University of Nigeria Research Publications
NWEZE, Augustine Uchechukwu
Aut
hor
PG/Ph.D/96/19170
Title
The Relation Of The Structure Of Equity Share Prices To
Historical, Expectational And Industrial Variables:
The Nigerian Experience
Facu
lty
BUSINESS ADMINISTRATION
Dep
artm
ent
BANKING AND FINANCE
Dat
e
2002
Sign
atur
e
UNIVERSITY OF NIGERIA ENUGU CAMPUS
SCHOOL OF POSTGRADUATE' STUDIES ' FACULTY OF BUSINESS ADMINISTRATION
DEPARTMENT OF BANKING AND FINANCE
THE RELATION OF THE STRUCTURE OF EQUITY SHARE.PRICES TO
- HISTORICAL, EXPECTATIONALeAND INDUSTRIAL VARIABLES:
THE NIGERIAN EXPERIENCE
BY
NWEZE, AUGUSTINE UCHECHUKWU PG/Ph.D./96/1,9170
BEING A THESIS SUBMITTED IN P.4RTIAL FUI,FILLMENT OF THE REQUIREMENT FOR THE AWARD
OF DOCTOR OF PHILOSOPHY (PH.D.) DEGREE IN BANKING AND FINANCE
ABSTRACT
From an extensive review of literature, it was established that a gap exists in
knowledge as regards the variables that influence equity share price behaviour in
Nigeria. Accordingly, the study is an investigation of the structure of equity prices in
the Nigerian capital market. It attempts to determine the variables that influence the
structure of share prices in Nigeria grouping them into three namely: historical,
expectational and industrial. An economic model is formulated to capture the
historical, expectational and industrial variables with a view to determining the
behaviour of share prices in the Nigerian Capital Market.
The approach adopted was hypothesis testing, rather than the phenomenological time
series analysis, because the researcher wanted to understand the economic
interrelationships which generate price volatility. Accordingly, a total of fifty (50)
publicly quoted companies (out of 102 as at 1990) drawn from fourteen industrial
classifications were studied. Companies were selected based on the active nature of
the shares for a decade from 1990. Data were generated from the Daily Official lists
(Equities) of the Nigerian Stock Exchange.as well as from audited accounts of the
companies. These data were analysed using various statistical tools and hypothesis
test statistics.
The major findings of the research include:
Out of 50 companies covered by the study, only 12 (24%) exhibited randomness in
their share price movements. The balance of 38 (76%) did not exhibit randomness.
The finding therefore is that the structure of share prices in the Nigerian Capital
Market is NOT purely random.
Of the 50 companies studied, only 7 (14%) showed a negative value of linear co-
efficient of correlation between dividends paid per share and prices per share. Also,
only 4 (8%) exhibited negative relationship between earnings per share and price per
share. Therefore, both dividends and earnings positively and robustly influence share
prices.
The average of the. co-efficient of regression for earnings is marginally higher than
that of dividends. Therefore, earnings have more impact on share prices than
dividends.
The result of a ranked correlation coefficient of change in share prices and volume of
business turnover is 0.66. Therefore, there exists a positive relationship between the
size of a company and the fluctuations in its share price.
Of the 50 companies studied, 7 (14%) had negative gradients and 43 (86%) had
positive gradients when dividends were regressed against prices. For earnings against
prices, the percentages were 8% (negative) and 92% (positive). Therefore, the higher
the expectation, the higher the share prices.
An econometric model of share price behaviour was formulated. Therefore, share
prices can be reasonably predicted.
DEDICATION
To my wife, Ngozichukwuka
and our children,
Odirachukwunma, Chukwuezukalum, Nmesonmachukwu, Ajuluchukwu and
Ebubechukwu.
CERTIFICATION
This is to certify that this Thesis written by NWEZE, AUGUSTINE
UCHECHIJKWU, PGlPh.D.196119 170, presented to the Department of Banking and
Finance, University of Nigeria, Enugu Campus is original and has not been admitted
for the award of any degree or diploma either in this or any other tertiary institution.
This is to certify that this research work by NWEZE, AUGUSTINE UCHECHUKWU, PG/Ph.D./96/19170, presented to the Department of Banking and Finance, University of Nigeria, Enugu Campus, was submitted in partial fulfillment for the award of Ph.D. in Banking and Finance.
.................................. DR. A. M. 0 . ANYAFO MNIM
Supervisor
L[u fL
ACKNOWLEDGEMENT
"Great discoveries and improvements invariably involve the cooperation of many minds. I may be given credit for having blazed the trail but when I look at the subsequent developments, I feel the credit is due to others rather than to myself' Alexander Graham Bell
Like a wife, who in Ibo culture remains "our wife" during the day but becomes
strictly "my wife" at night, this thesis is actually "our work" except that the final
degree, pleasing God Almighty, shall be awarded to me. Accordingly, I hereby
acknowledge the wonderful assistance I received from the following persons anlor
institutions
First and foremost, the author is eternally indebted to God ALMIGHTY for pushing
him up this far considering the fact that just some years ago, the possibility of
acquiring even a post primary school education was like an illusion. Yes, with God
nothing is impossible (LK. 1:37). Next, the author is ever grateful to Dr. A. M. 0.
ANYAFO, his Head of Department (as at the time of admission into the programme),
his supervisor and teacher of many years, whose wealth of knowledge, skill and
experience in financial matters in general and capital market in particular have been
brought to bear upon this work. He was so generous with his resources - time and
material that he could have ordinarily qualified as a co-author. Thank you, Dr.
Anyafo. The late Head of Department, ONWURA ANEKE whose dexterity with
statistical tools was properly harnessed in developing the model. Of particular
mention is the "distributed lag model". In short, he has succeeded in luring the
researcher into Econometrics. Then, the current Head of Department, Dr. C. U. Uche,
FCA. He was so concerned with the work that even while in the United Kingdom in
April 2001, he had time to source for very current and relevant materials for the
researcher from the British Library of Political and Economic Science. Dr. Uche, I
can not thank you enough for this your singular gesture. Head of Department, thank
you for your magnanimity.
Very deeply acknowledged are the constructive criticisms received from the DVC
(Deputy Vice Chancellor) University of Nigeria, Enugu Campus, Prof. Francis 0.
Okafor. Prof. you are indeed a guru in financial matters.
vii
In one batch, let me acknowledge the useful contributions of the following faculty
members during my Thesis Proposal defence. That was on 4Ih April 2001. They
include: Dr. A. M. 0 . Anyafo (Chairman); Mrs. Nnolim, the then Dean of the Faculty;
Prof. Ike ~ w o s u , the Dean of the Faculty; Onwura Aneke, the Acting Head of Dept;
Prof. E. Imaga, Dr. C. U. Uche; Dr. B E. Chikeleze; Dr. J. E. Ezeanyagu; Mrs. N. J.
Modebe, Mrs. E. N. Ogamba; Messrs E. U. Okoro-Okoro, D. N. Asomugha, C. E.
Ojiakor, and C. E. Nwude; Chief P. C. Unamka; the representative of the School of
Postgraduate Studies (SPGS) and the Secretary Christy E. Amaefule and other
lecturers in the Faculty. Also my co-doctoral colleagues who witnessed the Proposal
Defence, viz. Mr. Innocent Ike Okpe, who served as my Secretary, and Messrs
Godwin U. Owoh, FCA; G. A. Anugwom; M. C. Okeke and A. 0. Nwadibu and my
cousins, Sir Joseph Ohe Onyeke and Hon. Ifeanyi Ugwuanyi for their support in all its
ramifications.
Also worthy of mention are the following persons, namely, my mentor, Prof. Julius
Onuorah Onah, the then Vice Chancellor of (ESUT) Enugu State University of
Science and Technology (my employer) for providing me with the enabling
environment to pursue this programme; Prof. S. C. Chukwu, the then Dean, Faculty of
Management Sciences and the current Vice Chancellor of ESUT for taking me into
confidence when I was the Acting Head, Department of Accountancy, ESUT(161h
May 1996 through 1 3 ' ~ September 1999); Dr. Festus C. Eze, the then Registrar,
ESUT and Chief B. N. Uzoigwe, the current Registrar, ESUT for their brotherly
concern in the researcher; Messrs T. Ugwueze and F. Ugwuogo of SPGS, UNN;
Messrs Asadu and L. Odo of the Dean's office; and Messrs C. J. 0 . Ebirim (HOD),
Clifford Obiyo Ofurum and Kelvin Chinedu Okpani of the Department of
Accounting, University of Port Harcourt, who as a bye product of my external
moderation (January 3 - 6, 2001) assisted me to build up my data bank from the
Nigerian Stock Exchange, Port Harcourt. Also, all the members of staff of libraries
the researcher consulted particularly at the University of Nigeria, Nsukka and Enugu
Campuses, British Council, Enugu Central Bank of Nigeria.
Mention must be made of the staff of DCSI Computer Services where the initial
works were typed. Particularly, Nze Kris Nwatu, Njoku Sunday U. Ogechukwu Ani,
Nkechi Ikechukwu, and Mr. & Mrs. Jon Nwakalo (the proprietors). Also
... \'I11
., . ackno\&dged are the staff of REMS Consult (Mrs. G. E. Ugnuonah and MISS Oluchi
Edeh in particular) for assisting the researcher in data analysis and repackaging the
nark.
