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Validation of Asset Pricing Models during Crisis and
Non-Crisis Periods: A Comparative Analysis of Stock
Markets in Sri Lanka and in the US
By
D. A. I. Dayaratne
Registration No 2006/MPhil-PhD/EC/11
Date of Submission 21st December 2010
Thesis submitted for the Degree of Doctor of Philosophy to
The Department of Economics
University of Colombo
ii
Declaration
I certify that this thesis does not incorporate without acknowledgement any material
submitted for a degree or a diploma in any University. Also to the best of my
knowledge and belief it does not contain any material previously published or written
by another person except where due reference is made in the text.
Candidate: D. A. I. Dayaratne
Signature: Date: 21/12/2010
Approved for submission
Thesis Supervisor: Dr. Rajith W. D. Lakshman
Signature: Date: 21/12/2010
iii
Dedicated to
My Mother and Father
iv
Acknowledgements
Many people have helped and supported me throughout the preparation period of this
thesis. I would like to acknowledge my thesis supervisor, Dr. Rajith Lakshman, for
his guidance, valuable comments and his untiring effort to bring this thesis to the
current stage of completion. I also acknowledge with gratitude, Prof. Sunil
Chandrasiri, the coordinator of the program, for his invaluable advice, help and
guidance. I am also grateful to Prof. Athula Ranasinghe, the head of the Department
of Economics and Prof. Indralal De Silva, the Dean of the Faculty of Arts, University
of Colombo. Dr. Chandana Aluthge who helped me at the initial stage of the thesis
and all the staff members of the Department of Economics are also acknowledged. I
am also grateful to the National Centre for Advanced Studies in Humanities & Social
Sciences (NCAS) for funding my research.
My gratitude also goes to Dr. P. D. Nimal, University of Sri Jayewardenepura, who
provided valuable comments on my work in progress, particularly at the stage of
formation of variables of the research. The help of the director of Capitalstrust (pvt)
Ltd. Mr. Sarath Rajapaksa, to obtain weekly data series of CSE was also critical for
this work. My gratitude goes to Mr. K. M. M. I. Ratnayeka, who is currently reading
for his PhD at Utara University, for guiding me to many useful web resources. The
technical support of Ms. Wasana Chandraseekara and Ms. Dulani Rodrigo, both of
whom are graduates of the School of Computing, University of Colombo, is also
acknowledged. Mr. Malik Carder and Mr. Suanath in the Securities and Exchange
Commission (SEC) who helped me to gather information on Sri Lankan market must
be acknowledged. The valuable comments given by Prof. K. B. Palipane, Dean
Faculty of Applied Sciences of the Sabaragamuwa University of Sri Lanka and Dr.
Dissa Bandara, the Director Financial Services Academy during the several
discussions had with them must also be appreciated.
Last but not least I would like to thank my daughters, Sandamini and Dulmini, and
my wife Nirmala for enduring much hardship providing me the fullest support during
the long period of my study.
v
List of Abbreviations
AMEX American Stock Exchange
APT Arbitrage Pricing Theory
ASPI All Share Price Index
BE/ME Book-To Market Ratio
CAPM Capital Asset Pricing Model
CPI Consumer Price Index
CRSP Center for Research in Security Prices
CSE Colombo Stock Exchange
DCF Direct Cash Flow
E/P Earning Price Ratio
FF3F Fama and French Three Factor Model
GDP Gross Domestic Product
HML High minus Low
ICAPM Inter temporal Capital Asset Pricing Model
ICSS Iterated Cumulative Sum of Squares
IMF International Monetary Fund
ME Market Equity
MKT Market Factor
MPI Milanka Price Index
MPT Modern Portfolio Theory
NASDAQ National Association of Securities Dealers Automated Quotations
System
NYSE New York Stock Exchange
RE Return
RF Risk Free Rate
RM Risk Premium
SMB Small minus Big
TRI Total Return Index
vi
Abstract
This study investigates the validity of the Capital Asset Pricing Model (CAPM) and
Fama and French three factor model (FF3F) in predicting stock returns in the case of
the Sri Lankan and US stock markets during market crisis periods and non-crisis
periods. Past market crisis periods, defined as high volatility regimes, are identified
using the volatility break test of Inclan and Tiao (1994). Importantly, the periods
identified here were also identified as crisis periods in the previous work in finance.
This study investigates whether the fundamentals based and market based equity
market behavior as determined by the CAPM and the FF3F undergo changes as
markets are havocked by financial calamity. This study applies weekly data from both
markets for the empirical testing of the models. The methodology adopted for the
formation of portfolios is similar to the one used by Fama and French (1996). In
addition to the validation of the CAPM and the FF3F, this study further investigated
the existence of January effect for the same portfolios mentioned above in both
markets. Here the January effect is investigated for the same portfolios formed for the
purpose of testing the FF3F. It is one of the unique features of this study when
compared to other previous studies on January effect.
Findings suggest that in Sri Lankan market the CAPM does not work properly during
crisis and non-crisis periods, whereas it works well in the US market, both in crisis
and non-crisis periods. It is found that there are differences in the performance of the
FF3F during the identified crisis periods in the Sri Lankan market and the US market.
