitrage pricing theory.

Reisman (1988) extended the Chamberlain and Rothschild (1983) result to general

normal linear spaces. He showed that APT can be reduced to an approximation.

Competitive Equilibrium Derivations in APT

Imposing competitive equilibrium, an alternative to the approximation approach can

also derive APT. This gives a stronger pricing approximation, and links the APT with

other equilibrium-based pricing models. Considering a risk-averse investors utility

function, u(.), for end-of-period wealth, and the approximate factor model of returns

that includes the additional assumption that idiosyncratic risks are conditionally mean-

zero, gives the following factors:

0]|[ =fE ε (2.30)

If W0 is the investors wealth at time 0, then in a competitive equilibrium, the following

first order portfolio optimization condition would hold for every investor:


γιω nrrWuE =′′ ])([ 0 , (2.31)

for some positive scalar γ. For simplicity, letting W0 = 1, and inserting

[ ]r E r f ε= +Β + into 0[ ( ) ] nE u W r rω ι γ′ ′ = as well as separating three additive terms

and bringing constants outside, the expectations operator gives:

)]([

])([][ 0

ruE

ruErE

n

ωεωλλι

′′′′

+Β+=′ (2.32)

where λ0= / [ ( )]E u rγ ω′ ′ and [ ( ) ] / [ ( )]E u r f E u rλ ω ω′ ′ ′ ′= − . The competitive equilibrium

derivations of the APT assume a sufficient set of conditions so that the last term of the

above equation,[ ( ) ]

[ ( )]

E u r

E u r

ω εω

′ ′′ ′

, is approximately a vector of zeros.

Mean-Variance Efficiency and Exact Factor Pricing

The mathematics of mean-variance efficiency are often employed to reiterate the APT

pricing restriction. This is useful for economic modelling purposes. Considering a set

of unit-cost portfolios as linear combinations of n-vectors of asset returns, r, for any

portfolio return, rω, one can define the one-factor projection equation as:

ε++= bfrEr ][ (2.33)


where [ ]f r E rω ω= − . A single-beta-pricing model holds with respect to the above

equation if:

λλι brEn += 0][ (2.34)

for some scalars λ0 and λ. Defining a mean-variance efficient portfolio as a unit-cost

portfolio that minimizes variance subject to [ ]E r cω ′ = for some c, one can show

that 0

[ ] nE r bι λ λ= + is both the necessary and sufficient condition for the mean-

variance efficiency of ω. Thus 0[ ] nE r bι λ λ= + is equivalent to providing that ω is

mean-variance efficient.

This relationship between mean-variance efficiency and beta pricing can be extended to

a multi-beta model with a given n-vector of returns r. For any set of k portfolio returns,

rω1, rω2,…, rωk, with the projection equation [ ]r E r f ε= +Β + (where f j = rω j E[rω j] for

j =1,2,,k), linear pricing with respect to these factor-mimicking portfolios takes the form

0[ ]n

E r ι λ λ= + Β .

Dynamics in Asset Pricing

Dynamic versions of APT usually specify an exogenous factor model for the cash flows

(dividends) paid by firms while deriving the factor model for the prices of securities

endogenously. Often, discrete time dynamic models are useful to explain asset pricing

[Jagannathan and Viswanathan (1988); Connor and Korajczyk (1989, 1995)].


Even if factor loadings (betas) for the cash flow process are time invariant, the betas of

asset returns (relevant to factor-mimicking portfolios) will be functions of the current

information set. In the static APT one can replicate the priced payoff from a security

with the risk-less asset and factor-mimicking portfolios. Jagannathan and Viswanathan

(1988) showed that in a multi-period economy there exists a different set of riskless

assets for every maturity, that is, a discount bond with that maturity. Thus, although the

risky components of assets payoff are derived by say the one-factor model, asset

returns may follow an infinite factor structure corresponding to a portfolio mimicking

the single factor, plus the returns on discount bonds for every maturity [Connor and

Korajczyk (1989)].

Connor and Korajczyk (1989) developed a multi-period model in which they assumed

that per-share dividends, rather than asset returns, could be used in an approximate

factor model. They observed that expected returns follow the exact APT pricing

restriction at each date. Yet, the general format of their model could not be identified

since the beta coefficients and factor risk premium varied through time. Thus, they had

to add new conditions that give a statistically identified model. Among other works in

this field, extensions of dynamics into the continuous-time economy, intertemporal

equilibrium asset pricing and intertemporal capital asset pricing are notable

contributions to the literature [Reisman (1992a); Ohlson and Garman (1980);

Chamberlain (1988); Merton (1973); and Connor and Korajczyk (1989, 1995)].

In brief it is understood that factor analysis does not actually observe underlying

factors; rather it identifies the common sources of attributes or aptitudes (treating them


as factors) that help in explaining the performances of variables under study. Thus,

factors derived through factor analysis are not always amenable to appropriate

interpretation [Kritzman (1995)]. Parallel to factor analysis, principal component

analysis has been used by some researchers to identify the factors that influence stock

returns in finance. In this regard eigenvalues are calculated to construct relevant

eigenvectors which are similar to factors in factor analysis.

Summary

This chapter has reviewed finance theories that are related to security market behaviour

and pricing mechanisms. Both the popular theories of the capital asset pricing model

(CAPM) and APT are found useful for security market analyses or to describe stock

returns in an efficient market. Still, APT is popular as a superior alternative to the

CAPM. There are two forms of APT: the nonarbitrage pricing theory of Ross, and the

equilibrium APT. Rosss APT is more popular. Traditionally, the testing of APT is

done through factor analysis, as most researchers represented APT as a k-linear factor

model, where the number of common factors, k, is unknown. The Roll and Ross (RR)

method of testing APT has been popular within traditional applications. Our

contribution in this chapter has been to comprehensively review the asset pricing

literature from a theoretical perspective.


CHAPTER 3

EMPIRICAL FACADE OF ASSET PRICING THEORY

Generally, Arbitrage Pricing Theory (APT) indicates that an assets expected return is a

linear function of a set of sensitivity coefficients to systematic or common factors. The

number of common factors, k, and their nature, are not known. Hence, tests of the APT

model are often difficult to design. To avoid the confusion that arose in the literature

about the relationship between the theoretical underpinnings of APT and its empirical

tests, Dybvig and Ross (1985) noted that the empirical APT differs from the theoretical

APT. Yet, in deriving the empirical APT, one has to understand the underlying

theoretical premise of APT. The generalized theoretical APT states that asset returnsiR%

are generated by a factor model, 1

k

i i ij j i

j

R E β ε=

= + ∂ +∑ %% %, where

j∂% is a vector of systematic

risk factors that influence asset returns; iβ is a vector of factor loadings on asset i; Ei is

the expected return on asset i; and iε is the idiosyncratic noise term associated with

asset i. When assumed that iε% is independent across assets,

iε% is independent of the

factors with a mean zero, and that the factorsj∂% have also mean zero and that variances

exist, the empirical APT can be derived from the theoretical APT as suggested by

Dybvig and Ross (1985). Thus, the theoretical APT simply asserts that the new assets

expected returns are linear in factor loadings in the following form:

∑

=

+=k

j

ijjirE

1

βλ (3.01)


where r is a constant that equals the riskless rate of return if there is a riskless asset, and

λ is a vector of risk premia. The arbitrage in APT comes from the simple proof that

the theoretical version 1

k

i i ij j i

j

R E β ε=

= + ∂ +∑ %% % implies the empirical version

1

k

i j i j

j

E r λ β=

= + ∑ in the absence of arbitrage alone, for the case in which all the

iε% s

are zero. Customarily, the derivation of APT involves establishing that theiε% s can be

neglected when pricing assets. Most derivations are based on the intuition that the

idiosyncratic error terms represent diversifiable risks and therefore should not affect

asset pricing.

A good number of empirical studies, including Gehr (1978), tested the efficacy of APT

models without attempting to identify the risk factors. In these studies, portfolio returns

were decomposed using factor analysis. To test the ability of the factors to explain

mean returns, the factor loadings derived from factor analysis were used as independent

variables in a cross-sectional regression with mean portfolio rates of return.

Empirical Episodes of APT

The original APT of Ross (1976) hypothesized that the cross-sectional distribution of

expected returns of financial assets could be approximately measured by their

sensitivities, usually called factor loadings,κ, to k unknown economic factors.

Chamberlain and Rothschild (1983) extended Rosss (1976, 1977) APT, which

postulated that with a factor structure the mean returns are approximately linear


functions of the factor loadings. Rothschild (1983) accordingly provided a unique

approach, known as the principal components analysis.

Connor and Korajczyk (1988) have shown that Chamberlain and Rothschilds (1983)

findings hold good even for the sample covariance matrix. They have shown that

eigenvectors instead of statistical factor loadings can be used in the return generating

model for a large (infinitely many assets) economy.

Beggs (1986) provided an insight into APT operating in a finite economy by using

familiar quadratic preferences and standard regression analysis. He observed that the

standard APT result of a linear relationship between expected returns and the

covariance of returns is approximately true, although it does not hold exactly in a finite

economy. Beggs (1986) provided an expression for the error of the approximation,

suggesting some calculation procedures to keep the error small. However, principal

component analysis is found to be equivalent to factor analysis only when the

idiosyncratic risks of all firms are equal; otherwise the use of factor analysis is less

complicated [Shukla and Trzcinka (1990)].

McGowan and Francis (1991) used both multivariate analysis techniques and principal

component analyses in their study. They exploited the ability of multivariate statistical

analysis techniques (like factor analysis and principal component analysis) to discover

interesting empirical insights dependent upon the size and heterogeneity of the sample

and the approach of data analysis. Their research aimed at ascertaining the principal

components of stock price fluctuations as well as the principal components of


macroeconomic fluctuations during simultaneous sample periods. Then the

macroeconomic principal components were compared to principal components of stock

prices in an effort to determine primary relationships. To analyze the relationships, the

authors selected a highly diverse sample of macroeconomic data (consisting of 95

variables) in conjunction with the highly diverse sample of stock prices.

McGowan and Francis (1991) grouped each stock market index (consisting of 86

variables) under 10-factor classifications for which the index had the highest factor

loading. Their factor loading value (provided in the parentheses in Table 1) indicates

which industry indices were the most significant in explaining the stock price returns

for a factor. Thus, their principal component analysis grouped together those industries

that are most responsive to the same factor, that is, the risk component. They defined

their 10 industry factors into three broad groups, namely, primary, secondary, and

tertiary. The primary factor is an extracted factor composed of stock market indices that

had their highest factor loading on that factor. The secondary factor is a factor for

which no industry had its highest factor loading. That is, it was composed of indices

that were more highly related to a primary factor yet had a sufficient additional

common relationship with each other to be included in another grouping. The

remainder of the factors are tertiary factors, which had only one large industry factor

loading. Factors one to six, and nine were primary factor; factors seven and 10 were

secondary factors; and factor 8 was a tertiary factor. Details are presented in Table-3.1:


TABLE 3.1

Factor 1

Foods (0.52); Textile products (0.59); Textile-apparel manufacturers (0.79); Home furnishings (0.69); Containers-

paper (0.62); Publishing (0.70; Building materials-composite (0.73); Building materials-roofing & wallboard (0.62);

Tires & rubber goods (0.64); Shoes (0.71); Containers-metal & glass (0.52); Building materials-cement (0.61); Metal

fabricating (0.67); Building materials- GTG & PLMBG (0.54); Building materials-air conditioning (0.73); Machine

tools (0.63); Pollution control (0.61); Auto merch mach (0.61); Electric household appliances (0.53); Automobiles

(0.62); Automobile- except (0.65); Automotive-trucks & parts (0.73); Aerospace (0.62); Mobile homes (0.54); Toys

(0.70); Leisure time (0.78); Air transport (0.51); Air freight (0.56); Radio-TV broadcasters (0.72); Retail stores-

composite (0.56); Retail stores-discount (0.75); Retail stores-food chains (0.54); Investment companies (0.56);

Homebuilding (0.73); Hotels-Motels (0.80); Entertainment(0.62);Conglomerates (0.68)

Factor 2

Beverages-brewers (0.46); Beverages-distillers (0.48); Beverages-soft drinks (0.72); Tobacco (0.52); Drugs (0.83);

Hospital supplies (0.70); Soaps (0.75); Cosmetics (0.78); Office & business equipment (0.73); Office & business

equipment IBM (0.73); Electric & electronic-major (0.52); Electronic equipment (0.63); Restaurants (0.67)

Factor 3

Metals-miscellaneous (0.63); Coal-bituminous (0.63); Forest products (0.55); Paper (0.71); Chemicals (0.64); Steel-

except USS (0.76); Steel (0.77); Copper (0.62); Aluminum (0.75); Machinery-agriculture (0.56); Machinery-

construction & materials handling (0.55); Machinery-industrial & specialty (0.61); Rail road equipment (0.44); Rails

(0.52)

Factor 4

Telephone (0.71);Telephone-except ATT (0.64); Electric power (0.69); Natural gas- distribution (0.63); Natural gas-

pipe lines (0.48); Personal loans (0.54); S7L holding companies (0.60); Life insurance (0.58); Multiline insurance

(0.52); Property & casualty insurance (0.54)

Factor 5

Oil-composite (0.81); Oil-crude producers (0.62); Offshore drilling (0.50); Oil-intec domestic (0.75); Oil-intec

international (0.73); Oil well equipment & service (0.54)

Factor 6

Sugar refiners (0.68)

Factor 7

Offshore drilling (-0.39); Tires & rubber goods (0.34); Pollution control (-0.37); Automobile (0.43); Automobiles-

except (0.36)

Factor 8

Banks-NYS (0.46); Banks-outside NYS (0.40)

Factor 9

Gold mining (0.86)

Factor 10

Truckers (0.40); Air transport (0.37); Air freight (0.40)

Source: Adapted from McGowan and Francis (1991).


Connor (1995) presented an overview of the empirical procedures for the basic three

types of factor models, namely, macroeconomic, statistical, and fundamental models.

Input requirements, outputs and relevant estimation techniques corresponding to each

type of model are presented in the Table 3.2:

TABLE 3.2

Overview of the Empirical Procedures of Factor Models Model Type Inputs Estimation Technique Outputs

Macroeconomic Security Returns

Economic Variables

Time series regression Security factor betas

Statistical Security Returns Iterated time-series or Cross-

sectional regression

Statistical factors and

Security factor betas

Fundamental Security Returns

Security Characteristics

Cross-sectional Regression Fundamental factors

Source: Connor (1995).

Roll and Ross (1980) conducted their empirical tests of APT using data from individual

equities during the period 1962 to 1972. Their research design followed a two-step

procedure. In the first step, the expected returns and factor coefficients were estimated

from time series data on individual asset returns. The second step used the first stage

estimates to test the basic cross-sectional pricing conclusion. Since APT applies to

subsets of the universe of assets, it does not require a particular choice of a substitute

for the market portfolio, which is required for the capital asset pricing model. They

used data as described in Table 3.3.


TABLE 3.3

Data Description Source Daily Return File: Center for Research in Security Prices, Graduate School of

Business, University of Chicago, US.

Selection Criterion

By alphabetical order into groups of 30 individual securities from those listed on NY

or American Exchanges on both 3 July 1962 and 31 December 1972. The alphabetical

last 24 securities were not used since complete groups of 30 were required.

Basic Data Unit Return adjusted for all capital changes and dividends, if any, between adjacent trading

days, i.e., [ ], , , 1( )/ 1j t j t j tdρ ρ −+ − , where ρ =price, d = dividend, j = security

index, t = trading day index.

Maximum Sample Size

per Security

2619 daily returns.

Number of Selected

Securities

1260 (42 groups of 30 each)

Source: Roll and Ross (1980).

Brown and Weinstein (1983) proposed a new approach for estimating as well as testing

asset pricing models this was in the context of the bilinear paradigm of Kruskal

(1978). The bilinear paradigm suggests that testing of APT or asset pricing models does

not require that the factors common across securities have a multivariate normal

distribution. The authors found the approach relatively simple and general compared to

others. They described a bilinear model as the matrix of return observations, R = λ0 e ′ +

Ak Bk + U, where e is a column vector of ones, which can be re-written as R = AB + U.

This model generates observed returns in the context of an arbitrage pricing model with

a pre-specified k-number of factors. Thus, a simple test of the theory would be to check

whether the factor structure, factor prices, and implied risk-free rate given by the matrix

A are constant across groups of securities at each point in time.

Brown and Weinstein (1983) used the same set of data as considered by RR (Roll and

Ross, 1980). They started with 42 groups of 30 stocks each, arranged alphabetically,


and considered the daily returns (including dividends) for the period from 3 July 1962

to 31 December 1972. To be eligible for inclusion in a group, the stocks had to be listed

on one of the two major US stock exchanges on both the starting and ending dates for

the period. They combined two consecutive RR groups to form each of their 60 security

groups. They thus obtained 21 groups of 60 securities each. The results obtained

through the application of their approach of factor analyses for 30 security groups were

not identical with those of RR, for two reasons. First, their requirements were different

in the sense that they performed an analysis for 60 security groups to describe common

observations across 60 securities as opposed to the 30 securities of RR. Thus, each of

their runs used fewer observations than RR. Secondly, the results differed because they

used different data sources to RR.

Chen, et al. (1986) indicated that the systematic forces that influence US equity returns

are those that change discount factors, k, and expected cash flows, E(c). Since we are

only concerned with business institutions, stock prices can be defined as expected

discounted dividends p = ( )E c

k. The discount rate is an average of rates over time, and it

changes with both the level of rates and the term structure spreads across different

maturities. Unanticipated changes in the riskless interest rate will therefore influence

pricing. Through their influence on the time value of future cash flows, they will

influence returns. Unanticipated changes in the risk premium will also influence

security returns, because the risk premium is to an extent determined by the discount

rate. On the demand side, real consumption changes owing to the changes in the

indirect marginal utility of real wealth will influence pricing, and often such effects

show up as unanticipated changes in the risk premium.


Chen, et al. (1986) also inferred that expected cash flows change because of both real

and nominal forces. Changes in the expected rate of inflation influence nominal

expected cash flows as well as the nominal rate of interest. The unanticipated price

level change will have a systematic effect. Relative prices usually change with the

general inflation level. There can also be a change in asset valuation associated with

changes in the average inflation rate. Finally, changes in the expected level of real

production affect the current real value of cash flows. Thus, innovations in the rate of

productive activity have an influence on stock returns through their impact on cash

flows. Accordingly, Chen, et al. (1986) constructed two series of variables: a basic

series, and a derived series. Their basic series of variables along with their symbols,

definition/sources are as presented in Table-3.4:

TABLE 3.4

Glossary and Definitions of Basic Series Variables Symbol Variable Definition/Source

I Inflation Log relative of US Consumer Price Index

TB Treasury-bill rate End-of-period return on 1-month bills

LGB Long-term government bonds Return on long-term government bonds

IP Industrial Production Industrial production during month

Baa Low-grade bonds Return on bonds rated Baa and under

EWNY Equally weighted equities Return on equally weighted portfolio of NYSE listed

stocks

VWNY Value weighted equities Return on a value weighted portfolio of NYSE listed

stocks

CG Consumption Growth rate in real per capita consumption

OG Oil prices Long relative of Producer Price Index / Crude Petroleum

series

Source: Chen, et al. (1986).


The derived series of variables considered by Chen, et al. (1986) are as in Table 3.5:

TABLE 3.5

Glossary and Definitions of Derived Series Variables Symbol Variable Definition/Source

MP(t) Monthly growth, industrial production loge[IP(t)/IP(t-1)]

YP(t) Annual growth, industrial production loge[IP(t)/IP(t-12)]

E[I(t)] Expected inflation Fama and Gibbon (1984)

UI(t) Unexpected inflation I(t) E[I(t)|t-1]

RHO(t) Real interest (ex post) TB(t-1) I(t)

DEI(t) Change in expected inflation E[I(t + 1)|t] E[I(t)|t-1]

URP(t) Risk premium Baa(t) LGB(t)

UTS(t) Term structure LGB(t) TB(t-1)

Source: Chen, et al. (1986).

Faff (1988) examined empirically the issues concerning APT using Australian equity

data and employing the approach of Chamberlain and Rothschild (1983). He considered

a sample of 140 equities over 12 years from 1974 to 1985. He encountered problems

associated with missing data. A total number of 157 firms were detected having no

more than four missing observations; 94 firms did not have any missing information;

25 firms had four; 10 firms had three; 23 firms had two; and five firms had one missing

observation. The sample of 140 was achieved by a random selection of eight from 25 in

the group of firms having exactly four missing data points. Values of all missing

observations assigned the appropriate monthly average of available observations for

each affected firm. In his sample, Faff (1988) distributed the firms across industries in

the manner shown in Table 3.6 below:


TABLE 3.6

Distribution of Sample Firms Across Industries ASE Industry Group Number of Firms

1. Metals

2. Solid Fuels

3. Oil & Gas

4. Developers and Contractors

5. Building Materials

6. Electrical, Household Durable

7. Alcohol and Tobacco

8. Food, Household Goods

9. Textiles and Clothing

10. Automotive

11. Chemicals

12. Light Engineering

13. Heavy Engineering

14. Paper and Packaging

15. Banks and Finance

16. Insurance

17. Retail

18. Merchants and Agents

19. Transport

20. Media

21. Property Trust

22. Other Services

23. Miscellaneous, Diversified and Industrials

24. Diversified Resources

18

7

5

7

14

6

3

10

1

3

5

5

7

4

4

4

6

2

5

5

1

9

5

4

Source: Faff (1988).

Faff (1992) undertook a multivariate test of the equilibrium version of APT for the

Australian equity market applying the asymptotic principal component technique of

Connor and Korajczyk (1988). Faffs (1992) study aimed at extending and improving

his 1988 empirical examination of APT on Australian data. He observed that the

Connor and Korajczyk (1988) method performs well in relatively small sub-periods.

It uses a multivariate approach, permits time-varying factor risk premiums, and

incorporates monthly (seasonal) effects. The iterative process of the asymptotic

principal component technique followed by Faff (1992) can be understood from Table 3.7:


TABLE 3.7

The Iterative Process in Asymptotic Principal Component Technique 1. Form the cross-product matrix (Ω) of excess returns.

2. Calculate eigenvectors for the cross-product matrix.

[The first k-eigenvectors represent proxies for the independent variables of

1 1 2 2 .....it i t i t ki kt itr B F B F B F ε= + + + + , where rit = (Rit Rft), the excess return for asset i in period t;

and Fjt = ( )jt jtfγ + = 1,.,k, the realized risk premium plus the factor realization for factor j in period t].

3. For each individual asset in the sample run a regression of excess returns on the first k eigenvectors obtained

and calculate the standard deviation of residuals.

4. Scale the excess returns of each asset by its associated residual standard deviation obtained and form a new

scaled cross-product matrix of excess returns.

5. Repeat steps 2 to 4 until convergence achieved.

Source: Summarised from Faff (1992).

Faff (1992) gathered data from the price relatives file of the Centre for Research in

Finance (CRIF) at the Australian Graduate School of Management. His data set

covered the 165-month period from January 1974 to September 1987, which was

divided into three non overlapping 55-month sub-periods for analysis. Securities were

included in a sub-period sample if they had a complete price relative history in that

period. This produced sample sizes of 303, 158 and 340 for the three sub-periods

respectively. Faff (1992) used value weighted market index as supplied by CRIF, while

he estimated the risk-free rate from a series of monthly observations on 13-week

Treasury Notes. Likewise, he used portfolios rather than individual assets for analytical

convenience.

Hamao (1988) examined APT empirically using Japanese data. He considered

macroeconomic state variables similar to those used in Chen, et al. (1986). He utilized


neither the usual factor analysis nor mimicking portfolios analysis in deriving factors

that influence asset pricing in APT. Rather, he derived variables from the basic

economic theory of asset pricing that is applicable regardless of the location of the

markets and that reflects different magnitudes of parallel but different economy specific

economic conditions. Since the Japanese economy is heavily dependent on trade,

Hamao (1988) considered factors related to international trade in addition to basic

economic variables. He used the monthly return data on TSE Section I for the period

January 1975 to December 1984. The data were gathered from the Nomura Research

Institute. Out of 1066 companies, some were excluded because of missing

observations. The number of stocks excluded from the data series varied from month to

month. They varied from 53 to 188. For convenience, stocks were grouped into 20

equally weighted portfolios, with an approximately equal number of securities sorted

by size (that is, price to stock times outstanding volume) of a company at the end of the

previous month.

To determine the macroeconomic state variables, Hamao (1988) looked for exogenous

macro-variables that affect the future cash flows or the risk adjusted discount rate of

companies. He did not include equity related variables since the study aimed to identify

macroeconomic forces that only influence the stock market. Accordingly, Hamao

(1988) considered seven variables: industrial production, inflation, risk premium, term

structure, foreign exchange, market indices, and oil prices.

The structural specifications and/or definition of a priori variables considered by

Hamao (1988) are provided in Table 3.8.


TABLE 3.8

Structurally Specified Priori Variables A Priori Variable Structural Specification

Industrial Production

The monthly index of production, IP(t), obtained from Ministry of International

Trade and Industry statistics. The growth rate of industrial production:

( ) ln ( ) ln ( 1)MP t IP t IP t= − −

It was moved forward by one month since MP(t) actually reflects the production

change in month t-1 (at least in part). The average MP over the previous five years

for the same month was subtracted from the MP series to yield the variable MPSA(t).

Inflation

Used the Fama and Gibbons (1984) methodology as in Chen, Roll and Ross to derive

the expected inflation variable. Following the Fisher theorem, the one month interest

rate GR(t-1) observed at the end of month t-1 applicable to month t was broken down

into: an expected real return for month t and expected inflation rate:

( 1) [ ( ) | 1] [ ( ) | 1]GRt E p t t E I t t− = − + −

With some modification and adjustments in the process of estimation, monthly

inflation variables were constructed as:

( ) ( ) [ ( ) | 1]UI t I t E I t t= − − and

( ) [ ( 1) | ] [ ( ) | 1]DEI t E I t t E I t t= − − −

where UI is unanticipated inflation and DEI is the change in expected inflation. If the

inflation forecast is based on information other than the previous forecast errors, DEI

would have different information from UI.

Risk Premia

Changes in the risk premium in the financial market affects the value of an asset

through changes in discount rates. Through a process of treating the spread between

government and corporate bonds yields of long-term and short-term maturity or high-

grade and low-grade bonds yield differentials; and well-diversified managed

portfolio, the constructed risk premia variables are:

( ) ( ) ( )UPREL t EL t LGB t= − and

( ) ( ) ( )UPRMF t MF t LGB t= −

where EL(t), LGB(t), and MF(t) are the returns on electricity bonds, long-term

government bonds, and the managed funds respectively.


Term Structure

To capture the effects of changes in interest rates, the return difference between long

bonds and Gensaki considered. The constructed term structure variable is:

( ) ( ) ( 1).UTS t LGB t GRt= − −

The interpretation here is that if UTS is positive, then long bonds have risen implying

that their yield has fallen which lowers the slope of the yield curve.

Foreign Exchange

To capture the economys heavy orientation towards international trade, the volatility

in foreign exchange rates were considered as having substantial systematic effects

upon Japanese equities. With appropriate assumptions concerning risk-neutrality,

efficiency of the forward exchange market, and forecasting of spot rate, the exchange

rate change variable is:

1( ) ln lnt t tUYEN t F S−= −

Additionally, the terms of trade have some direct effect on the economy that

influences its exchange rate. Considering terms of trade (TT) data, and the definition

of TT = (Price index of export goods)/(Price index of import goods), the change in TT

is:

( ) ln ( ) ln ( 1).DTT t TT t TT t= − −

Market Indices

To capture unexpected shocks to the economy, market indices were included. The two

market indices included in the analysis are: return on the value weighted TSE-I index

including dividends, VW(t); and return on the equally weighted TSE-I index including

dividends, EW(t).

Oil Prices

Since the Japanese economy is heavily dependent on foreign oil, the price of oil were

included as a systematic factor influencing the Japanese stock market. The oil price

(growth) variable, OG, constructed as the monthly log difference of the Arabian Light

Spot price translated into Japanese yen using month-end spot exchange rates.

Source: Derived from Hamao (1988).

Fama and French (1992a) studied the joint roles of the market beta, firm size, E/P,

leverage, and book-to-market equity in the cross-section of average stock returns. Their

results suggested two empirically determined variables, the size and book-to-market

equity, which explained satisfactorily the cross-section of average returns on the

NYSE, AMEX, and NASDAQ stocks for the period 1963 to 1990.


Later, Fama and French (1993) extended Fama and French (1992a) in three ways. First,

they expanded the set of asset returns for explanation. Secondly, they expanded the set

of variables to explain returns. Finally, they employed a different approach to testing

asset pricing models. Monthly returns on stocks and bonds were regressed against the

returns on a market portfolio of stocks and mimicking portfolios for size, book-to-

market equity, and term structure risk factors in returns. They used the time series

regression approach of Black, Jensen, and Scholes (1972). In their explanatory

variables of the time series regression, they included the returns on a market portfolio

of stocks and mimicking portfolios. They sought explanations for the returns on

government bond portfolios in two maturity ranges, corporate bond portfolios in five

rating groups, and 25 stock portfolios formed based on size and book-to-market equity.