And to the members of my immediate family for'their wonderful contributions: nly
. btep father, Hon.'Justice Dr. Centus Chima Nweze whose superlative perLormances both at the Bar (then) and now at the Bench have always been sources of inspiration
to me. "My Lord", I think, "the wall of poverty has been broken and dismantlecl". m mother, Lady Elizabeth Nweze (Mrs.) who sacrificed "eve~ything" to keep me afloat:
mJr younger brother Anthony - the ball is n o h in ,your court: and my father. Pa John
U. Eze (of blessed memory). Also. I thank my wife, Bernadine and our children,
-Alexius, Kizito, Cordis-Mariae, Jose-Mariae and JohnBosco for the time I could have
spent with them instead.
In a very special way7 let me acknowledge the two disciplined proressional bodies I
belong to, viz.:
. - C Institute of Chartered and Accountants of Nigeria (ICAN) ,and
P Chartered Institute of Taxation of Nigeria (CITN)
for the immeasurable value added to me and the highly rewarding esposure through
the Mandatory Continuing Professional Education (MCPE)
And finally. to the University of Nigeria. for making me a tr~ple "Llon" and as a
corollary, adequately restoring the "dignity of man" in me.
-TO GOD BE THE GLORY - AMEN. AUSTIN NWEZE
2002
Title Page: . . . . . . Abstract . ...
. . . . . . Dedication ... Certification
Acknowledgement
Table of Content
List of Appendices
... List of Tables
TABLE OF CONTENTS
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
.... .... ... a , .
... 9 . . 1 . .
... ... 11
... ... iv
... ... V
... .... vi
... ... ix
... ... xii
... .... xvi
CHAPTER ONE: INTRODUCTION
... Background of the Study: ...
... Statement of the Problem: ...
... Objectives of the Research: ...
... Research Questions: ... ...
... Research Hypotheses: ...
... Significance of the Study: ... Scope of the Study and its Delimitation:
... Limitation of the Study ...
... Definition of Terns: ... ...
... ... ... References ...
CHAPTER TWO: LITERATURE REVIEW AND THEORETICAL CONSIDERATION
... ... ... Background to Share Price Behaviour 19
... ... ... Theories of Share Price Behaviour ... 20
... Variables that influence the Structure of Share Prices 41
... ... ... Factors affecting the Share Prices ...... 46 The Place of Dividends and Retained Earnings
... ... ... ... ... ... on Share Prices 49 The Impact of Company Size and Industrial
... ... ... Classification on Share Prices ... 54
... ... ... Expectation and Share Prices ... 55
... ... ... ... Share Valuation Models ... 56
... ... ... ... ... References .. ... 75 CHAPTER THREE
RESEARCH DESIGN AND METHODOLOGY
... ... ... ... Research Design: .. . ... 83 ... ... Sources of Primary and Secondary: ... ... 83 ... ... ... Methods of Data Collection: ... ... 85
Validation and Reliability of Data Collection ... ... ... ... ... Instrument . . . . . . ... 85
... .... ... ... ... Population and Sample: 86
... ... ... ... Methods of Data Analysis: ... 92
... ... ... ... ... The Model: ... ... 92
... ... ... . . . Statement of Hypotheses: ... 93 ... ... ... Hypotheses Test Statistic: ... . , . 94
... ... ... ... References ... ... ... 98
CHAPTER FOUR PRESENTATION AND ANALYSIS OF DATA
Analysis of the Structure of Share Prices in the Nigerian ... ... ... 9 . . ... Capital Market ... 100
Determination of the Variables that influence the ... ... ... Structure of Share Prices in Nigeria ... 103
An Estimation of the Influence of Dividends. Retained Earnings and Quality of Returns Retained Earnings
... ... ... ... on Share Prices ... 104 Analysis of the Impact of Company Size and Industrial
... ... ... ... Classification on Share Prices ... 108
Determination of the Influence of Expectational ... ... Variables on Share Price Behaviour ... ... 114
Construction of a Model of Share Price Behaviour which takes into Account Historical. Expectational
... ... ... ... and Industrial Variables ... 114
... ... . a . ... ... Testing of Hypotheses ... 120 ... ... ... ... ... References ... ... 128
CHAPTER FIVE SUMMARY OF FINDINGS. CONCLUSIONS AND RECOMMENDATIONS
5.1 Summary of Findings . . . . . . . . . . . . . . . ... 129 5.2 Conclusions: ... ... ... ... ... ... ... 132
5.3 Recommendations ... ... ... ... ... ... 134 5.4 Suggested Future Research Path ... ... ... ... 135 Bibliography ... ... ... ... ... ... ... ... 136
xii
LIST OF APPENDICES
111.
IV
v VI
VII
VIII
IX
X
XI
XI1
XI11
XVI
xv XVI
XVII
XVIII
XIX
XXI
XXII
XXIII
Nigerian Stock Exchange Daily Official List (Equities) as at January 2, 1990 . . . . . . . . . . . . . . . Nigerian Stock Exchange Daily Official List (Equities) as at 3 1 " December, 1999 . . . . . . . . . . . . Proportional Distribution of the Sample Size.. . . . . History of Dividends paid per share, from 1990 - 1999
History of Earnings paid per share, from 1990 - 1999
History of Price - Earnings Ratio from 1990 - 1999 . . . History of Share Prices from 1990 - 1999 . . . ... Weekly Share Price Changes, January - December 1990
Weekly Share Price Changes, January - December 1991
Weekly Share Price Changes, January - December 1992
Weekly Share Price Changes, January - December 1993
Weekly Share Price Changes, January - December 1994
Weekly Share Price Changes, January - December 1995
Weekly Share Price Changes, January - December 1996
Weekly Share Price Changes, January - December 1997
Weekly Share Price Changes, January - December 1998
Weekly Share Price Changes, January - December 1999
Annual number of runs for Dunlop, Intra-Motors, R. T. Briscoe, First Bank and Owena Bank . ..
Annual number of runs for United Bank, Union Bank, Golden Guinea, Guiness Breweries and NBL.. . . . .
Annual number of runs for Nigerian Ropes, Nigerian Wires, WAPCO, Berger Paints and CAP Plc. . . Annual number of runs for International Paints, K. Challarams, Morison, NCR and Thomas Wyatt . . . Annual number of runs for Wiggins Teape, CFAP, John Holt, Lever Brothers and PZ . . . . . . . . . Annual number of runs for SCOA, UACN, UTC, Cappa D7Alberto and Dumez . . . . . . ... . . . Annual number of runs for G.Cappa, Julnas Berger, 7-Up, Cadbury and NBC Plc. . . . . . . . . . . . . . Annual number of runs for NTC, ALUMACO, Nigerian Enamel Ware, Vita Foam and Vono . . .
XXVI
XXVII
XXVIII
XXX
XXXI
XXXII
XXXIII
XXXIV
XXXV
XXXVI
XXXVII
XXXVIII
... X l l l
Annual number of runs for BAICO, Niger Insurance, AP, Agip and Mobil ... ... ... ... ... ..203 Annual Number of runs for National Oil, Texaco, Total, Afprint and UNTL ... , . . ... ... ..204 Annual number of "Minuses", "Zeros" and "Pluses" for Dunlop, Intra Motors, R. T. Briscoe, First Bank
... and Owena Bank ... ... ... ... .. .205 Annual number of "Minuses", "Zeros" and "Pluses" for UBA, Union Bank, Golden Guinea, Guiness Breweries and Nigerian Breweries .... .... ... ... .. .206 Annual number of "Minuses", "Zeros" and "Pluses" for Nigerian Rope, Nigerian Wires, WAPCO, Berger Paints and CAP Plc ... ... ... ... ... .. .207 Annual number of "Minuses", "Zeros" and "Pluses" for International Paints, K. Challaram, Morison, NCR and Thomas Wyatt.. . ... ... . . . ... ... .. .208 Annual number of "Minuses", "Zeros" and "Pluses" for Wiggins Teape, CFAO, John Holt, Lever Brothers and PZ ..209
Annual number of "Minuses", "Zeros" and "Pluses" for SCOA, UACN, UTC, Cappa D'Alberto and Dumez ... 210 Annual number of "Minuses", "Zeros" and "Pluses" for G. Cappa, Julius Berger, 7-Up, Cadbury and NBC Plc . ..211 Annual number of "Minuses", "Zeros" and "Pluses" for NTC, ALUMACO, Nigerian Enamel Wares, Vita Foam and Vono ... ... ... ... ... ... 212
Annual number of "Minuses", "Zeros" and "Pluses" for BAICO, Niger Insurance, AP, Agip and Mobil ... ... 213
Annual number of "Minuses", "Zeros" and "Pluses" for National Oil, Texaco, Total, Afprint and UNTL ... .. .214
Regression analysis - Dividends against prices for Dunlop, Intra Motors and R. T. Briscoe, First Bank, Owena Bank, and UBA ... ... ... ... ... ... ... 215
Regression analysis - Dividends against prices for Union Bank, Golden Guinea, Guiness Nigeria Plc, Nigerian Breweries, Nigerian Ropes and Nigerian Wires .. .2 16
Regression analysis - Dividends against prices for WAPCO, Berger Paints, CAP Plc., International Paints, K. Challaram and Morison ... ... ... ... ... ... ... 217
xiv
XLI
XLII
XLIII
XLIV
XLV
XLVI
XLVII
XLVIII
XLIX
LI
LII
LIII
LIV
Regression analysis - Dividends against prices for NCR, Thomas Wyatt, WTN, CFAO, John Holt and Lever Brothers .. ... ... ... ... 218
Regression analysis - Dividends against prices for PZ, SCOA, UAC, UTC, Cappa D'Alberto and Dumez ... 219
Regression analysis - Dividends against prices respectively for G. Cappa, Julius Berger, 7-Up, Cadbury, NBC Plc.