The findings on FF3F are mostly consistent with Fama and French (1996). In
particular, significant differences are found among SMB and HML during crisis and
non-crisis periods in both markets. The empirical evidence also confirms that the
FF3F model is sensitive to the January effect. Finally, the findings of this study may
be interpreted as a warning against using the model on long series of data punctuated
by random crisis periods. This will enable more specific generalization of findings for
crisis and non-crisis periods. The findings of this study are mostly consistent with
everal previous studies; for example, Wai and Gordon (2005) and Charitou and
Constantinidis (2004).
vii
Table of Contents
Declaration ii
Acknowledgements iv
List of Abbreviations v
Abstract vi
Table of Contents vii
List of Tables xiv
List of Figures xvi
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Research Objectives and Questions 2
1.3 Distinguishing Characteristics and Contributions 4
1.4 Structure of the thesis 5
1.5 Limitations of the study 8
1.6 Summary and conclusion 9
Chapter 2 Theoretical and Empirical Literature on Asset Pricing 10
2.1 Introduction 10
2.2 The pre-CAPM Era 10
2.2.1 Value Investing and Intrinsic Value 11
2.2.2 Portfolio Selection and Modern Portfolio Theory 12
viii
2.2.3 Liquidity Preference Model 14
2.2.4 Dividend Valuation Model 17
2.3 The CAPM 18
2.3.1 William F. Sharpe 19
2.3.2 John Lintner 22
2.3.3 Fisher Black 23
2.3.4 The CAPM as it stands today 26
2.3.5 Capital Market Line (CML) and the CAPM 28
2.4 Major issues of the model and empirical tests 30
2.4.1 The Asset Returns in CAPM 30
2.4.2 Econometric Problem of the Model 30
2.4.3 The CAPM and the Real World Market 31
2.4.4 Empirical studies of the CAPM and Different versions of CAPM 32
2.4.5 Empirical Contradiction of the CAPM 33
2.4.6 Roll‘s Critique of Tests of the CAPM 35
2.5 Post CAPM and Pre-FF3F Development of Literature 36
2.5.1 January effect 36
2.5.2 Size effect 39
2.5.3 Momentum effect 40
2.5.4 The Black, Jesnsen and Scholes Test (1972) 41
ix
2.5.5 Fama–Macbeth Study (1974) 42
2.6 Emergence of Fama and French three factor model 43
2.6.1 Properties of the FF3F 44
2.6.2 Risk Proxies of the model 44
2.6.3 Empirical studies of the model. 45
2.6.4 CAPM and FF3F similarities and Differences 45
2.6.5 CAPM, FF3F and Multi-Risk Factor Models 46
2.7 Economic Crises and Stock Market Crashes 48
2.7.1 General overview of Economic Crisis and Stock Market Crashes 48
2.7.2 Information effect on Crisis 50
2.7.3 Historical Empirical Evidence of Market Crisis 51
2.7.4 Evidences on Volatility, Crisis and other Events 52
2.7.5 Main Causes of Volatility of Stock Returns 54
2.8 Patterns and gaps in the empirical literature 54
2.9 Summary and Conclusion 57
Chapter 3 Data and Methodology 59
3.1 Introduction 59
3.2 The Capital Assets Pricing Model (CAPM) 60
3.3 The Fama and French 3 Factor (FF3F) Model 61
3.4 Data preparation 62
x
3.4.1 The generic description of portfolio creation 63
3.4.2 The formation of the FF3F portfolios: the Sri Lankan peculiarities 64
3.4.3 The creation or generation of data for additional risk factors 66
3.5 The Data 67
3.5.1 Sri Lankan stock market data 67
3.5.2 The US stock market data 71
3.5.3 Interlinks among the six portfolios and the market portfolio 74
3.6 Crisis identification and Inclan and Tiao (1994) 75
3.6.1 Iterated Cumulative sum of squares (ICSS) Algorithm 76
3.6.2 The ICSS and the periods of crisis in the CSE 78
3.6.3 ICSS and periods of crisis in the NYSE 82
3.6.4 Descriptive statistics for crisis and non-crisis periods 85
3.6.5 The correlation analysis of the crisis and non-crisis periods 88
3.7 Summary and Conclusion 91
Chapter 4 Test of Pricing Models and Anomalies in Colombo Stock Exchange 92
4.1 Introduction 92
4.2 Main Features of Emerging stock markets 93
4.3 Investing in Sri Lanka and the CSE 93
4.3.1 Sri Lanka: the economy in general 94
4.3.2 An overview of the Colombo Stock Exchange 96
xi
4.3.3 Impact of Recent Global Crisis on the CSE 98
4.4 Test of the CAPM using the FF3F portfolios 99
4.5 Test Results for the FF3F 102
4.6 Test for Explanatory Power of SMB and HML 108
4.7 Market anomalies and the January Effect in the CSE 113
4.7.1 Preliminary evidence of January effect in the CSE 113
4.7.2 The CSE, January effect and the FF3F 115
4.8 Summary and Conclusion 118
Chapter 5 Testing of Asset Pricing Models for the US 119
5.1 Introduction 119
5.2 The US Economy 120
5.3 Tests for the CAPM and the FF3F 128
5.3.1 The CAPM test results in the US 128
5.3.2 Testing Results of Three Factor Model 130
5.4 Test for Explanatory Power of SMB and HML 134
5.5 Test Results of January effect US Market 138
5.5.1 Preliminary evidence of January effect US Market 138
5.5.2 Response of the FF3F to the January effects in the US 140
5.6 Summary and Conclusion 142
Chapter 6 A Comparative Analysis of the Impact of Market Anomalies in Sri
Lanka and in the US 143
xii
6.1 Introduction 143
6.2 The current economic trends 144
6.2.1 Sri Lankan and the US economies: a recent snap shot 144
6.2.2 The stock markets: The key performance indicators 148
6.3 Risk and rewards comparison using summary statistics and pair-wise
correlations 150
6.4 Market wise comparison of major findings 152
6.4.1 Analysis of the Results of the CAPM in CSE and US 152
6.4.2 Comparison of the results of the FF3F 154
6.4.3 Comparison of explanatory power of SMB and HML 157
6.4.4 Differences and Similarities of January effect in both markets. 161
6.5 Summary of the findings 163
6.6 Conclusion 165
Chapter 7 Summary of the Findings and Conclusion 166
7.1 Introduction 166
7.2 Summary of key findings 166
7.3 Answers for research questions 167
7.4 Country specific findings in the Sri Lankan market 169
7.5 Country specific findings in the US Market 171
7.6 Contribution of this thesis 172
7.7 Policy implications of the findings 173
xiii