Hughes (1985) tested APT using monthly security returns for Canadian data. He found

the existence of multiple factors in generating Canadian security returns for the period

1971 to 1980. His empirical procedures include classical factor analysis. His

formulated minimum variance portfolios attempt to derive the time series of returns on

general economic factors, sensitivities of returns for each of 220 firms to that of each

factor, and expected returns on the factors. At least 12 common factors were found to

be those which generate Canadian security returns. Out of the 12 factors, three to four

factors had statistically significant risk premia. Hughes generated an APT functional

relationship based on the notion that all individuals believe that security returns are

generated by the same small number of common factors.


Dynamic versions of APT usually specify an exogenous factor model for the cash flows

(dividends) paid by firms while deriving the factor model for the prices of securities

endogenously. Often, discrete time dynamic models are useful to explain asset pricing

[Jagannathan and Viswanathan (1988); Connor and Korajczyk (1989, 1995)]. Even if

factor loadings (betas) for the cash flow process are time invariant, the betas of asset

returns (relevant to factor-mimicking portfolios) will be functions of the current

information set. In the static APT one can replicate the priced payoff from a security

with the risk-less asset and factor-mimicking portfolios. Jagannathan and Viswanathan

(1988) showed that in a multi-period economy there exists a different set of riskless

assets for every maturity, that is, a discount bond with that maturity. Thus, although the

risky components of an assets payoff are derived by, say, a one-factor model, asset

returns may follow an infinite factor structure corresponding to a portfolio mimicking

the single factor, plus the returns on discount bonds for every maturity [Connor and

Korajczyk (1989)].

Connor and Korajczyk (1989) developed a multi-period model in which they assumed

that per-share dividends, rather than asset returns, could be used in an approximate

factor model. They observed that expected returns follow the exact APT pricing

restriction at each date. Yet, the general format of their model could not be identified

since the beta coefficients and factor risk premium varied through time. Thus, they had

to add new conditions on preferences and the stochastic process for dividends that give

a statistically identified model. Among other works in this field, extensions of

dynamics into the continuous-time economy, intertemporal equilibrium asset pricing

and intertemporal capital asset pricing are notable contributions to the literature


[Reisman (1992a), Ohlson and Garman (1980), Chamberlain (1988), Merton (1973),

and Connor and Korajczyk (1989, 1995)].

Aitken, et al. (1996) studied the Australian trading system. They found price clustering

pervasive, tending to follow an overall pattern somewhat similar to that found in US

security markets. They noticed that clustering resulted from imprecise beliefs or

haziness about firm value and firm conventions. Thus they found that the clustering

increases with the price of stock (reflecting imprecision in beliefs about firm value) and

higher market-wide volatility, own stock volatility, trade size, and the size of bid-ask

spread. Clustering is lower when price discovery is likely to be more efficient.

Brailsford and Easton (1991) examined the impact of the seasonality factor on

Australian equity returns for the period 1936 to 1957. Their major finding was that

equity returns in January are consistently higher than returns in any other month, and

that returns in February and June are consistently lower than returns in other months.

Also, the returns in July were higher, and in March were lower. However, January,

February and June were significant in their study.

Easton and Faff (1994) conducted a study of the robustness of the day-of-the-week

effect in Australia. Their results showed that sample size could distort the interpretation

of classical test statistics unless the significance level is adjusted downward. They

noticed that the Australian day-of-the-week effect was independent of that of US.


Faff and Heaney (1999) analyzed the relationship between inflation and equity returns

in Australia over the period January 1974 to March 1996. Their analysis was based on

monthly and quarterly data and they used value weighted equity indices at both the

aggregate market and industry level. Three price indices, the quarterly consumer price

index, the manufactured materials used index, and the manufacturing articles produced

index, both as monthly and quarterly values, were used to measure inflation. The result

showed the impact of expected inflation on industry returns varied considerably over

three sub-period observations. Changes in government inflation policy appeared to

have the greatest impact on expected company inflation in Australia.

Faff and Brailsford (1999) investigated the sensitivity of Australian industry equity

returns to an oil price factor over the period 1983 to 1996. They employed an

augmented market model to establish the sensitivity. The important findings were as

follows. First, beyond the influence of the market, they detected a degree of

pervasiveness of an oil price factor across some Australian industries. Secondly, oil

price sensitivity was found to be significantly positive in the oil, gas and other

diversified resources industries. Similarly, they found significant negative oil price

sensitivity in the paper and packaging, and transport industries. They observed that

long-term effects persist in the market, although some firms passed on oil price changes

to its customers or hedged the risk.


Akin Methods

Analyses of the factor structure of systematic risks in security markets returns actually

predate the APT. In addition to the pricing implications, the need for describing the

covariance structure of asset returns, Σ, becomes significant in the literature [Connor

and Korajczyk (1995)]. The covariance matrix of asset returns is a major component of

portfolio optimization problem. Estimation of the unrestricted covariance matrix of n

securities requires the estimation of n×(n+1)/2 distinct elements. The single-index or

diagonal model of Sharpe (1963) postulated that all of the common elements of returns

were due to assets relationship with the index. Thus, only 3×n parameters needed to be

estimated: n betas relative to the index, n unique variances, and n intercept terms. This

approach reduced much of the noise in estimating Σ. The single-index model can be

viewed as a strict one-factor model with a pre-specified factor. Specifically, the single-

index model does not describe all of the common movements across assets, which

means the residual matrix is not diagonal. On the other hand, with k factors there are

only n×(k+2) parameters to estimate: n× k betas, n intercepts or means, and n unique

variances.

If one becomes primarily interested in the evidence regarding the pricing implications

of APT, one main implication is that expected returns on assets are approximately

linear in their sensitivities to the factors, that is, 0[ ] nE r ι λ λ≈ +Β . With some additional

restrictions, it is possible to obtain the pricing relation of APT as an equality. Since

standard statistical methods are not amenable to testing approximations, most empirical

tests evaluate whether 0[ ] nE r ι λ λ≈ +Β holds as an equality. Often, joint tests of APT


with any ancillary assumptions are performed for obtaining the exact pricing relation,

that is, 0[ ] nE r ι λ λ= +Β [Shanken (1985)].

Once the relevant factors are identified or estimated, approaches to analyzing and

testing APT proceed in most cases by analyzing and testing other competitive asset

pricing models, for example, the capital asset pricing model, and by investigating

various aspects of 0[ ] nE r ι λ λ= +Β . Some researchers have focused on evidence

regarding the size and significance of the factor risk premium vector, λ. One testable

restriction of the model is that the implied risk premiums are the same across subsets of

assets. This implies that, if we partition the return vector, r, into components, r1, r

2,…,

rs, with B

i representing the same partitioning of B, the subset pricing relations become

0[ ]i n i i iE r ι λ λ= +Β , where i = 1, 2, , s. It follows that 0 0

iλ λ= and iλ λ= for all i. An

additional restriction implied by the pricing model is that variables in the agents

information set should not allow investors to predict expected returns which differ from

the relation in0[ ] nE r ι λ λ= +Β . These restrictions form the basis for testing APT.

Now, the exact pricing relation,0[ ] nE r ι λ λ= +Β , along with the factor model for the

return generating process, [ ]r E r f ε= +Β + , imply that the n-vector of returns at time t,

rt, is given by:

0, 1 1

( )n

t t t t tr fι λ λ ε− −= +Β + + (3.02)


The riskless rate of return,0, 1tλ −

, and the risk premia, λ t-1, have a time t-1 subscript since

they are determined by expectations conditional on information at time t-1. If one

observes the return on the risk-free asset, 0, 1tλ −

, one would obtain an equivalent relation

between returns in excess of the risk-free rate 0, 1

n

t t tR r ι λ −= − , B, and the factor returns,

1t tfλ − + . This relationship takes the following form:

1

( )t t t t

R fλ ε−= Β + + (3.03)

Almost every empirical study of APT involves analyses of a panel of asset returns in

which we observe a time series of returns (t = 1,2,,T) on a cross-sectional sample of

assets or portfolios (the n individual assets in rt or Rt). Although all empirical studies

combine cross-sectional and time series data, it is common to classify them as cross-

sectional or time series studies on the basis of the approach used in the final testing

stage of the analysis. A study conditional on B, 0, 1 1( )

n

t t t t tr fι λ λ ε− −= +Β + + , and

1( )t t t tR fλ ε−=Β + + , can be thought of as a cross-sectional regression in which the

parameters being estimated are 0, 1t

λ − and (

1t tfλ − + ). Conversely, conditional on

0, 1tλ −

,

the formulae (1t t

fλ − + ), 0, 1 1

( )n

t t t t tr fι λ λ ε− −= +Β + + , and

1( )

t t t tR fλ ε−= Β + + can be

thought of as a time series regression in which the parameters being estimated are

estimates of B only. Some studies, however, jointly estimate the model in one step.

A recent study by Merville, Hayer-Yelken and Xu (2001) agreed that stock returns can

be better understood using several dimensions. Accordingly, they investigated two


matters. First, they studied the number of fundamental factors [Fama and French

(1992)] that drive the returns. Secondly, they tried to bridge the gap between the

statistical factors and economic factors by interpreting the former using the latter. They

used both principal components analysis as well as the mispricing approach of Connor

and Korajcyzk (1993) to determine the number of pricing factors. They relied on

principal components analysis because it does not require pre-specifying the number of

explanatory factors or variables. The principal components analysis helped them

identify the meaning of the factors found in the portfolio analysis because they relied

on the correlation structure of the data inputs. Accordingly, through principal

components analysis they were able to study both the number and the nature of the

factors driving returns over time without pre-specifying them. Once factors are

constructed, regression analysis is used to determine the consistency of the factor

model with the corresponding APT model. This technique also allowed them to

calculate a relative measure of the importance of each factor found through principal

components analysis. Their results indicate that there are most likely three significant

fundamental factors that explain common stock prices: (i) market return, which also

includes idiosyncratic return; (ii) market capitalisation; and (iii) the investment

opportunity set. Moreover, they found that higher-order factors are uniquely identified

with macroeconomic variables.

The research work of Bai and Ng (2002) attempted to determine the number of factors

in approximate factor models. Their study proposes econometric theory for factor

models of large dimensions. Their idea is that variations in a large number of economic

variables can be modelled by a small number of reference variables and this can be


analyzed. Their focus was to determine the number of factors, r, which is an unresolved

issue in the rapidly growing literature on multi-factor models. They first established the

convergence rate for the factor estimates that will allow consistent estimation of r. They

then proposed some panel criteria and showed that the number of factors can be

consistently estimated using the criteria. A theory has been developed under the

framework of large cross-sections, N, and large time dimensions, T. They later

conducted simulations that showed that the proposed criteria have good finite sample

properties in many configurations of the panel data encountered in practice.

They considered the following model, which treats Xit as observed data for the ith

cross-

section unit at time t, for i =1,,N, and t =1,,T:

i t i t i tX F eλ ′= + (3.04)

Ft is a vector of common factors; t

λ is a vector of factor loadings associated with Ft,

and eit is the idiosyncratic component of Xit. The product i tFλ ′ is called the common

component of Xit. The above equation then becomes the factor representation of data.

As the factors, their loadings, and the idiosyncratic errors are not observable, this type

of factor analysis allows for dimension reduction and is in that sense a useful statistical

tool. Usually, many economic and financial analyses including APT fit naturally into

this framework.


However, as security prices are responsive to external factors, the relationship between

equity markets and exogenous variables is not necessarily unidirectional. Various

researchers considered diverse a priori (pre-specified or choice) variables. Chen, et al.

(1986) considered nine a priori macroeconomic variables. They were inflation, the

treasury-bill rate, long-term government bonds rate, industrial production, low-grade

bonds, equally weighted equities, value weighted equities, consumption, and oil prices.

On the other hand, Fama and French (1993) considered five variables that can explain

average returns, but do not have any special standing in conventional asset pricing

theory. Those specific financial variables were size, leverage ratio, earnings/price ratio,

book-value/market-value ratio, and overall market beta.

McGowan and Francis (1991) considered 25 representative macroeconomic factors

(chosen from between 86 and 95 variables) in their research design to identify

relationships between APT factors and macroeconomic variables in a broader fashion.

McGowan and Francis (1991) factors were: overall production; inflation; money

supply; personal consumption; interest rates; weekly wages; wholesale sales; lagging

indicators; labour force; building construction; total federal debt; federal budget

financing; total construction; new one-family houses; business formation; exports and

imports; population; inventories; leading indicators; non market interest bearing debt;

average weekly hours of service workers; free reserves of all banks; budget deficit and

current liabilities; consumer credit outstanding; commercial banks asset value; and net

budget receipt plus money stock.


Johansen (2000) pointed to the appropriateness of applying cointegration techniques

even for APT, as testing the arbitrage pricing theory often describes a one-period model

for asset prices and it derives a restriction on the mean return by assuming that there

should be a nonarbitrage opportunity by creating a portfolio with positive excess mean

return and no risk. Although the exact factor model does not allow this possibility, the

lack of the restriction opens an approximate arbitrage opportunity by diversification

over many assets. Johansen indicated that if we consider a multi-period model, and

instead of the asset returns consider the cumulated asset returns or the log prices, then

these variables are found to be nonstationary. Johansen and Lando (1999) suggested

that, if we fit a cointegration model with a linear term restricted to the cointegrating

relations, we will get a model for a rebalanced portfolio. The nonarbitrage condition

would be that any portfolio with linearly increasing mean and constant risk must have

the same mean return. Thus, the APT hypothesis is a restriction on the deterministic

terms and the cointegrating vectors [Johansen (2000)].

Summary

We have reviewed empirical APT in this chapter to ascertain whether the theoretical

underpinnings of APT and its empirical forms are the same. We observed that empirical

APT differs from theoretical APT in many ways. Still, theoretical APT implies an

empirical version of APT. We saw that traditional approach to test an APT model

follows statistical factor analysis, although many researchers used other methods,

including regression and principal component analyses. From a number of legitimate

versions of APT, the Roll and Ross two-step procedure is found popular in empirical


analysis. And yet, many researchers tried various other testing methods, including

cointegration, on different versions of APT, including the dynamic version of APT.

Any empirical approach to APT always maintained harmony with the corresponding

school of thought on the factors (either latent or pre-specified). In this chapter we

reviewed the relevant empirical works of APT for the purposes of identifying an

appropriate approach to quantitative analysis.


CHAPTER 4

FUNCTIONAL SECURITY PRICING FROM A MARKET

VIEWPOINT

A clear view of security market pricing procedures and related issues are important to

an astute investor. This chapter will briefly review those studies in asset pricing

analysis that are particularly relevant from a security market viewpoint.

Security market prices are represented by security market indices, which are often

measured by a stock price index, a way of measuring the performance of a market over

time. Indices are regarded as an important indicator by the finance industry and the

investing public at large. An index can be used as a benchmark by which an investor or

fund manager compares the returns of their own portfolio. As the share market index

represents the return of the market as a whole, one can easily evaluate market or

industry performance using this index. The market index can also be used to define the

universe from which investors or fund managers pick their stocks. Furthermore, indices

are useful to form indexed portfolios as the basis for estimating the risk of an investors

own portfolio. Fund managers portfolios can either be indexed (risk-neutral),

overweight or underweight, compared to the weights in their benchmark [Standard and

Poors (2002)].

We also acknowledge that significant risk factors need to be priced. Hence,

understanding systematic risk factors and determining whether these factors are being

appropriately priced for both an individual asset and stock indices are important to any


CHAPTER 4

FUNCTIONAL SECURITY PRICING FROM A MARKET

VIEWPOINT

A clear view of security market pricing procedures and related issues are important to

an astute investor. This chapter will briefly review those studies in asset pricing

analysis that are particularly relevant from a security market viewpoint.

Security market prices are represented by security market indices, which are often

measured by a stock price index, a way of measuring the performance of a market over

time. Indices are regarded as an important indicator by the finance industry and the

investing public at large. An index can be used as a benchmark by which an investor or

fund manager compares the returns of their own portfolio. As the share market index

represents the return of the market as a whole, one can easily evaluate market or

industry performance using this index. The market index can also be used to define the

universe from which investors or fund managers pick their stocks. Furthermore, indices

are useful to form indexed portfolios as the basis for estimating the risk of an investors

own portfolio. Fund managers portfolios can either be indexed (risk-neutral),

overweight or underweight, compared to the weights in their benchmark [Standard and

Poors (2002)].

We also acknowledge that significant risk factors need to be priced. Hence,

understanding systematic risk factors and determining whether these factors are being

appropriately priced for both an individual asset and stock indices are important to any


investor or fund manager. If systematic risk factors are cointegrated with security

market prices, this knowledge is useful to investors in their decision making processes.

This type of study is becoming a focal point in finance. The studies suggest that stock

market returns are predictable from a variety of financial and macroeconomic variables.

The results of various studies suggest that financial and macroeconomic variables

influence stock prices across a variety of markets and time horizons [Campbell (1987),

French, Schwert and Sambaugh (1987), Fama and French (1989), Balvers, Cosimano

and McDoanld (1990), Been, Glostone and Jagannathan (1990), Cochrane (1991),

Campbell and Hamao (1992), Ferson and Harvey (1993), Glosten, Jagannathan and

Runkle (1993), Pesaran and Timmerman (1995, 2000), and McMillan (2001)].

Both international investors and researchers have been focusing their attention on stock

markets and fundamental macroeconomic dynamic interactions in countries (including

ASEAN) that provide attractive investment opportunities to foreign investors

[Wongbangpo and Sharma (2002)]. A number of studies, for example, modelled

relationships between US share prices and real economic activity [Fama (1981), Geske

and Roll (1983), Huang and Kracaw (1984), Chen, Roll and Ross (1986), Chen (1991),

Dhakal, Kandil and Sharma (1993), Abdullah and Hayworth (1993)]. Poon and Taylor

(1991) and Cheng (1995) investigated the relationships between the UK stock market

and macroeconomic factors, while Hamao (1988), Brown and Otsuki (1990), and

Mukharjee and Naka (1995) studied the Japanese market. Moreover, Fung and Lie

(1990) considered the Taiwanese market and Kwon, Shin and Bacon (1997)

investigated the Korean market for any relationship with their respective macro-

variables. The outcomes of all these studies suggest that, with minor degrees of


variation, fundamental macroeconomic dynamics are indeed influential factors for

stock market returns.

The cointegration approach has been used by many researchers to analyse pricing

factors and to observe the relationships between economic variables and stock markets.

Despite the fact that the cointegration approach is still evolving within the realm of

time series analysis, it has become popular in empirical work in both economics and

finance since its introduction in the 1980s by Granger (1981) and Engle and Granger

(1987).

There has been a noticeable tendency to shift from the classic testing approach to

testing APT with cointegration techniques as it is a more efficient method. The shift

can partly be explained by the fact that researchers are now assessing whether

systematic risk factors or a priori variables are priced in stock markets rather than just

condensing factors dimensions for analyzing the asset pricing of particular markets

[Ackert and Racine (1999), Nasseh and Strauss (2000), McMillan (2001), Mookerjee

and Yu (1997), Maysami and Koh (2000), Shamsuddin and Kim (2000, 2003)].

Researchers are aiming to investigate both the long-run and dynamic relationships

between a priori variables and stock market prices. The trend is towards the

cointegration technique. Empirical frameworks are being developed in line with the

cointegration techniques of Engle and Grager (1987), Granger (1988) and Johansen

(1988, 1991, 1995, and 2000).


McMillan (2001), using US data, undertook to test whether a cointegrating vector

exists between stock market indices and industrial production, inflation, money supply

and the interest rate. The results provided positive evidence of cointegration between

both the US market index (S&P 500) and the Dow Jones Industrial Average index

(DJIA) and macroeconomic activity variables. McMillan (2001) focused his research

on both the long- and short-run relationships between stock markets rather than on

individual stock returns and financial and macroeconomic variables. He pointed to the

fact that research on long-run relationships between stock markets and the unit root

components of economic activity variables is yet to receive significant attention.

By using the concept of cointegration, McMillan (2001) investigated empirically long-

run equilibrium relationships between stock market indices and pre-selected economic

and financial variables. He also used variance decompositions to see which

macroeconomic factors explain a substantial part of the variation in stock prices over

the short and medium-run, namely, one, four and eight years. Variance decompositions

are constructed from a vector autoregression (VAR) with orthogonal residuals and can

directly address the contribution of macroeconomic variables in forecasting the

variance of stock prices [Sims (1980), Litternman and Weis (1985)].

McMillan (2001) used Johansens (1991, 1995) vector error correction model (VECM)

for ascertaining the cointegrating relationship between integrated time series through

representation by a vector autoregression. He asked whether each series was integrated

of the same order by considering both the Augmented Dickey-Fuller and Phillips-Peron

tests. He assumed that each series contained a single unit root, and thus was integrated


of the same order. He found a potential for co-movement between these series exists,

meaning a linear combination of this co-movement is stationary. This suggests a long-

run relationship between these variables.

Researchers who have investigated long-run relationships between macroeconomic

variables and stock market indices focused their attention on determining the dynamic

relationships between a priori variables and a representative stock market index

[Maysami and Koh (2000), Mookerjee and Yu (1997), Shamsuddin and Holmes

(1997), Mallik, et al. (2001), Shamsuddin and Kim (2000, 2003), Nasseh and Strauss

(2000)]. The proxy variables chosen by these researchers varied from one stock market

to another. Also, the analytical methods varied noticeably. Yet, the basis of all these

studies in security pricing originated from the theoretical perspective of APT.

To assess the impact of economic forces on the stock market, Maysami and Koh (2000)

related monthly stock market levels and monthly stock returns using Johansens

VECM. Maysami and Koh (2000) adopted Mukharjee and Nakas (1995) lesson for

Singapore. Shamsuddin and Kim (2000, 2003) examined cross-country stock market

relationships by employing the cointegration technique of Johansen (1988). Chen

(1995) and Clare, Maras and Thomas (1995) used pair-wise cointegration in studying

the performances of a group of countries.

While examining the dynamic relationships between the Singapore stock market and

the two well-developed stock markets of the US and Japan, Maysami and Kohs (2000)

process of selecting macroeconomic variables for the Singapore stock market was


based on the simple and intuitive financial theory suggested by Mukherjee and Naka

(1995), and Chen, et al. (1986). They recognized that although the Engle and Grager

(1987) two-step error correction model (ECM) was suitable for use in the multivariate

context, VECM yielded efficient estimators of cointegrating vectors. This was because

VECM is a full information maximum likelihood estimation method. It allows

cointegration to be tested in a whole system of equations in only one step without

requiring a specific normalized variable. VECM avoids carrying over the errors from

the first step into the second, and it does not require prior assumptions about the

variables (endogenous or exogenous).

In estimating a VECM, Maysami and Kho (2000) first checked for stationarity and unit

roots by performing the Augmented Dickey-Fuller and Phillips-Peron tests on the

variables in levels and first differences. Only variables integrated of the same order

seemed cointegrated, and the unit root tests helped them to determine which variables

were integrated of order one, or I(1). They chose lag lengths using Sims likelihood

ratio test. For simplicity, they used the multivariate forms of the Akaike Information

Criterion and Schwartz Bayesian Information Criterion. Their choice of the number of

maximum cointegrating relationships was based on the trace

λ tests. The max

λ test is used

to test specific alternative hypotheses.

Having determined the order of cointegration, Maysami and Kho (2000) analyzed the

relevant cointegrating vector and the speed of adjustment coefficients. They performed

tests on the parameters of the cointegrating vector using the likelihood ratio test. This

was required for understanding whether stock prices contributed to the cointegrating


relation and also if the macroeconomic variables were significant in the cointegrating

relationship.

Maysami and Kho (2000) used monthly time series in natural logarithms of these

variables: share price index (LSESt), M2 money supply (LM2t), consumer price index

(LCPIt), industrial production index (LIPt), domestic export (LTDEt), bank rate

(LSTBt), and yield on government securities (LLTBt). They gathered time series data

from various sources including the Public Access Time Series System, an online

service of the Singapore Department of Statistics. Data on the exchange rate (LERt)

was obtained from the International Financial Statistics, published by the International

Monetary Fund. Both the US stock market price (LUSt) and the Japanese stock market

price (LJPNt) were obtained from the US Bureau of Labour Statistics. Definitions and

transformations of these variables are presented in Tables 4.1 and Table 4.2

respectively.

TABLE 4.1

Definitions of Variables Variables Definitions of Variables

LSESt Natural logarithm of the index of the market-value weighted average of month-

end closing prices for all shares listed on the Stock Exchange of Singapore

LERt Natural logarithm of the month-end exchange rate of the Singapore

LM2t Natural logarithm of the month-end M2 money supply in Singapore.

LCPIt Natural logarithm of the month-end Consumer Price Index.

LIPt Natural logarithm of the month-end Industrial Production Index.

LSTBt Natural logarithm of the month-end 3-month Interbank Offer Rate.

LLTBt Natural logarithm of the month-end yield on 5-year government securities.

LUSt Natural logarithm of the month-end stock-price index of the United States.

LJPNt Natural logarithm of the month-end stock price index of Japan.

LTDE Natural logarithm of the month-end Total Domestic Export from Singapore.

Source: Maysami and Kho (2000).


TABLE 4.2

Time-Series Transformations Transformation Definitions of Transformations

∆SESt = LSESt LSESt-1 Monthly return on the Singapore stock market (ex-dividend).

∆ERt = LERt LERt-1 Monthly change in exchange rate.

∆M2t = LM2t LM2t-1 Monthly growth rate of money supply.

∆CPIt = LCPIt LCPI.t-1 Monthly realized inflation rate.

∆IPt = LIPt LIPt-1 Growth rate of industrial production.

∆STBt = LSTBt LSTBt-1 Monthly return on 3-month interbank market (short- term).

∆LTBt = LLTBt LLTBt-1 Monthly return on government bonds (long-term).

∆USt = LUSt LUSt-1 Monthly return on US stock market (ex-dividend).

∆JPNt =LJPNt LJPNt-1 Monthly return on Japanese stock market (ex-dividend).

∆LTDE = LTDEt LTDEt-1 Monthly change in Singapores total domestic exports

Source: Maysami and Kho (2000).

Maysami and Kho (2000) used seasonally adjusted month-end data for the period from

January 1988 to January 1995. The index they used was a value weighted index of all

the shares listed, which provided them with a broad measure of market levels. Based on

their test results, Maysami and Kho (2000) concluded that there were two cointegrating

relationships at the 5% level of significance.

Earlier, Mookerjee and Yu (1997) studied the Singapore stock market pricing

mechanism by investigating whether there were long-term relationships between

macroeconomic variables and stock market pricing. They chose the all-share price

index to broadly represent Singapore stock market prices. They found that three out of

four macroeconomic variables were cointegrated with stock market prices. To test for

informational efficiency they employed cointegration and causality techniques because

these techniques allowed for any potential linkages between variables in the long-run as

well as in the short-run.


Mookerjee and Yu (1997) began by conducting tests of nonstationarity. They

considered four pre-selected macroeconomic variables that included the narrow money

supply, the broad money supply, nominal exchange rates, and foreign currency reserves

to ascertain whether these variables were related to Singapore stock market prices in

both the long- and short-runs. In their unit root testing process, Mookerjee and Yu

(1997) could not reject the hypothesis for all five variables at the 1% significance level.

But the hypothesis could be rejected in first differences at the 5% significance level.

The authors used the Engle and Granger (1987) method for identifying causality and

cointegration between stock market prices and macroeconomic variables. They also

employed the Johansen (1991) approach for further confirmation of their results. The

Engle-Granger tests of cointegration suggested that the Singapore stock market was

efficient in the long-run with respect to its exchange rate. Alternatively, they used the

causality test of Granger (1996) for short-run informational efficiency. As the test of

causality is sensitive to lag length selection as per Thornton and Batten (1985), they

conducted causality tests between stock price change and each macroeconomic variable

series up to the 12th lag. They observed that changes in Singapore stock prices had a

causal relationship only with the narrow money supply. To obtain concrete evidence

concerning the efficiency of the Singapore stock market, Mookerjee and Yu (1997)

conducted further tests that entailed calculating the forecasted or anticipated

components of macroeconomic variables.

Nasseh and Strauss (2000) also found support for the existence of significant long-run

relationships between stock market prices (represented by relevant share price indices)

and domestic and international economic activity in six countries that included France,


Germany, Italy, Netherlands, Switzerland and the UK. In their study Johansens

cointegration tests demonstrated that stock price levels were significantly related to

industrial production, business surveys of manufacturing orders, short- and long-term

interest rates as well as foreign stock prices, short-term interest rates, and production.