... and NTC ... ... ... . . . ... 220
Regression analysis - Dividends against prices for ALUMACO, Nigerian Enamel Wares, Vita Foam, Vono, BAICO, and Nigerian Insurance . . . . . . . . . 22 1
Regression analysis - Dividends against prices for AP, Agip, Mobil, National Oil, Texaco and Total.. . ... 222
Regression analysis - Dividends against prices for Afprints and UNTL ... ... ... ... ... 223
Regression analysis - Earnings against prices for Dunlop, Intra Motors and R. T. Briscoe, First Bank, Owena Bank, and UBA ... ... ... ... ... 224
Regression analysis - Earnings against prices for Union Bank, Golden Guinea, Guiness Nigeria Plc, Nigerian Breweries, Nigerian Ropes and Nigerian Wires ... 225
Regression analysis - Earnings against prices for WAPCO, Berger Paints, CAP Plc., International Paints, K. Challaram and Morison ... ... ... ... 226
Regression analysis - Earnings against prices for NCR, Thomas Wyatt, WTN, CFAO, John Holt and Lever Brothers ... ... ... ... ... ... 227
Regression analysis - Earnings against prices for PZ, SCOA, UAC, UTC, Cappa D'Alberto and Dumez ... 228
Regression analysis - Earnings against prices respectively for G. Cappa, Julius Berger, 7-Up, Cadbury, NBC Plc. and NTC ... ... ... ... ... 229
Regression analysis - Earnings against prices for ALUMACO, Nigerian Enamel Wares, Vita Foam, Vono, BAICO, and Nigerian Insurance ... ... 230
Regression analysis - Earnings against prices for AP,
Agip, Mobil, National Oil, Texaco and Total.. . ... 231
LV
LVI
LVII
LVIII
LIX
LXI
LXII
LXIII
LXIV
LXV
LXVI
Regression analysis - Earnings against prices for ... ... Afprints and UNTL ... ... 232
Yearly structure of share prices 1990 - 1999 for Dunlop, Intra Motos, R. T. Briscoe, FBN, Owena Bank, UBA, UBN and Golden Guinea ... ... ... ... 233
Yearly structure of share prices, 1990 - 1999, for Guiness, Nigerian Breweries, Nigerian Ropes, Nigerian Wires, WAPCO, Berger Paints, CAP Plc and International Paints 234
Yearly structure of share prices, 1990 - 1999 for K. Challarams, Morison, NCR, Thomas Wyatt, WTN, CFAO, John Holt and Lever Brothers ... ... 235
Yearly structure of share prices, 1990 - 1999 for PZ, SCOA, UACN, UTC, Cappa D'Alberto, Dumez, G. Cappa and Julius Berger ... ... ... ... 236
Yearly structure of share prices, 1990 - 1999 for 7-Up, Cadbury, NBC, NTC, ALUMACO, Nigerian Enamel Ware, Vita Foam and Vono ... . . . ... ... 237
Yearly structure of share prices, 1990 - 1999 for BAICO, Niger Insurance, AP, Agip, Mobil, National Oil, Texaco and Total ... ... ... ... ... 238
Yearly structure of share prices, 1990 - 1999 for Afprint and UNTL.. . . . . ... ... ... ... 239
Calculation of the Critical Values of the Model ... 240
Calculation of the Regression Coefficients ... ... 286
Table of Expectational Variables ... ... ... 326
Table of Values ... ... ... ... ... 328
xvi
LIST OF TABLES
... ... Companies under study ... ... ... ... 9
... ... Industries under study ... ... ... ... 11 ... ... Results from Cross-sectional Estimates ... ... 60
... Distribution of quoted companies as at January 2. 1990 ... 87 Distribution of quoted companies as at December 3 1. 1999 .. ... 88 Proportional distribution of sample size ... ... ... ... 91 Comparative analysis of observed and expected
... number of runs ... ... ... ... ... 101 Regression results: Dividends (xl) against prices . . . . . . ... ... 104
Regression results: Earnings (x2) against prices . . . ... ... 106 Percentage changes in share prices with 1990 as the base year ... ... ... ... ... ... ... ... 108 Industrial average gain (loss) in share prices between the base year 1990 and 1999 ... ... ... ... ... ... 110
... Business turnover of quoted companies by sector ... ... 111
Rank Correlation of Price Indices and Sectorial Business Turnover ... ... ... ... ... ... ... 112
CHAPTER ONE
INTRODUCTION
"It is dlSJicult to say what is impossible, for the dream of yesterday is the hope of today crnd the reality of tomorrow".-
Robert H. Coddard
1.1 Background of Study
Of all economic time series, according to Roberts (1959), the history of security
prices, both individual and aggregate, has probably been the most widely and
intensively studied. While financial analysts agree that underlying economic factors
and relationships are important, many also believe that the history of the market itself
contains "patterns", that give clues to the future, if only these patterns can be properly
understood. The questions often asked are:
Can share prices be predicted? Are share prices determined by their intrinsic values?
Are share price movement random in nature - as exemplified by the movement of a typical drunk or mad man in the centre of a large field who is equally likely to move
in any one direction as the other? In Nigeria, previous researchers, for example
(Ezirim, 1999), (Ayadi, 1984) favoured the random work hypothesis. Yet, for Bower
and Bower (1969: 349) it is quite reasonable and quite acceptable among both
academic researchers, for example, Gordon and Shapiro (1956), Walter (1956),
Modigliani and Miller (1961), Malkiel (1963) and professional security analysts
namely Molodovsky (1959; 1960, 1965), and Bauman (1965) to view the price of a
share of stock as the present values of future dividends expected from the share
discounted at a rate which reflects the risk borne by an owner of the share.
From the foregoing discussion, one can infer and at a reasonable confidence level too
that any study on share price behaviour particularly in a developing economy like
Nigeria is a worth while venture. Yet, only few academics to the best of the
researcher's knowledge namely Samuels and Yacout (1981), Anyafo (1982),
Osisioma (1983), Ayadi (1984) and Osaze (1997) have done scientific studies on
share price behaviour. Even then, each of them just concluded by confirming the
Random walk hypothesis. None tried to explain in details the underlying forces
2
responsible for the randomness by identifying the various variables influencing share
price behaviour. What is this randomness all about?
Also, Malliaris and Stein (1999: 1614) pointedly posited that:
The issue of where price variance comes from involves the concept of randomness. The concept of randomness is profound. By randomness one means that knowing all past events is no help in predicting the future. The rolling of dice or tossing of a coin are taken as the prime examples. But the world is determined by physical laws. IJ'we knew the velocity and spin of the thrown dice or coin, we would be able to predict the out come of a toss.
Ekeland (1988) as quoted by Malliaris and Stein (1999) put the matter lucidly:
Randomness appears because the available information, though accurate, is incomplete. IJ' determinism means that the past determines the future, it can only be a proper& of reality as a whole, of the total cosmos. As soon as one isolates, from this global reali& a sequence of observations to be described and analyzed, one runs the risk of finding only randomness in that particular projection of the deterministic whole.
Central to this thesis, therefore, is an attempt to "know the velocity and spin of the
thrown dice or coin to enable us predict the outcome of a toss" by relating the
structure of share prices to historical, expectational and industrial variables.
The historical variables include past growth rates of various financial variables.
(a) End-of-year market price per share
(b) Total dividends paid per share (adjusted to number of shares
outstanding at year end).
(c) Reported earnings per share (adjusted to exclude nonrecurring items).
(d) Average dividend pay out ratio.
As for the expectational variables, Malkiel and Cragg (1970) submitted that the most
important of the expectational variables employed are forecasts of short-term and
long-term eamings growth, estimates of the "normal earning power" of each company
and estimates of the instability of eamings stream. Yet, according to Malkiel and
Cragg (1970), the critical dependence of share prices on expectational variables has
proved to be a major obstacle for empirical investigators.
3
Industrial variables are mainly qualitative variables (such as extent of Government
regulation, extent of susceptibility to changes in fiscal and monetary polices) that
collectively influence the perception of investors as well as potential investors.
Consequently, this thesis is focused on the relation of historical, expectational and
industrial variables to share price behaviour. This by the researcher's thinking is very
apt since for many years economists have emphasized the importance of expectations
in a variety of problems. Yet one area in which expectations are highly important is
the valuation of the common stock of a corporation (Cragg and Malkiel, 1968). After
all, according to Williams (1938), the price of a share, is-or should be determined
primarily by investor's current expectations about the future values of variables that
measure the relevant aspects of corporation's performance and profitability,
particularly the anticipated growth rate of earnings per share. From the foregoing,
one can infer that without the proper expectational variables, it will be impossible to
untangle the true influence of the many factors influencing the structure of price-
earnings multiples (Malkiel and Cragg 1970).
1.2 Statement of the Problems:
Investment, in common stock (ordinary shares) is, in essence, a present sacrifice in
exchange for expected future benefits. Since the present is known, this investment
becomes a certain sacrifice for an uncertain risky benefit (Pinches and Kinney,
1997: 1 19) And yet, philosophically speaking, today is the tomorrow we were afraid of
yesterday. By deduction, therefore, there exists a very strong link between yesterday,
today and tomorrow. The researcher posits: can we carry this link into the structure of
share price behaviour? Put differently, can we use our knowledge of share price
behaviour yesterday to determine its price today and as a corollary estimate or predict
the share price tomorrow? There are principally three schools of thought.