7.8 Suggested areas for future research 175
7.9 Final remarks 176
References 177
Appendix A: The companies in the CSE 186
New Listing and De-Listing of Companies 1999-2008 186
Appendix B: Classification of Sectors of the CSE 188
Appendix C: VB codes 189
Codes for Matching BE and ME values for all companies 189
xiv
List of Tables
Table 2.1: Characteristics of the Models ..................................................................... 25
Table 3.1: Descriptive Statistics for the weekly data from the CSE (1999-2008). ...... 70
Table 3.2: Descriptive Statistics for the US stock market (1985-2007) ...................... 73
Table 3.3: Pair-wise correlations for FF3F portfolios and the market ......................... 75
Table 3.4: Volatility breaks and crisis periods in the CSE .......................................... 81
Table 3.5: Volatility Breaks and Market Crashes- NYSE ........................................... 82
Table 3.6: Descriptive statistics for the CSE. .............................................................. 85
Table 3.7: Descriptive statistics for the US ................................................................. 87
Table 3.8: Pair-wise correlations of portfolios in the CSE .......................................... 89
Table 3.9: Pair-wise correlations of portfolios in the US ............................................ 90
Table 4.1: Test of CAPM in the CSE ........................................................................ 100
Table 4.2: The FF3F results for the CSE based on weekly data. ............................... 103
Table 4.3: A test of explanatory power of SMB and HML. ...................................... 110
Table 4.4: Mean excess returns for the CSE portfolios. ............................................ 114
Table 4.5: Testing of responses of FF3F to the January effect 1999 to 2008 in CSE 117
Table 5.1: Macro Variables of US Economy ............................................................ 121
Table 5.2: Financial Indicators of US Economy ........................................................ 123
Table 5.3: Test of CAPM in the US market ............................................................... 129
Table 5.4: The FF3F results for the US based on weekly data. ................................. 131
xv
Table 5.5: A test of explanatory power of SMB and HML. ...................................... 136
Table 5.6: Percentage return of January & Non January 1964-2008. ........................ 139
Table 5.7: Testing of responses of FF3F to the January effect in US Market ........... 141
Table 6.1: Comparison of Key Economic Indicators. ................................................ 145
Table 6.2: Important Performance Indicators of Sri Lankan Market and US Market149
Table 6.3: Measuring Explanatory Power of SMB and HML ................................... 158
Table 6.4: January Seasonality of CSE and US ......................................................... 162
Table 6.5: Sensitivity of FF3F to January Effect ....................................................... 162
Table 6.6: Gravity of major findings ......................................................................... 164
xvi
List of Figures
Figure 1.1: Overview of the thesis ................................................................................. 7
Figure 2.1: Efficient combination of E-V rule. ............................................................ 13
Figure 2.2: Portfolio Selection at Various Interest Rates ............................................ 15
Figure 2.3: The Investment Opportunity Curve. .......................................................... 21
Figure 2.4: Capital Market Line ................................................................................... 29
Figure 2.5: Analysis of empirical literature ................................................................. 56
Figure 3.1: Weekly time series plots for the CSE.. ...................................................... 69
Figure 3.2: Weekly time series plots for the US.. ........................................................ 72
Figure 3.3: The application of Inclan and Tao (1994) to the CSE. .............................. 80
Figure 3.4: The application of ICSS to the NYSE returns series................................. 84
Figure 4.1: Contribution by each sector to the economy of Sri Lanka. ....................... 94
Figure 4.2: ASPI and identified crisis periods for the CSE. ........................................ 98
Figure 5.1: Some economic and financial variables for the US. ............................... 124
Figure 5.2: Mean returns of the FF3F portfolios for the US Market (1964-2008). ... 140
Figure 6.1: Relationship between CAPM betas and excess return of portfolios. ...... 153
Figure 6.2: Multi factor beta of small and big portfolios.. ......................................... 156
Figure 6.3: Analysis of SMB Loading. ...................................................................... 159
Figure 6.4: Analysis of HML Loading. ..................................................................... 160
1
Chapter 1
Introduction
1.1 Introduction
Over the years, empirical finance research has subjected the stock markets in
developed countries to rigorous examination. For example, in the US and in other
developed markets the cross-sectional relationship between stocks returns and
fundamental variables has been studied extensively. In contrast, only a limited volume
of work is available for developing or emerging stock markets. This is inadvertently
related to the fact that the developing/emerging segment of the global financial
architecture is minute in comparison to developed markets, particularly in the US
market. For example, stock markets in developing countries represented only 4.73
percent of the global market capitalization in 2005 (Standard and Poors, 2005).