Nasseh and Strauss (2000) also used variance decomposition methods that supported

the strong explanatory power of macroeconomic variables in contributing to the

forecast variance of stock market prices. They recognized the usefulness of Johansens

framework for analyzing stock market and macroeconomic activity it incorporates

dynamic co-movements or simultaneous interactions, allowing the researchers to study

the channels through which macroeconomic variables affected asset pricing, as well as

their relative importance. Their variance decomposition methods, based on a vector

autoregression with orthogonal residuals, showed that macroeconomic factors

explained a substantial part of the variation in stock prices in the medium and short-

runs. Nasseh and Strauss (2000) found that although stock prices were explained by

economic fundamentals in the medium and short-run, the underlying volatility inherent

in stock prices was related to macroeconomic movements in the long-run.

Using US equity market index data, Actert and Racine (1999) examined whether spot

and futures equity markets were cointegrated. Their analytical model was based on the

nonarbitrage, cost-of-carry pricing model of Brenner and Kroner (1995). They assumed

that a stock index and its futures price was cointegrated if the cost of carry was

stationary, otherwise the cointegrating relationship would be trivariate. They found that

the S&P500, associated futures series, and the interest rate were all nonstationary. In

addition, their cointegrating relationships included the index, futures price, and the cost


of carry. Their findings were consistent with the nonarbitrage pricing model and did not

appear to be sensitive to the presence of structural breaks in the series.

Based on practical experience, Duy and Thoma (1998) noticed that although the issue

of identifying cointegrating relationships between time series variables was of

increasing importance, researchers had to reach an agreement on the appropriate

manner of modelling such relationships. They attempted to distinguish between

modelling techniques through a comparison of forecast statistics, at the same time

focusing on the issue of whether or not imposing cointegrating relations via an ECM

(error correction model) improved long-run forecasts. They found that imposing

cointegrating restrictions often improved forecasting power.

Duy and Thoma (1998) constructed a model that took into account zt, an n×1 vector of

nonstationarity, I(1) and time series variables. They assumed that two or more of the

elements of zt form a stationary, I(0), linear combination. Their ECM representing such

a system of variables is:

1 1

1

jE C

t t i t t

i

z w zα γ ε− −=

∆ = + ∆ +∑ (4.01)

where t t

w zβ ′= is the cointegration term;β is an n×1 vector of coefficients in the

cointegrating vector; α is an n×1 vector of coefficients; and EC

tε is a vector of

Gaussian error terms. Duy and Thoma determined the elements of the cointegrating

vector both theoretically and empirically. In doing so they first considered a vector


autoregression (VAR) model in pure differences for examination because if

cointegration was not present in the variables zt then the above error correction models

would be misspecified. This type of model is often recommended when the elements of

zt are difference stationary but not cointegrated. They also considered that a VAR

model in pure levels which estimates a VAR in levels avoids the possibility of

imposing false restrictions on the model. These VARs are:

1

jD

t t t i t

i

z zγ ε−=

∆ = ∆ +∑ (differences) (4.02)

and

1

jL

t t t i t

i

z zγ ε−=

= +∑ (levels) (4.03)

Duy and Thoma (1998) thus tested cointegration within their three systems of equations

by using the Johansen maximum likelihood procedure, which they found satisfactory.

Paul and Mallik (2001) investigated the long-run relationship between three pre-

specified macroeconomic factors and stock prices in the banking and finance sector in

Australia by using cointegration techniques. As a proxy for stock prices, they used time

series data on ASX bank and finance share market indices. All data were quarterly

observations for the period 1/1980 to 1/1999. They measured inflation as the change in

the quarterly consumer price index. They considered three-monthly bank bill rates as

interest rates, and logged seasonally adjusted gross domestic product (GDP) at 1997-98

base prices as a proxy for GDP growth. Upon detection of any cointegrating


relationship, for estimation of their model they constructed an error correction

autoregressive distributed lag (ARDL) model in line with Pesaran and Shin (1995).

Their ARDL error correction model was as follows:

10 1 2 3 1

1 0 0

ln ln lnp r s

t t i t k t

t k l

BP BP INT INFφ φ φ φ− − −− = =

∆ = + ∆ + ∆ + ∆∑ ∑ ∑

4 1 1

0

lnq

t j t t

j

G D P eφ ρ µ− −=

+ ∆ + +∑ (4.04)

where ∆ denotes a first difference operator; µt-1 is an error correction term; p, q, r and s

are the lag lengths; and et is the random disturbance term. Although their results could

not show any significant effect of inflation on stock prices, they found both the interest

rate and GDP growth significant. The interest rate had a negative effect, whereas GDP

growth had a positive effect on the banking and finance sectors stock price.

Earlier, Lim and McNelis (1998) studied the effect of US and Japanese stock market

price movements on that of Australian markets by examining the influence of shocks in

the Japanese Nikkei index and in the US S&P index on the Australian All Ordinaries

index. They considered logged daily data series from 28 September 1990 to 12

September 1996, and used three models including an autoregressive linear model.

More recently, Wongbangpo and Sharma (2002) investigated the role of five

macroeconomic variables, namely, gross national product, consumer price index,

money supply, interest rate, and exchange rate on the stock prices in five ASEAN

countries (Indonesia, Malaysia, the Philippines, Singapore, and Thailand). They


observed both long- and short-term relationships between stock prices and their

macroeconomic variables for the period 1985 to 1996. They used monthly data that

were found to be integrated of order one from the Augmented Dickey-Fuller and

Phillips-Peron tests. They also used maximum likelihood based trace

λ and max

λ statistics

through the cointegration analysis technique of Johansen (1988, 1991) and Johansen

and Juselius (1990) for tracing any causal relationship within the framework of the

VECM. Their system of the short-run dynamics of the stock price series (SPt) was as

under:

1 1 1 1 1 1

1 1 1

k k k

t t i t i i t i i t i

i i i

SP EC SP G N P C PIα β δ θ ξ− − − −= = =

∆ = + + ∆ + ∆ + ∆∑ ∑ ∑

1 1 1 1

1 1 1

k k kS P

i t i i t i i t t

i i i

M S I R E Rρ ω τ ε− − −= = =

+ ∆ + ∆ + ∆ +∑ ∑ ∑ (4.05)

where ECt-1 is the error correction term obtained from the cointegration vector,

, , , , , ,β δ θ ζ ρ ω τ are parameters; k is the lag length; and SP

tε are a stationary random

process with mean zero and constant variance.

Summary

This chapter has reviewed the trend towards analyzing the relationship between the

security market movement and a priori variables, while retaining the basic attributes of

asset pricing theory. As has been seen, many researchers have studied the long-term

relationship between stock indices and macroeconomic variables as well as short-term

dynamics using the cointegration technique. It has become apparent in this chapter that


using the cointegration approach one can efficiently analyse the long-run relationship

between a priori variables that are considered as a proxy for systematic risk factors and

security market prices. We have also seen in this chapter that an additional cross-

country study which traces the interrelationship between various stock markets is useful

for understanding the global impacts on a specific stock markets price movements.

Our contribution here has been to find that an empirical study in asset pricing imposes

no limits within the boundaries of its traditional methods nor models. We deem both

the cointegration method and an autoregressive model based on the market stock prices

is more suitable for us. We will examine the cointegration approach as our preferred

method of analysis in further detail in Chapter 5.


PART III

EMPIRICAL APPROACHES TO SECURITY MARKET

PRICING

The third part of the thesis considers our empirical work. This part consists of two

chapters. Chapter 5 investigates the approaches used to derive our methodological

framework. Chapter 6 systematically derives the methodology suitable for developing

the appropriate model for our research.


CHAPTER 5

METHODOLOGICAL OUTLINE

Many methods are available to analyse empirically the asset pricing mechanism and

determine the relationship, if any, between stock market returns and a priori variables.

As is evident from preceding chapters, the influences of systematic risk factors on the

stock pricing process can be detected by employing various models. A record of the

analytical techniques used in various studies is provided in Table 5.1.

TABLE 5.1 Methods Used for Investigating Asset Pricing

Analytical Methods Recorded Studies

Factor Analysis Ross (1976, 1977); Ross and Roll (1980); Chen, Roll and Ross (1983, 1986); Gehr (1978); Fogler, et al. (1981); Hughes (1985); Beenstock and Chan (1983, 1984); Winkelmann (1984); Dumontier (1986); Kim and Lee (!995); Connor and Korajezyk (1989); McGowan and Francis (1991); Brailsford and Heaney (1998); Connor (1995); Bai and Ng

(2002); and Fama and French (1992, 1993).

Asymptotic Principal Component Chamberlain and Rothschild (1983); Anckonle (1983); Connor and Korajczyk (1986, 1988, 1989); McGowan and Francis (1991); Shukla and Trzcinka (1990); Faff (1988, 1992); and Merville, et al. (2001).

Standard, Cross-Section and Time Series

Regression Analyses

Beggs (1986); Merton (1973); Kritzman (1995); Fam and French

(1992, 1993); Brown and Weinstein (1983); Aitken, et al. (1996); Brailsford and Easton (1991); Faff and Brailsford (1999); Hamao (1988); Faff and Heaney (1999); and Easton and Faff (1994).

Generalised Method of Moments

Zhou (1999); and Velu and Zhou (1999).

Maximum Likelihood Handa and Linn (1993).

Autoregressive Conditional

Heteroskedasticity

Brailsford and Faff (1996)

Cointegration Maysomi and Kho (2000); Johansen (1988, 1991, 1995, 2000); Pesaran and Timmerman (1995); McMillan (2001); Mukharjee and Naka (1995); Cheung and Ng (1998); Ackert and Racine (1999); Nasseh and Stranss (2000); Mukharjee and Hoh (2000); Shamsuddin and Holmes (1997); Cheung and Ng (1998); Paul and Mallik (2001); Roca (1998); and Shamsuddin and Kim (2000, 2003).


Underpinning any methodological approach adopted by empirical studies in finance is

regression analysis. The most common methods are investigated in this chapter to

ascertain the most appropriate for a system which is considered to be a group of

equations containing unknown parameters. In general terms, a system can be estimated

using a number of techniques that take into account the interdependencies among the

equations within the system. This form of system is represented by

( ), ,t t t

F y x β ε= (5.01)

where yt is a vector of endogenous variables; xt is a vector of exogenous variables; and

εt is a vector of possibly serially correlated disturbances. The task of estimation is to

find estimates of the vector of parameters β.

Almost all systems in finance deal with multiple variables so that the methodology falls

within the field of multivariate analysis as well as multiple regression analysis.

Multivariate analysis refers to the analysis of multiple variables singly or in a set of

relationships. Although there are nonlinear relationships, studies for linear relationships

are common. The basis of multivariate analysis is the variate, a linear combination of

variables with empirically determined weights [Hair, et al (1995)]. Usually, a linear

combination of variables with empirically determined weights is the variate value,

whereas multiple regression analysis is a statistical technique that can be used to

analyse a relationship between a single dependent (criterion) variable and several

independent (predictor) variables. The objective of multiple regression analysis is to

use independent variables whose values are known to predict the dependent variable.


The basic motivation for estimating all regression relationships is correlation, which

measures the association between two variables. In regression analysis, the correlation

between the independent variables and the dependent variable provides the basis for

forming the regression variate by estimating regression coefficients (weights) for each

independent variable that maximize the prediction (explained variance) of the

dependent variable.

When more independent variables are added to the variate, the process must also

consider the inter-correlations among independent variables. If the independent

variables are correlated, they share some of their predictive power. Because only the

prediction of the overall variate is used, the shared variance must not be double counted

by using the direct correlations. In these cases, some additional forms of correlation

that represent shared effects are to be calculated for an accurate prediction of the

dependent variable. Partial correlation is the appropriate tool, where correlation of an

independent and dependent variable is obtained by removing the effects of other

independent variables.

To answer any empirical research question and formulate an appropriate model, one

needs to choose an appropriate technique or method for data analysis.


Empirical Methods in Asset Pricing

General Linear Regression

Most of the techniques for asset pricing analyses are special applications of the general

linear regression model (GLM). Within the GLM, a simple form of regression is

A + βX + e = Y (5.02)

where β is the change in Y associated with a one-unit change in X; A is a constant

representing the expected value of Y when X is zero; and e is a random variable

representing the error of prediction.

If X and Y are converted to standard z scores, then zx and zy are measured on the same

scale. The constant A automatically becomes zero, because zy is zero when zx is zero.

Standardising the variance to 1, the closer the β to ± 1 the better the prediction of Y

from X (or vice versa). The equation becomes βZx + e = Zy. When this simple bivariate

form of the GLM adds more independent variables, Xs, to predict Y, it takes the shape

of a multivariate form of the regression:

1

k

i x i y

i

Z e Zβ=

+ =∑ (5.03)


The generalised linear model takes a major leap when the Y side of the equation is

expanded. More than one equation may be required to relate the Xs to the Ys. A full

multivariate form of the regression is

1 1

pk

im x im jm y j m

i j

Z e Zβ γ= =

+ =∑ ∑ (5.04)

where m equals k or p, whichever is smaller, and γ are regression weights for the

standardised Y variate. Generally, there are as many equations as the number of X or Y

variables, whichever is smaller.

Maximum Likelihood

The maximum likelihood (ML) method of estimation is often found useful in stock

pricing analyses. In simple terms, the maximum likelihood estimator (MLE) is that

value of estimated parameter/s that is most likely to have generated the observed sample

values, where most likely is defined as meaning those values of the population

parameters which have the greatest probability of giving rise to the sample values

actually obtained. The advantage of the ML method of estimation is that, under general

conditions, MLEs are consistent and asymptotically efficient. They have desirable large

sample properties. Given the circumstances, MLEs frequently have an important role to

play in multiple regression analysis. MLE is often viewed as an alternative method to

ordinary least squares (OLS), a technique which minimises the sum of squared

residuals for each equation as OLS is MLE when residuals are normally distributed.


Generalised Method of Moments

Many studies analysing asset pricing have used the generalised method of moments

(GMM) in estimating parameters drawn from a random sample, as moments are

essentially the sums of observations. GMM estimation is a direct extension of the

method of moments which is a consistent estimation technique. The method is

applicable both in estimating a single equation and multiple system models. The basis

of this method is that, in random sampling, a sample statistic will converge in

probability to some constant [Greene (2000)]. The GMM estimator belongs to a class

of estimators known as M-estimators that are defined by minimising some criterion

function [EViews (1998, and 2001)]. This is based upon the assumption that the

disturbances in the equations are uncorrelated with a set of instrumental variables.

GMM can be made robust to heteroskedasticity and/or autocorrelation of unknown

form.

Seemingly Unrelated Regression

Sometimes the parameters of a system of equations are estimated by using the

seemingly unrelated regression (SUR) estimation method accounting for

heteroskedasticity and contemporaneous covariance in the errors across equations. SUR

is also known as multivariate regression, or Zellners seemingly unrelated regressions

method. The estimates of cross-equation covariance matrix are based upon parameter

estimates of the unweighted system. The SUR method allows for cross-equation


restrictions on parameters and it is superior to the OLS method in such a situation. In

some special cases for asset pricing analyses this approach is found suitable.

Factor Analysis

The statistical approach called factor analysis has been used to analyse asset pricing

it describes the basis of interrelationships among a large number of financial and

economic a priori variables. The method explains the variables under consideration in

terms of their common underlying dimensions (factors). The objective is to find a way

of condensing the information contained in a number of original variables into a

smaller set of variables (factors), with a minimum loss of information [Hair, et al

(1995)].

Simple factor analysis begins with calculating the equal interval stock returns during

some period and isolating the factors that explain stock market performance. It

computes the correlation between the (daily or specified equal interval) returns of each

stock and the returns on every other stock to isolate the factors. Then it identifies the

groups of stocks that are highly correlated with each other but not with the stocks

outside the group. Similarly, it proceeds to isolate other groups of stocks whose returns

are highly correlated with each other within their own group, until it isolates all the

groups that seem to respond to a common source of risk. Thereafter, factor analysis

attempts to identify the underlying sources of risk for each group. In the first instance,

it relies on intuition to identify the factor that underlies the common variation in returns

among the stocks. Then it tests the intuition. In doing so, the approach defines a


variable that serves as a proxy for the unanticipated change in the factor value. Finally,

it regresses the returns of stocks that appear to depend on the hypothesized factor with

the unanticipated component of the factor value [Kritzman (1995)].

Customarily, factor analysis reveals covariation in returns and attempts to identify the

sources of this covariation, whereas cross-sectional regression analysis requires

specifying the sources of return covariation and attempts to affirm that these sources do

indeed correspond to differences in return. Based upon intuition and prior research,

researchers often infer attributes, rather than factors, that they deem correspond to

differences in stock returns. Once a set of attributes is specified, a measure of

sensitivity to the common sources of risk can be detected. Then we regress the returns

across a large sample of stocks during a given period on the attribute values for each

stock as at the beginning of the period. This regression is repeated over many different

periods. If the coefficients of the attribute values are not zero and are significant in a

sufficiently high number of the regressions, it is concluded that differences in return

across the stocks relate to differences in their attribute values [Kritzman (1995)].

More often than not, security returns used to be characterized by very large cross-

sectional samples (often, more than 10,000 simultaneous return observations) with

strong co-movements. The fundamental sources of these co-movements are not always

obvious and are not easily measurable. Such a statistical system, where a few

unobservable sources of system-wide variation affect many random variables, leads to

factor modelling. Arbitrage pricing theory begins by assuming asset returns follow a

factor model. There exist n assets and k factors; f denotes the k-vector of random


factors; β refers to the n×k matrix of linear coefficients representing assets sensitivities

to movements in the factors (factor loading). One can write an n-vector of returns, r, as

expected returns, E[r], and the sum of two sources of random returns, that is, a factor

return, Bf, and an idiosyncratic return, ε:

[ ]r E r f ε= + Β + (5.05)

where E[f] = 0, E[ε] = 0, and [ ] 0E f ε ′ = . B is defined by the standard linear projection

1[( [ ]) ]( [ ])E r E r f E ff −′ ′Β = − (5.06)

Given a vector of returns, r, and a vector of zero mean-variances, f, the standard linear

projection divides the returns into expected returns, k-linear components correlated

with f, and zero mean idiosyncratic returns uncorrelated with f [Connor and Korajczyk

(1995)].

Additional structural appearances of [ ]r E r f ε= +Β + appear in the literature providing

support for the hypothesis that the idiosyncratic returns are diversifiable risks. In

application, the strict factor models as well as the approximate factor models provide

additional support for this hypothesis. Often, conditional factor models rewrite the

equation with an explicit time subscript to capture the time-varying or dynamic nature

of the return generating process.


Strict Factor Model

Since the factors and idiosyncratic risks are uncorrelated in strict factor models, the

covariance matrix of asset returns denoted by [( [ ])( [ ]) ]E r E r r E r ′∑ = − − is treated as

the sum of two matrices:

[ ]ff V′ ′∑ = ΒΕ Β + (5.07)

where V=E ][ εε ′ and the idiosyncratic returns are assumed uncorrelated with one

another. This means that the covariance matrix of the idiosyncratic risks, V, is a

diagonal matrix. The covariance matrix can be decomposed as the sum of a matrix of

rank k and a diagonal matrix of rank n. This imposes strict restrictions on the

covariance matrix as long as k < n.

This method divides the vector random process into k, common sources of randomness

and, n, asset-specific sources of randomness. Considering n is large and the

idiosyncratic variance of a portfolio with portfolio proportion (weights) as ω,

2 2 2 2

1 1

( m a x )n n

i i i ii

i i

Vω ω ω σ σ ω= =

′ = ≤∑ ∑ (5.08)

Since the portfolio weights sum to one, the average portfolio weight is 1/n. If the

holdings are spread widely over the n assets, then the sum of squared portfolio weights

approaches zero as n goes to infinity. As long as there is an upper bound on the


idiosyncratic variances of individual assets, the idiosyncratic variance of any well-

spread portfolio will be near zero. Thus, given a strict factor model and many assets,

the idiosyncratic returns contain only diversifiable risks [Connor and Korajczyk

(1995)].

Approximate Factor Model

Ross (1976, 1977, 1990) used the factor model assumption to show that idiosyncratic

risks are diversifiable in many asset portfolios. The strict diagonality of V (as it is

assumed that [ ]V E εε ′= is a diagonal matrix) is a sufficient but not a necessary

condition for the diversification argument of Ross. To overcome the condition,

Chamberlain (1983) and Chamberlain and Rothschild (1983) proposed an asymptotic

statistical model for asset returns data called the approximate factor model. This model

retains the diversifiability of idiosyncratic returns but weakens the diagonality

condition on V. It imposes an additional condition that the factor risks are not

diversifiable.

The approximate factor model relies on limiting conditions as the number of assets

grows larger. The model performs a factor decomposition task where the εs are

diversifiable and the fs are pervasive. The diversifiable risk condition is equivalent to a

finite upper bound on the maximum eigenvalue of Vn as n tends to infinity. In addition,

the pervasiveness condition is equivalent to the minimum eigenvalue of nn ΒΒ '

when n

approaches infinity. Here, the covariance matrix of returns is the sum of two

components, 'nnΒΒ and V

n. Thus,

'nnΒΒ has all of its eigenvalues approaching to


infinity, whereas Vn has a bound on all its eigenvalues. Chamberlain and Rothschild

(1983) showed that these bounds carry over to the covariance matrix. The k largest

eigenvalues of the covariance matrix go to infinity with n, and the k+1st largest

eigenvalue is bounded for all n. The model thus proves both the sufficient and

necessary conditions.

Conditional Factor Model

To accommodate time-varying or dynamic conditions in the modelling, the factor

model is mathematically expressed as:

1 1[ ]

t t t t t tr E r f ε− −= + Β + (5.09)

Let 1t−Β be chosen by the conditional projection of rt on ft. That means

1

1 1 1 1[( [ ]) ][( [ ] ]

t t t t t t t t tE r E r f E f f −

− − − −′ ′Β = − so that 1[ ] 0

t t tE fε− ′ = . Now the conditional

covariance matrix is:

1 1 1 1 1t t t t tV− − − − −′Σ = Β Ω Β + (5.10)

where 1 1

[ ]t t t t

E f f− − ′Ω = and 1 1

[ ]t t t t

V E ε ε− − ′=

Even if Vt-1 is diagonal for all t, the system is not statistically identified in this general

form. Connor and Korajczyk (1995) pointed out that to estimate the returns on n


securities for T periods, one has to estimate the n elements of Vt-1, the nk elements of Bt-

1, and the k2 elements of Ωt-1 for each date t. This would provide a total of T(n+nk+ k

2)

parameters to estimate from nT return observations under a structured identifiable

model. To develop a dynamic model from the static model, some but not all of the

rotational indeterminacy of static models must be eliminated. Engle, et al. (1990)

suggested that, conditional on the assumed source of time variation (Bt-1 or Ωt-1) and

the assumed time series properties, it is assumed that the factors follow a GARCH

process. Sentana (1992) indicated that the dynamic structure here eliminates a notable

number of standard rotational indeterminacies of static models. Thus, the conditional

factor models allow for time variation in expected returns so that Et-1[rt] is not constant.

Multi-Factor Models

In their recent study, Merville, Hayes-Yelken and Xu (2001) pointed to a theoretical

perspective of asset pricing approaches. They acknowledged that although the capital

asset pricing model of Sharpe (1964) has limitations in terms of its assumptions and

rational implications in empirical asset pricing literature [Fama and French (1992)], the

multi-factor model that includes the market return should be used in practice to capture

the cross-sectional differences in the average returns of individual stocks. This practice

is generally seen in the arbitrage pricing theory analysis of Ross (1976). As the theory

does not provide any guidelines about factors, researchers often rely on a number of

methods that include statistical factor analysis, principal component analysis, and

attributes of macroeconomic and fundamental variables as asset pricing factors.


With some blurring at the boundaries, the methodology that uses multi-factor models of

asset returns can be divided into three types: (i) macroeconomic factor model; (ii)

statistical factor model; and (iii) fundamental factor model [Connor (1995)]. A

macroeconomic factor model is typically intuitive and the simplest, requiring data on

security returns and macroeconomic variables. The pioneering studies of Chen, Roll

and Ross (1983), Berry, Chan, Chen and Hsieh (1985), and Burmeister and McElroy

(1988) all covered macroeconomic factor modelling which uses time series regression

to estimate security factor betas. The statistical factor model usually follows maximum

likelihood and principal component techniques of data analysis. It requires cross-

sectional or time series samples of security returns to identify the pervasive factors in

the return generating process of securities, and it also uses time series regression to

estimate the factor beta. The fundamental factor model does not requires time series

data or time series regression; rather it relies on attributes relevant to listed companies,

namely, the firm size, the dividend yield, book-to-market ratio, and industry

classification. The fundamental factor model uses observed company attributes as

factor betas, whereas both the macroeconomic and statistical factor models estimate a

firms factor beta by using a time series regression that requires a long and stable

history of returns. Connor (1995) studied the explanatory power of these three types of

multi-factor models and estimated a particular specification of each of the models based

on the work of Connor and Korajczyk (1993). Connor (1995) found that both statistical

and fundamental factor models substantially outperform the macroeconomic model and

the fundamental model slightly outperforms the statistical model. Although Connors

(1995) study was based only on the explanatory power criterion to evaluate the relative

strength of the three approaches to multi-factor modelling, he acknowledged that other


criteria, namely, theoretical consistency and intuitive appeal, are significant in the

literature and deserve attention. In considering other criteria to assess the relative

strength of the models, Connor (1995) observed that the performance of the

macroeconomic factor model became the strongest rather than the weakest.

Time Series Analysis

In general econometrics, the analysis of autocorrelation in disturbances belongs in the

realm of time series analysis. Time series analysis requires some interpretation of both

data generation and sampling. A time series model will typically describe the path of a

variable yt in terms of contemporaneous and perhaps lagged factors xt, disturbances or

innovations εt and its own past yt-1, .

1 2 3 1t t t ty x yβ β β ε−= + + + (5.11)

Essentially, a time series is a single occurrence of a random event. The properties of yt

as a random variable in a cross-section are straightforward. It is common to assume that

disturbances are generated independently from one period to the next.

Cointegration

In the time series area, the most recently developed alternative approach to examine the

relationship between time series variables is cointegration analysis. The cointegration

analysis technique is still evolving and has many forms, as is evident from the literature


which might sometimes seem confusing to the first timer. Often the terms causality and

cointegration are synonymous. The notion of causality has existed as an operational

concept in the empirical macroeconomic and financial literature since Granger (1969)

[Hansen and Mittnik (1998)]. As correlation does not necessarily imply causation in

any meaningful sense of that word, the Granger (1969) approach to the question of

whether the x variable causes y is to see how much of the current y can be explained by

past values of y and then to see whether adding lagged values of x can improve the

explanation. In the view of Granger (1969), y is said to be Granger-caused by x if x

helps in the prediction of y, or equivalently, if the lagged xs are statistically significant.

Usually, two-way causation is checked: x Granger causes y; and y Granger causes x.

The Wald test has been widely used for testing zero restrictions implying Granger non

causality.

It is important to find the causal structure of a vector autoregressive analysis since all

variables are assured to be endogenous in the sense of Sims (1980). During the late

1980s, Engle and Granger (1987) and Granger (1988) introduced a relatively clearer

concept of cointegration and error correction mechanism. Later, Johansen (1988)

proposed a vector autoregressive error correction model based on the concept of

canonical correlation and full information maximum likelihood estimation. Johansen

and Juselius (1990) provided further directions for cointegration analysis and showed

how to handle identification problems and impose necessary restrictions.

A simple exposition of the cointegration approach is that a set of time series variables

are said to be cointegrated if they are integrated of the same order and a linear


combination of them is stationary [Maysami and Koh (2000)]. Such linear

combinations would then point to the existence of a long-term relationship between the

variables [Johansen and Juselius (1990)]. In other words, cointegration means that

despite being individually nonstationary, a linear combination of two or more time

series variables can be stationary in the long-run [Gujarati (1995)]. Although unit roots

or nonstationarity in variables are important for cointegration analysis, Spanos (1990)

argued that the question of whether a priori variables exhibit a unit root is ill-posed, as

it is not generally the case that the unit root found in the autoregressive representation

of a series will model in the context of a vector autoregressive representation. Caporale,

Hassapis and Pittis (1998) showed how the issue of unit roots is an invariant feature of

a time series that relates to long-run causality. They recognized that there are two steps

to model specification, variable selection and the imposition of a structure which draws

upon economic and/or finance theory. Pesaran and Shin (1994) also contributed to the

structural approach to cointegration analysis by developing a method of identification

for the long-run relations.

It may be noted that numerous techniques are available for empirical investigation

using cointegration analysis. We investigate some applications of cointegration analysis

so that we can choose which technique is suitable for our modelling and empirical

analyses.