In the words of Ayadi (1984), two distinct and opposing views have been presented
explaining the behaviour of stock (share) prices. The first school of thought is the
random walk school. This school holds the view that stock market prices follow an
unpredictable path and hence the knowledge of past price movements cannot be used
to predict future prices. On the other hand, the technical analysis school holds the
4
view that stock price follow a predictable path. To predict future prices would only
involve a knowledge of past price movements. In addition, Okafor (1983) and
Pilbeam (1995) recognized the third school of thought - the fundamentalist theory.
This theory holds that it is the prospective changes in economic fundamentals that
move the share prices.
If investors and researchers accept the random walk hypothesis, then most of all the
beautiful share valuation models would have been rendered "impotent" since the
future value cannot be predicted with an iota of mathematical precision. On the other
hand, if the technical analysis is accepted then it follows that the price of a share can
be predicted far into the future even when the going concern concept has become
inapplicable. As for the fundamentalists, how do we qualify prospective changes in
economic fundamentals that move the share prices? Contributing towards the
resolution of the conflicting positions, Okafor (1983: 186) observed:
The randonz walk hypothesis simply states that the current market price of any security ftilly reflects the iizformation content of its historical sequence of prices. Coirsequently, knowledge of the historical prices of a security and/or detailed analysis based on such knowledge would not enlzaizce the quality of irrvestnient decisions. This assertion is a complete negation of the methods nrzd spirit of tecliiiicnl analysis. If' the past seqtieizce of prices cnrrnot be used to predict jiiture trends, then there would be iro value in charting or in all other procedzwes adopted by technicians.
Reasoning by deduction therefore, Okafor (1983) was in sympathy with the
technicians.
Yet others have a contrary view. Hence, Samuels and Yacout (l981), Anyafo (1982),
Osisioma (1983), and Ayadi (1984) have been able to validate the random walk
hypothesis. However, NONE of them tried to study the underlying variables that
influence share price behaviour. Each of them just accepted the prices as given by the
Nigeria Stock Exchange. No wonder Ekechi (2002) pointedly observed that the quest
for standardized model of security price behaviour in the United States securities
market has not proven conclusive. For Nigerian market, work has begun and further
available data are very fragmentary. It therefore means that there is a gap in
knowledge of share price behaviour in the Nigerian context.
5
The current thinking, however is that since the world is governed by physical laws,
researchers must NOT just stop at validating the random walk hypothesis. Efforts
must be made to predict future share prices. Malliaris and Stein (1999: 1614) while
giving thelrolling of dice or tossing of a coin as the prime examples of randomness
submitted that if we knew the velocity and spin of the thrown dice or coin, we would
be able to predict the outcome of a toss. "Rolling of dice or tossing of a coin" can be
likened to a decision to invest in a share in a capital market. The "velocity of the
thrown dice or coin" is comparable to a share price movement. The "outcome of a
toss" may be considered akin to the outcome of a stock-market investment.
Borrowing the phrase by Malliaris and Stein, we may view the focus of this research
as an attempt to "know the velocity and spin of the thrown dice or coin to enable us
predict the outcome of a toss". This is the task the researcher attempted to accomplish
by relating the structure of share prices to historical, expectational and industrial
variables. This led to the development of an econometric model that expresses the
share price-earnings ratio as a function of these variables.
1.3 Objectives of the Study:
In the words of Bell (1974), one of the most important problems confronting stock
market analysts is the valuation of stocks at any point in time. In fact, the name of the
game is to determine whether stocks are selling above or below their real worth.
Presumably, "real worth" is synonymous with economic equilibrium based upon the
correct" model of common stock valuation. Deviations from equilubrium will
eventually be corrected by the market mechanism and this is the stuff of which profits
and losses are made.
The objectives of this research are:
(i) To find out the structure of share prices in the Nigerian Capital Market;
(ii) To determine the variables that influence the structure of share prices
in Nigeria.
(iii) To estimate the influence of dividends, retained earnings and quality of
the returns streams on share prices.
G
(iv) To determine the impact of company size and industrial classifications
on share prices.
(v) To estimate the influence of expectational variables viz, forecasts of
short-term and long-term earnings growth; and forecasts of the normal
earnings streams on share price behaviour.
(vi) To construct a model of share price behaviour which takes into account
historical, expectational and industrial variables.
(vii) To make recommendations based on the findings of the research which
shall hopefully improve the efficiency of the Nigerian Capital Market.
1.4 Research Questions
This research answered the following questions:
What is the structure of share prices in the Nigerian Capital Market?
What are the variables that influence the structure of share prices in
Nigeria?
Can the influence of dividends, retained earnings and quality of returns
streams on share prices be estimated?
Do company size and industrial classifications impact positively or
negatively on share prices?
Do expectational variables such as force\casts of short term and long-
term earnings growth; forecast of the normal earnings power of each
company and forecast of the instability of the earning stream influence
share price behaviour?
Can a model be constructed to incorporate historical expectational and
industrial variables with respect to the structure of share prices?
1.5 Research Hypothesis:
The hypotheses tested by this study were derived from the three schools of thought
regarding the share price behaviour. These are:
(i) The fundamentalist theory.
(ii) The technical analysis and
(iii) The Random Walk Hypothesis (RWH).
Before presenting the hypotheses to be tested, we summarize the key issues advanced
by each school of thought. The fundamentalist theory holds that it is the prospective
changes in economic fundamentals that move share prices (Pilbeam, 1995).
Technical analysis includes many different approaches requiring a good deal of
subjective judgment in application (Roberts, 1959). In part, these approaches are
purely empirical; in part, they are based on analogy with physical processes, such as
tides and waves. Yet, according to Dockery and Vergari (1997: 629), considerable
attention has been paid to testing the theory of random walk which claims that for
stock returns to follow a random walk process, successive stock returns must be
identically distributed and independent so that the correlation between one period's
return and the immediate following period is zero. This position was taken by Fama
(1965), D'Ambrosio (1980), Cooper (1983), Shiller and Perron (1985); Lo and
Mackinlay (1988) and Um~tia (1995). Malliaris and Stein (1999: 1605) points out
that the random walk hypothesis assumes that price volatility is exogenous and
unexplained. Randomness means that a knowledge of the past cannot help to predict
the future. Put differently, randomness is a situation where the future appears to be
independent of the past and is unpredicatable, whereas determinism is a situation
where the future is predictable once we know the initial conditions and the dynamic
equations.
Majority of the previous researchers have been able to validate the random walk
hypothesis. However, the current thinking is that the random walk hypothesis can
only be accepted with reservations because of the practical implications. If this
hypothesis is correct, it implies that no trading rule based on past prices will earn an
economic profit (Hagerman and Richmond 1973). Also if this hypothesis is correct,
it implies that most of our beautiful share price valuation models would have been
rendered impotent.
Therefore, this thesis attempted to establish that share price movements are not purely
random since share prices can be predicted by an optimum mix of historical,
8
eipectational and industrial variables. Accordingly, the following hypotheses were
tested.
Hypothesis One:
The structure of share prices is not purely random.
Hypothesis Two:
Dividends, and retained earnings do not influence share prices
Hypothesis Three:
Dividend payments in Nigeria do not have more influence on share prices than
earnings.
Hypothesis Four:
Industry character and company size do not impact positively on share prices.
Hypothesis Five:
Share prices are not critically dependent on expectational valuables.
1.6 Significance of the Study:
In most economies of the world, the financial system will be incomplete without a
capital market. The primary role of a capital market is the provision of medium to
long-term finance for development. A capital market can be subdivided into a
primary capital market and a secondary capital market. In the former, new securities
are traded while in the latter only existing securities are traded. A stock exchange is a
good example of a secondary market.
According to Anyanwu (1 998), our empirical results suggest that the Nigerian stock
market development is positively and robustly associated with long-run economic
growth. Any wonder therefore that Ayadi (1984) opined that the importance of a
stock market in the economy can not be over emphasized. It helps to allocate and
reallocate the ownership of the economy's capital resources. Against the above
background and bearing in mind that Nigeria is currently privatizing and
9
commercializing a reasonable chunk of her public enterprises, the researcher hereby
asserts that the study came at the most appropriate time.
On the understanding that the outcome of this research will ultimately be published,
the significance of the study include the following:
It would create awareness among the investing public, capital market
operators as well as academics about share price behaviour.
Factors affecting share prices would be highlighted
Potential investors would get to know that investing in financial assets
is a good form of investment comparable with investing in real assets.
As a guide, a model was developed expressing share prices as a
function of historical, expectational and industrial variables.
1.7 Scope of the Study and its Delimitation:
This study covered a period of one decade, 1990-1 999.
Fifty (50) publicly quoted companies (as at 1990) were studied-from fourteen
industrial classifications. This led us to a stratum of fourteen layers viz:
Table 1.1: Companies Under Study
CODE NO.