Though this situation has led to a relative dearth of research on the function and
operation of stock markets in developing countries, the lessons that can be learnt from
studying them are nevertheless valuable. This thesis, therefore, examines a
particularly important model used in finance; namely the Capital Asset Pricing Model
(CAPM) and an important caveat thereto, the Fama and French Three Factor model
(FF3F), in the context of a rarely studied developing country, Sri Lanka.
The CAPM due to Sharpe (1964), Lintner (1965) and Black (1972) which is discussed
in more detail later, asserts that the return from a particular stock is primarily
determined by movement in the market return which led it to be identified as the
single factor model. As a model that was developed and tested in developed countries,
it can be challenging to adopt or even adapt the model for developing/emerging
markets. This difficulty can be at two levels. First, the model‘s assumptions may not
be valid for the developing markets. Second, the data availability issues could obstruct
its implementation. The current thesis circumvents these problems to provide a unique
example of an application and validation of the CAPM in developing countries. The
lessons learned here are reinforced by a rigorous comparative analysis involving the
2
results from the application of the CAPM to the US. In fact, this comparative thread is
visible throughout this work.
A Large volume of scholarly articles that stemmed from previous work on the CAPM
is the literature on market anomalies which primarily disputes the single factor models
in favor of models with multiple factors. In fact, the present research places much
emphasis on the matter and painstakingly adopts the anomalies model due to Fama
and French (1992) for the case of Sri Lanka. The model is popularly dubbed as the
Fama and French three Factor (FF3F) model owing to the number of factors that is
proposed in the model. The new factors proposed in the model are argued to be more
important than the market factor flagged in the CAPM. As the use of the FF3F in
literature has largely excluded developing countries, the present implementation of
the model with Sri Lankan data stands to contribute non-trivial lessons to finance
literature. The application of the FF3F to Sri Lanka is also done, while carefully
drawing parallels with the US. Additionally, the work also purports to examine other
important CAPM anomalies, such as the January effects.
The rest of this introductory chapter is structured as follows. Section 1.2 examines in
detail the research questions that are raised and the approaches made to address these
questions. This is followed by a section which draws the attention of the reader to the
specific contributions of this thesis which distinguishes it from the rest of the
literature. Section 1.4 provides an overview of the thesis, while Section 1.5 flags some
of its limitations. This is followed by the summary of the chapter and some
conclusions.
1.2 Research Objectives and Questions
The main objective of this research is the application of asset pricing models to
developing country stock markets, represented by the Sri Lanka‘s Colombo Stock
Exchange (CSE). In order to achieve this, the present research undertakes to prepare
and organize the CSE data which takes much time and effort. For instance,
implementing a model such as FF3F demands that the stock price data be sorted and
3
organized in various ways to construct dynamic portfolios (this process will be
examined in more detail in Chapter 3).
In addition to the main objective explained above, the study attempts to explore two
other important objectives that are identified as secondary objectives of this study.
First, is to understand whether the findings in Sri Lanka are peculiar to developing
countries. This objective will be achieved by focusing on the US for comparative
purposes. This comparison provides a new perspective of how these models operate in
developing countries. Second, in the backdrop of the recent financial crisis that
havocked the world, it was apparently important to ascertain whether the pricing
models behaved differently in crisis settings than in non-crisis settings. Investigation
of crisis sensitivity of asset pricing models is an important link which was missing in
the literature up to date. In view of the main and secondary objectives, the following
specific research questions will be addressed in this work.
1. The primarily concern of the study is to ascertain which of the two models
(CAPM and FF3F) is more powerful in explaining the differences of stock returns
in stock markets in Sri Lanka and the US?
2. Does the FF3F model outperform the CAPM?
3. Which one of the three factors (MKT, SMB and HML) modeled under FF3F is
more prominent in the CSE and in the US?
4. Can the CAPM be used as a valid model in capturing the differences of small and
big portfolios in CSE and NYSE?
5. Are there any significant differences in the behavior of FF3F in the months of
January for Sri Lanka and for the US?
6. Have the answers for the above questions 1 to 4 significantly changed during
market crisis periods?
4
1.3 Distinguishing Characteristics and Contributions
In achieving the above objectives and answering the research questions the study
contributes to the literature on asset pricing in important ways. Firstly, the CAPM is
extended in several ways in this research. The most interesting aspect of this is the
testing of CAPM using the portfolios constructed for the FF3F methodology. This
portfolio wise testing of CAPM is also subjected to tests of crisis sensitivity which is
an important extension of the CAPM literature.
Secondly, the use of the FF3F in this work demonstrates some unique features. The
most prominent among these is the comparison of the behavior of the CAPM and the
FF3F in an emerging small market vis-à-vis a developed market. The test of the FF3F
for objectively identified crisis periods is also unique: the study examines the
behavior of the model during crisis and non-crisis periods within the sample used.
This constitutes an important measure of the impact of economic/financial crises on
asset pricing pattern of emerging and developed Markets. This provides a unique
opportunity to look into the modalities of how the CAPM and FF3F work in crisis
settings. No earlier research has investigated into this aspect before.
Thirdly, even though much work has been done on the US using FF3F, none of this
previous work used weekly data. The use of weekly data, instead of monthly, allows
the researchers to work with a larger number of observations. Though this does not
have obvious advantages for markets like the US which has centuries of historical
data, it makes a significant difference to markets like CSE with only few decades of
historical data to work with. In fact, had the investigator not used this approach the
work on Sri Lanka might not have been possible. Weekly data, obviously, captures
shorter terms movements of prices than monthly data, which therefore can bring out
the different aspects of investor behavior in a market.
Fourthly, the way crisis periods are identified in this work is unique in the literature.