Applications of Cointegration Analysis

For any cointegration test it is necessary that a unit root in the time series for

nonstationarity is found at the outset. The test statistics can be based on the ordinary

least squares (OLS) results for a suitably specified regression equation. The following

are two forms of Augmented Dickey-Fuller (ADF) [Dickey and Fuller (1979, 1981)]

regression equations for a time series Yt:

0 1 1

1

p

t t j t j t

j

Y Y Yα α γ ε− −=

∆ = + + ∆ +∑ (5.12)

0 1 1 2

1

p

t t j t j t

j

Y Y t Yα α α γ ε− −=

∆ = + + + ∆ +∑ (5.13)

where we assume that t

ε for t = 1,.., N is a white noise process which has no

discernible structure with constant mean or constant variance σ2

and is uncorrelated

with other variables. The first of the above equations has a constant with no trend,

whereas the second equation has a constant with a trend. The number of lagged terms p

is chosen to ensure the errors are uncorrelated. Later, test statistics such as z-test, t-test,

and F-test with or without drift are calculated for both equations against the null

hypothesis to ascertain if there is a unit root. Table 5.2 depicts formats of test statistics

corresponding to each null hypothesis:


TABLE 5.2

ADF Unit Root Testing Formats Null hypothesis | Test Statistic

For equation: 0 1 1

1

p

t t j t j t

j

Y Y Yα α γ ε− −=

∆ = + + ∆ +∑

1

1

0 1

0

0

0

ααα α

=== =

1

1

N

t ratio

F test

α

φ−−

( )

z test

test

Unitroot test zerodrift

τ−−

−

For equation: 0 1 1 2

1

p

t t j t j t

j

Y Y t Yα α α γ ε− −=

∆ = + + + ∆ +∑

1

1

0

0

αα

==

1N

t ratio

α−

z test

testτ−−

Source: Adapted from Dickey and Fuller (1979, 1981), Brooks (2002), EViews, Green (2000), Verbeek (2000) and Dhrymes (1998).

This method is capable of producing test statistics against each null hypothesis

considering both constant with or without trend and even no constant. The constant

with trend and drift are presented as 0 1 2 0α α α= = = and

1 2 0α α= = . Here, 0α is the

drift, 1α represents a unit root, and

2α indicates a trend. The presence of one unit root is

represented by I(1), whereas I(0) stands for no unit root. The presence of a unit root is

derived from test statistics and critical values for the same. When the null hypothesis

cannot be rejected the resulting outcome indicates the presence of a unit root, I(1), and

we say that the series is integrated of order one.

The Engle-Granger (1997) approach to cointegration analysis often uses the

Augmented Dickey-Fuller (ADF) tests on the OLS residuals applying critical values.

The approach requires running a regression of Y1t (being the first element of Yt) against

the other k-1 variables, Y2t, , Ykt, and testing for a unit root in the residuals. If the unit

root hypothesis is rejected, the hypothesis of non cointegration is also rejected.


Phillips and Ouliaris (1990) indicate that the Phillips test is a non parametric approach.

Engle and Granger (1987) considered the same regression equation while undertaking

the Phillips test as in ADF, 0 1

1

k

t t j t j t

j

e e eδ δ η− −=

∆ = + ∆ +∑ , assuming k=0, τ *= t-ratio on

the estimate of δ0, te∆ is the first differenced series, and tη the residuals from the least

squares fit. The Phillips test statistic for a sample of n-observations is then

( )2 2

*

2

2 te

η ω σσττω ω

−= −

∑ (5.14)

where 2 1 2tnσ η−= ∑

and ( )2 1 2

1 1 1

2 ,n k n

t t t j

t j t j

n j kω η ω ηη−−

= = = +

= +

∑ ∑ ∑ (5.15)

employing 1( , )

( 1)

jj k

kω −=

+

where k is chosen sufficiently large to account for all non zero autocorrelations.

Under the null hypothesis of non cointegration, Loughran and Newbold (1997)

observed that both the ADF and Phillips tests provide the same asymptotic (large

sample) distribution. Shamsuddin and Holms (1997) point to a couple of limitations of

ADF, namely, that the arbitrary choice of the dependent variable in the cointegrating

regression often leads to a sequence of residual series based on which variable is

considered as dependent; and the ADF cannot be used to identify the existence of


multiple cointegrating vectors. Their view is that these limitations of ADF can be

overcome by the Johansen procedure.

It is also possible to use the Durbin-Watson (DW) test statistic or the Phillips-Perron

(PP) approach for nonstationarity of residuals. If the DW test is applied to the residuals

of potentially cointegrating regression, it is known as the Cointegrating Regression

Durbin Watson (CRDW). Under the null hypothesis of a unit root in the errors, CRDW

≈ 0 (that is, CRDW is equivalent to zero), so the null of a unit root is rejected if the

CRDW statistic is larger than the relevant critical value which is approximately 0.5

[Brooks (2002)]. Thus, the null hypothesis Ho: ût ~ I(1) can be tested against the

alternative hypothesis H1:ût ~ I(0) using CRDW.

As most empirical studies in economics and finance involve both nonstationary and

trending variables, differencing and other transformations including seasonal

adjustments for reducing them to stationarity and then analyzing the resulting series are

appropriate. Yet, recent researches show more interesting and efficient analytical ways

for dealing with trending variables that are integrated of order one. In any fully

specified regression model, there is a presumption that the disturbance (tε ) is a

stationary, white noise series. However, this presumption is unlikely to be true if both

endogenous (Yt) and exogenous (Xt) series are integrated. Generally, if two series are

integrated to different orders, then linear combinations of them will be integrated to the

higher of the two orders [Green (2000)]. Thus, if both endogenous (Y) and exogenous

(X) variables at a period (t) are I(1), then we would normally expect Yt β Xt to be of


I(1) regardless of the value of β . On the other hand, if the two series are both I(1),

there may be a β such that:

t t tY Xε β= − is I(0) (5.16)

Intuitively, if the two series are both I(1), then this partial difference between them

might be stable around a fixed mean. The implication of this would be that the series

are drifting together at roughly the same rate. Whenever two series satisfy this

condition, they are said to be cointegrated and the vector [1, β− ] or any multiple of it is

a cointegrating vector. In such a case we can ascertain a long-run relationship between

Yt and Xt and identify the manner in which the two variables drift upward together.

Alternatively, one can observe the short-run dynamics through the relationship between

deviations of Yt from its long-run trend and deviations from Xt from its long-run trend.

In this case, differencing of the data would be counterproductive, since it would

obscure the long-run relationship between Yt and Xt. Studies of cointegration and related

techniques such as vector autoregressive regression (VAR) and vector error correction

model (VECM) are concerned with methods of estimation that preserve information

about both techniques on covariation [Engle and Granger (1987), and Watson (1994)].

VAR is commonly used for forecasting systems of interrelated time series as well as for

analyzing the dynamic impact of random disturbances on the system of variables. The

VAR representation sidesteps the need for structural modelling by treating every

endogenous variable in the system as a function of the lagged variables of all the

endogenous variables. The VAR may be in the form


1 1 ............t t p t p t tY Y Y Xψ ε− −=∏ + +∏ + + (5.17)

where Yt is a k vector of endogenous variables; Xt is a d vector of exogenous variables;

1∏ , , p∏ and ψ are matrices of coefficients to be estimated; and

tε is a vector of

innovations that may be contemporaneously correlated with each other but are

uncorrelated with their own lagged values and uncorrelated with all of the right hand

side variables (EViews).

Since only lagged values of the endogenous variables appear on the right hand side of

each equation, there is no issue of simultaneity and OLS may be the appropriate

technique of estimation. The disturbances are not serially correlated which means it is

unrestrictive since any serial correlation could be absorbed by adding more lagged Ys.

By employing any suitable econometrics software, one can estimate the parameters of

the VAR and then do either cointegration or Granger causality tests to see the long-run

relationship between variables of interests. One can test Granger causality by running a

VAR on the system of equations and testing for zero restrictions on the VAR

coefficients. Often, an alternative approach disregards testing for Granger causality.

The VAR model then generates an error correction mechanism which is accommodated

within the VECM. In this process, it is imperative that lagged length is identified

beforehand. Instead of a trial and error method, the most efficient way of getting the

information about the lagged value could be from either the Akaike Information


Criteria or the Schwarz Bayesian Criteria. In this connection, the residual covariance

Ω is computed as

d e t /t t

t

Tε ε ′Ω = ∑ (5.18)

where tε is the k vector of residuals from k equations or parameters with T

observations . The log-likelihood value, l , is computed assuming a multivariate normal

(Gaussian) distribution as

( ) 1 lo g 2 lo g2 2

T k Tπ= − + − Ωl (5.19)

The two above mentioned information criteria about the length of the lag are as under:

2 / 2 /AIC T n T= − +l (5.20)

2 / log /SBC T n T T= − +l (5.21)

where n = k(d + pk) is the total number of estimated parameters in the VAR. Apart

from these popular criteria, there is another called the Hannan-Quinn Criterion. The

smaller the value of the information criteria, the better is the model.

Further, one might have to compute an impulse response function for each innovation

and endogenous variable pair. Essentially, these trace the effects of a shock to an

endogenous variable on the variables in the VAR. Accordingly, a four-variable VAR


has 16 potential impulse response functions. Variance decomposition provides a

different method of depicting the system dynamics. Variance decomposition gives

information about the relative importance of each random innovation to the variables in

the VAR.

As a VECM is nothing but a restricted VAR that has cointegration restrictions built into

the specification, it is designed for use with nonstationary series that are known to be

cointegrated. The VECM specification restricts the long-term behaviour of the

endogenous variables to converge to their cointegrating relationships while allowing a

wide range of short-term dynamics. The cointegration term is known as the error

correction term since the deviation from long-term equilibrium is corrected gradually

through a series of partial short-term adjustments. We can consider a simple two-

variable system with one cointegrating equation and no lagged difference terms as:

2 , 1 ,t ty yβ= and (5.22)

the VECM as:

1, 1 2, 1 1, 1 1,( )t t t ty y yλ β ε− −∆ = − + and (5.23)

2, 2 2, 1 1, 1 2,( )t t t ty y yλ β ε− −∆ = − + (5.24)


In this model the only right hand side variable 2, 1 1, 1( )t ty yβ− −− is the error correction

term. In long-run equilibrium, this term is zero. However, if y1 and y2 deviated from

long-run equilibrium last period, the error correction term is nonzero and each variable

adjusts to partially restore the equilibrium relation. The coefficients 1λ and

2λ measure

the speed of adjustment. The two endogenous variables y1,t and y2,t will have nonzero

means but the cointegrating equation will have a zero intercept. The VECM will take a

different form by including an intercept term when endogenous variables do not have a

trend. The cointegrating equation has an intercept as

1, 1 2, 1 1, 1 1,

( )t t t t

y y yλ µ β ε− −∆ = − − + and (5.25)

2, 1 2, 1 1, 1 2,( )t t t ty y yλ µ β ε− −∆ = − − + . (5.26)

Both a linear trend and an intercept can be accommodated in the VECM as

1, 1 1 2, 1 1, 1 1,( )t t t ty y yδ λ µ β ε− −∆ = + − − + and (5.27)

2, 2 1 2, 1 1, 1 2,( )t t t ty y yδ λ µ β ε− −∆ = + − − + . (5.28)

It is also possible to include lagged differences instead on the right hand side to meet

the specific research demand.


Given a group of nonstationary series, one may determine whether the series are

cointegrated, and if they are, one can ascertain long-term equilibrium relationships.

Any VAR based cointegration tests can be conducted by using the methodology

developed by Johansen (1988, 1991, 1995a). Johansens method tests the restrictions

imposed by cointegration on the unrestricted VAR involving the series. To explain, we

consider a VAR of order p:1 1 ........t t p t p t ty A y A y Bx ε− −= + + + + , where yt is a k-vector

of nonstationarity; I(1) variables; xt is a d-vector of deterministic variables; and tε is a

vector of innovations. The reduced form of VAR takes the following shape:

1

1

1

p

t t i i t i t t

i

y y y B x ε−

− −=

∆ = + Γ ∆ + +∑∏ (5.29)

where 1

p

i

i

A I=

∏ = −∑ and

1

p

i j

j i

A= +

Γ = − ∑

Grangers representation theorem asserts that if the coefficient matrix Π has reduced

rank r k< , there exist k r× matrices α and β each with rank r such that αβ ′Π = and

tyβ ′ is stationary. Here, r is the number of cointegrating relations and each column of

β is the cointegrating vector. The element of α are known as the adjustment

parameters in the VECM. Johansens method is to estimate the Π matrix in an

unrestricted form, then test whether the restrictions implied by the reduced rank of Π

can be rejected.


Shamsuddin and Holms (1997) applied the Johansen test from their equation

system1 1 1t tx A x ε−= + , where xt was the vector of parameters and εt was the vector of

errors. Subtracting xt-1 from both sides and denoting π = (A1 I), they obtained

expressions such as ∆xt = - T ttx ε+−1 .

As a common practice, the Johansen test involves testing the rank r of Π . The rank of

Π gives the number of independent cointegrating vectors and the following test

statistic is used to determine the rank:

0

0

1

( ) ln (1 )k

t ra ce j

j r

r Tλ λ= +

= − −∑ (5.30)

where ^

jλ =estimated eigenvalues of the ^

Π matrix and T = the effective number of

observations. This is the so-called trace test that checks whether the smaller k-r0

eigenvalues are significantly different from zero. The results on the Johansen trace test

for cointegration are the λ trace statistic. If the null hypothesis 0 0:H r r≤ cannot be

rejected against the alternative hypothesis1 0:H r r k< ≤ , this would mean that there

exists no cointegrating relationship between the variables in the system. Alternatively,

one can test 0 0:H r r≤ versus the more restrictive alternative

0: 1iH r r= + using

0max 0 1

( ) ln(1 )rr Tλ λ += − − (5.31)


This is called the maximum eigenvalue test, as it is based on the estimated

0( 1)r th+ largest eigenvalue. The above two tests are often known as likelihood ratio

tests. They do not have the usual chi-squared distributions; rather, their appropriate

distributions are multivariate extensions of the Dickey-Fuller distributions. As with the

unit root tests, the percentiles of distributions depend on whether a constant and/or a

time trend are included [Verbeek (2000)].

Lutkepohl and Saikkonen (2000) investigated the cointegrating rank of a VAR process

with a time trend. They noticed that standard tests for the cointegrating rank of a VAR

have nonstandard limiting distributions which depend on the characteristics of intercept

terms and time trends in the system. Often these characteristics are unknown. As a

result, they modified the tests that allowed for deterministic linear trends in the data

generation process. Their modified tests were based on the lagrange multiplier principle

and, in contrast to likelihood ratio tests, accounted for the cointegrating rank specified

under the null hypothesis in estimating the trend parameters. Those tests had

nonstandard limiting disturbances which did not depend upon deterministic terms and

had better local power as well as small sample properties in many situations compared

to the competing likelihood ratio tests. Considering a time series of n-dimension,

yt=(y1t,,ynt), t= 1,,T, they generated their initial model:

0 1t ty t xµ µ= + + t = 1, 2, . (5.32)


where 0 ( 1)nµ × and

1( 1)nµ × are unknown parameters which may, of course, be zero,

and xt is an unobservable error process. It is assumed that xt follows a pth-order VAR

process:

1

..........t t t p t p t

x A x A x ε− −= + + + t=1, 2, . (5.33)

where the Aj are (n×n) coefficient matrices. This process was written in error correction

form as:

1

1

1

p

t t j t j t

j

x x x ε−

− −=

∆ = Π + Γ ∆ +∑ t= 1, 2, .. (5.34)

where 1( ....... )n pI A AΠ = − − − − is (n×n), the

1( .... )j j pA A+Γ = − + + , (n×n), are

unknown parameters and ∆ is the usual differencing operator. The error term tε is white

noise, that is, tε ~ (0, )Ω with Ω positive definite.

Andersson and Gredenhoff (1999) examined the usual maximum likelihood procedure

under a fractional equilibrium error situation. Their lagrange multiplier test has the

ability of detecting cointegration relationships when deviations from equilibrium are

persistent.

Otero and Smith (2000) studied the effects of increasing the frequency of observation

and the data span of Johansen cointegration tests. They observed that the ability of the

Johansen tests to detect cointegration is more dependent on the total sample length than


the number of observations. They utilized the procedures of both the Augmented

Dickey-Fuller and the Phillips-Perron tests in their study. They also did simulations by

using both Monte Carlo and relevant empirical applications. The overall results suggest

that when interested in long-run relationships, practitioners ought to rely on data

collected over a long period of time rather than on a large number of observations

collected over a relatively short period.

Pesaran and Shin (1995) acknowledged that economic analysis of long-run

relationships has been the focus of much theoretical and empirical research. They

followed the general practice, instead of cointegration, when the variables in the long-

run relationship were trend stationary. They attempted to de-trend the series and model

the de-trended series as a stationary distributed lag or autoregressive distributed lag

(ARDL) model. Estimation and inference concerning the long-run properties of the

model was then carried out using standard asymptotic normal theory in the context of

the ARDL model [Hendry and Sargan (1984), Wickens and Breusch (1988)]. Typically,

for a large sample, an estimator α is considered a consistent estimator of α when α is

asymptotically unbiased; and var( α ) decreases as the sample size increases [Lardaro

(1993)]. However, the analysis of Pesaran and Shin (1995) became more complicated

when the variables were difference stationary or integrated. They recognized that in the

presence of integrated or I(1) variables the traditional ARDL approach does not work.

Consequently, they choose an alternative estimation and hypothesis testing procedure

for the analysis of those I(1) variables in line with Engle and Granger (1987), Johansen

(1988, 1991), Phillips (1991), Phillips and Hansen (1990), and Phillips and Loretan

(1991).


Hassapis, et al. (1999) showed that sufficient conditions for unit roots found in VAR

systems amount to Granger non causality in any direction among the variables

involved. This implies that a necessary condition for the disappearance of one unit root

in a VAR system implies Granger causality in at least one direction. The researchers

also noticed that causality and cointegration inference is strongly affected by the

omission of an important causal variable. For first order models with non explosive

variables, Granger causality is also sufficient for cointegration.

Lau (1999) attempted to complement empirical studies applying unit root and

cointegration methods and showed that integration and cointegration properties arise

intrinsically in stochastic endogenous growth models under fairly general conditions.

This implies that a unit root has to be present in the autoregressive polynomial of the

variables generated by an endogenous model so as to produce a steady state in the

absence of exogenous elements. The endogenous modelling induces difference

stationarity of the variables even though the external impulses are stationary, and it

leads to the phenomenon of cointegration if the variables satisfy a state-space

representation. The unit root propagation mechanism is the time series analogue of the

constant returns condition. The time series properties of endogenous models combined

with their counterparts for exogenous models lead to testable implications for

distinguishing between these two classes of models.

Johansen (1991) presented new results on maximum likelihood estimators and

likelihood ratio tests for cointegration in Gaussian VAR models with a constant term


and seasonal dummies [Johansen (1991)]. He considered a general VAR model with

Gaussian errors written in error correction form:

1

1

k

t i t i t k t t

i

X X X D µ ε−

− −=

∆ = Γ ∆ + ∏ + Φ + +∑ (t = 1, , T) (5.35)

where Dt are seasonal dummies and µ is a constant term. Further,tε and (t = 1, ..,T)

are independent p-dimensional Gaussian variables with mean zero and variance matrix

Λ . The first k data points X1-k, ., X0 are considered fixed and the likelihood

function is calculated from given values of them. The parameters 1 1,......., , ,k µ−Γ Γ Φ

and Λ are assumed to vary without restrictions, and Johansen formulated the

hypotheses of interest as restrictions on∏ . This model of Johansen (1991) was denoted

by H1 and his hypothesis of at most r cointegration vectors H2 was formulated as:

2 :H α β ′∏ = (5.36)

where β referred to cointegrating vectors, and α, the adjustment coefficients, were p×r

matrices. When comparing models with different numbers of cointegration vectors,

Johansen used the notion H2(r). His objective was to conduct inference on the number

of cointegrating relations as well as their structure without imposing an a priori

structural relationship. This was accomplished by fitting the general VAR model:

1

1

k

t i t i t k t t

i

X X X D µ ε−

− −=

∆ = Γ ∆ + ∏ + Φ + +∑ (5.37)


for describing the variation of data, and formulating questions concerning structural

economic relationship as hypotheses about the parameters of the VAR model. Johansen

(1991) tested these hypotheses using likelihood ratio statistics.

In 2000, Johansen presented an insight into the modelling of cointegration in the VAR

model and examined some results that were obtained from the cointegrating VAR. The

Granger representation theorem was evaluated and the notions of cointegration and

common trends were defined. Johansen defined the related statistical model for

cointegrated I(1) variables, demonstrated how hypotheses on the cointegrating relations

can be estimated under suitable identification conditions in the light of asymptotic

theory, and indicated some applications of the cointegration model in economic

research [Johansen (2000)].

Johansen (2000) also presented some definitions based on the Granger representation

theorem with essential proofs that are suitable for various conditions of modelling

cointegration in a VAR system, and also demonstrated how to express the stochastic

properties of the solution of the autoregressive equations under various assumptions

about the parameters. Johansen derived a reduced error correction model as:

1

1

k

t t i t i t t

i

X X X D ε− −=

∆ = + Γ ∆ + Φ +∑∏ (t = 1, ., T) (5.38)


where Dt are deterministic dummies and the tε are i.i.d. (0, )nN Ω . The equations

determine the process Xt as a function of initial values X0, ., X-k, the ε and

dummies Dt. From the 5.38 equation Johansen then derived a matrix A(z) of n×n order

as:

1

( ) (1 ) (1 )k

i

i

i

A z z I z z z=

= − −∏ − Γ −∑ (5.39)

Allowing ( )A z to denote the determinant, and ( )adjA z the adjoint matrix:

( ( ) )( )

( )

t a d j A zA z

A z

− = (5.40)

The main assumption here is that the polynomial A(z) satisfies the condition ( ) 0A z =

implying either |z| > 1 or z = 1.

Further, based on the Granger representation, Johansen (2000) examined the model

describing an I(1) process having cointegration and αβ ′∏ = . The reduced form of

error correction model (Hr) thus takes the following shape:

t 1

1

Xk

t i t i t t

i

X X Dαβ ε− −=

′∆ = + Γ ∆ + Φ +∑ (t = 1, ..., T) (5.41)


where α and β are n×r, and 1,......, Tε ε are independent Gaussian (0, )nN Ω , and the

variables Dt are deterministic terms. The parameters 1( , , ,......, , , )kα β Γ Γ Φ Ω are freely

varying.

Johansen then formulated a nested sequence of hypotheses 0 .... ....r nH H H⊂ ⊂ ⊂ ⊂ .

The test of Hr in Hn was that there are at most r cointegrating relations. Thus, H0 is just

a VAR model for Xt in differences and Hn the unrestricted autoregressive model for Xt

in levels, and the models in between H1, ,Hn-1 give the possibility to exploit the

information in the reduced rank matrix ∏, and contain information about the long-run

relationships in the economy [Johansen (2000)].

The Johansen approach [Johansen (1988, 1989, 1991, 1995, 2000); Johansen and

Juselius (1988, 1990)] to cointegration analysis seems attractive to many researchers,

although competing approaches like the Engle-Granger two-step method [Engle and

Granger (1987); Granger (1983, 1994)] and the ARDL method [Pesaram and Shin

(1995)] are also popular in practice.

Summary

This chapter investigated various empirical techniques that are suitable for detecting the

relationship between stock market returns or price movements and a priori variables. It

observed that various researchers investigated this relationship by employing different

methods. The analytical periphery depends on the availability of resources including

computer software and data at hand. The recent breakthrough in computing capacity


and speed coupled with the development of statistical and econometric software has

enabled researchers investigating the security pricing process and other relevant issues

to adopt approaches, namely, cointegration analysis, which are more efficient than

traditional approaches such as ordinary regression analysis and/or factor component

analysis. We have observed that, depending on the research objectives and available

resources, different researchers have applied different techniques for cointegration

analysis there is no hard and fast rule as to which technique is to be employed for

investigating both long-run and short-run relationships among pre-identified variables.

In practice, at least three techniques for cointegration analysis are popular we intend

to use Johansen approach.

The empirical methods that are applied and practiced by various researchers suggest

that we can follow any or a combination of techniques for analyzing our research

problems and still achieve results of similar or even better standards. We have

contributed in this chapter by exploring the cointegration technique. In Chapter 6 we

will develop a model suitable to our research purpose.


CHAPTER 6

MODELLING

As stated at the outset, the aim of this thesis is twofold. First, we intend to identify any

long-term relationships between systematic risk factors and Australian stock market

returns based on theories of economics and finance. In line with this research objective,

we have chosen a priori variables to proxy for Australian systematic risk factors. Based

on theoretical and empirical evidence as well as the methodological and analytical

strengths of available econometrics software, we have attempted to develop a model

which makes use of the most recent methodology. We have thus used a modern

empirical approach to ascertain whether a priori variables have influenced Australian

stock market prices movements as well as returns.

Secondly, we aim to study cross-country stock market relationships to determine

whether the Australian stock market is cointegrated with other developed markets

under prevailing global economic and technical settings. Our second analysis is

performed after we have conducted our first analysis the base study using the

method of cointegration. To meet both research objectives, we have developed our

models in terms of cointegration analysis.

Pool of a priori variables

Based on the literature reviews in Chapters 2, 3 and 4, there exists no hard and fast rule

in choosing a priori variables to proxy systematic risk factors for consideration in our


first empirical objective. Often, the decision was made arbitrarily. Yet, it appeared that

the proxy variables considered were based on plausible economic, finance or

accounting theories. Further studies showed that researchers choice of the number of a

priori variables was based on the capabilities of the software that they employed

[Brooks (1997)]. Although rationales for choosing a priori variables may vary from

researcher to researcher, they have to be consistent with prevailing theories, familiar

intuition and research objectives.

Most of the studies in this field, including Roll and Ross (1980), Sinclair (1982), Chen,

et al. (1986), Hamao (1986), Faff (1988), and McGowan and Francis (1991), provided

mixed support for arbitrage pricing theory having three to five proxy variables or

factors. The variables that explained stock returns were changes in industrial

production, inflation, money supply, personal consumption, and interest rates. Fama

(1981) studied the relationship between common stock returns and real economic

variables, namely, capital expenditure, industrial production, gross national product,

money supply, lagged inflation, and the interest rate. Chen, Roll and Ross (1986) used

industrial production, money supply, inflation, the exchange rate, and long- and short-

term interest rates to investigate their effect on stock returns. Chen (1991) found that

the lagged production growth rate, the default premium, the term premium, the short-

run interest rate, and the market dividend-price ratio are the domestic macroeconomic

variables which have a significant direct and indirect impact on changes in stock prices.

Wongbangpo and Sharma (2002) used a model with five macroeconomic a priori

variables gross national product, the consumer price index, money supply, the


nominal interest rate, and the exchange rate to investigate the relationship between

these variables and US stock price indices. Valentine (2000) argued that corporate

profits, interest rates, the exchange rate and overseas influences are relevant to stock

pricing. Maysami and Koh (2000) found six macroeconomic variables to be relevant,

namely, the exchange rate, short- and long-term interest rates, inflation, the money

supply, domestic exports, and industrial production. Paul and Mallik (2001) considered

quarterly observations of inflation, interest rates, and gross domestic product as their

proxy and they found both the interest rate and gross domestic product growth

significant in the Australian banking sector market pricing process.

It is apparent that capital markets around the globe are undergoing tremendous changes

with the impact of the information revolution and changes in household/consumer

tastes. To cope with these changes, market liberalization or financial deregulation often

provides a boost in market activity. Market liberalization also tends to make markets

efficient, where no under- or over-valued securities exist, based on the available

information set [Drew (2000)]. Likewise, available computable general equilibrium

(CGE) models (including ORANI and MONASH) often provide significant inputs to

the development process of an efficient stock market like Australia. Additionally,

global market indices viewed as benchmarks play an important role in the process of

asset pricing.

A list of a priori variables frequently used in various studies is presented in Table 6.1.