(A)
0 1
02
03
(B)
04
05
06
INDUSTRIAL CLASSIFICATION
AUTOMOBILE AND TYRE
DUNLOP NIGERIA PLC
INTRA MOTORS PLC
R. T. BRISCOE PLC
BANKING
FIRST BANK OF NIGERIA PLC
OWENA BANK PLC
UNITED BANK FOR AFRICA PLC
07
( c )
08
09
10
UNION BANK OF NIGERIA PLC
BREWERIES
GOLDEN GUINEA PLC
GUlNESS NIGERIA PLC
NIGERIAN BREWERIES PLC
I
(H) I CONGLOMERATES I
22 1 CFAO NIGERIA PLC
I 25 1 PZ INDUSTRIES PLC
L
23
24
JOHN HOLT PLC
LEVER BROTHERS PLC
I 3 1 1 G. CAPPA PLC
26
27
28
(1)
29
30
SCOA NIGERIA PLC
UACN PLC
UTC PLC
CONSTRUCTION
CAPPA & D'ALBERTO PLC
DUMEZ NIG. PLC
I 39 I VITA FOAM NIGERIA PLC
L
32
(J)
33
34
35
3 6
(K)
37
38
I 40 I VONO PRODUCTS PLC
JULIUS BERGER PLC
FOOD AND BEVERAGES
7-UP BOTTLING CO. PLC
CADBURY NIGERIA PLC
NIGERIAN BOTTLING CO. PLC
NIGERIAN TOBACCO CO. PLC
INDUSTRlALlDOMESTlC PRODUCTS
ALUMACO PLC
NIGERIAN ENAMEL WARE PLC
- --- INSURANCE
-- . - - - - - - - -. PETROLEUM
--
AFRICAN PETROLEUM PLC ---- - -.
N i l P (NIGERIA) P1.C -.
MOI31L NIGERIA PLC
Source: Nigerian Stock Escl~ange Dailj. Ollicial I..isl.
Monday (first \\.orking da! of the week), prices arid price changes were obtninetl fro111
1990 to 1999. The above data amounted to about 26.000 prices ruid itbout 26.000
price changes. Even though this is not the entire population. the re?earclier is
confident that the data are sufficiently represetitative and as a corollary they \\~oultl
not differ materially had the entire population been studied As quoted in Osisior~ln
(1984). the sampling procedure involves the selection and use of a sn~all part of a
large group to make conclusiot\s or forecasts about tlie entit-e population. 'The theon.
is based on the assunlptinn that the elm-acleristics of' an ntleqirate sample are
representati\:e of the \\.hole ol'\\.hich it is a par[. "
In sum, therefore. the scope nf h e research \ifas delimited xq rollo\\s.
Scope: F i b (50) publicl!. quoted companies r b m i , ~ ~ ,fi.orn jimrreen i~thrstricrl
groupings, nnnwiy:
, Table 1.20: Ind~~stries Under. Study
( (a) 1 Auto Mobile a~itl Tyre
. ( (Q I Commercial
(i) 1 Construction 1 1
2
3
7
I
(g)
(h)
I I
Computer and Office Equipment
Conglomerates
(k)
(1)
4 (j)
(m)
(n)
Period: The period covered by the study is from 1990 to 1999 (inclusive).
Food and Beverages
Industrial/Domestic Products
Insurance
Total
Activity level: Weekly (as against daily) prices and price changes were collated and
4
2
Petroleum
Textiles
5 0
empirically investigated.
6
2
1.8 Limitation of Study
The study was limited by the following factors:
1. The prices as published by the Nigerian Stock Exchange were used.
Therefore, any inherent inaccuracy on the listed prices may have affected
the work. The much the researcher could do was to avoid transmission
errors.
ii . Only weekly (Mondays) share prices were used in the study. Assuming,
therefore, that Monday share prices had a definite pattern or sequence,
then, that would have affected the results.
iii. Non-application of electronic pricing method. This affected the speed and
accuracy of generating data. Elsewhere, electronic pricing method, has
facilitated studies on share prices at hourly intervals.
iv. Infrequent Trading. Nigerian Stock Market is shallow in relation to the
major developed country markets in terms of transaction volume and the
number of listed securities. Even among the listed securities, a large
majority is infrequently traded. This infrequent trading augments the risk
borne by the Market marker and thus contributes to higher bid-ask spreads.
Further, the lack of information in the market could result in negative
oscillates in prices about the intrinsic value for thinly traded stocks.
v. Inefficiency of Information. Market inefficiency arises from obstacles to
the diffusion of information and may construe itself in serially correlated
return. The knowledgeability to a new relevant information may result in
low cost of speculation and the return to show positive serial correlations.
The obstacle of information diffusion depends positively on the real cost
of capital to speculators and negatively to the speed of diffusion of
information. It is not surprising to mention that the cost of capital for
speculators is higher in Nigeria because of suppression and market
imperfections (larger inconsistency between the lending and borrowing
rates, higher transaction costs, etc.) and rules of insider trading are lacking
and if it exist, it is unenforceable. Moreso, firms in Nigeria disclose less
information with a relatively longer time lag, which defeat the speed of
information diffusion, (Ekechi, 2002: 49).
1.9 Definition of Terms:
Historical Variables
These variables are discernable from the annual reports and accounts. They include:
(a) End-of-year market price per share.
(b) Total dividends paid per share (adjusted to number of shares
outstanding at year end).
(c) Reported earnings per share (adjusted to exclude non-recurring items).
(d) Average dividend pay-out ratio.
Expectatioizal Variables
These variables are futuristic in nature. They include:
(a) Forecasts of short-term and long-term earnings growth
(b) Estimates of the normal earning power" of each company and
(c) Estimates of the instability of the earnings stream.
Industrial, Variables:
These variables are related to the nature of the business and hence the perception of
the investing public and government.
They include;
(a) Extent of government regulation
(b) Vulnerability to government action
(c) Management resilience
Stochastic Trend
Informally, a stochastic trend is defined as the part of time series which is expected to
persist into the indefinite future, yet it is not predictable from the past.
Formally, a series is said to contain a stochastic trend "if it is non-stationary in levels
even after removing a linear trend, whereas the process is stationary in differences"
(Bernard and Durlauf, 199 1).
Bayesian Error
The Bayesian error is the difference between the true or full information expectation
of the fundamentals and the subjective expectation.
Autocorrelation (Serial Correlation)
It is possible to attempt to correlate values of a variable X at certain time with
corresponding values of x at earlier times. Such correlation is often called
autocorrelation (Spiegel and Stephens, 1999: 3 16).
Also, according to Horngren, Forster and Datar (1997: 362), serial correlation (also
called autocorrelation) means that there is a systematic pattern in the sequence of
residuals such that the residual in observation n conveys information about the
residuals in observation ntl, nt2 and so on. In time series data, inflation is a common
cause of autocorrelation because it causes costs (and hence residuals) to be related
over time.
~utocorrelation can also occur in cross-sectional data.
Residuals
The vertic,al deviation of the observed value Y from the regression line, estimate y is
called the residual term, disturbance term or error term,
Homoscedasticity (constant variance)
The assumption of constant variance implies that the residual terms are unaffected by
the level of the independent variables. The assumption also implies that there is a
uniform scatter or dispersion of the data points about the regression line. The scatter
diagram is the easiest way to check for constant variance. Constant variance is also
known as homoscedasticity.
Heteroscedasticity
In a regression analysis, once the scatter is not uniform around the line of best fit, that
is, once there is a violation of the assumption of constant variance, we refer to the
situation as heteroscedasticity.
Heteroscedasticity does not affect the accuracy of the regression estimates a and b. It
does however, reduce the reliability of the estimates of the standard errors and thus
affects the precision with which inferences can be drawn.
Multicollinearity
Multicollinearity (also known as simultaneous relationship) exists when two or more
independent variables are highly correlated with each other. Generally, users of
regression analysis believe that a coefficient of correlation between independent
variables greater than 0.70 indicates multicollinearity. Multicollinearity increases the
standard errors of the coefficients of the individual variables. The result is that there
is greater uncertainty about the underlying value of the coefficients of the individual
independent variables. That is, variables that are economically and statistically
significant will appear insignificant (Homgren et al, 1997: 366).
REFERENCES
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Anyanwu, John (1998). "Stock Market Development And Nigeria's Economic Growth", Nigerian Financial Review. Vol. 17, No. 2, pp. 6-14.
Ayadi, Olusegun (1984). "The Random Walk Hypothesis and the Behaviour of share prices in Nigeria," The Nigerian Journal of Economic and Social Studies. Vol. XXVI, NO 1, Pp. 57-7 1.
Bauman, Scott (1965). "The Investment Value of Common Stock Earnings and Dividends", Financial Analysts Journal. Vol. XXI, No. 6, pp. 98-104.
Bell, Fredrick (1974). "The Relation of the Structure of Common Stock Prices to Historical, Expectational and industrial variables", Journal of Finance. Vol. XXTX, NO. 1, pp. 187-1 97.
Bernard, A. B. and Durbauf, S. N. (1991). "Convergence of International Out Movements," Working Paper. No. 3717, National Bureau of Economic Research.
Bower, Richard and Dorothy H Bower (1969). "Risk" and the valuation of Common Stock, "Journal of Political Economy. Vol. 77, May-June, pp. 349-362.
Cooper, J. C. (1983). "The Korean Stock Exchange: a qualitative and quantitative assessment," The Investment Analysts. Vol. 70, pp. 5 - 12.
Cragg, J. G , and Malkiel, B. G. (1968). "The Consensus and Accuracy of some Predictions of the Growth of Corporate Earnings", Journal of Finance. Vol. XXIII, NO. 1, pp. 67-84.