Inclan and Tiao (1994) methodology used to identify volatility breaks in return series
such as stock returns is used for this purpose here. The thesis uses volatility
breakpoints in market return series indentified by using Inclan and Tiao (1994) to
5
separate high and low volatile periods in the CSE and the US markets. The high
volatility in the series is taken to imply or reveal crisis periods and the low volatility
the non-crisis periods. This objective identification of crisis periods enhances the
validity of the findings of the present work.
1.4 Structure of the thesis
This thesis is structured in seven chapters. The links between these chapters and how
they contribute to one another are presented in this section using Figure 1.1. Chapter 1
outlines the objectives of the thesis. The contextual background provided in this
chapter presents an overview of the research questions that are discussed in detail in
subsequent chapters.
Chapter 2 is a review of the literature that is central to this work. This chapter reviews
key developments in empirical studies on the CAPM and the FF3F, as well as some of
theoretical contributions that support these developments. The chapter also looks at
the historical evolution of asset pricing models with a view to explaining how various
developments in the stock markets around the globe has affected this literature.
Chapter 3 is a central link in this work. It uses existing literature (Chapter 2) to
generate the methodological foundation for the key empirical works in Chapters 4 and
5. This centrality is brought out in Figure 1.1. The use of the CAPM and the FF3F in
this work is formalized in Chapter 3. This is followed by a data section which uses
much space to discuss in detail the formation of six portfolios for implementing the
FF3F. The portfolios for the Sri Lankan study rely on data inputs from the CSE and
the Central Bank of Sri Lanka in an unprocessed form. Converting this data into
portfolios is involves many procedures which are explained in detail in Chapter 3.
However, these steps are however not needed for the case of US, as the weekly
returns of the six portfolios needed to implement FF3F for the US is available free
from (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french). This distinction
across the two sources of data is illustrated by the areas marked out using the
perforated line in Figure 1.1. While discussing the data issues, the chapter also
explains the use of Inclan and Tiao (1994) for the identification of market crisis
6
periods in both Sri Lanka and the US. The chapter uses daily prices of market indices
for the CSE and the US in implementing Inclan and Tiao (1994).
Chapter 4 and Chapter 5 implement the empirical testing of the models for the case of
Sri Lanka and the US respectively. They use the same methodology and generate
similar outputs for the cases of Sri Lanka and the US. The contributions of these
chapters are highlighted in Figure 1.1.
The rest, apart from the data sections in Chapter 4 and in Chapter 5, are similar in
approach and implements CAPM and FF3F for Sri Lanka and the US respectively.
Apart from the validating the models, these chapters also deal with the measuring of
the sensitivity of FF3F to January months in both countries. Both chapters are based
on Chapter 3 as shown in Figure 1.1.
The comparison of the results of CSE and US is discussed in Chapter 6. The inputs to
this chapter come from Chapters 4 and 5. The comparisons made here is twofold: (1)
Comparison of CAPM, FF3F and sensitivity of the model (FF3F) to January seasonal
effect, and (2) Comparison of impact of financial crises on the models and their
predictions for both markets.
Chapter 7 summarizes the main findings of this work and offers some concluding
remarks. This also provides a discussion of how the objectives of the research have
been attained by the outcome of this work. An important contribution of the chapter is
the discussion of the policy implications of this thesis, especially for the Sri Lankan
case.
7
Figure 1.1: Overview of the thesis
Ch 1Introduction
Ch 6Comparative analysis
of Sri Lanka vs. the US
Ch 5Validation of CAPM
and FF3F for the US.Test of crisis sensitivity.
January effect in the US.Test of power of FF3F variables.
Ch 4Validation of CAPM and
FF3F for Sri Lanka.Test of crisis sensitivity.
January effect in CSE.Test of power of FF3F variables.
Ch 3Methodology and data.
Data preparation and creation of the
six portfolios for the CSE.
Data description (Sri Lanka and US)
Identify Crises in Sri Lanka and the US using Inclan and Tiao (1994)
Ch 2Literature on asset pricing (including
CAPM and FF3F)Literature on financial crises
Ch 7Policy
implications and Conclusions
Six
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8
1.5 Limitations of the study
Finance research in developing countries, particularly those involving stock markets,
is challenging due to the limited availability of data. By overcoming these challenges
the present study contributes to the literature existing on many fronts. However, it
does not mean that all such issues are solved here. In particular, this research in its
current form has some limitation that needs to be identified and appreciated. This
exercise will place the findings of this work in proper perspective and make them
more useful.
The main limitation of the study still involves data, particularly in the case of Sri
Lanka. An unavoidable issue in this regard is the unavailability of historical data. The
lack of information from the CSE is due to the relatively young existence of the
market. Also the automated trading is a relatively recent phenomenon which implies
that data from earlier periods are not available in digital form.
Another important limitation that could not be avoided in the present study, but which
could easily be rectified in future work, is that the 2008 crisis has not been covered in
it. As the data collection for this study predates the crisis, it is not possible to bring in
a meaningful discussion of the impact of the present crisis on Sri Lanka or the US.
This was primarily hampered by the colossal amount of work that needs to be done in
order to prepare data for the Sri Lankan study.
In addition to the above limitations, the study also faced other limitations inherent in
any study of stock markets in developing countries. These include issues of
new-listing/de-listing of companies, and the issue of thin trading.
9
1.6 Summary and conclusion
This chapter explores the main objectives of this study and examines how they are to
be achieved. Six research questions that are identified alerts the reader to the various
sub focuses of the research. In addition, this chapter usefully identifies academic and
empirical contributions of the thesis. The outline of the thesis was used to identify
where in the thesis these contributions arise. Finally, some limitations that restricted
the scope of the thesis, particularly data limitations, have been outlined.