TABLE 6.1

Record of A Priori Variables Used in Various Studies Popular a priori variables Referred studies

Industrial Production; Inflation; Interest rates; Treasury

bill rates; Long and short-terms Govt. bond rates;

Corporate bond rates; Equity returns; Per capita

consumption; Risk Premium; Term structure; Foreign

exchange rate; Market indices; Oil price; Overall

production; Gross Domestic Production; Gross national

product; Weekly wages; Money supply, Wholesale sales;

Labour force; Building construction; Federal debt;

Federal budget financing; Housing construction;

Exports and Imports; Population; Inventories; Book-to-

market equity value; Dividend yields; Spread of long-

and short-runs bond yield; High and low-grades bond

yield; Current liabilities; Consumer credit outstanding;

Commercial bank asset value; Money stock; Consumer

price index; Price-earnings ratio; Farm size; Corporate

profit; International or global index

Roll and Ross (1980); Chen, Roll and Ross (1986); Zhou (999); Kim and Lee (1995); Wongbangpo and Sharma (2002); Maysami and Koh (2000); Gehr (1978); Fogler, et al. (1981); Hughes (1985); Beenstock and Chan (1983, 1984); Winkelmann (1984); Dumontier (1986); Kim and Lee (!995); Connor and Korajezyk (1989); McGowan and Francis (1991); Brailsford and Heaney (1998); Connor (1995); Bai and Ng (2002); Fama and French (1992, 1993); Chamberlain and Rothschild

(1983); Anckonle (1983); Connor and Korajczyk (1986, 1988, 1989); McGowan and Francis (1991); Shukla and Trzcinka (1990); Faff (1988, 1992); Merville, et al. (2001); Beggs (1986); Merton (1973); Kritzman (1995); Fam and French (1992, 1993); Brown and Weinstein (1983); Aitken, et al. (1996); Brailsford and Easton (1991); Faff and Brailsford (1999); Hamao (1988); Faff and Heaney (1999); Easton and Faff (1994); Zhou

(1999); Velu and Zhou (1999); Brailsford and Faff (1996); Maysomi and kho (2000); Johansen (1988, 1991, 1995, 2000); Pesaran and Timmerman (1995); McMillan (2001); Mukharjee and Naka (1995); Cheung and Ng (1998); Ackert and Racine (1999); Nasseh and Stranss (2000); Mukharjee and Hoh (2000); Shamsuddin and Holmes (1997); Cheung and Ng (1998); Paul and Mallik (2001); Roca (1998); Shamsuddin and Kim (2000,

2003); Valentine (2000).

We have so far learned that there is a wide range of variables that we can consider as

proxies for systematic risk factors in Australian stock market pricing. To derive the

series of a priori variables, we often need to do some form of transformation or

manipulation of available basic data series. It appears that some types of economic,

financial, and accounting indicators represent the elements of systematic risk that

influence the return generating series of any stock market. Initially, we have decided to

consider a priori variables that have both theoretical and practical implications for our

empirical investigation and analyses. We also understood that transformations might

provide inefficient outcomes when investigating long-run relationships. The

recommendation in the literature is that base level data do not generally provide

information when they are nonstationary. However, a handful of a priori variables were


considered at the beginning based on theoretical consistency that are later reduced to a

workable number based on the data and the analytical capabilities of available

econometric software.

Variables for Modelling

Stock indices represent the returns on the market as a whole. Most stock indices are

price weighted and use market capitalization based weights. These indices act as

market indicators and set up a performance benchmark in the stock market. They thus

provide a sensible and realistic proxy for the security market pricing profile.

Accordingly, we have considered the time series of index values in our analysis

because they represent the Australian stock market performance.

Nearly 100 different Australian Stock Exchange (ASX) share price indices are

currently produced. Some cover shares in specific industries, namely, metal, oil and

gas, banking, insurance, retail, media, and so on. Others cover combinations of these,

namely, all resources, all industrials, all ordinaries, and so on. Further indices cover

combinations of various leaders in the market, namely, S&P/ASX 20, S&P/ASX 50,

S&P/ASX 200, S&P/ASX 300, S&P/ASX MidCap, S&P/ASX SmallCap, and so on. In

each case the value of the stock price index represents the current market capitalization

of all the shares concerned, expressed as a number relative to a base number. Australian

stock indices thus give a quick picture of weighted average price movements in the

market either as a whole or for a sector of the Australian share market [Renton (1998)].

The indices for the Australian stock market are constructed by Standard and Poors,


implying that they are of world standard and accurately represent Australian stock

market performance. Although both the S&P/ASX 200 and the All Ordinaries indices

are comprehensive, we have used the All Ordinaries (ALLORDS). It is a standard

proxy of Australian stock market prices movements/returns over the period lasting from

the 1st quarter of 1983 to the 2

nd quarter of 2002.

As for our a priori variables, we initially selected 15 variables based on both theoretical

and intuitive considerations. For further analysis and modelling we have reduced the

number of a priori variables to six. These ultimate a priori variables for our first

empirical analysis, presented in Chapter 7, are the bank variable interest rate, industrial

production, the exchange rate, the dividend yield, the price-earnings ratio, and the

global stock market index.

For our supplementary objective, that of cross-country stock market cointegration

analysis, we have considered the comprehensive stock market indices of the US, the

UK, Germany, Canada, France, Japan, and Australia. This study concentrated on the

annual data series of all seven stock markets from 1945 to 2002. We have used the

DJIA, FTA, DAX, SBF250, S&P/TSX300 and NIKKEI to represent the stock market

performances of the US, the UK, Germany, France, Canada and Japan respectively for

our second empirical study, presented in Chapter 8.


Modelling

Variables for our first study have drawn upon both prevailing theories and intuition.

Our intention here is to ascertain whether the a priori variables (Xit) have any long-run

effect in explaining the dependent variable (Yt), and if they do, which ones are

influential. To undertake an empirical investigation on the first research question, we

have developed a basic model, which is then extended by necessary transformations to

suit our specific modelling needs.

We start with a simple structural relationship of our variables Yt and Xit may be

presented in either this manner:

1( , .. . ., )t t k tY f X X= (6.01)

or

1

k

t i i t

i

Y X=

= Γ∑ (6.02)

where Yt is the criterion variable representing the security market prices generated from

the quarterly series of the ALLORDS, Xit =X1t, ,Xkt refer to our a priori variables, and

t = study period (that is, 1/1983 to 2/2002 for our first analysis, and 1914 to 2002 for

our second).

Including the error term,tε , in this relationship we have:


( , )t i t t

Y f X ε= (6.03)

The above relationship could also be expressed as:

1

i

k

t it t

i

Y Xδγ ε

=

= ∏ (6.04)

where tε refers to the disturbance or error term; γ is a constant or intercept; and

iδ is

the parameter. Also, here the relationship between predictors or explanatory variables

and between the predictors and the error is assumed to be multiplicative.

Transforming 6.04 into a logarithmic function, the relationship can now be specified in

linear form as:

0

1

k

t i it t

i

y x uµ δ=

= + +∑ (6.05)

where yt = lnYt; µ0 = lnγ; xit = lnXit; δi is the parameter; ut = lnεt; and that ln refers to

natural log.

Further, we can write this equation in another form as:

y X uδ= + (6.06)


where y is of dimension T×1; X is of dimension T×k; δ is of dimension k×1; and u is

of dimension T×1. The represented model is:

t t ty x uδ= + , t = 1, 2, ,T (6.07)

To construct a structural linear regression model, we consider the k regressors or

independent variables, xi, where i=1, ,k and t =1,,T. Through transformation, our

generalized linear multiple regression (GLM) model is:

1 2 2 3 3t t t k kt ty x x x uδ δ δ δ= + + + + +LL (6.08)

The model in matrix form is

11 121 1

2 22 22 2

21 11

1

1

1

k

k

kT TT kTT TkT k

y ux x

xy x u

y ux x

δδ

δ× ×××

= +

L

L

M MM M MM (6.09)

so that the xij element of the matrix X represents the jth

time observation on the ith

variable.


When using a structural model like the GLM, it would be necessary to examine if the

model specifications and variables included in the model are correct. To achieve this

effect a Ramsey Regression Specification Error test is useful. Thus, our generalised

linear model (GLM) or basic structural regression model is

0

1

( | )k

t it i it t

i

E Y X X uµ η=

= + +∑ (6.10)

where ut is assumed to satisfy all the usual assumptions about the regression errors.

In multivariate time series analysis, where the stochastic process is the moving average

process and lags of variables are important to consider in the modelling, the above

basic structural type of model becomes inappropriate. A special type of model is

necessary, one which is valid with autocorrelation and/or other unavoidable

complexities. Although the typical structural approach to simultaneous equation

modelling is often used in describing the basic relationship between endogenous

(dependent) and exogenous (independent) variables of interest in many fields of study,

an autoregressive approach provides outcomes that are more accurate and consistent

with the theory underlying economics and finance. This is because the theory is not

always capable of providing a structured specification to express the dynamic

relationship between variables and/or it becomes complicated and confusing to make

inferences when it is difficult to specify whether endogenous variables appear only on

the left hand side or on both sides of an equation. Additionally, the structural equation

framework is often inadequate in handling problems arising from nonstationarity of the

time series variables, resulting in spurious regressions [Verbeck (2000)].


An autoregressive approach in essence sidesteps the problems associated with structural

equations and endogeneity of variables by modelling all endogenous variables in the

system. By adding additional lagged variables of the dependent variable, this estimation

takes care of serial correlation between the disturbances [Self and Grabowski (2002)].

In order to find long-run relationships between the endogenous and exogenous

variables in our model, we need to accommodate any changes in a variable by reference

to the movements in the current or past values of the variables. A vector autoregressive

(VAR) model incorporates past values of variables into the process. It is a system

which accommodates more than one dependent variable as an alternative to a large-

scale simultaneous equation structural model [Brooks (2002)]. A VAR is a flexible and

generalised model that is extendable to the case where the model needs to include first

difference terms for ascertaining any cointegrating relationships among its variables.

Based therefore on the empirical needs of our twofold research objectives, we have

transformed our basic structural model (GLM) into a non structural autoregressive

VAR model as:

0

1

k

t i t i t

i

y y uµ η −=

= + +∑ (6.11)

where yt is 1p× vector of variables that contains all variables (including Xs) as

endogenous and is determined by k lags of all p variables in the system; ut is

1p× vector of error terms; 0µ is 1p× vector of constant term coefficients; and

iη are


p p× matrices of coefficients on the ith

lag of y and t = 1, ., T. A VAR model can

be constructed with first differenced variables if these first differenced variables (∆yt)

are found to be nonstationary (that is, I(1)) and/or the underlying theory permits us to

do so. In such a special case, the VAR would look like

0

1

k

t i t i t

i

y y uµ η −=

∆ = + ∆ +∑ (6.12)

To detect long-run equilibrium relationships as well as short-term dynamic adjustments

among the variables, an error correction term (ECT) is very useful because the

cointegration term (CT) is closely associated with the error correction term or error

correction mechanism (ECT or ECM). Sargan (1964) first applied the concept of ECM

and Engle and Granger (1987) later corrected it for disequilibrium. A vector error

correction model (VECM) is simply a restricted VAR which requires accommodating

the error correction term (ECT/ECM). By identifying the lagged number from either

the Akaike Information Criteria or Schwarz Bayesian Criteria and other suitable

criterion, we have the VECM as

1

0 1

1

p

t t i i t i t

i

y y yµ ε−

− −=

∆ = + + Γ ∆ +∑∏ (6.13)

or, following Johansen, the reduced form of VECM without a constant as:

1

1

1

p

t t i i t i t

i

y y y ε−

− −=

∆ = + Γ ∆ +∑∏ (6.14)


where tε ~ (0, ), 1,...,N t TΩ = ;

1

p

i

i

A I=

∏ = −∑ ; and 1

p

i j

j i

A= +

Γ = − ∑

We note that, at equilibrium, the reduced form of Johansens VECM would be viewed

as 1t ty y −∆ = ∏ . The equation

1

1

p

i i t i

i

y−

−=

Γ ∆∑ would not exist in equilibrium, all t iy −∆

will be zero and setting the error term tε to their expected value of zero will leave

1 0ty − =∏ [Brooks (2002)]. Within the VECM system, П contains both dynamic

adjustment parameters (α ) and cointegrating relationships (β ′ ).

The VECM distinguishes between the short- and long-run forms of causality, which the

standard Granger causality test cannot accomplish. While the joint F-tests on the

coefficients of the differenced terms in the VECM are used to test short-run causality, t-

tests on the coefficients of the lagged ECTs are utilized to determine the long-run

causal relationships since these are derived from the cointegrating relations between the

relevant variables [Self and Grabowski (2002)].

The modified or restricted VAR is the VECM which accommodates the ECM or ECT

often presented in the form that changes in the dependent variable are a function of

both the explanatory variables and the ECT. This captures the level of disequilibrium in

the relationship. This form of VECM (with optional constant µ0) is often written as:

1

0 1

1

p

t i i t i t t

i

y y ECTµ δ ε−

− −=

∆ = + Γ ∆ + +∑ (6.15)


where ECTt-1 contains the error correction terms derived from the cointegrating vectors

and δ records the response of the dependent variable in each period t from equilibrium.

Granger (1988) also recognized this notion by pointing that there are two channels of

causality when using vector error correction (VEC); one is through the lagged values of

the variables and the other is through δ, if δ is significant [Self and Grabowski (2002)].

However, after the cointegrating vector has been normalized, the initial relationship for

yt can be written as

1 1t t i t iy y yη η− −= + +L (6.16)

whilst the equation for ECTt is:

1 1 1t t t i t iECT y y yη η− − −= − − −L (6.17)

Summary

This chapter has developed the models that will be adapted to our specific data series

for empirical analyses in Part IV. As our aim of this research is twofold, we need to be

able to use our models for both purposes. Our models consist of the basic model

(GLM), the VAR and the VECM. The GLM contained both endogenous (yt) and

exogenous (xit) variables, whereas the VAR/VECM model bypassed the structural

GLM model by considering all variables as endogenous yt series. Thus, both yt and xit

series of GLM turned into one endogenous series of yt in VAR/VECM. Our models are:


Structural Model

0

1

( | )k

t i t i i t t

i

E Y X X uµ η=

= + +∑

Non Structural/Autoregressive Models

VAR

0

1

k

t i t i t

i

y y uµ β −=

= + +∑

or

0

1

k

t i t i t

i

y y uµ β −=

∆ = + ∆ +∑

VEC

1

0 1

1

p

t i i t i t t

i

y y E C Tµ δ ε−

− −=

∆ = + Γ ∆ + +∑ ;

or

1

1

1

p

t t i i t i t

i

y y y ε−

− −=

∆ = + Γ ∆ +∑∏

Depending on the nonstationarity condition of our variables, model estimation

criterion, econometrics software packages and research objectives, we will use one or a

combination of suitable model/s from the above pool of models for our empirical

analyses in Chapters 7 and 8.


PART IV

METHODOLOGY

As the objective of this thesis is twofold, it is necessary to perform two separate

analyses. The first analysis examines which a priori variables are cointegrated with

Australian stock market returns, while the second analysis tests both long-run cross-

country relationships and short-term dynamics. Part IV thus contains two chapters.

Chapter 7, to address the first objective, carries out the necessary empirical analysis and

reports the outcomes. Chapter 8, to fulfill the second objective, analyses relevant data

and details the results.


CHAPTER 7


ANALYSIS OF SYSTEMATIC RISKS FOR THE

AUSTRALIAN STOCK MARKET

In the literature on investment risk, the total risk is divided into two components,

namely, systematic risk and unsystematic risk. This classification is conceptualised by

the standard deviation of an investment return from the point of view of diversification.

The diversifiable risk is the unsystematic risk, while non diversifiable risk is systematic

risk. The systematic risk principal states that the reward for bearing risk depends only

on the systematic risk of an investment and thus the expected return on a risky asset

depends only on that assets systematic risk. Accordingly, systematic risk is also

market risk.

From the literature review we have seen that asset pricing theories do not specify the

underlying economic forces or systematic risk factors that drive securities prices. The

empirical analysis uses particular software and depends on both the availability of data

and established statistical criteria that are frequently used in the selection of variables.

Accordingly, the rationale for the selection of variables is essentially based on intuitive

financial theory [Chen et. al. (1986), Mukharjee and Naka (1995), McMillan (2001)].

Although the preliminary a priori variables for this study were pre-identified based on

theory as well as intuition and, accordingly, necessary data had been collected, some

prior tests needed to be carried out to select the appropriate variables for cointegration

analysis.


Data and Variables

The preliminary variables identified for the basic model are a priori variables that have

been derived from both theory and practice. Theories in economics and finance suggest

that macroeconomic variables such as growth in gross domestic product, changes in

industrial production, the interest rate, the unemployment rate, the exchange rate, and

net exports are likely to be relevant in predicting stock market performance. Likewise,

principles of accounting as well as financial theories point to the importance of

corporate profits, the price-earnings (P/E) ratio, the dividend yield, and global equity

indices for the local stock market as significant determinants of stock market

performance. To address the first objective of this research, 15 initial a priori variables

were considered. The data were assembled from various sources. The data on gross

domestic product (GDP), per-capita GDP (GDPPC), the industrial production index

(IPI), the manufacturing commodity price index (MPI), the unemployment rate (UR),

imports and exports to derive net exports (NX), and the consumer price index (CPI)

were collected from the Australian Bureau of Statistics (ABS). The data on the M3

money supply (MS), the standard variable bank interest rate (BVIR), the 11AM cash

rate (IR11AM) and net exports (NX) were collected from both the ABS and the

Reserve Bank of Australia. The net export (NX) figures were derived from the imports

and exports of all goods and services of Australia during the period under study

as ( )NX EXPORTS IMPORTS= − . Company or corporate profits (CP), the price

earnings or P/E ratio (PER), dividend yields (DY), and the Australian to US dollar

exchange rate (ER) were obtained from the Reserve Bank of Australia. Data on the

Morgan Stanley capital international world index (MSCI) was used as a proxy for


global equity market influences and was obtained from the Morgan Stanley worldwide

website.

The All Ordinaries index (ALLORDS) was used to obtain a measure of the market

price movements of Australian securities since this index is comprehensive and

available for our both analyses. Share prices were collected from the Securities Industry

Research Centre of the Asia-Pacific and ABS sources. Depending on the availability of

data, we constructed quarterly time series for the period from the first quarter of 1983

to the second quarter of 2002 (1/1983to 2/2002). Most of the data series were balanced

except for corporate or company profits where there were a few missing observations.

Given the unavailability of a longer period and given a lower frequency of data, the

quarterly data seemed satisfactory for the intended empirical analyses.

Because the selection of variables for inclusion in a model is an important step in the

analysis, to ensure that the model neither includes any irrelevant variable nor omits any

important variable and that the parameters are stable, several statistical tests were

performed. The first was to use the correlation values of a priori variables and stock

market returns from Annexure 1. Other diagnostic tests such as multi-collinearity were

also taken into account (Annexure 1). However, some of the variables were eliminated

as they were thought to be irrelevant. Accordingly, our initial 15 a priori variables were

reduced to six for the final analysis, based on its statistical correlations with the

Australian security market price movement, possible multi-collinearity among the

variables, and both theoretical and intuitive weights. These six final a priori variables

are industrial production, the bank variable interest rate, corporate profits, the dividend


yield, the price earnings ratio, and MSCI. We used logged values of all series of

variables.

To validate the above variable selection decision, a data reduction procedure was

followed using the SPSS 11 statistical software to develop an idea about the number of

components or factors based on eigenvalue. This procedure extracted one component or

factor based on eigenvalues of more than 0.1 from the initial 16 variables, including the

ALLORDS. Graph 7.1 plots the extracted components/factors, while Table 7.1 reports

the component matrix.

GRAPH 7.1

Component/Factor Plot

Scree Plot

Component Number

16151413121110987654321

Eig

en

va

lue

500000

400000

300000

200000

100000

0


TABLE 7.1

Component Matrix Raw Rescaled

Component Component

1 1

LNALLORDS 622.675 1.000 LNMSCI .282 .952

LNGDPPC .084 .919 LNGDP .126 .893

LNIPI .085 .839 LNER -.106 -.793 LNCP .302 .769

LNMS .290 .757 LNMPI .080 .681 LNCPI .091 .677

LNBVIR -.254 -.609 LNIR11AM -.244 -.592

LNDY -.135 -.545 LNUR -.083 -.467

LNPER .079 .199

LNNX .253 .158 Extraction Method: Principal Component Analysis.

a 1 components extracted.

The descriptive statistics of the seven variables (which include the six a priori and the

ALLORDS return) are reported in Table 7.2. Table 7.2 shows no major discrepancies,

meaning that the selected seven variables are consistent with conventional research norms.

TABLE 7.2

Descriptive Statistics LNALLORDS LNBVIR LNCP LNDY LNIPI LNMSCI LNPER

Mean 7.570596 2.097070 8.472301 1.373518 4.570115 5.974402 0.012789 Median 7.539122 1.991859 8.504892 1.340665 4.551235 5.997631 0.011196 Maximum 8.101006 2.904633 9.234838 1.903102 4.774069 6.548168 0.337367

Minimum 6.894670 1.448980 7.473069 0.946497 4.326778 5.174042 -0.521375 Std. Dev. 0.315845 0.487376 0.430099 0.199241 0.123883 0.344317 0.130132 Skewness 0.063872 0.394773 -0.284654 0.758343 -0.171726 -0.234526 -0.772756 Kurtosis 2.080722 1.586991 2.358626 3.123477 2.202477 2.329086 6.608913

Jarque-Bera 2.368826 7.204940 2.022549 6.367846 2.073507 1.842875 42.38536 Probability 0.305926 0.027256 0.363755 0.041423 0.354604 0.397947 0.000000

Sum 499.6593 138.4066 559.1719 90.65220 301.6276 394.3106 0.844104 Sum Sq. Dev. 6.484260 15.43977 12.02406 2.580292 0.997554 7.706014 1.100737

Observations 66 66 66 66 66 66 66


Hypothesized Relationships of Variables

We aim to investigate the interrelationship between Australian security market returns,

the set of a priori variables that represent the money market, the goods market, the

foreign exchange market and the global stock market performance. Here we have

considered industrial production (IPI) to represent the goods market. The money market

is represented by the bank variable interest rate (BVIR) which is also linked to the

exchange rate (ER) representing the foreign exchange market. The security market is

represented by the stock price index (ALLORDS), which is also linked to the dividend

yield (DY) and the price earnings ratio (PER). The global stock market is represented

by the performance of the global index MSCI which might impact under globalization

on individual markets. In line with previous studies (referred to in earlier chapters), we

expect that our a priori variables will show a linkage with stock market performance.

This study will thus investigate both the long-run and short-run relationship between

the Australian stock market price movements or returns ( ALLORDS∆ ) and the changes

in selected six a priori variables (BVIR, IPI, CP, DY, MSCI and PER). Usually, the

simple model is specified in the following form:

( , , , , , )t t t t t t t

ALLORDS f BVIR CP DY IPI MSCI PER∆ = ∆ ∆ ∆ ∆ ∆ ∆ (7.01)

The relationship between interest rates and stock prices from the perspective of asset

portfolio allocation is commonly negative. An increase in interest rates raises the

required rate of return, which in turn inversely affects the value of the asset. Measured

as opportunity cost, the nominal interest rate will affect investors decision on stock


holdings. A rise in the opportunity cost will, however, motivate investors to substitute

shares for other assets in their portfolios. Also, an increase in interest rates may cause a

recession and thus cause a decline in future corporate profitability, as corporate

financial costs may rise due to increased interest payments. Further, higher interest

rates have a discouraging effect on mergers, acquisitions and buyouts. Interest rates

might have a positive relationship with stock returns, as an increase in the rate of

interest raises the opportunity cost of holding cash and is likely to lead to a substitution

effect between stocks and other interest bearing securities/accounts. Changes in interest

rates are expected to affect the discount rate in the same direction through their effect

on the nominal risk-free rate [Mukharjee and Naka (1995)]. However, nominal interest

rates are assumed to contain information about future economic conditions and to

capture the state of investment opportunities in stocks; in addition, studies have found

that short-term interest rates have a significant negative influence on the stock market.

Thus, we hypothesize a negative relationship between interest rates (BVIR) and stock

prices (ALLORDS).

We hypothesize a positive relationship between ALLORDS and industrial production

(IPI), as IPI typically has a positive relationship with the stock market. An increase in

production is likely to influence stock prices through its positive impact on gross

domestic product and corporate profitability. An increase in output may increase

expected future cash flows and thereby raise stock prices, while the opposite effect

would occur in a recession.


We hypothesize a negative relationship between the exchange rate and the stock price,

as changes in the exchange rate affect the performance of the stock market through its

impact on net exports and thus the current account position of an export focused

country like Australia. A number of commentators have suggested that currency

depreciation will have a favourable impact on a domestic stock market [Ma and Kao

(1990), Mukharjee and Naka (1995)]. Thus, an Australian dollar depreciation against

the US dollar implies that products exported from Australia become cheaper in the

world market. If the demand for exportable items is elastic, the volume of exports from

Australia would increase, which in turn causes higher cash flows, corporate profits and

stock prices of Australian companies. However, the contrary relationship may be found

under different circumstances.

Movements in the dividend yield are thought to be related to long-run business

conditions and they represent a predictable component of stock market returns.

We hypothesize that the dividend yield has a positive relationship with stock prices.

However, in the short-run, the price would drop immediately after the dividend payout

for a specific stock due to speculation about the lack of an immediate profit-taking

opportunity and/or a longer holding period to receive another dividend payout.

We hypothesize a positive relationship between corporate profits and market stock

price, because it captures predictable elements in future return series. This often relates

to the price-earnings ratio which boosts the confidence of investors by encouraging

them to invest in the stock market.


Finally, we consider that the global stock market price index (MSCI) has some impact

on a developed stock market like Australia. Changes in the MSCI could pose either a

direct or indirect impact on the local stock market depending on the trading relationship

with other markets. We hypothesize a direct and positive relationship between

ALLORDS and MSCI.

The hypothesized relationship may hold or be rejected depending on the methodology

used in the analysis. In this connection, we note that, amongst others, Verbeck (2000)

pointed to the fact that to apply standard estimation or testing procedures in a dynamic

model, it is typically required that the variables are stationary since regressing a

nonstationary I(1) endogenous variable like LNALLORDS on nonstationary I(1)

exogenous variables such as LNIPI, LNBVIR, LNCP, LNDY, LNPER, and LNMSCI

may lead to so called spurious regression when we use the standard regression model,

where estimators and test statistics are misleading. An exception to this rule occurs

when two or more I(1) variables are cointegrated, meaning that there is a linear

combination of these nonstationary I(1) variables which is stationary I(0). In such cases

a long-run relationship between these variables exists and this also has implications for

the short-run behaviour of the I(1) variables. To capture this relationship for both the

long- and short-runs, there has to be some mechanism that drives the variables and their

short-run unstable behaviors to their long-run equilibrium relationship. This mechanism

is modelled by an error correction mechanism, in which the equilibrium error also

drives the short-run dynamics of the series. Accordingly, we intend to employ the error

correction model discussed in Chapter 6 for the empirical examination.


Unit Root and Breakpoint Tests

For cointegration analysis, it is important to check whether all the time series variables

are nonstationary with unit root I(1) and stationary with unit root I(0) at difference

before using them in cointegration analyses. This is because the standard inference

procedures that are relevant to the standard regression model do not apply in

cointegration analysis it bypasses the standard regression modelling structure.

Cointegration analysis requires us to use only those variables that are nonstationary

with unit root I(1). We have tested the stationarity of all these series using EViews

econometric software. We tested for unit roots both in levels and first differences for all

three possible states of the model in relation to intercept and trend. The tested models

were with intercept but no trend, intercept with trend, and no intercept or trend.

We used both the Augmented Dickey-Fuller and the Phillips-Perron test procedures in

EViews3.1. Results of the unit root tests are presented in Table 7.3.

TABLE 7.3

Unit Root Test Results

Augmented Dickey-Fuller (ADF) Phillips-Perron (PP) Variables Intercept,

No trendA Intercept

with trendB No intercept,

No trendC Intercept, No trendA

Intercept with trendB

No intercept, No trendC

At level LNALLORDS -0.7693 -2.5204 1.6447 -0.9158 -3.1529 1.8879 LNBVIR -1.0780 -2.8031 -0.7916 -1.1332 -2.2060 -1.1586 LNMSCI -2.0051 -2.5200 2.4765 -2.7021 -3.4094 2.6647 LNIPI -1.5737 -3.0819 3.2505 -1.9306 -3.1799 4.5530 LNER -1.5525 -2.1974 0.3993 -1.6695 -2.2856 0.4539 LNDY -2.0014 -2.6032 -0.5466 -2.4353 -2.7896 0.8648

LNPER -1.8346 -2.9635 0.2156 -1.8475 -2.5987 0.4182 At 1st diff. ∆LNALLORDS -6.7377 -6.6898 -5.9812 -11.9180 -11.8279 -11.0715 ∆LNBVIR -4.5835 -4.6497 -4.6254 -6.0566 -6.0173 -6.0533 ∆LNMSCI -6.0321 -6.1883 -5.2225 -9.1863 -9.3631 -8.4619 ∆LNIPI -4.6453 -4.7518 -3.3183 -9.1809 -9.2496 -7.5641 ∆LNER -3.9624 -3.9067 -3.8699 -7.8623 -7.8127 -7.8161 ∆LNDY -4.9831 -4.9657 -5.0108 -8.3097 -8.2527 -8.3542 ∆LNPER -4.4205 -4.3887 -4.4167 -6.5535 -6.5088 -6.5723

Note: MacKinnon Critical values at level: for model A. -2.9851; model B. -3.469; model C. -1.9439, and at 1st difference: for model A. -2.8955; model B. -3.4626; model C. -1.9445


The test results are compared against the MacKinnon (1991) critical values for the

rejection of the null hypothesis of no unit root. Table 7.3 shows that all seven a priori

variables are integrated of order one I(1) in levels and of order zero I(0) in first

differences, meaning that they are nonstationary in levels and stationary in first

differences.