D'Ambrosio, C. (1980). "Random Walk and the Stock Exchange of Singapore," Financial Review. pp. 1 - 12.
Dockery, E. and Vergari, F. (1997). "Testing the Random Walk Hypothesis: Evidence for the Budapest Stock Exchange," Applied Economic Letters. Vol. 4, No. 10, pp. 627 - 629.
Ekechi, Augustine 0 . (2002). "The Behaviour of Stock Prices on the Nigerian Stock Exchange: Further Evidence," FBN Quarterly Review. ISSN: 11 15 - 633, March, pp. 44 - 59.
Ekeland, 0 . (1988), "Calcul, I'mprevu" and "Au hazard", Translated.
Ezirim, Chinedu (1999). "Intermediation Functions of the Financial superstructure and Economic Growth: Evidence from Nigeria." Ph.D Thesis, Department of Economics, University of Port Harcourt - Nigeria.
Fama, Eugene (1 965). "The Behaviour of Stock Market Prices," Journal of Business Finance. Vol. .37, pp. 934 - 1003.
Gordon, M. J. and Shapiro Eli (1956). "Capital Equipment Analysis: The Required Rate of Profit," Management Science 111.-No. 2, pp. 102-1 10.
Hagerman, Robert and Richmond Richard (1973). "Random Walks, Martingales and the OTC," Journal of Finance. Vol. XXVIII, No. 4, Pp. 897 - 909.
Horngren, C. T, Foster, G. and Datar, S. M. (1997). Cost Accounting: A Managerial Emphasis. 9th ed. (New Delhi: Prentice Hall Inc.).
Lo, A. and Mackinlay A. C. (1988). "Stock Market Prices Do Not Follow Random Walks: Evidence from a simple Specification test," Review of Financial Studies. Vol. 1, Pp. 41 - 66.
Malkiel, Burton and John G. Cragg (1970). "Expectations and the Structure of Share Prices", The American Economic Review. Vol. 60, pp. 601-61 7.
Malkiel, Burton G. (1963). "Equity Yields Growth and the Structure of Share Prices", American Economic Review. Vol. LIII, No. 5, pp. 1004-103 1.
Malliaris, A. G. and Stein J. L. (1999). "Methodological Issues in Asset Pricing: Random Walk or Chaotic Dynamics", Journal of Banking and Finance. Vol. 23, pp. 1605 - 1635.
Modigliani, Franco and Miller Merton (1961). "Dividend Policy, Growth and the Valuation of Shares," Journal of Business. Vol. XXXIV, No. 4, pp. 41 1-433.
Modovsky, Nicholas (1959). "Valuation of Common Stocks", Financial Analysts Journal. Vol. XV, No. 1, pp. 23.
Okafor, Francis (1983). Investment Decisions: Evaluation of Securities. (London, Cassel).
Osisioma, Benjamin (1 983). "Capital Market Efficiency in Nigeria; A test of Random Walk Hypothesis", PhD. Thesis. Department of Banking and Finance, University of Nigeria.
Pilbeam Keith (1 995). "The Profitability of Trading in the Foreign Exchange Market: Chartists, Fundamentalists and Simpletons", Oxford Economic Papers. Vol. 47, NO. 3, pp. 437 - 52.
Pinches, George and Kinney William (1971). "The measurement of volatility of common stock prices", Journal of Finance. Vol. LXXVI, pp. 119-125.
Roberts, Harry (1959). "Stock-market "Patterns" and financial analysis: Methodological suggestions." Journal of Finance Vol. XIV, No. 1, pp. 1-1 0.
Samuels, J. M. and Yacout (1981). "Stock Exchanges in Developing Countries", Savings and Development. No. 4, pp. 217-230.
18
Schwarts, Robert and Edward Altrnan (1973). "Vollatility Behaviour of Industrial Stock Price Indices", Journal of Finance. Vol. XXVIII, No. 4, pp. 957-971.
Shiller, R. J. and Perron, P. (1985). "Testing the Random Walk Hypothesis Power versus Frequency Observations," Economic Letters. 18, pp. 381 - 386.
Spiegel, M. R. and Stephens, L. J. (1999). Schaum's Outlines: Statistics. 3rd ed. (New York: McGraw-Hill).
Urmtia J. L. (1995), "Test of Random Walk and Market Efficiency for Latin American Emerging Equity Markets," Journal of Financial Research. Vol. 18, pp. 299 - 309.
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Williams, J. B. (1938). The Theory of Investment Value. (Cambridge Harvard University Press).
CHAPTER TWO
LITERATURE REVIEW AND THEORETICAL CONSIDERATIONS
"Nothing gives an author so much pleasure as to find his works respectjblly quoted by other learned authors"
- Benjamin Franklin
"When you take stufli-om one writer, it's plagiarism; but when you take it froin many writers, it's research"
- Wilson Mizner 2.1 Background to Share Price Behaviour
Over the years, it has been a daunting task for both financial analysts and academic
researchers to come out with generally acceptable models, expressing the prices of
shares in terms of all the possible factors influencing prices. While some hold the
view that the prices of shares are dependent on earnings, others assert that share prices
are dependent on dividends. Yet, others are of the view that besides dividends or
earnings, share prices can be related to historical, expectational and industrial
variables.
In the same vein, it is equally arguable whether share price behaviours can be
predicted with any mathematical precision or that the share prices move in a random
nature - as exemplified by the movement of a typical drunk or mad man in the center
of a large field who is equally likely to move in any one direction as the other (Ezirim,
1999), (Ayadi 1984). (As exhibited in Appendices VIII - XVI).
How can one describe the structure of share prices?
Since share prices are given over a period of time, it becomes very necessary to study
the pattern exhibited. After all, according to Harry (1959), of all economic time
series, the history of security prices both individual and aggregate, has probably been
most widely and intensively studied.
The truth is that there is a pattern. But the question is: What is the nature of the
pattern?
Other follow - up questions are:
Is it a mathematical function?
If yes, what type of function?
(a) Linear?
Price
The pattern can not be linear since linearity implies proportionate change in price as
time changes or as the number of share increases.
(b) Quadratic?
(c) Inverse?
(d) Hyperbolic?
(e) Asymptotic?
(f) Normal?
(g) Leptokurtic?
Broadly speaking, there are four theories about the share price behaviour. These are
the fundamentalist; the technical analysis, random walk and the efficient market
theory.
2.2 Theories of Share Price Behaviour
The Fundamentalist Theory:
According to Pilbeam (1995), the fundamentalist theory holds that it is the
prospective changes in economic fundamentals that move the share prices.
The fundamental approach assumes that:
I. Every security has an intrinsic value.
. * 11. The intrinsic value of every security is reflected by its market price.
iii. Basic economic facts about a firm determine the intrinsic value of
securities issued by it. (Okafor 1983: 12 1).
Continuing, Okafor (1983), opined that without agreeing on specifics, fundamentalists
use three basic performance indicators in predicting intrinsic values. These are the
earnings record, some index of risk and a time - value conversion rate for funds.
Also, according to Okafor (1983), specifically four major forms of analyses are
conducted by the fundamentalists: They are:
(a) Analysis of general economic conditions.
(b) Industry conditions
(c) Company analysis and
(d) Financial analysis.
(a) Economic Conditions
These include the following macro-economic indices:
(i) Gross National Product (GNP). This represents the total value of
goods and services produced in an economy over a fiscal period plus
net overseas transfers.
(ii) Index of production
(iii) The general price index
(iv) External trade indices
(v) Index of retail sales
(b) Industry Factor
Industry factors affect corporate activities in general. A company's profit
performance, in particular, is very much influenced by industry factors.
(c) Company Analysis
Company analysis focuses on four major issues: the nature of a company's products,
its competitive position in the industry, characteristics of the company's factor market
and the issue of management.
22
(a) Financial Performance: Fundamental analysis relies ultimately on an evaluation of the past, the present and
the expected financial performance. Corporate financial performance is summarized
in various financial statements, namely:
>i The Profit and Loss Account
P The Value Added Statement
P The Cash flow Statement
P The Five Year Summary
The Clzartists/Teclznical Analysts Theory:
The major tenents of the method, according to Reilly and Norton (1999: 490) and
Okafor (1983: 167) could be summarized as follows:
(a) The value (price) of securities is determined by forces of demand and
supply.
(b) Demand and supply forces are influenced by both rational and
irrational factors.
(c) Movements in stock prices tend to follow identifiable systematic, self
sustaining and recurring trends.
(d) Market trends constitute solid foundations on which profitable trading
rules can be erected.
Of all the tools used in technical analysis, the Dow Theory is the oldest and perhaps
the most popular. In essence, the Theory is a mechanical device which uses previous
highpoints and low points in a stock market index as indicators for predicting trends
and reversal in the market.
According to Charles Dow, the originator of the theory, all price actions on the
exchange comprise three contemporaneous movements:-
(a) The primary movement
(b) The secondary movement and
(c) The minor movements (Okafor, 1983 : 169).
23
According to Roberts (1959), a common and convenient name for analysis of stock
market pattern is technical analysis. Perhaps, no one in the financial world
completely ignores technical analysis - indeed, its terminology is ingrained in market
reporting-and some rely intensively on it. Technical analysis includes many different
approaches, most requiring a good deal of subjective judgment in application. In part
these approaches are purely empirical; in part, they are based on analogy with
physical process, such as tides and waves.