10
Chapter 2
Theoretical and Empirical Literature on Asset Pricing
2.1 Introduction
This chapter reviews the literature on asset pricing, with a specific focus on
theoretical and empirical work that highlights the literature on the CAPM and the
FF3F—the focus of this work. This focus demands, however, that the literature
review focus on the literature that provides the backdrop to the works on the CAPM
and its anomalies. The chapter is organized around the CAPM in a specific and
perhaps obvious chronological order: it starts by examining precursors to the CAPM,
followed by the CAPM itself and the aftermath of the CAPM. In covering this ground
the chapter is able to identify a gap in the literature which is to be filled by the present
work.
The chapter gives an overview of the initial stages of the development of this
literature in Section 2.2 focusing on pre-CAPM literature. This is followed by Section
2.3 which deals with the emergence of important literature of the CAPM. Here the
discussion is mainly focused on the evolution of the CAPM to date placing, with
much emphasis on the practical application of the model. Section 2.4 discusses the
CAPM anomalies with special reference to the January effect. The theoretical
background and emergence of the FF3F is covered in Section 2.5. Section 2.6
establishes the impact of the financial crisis on asset pricing models and major market
crises experienced in the history of capital markets in the world. The contribution of
this study to the body of knowledge of this area is summarized in Section 2.7. The
final section concludes the chapter.
2.2 The pre-CAPM Era
This section looks at the literature that led to the development, later known as the
asset pricing literature spearheaded by the CAPM. As such much emphasis is put on
the evolution of asset pricing concept. Even though asset pricing per se was rarely
examined in the literature prior to the CAPM, there were some key pre-CAPM
11
contributions that had much impact on the latter development of asset pricing theory
in finance.
2.2.1 Value Investing and Intrinsic Value
Historically, the Wall Street crash of 1929 inspired investors and other professionals
to look for better practices of investment which were conservative and safe. This
interest was also fueled by the abandonment of the gold standard in the early 1930s
and the resulting depreciation of many currencies. The concept of value investing
introduced by Graham and Dodd (1934) was an important contribution to the
literature during this time. The currency of the concept highlights the continued used
of it even today (the sixth, and the latest edition of this work was published in 2008).
The concept of value investing contends that in order to make profits in the stock
markets, the investors should buy stocks at a price lower than their intrinsic value.
Graham and Dodd (1940 : 20-21) agreed that:
an elusive concept and in general terms it is understood to be that value
which is justified by the facts, e.g., the assets, earnings, dividends,
representative of what may be expected in the future.
With its emphasis on future earnings, the concept of intrinsic value alludes to
something beyond mere economic value to an investor. It also emphasizes the
importance of the adequacy of the value of investment to protect the investor. This is
further emphasized by the concept of ―safety of principal‖ also defined by Graham
and Dodd (1940: 63) as:
An investment operation is one which upon through analysis premises
safety of principal and a satisfactory return. Operations not meeting
these requirements are speculative.
This concept gained due recognition from the practitioners and other researchers
during 1930s and 1940s. This empirical concern spearheaded by the work of Graham
and Dodd led the way to formalizing the theoretical relationships between a safety of
an investment and its returns. This concern also sprouted other works that looked at
12
ways to increase the ―safety of principal‖. Hayes (1950), for instance, examines issues
involved in appraisal of safety of investment in common stocks and suggests
diversification of investments as a method of obtaining safety.
2.2.2 Portfolio Selection and Modern Portfolio Theory
As noted above, the importance of diversification in view of conservative and safe
investing was getting established during the 1950s. The helm of this movement is
undoubtedly the advent of the Modern Portfolio Theory (MPT) due to the 1990 Noble
Prize winner Harry Markowitz. Markowitz (1952) proposing "expected returns-
variance of returns" rule as the best, and also the safest rule of investment. Markowitz
(1952: 82) states his rule as follows:
The E-V rule states that the investor would (or should) want to select
one of those portfolios which give rise to the (E, V) combinations
indicated as efficient in the figure; i.e., those with minimum V for
given E or more and maximum E for given V or less.
The figure in the above quote is reproduced in Figure 2.1. The figure presents the
attainable combinations and efficient combinations (the thick arc) under the E-V rule.
The rational investor should invest in such a manner that he/she achieves any efficient
E, V combination. The figure also illustrates that the efficient combinations are a
subset of the attainable E, V combinations. Markowitz goes on to prove that an
investor, using stocks of a given set of companies, can easily position him/her self
anywhere in the attainable set of E, V combinations. Perhaps within the purview of
this thesis, the most significant contribution of the Markowitz‘s work is this.
13
Figure 2.1: Efficient combination of E-V rule.
attainable E ,Vcombinations
efficient E,Vcombinations
V
E
Source: Fig 1 of Markowitz (1952)
To explain the above proposition Markowitz (1952: 81) derived the expected value
(E) and the expected variance (V) of a portfolio of N number of stocks (i) and stock
return (ui) as follows:
N
i
iiuXE1
(2.1)
ji
N
i
N
ji
ji XXσV
1
(2.2)
where ji is the covariance between returns of stock i and stock j, Xi and Xj are the
weights of each stock within the portfolio (i=j=1,2,…,N). Equation 2.2 captures an
important result which revolutionized the asset pricing literature. Namely, the
covariance between stocks is critical for the variance of the portfolio. Markowitz
(1952: 89) states:
14
In trying to make variance small it is not enough to invest in many
securities. It is necessary to avoid investing in securities with high co-
variances among themselves.