We plotted the residuals of the Australian stock market data in Graph 7.2 to identify

whether there was any break in the series owing to the stock market crash of October

1987. We also graphed the residuals of the a priori variables series in Graph 7.3. Both

graphs indicate that all series contain an outlier in the fourth quarter of 1987 which

suggests a break point dummy variable for the analysis to capture the impact of the 12

October 1987 stock market crash.

GRAPH 7.2

Plot of Residuals and Two StandardError Bands

Quarters

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

0.0

0.1

0.2

0.3

1985Q4 1988Q2 1990Q4 1993Q2 1995Q4 1998Q2 2000Q4 2001Q4


GRAPH 7.3

We also conducted a statistical test called the Chow Breakpoint test using EViews4 to

ascertain if the null hypothesis of no significant break in 1987.4 data series can be

rejected. The Chow Breakpoint test produced an F-statistic of 6.547176 (probability

0.000015) and a log likelihood ratio statistic of 41.71134 (probability 0.000001), as

reported in Table 7.4.

TABLE 7.4

Chow Breakpoint Test Chow Breakpoint: 1987:4

F-statistic 6.547176 Probability 0.000015

Log likelihood ratio 41.71134 Probability 0.000001

Note: Critical values of F-statistic (1df) are 2.71, 3.84 and 6.63 at 10%, 5% and 1% significance levels respectively.

The Chow Breakpoint test rejected the null hypothesis of no-effect of the October 1987

(1987.4) stock market crash in the movement of Australian stock prices against the

alternative hypothesis. Thus the breakpoint test implies that the October 1997 stock

market crash is significant for consideration in our analysis. We have included a break-

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

84 86 88 90 92 94 96 98 00 02

RESIDLNIPIRESIDLNMSCIRESIDLNBVIR

RESIDLNERRESIDLNDYRESIDLNPER

RESIDUL PLOT OF A PRIORI VARIABLES


point dummy (which takes the value one for the 4th quarter of 1987 and zero elsewhere)

as an exogenous variable in the model for the investigation of the cointegrating

relationship between the Australian stock market returns and our a priori variables.

Lag Length Selection

As the autoregressive model is sensitive to the lag operator chosen, we have to

ascertain the appropriate lag length before we conduct the cointegration analysis in line

with Johansen. We have used both Microfit 4.1 and EViews4 to determine the optimal

lag length based on the Akaike Information Criteria (AIC) or Schwarz Bayesian

Criteria (SBC) criteria.

Both the likelihood ratio (LR) and the adjusted LR statistics for selecting the optimal

VAR order by using Microfit 4.1 suggested that optimal lag length should be one.

The same conclusion was suggested by the SBC tests through employing EViews 4.

The results are provided in Tables 7.5A and 7.5B.

TABLE 7.5A Test Statistics and Choice Criteria for Selecting the Order of the VAR Model --------------------------------------------------------------------------------------------------------------------------------------------

List of variables included in the unrestricted VAR: LNALLORDS LNBVIR LNCP LNDY LNIPI LNMSCI LNPER =================================================================================== Order LL AIC SBC LR test Adjusted LR test 5 922.6844 677.6844 419.1023 ------ ------

4 853.5152 657.5152 450.6496 2χ ( 49)= 138.3383[.000] 58.9639[.156]

3 766.6831 619.6831 464.5339 2χ ( 98)= 312.0025[.000] 132.9847[.011]

2 711.1570 613.1570 509.7242 2χ (147)= 423.0547[.000] 180.3184[.032]

1* 632.4021 583.4021 531.6857 2χ (196)= 580.5645[.000] 247.4537[.007]

0 -22.6793 -22.6793 -22.6793 2χ (245)= 1890.7[.000] 805.8838[.000]

Test Statistics and Choice Criteria for Selecting the Order of the VAR Model using Microfit4. Probability in [ ].


TABLE 7.5B VAR Lag Order Selection Criteria Endogenous variables: LNALLORDS LNBVIR LNCP LNDY LNIPI LNMSCI LNPER Exogenous variables: C Sample: 1983:1 2002:2 Included observations: 61

Lag LogL LR FPE AIC SC HQ

0 301.7397 NA 1.50E-13 -9.663595 -9.421364 -9.568662 1 646.5622 599.1998 9.29E-18 -19.36269 -17.42484* -18.60323 2 719.4107 109.8700 4.52E-18 -20.14461 -16.51114 -18.72062 3 779.4621 76.78697 3.71E-18 -20.50695 -15.17786 -18.41843 4 866.4853 91.30303* 1.51E-18* -21.75362 -14.72890 -19.00057*

5 934.6668 55.88645 1.53E-18 -22.38252* -13.66219 -18.96494

* indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion

Test Statistics and Choice Criteria for Selecting the Order of the VAR Model using EViews4

Even though the SBC and Hannan-Quinn Criterion (HQ) criteria suggested a higher lag

length, we could not take the risk of over-parameterization by considering higher lags

because our data series are quarterly and we have a short time series with only 78

observations, out of which 61 are balanced. We therefore chose one lag for the model

which also seemed in conformity with finance theory and investors intuition that the

stock market is very volatile.

Cointegration Analysis

For the cointegration analysis, we considered a vector autoregressive (VAR) model

which has a constant (but no trend) and included the breakpoint dummy as exogenous,

as in the following:

0

1

k

t i t i t t

i

y y D uµ β ϕ−=

= + + +∑ (7.02)


where ( , , , , , , )t

y LNALLORDS LNBVIR LNCP LNDY LNIPI LNMSCI LNPER ′= a 7×1

vector of I(1) variables considered as endogenous in the model; Dt is a vector of

breakpoint dummy exogenous variable; µ0 is a constant and ut is white noise.

In order to perform Johansens cointegration analysis we have converted the VAR into

a vector error correction model (VECM) by incorporating error correction term or error

correction mechanism (ECM-1) into the system. Thus, our transformed VECM is

1

0 1

1

p

t i i t i t t t

i

y y E C M Dµ δ ϕ ε−

− −=

∆ = + Γ ∆ + + +∑ (7.03)

or 1

0 1

1

p

t i i t i t t t

i

y y y Dµ α β ϕ ε−

− −=

′∆ = + Γ ∆ + + +∑ (7.04)

where t

ε ~ (0, )iidN Ω .

Considering the previously identified lag length one as the order of the VAR, we have

employed EViews4 to perform our analysis following Johansen (1991). Accordingly,

we have performed a likelihood ratio (LR) test, the maximum eigenvalue (max

λ ) test

and the trace (trace

λ ) test for the cointegration analysis. The cointegration results along

with test statistics are presented in Table 7.6.


TABLE 7.6

Cointegration Results Hypothesis Critical Value

Null Alternative

Test Statistic 5% 1%

Eigenvalue

(A) Cointegration testa

Test Statistic: Maximal Eigenvalue (max

λ )

r = 0 r = 1 82.50867 45.28 51.57 0.724508 r ≤ 1 r = 2 56.39844 39.37 45.10 0.585725 r ≤ 2 r = 3 37.22766 33.46 38.77 0.441043 r ≤ 3 r = 4 30.79637 27.07 32.24 0.381955

r ≤ 4 r = 5 14.77187 20.97 25.52 0.206110 r ≤ 5 r = 6 6.831499 14.07 18.63 0.101243 r ≤ 6 r = 7 0.393115 3.76 6.65 0.006124

Test Statistic: Trace (trace

λ )

r = 0 r ≥ 1* 228.9276 124.24 133.57 0.724508 r ≤ 1 r ≥ 2 146.4189 94.15 103.18 0.585725 r ≤ 2 r ≥ 3 90.02050 68.52 76.07 0.441043 r ≤ 3 r ≥ 4 52.79285 47.21 54.46 0.381955

r ≤ 4 r ≥ 5 21.99648 29.68 35.65 0.206110 r ≤ 5 r ≥ 6 7.224615 15.41 20.04 0.101243 r ≤ 6 r = 7 0.393115 3.76 6.65 0.006124

(B) The long-run equationb

LNALLORDS(3.5776) = 0.3557LNBVIR(5.4923) + 1.2869LNCP(24.4554) +

0.8600LNDY(4.7723) 4.24174LNIPI(8.1860) 0.9201LNMSCI(2.3277)

0.0047LNPER(0.0010) or

LNALLORDS(3.5776) + 0.3557LNBVIR(5.4923) 1.2869LNCP(24.4554)

0.8600LNDY(4.7723) + 4.24174LNIPI(8.1860) + 0.9201LNMSCI(2.3277) +

0.0047LNPER(0.0010) = 0

r = the number of cointegrating vectors. a. Optimal lag structure is 1 and the VAR contains a constant without trend and breakpoint dummy as exogenous to the model. b. The cointegrating vector is normalised on the Australian stock price index (LNALLORDS). The LR test statistics, given in parentheses, are used to test the null hypothesis that each coefficient is statistically zero. The test statistic is

asymptotically distributed as a chi-square distribution with 1 degree of freedom. The critical values of chi-square distribution at 5% and 10% significance levels are 3.841 and 2.706 respectively.

It is evident from the results in Table 7.6 that we can reject the null hypothesis of

0r = against the alternative 1r = from the max

λ test. The same outcome is achieved

from the trace

λ test which has rejected 0r = against 1r ≥ . We have ascertained that in

our model only one stationary linear combination of variables is cointegrated in the


long-run. Coefficients of the cointegrating equation (B) in Table 7.6 are normalized

by11

S Iβ β = as an identification process of the Johansen (1995) procedure, since the

long-run multiplier matrix Пy does not generally lead to a unique choice for the

cointegrating relations. The identification of β in y y

α β ′Π = requires at least r

restrictions per cointegrating relation (r). As we have found that r =1, one restriction

should be enough to identify the cointegrating relationship which is the normalizing

restriction applied to the LNALLORDS variable. LNALLORDS is considered as the

cointegrating equation, because it is the vector that contains the maximum eigenvalue.

Although the normalization is convenient from the mathematical point of view, it may

not always be meaningful otherwise. It has an advantage because such a normalization

is made without assuming anything about which variables are cointegrated, that is, it

serves the purpose without normalizing β.

It appears from the likelihood ratio (LR) test results of restrictions concerning each

variable in equation (B) of Table 7.6 that we can reject the null hypothesis of no

significance in relation to four a priori variables, including interest rate (LNBVIR),

corporate profit (LNCP), dividend yield (LNDY) and industrial production (LNIPI) at

the 5% level. Although in terms of LR test results both LNMSCI and LNPER do not

seem significant even at the 10% level, the global stock market index is significant

when we look at the t-statistic (2.7196) for LNMSCI. Respective t-statistics for

LNBVIR, LNCP, LNDY, LNIPI, LNMSCI, and LNPER are 3.5762, 11.3262, 4.4858,

4.2826, 2.7196 and 0.0484. From these results we can see that four to five of our a

priori variables have significant long-run influence on Australian stock price

movements or returns.


Our results therefore suggest that although the linear combination of all our modelled

variables are found cointegrated, all variables are not equally influential. The

significantly influential a priori variables in the long-run cointegrating relationship for

the Australian stock market are the bank variable interest rate, corporate profitability,

dividend yield, and industrial production. The global stock market index also has some

influence. The price-earnings ratio seems to have insignificant influence from the

results of both the likelihood ratio and t tests statistics of EViews4.

Results of dynamic time series models and their corresponding error correction

mechanisms (ECM -1) are presented in Table 7.7.


TABLE 7.7

Multivariate Dynamic Time Series (Short-Run) Models Entry Coefficient Standard Error t statistic[probability]

LHS variable: ∆LNALLORDS

∆LNALLORDS(-1)

∆LNBVIR(-1)

-0.4259

-0.2139

0.0391

0.1091

-4.8797

-1.9595

∆LNCP(-1) 0.0239 0.0362 0.6593

∆LNDY(-1) 0.3247 0.2233 1.4540

∆LNIPI(-1) 0.7837 0.1938 1.2332

∆LNMSCI(-1) 1.0964 0.6355 4.8393

∆LNPER(-1) -0.1174 0.0727 -1.6148

ECM(-1) -0.0401 0.0391 -1.0270

CHSQ(1) 0.6852 [0.4078]

LHS variable: ∆LNBVIR

∆LNALLORDS(-1) ∆LNBVIR(-1)

-0.1143 0.3978

0.1018 0.1279

-1.1231 3.1116

∆LNCP(-1) -0.0378 0.0424 -0.8914

∆LNDY(-1) -0.0087 0.2616 -0.0334

∆LNIPI(-1) 0.1963 0.7446 0.2636

∆LNMSCI(-1) 1.0964 0.2654 0.7091

∆LNPER(-1) -0.1174 0.0852 -0.4702

ECM(-1) 0.1048 0.0458 2.2884

CHSQ(1) 4.9172 [0.0266]

LHS variable: ∆LNCP

∆LNALLORDS(-1)

∆LNBVIR(-1)

0.7380

0.5079

0.2997

0.3764

1.3494

3.5824

∆LNCP(-1) 0.4471 0.1248 2.8126

∆LNDY(-1) 2.1662 0.7701 -0.6995

∆LNIPI(-1) -1.5333 2.1920 2.0367

∆LNMSCI(-1) 1.5916 0.7815 -0.6752

∆LNPER(-1) -0.1694 0.2508 -0.3242 ECM(-1) -0.0104 0.1348 -6.9414

CHSQ(1) 20.4846 [0.0000]

LHS variable: ∆LNDY

∆LNALLORDS(-1)

∆LNBVIR(-1)

-0.0674

0.15245

0.1061

0.1332

-0.6360

1.1443

∆LNCP(-1) 0.0288 0.0442 0.6529

∆LNDY(-1) 0.1948 0.2726 0.7147

∆LNIPI(-1) 0.1240 0.7758 0.1599

∆LNMSCI(-1) 0.1138 0.2766 0.4115

∆LNPER(-1) -0.0047 0.0888 -0.0529

ECM(-1) -0.0102 0.0477 -0.2135

CHSQ(1) 0.0470 [0.08284]

LHS variable: ∆LNIPI

∆LNALLORDS(-1)

∆LNBVIR(-1)

-0.0081

-0.0331

0.0183

0.0230

-0.4431

-1.4404 ∆LNCP(-1) -0.0005 0.0076 -0.0640

∆LNDY(-1) 0.0354 0.0471 0.7519

∆LNIPI(-1) 0.0454 0.1339 0.3389

∆LNMSCI(-1) 0.0673 0.0478 1.4104

∆LNPER(-1) 0.0075 0.0153 0.4876

ECM(-1) 0.0010 0.0083 1.2111

CHSQ(1) 1.3005 [0.2541]

LHS variable: ∆LNMSCI

∆LNALLORDS(-1)

∆LNBVIR(-1)

0.0786

-0.1339

0.1000

0.1254

0.7871

-1.0672

∆LNCP(-1) -0.0384 0.0416 -0.9227

∆LNDY(-1) 0.1190 0.2566 0.4637

∆LNIPI(-1) 0.2943 0.7303 0.4030

∆LNMSCI(-1) 0.2641 0.2604 1.0144

∆LNPER(-1) -0.0592 0.0836 -0.7081 ECM(-1) 0.0414 0.0450 0.9220

CHSQ(1) 0.8991 [0.3568]

LHS variable: ∆LNPER

∆LNALLORDS(-1)

∆LNBVIR(-1)

0.2271

-0.3612

0.1416

0.1779

1.6040

-2.0305

∆LNCP(-1) 0.0087 0.0590 0.1483

∆LNDY(-1) 0.9716 0.3639 2.6697

∆LNIPI(-1) -0.7002 1.0358 -0.6760

∆LNMSCI(-1) 0.0060 0.3693 0.5433

∆LNPER(-1) 0.6022 0.1185 5.0807

ECM(-1) -0.0715 0.0637 -1.1223

CHSQ(1) 1.2293 [0.2675]

Note: Critical values for t-statistics (2-sided test) are 1.64, 1.96 and 1.58 at10%, 5% and 1% significance levels respectively.


The identified long-run cointegrating relation amongst seven variables in this study

from the perspective of the Australian stock market is plotted in Graph 7.4:

GRAPH 7.4

State of Equilibrium Pricing in the Australian Stock Market

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

84 86 88 90 92 94 96 98 00

Cointegrating relation of Australian Stock Market and apriori variables

Note: The cointegration plot shows the pattern of integration in the long-run.

Taking ∆LNALLORDS as the left hand side variable in the short-run model in Table

7.7 (which may be thought as the dependent variable in structural time series), it may

be suggested that the Australian stock market is dynamic and has been continually

corrected from its own disequilibrium of the previous quarter at a speed of 4%, while

all individual variables are contributing to the process of adjustment for equilibrium.

The bank interest rate (∆LNBVIR), global influence (∆LNMSCI) and the previous

performance of Australian market itself (∆LNALLORDS) are found significant in the

dynamic adjustment process, although the error correction mechanism (ECM1) is not

very efficient. The interest rate (∆LNBVIR) and company profits (∆LNCP) are found

to significantly contribute towards long-run equilibrium as their related error correction

mechanisms are significant.


From another angle, coefficients of our long-run parameter β ′ upon normalization for

LNALLORDS are 0.3557, 1.2869, 0.8600, 4.2418, 0.9201 and 0.0047 for

LNBVIR, LNCP, LNDY, LNIPI, LNMSCI and LNPER respectively. Resulted

corresponding t-statistics are 3.5762, 11.3262, 4.4858, 4.2826, 2.7196 and 0.0484.

Thus, our estimated normalized ALLORDS

β with corresponding t-values in the

parentheses is:

11

( 3.5762)21

(11.3262)31

41 (4.4858)

51 ( 4.2826)

61 ( 2.7196)

71( 0.0484)

1.000000

0.3557

1.2869

0.8600

4.2418

0.9201

0.0047

ALLORDS

βββ

β ββββ

−

−

−

−

− = = − − −

(7.05)

This suggests that the LNBVIR, LNCP, LNDY, LNIPI and LNMSCI variables are

significant in the long-run cointegrating relationship for Australia as they are

significant when compared with the critical value for the t-statistic (1.96) at the 5%

significance level.

The short-run dynamic system provided us with coefficients of α corresponding to

∆LNALLORDS, ∆LNBVIR, ∆LNCP, ∆LNDY, ∆LNIPI, ∆LNMSCI and ∆LNPER.

The coefficients of α in respective order are 0.0401, 0.1048, 0.0104, 0.0102,

0.0010, 0.0414, and 0.0715. Corresponding t-values for α are 1.0270, 2.2884,


6.9414, 0.2135, 1.2111, 0.9220 and 1.1223 respectively. This information can be

presented as:

( 1.0270)11

(2.2884)21

( 6.9414)31

41 ( 0.2135)

51 (1.2111)

61 (0.9220)

71( 1.1223)

0.0401

0.1048

0.0104

0.0102

0.0010

0.0414

0.0715

ααα

α αααα

−

−

−

−

− − = = − −

(7.06)

wherein the ECM-1 for the LNALLORDS is ALLORDSα =

11α = 0.0401, which is the

adjustment parameter in the cointegrating equation for Australia. The t-statistic in

parentheses corresponding to11α indicates that ECM-1 for LNALLORDS is not very

significant although the linear combination of all variables are found cointegrated. This

might mean that the Australian stock market is yet to be efficient in terms of its auto

correction.

We have obtained the estimates of the short-run parameters for the Australian market

ALLORDSΓ as 0.4259, 0.2139, 0.0239, 0.3247, 0.7837, 1.0964, and 0.1174 for

∆LNALLORDS -1, ∆LNBVIR -1, ∆LNCP -1, ∆LNDY -1, ∆LNIPI -1, ∆LNMSCI -1 and

∆LNPER -1 respectively. The corresponding t-statistics for ALLORDSΓ are 4.8797,

1.9595, 0.6593, 1.4540, 1.2332, 4.8393, and 1.6148. This suggests that in the process

of the short-run adjustment for the Australian stock market, ∆LNALLORDSt-1,

∆LNBVIRt-1 and ∆LNMSCIt-1 are significant at the 5% level. This means that


Australian stock market prices are being adjusted each quarter dominantly by the

influences of the markets own performance as well as interest rate and global stock

market movements of previous quarter.

We thus present the short-run estimated parameter ALLORDSΓ as:

( 4.8797)

( 1.9595)

(0.6593)

(1.4540)

(1.2332)

(4.8393)

( 1.6148)

0.4259

0.2139

0.0239

0.3247

0.7837

1.0964

0.1174

ALLORDS

−

−

−

− − Γ = −

(7.07)

Based on the above results, we present the estimated model (VECM) for Australia in

equations 7.08 and 7.09. Our estimated model takes the following shape:

∆LNALLORDSt = −0.0401*[ 1*LNALLORDS -1 −0.3557*LNBVIR -1 +

1.2869*LNCP -1 + 0.8600*LNDY -1 − 4.2418*LNIPI-1 −

0.9201*LNMSCI-1 − 0.0047*LNPER-1]

[−0.4259*∆LNALLORDS-1 0.2139* ∆LNBVIR-1 +

0.0239* ∆LNICP-1 +0.3247* ∆LNDY-1+ 0.7837* ∆LNIPI-1 +

1.0964* ∆LNMSCI-1 − 0.1174*∆LNPER-1 ]. (7.08)

or


∆LNALLORDSt = − 0.0401*LNALLORDS -1 + 0.0143*LNBVIR -1 −0.0516*LNCP-1

− 0.0345*LNDY -1 + 0.1701*LNIPI-1 + 0.0369*LNMSCI-1 +

0.0002*LNPER-1 + 0.4259* ∆LNALLORDS-1 + 0.2139*∆LNBVIR-1 +

0.0239*∆LNCP-1 0.3247* ∆LNDY-1 − 0.7837*∆LNIPI -1

1.0964*∆LNMSCI -1 + 0.1174*∆LNPER -1 . (7.09)

In long-run equilibrium, the second part of the above model would not exist; therefore,

our solved model in reduced form is as follows:

∆LNALLORDSt = −0.0401*LNALLORDS -1 + 0.0143*LNBVIR -1 − 0.0516*LNCP-1

− 0.0345*LNDY -1 + 0.1701*LNIPI -1 + 0.0369*LNMSCI -1 +

0.0002*LNPER -1 (7.10)

These results are interesting and useful in understanding the Australian stock market

pricing mechanism as well as its return generating process. The cointegrating analysis

presented in Table 7.6 shows that all our variables are cointegrated in the long-run,

although only four to five variables are influential in the pricing process. These

variables are interest rate, corporate profit, dividend yield, industrial production, and

global stock market movements.

Although the presence of cointegration among variables does not necessarily imply that

all variables will contribute the process of integration equally, some might like to see

what happens if the insignificant variable/s is/are dropped from the model and rerun the

analysis. We have done so by dropping our insignificant variable the price earnings

ratio (LNPER). This additional cointegration analysis shows that there exists a


cointegrating relationship between the variables considered and that all variables are

significantly influential. This additional analysis thus corroborates the earlier claim that

our a priori variables as proxy to systematic risk factors for Australian stock market are

being priced in the long-run.

Caution

The results of this analysis should not be treated as conclusive for an investment. Apart

from understanding Australian stock market pricing based on the contributions of our

significant a priori variables, there remains other important issues that affect the return

generating process. These issues are the cost of equity capital, asset valuation, industry

analysis, a firms management and operational efficiency analysis, and so on.

An Australian investor should consider all relevant sources of information when

making an investment decision. Even within the arena of systematic risk analysis for

assets, one should identify both business and financial risks and analyse them while

selecting a stock in their portfolio for investment. The business risk of a firm depends

on the systematic risk of a firms assets. The greater a firms business risk, the greater

the firms cost of equity. The other component in the cost of equity is determined by a

firms financial structure which also needs assessment while selecting stocks for an

investment portfolio. This extra risk that arises from the use of debt financing is called

the financial risk of a firms equity. The well known propositions of Franco Modiglini

and Merton Mills are useful in analysing the value of a firm as well as its cost of equity.

Their first proposition is that the value of a firm is independent of a firms capital

structure, while their second proposition states that the cost of equity depends on the


required rate of return on a firms assets, its firms cost of debt, and its firms debt-

equity ratio. When investigating portfolio investment, an investor should analyse two

types of risks, the total systematic risk of the firms equity consisting of business

risk, and financial risk [Ross, et. al. (1998)].

It is more useful for our purposes to know that the linear combination of modelled

variables contains a relationship the variables are cointegrated and our a priori

variables explain the price movements as well as the return generating process of the

Australian stock market in both the long- and short-runs.

Summary

In this chapter, we performed necessary analyses to answer the research question of

whether some of our identified a priori variables as proxy to systematic risk factors for

Australian stock market explain return generating as well as pricing process. We

followed the model that was presented in Chapter 6 and used the most current

econometrics software procedures for the empirical analysis. The outcome is in line

with current theory, yet interestingly different on some points. We found that four to

five of our identified a priori variables explain the Australian stock market pricing

mechanism these variables have a long-term relationship with Australian stock

returns. Further interpretations of the results will be discussed in the research

conclusion Chapter 9. We now progress to our second analysis, in Chapter 8.


CHAPTER 8


INTERDEPENDENCE OF STOCK MARKETS UNDER

GLOBALIZATION

The common intuition is that under the prevailing globalized world economic order, the

stock markets of most developed nations are becoming increasingly interrelated.

Capital and investment funds now flow freely from one country to another. Due to

internet technology and the speedy transfer of information the world has become one

interdependent market place. As a result, it is likely that the stock market performance

of one country will be influenced by that of others. This is especially true for efficient,

developed markets.

We aim to examine the common intuition from an Australian perspective. Our

investigation was carried out, in the first instance, in a straightforward way the aim

was to ascertain whether the Australian stock market is cointegrated with the US, UK,

Canadian, German, French and Japanese stock markets. Based on annual data series

from 1945 to 2002 we have studied both the long-run relationships and the short-run

dynamics operating between the seven markets under the global economic and financial

system.

In addition, we have investigated the issue of global integration and considered the

impact of foreign exchange on the model, in order to understand the exchange rate risk


element. We have analyzed two models: the structural model, and the TWI weighted

autoregressive model.

Background

Although we aim to examine empirically whether the common intuition about the

integrated global financial market stands, the prevailing literature needs to be reviewed.

The theoretical basis of the common intuition is traced in early mean-variance analyses

of international share price integration or international asset pricing analyses, namely,

the international asset pricing model (IAPM) and international arbitrage pricing theory

(IAPT) [Solnik (1974a), Sutlz (1981)]. IAPM is an extended version of the capital asset

pricing theory (CAPM) of Sharpe (1963, 1964) and Lintner (1965) while IAPT is

influenced by the arbitrage pricing theory (APT) of Ross (1976), Roll (1977), and Roll

and Ross (1980). The portfolio theory of Markowitz (1952) has been the foundation of

all asset pricing theories. Other studies aimed to assess integration patterns of global

stock markets through correlation and other methods. These include Grubel (1968),

Levy and Sarnat (1970), Solnik (1974b, 1983), Sutlz (1981), Lessard (1973), Ripley

(1973), Panton, et al (1976), Eun and Resnick (1984), Errunza (1983), Chan, et. al

(1992), Maldanado and Saunders (1981), Phillippatos, et al (1983), Arshanapalli and

Doukas (1993), Aggarwal and Rivoli (1980), Bekart and Harkey (1995), Eun and

Beswick (1984), Janakiramannan and Lamba (1998), Joen and Chiang (1991), and Cha

and Oh (2000).


Mills and Mills (1991), Kasa (1992), Cheung and Mak (1992), Arshanapalli and

Doukes (1993), Nasseh and Strauss (2000), Lim and McNelis (1998), Maysami and

Kho (2000), Leong and Felmingham (2001), and Shamsuddin and Kim (2003),

amongst others, have studied the interrelationship between various markets by applying

cointegration analysis to international share prices. Further support for studying the

interdependence of share markets is found in studies on market efficiency or efficient

market hypothesis, including those of Roca (1999), Roca, et al (1998) and Chan and Oh

(2000).

Generally, any potential gain from the international diversification of a portfolio is

inversely related to the extent of stock market integration. A low correlation between

returns of national and overseas indices allows investors to minimize portfolio risk

through international diversification. Thus, an analysis of the long-run co-movement of

national stock prices with that of overseas stock prices and the short-run temporal

relationship between the two is important for managing an international portfolio.

Additionally, interdependent international stock prices reflect economic integration in

the form of trade linkages and foreign direct investment. Co-movement of underlying

macroeconomic variables across nations may lead to co-movement of stock prices

[Bracker, et al. (1999)]. Still, foreign exchange risk is thought to be an important

consideration by some investors buying foreign stocks.