In the light of this intense patterns and of the publicity given to statistics in recent
years, it seems curious that there has not been widespread recognition among
financial analysts that the pattern of technical analysis may be little, if anything, more
than a statistical artifact.
As an alternative to the technical analysis, Sidney (1 961) argued that the random walk
and martingale efficient market theories of security price behaviour imply that stock
market trading rules based solely on the past price series can not earn profits greater
than those generated by a simple buy-and-hold policy. Technical analysts or chartists,
however, have insisted that this evidence does not imply their methods are invalid and
have argued that the dependences upon which their rules are based are much too
subtle to be captured by simple statistical tests (Jenson and Benington, 1970).
#,,mpu,m4 mi+ u*.wr The Random Walk Hypothesis (R WH): r -- * 7 *Y - & The basic hypothesis of the random walk theory is that a particular price series behave
as a simple stochastic process. Successive price changes are independent random
variables implying that the past history of a series generates no information predicting
future price changes. Continuing, Malliaris and Stein (1999: 1633), noted that the
random walk hypothesis assumes that price volatility is exogenous and unexplained.
Randomness means that the knowledge of the past cannot help to predict the future.
We accept the view that randomness appears because information is incomplete.
Ekeland (1988), quoted in Malliaris and Stein (1999: 1625) put the matter lucidly:
Randomness appears because the available information though accurate is incomplete. vdeterminisnt means that the past determines the ft~ture it car? only be a property of reality as a whole of the total cosmos. As soon as orie isolates from this global reality a sequence of observations to be described and artalysed one runs the risk offitding
only randomness in that particular projection of' the deterministic whole.
In his contribution, Debby et. al. (2000) submitted that the random walk hypothesis
has three components: that the price increments are independent, symmetric about
zero, and identical
As discussed by Ayadi (1984: 60-61), the original and analytical empirical work on
the random walk theory was done by Bachelier (1900). He was the first to point out
that security prices and prices of other speculative commodities follow a random
walk. His study was not recognized until Working (1934) confirmed the same result.
Kendall (1953) examined the behaviour of weekly changes in 19 indices of British
Industrial share price, spot prices for cotton in New York and wheat in Chicago. He
found successive arithmetic differences in British stock price averages to be largely
uncorrelated. Other studies in support of the random walk theory include Roberts
(1 959), Osborne (1 959), Moore (1 962), Morgenstern and Granger (1 963), Fama
(1965), Samuelson (1965), Mandelbrot (1967), Black and Scholes (1972), and more
recently in Nigeria, Samuels and Yacout (1 98 I), Anyafo (1 982), Osisioma (1 983),
and Okafor (1 983).
Specifically, Osborne (1959) found a very high degree of conformity between the
movements of stock prices and the law governing Brownian Motion. Moore (1962)
examined the weekly changes of 29 randomly selected New York Stock Exchange
(NYSE) stocks from 1951 to 1958 and found an average serial correlation coefficient
of - 0.06. With the aid of a statistical technique called spectral analysis, Morgenstem
and Granger (1963) found no substantial relationship between one period's security
returns and the returns in prior periods.
Of more direct relevance to this study was the study by Samuels and Yacout in 1981
on the Nigerian data. They tested for several correlations in the weekly prices of
shares in 21 companies quoted on the Nigerian Stock Exchange between July 1977
and July 1979. They found a trace of dependence with a one-week lag in only seven
shares and a two-week lag in four shares. The absolute mean serial correlation
coefficient was 0.146 with one-week lag and 0.086 with a two-week lag. The results
of these tests support the theoiy that prices follow a random walk.
– here are, however, conflicting evidence against the random walk theory. Alexander
(1961, 1964), applied the filter test to the daily closing prices of two stock market
indices: Dow Jones and Standard and Poor. Taken altogether, the evidence runs
strongly against the random walk hypothesis. Levy (1 966, 1967, 1968) posed a more
serious challenge to the random walk hypothesis. He used various technical portfolio
upgrading. On the basis of his evidence, Levy concluded that "the theory of random
walks has been refuted". Other scholars who contradicted the random walk
hypothesis include Shiskin (1968), Cheng and Deets (1971), and Kemp and Reid
(1 972).
In the words of Dockery and Vergari (1997: 627), considerable attention has been
paid to testing the theory of random walk which claims that for stock returns to follow
a random walk process, successive stock returns must be identically distributed and
independent so that the correlation between one period's return and the immediate
following period is zero; see for examples, Fama (1965), D'Ambrosio (1980) Cooper
(1983), Shiller and Peiron (1985), Lo and Mackinlay (1988) and Urmtia (1995).
Kendall, as quoted in Roberts (1959), found that changes in security prices behaved
nearly as if they had been generated by a suitably designed roulette wheel for which
each outcome was statistically independent of past history and for which relative
frequencies were reasonably stable through time. Also, Leuthold (1977) opined that a
notable and provocative development in the recent literature has been the application
of the theory of random walks to the analysis of price behaviour in the stock and
commodity futures market.
Testing for Randomness:
Currently, there are three principal methods for testing for randomness in share price
behaviour. These methods are:
(i) The sign tests, examples of which are: Wald - Wolfowitz test, number-
of-runs test, and the estimation test
(ii) The variance ratio approach used by Dockery and Vergari (1997) and
Lo and Machinlay (1988)
(iii) The unit-root test as propounded by Dickey-Fuller (1979).
A brief discussion of the various methods now follows:
i. The sign tests:
Anyafo (1982), Osisioma (1983) and Ayadi (1984) while testing the random walk
hypothesis in the Nigerian Capital Market applied extensively the sign test.
Two major types of non-parametric and one parametric statistical tests are employed:
(1) Wald - Wolfowitz test
(2) The number-of-runs test, and
(3) The estimation test
These are used to test the null hypothesis that successive stock price changes are
independent and hence unpredictable. The alternative hypothesis will then be that
successive price changes are dependent and predictable.
That is:
Ho: Successive stock price changes are independent and unpredictable.
HI : Successive stock price changes are dependent and predictable.
The procedures are summarized below:
To apply this test, one should classify the sequences of price changes into three, an
increase in price over the preceding price, a decrease, and a situation of no change. A
price rise is denoted by a plus (+), a decrease, a minus (-), and a situation of no
change, a zero (0) sign. That is, given a series of prices (Pt) for consecutive Mondays
(t = 1,2,3, n) the price change X, = P, - P,-, are calculated producing a series of share
price changes. If X is positive, it is denoted by '+', if negative '-' and if zero, it is denoted by '0'. See Appendices VIII to XVII.
These series of sequences and reversals are arranged in order of occurrence and the
number of runs observed for each share determined. A "run" is a consecutive
sequence of the same symbol, for example the sequence ++ --- 000 + - + has six runs.
The Wald-Wolfowitz run test takes cognizance of sequences and reversals only, that
is, "pluses" and "minuses" but not zeros. For a large number of observations as in
27
this case'the sampling distribution of the expected runs is approximately normally
distributed. The mean of such a distribution represents the expected number of runs.
The standard deviation of the sampling distribution is also calculated. Both the
observed and the mean number of runs are compared by calculating the standard
score. The values of the standard normal variable under the null hypothesis are
approximately normally distributed with zero mean and unit variance. The
significance of any observed value of Z computed may be determined by reference to
the normal curve table. The normal curve table gives the one-tailed probability
associated with the occurrence under Ho of values as extreme as an observed Z. The
decision rule is that Ho be accepted if the computed Z is significantly higher than or
equal to the standard Z score obtained from Table at the level of significance chosen.
In other words, if successive price changes are independent one would expect a Z
score of at least 2.33 at one percent critical region.
The estimation theory is applied on any two independent random samples. It is used
to determine whether or not the two samples are from the same population. If they
are, it means that samples are dependent otheiwise, they are independent. The null
hypothesis is that there is no difference between the population means or that two
samples means may be regarded as means of samples drawn from the same
population. In this case, the two random samples are the expected and observed runs.
The difference between the two are finally converted to a critical value. If the
difference between them is significant, we will reject the null hypothesis.
The sampling distribution under the number-of-runs test (with zero) is again
approximately normal. The only difference between this test and the Wald-Wolfowitz
is that, while the Wald-Wolfowitz test neglects zero observation, this test recognizes
them. If the observations are independent the Z score obtained will not be significant.
If it is significant, then the null hypothesis that the observations are independent will
be rejected. That is, for successive price changes to be independent, the Z score so
obtained should fall within the range of - 1.96 and + 1.96 at a level of significance of 5 percent.
Application of the Wald- Wolfowitz Test
According to Murray and Larry (1999: 405), the expression for determining the mean,
standard deviation and the Z-score for purpose of applying the Wald-Wolfowitz test
are given below:
2n1 n;? (2111 n2 - n~ - n2) Standard deviation =
(nl + n212 (n, + n2 - 1)
Observed - Mean Runs 2 score = Standard Deviation
Where
nl = number of "pluses"
n2 = number of "minuses"
Application of Num ber-ofRuns Test
Formula
Mean = n(n+l) - ni2
Standard deviation
Z - score
Cni2 - n (n-r + % ) - - Cni2 + n(n+l) - 2nCni3 - n3 1
Where
ni - - nl, n2, no
BI = number of "pluses"
n2 - - number of "minuses"
no - - number of "zeros" - r , - observed number of runs.