This work was pivotal in establishing the significance of the co-movement of stock
prices as a component of risk. In later developments many authors build upon this to
establish the concept of systematic risk which is an important piece of historical
evolution that is being mapped here.1
2.2.3 Liquidity Preference Model
James Tobin (1958) in his seminal work used traits of MPT and the theory of liquidity
preference developed by Keynes (1937). He used a micro model to examine the
behavior of an investor when he/she maintains a portfolio of assets. As Tobin‘s work
has advanced the understanding of liquidity preference behavior it also has a non
trivial impact on the literature on asset pricing.2
It is interesting that the main idea of Markowitz‘s (1952), which was dubbed the E-V
rule in Section 2.2.2, is used by Tobin (1958) in a different context. Both use the idea
that a portfolio can potentially have many E-V combinations. The only difference is
where as Markowitz uses a portfolio of common stocks. Tobin uses a portfolio of cash
and bonds.3
1 see for example Hirshleifer Hirshleifer, J. (1961). "The Bayesian Approach to Statistical Decision An
Exposition." Journal of Business 34(4): 471-489.
. 2 A Google Scholar search revealed that Tobin (1958) has been cited in 2910 studies at the time of
writing. 3 Tobin called these consols.
15
Figure 2.2: Portfolio Selection at Various Interest Rates and Before and After Taxation.
0 1
Source : Adapted from Figure 1 of Tobin (1958)
T1
T2
C1
C2
B
A2(r1)
A2(r1)
A1(r1)
A1(r1)
A11
0
σRσg
I1
I2
Figure 2.2, which is adapted from Tobin (1958: 73), graphically presents the decision
making process of an investor within Tobin‘s liquidity preference model. In the upper
half of Figure 2.2 the vertical axes represents expected return and the horizontal axis
risk. There the investor decides how to construct a portfolio consisting of two
components, cash and consols. The decision of the investor involves the proportion
16
of his/her investment that goes into cash A1 and so the proportion that would go into
consols is (A2 = 1 - A1); . Tobin assumed that A1 and A2 do not depend on absolute size
of the initial investment balance in dollars. The return on this portfolio of cash and
consols, R, is:
)(2 grAR 10 2 A (2.3)
where r is the interest rate from consols and g is the capital gain or loss from investing
in consols. The variable g is assumed to have an expected value of 0 in which case the
expected value of R can be written as:
rARE R 2)( (2.4)
As shown in Figure 2.2 standard deviation of R depends on the standard deviation of
g, σg, and on the amount invested in the consols:
gR A 2 (2.5)
The conditions in equation 2.3 indicate that the proportion the investor holds in
consols A2 determines both his expected return µR and his σR. The terms in which the
investor can obtain greater expected return at the expense of assuming more risk can
be derived from (2.4) and (2.5):
R
g
R
r
gR 0 (2.6)
This opportunity locus is shown as 0C1 in the figure. The slope of this locus is g
r
1 .
For a higher r2 the opportunity locus is shown as 0C2. Similarly, cash holding (A1) can
be read on the right-hand vertical axis. The investor is indifferent between all pairs
(µR, σR) that lie on a curve as shown in I1. Points on I2 are preferred to those on I1, for
given risk an investor always prefers a greater to a small expectation of return. These
indifference curves are similar in spirit to the efficient E-V combinations of
Markowitz (1952) shown in Figure 2.1. Tobin (1958) showed that the efficient E-V
17
combinations for a portfolio of cash and consols are in fact sensitive to the interest
rate.
The work of Tobin (1958) on liquidity preference has been later improved by several
others Feldstein (1969) and Chang, Hamberg and Hirata (1983). These, however, do
not in anyway take away Tobin‘s important contributions to the theory of asset
pricing.
2.2.4 Dividend Valuation Model
The Dividend Valuation Model is also known as the Gordon Model after the author of
Gordon (1959) who proposed the model. The model attempts to build up on the
concept of intrinsic value of Graham and Dodd (1934) discussed in Subsection 2.2.1
in p.11. Gordon proposes an empirical model to capture the intrinsic value of a stock
using its future dividends. Though Graham and Dodd (1934) alluded to a link between
dividend and earnings, it was Gordon (1959) who first empirically tested it. For
instance Gordon (1958: 99) states:
Graham and Dodd go so far as to state that stock prices should bear a
specified relation to earnings and dividends, but they neither present
nor cite data to support the generalization.
Gordon (1959) effectively uses cross-sectional stock prices to build an elementary
theory of variation of stock prices in relation to dividends and earnings. The empirical
literature on asset pricing is proliferated with this important application of statistical
technique. Gordon (1959) observed that stockholders are interested in both dividends
and income per share and derived a model to prove this phenomenon:
YDP 210 (2.7)
where P = the year end price, D = the year‘s dividend, Y = the year‘s income. The
coefficients 1 and 2 are the values that the market places on dividends and
earnings respectively. Gordon did not restrict and went on to test the model
empirically in a real market situation.
18
Two hypotheses were developed by the investigator in the model. The first was the
dividend hypothesis which assumed that the investor buys dividend when he buys
shares. In implementing this hypothesis it must be recognized that the stockholder is
interested in the entire sequence of dividend payments that he may expect and not
merely the current value. The other hypothesis assumes that the investor buys income
for shares when he acquires a share of stock. More specifically, the value of equity
can be written as the present value of expected dividends during the non-stable
growth phase and the present value of price at the end of the high growth phase are
usually computed using equation 2.3.