Studies on stock market integration may be classified into two categories, both based

on the foreign exchange risk component: (i) studies that considered the exchange rate

factor in the analysis [Taylor and Tonks (1989), Bekaert and Harvey (1997)]; and (ii)


studies that ignored the exchange rate risk component. The second category may be

further divided into two sub-groups, based on their assumptions: (i) ignore the

exchange rate and use local currency in the analysis because the foreign exchange risk

can be hedged while investing in overseas markets [Bracker, et al (1999), Ragunathan,

et al (1999)]; and (ii) ignore the exchange rate risks because they are priced in

international asset markets [Dumas and Solnik (1995), Iorio and Faff (2000), Khoo

(1994), and Choi, et al (1998)].

In this chapter, we investigate the global stock market integration issue considering

both ideas on the exchange rate risk element. We therefore have two analyses. One

considers the idea that the foreign exchange component is important for consideration

in assessing the stock market integration under globalization. The second follows the

idea that the foreign exchange component is irrelevant. In our first analysis, we have

used structural and autoregressive approaches to empirical analysis. In our second

analysis we did not go as far as exploring other effects of risks including exchange rate

risk, currency depreciation and impact of inflation. Instead, we have investigated the

cross-country interrelationship in a straightforward way, that is, by using the

cointegration technique of Johansen, based on an autoregressive error correction model.

For our first analysis, we have deliberately ignored the exchange rate component

because of the belief that an astute investor would hedge the exchange risk this is a

diversifiable risk factor is most cases. We acknowledged Solnik (1983) who showed

that if a factor model is believed to hold when asset returns are expressed in some

arbitrary chosen currency, the factor structure as well as its major conclusions is


invariant to the currency chosen. For analogous reasons, we have also ignored the

possible influence of the share return parity. Our first analysis is straightforward in that

it aims to ascertain whether the Australian stock market is integrated with selected six

overseas markets and it aims to identify the short-run dynamics behind it.

For our second analysis, we have used the trade weighted index (TWI) of Australias

major trading partners to represent the foreign exchange risk element. We undertook

investigations considering structural and autoregressive models. The structural model

incorporated exchange risk and share-return parity issues. In analyzing our TWI

adjusted structural model, the ordinary least squares (OLS) estimation technique is

followed.

Data and Variables

We have considered the national stock index of seven developed countries Australia,

the US, the UK, Canada, Germany, France, and Japan. As the S&P/ASX 200 index or

accumulated index series was unavailable for the entire period under investigation, we

used the All Ordinaries index (ALLORDS) to represent the performance of Australian

stock market. Accordingly, our data series consist of the yearly index values of the

ALLORDS, DJIA, FTA, SBF250, DAX, TSX300, and NIKKEI for Australia, the US,

UK, Canada, Germany, France, and Japan respectively. The data have been gathered

from sources that include the Australian Bureau of Statistics, the Reserve Bank of

Australia, and the worldwide website of Harcourt College Publishers. The period of

study is based on the collected data series 1945 to 2002. Annual data series are


considered for the purposes of studying both the long-run relationships as well as the

short-run dynamics operating between the selected seven stock markets. In all of our

analyses we have used logged values of selected variables.

Preliminary Tests

At the outset, the data for this study were checked from descriptive statistical

viewpoints. These are presented in Table 8.1.

TABLE 8.1

Descriptive Statistics AUSTRALIA USA UK CANADA GERMANY FRANCE JAPAN

Mean 5.245621 6.221484 4.771890 4.228871 3.296500 6.437833 6.334756 Median 5.023436 6.369301 4.203049 4.893704 3.285783 6.305764 6.502100 Maximum 8.119666 9.349852 8.083964 8.245610 6.100207 9.097584 10.56916 Minimum 2.860394 3.999668 3.083139 0.548757 0.415283 4.594600 2.789827

Std. Dev. 1.522504 1.415010 1.524519 2.228121 1.359712 1.328497 2.619283 Skewness 0.345815 0.467197 0.809055 -0.053329 0.188878 0.393691 0.073577 Kurtosis 2.016226 2.338045 2.311779 1.821935 2.065949 1.912129 1.403392

Jarque-Bera 5.362856 4.862655 11.46589 5.188750 3.764519 6.687736 9.533426 Probability 0.068465 0.087920 0.003238 0.074693 0.152246 0.035300 0.008508

Sum 466.8603 553.7121 424.6982 376.3695 293.3885 572.9671 563.7933

Sum Sq. Dev. 203.9858 176.1982 204.5260 436.8778 162.6959 155.3116 603.7366

Observations 89 89 89 89 89 89 89

It appears from Table 8.1 that our data series consisting of 89 observations have

probabilities of being significant at around the 10% level in terms of various

preliminary statistical measures, including the mean, the standard deviation, skewness,

kurtosis, and the Jaque-Bera statistic.


Analysis 1

In selecting the optimal lag length for our first analysis, we have conducted the

necessary tests using EViews4, as presented in Tables 8.2A and 8.2B. The results of the

correlogram in Table 8.2A indicates that the appropriate lag length is two, while the lag

length selection test statistics of LR, FPE, SBC and HQ in Table 8.2B clearly suggest

that a lag of one period is the optimal lag length. Although the AIC and correlogram

criteria suggested differently, the other tests suggested that a lag of one year is

appropriate. Accordingly, we have taken the lag length as one in the model for analysis.

TABLE 8.2A

Correlogram of Residuals Sample: 1945 2002

Included observations: 58

Autocorrelation Partial Correlation Lag AIC PAC Q-Stat Prob

. |*******| . |*******| 1 0.943 0.943 54.324 0.000 . |*******| . | . | 2* 0.887 -0.029 103.17 0.000 . |****** | . | . | 3 0.836 0.021 147.34 0.000

. |****** | .*| . | 4 0.779 -0.075 186.47 0.000 . |****** | . | . | 5 0.724 -0.020 220.88 0.000 . |***** | . | . | 6 0.674 0.009 251.24 0.000

. |***** | . | . | 7 0.624 -0.019 277.82 0.000 . |**** | . | . | 8 0.575 -0.025 300.83 0.000 . |**** | .*| . | 9 0.518 -0.101 319.92 0.000

. |**** | . | . | 10 0.461 -0.047 335.31 0.000 . |*** | . | . | 11 0.410 0.021 347.77 0.000 . |*** | .*| . | 12 0.356 -0.061 357.37 0.000

. |** | . | . | 13 0.310 0.034 364.77 0.000 . |** | .*| . | 14 0.256 -0.118 369.94 0.000 . |** | . | . | 15 0.209 0.036 373.48 0.000

. |*. | . | . | 16 0.168 0.003 375.83 0.000 . |*. | .*| . | 17 0.121 -0.076 377.08 0.000 . |*. | . | . | 18 0.081 0.024 377.65 0.000

. | . | . | . | 19 0.048 0.008 377.86 0.000 . | . | . | . | 20 0.014 -0.029 377.87 0.000 . | . | . | . | 21 -0.014 0.026 377.89 0.000

. | . | .*| . | 22 -0.051 -0.124 378.14 0.000 .*| . | . | . | 23 -0.089 -0.036 378.92 0.000 .*| . | . |*. | 24 -0.108 0.109 380.11 0.000


TABLE 8.2B

Lag Length Selection VAR Lag Order Selection Criteria Endogenous variables: AUSTRALIA USA UK CANADA GERMANY FRANCE JAPAN

Exogenous variables: C Date: 11/22/03 Time: 17:51 Sample: 1945 2002 Included observations: 58

Lag Log likelihood LR FPE AIC SBC HQ

0 -124.1068 NA 2.17E-07 4.520924 4.769598 4.617787 1 199.0015 557.0832* 1.72E-11* -4.931085 -2.941691* -4.156176* 2 237.1254 56.52862 2.69E-11 -4.556048 -0.825936 -3.103094 3 283.5171 57.58967 3.58E-11 -4.466106 1.004725 -2.335107 4 337.6588 54.14168 4.53E-11 -4.643406 2.568145 -1.834361 5 414.9343 58.62285 3.75E-11 -5.618425* 3.333844 -2.131336

* indicates lag order selected by the criterion LR: sequential modified likelihood ratio (LR) test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SBC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

We could not find any significant effect of the stock market crash of October 1987 in

our series from the Chow Breakpoint test [Chow (1960)]. This is because we failed to

reject the hypothesis of no breakpoint effect in the 1987 data even at the 10% level. We

observed the F-statistic 0.814644 with p-value 0.580112, and the log likelihood ratio

statistic 7.068216 with corresponding p-value of 0.421812. These are not significant at

acceptable levels. As a result, we did not consider any exogenous dummy variable in

the model.

Furthermore, to undertake cointegration analysis in the spirit of Johansen, we have

conducted the necessary unit root tests using both the ADF [Dickey and Fuller (1979,

1981)] and PP [Phillips and Perron (1988)] test procedures. These are presented in

Table 8.3.


TABLE 8.3

Unit Root Test Results

Augmented Dickey-Fuller (ADF) Phillips-Perron (PP) Variables Intercept,

No trendA Intercept

with trendB No intercept,

No trendC Intercept, No trendA

Intercept with trendB

No intercept, No trendC

At level

AUSTRALIA -0.0861 -2.2462 3.2128 -0.3195 -2.9038 3.0873

USA -0.0151 -1.1831 3.4482 -0.2368 -1.5074 3.7666

UK 0.0253 -2.2697 2.6029 -0.2431 -2.6681 2.4349

CANADA -0.9264 -2.0602 2.1724 -1.0656 -2.2391 2.3153

GERMANY -0.9647 -2.8672 0.9940 -1.1078 -3.0808 0.8983

FRANCE -0.7003 -2.7838 3.8898 -0.9017 -3.6897 3.6777

JAPAN -2.6085 -0.0516 1.6254 -2.6789 -0.1857 1.7593

At 1st diff.

∆AUSTRALIA -4.9478 -4.4088 -3.7166 -8.8982 -8.8172 -7.7549

∆USA -4.1458 -4.0870 -2.9673 -7.6233 -7.5492 -6.3772

∆UK -5.7611 -5.7935 -4.4700 -8.3472 -8.2862 -7.6105

∆CANADA -3.9954 -3.8950 -3.2572 -7.8111 -7.7395 -7.0719

∆GERMANY -5.1658 -5.0782 -4.8364 -8.2049 -8.1195 -8.0446

∆FRANCE -5.4494 -5.3924 -3.5407 -8.5461 -8.4742 -7.0986

∆JAPAN -3.1398 -3.9737 -2.6973 -6.0568 -6.7411 -5.5385

Note: MacKinnon Critical values at level: for model A. -2.9851; model B. -3.462; model C. -1.9439, and at 1st difference: for model A. -2.8955; model B. -3.4626; model C. -1.9440

The test results reported in Table 8.3 are compared against the MacKinnon (1990)

critical values for rejection of the null hypothesis of no unit root. It clearly suggests that

all of the seven series are integrated to order one I(1) in levels and are of order zero I(0)

in first differences, meaning that they are nonstationary in levels and stationary in first

differences.

Cointegration Analysis

To determine both the long- and short-run relationships operating between the

Australian stock market and those of the six other major markets, we have treated all of

the seven series or variables as an endogenous series:


( , , , , , , )ty AUSTRALIA USA UK CANADA GERMANY FRANCE JAPAN ′=

where the logged stock market indices of seven countries are assumed to be integrated

of order one, I(1), and also they are thought to be cointegrated. We have adapted the

generalised vector autoregressive (VAR) model with k lags containing all variables (g

=7), as under:

1 1 2 2t t t k t k ty y y y u− − −=Φ +Φ + +Φ +L (8.01)

where yt is a vector of order 7 1× , Φ is a 7 7× matrix, and ut is a 7 1× vector. Johansen

cointegration requires us to convert the above VAR into an error correction form. The

vector error correction model (VECM) takes the following form:

1 1 1 ( 1)t t k t k t k ty y y y ε− − − − −∆ =∏ +Γ∆ + +Γ ∆ +L (8.02)

where 1

( )k

i gi

Iβ=

∏ = ∑ − is the long-run coefficient matrix of the lagged yt, 1

( )i

i j gj

Iβ=

Γ = ∑ −

is a coefficient matrix of k-1 lagged difference variables, and ∆yt, on the right hand side

of the equation refers to short-run dynamics. Accordingly, the reduced form VECM for

the seven cross-country cointegration analysis is:

1

1

k

t t k i t i ti

y y y ε−

− −=

∆ = ∏ + ∑ Γ ∆ + (8.03)


where αβ ′∏ = as per Johansen (1988, 1996, 2000).

By considering 1st order VAR and employing EViews4 to perform the analysis

following Johansen (1988, 1991, 1995a, 1995b, 1996, 1999, 2000), we have obtained

test results. It is evident from the results that although we cannot reject the null

hypothesis of no cointegration from the test result ofmaxλ , we can reject the null

hypothesis of 0r = from the traceλ test against the alternative 1r = . As per the trace

tests results there are at most two cointegrating equations. Since the first equation

provides the relationship from the perspective of the Australian stock market, we can

say that the Australian stock market is cointegrated with the other six markets. In other

words, movements in Australian stock prices are influenced by major developed

markets. Graph 8.1 plots the cointegrating relationship between Australia and the other

six markets under study.

GRAPH 8.1

Pattern of Australian Stock Market Integration under Globalization

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

1950 1960 1970 1980 1990 2000

Cross-Country Cointegrating relation for AUSTRALIA


For convenience, the coefficients of the first cointegrating equation have been

normalized. To ascertain the strength of the relationship and the extent of influences,

the likelihood ratio (LR) test results are produced by imposing appropriate restrictions

in the model solutions. We have used EViews4 to perform the necessary tests in this

regard. The cointegration results along with test statistics are presented in Table 8.4.

TABLE 8.4

Cointegration Results Hypothesis Critical Value

Null Alternative

Test Statistic At 5% level At 1%

Eigenvalue

(A) Cointegration testa

Test Statistic: Maximal Eigenvalue (maxλ )

r = 0 r = 1 41.7013 45.28 51.57 0.5128 r ≤ 1 r = 2 33.4656 39.37 45.10 0.4384 r ≤ 2 r = 3 25.7108 33.46 38.77 0.3581 r ≤ 3 r = 4 17.8657 27.07 32.24 0.2651 r ≤ 4 r = 5 8.9440 20.97 25.52 0.1429 r ≤ 5 r = 6 5.5932 14.07 18.63 0.0919 r ≤ 6 r = 7 3.4890 3.76 6.65 0.0584

Test Statistic: Trace (traceλ )

r = 0 r ≥ 1* 136.7697 124.24 133.57 0.5128

r ≤ 1 r ≥ 2* 95.0683 94.15 103.18 0.4384 r ≤ 2 r ≥ 3 61.6028 68.52 76.07 0.3581 r ≤ 3 r ≥ 4 35.8919 47.21 54.46 0.2651 r ≤ 4 r ≥ 5 18.0262 29.68 35.65 0.1429 r ≤ 5 r ≥ 6 9.0822 15.41 20.04 0.0919 r ≤ 6 r = 7 3.4890 3.76 6.65 0.0584

(B) The long-run equationb

AUSTRALIA(8.1862) = 0.2088USA(0.4818) 0.8222UK(8.1032) +

0.3154CANADA(1.6272) 0.2155GERMANY(2.3006) + 0.0572FRANCE(0.0354)

0.0461JAPAN(0.2461)

or

AUSTRALIA(8.1862) 0.2088USA(0.4818) 0.8222UK(8.1032) +

0.3154CANADA(1.6272) 0.2155GERMANY(2.3006) + 0.0572FRANCE(0.0354)

0.0461 JAPAN(0.2461) = 0

r *= the number of cointegrating vectors.

a. Optimal lag structure is one and the VAR contains constant without trend and breakpoint dummy as exogenous to the model.

b. The long-run cointegrating vector is normalised on the logged Australian All Ordinaries index (AUSTRALIA). The Likelihood

Ratio (LR) test statistics, given in parentheses, are used to test the null hypothesis that each coefficient is statistically zero. The test

statistic is asymptotically distributed as a chi-square distribution with one degree of freedom. The critical values of chi-square

distribution at 5% and 10% significance levels are 3.841 and 2.706 respectively.


TABLE 8.5

Multivariate Dynamic Time Series (Short-Run) Models

Item Coefficient Standard Error t-ratio LHS variable: ∆AUSTRALIA

∆AUSTRALIA(-1)

∆USA(-1)

0.1096

-0.0352

0.2322

0.2760

0.4722

-0.1276

∆UK(-1) -0.0399 0.1822 -0.2188

∆CANADA(-1) -0.1340 0.1320 -1.0153

∆GERMANY(-1) 0.0155 0.0922 0.1676 ∆FRANCE(-1) -0.2354 0.2804 -0.8396

∆JAPAN(-1) -0.0237 0.1082 -0.2191

ECM(-1) -0.3286 0.1659 -1.9812

F-Statistic 1.0998

LHS variable: ∆USA

∆AUSTRALIA(-1)

∆USA(-1)

-0.1242

0.2359

0.1861

0.2213

-0.6672

1.0660

∆UK(-1) 0.1104 0.1461 0.7560

∆CANADA(-1) 0.0198 0.1058 0.1875

∆GERMANY(-1) 0.0812 0.0739 1.0985

∆FRANCE(-1) -0.4521 0.2248 -2.0112

∆JAPAN(-1) -0.0669 0.0868 -0.7714

ECM(-1) 0.1171 0.1330 0.8807

F-Statistic 1.2186

LHS variable: ∆UK ∆AUSTRALIA(-1)

∆USA(-1)

0.1790

0.5074

0.2779

0.3304

0.0644

1.5355

∆UK(-1) -0.1539 0.2181 -0.7054

∆CANADA(-1) -0.1397 0.1580 -0.8842

∆GERMANY(-1) 0.1141 0.1104 1.0342

∆FRANCE(-1) -0.7435 0.3357 -2.2151

∆JAPAN(-1) -0.0421 0.1295 -0.3253

ECM(-1) 0.0483 0.1986 0.2433

F-Statistic 1.1926

LHS variable: ∆CANADA

∆AUSTRALIA(-1)

∆USA(-1)

-0.1502

-0.0834

0.2886

0.3432

-0.5205

-0.2430

∆UK(-1) 0.0618 0.2266 0.2730

∆CANADA(-1) -0.1844 0.1641 -1.1233

∆GERMANY(-1) 0.1610 0.1146 1.4051

∆FRANCE(-1) 0.1979 0.3486 0.5675 ∆JAPAN(-1) 0.0818 0.1345 0.6082

ECM(-1) -0.3848 0.2062 -1.8689

F-Statistic 1.3739

LHS variable: ∆GERMANY

∆AUSTRALIA(-1)

∆USA(-1)

-0.7132

0.0783

0.4086

0.4858

-1.7457

0.1613

∆UK(-1) 0.6448 0.3207 2.0105

∆CANADA(-1) 0.0470 0.2324 0.2023

∆GERMANY(-1) -0.0960 0.1623 -0.5918

∆FRANCE(-1) 0.0270 0.4935 0.0547

∆JAPAN(-1) -0.1870 0.1905 -0.9818

ECM(-1) 0.4064 0.2919 1.3921

F-Statistic 0.8088

LHS variable: ∆FRANCE

∆AUSTRALIA(-1) ∆USA(-1)

0.0796 -0.0601

0.1893 0.2251

0.4203 -0.2673

∆UK(-1) 0.1244 0.1486 0.8371

∆CANADA(-1) -0.0891 0.1076 -0.8278

∆GERMANY(-1) 0.0709 0.0752 0.9428

∆FRANCE(-1) -0.2445 0.2287 -1.0695

∆JAPAN(-1) 0.0037 0.0882 0.0415

ECM(-1) -0.1372 0.1352 -1.0147

F-Statistic 0.8210

LHS variable: ∆JAPAN

∆AUSTRALIA(-1)

∆USA(-1)

-0.4194

-0.1847

0.3136

1.3729

-1.3374

-0.4953

∆UK(-1) 0.5669 0.2462 2.3028

∆CANADA(-1) 0.0772 0.1783 0.4330

∆GERMANY(-1) 0.0734 0.1245 0.5895

∆FRANCE(-1) -0.0198 0.3788 -0.0523 ∆JAPAN(-1) 0.0807 0.1462 0.5523

ECM(-1) 0.5157 0.2241 2.3014

F-Statistic 1.3077


It appears from the LR test statistics and the estimated coefficients corresponding to

each market in (B) of Table 8.4 that the movements of UK stock prices significantly

influence the movement in Australian stock prices at the 5% level. The Australian

market is corrected at the rate of 33% from its previous years disequilibrium as shown

in the dynamic solution presented in Table 8.5.

The first cointegration equation contains both a long-run relationship and the short-run

dynamics of the VECM, 1 1t i iy y yα β − −′∆ = + Γ ∆ , where ∆yt =∆AUSTRALIA,

normalized β ′ = 1, 0.21, 0.82, 0.32, 0.22, 0.06, 0.05 and corresponding t-statistics

for the US, the UK, CANADA, GERMANY, FRANCE, and JAPAN are 1.51551,

8.89530, 2.62820, 2.66750, 0.31799, and 1.02482 respective. The estimated β for

Australia and the estimated α with its corresponding t-statistics in parentheses are

provided in the following:

11 11

( 1.516)21 21

( 8.895)31 31

41 (2.628) 41

51 51( 2.668)

61 61(0.318)

71 71( 1.025)

1.00

0.21

0.82

0.32 ;

0.22

0.06

0.05

AUSTRALIA

β αβ αβ α

β β α αβ αβ αβ α

−

−

−

−

− − = = = − −

( 1.981)

(0.881)

(0.243)

( 1.866)

(1.392)

( 1.015)

(2.301)

0.33

0.12

0.05

0.38

0.41

0.14

0.52

−

−

−

− = − −

(8.04)

The resultant t-statistics for AUSTRALIAβ in the above equation suggests that three markets

are influential for Australia in the long-run as they are significant at 5% levels. These

three markets are UK, Canada, and Germany. In the same cointegrating vector for

Australia, α = (0.33, 0.12, 0.05, 0.38, 0.41, 0.14, 0.52) where ECM-1 = 11α = 0.33


is relevant to the long-run equation for Australia. Corresponding t-values of α are

1.98124, 0.88070, 0.24332, 1.86585, 1.39216, 1.01473 and 2.30141. From t-statistics

for α in the above equation, it is evident that the error correction mechanism ECM-1

for Australia is significant at the 5% level.

The coefficients of the short-run adjustment parameters 1i y−Γ ∆ are 0.11, 0.04, 0.04,

0.13, 0.02, 0.24, and 0.02, with t-values as 0.47218, 0.12758, 0.21883, 1.01529,

0.16760, 0.83956, and 0.21907 respectively. Based on these results, the solved

model is presented in equations 8.05 and 8.06:

∆AUSTRALIA t = 0.33*[AUSTRALIA -1 + 0.21*USA -1 0.82*UK -1

+ 0.32*CANADA -1 0.22*GERMANY-1 + 0.06*FRANCE -1

0.05*JAPAN -1] + [0.11*∆AUSTRALIA -1 0.04*∆USA -1

0.04*∆UK -1 0.13*∆CANADA -1 + 0.02*∆GERMANY -1

0.24*∆FRANCE -1 0.02*∆ JAPAN -1] (8.05)

∆AUSTRALIA t = 0.33*AUSTRALIA -1 0.07*USA -1 + 0.27*UK -1

0.10*CANADA -1 + 0.07*GERMANY-1 0.02*FRANCE -1

+ 0.02*JAPAN -1 + 0.11*∆AUSTRALIA -1 0.04*∆USA -1

0.04*∆UK -1 0.13*∆CANADA -1 + 0.02*∆GERMANY -1

0.24*∆FRANCE -1 0.02*∆ JAPAN -1. (8.06)

The estimated long-run model for Australia in equilibrium, where the short-run

equation does not exists, is presented by equation 8.07:

∆AUSTRALIA t = 0.33*AUSTRALIA -1 0.07*USA -1 + 0.27*UK -1

0.10*CANADA -1 + 0.07*GERMANY-1 0.02*FRANCE -1

+ 0.02*JAPAN -1. (8.07)


The above solved model (8.07) indicates that Australian stock market returns are

influenced by the previous years stock market performance of the US at 7%, the UK at

27%, Canada at 10%, Germany at 7%, France at 2%, Japan at 2%, and Australian

market performance at 33%. It is evident from the t-tests for AUSTRALIAβ presented in the

parentheses of equation 8.04 that in addition to the UK, the Canadian and German

markets also have significant influence on the Australian stock market in the long-run.

Both the LR test statistics in (B) of Table 8.4 and the t-value corresponding to the UK

in equation 8.04 suggest that the influence of the UK market alone is highly significant

for Australia. During this process, the Australian market is corrected from its own

preceding disequilibrium at a speed of 33%.

We have ascertained that the movement of Australian stock market prices is linked with

developed overseas stock markets in the long-run as the linear combination of all

markets under investigation is found cointegrated. Yet, only one to three overseas

markets are found significantly influencing the Australian stock returns based on LR

and t-tests statistics. As the t-test is also relevant, we find the UK, Canada and

Germany are significant at 5% levels, while insignificant markets in the cointegrated

equation are the US, France and Japan.

Supplementary Tests

To corroborate the outcomes we undertook additional analysis by considering only the

significant variables. We have re-estimated the equation dropping insignificant

markets. The additional cointegration analysis was set on two lags because this


appeared to be reasonable. The trace test indicates the presence of one cointegrating

vector at both 5% and 1% significance levels, meaning that all three markets are

cointegrated. Estimation of the long-run equation shows that all cointegrated markets

are significant at 5% levels from the resulted t-statistics. From the LR test it appears

that all variables are significant at 10% levels. The t-test result corroborates the earlier

findings that the UK market is the most dominating market for Australia, although the

LR test indicated otherwise. As per the LR test results, both the German and Canadian

markets are significant at 5% levels, while the UK market is significant at 10% levels.

The German market is found dominating within the cointegration relationship. It is

worth noting that the additional test result corroborated our findings that all three

markets, namely, the UK, Canadian, and German markets, are linked with the

Australian market in the long-run and they appeared to be significant at acceptable

levels.

Analysis 2

Here we have followed two test procedures using TWI adjusted data. The first followed

a structural regression method on the adjusted data, while the second followed the same

cointegration approach used in our first analysis. As we aim to verify if the selected

overseas stock markets are linked to the Australian market even when the foreign

exchange risk component is taken into consideration, we used the trade weighted index

(TWI) as proxy for our adjusted data series. We have considered the relative weight of

each country in the TWI composed by the Reserve Bank of Australia [Becker and

Davies (2002)]. The percentage weights in TWI for the US dollar, UK pound, Canadian


dollar, and Japanese yen in 2002-2003 were 15.07, 5.14, 1.57, and 17.21 respectively.

Since both France and Germany now use common currency, the TWI weight for the

European euro was considered for these countries. The percentage weight of euro for

all common currency affiliated European countries (except the UK) was 12.40 in terms

of the Australian dollar. Since we are interested in the TWI for euro relevant to our

study, we have readjusted the weight based on the % trading relationships. The %

positions of the average international trades (exports and imports) between Australia

and both France and Germany are 13.8% and 23.4% respectively. Accordingly, our

adjusted TWI values for France and Germany become 1.7 (=12.4 × 13.8%) and 3.0

(=12.4 × 23.4%) respectively. For both analyses, the natural logarithms of data are

used.

Structural Approach

We considered a structural regression model in the following manner:

1

p

A j j

j

R T R T W I=

= + ∆∑ (8.08)

where AR is the return on the Australian market, jR refer to returns in selected overseas

stock markets, 1,( , )j pT t t= L is the weight of corresponding currency of selected

overseas markets in the TWI, and TWI∆ is expected depreciation of the TWI or error

term. Again, 1 1 2 2 n nt e t e t e TWI+ + + =∆L and

1 2

1

1n

i n

i

t t t t=

= + + + =∑ L for all currency

specific countries in TWI for Australia where ( , , )i i nT t t= L . The above model is


derived from the notion of share-return parity reflected in the generalised nature

equation 1 2 1 1 2 2 1 1 2 2( ) ( ) ( )n A n n n nt t t R t R t R t R t e t e t e+ + + = + + + + + + +L L L .