(ii) The Variance Ratio Approach:
While testing the random walk hypothesis for the Budapest Stock Exchange (in
Hungary), which is relatively underdeveloped in comparison with the stock markets in
other mature industrialized economies, Dockery and Vergari (1997) applied the
variance test ratio. The methodology is summarized hereunder:
To test the hypothesis of random walk for the BSE (Budapest Stock Exchaige) we apply the variance ratio approach of Lo and Mackinlay (1988). According to this approach, if the r~atural logarithm of a time series Pt is a pure randoin walk, the variance of its k-dfference grows proportionally with the difference k.
The variance ratio, VR(k), is defined as:
where o2 (k) is the unbiased estimator of l/k of the variance of the kth difference of
the log stock price (P, - PI-,) and o2 (1) is an unbiased estimator of the variance of the
log of stock price Pt - P,-1 The whole purpose of estimating a variance ratio is to
estimate the magnitude of the random walk. Thus, if stock prices follow a random
walk process, the variance of k-period returns should then equal k times the variance
of one period returns and, in turn, the variance ratio should be equal to unity.
Lo and Mackinlay (1988) show that the estimators we have described may be
calculated as follows:
02 (k) = 1 C (P, - P,-k - kPl2 m t=k
Where
and 1 - n k
o2 (k) = (nk- 1) C (Pt -PI-, - p) 1= I
in which I
and where Po and P,k are the first and last observations of time series. The first test
statistics, z(k), is developed under the maintained hypothesis of homoscedasticity,
while the asymptotic variance of the variance ratio under homoscedasticity, 0 ( k ) is:
The standard Z test statistic under the assumption of homoscedasticity, Z(k), is then:
Where a indicates that the distribution equivalence is asymptotic. It is well known + that the variance of most stock returns are conditionally heteroscedastic with regard to
time; see, inter a h , Hamao et al, (1993), Theodossiou and Lee (1993) and Koutmous
et al. (1994). To overcome this problem, Lo and Mackinlay (1988) advanced the
heteroscedasticity-consistent asymptotic variance estimator of the variance-ratio, 0"
(0):
+*(k) = C- 6 (j) j= l k
in which k- I P - P - ) ( j - Pt-j-I - ~1)' Fj+ I
The variance ratio statistic can be standardized asymptotically to a standard normal
test-statistic, Z* (k) which, as refined by Lo and Mackinlay (1988), is: f 3
Where 0* (k) is the asymptotic variance of the variance ratio consistent with the null
hypothesis.
3 1
Also, Urrutia (1992: 458) noted that the traditional Dickey and Fuller (1979, 1981)
tests of random walk are based on regression models. They assume that the
regression disturbances are independent identical distribution (i.i.d). Gaussian
random variables. Such tests have relatively low power. Lo and Mackinlay (1988)
have developed a test of random walk that is robust with respect to heteroscedasticity
and non-normal disturbances. It is known as the variance ratio test. Indeed, Lo and
Mackinlay (1989) show that the variance ratio statistic compares favourably to the
Dickey and Fuller procedures in tests of random walk behaviour. Lo and Mackinlay
(1988) and Poterba and Summers (1988) have used the variance ratio test to partially
reject the random walk behaviour in stock markets. Cochrane (1988) employed the
variance ratio approach to reject the random walk hypothesis for the GNP.
The intuition behind the variance ratio test is the following: if the natural logarithm
of a time series denoted Y, is a pure random walk of the form:
then, the variance of its k-differences grows linearly with the difference k (that is, the
variance increases proportionally with time). For example, the variance of annually
sampled series must be 12 times as large as the variance of a monthly sampled series.
Thus, if the series follows a random walk, it must be the case that the variance of k-
differences is k times the variance of the first differences:
Therefore, a test of random walk is equivalent to testing the null hypothesis that ( l k )
times the variance of the k-differences over the variance of the first difference, that is,
the variance ratio, is equal to one:
Ho: (1 k) var (Y, - Y,.k)/var(Yt - Y,,) = 1.
In order to simplifjr the notation let us define:
2 ( l k ) var (Y, - Y,-k) = o k
thus, our null hypothesis of random walk becomes:
(iii) The Unit Root Test:
According to Goerlich (1992: 151), it is widely known that the Dickey-Fuller (1979)
t-statistic obtained from a regression with a linear trend is asymptotically normal if
the Data Generating Process (DGP) is a random walk with a linear trend.
Unit root testing has become very popular in macroeconomic modelling. It is
nowadays entirely common to approach applied work running some Dickey-Fuller
(1979) tests to determine if a given series should be differenced to achieve
stationarity. Given the data generating process (DGP) y, = pyt-l + E 1 - iid (0, 02), and the null hypothesis of interest Ho : p = 1 against HI : p < 1, Dickey and Fuller (1 979)
suggest the use of the t-statistic on n = p - 1 in the regression model Ayt = nyt-l + E to test Ho : p = 1, with rejection if the t-statistic is sufficiently negative. Since the
distribution of this t-statistic under the null is non-standard, Dickey and Fuller (1979)
tabulate it by numerical methods; see Fuller (1 976, p. 373).
The above procedure is only valid when the mean of the series is zero. However,
most macroeconomic time series exhibit growth so the appropriate alternative to a
difference stationary model is a trend stationary model in which the series is
stationary around a deterministic trend [(Nelson and Plosser (1982)l. Accordingly,
unit root test usually begins with regressions of the form Ayt = a + b.t + ny,-l + E 1 where under the alternative the growth in y, is picked up by the linear trend. Dickey
and Fuller (1 979) also tabulate by simulation the distribution of the t-statistic on n in
this case under the null of a unit root.
It should be noted, however, that under the null hypothesis, Ho : p = 1, the trend term
should be zero, so in this case the growth in the series is picked up by a non-zero drift.
When this is not the case, i.e. the DGP is Y, = a + P.t + y1.1 + E 1 , P + 0; then the t- statistics in the above regression model are all asymptotically normal. Consequently
some authors, Dolado and Jenkinson (1987), recommend that when a linear trend is
significant under the null of a unit root the normal tables should be used instead of the
Dickey - Fuller tables, as use of the later will result in too few rejections of the unit
root hypothesis asymptotically.
33
~ h ; same phenomenon appears when the form of the DGP is yt = a + yt-1 + E 1, a # 0.
The t-statistics of the regression model Ay, = a + 7cyt-l + E 1 are all asymptotically normal [West (1988), Sims, Stock and Watson (1990)], so the recommendation is that
the normal tables should be used also in this situation. Hylleberg and Mizon (1989)
and Schmidt (1990) have noted that, in finite samples, the drift has to be quite large
for the normality result to apply, so in practice the Dickey-Fuller tables may give a
better approximation to the true distribution.
This note investigates the small sample distribution of the Dickey-Fuller (1979) t-
statistic on when both, DGP and regression model, contain a linear trend, to see under
what conditions the normality result can be considered as a good approximation.
The sinall distribution
Consider the DGP for t = 0, 1,2, .. .., T,
With P # 0 and E 1 - iid (0, 02). Integrating (1) with respect to t, it is seen that: Yt = yo + a . t + p.t (t + 1)/2 + C
j= 1
Which shows that y, consists of a quadratic trend comp,onent,
p.t2/2, and a stochastic trend component, St = C € 1 , j= 1
Given that the sample variability of the quadratic trend is of order 0p(P) and the
sample variability of the stochastic trend is of order. 0p(T?) the quadratic term will
dominate the integrated process asymptotically; in fact it is not difficult to show that
Therefore if the unit root process contains a linear trend its variability will be
dominated by a quadratic trend. This can be seen more clearly if we compare the
series z, = pt2/2
where Ef , 7 = p2/4) T (T + 1) (2T + 1) ( 3 ~ ~ + 3~ - l)/3O with S, ( = I z ! J
the z, component dominates the St component.
Asymptotically yt behaves like a deterministic trend and the asymptotic normality of
the ordinary least squares (OLS) estimators in the regression.
follows from the general results in Sims, Stock and Watson (1 990) since no regressor
in (3) is dominated by stochastic trends.
Also, Zhu (1 998) while testing the random walk of stock prices by adducing evidence
fiom a panel of G-7 countries (the US, Japan, Germany, the UK, Canada, Italy and
France) noted that:
To overcome the weak power problem of the conventional unit-root tests such as Dickey Fuller (1979) and Philips and Perron (1988) tests, Leviiz and Lin (1992, 1993) proposed a method to test for unit root in panel data. They show that the power of the tests improves substantially when the tests are applied to a panel data even when the cross-section of the data is small and the length of the sample is shot. SpeciJically, consider a cross section of N units observed quarterly over T quarters. We assume that the variable Zit follows an AR(1) process in t and has a unit specijk eflect 771 for each unit I, or
Levin and Lin (1 979, 1993) showed that the asymptotic distribution of the t-statistic
for p follows the non-central normal distribution and the statistic is not affected by the
inclusion of a constant intercept, a time trend, or time specific fixed effects in the
model. In a more general case where the error terms are serially correlated, they
suggested that we can adopt a method similar to the Augmented Dickey-Fuller tests to
include lagged differenced dependent variable in the regression equation. The
distribution of the test statistic under the null will be independent of the serial
correlation in the error terms after the serial correlation has been corrected for.
To implement the tests, we can estimate the following equal test for unit root in the
series:
where i = l1, 2, ..., N, t = 1, 2 ,... T vt the time specific fixed effect. We can estimate
the above model by the usual method of panel data transformation, which subtracts
the individual mean and time-specific mean from all variables involve