To estimate equation 8.08 we have applied both the ordinary least squares (OLS) and

generalized method of moments (GMM) approaches. Both the OLS and GMM

estimations results in relation to equation 8.08 are presented in Tables 8.6 and 8.7:

TABLE 8.6

Dependent Variable: RAUSTRALIA

Method: Least Squares (OLS)

Sample(adjusted): 1946 2002

Included observations: 57 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

RUSA 0.028059 0.152705 0.183749 0.8550

RUK 0.104235 0.024912 4.184088 0.0001

RCanada 0.018028 0.005080 3.548912 0.0009

RFrance 0.224051 0.077894 2.876367 0.0059

RGermany 0.001662 0.001833 0.906372 0.3691

RJapan -0.042002 0.041872 -1.003104 0.3206

C 0.002888 0.003341 0.864475 0.3915

R-squared 0.568987 Mean dependent var 0.011297

Adjusted R-squared 0.517265 S.D. dependent var 0.031709

S.E. of regression 0.022031 Akaike info criterion -4.678109

Sum squared residual 0.024269 Schwarz criterion -4.427208

Log likelihood 140.3261 F-statistic 11.00096

Durbin-Watson stat 2.398591 Probability of F-statistic 0.000000


TABLE 8.7 Dependent Variable: RAUSTRALIA Method: Generalized Method of Moments (GMM) Sample(adjusted): 1946 2002 Included observations: 57 after adjusting endpoints Kernel: Bartlett, Bandwidth: Fixed (3), No prewhitening Simultaneous weighting matrix and coefficient iteration

Convergence achieved after: 1 weight matrix, 2 total coefficient iterations Instrument list: RUSA RUK RCANADA RFRANCE RGERMANY RJAPAN

Variable Coefficient Std. Error t-Statistic Prob.

RUSA 0.028059 0.143685 0.195284 0.8460

RUK 0.104235 0.017845 5.841229 0.0000

RCanada 0.018028 0.005290 3.407572 0.0013

RFrance 0.224051 0.090421 2.477875 0.0166

RGermany 0.001662 0.000563 2.951147 0.0048

RJapan -0.042002 0.035899 -1.170002 0.2475 C 0.002888 0.002527 1.142799 0.2586

R-squared 0.568987 Mean dependent var 0.011297 Adjusted R-squared 0.517265 S.D. dependent var 0.031709 S.E. of regression 0.022031 Sum squared resid 0.024269 Durbin-Watson stat 2.398591 J-statistic 1.56E-32

The results of the OLS estimation provided in Table 8.6 indicate that coefficients of

three variables are significant at 5% levels based on t-statistics. These variables are the

stock market returns of the UK, Canada, and France. From the results of the GMM

estimation in Table 8.7 it appears that coefficients of four variables are significant at

5% levels. These markets are the UK, Canada, France and Germany. From the t-

statistics we can see that out of four markets, the UK market is dominating in the

process maintaining linear relationship. Although the R2 and adjusted R

2 for both tests

do not show very strong fits, other parameters, including the log likelihood, Durbin-

Watson, F-tests statistics and probability in both tests, are within satisfactory levels.

The above structural analysis gives us information about the linkages between the

Australian stock market and other developed overseas markets under globalization with

due consideration given to the exchange risk component. We understand that three to


four overseas markets are linked with the Australian stock market. These are the UK,

Canada, France and Germany, with the UK market the most influential.

Autoregressive Approach

Using both the Augmented Dickey-Fuller and Phillips-Peron procedures, we have

utilised our adjusted series in natural logarithms to identify if they are integrated to

order one in levels and to order zero in first differences. We found all variables are I(1)

in levels and I(0) in first differences. We also tested for appropriate lag length using

standard techniques of likelihood ratio, Akaike Information Criterion, Schwartz

Bayesian Information Criterion, Hannan-Quinn Criterion and Final Prediction Error.

We observed that appropriate lag length is one.

We progress with our analysis using the cointegration approach of Johansen, same as

for our first analysis. Both trace and max-eigenvalue tests show the existence of

cointegrating relationship at the 5% levels. The tests also indicate that the linear

combination of all variables is cointegrated in the long-run while there are short-term

dynamics within the markets for error correction. The cointegration analysis in our

second analysis provides results that are different from our first analysis. From the t-

statistics it appears that within the cointegrating equation five markets are significant

for Australia at the 5% level. These are the US, the UK, Canada, Germany and Japan.

From the likelihood ratio (LR) tests it is revealed that only three markets are significant

between the 5% and 10% levels. These markets are the UK, Germany and Japan, with

the UK the most significant at the 10% level and remainder markets significant at the


5% level. With respect to short-run dynamic adjustment, the Australian market is being

auto corrected at the speed of 9.4%. Still, the error correction mechanism ECM-1 for

Australia is insignificant.

Supplementary Tests

As the error correction mechanism ECM-1 for Australia is insignificant and not all

markets are sufficiently significant, we have further tested our model by dropping the

insignificant market/s. To find the error correction mechanism ECM-1 for Australia as

well as considered markets significant enough, we required three extra tests. The first

extra test indicated that although five overseas markets are cointegrated with the

Australian market and all variables are significant at 5% levels from their

corresponding t-statistics, the ECM-1 for Australia was insignificant. From LR test

results we found that the US market is insignificant as well. We therefore ran our model

again dropping the US from the equation. The second extra test result indicated that we

should run our model one more time dropping the Japanese market because it seemed

insignificant in addition to the insignificant error correction mechanism ECM-1 for

Australia. We therefore conducted our final test by considering only three overseas

markets, namely, the UK, Canada and Germany. We obtained the ECM-1 for Australia

as significant at 5% levels, while all variables are also significant at 5% levels from

both t-test and LR test statistics. The linear combination of the markets of Australia, the

UK, Canada and Germany are also found cointegrated. The results of all undertaken

cointegration tests in this part of the analysis are provided in Table 8.8.


TABLE 8.8

Items

Test on Model 1 for Australia




Variables in model

AUSTRALIA, USA, UK, CANADA, FRANCE, GERMANY, JAPAN

AUSTRALIA, USA, UK, CANADA, GERMANY, JAPAN

AUSTRALIA, UK, CANADA, GERMANY, JAPAN

AUSTRALIA, UK, CANADA, GERMANY

Test relationship

Cointegrated Cointegrated Cointegrated Cointegrated

Significance of ECM-1 for Australia

Not significant Not significant Not significant Significant

Overseas markets Significance from t- test at 5% level

USA, UK, CANADA, GERMANY, JAPAN

UK, CANADA, GERMANY, JAPAN


UK, CANADA, GERMANY

Overseas markets

Significance from LR test at 5% level

GERMANY,

JAPAN

UK, CANADA,

GERMANY, JAPAN

UK,

CANADA, GERMANY

UK,

CANADA, GERMANY

Overseas markets Significance from LR test at 10% level

UK, GERMANY, JAPAN


UK, CANADA, GERMANY

UK, CANADA, GERMANY

Australian markets significance from

LR test at 5% level

Not significant

Not significant

Significant

Significant

It appears from Table 8.8 that the result of the cointegration tests on Model 4 is very

satisfactory from every aspect. All modelled variables are cointegrated as well as

significant. The error correction mechanism ECM-1 for Australia is significant at 5%

levels from both LR and t-tests. The complete test results are provided in Table 8.9:


TABLE 8.9

Vector Error Correction Estimates

Sample(adjusted): 1947 2002 Included observations: 56 after adjusting endpoints

Standard errors in ( ) and t-statistics in [ ]

Cointegrating Equation: Equation for Australia

AUSTRALIA (-1) 1.000000

UK(-1) -0.937789

(0.06728) [-13.9396]

CANADA(-1) 0.393356 (0.10603) [ 3.70977]

GERMANY(-1) -0.320276

(0.08100)

[-3.95390]

C -4.134737

Error Correction: D(AUSTRALIA) D(UK) D(CANADA) D(GERMANY)

Cointegrating Equation 1 -0.428136 0.083469 -0.466556 0.541700 (0.16804) (0.21344) (0.19543) (0.29481) [-2.54782] [ 0.39105] [-2.38730] [ 1.83746]

D(AUSTRALIA(-1)) 0.087336 -0.059234 -0.075148 -0.790582 (0.20737) (0.26340) (0.24117) (0.36381) [0.42116] [-0.22488] [-0.31159] [-2.17308]

D(UK(-1)) -0.127143 -0.050664 0.045764 0.735829

(0.17052) (0.21660) (0.19832) (0.29917)

[-0.74560] [-0.23390] [ 0.23076] [ 2.45958]

D(CANADA(-1)) -0.195267 -0.180547 -0.182048 0.061660

(0.13014) (0.16530) (0.15135) (0.22832) [-1.50045] [-1.09222] [-1.20280] [ 0.27006]

D(GERMANY(-1)) -0.005672 0.152919 0.144629 -0.064803 (0.08775) (0.11146) (0.10205) (0.15394) [-0.06464] [ 1.37200] [ 1.41721] [-0.42095]

C 0.085081 0.080176 0.080938 0.047939 (0.02677) (0.03400) (0.03113) (0.04696)

[ 3.17871] [ 2.35825] [ 2.60008] [ 1.02089]


The final cointegration relationship can be seen in Graph 8.2.

GRAPH 8.2

Final Relationship for Australia under Prevailing Influences of Globalization

-.5

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

-.5

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

1950 1960 1970 1980 1990 2000

Cointegrating relation between three significant overseas markets and the Australian market

The above results are in line with the common intuition about the present global

system. The significant stock markets in our cointegration analysis infer that the UK,

Canadian, and German stock markets are moving in the same way as Australias.

Australian investors have thus little scope to diversify their portfolios by including UK,

Canadian and German stocks when Australian stocks are bearish. In contrast, there will

be opportunities for effective diversification vis-a-vis the US, French and Japanese

markets. Investors should consider additional issues such as the cost of overseas

capital, stock values, and so on. Attention should therefore be focused on analyses of

fundamentals and related risk factors including foreign exchange risk, overseas

inflation, and specific industry risk factors.


Summary

This chapter has examined the cointegrating relationship between Australian stock

price movements and that of six overseas markets using the Johansen cointegration

approach. The analysis confirmed that the Australian stock market has a long-run

relationship with overseas equity markets. The significant overseas markets for

Australia are the UK, Canada and Germany. The Australian stock markets error

correction mechanism is found to be significant at the 5% level.

Although developed stock markets are cointegrated with each other, Australian

investors can still diversify their portfolio risks by considering US, French and

Japanese stocks because these markets are insignificant for Australia in the

cointegrating equation. In addition to knowing about the nature of global stock market

co-movements, Australian investors diversifying their portfolios should consider issues

such as the cost of foreign capital, fundamental values of international stocks, foreign

exchange, and other relevant risks. Upon appropriate assessment of all risk factors,

including both systematic and unsystematic risks, prudent investors should be able to

form effective portfolios that include both local and international stocks and thus for

better returns.


PART V

CONCLUSION

This is the last part of the thesis and consists of one chapter only. Chapter 9 discusses

our outcomes, provides some interpretations and makes recommendations for future

research.


CHAPTER 9

CONCLUSION AND RECOMMENDATION

Outcomes

The aim of this thesis was twofold. First, we aimed to find out which systematic risk

factors are priced in the long-run return generating process in the Australian stock

market. Secondly, we attempted to ascertain if the Australian stock market is integrated

under the influence of globalization. To answer these two questions we focused on

finding reasonable empirical answers. The literature review of asset pricing led us to

ask the two questions. It is clear from the finance literature that the stock market and its

pricing behaviour is highly relevant to both investors and researchers. The performance

of any stock market will always be volatile. And yet, investors are faced with much

risks exposure. To survive the process and gain from their investment, investors need to

be efficient in managing their investment risk.

There have been many studies done on stock market volatility and associated topics.

The various theories provide clear information about the various types of risks

associated with investing in stocks or equity. Investment risk is of two generic types,

based on efficacy of diversification. The type of risk that can be diversified away is

called unsystematic risk, while the other type that cannot be diversified away is called

systematic risk. Unsystematic risk is also asset-specific or unique risk. The

unsystematic risk is negligible for a well diversified portfolio. Essentially all of the risk


in such a portfolio is systematic. In this context, the systematic risk principle states that

the expected return on a risky asset depends only on the assets systematic risk as the

unsystematic risk is supposed to be eliminated by diversification. Although the

systematic risk is thought to be the market risk, the beta coefficient does not refer to the

entirety of systematic risk. The beta coefficient only refers to the amount of systematic

risk that is present in a particular risky asset relative to that of an average risky asset.

Diversifiable risk ought to be managed for efficiency and improved performance under

the competitive market environment. Non diversifiable risk, on the other hand, is

beyond the scope of a firms normal operations. Thus, studying the systematic risk of

an investment is an important issue to investors, one which requires special attention

their investment decision making.

The movement of stock prices has been the focus of many finance studies. Current

theories have already answered vital questions associated with asset pricing and

investment decision making. Still, answers to certain questions are inadequate and often

they require thorough research. We therefore aimed to extend current knowledge by

identifying systematic risk factors significant for the Australian stock market and

examining the nature of stock market integration under the influence of globalization.

We used the most up-to-date methods of empirical data analysis. We also used up-to-

date econometrics knowledge and software. An intensive literature review was

conducted to help identify the most common systematic risk factors. The empirical

investigation conducted to ascertain the causal relationship between Australian stock


market returns and the common systematic risk factors and also the movements of

overseas markets under globalization was carried out through testing our generated

models. We acknowledged that the idea of causality of any nature must come from

reality, as empirical or statistical relationships per se cannot logically explain causation

[Gujarati (1995)]. Accordingly, to ascribe causality we opted to appeal to theory. In

assessing statistical relationships among variables, we essentially dealt with randomness

that is nonstationary by its nature and developed autoregressive models to that effect.

This research questions considered here evolved from both theory and real life

situations relevant to many investors and fund managers in the Australian marketplace.

Theoretical and practical aspects have been intensively explored to help answer the

questions of which systematic risk factors are priced in the Australian stock market and

whether there is any cross-country relationship between Australian and other developed

markets in the both long- and short-terms.

We saw from our reviews in Chapters 2, 3 and 4 that many researchers have dealt with

the problems of identifying systematic risk factors to explain stock returns. Most have

followed the Roll and Ross method, in line with arbitrage pricing theory (APT) rather

than the capital asset pricing model of Sharpe and Lintner. Researchers who conducted

studies in line with APT followed two different approaches in dealing with factors.

Some researchers considered the nature of common factors as latent, while others

preferred to pre-specify their variables by considering these factors as a priori. In this

research we treated our factors as pre-specified or a priori. We saw in the literature

review chapters that modern researchers have been attempting to find out if a priori


variables can explain the returns generating process of a stock market considering the

comprehensive market index to proxy for their market returns.

It was also seen from the literature review in Chapters 3 and 4 that different researchers

used different methodologies in their analytical process, including factor analysis,

principal component analysis, general regression analysis, generalized method of

moments, time series regression analysis, causality analysis, and residual based as well

as autoregressive cointegration approaches. From available methods of cointegration

analysis, the lately developed approach of Johansen is considered more suitable over

earlier ones. This is because the cointegration approach of Johansen has the built-in

capacity to show both the long-run relationship between variables and the short-run

dynamics of the model. Thus, we used the Johansens cointegration method for the

purpose of both our analyses in Chapters 7 and 8, generating reliable results by

identifying which of our a priori variables are influencing the stock market returns in

both the long- and short-runs, and providing clarity about the dynamics of our models. The

outcomes are in line with both theory and general intuition in finance and investment.

In Chapter 7 we ascertained that at least four a priori variables are significant at the 5%

level, including the interest rate, corporate profit, dividend yield and industrial

production. Although the likelihood ratio test indicated that both the global stock

market index and price-earnings ratio are insignificant even at the 10% level, yet the

global stock market index was found significant at the 5% level, along with the interest

rate, corporate profit, dividend yield, industrial production, and price-earnings ratio

from the t-statistics. We observed that the linear combination of all our modelled


variables is cointegrated even though not all variables are significantly influential.

We concluded that four to five of our a priori variables have significant long-run

influences on Australian stock price movements or the return generating process and

they are priced in the market.

The findings of our second analysis in Chapter 8 demonstrated that in longer run, the

Australian stock market is linked to these major developed markets: the US, the UK,

Canada, Germany, France and Japan. All were found cointegrated with the Australian

stock market. The likelihood ratio test result indicated that within the global stock

market set-up, the significant overseas markets for Australia are the UK, Canada and

Germany, with the UK being heavily influential.

Through the literature reviews of Chapters 2, 3, and 4 we established both theoretical

and practical knowledge about variables to proxy systematic risk factors. Initially we

identified a larger number of proxy variables, which we then reduced for efficient

modelling. We specified the a priori variables to consider in our appropriate model. In

Chapter 6, we developed suitable models in both structural and autoregressive fashions.

We tested our models empirically in Chapters 7 and 8. The outcomes of Chapter 7

showed us that Australian stock market price movements respond to changes in our a

priori variables and some of these systematic risk factors are influential in the long-run

while short-run dynamics are also present. We learnt from Chapter 8 about the nature

of the global stock market integration mechanism. We saw that the Australian stock

market is integrated with major overseas markets under the influence of globalization,

with some overseas markets more influential than others.


Recommendations

We recommend that Australian investors and fund managers closely watch any sharp

movement in the a priori variables which we found influential for Australia. As the

scope of this thesis was necessarily limited, our outcomes do not suggest that

Australian investors invest exclusively on the basis of this study there are other

types of risks that also warrant proper investigation before making any investment

decision. Some of these risks are company specific, while others are industry specific.

Investors own studies on the fundamental valuation of assets and the costs of capital

are important for superior investment returns. The lessons of this thesis will only be

effective if investors treat the outcomes here as complementary to other types of

knowledge, knowledge which an Australian investor should pursue as part of their

ongoing investment decision making processes.

Future Research

Many other questions remain unresolved; these can be carried over for further study.

An interesting area of future study relates to the long-run relationship between

Australian and emerging stock markets. Additional research projects may be developed

on matters such as asset pricing bubbles and asset valuation problems, testing the

efficient market hypothesis for emerging markets, and how to set a universal best

practice norm for global stock trading.


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Annexure 1

Pair-wise Correlation Matrix on Base Data

ALLORDS BVIR CP CPI DY ER GDP GDPPC IPI IR11AM M3 MPI MSCI NX PER UR

ALLORDS 1.000

BVIR -0.685 1.000

CP 0.838 -0.654 1.000

CPI 0.908 -0.749 0.775 1.000

DY -0.547 0.626 -0.415 -0.377 1.000

ER -0.767 0.436 -0.562 -0.640 0.563 1.000

GDP 0.968 -0.744 0.863 0.945 -0.478 -0.738 1.000

GDPPC 0.971 -0.711 0.869 0.929 -0.468 -0.748 0.998 1.000

IPI 0.953 -0.731 0.856 0.974 -0.408 -0.697 0.987 0.982 1.000

IR11AM -0.674 1.000 -0.652 -0.742 0.615 0.410 -0.738 -0.704 -0.724 1.000

M3 0.951 -0.772 0.843 0.954 -0.473 -0.721 0.994 0.985 0.982 -0.770 1.000

MPI 0.905 -0.733 0.781 0.998 -0.358 -0.653 0.939 0.924 0.973 -0.726 0.948 1.000

MSCI 0.985 -0.737 0.843 0.944 -0.555 -0.749 0.981 0.978 0.974 -0.730 0.974 0.939 1.000

NX -0.301 0.143 -0.425 -0.182 0.206 0.181 -0.310 -0.335 -0.276 0.164 -0.258 -0.170 -0.276 1.000

PER 0.535 -0.729 0.365 0.619 -0.573 -0.512 0.571 0.542 0.568 -0.725 0.597 0.619 0.585 -0.135 1.000

UR -0.482 -0.205 -0.317 -0.298 -0.162 0.385 -0.434 -0.483 -0.423 -0.245 -0.369 -0.311 -0.414 0.318 0.245 1.000


Common Sample Correlation Matrix on Base Data

Annexure 1 (Contd.)

ALLORDS BVIR CP CPI DY ER GDP GDPPC IPI IR11AM M3 MPI MSCI NX PER UR

ALLORDS 1.000

BVIR -0.703 1.000

CP 0.838 -0.654 1.000

CPI 0.842 -0.838 0.775 1.000

DY -0.534 0.599 -0.415 -0.315 1.000

ER -0.676 0.427 -0.562 -0.429 0.588 1.000

GDP 0.956 -0.770 0.863 0.929 -0.434 -0.625 1.000

GDPPC 0.961 -0.731 0.869 0.902 -0.421 -0.636 0.997 1.000

IPI 0.924 -0.783 0.856 0.960 -0.351 -0.529 0.985 0.977 1.000

IR11AM -0.700 1.000 -0.652 -0.836 0.599 0.423 -0.768 -0.728 -0.781 1.000

M3 0.936 -0.799 0.843 0.957 -0.424 -0.611 0.993 0.981 0.985 -0.797 1.000

MPI 0.839 -0.824 0.781 0.996 -0.291 -0.447 0.924 0.897 0.959 -0.822 0.953 1.000

MSCI 0.977 -0.777 0.843 0.906 -0.545 -0.638 0.975 0.970 0.957 -0.775 0.966 0.901 1.000

NX -0.317 0.138 -0.425 -0.161 0.211 0.189 -0.336 -0.369 -0.293 0.142 -0.273 -0.141 -0.293 1.000

PER 0.396 -0.714 0.365 0.516 -0.542 -0.414 0.455 0.417 0.446 -0.715 0.494 0.519 0.465 -0.108 1.000

UR -0.350 -0.340 -0.317 -0.062 -0.276 0.204 -0.281 -0.345 -0.252 -0.343 -0.204 -0.078 -0.251 0.320 0.460 1.000


Pair-wise Correlation Matrix on LNDATA

Annexure 1 (Contd.)

LNALLORDS LNBVIR LNCP LNCPI LNDY LNGDP LNER LNGDPPC LNIPI LNIR11AM LNMPI LNMS LNMSCI LNNX LNPER LNUR

LNALLORDS 1.000

LNBVIR -0.690 1.000

LNCP 0.804 -0.699 1.000

LNCPI 0.929 -0.750 0.755 1.000

LNDY -0.534 0.653 -0.383 -0.372 1.000

LNGDP 0.943 -0.792 0.839 0.945 -0.482 1.000

LNER -0.720 0.529 -0.496 -0.604 0.591 -0.723 1.000

LNGDPPC 0.940 -0.764 0.844 0.920 -0.481 0.996 -0.742 1.000

LNIPI 0.946 -0.762 0.840 0.972 -0.408 0.988 -0.675 0.979 1.000

LNIR11AM -0.678 1.000 -0.697 -0.741 0.638 -0.782 0.495 -0.752 -0.752 1.000

LNMPI 0.927 -0.740 0.763 0.998 -0.358 0.943 -0.618 0.919 0.973 -0.731 1.000

LNMS 0.935 -0.796 0.796 0.987 -0.425 0.981 -0.656 0.963 0.989 -0.788 0.985 1.000

LNMSCI 0.987 -0.729 0.808 0.963 -0.527 0.953 -0.690 0.942 0.963 -0.719 0.960 0.962 1.000

LNNX 0.174 0.045 -0.122 0.255 0.235 0.229 -0.058 0.223 0.224 0.036 0.248 0.234 0.158 1.000

LNPER -0.006 0.079 -0.222 -0.002 -0.052 -0.036 0.040 -0.048 -0.055 0.082 -0.012 -0.007 0.009 0.194 1.000

LNUR -0.456 -0.135 -0.275 -0.303 -0.128 -0.422 0.404 -0.479 -0.418 -0.185 -0.318 -0.329 -0.390 -0.277 0.085 1.000


Common Sample Correlarion Matrix on LNDATA

Annexure 1 (Contd.)

LNALLORDS LNBVIR LNCP LNCPI LNDY LNGDP LNER LNGDPPC LNIPI LNIR11AM LNMPI LNMS LNMSCI LNNX LNPER LNUR

LNALLORDS 1.000

LNBVIR -0.622 1.000

LNCP 0.766 -0.690 1.000

LNCPI 0.656 -0.725 0.612 1.000

LNDY -0.592 0.589 -0.392 -0.119 1.000

LNGDP 0.867 -0.730 0.775 0.910 -0.296 1.000

LNER -0.739 0.562 -0.709 -0.506 0.474 -0.722 1.000

LNGDPPC 0.890 -0.679 0.789 0.857 -0.297 0.992 -0.755 1.000

LNIPI 0.811 -0.713 0.753 0.940 -0.203 0.991 -0.660 0.976 1.000

LNIR11AM -0.607 0.999 -0.681 -0.716 0.589 -0.715 0.543 -0.664 -0.701 1.000

LNMPI 0.655 -0.721 0.633 0.997 -0.102 0.913 -0.544 0.863 0.943 -0.711 1.000

LNMS 0.738 -0.753 0.680 0.991 -0.191 0.955 -0.572 0.913 0.972 -0.743 0.988 1.000

LNMSCI 0.956 -0.737 0.726 0.773 -0.619 0.908 -0.713 0.905 0.868 -0.726 0.765 0.834 1.000

LNNX 0.092 0.158 -0.122 0.216 0.271 0.221 -0.137 0.228 0.217 0.169 0.211 0.201 0.070 1.000

LNPER -0.043 -0.062 -0.345 0.083 -0.124 -0.087 0.246 -0.148 -0.098 -0.069 0.067 0.046 0.018 0.207 1.000

LNUR -0.420 -0.308 -0.275 -0.076 -0.229 -0.338 0.382 -0.434 -0.319 -0.328 -0.101 -0.142 -0.241 -0.325 0.408 1.000


Pair-wise Correlation Matrix on 1st Differenced Data

Annexure 1 (Contd.)

DALLORDS DBVIR DCP DCPI DDY DER DGDP DGDPPC DIPI DIR11AM DMPI DMSCI DNX DUR DPER DMS

DALLORDS 1.000

DBVIR -0.046 1.000

DCP -0.056 0.005 1.000

DCPI 0.021 -0.115 -0.113 1.000

DDY -0.426 0.224 0.139 -0.012 1.000

DER -0.037 -0.166 -0.043 -0.047 -0.103 1.000

DGDP -0.057 0.117 0.235 0.004 0.191 0.034 1.000

DGDPPC -0.047 0.117 0.233 0.014 0.186 0.018 0.989 1.000

DIPI -0.119 0.094 0.128 -0.054 0.211 -0.156 0.401 0.407 1.000

DIR11AM -0.040 0.996 -0.009 -0.115 0.231 -0.192 0.105 0.107 0.084 1.000

DMPI 0.071 0.204 0.233 -0.085 0.286 -0.242 -0.118 -0.093 0.226 0.194 1.000

DMSCI 0.488 -0.051 -0.152 -0.064 -0.803 0.137 -0.045 -0.047 -0.110 -0.059 -0.080 1.000

DNX 0.056 -0.113 -0.192 -0.002 0.067 -0.135 -0.121 -0.130 -0.055 -0.097 0.171 -0.024 1.000

DUR -0.154 -0.270 -0.229 0.076 -0.279 -0.131 -0.375 -0.380 -0.028 -0.271 -0.124 0.075 0.050 1.000

DPER 0.092 -0.106 0.001 0.015 -0.377 -0.001 0.054 0.044 -0.090 -0.113 -0.101 0.321 -0.067 0.194 1.000

DMS -0.098 0.037 0.095 -0.092 0.099 -0.027 0.228 0.173 0.136 0.074 -0.097 0.065 -0.065 -0.070 0.085 1.000


Common Sample Correlation Matrix on 1st Differenced Data

Annexure 1 (Contd.)

DALLORDS DBVIR DCP DCPI DDY DER DGDP DGDPPC DIPI DIR11AM DMPI DMSCI DNX DUR DPER DMS

DALLORDS 1.000

DBVIR 0.020 1.000

DCP -0.056 0.005 1.000

DCPI 0.021 -0.158 -0.113 1.000

DDY -0.440 0.175 0.139 -0.015 1.000

DER -0.046 -0.049 -0.043 -0.067 -0.164 1.000

DGDP -0.077 0.136 0.235 0.010 0.252 -0.021 1.000

DGDPPC -0.076 0.129 0.233 0.024 0.263 -0.028 0.995 1.000

DIPI -0.144 0.071 0.128 -0.053 0.305 0.012 0.475 0.484 1.000

DIR11AM 0.029 0.996 -0.009 -0.157 0.181 -0.054 0.127 0.120 0.048 1.000

DMPI 0.044 0.225 0.233 -0.083 0.331 -0.222 -0.123 -0.109 0.195 0.200 1.000

DMSCI 0.527 -0.022 -0.152 -0.066 -0.826 0.199 -0.057 -0.065 -0.152 -0.043 -0.084 1.000

DNX 0.097 -0.138 -0.192 -0.002 0.081 -0.115 -0.123 -0.128 -0.070 -0.118 0.206 -0.037 1.000

DUR -0.160 -0.363 -0.229 0.075 -0.248 -0.092 -0.371 -0.372 -0.045 -0.366 -0.141 0.050 0.027 1.000

DPER 0.107 -0.108 0.001 0.014 -0.367 0.008 0.054 0.048 -0.113 -0.119 -0.099 0.307 -0.085 0.175 1.000

DMS 0.027 0.180 0.095 -0.147 0.188 -0.001 0.389 0.345 0.173 0.161 -0.052 -0.049 -0.184 -0.237 0.028 1.000

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