Subsequently, in order to simplify the complexity of the Gordon model, the
researchers found some variants to the original model. For instance, Chen (1967)
examined the validity of the Gordon‘s model in valuing stocks in levered firms that
are highly regulated. Furthermore, recently the H- Model was developed by Fuller
and Hsia (1984). This model avoids the problems associated with the growth rate
dropping precipitously from the high growth to the stable growth phase, but it does so
at a cost. First, the decline in the growth rate is expected to follow the strict structure
laid out in the model and it drops in linear increments each year based upon the initial
growth rate, the stable growth rate and the length of the extraordinary growth period.
While small deviations from this assumption do not affect the value significantly,
large deviations can cause problems. Second, the assumption that the payout ratio is
constant through both phases of growth exposes the analyst to an inconsistency
because as the growth rates declines, the payout ratio usually increases. H-Model
assumes that firm‘s growth rate declines in a linear passion from an above normal rate
to a normal long term rate. The H-Model is more practical than the general discount
model.
2.3 The CAPM
The CAPM is considered the backbone of modern price theory for financial markets.
The CAPM basically explains the relationship between average stock return and
market portfolio and is widely used in empirical analysis of securities. Moreover, the
model is applied extensively by practitioners and has therefore become an important
19
basis for decision-making in different areas in corporate finance. In the present
section, the CAPM and its arguments are introduced in some detail using material
from the work of Sharpe (1964), Lintner (1965), and Black (1972). This section traces
the evolution of asset pricing theory through the prominent works in the pre-CAPM
literature (some of these were discussed in Section 2.2) up to the level of the CAPM.
2.3.1 William F. Sharpe
William Sharpe won the 1990 Nobel Prize in economics for the contribution of the
CAPM to financial economics in the reputed piece Sharpe (1964). Of course the
model was not named the CAPM till Fama (1968: 34):
Fortunately, it is shown that the measure of the risk of an individual
asset and the equilibrium relationship between risk and expected return
derived from the capital asset pricing model will be essentially the
same whether or not it is assumed that such riskless borrowing-lending
opportunities exist.
Sharpe (1964), heavily influenced by Markowitz (1952) as discussed in Section 2.2.2,
attempts to offer a micro analysis to market analysis of price formation for financial
assets. The basis of the CAPM is that an individual investor can choose exposure to
risk through a combination of lending and borrowing and a suitably composed
(optimal) portfolio of risky securities. Sharpe specifically stated that the composition
of this optimal risk portfolio depends on the investor's assessment of the future
prospects of different securities, and not on the investors' own attitudes towards risk.
The latter is reflected solely in the choice of a combination of a risk portfolio and risk-
free investment (for instance treasury bills) or borrowing. In the case of an investor
who does not have any special information, i.e., better information than other
investors, there is no reason to hold a different portfolio of shares than other investors,
for example a so-called market portfolio of shares.
Sharpe (1964) assumed that an individual views the outcome of an investment in
probabilistic terms that is in terms of probability distribution. In assessing the
desirability of an investment he recommended two parameters; namely, expected
20
value and standard deviation. Sharpe (1964) stated that the expected value and
standard deviation can be represented by a total utility function given below:
),( WWEfU (2.8)
Where EW indicates expected future wealth and σw the predicted standard deviation of
the possible divergence of actual future wealth from EW. To simplify the presentation,
Sharpe (1964) assumed that investor has decided to commit a given amount (W1) of
his present wealth to investment. Letting (Wt ) be his/her terminal wealth and R the
rate of return on the investment:
1
1
W
WWR t
(2.9)
11 WRWWt (2.10)
This relationship makes it possible to express the investor‘s utility in terms of R, since
terminal wealth is directly related to the rate of return.
Figure 2.3 summarizes investor preferences in a family of indifference curves. Such
indifference curves can also be derived by assuming that the investor wishes to
maximize expected utility and that his/her utility can be represented by quadratic
function of R with decreasing marginal utility. As previously explained in Subsections
2.2.2 and 2.2.3 respectively, both Markowitz and Tobin present such a derivation.
21
Figure 2.3: The Investment Opportunity Curve.
.C
σR
II
III
.
X
. D
ER
Source : Adopted from Figure 2 of Sharpe (1964)
.
I
.B
F
Z
.
.
The model of investor behavior considers the investor as choosing from a set of
investment opportunities that as maximizes his/her utility. Every investment plan
available to the investor may be represented by a point in a point in the ER, σR plane. If
all such plans involve some risk, the area composed of such points will have an
appearance similar to that shown in Figure 2.3. The fundamental concept behind the
selection of portfolios is similarly to what Markowitz stated. As described in
Subsection 2.2.2 Markowitz introduced E-V combination instead of ER, σR plane for
the selection of optimal portfolios, as both concepts fundamentally explains the same
procedure.
The investor will choose from among all possible plans the one placing him on the
indifference curve representing the highest level of utility, point F in Figure 2.3. The
decision can be made in two stages: first find the set of efficient investment plans and
second choose one from among this set. A plan is said to be efficient if there is no
alternative with either (1) the same ER, and a lower σR , (2) the same σR and a higher
22
ER, or (3) a higher ER, and a lower σR. Thus, investment Z is inefficient since
investments B, C and D dominate it. The only plans which would be chosen must lie
along the lower right-hand boundary (AFBDCX) which is the investment opportunity
curve for an individual investor.
2.3.2 John Lintner
In the late 1960s several extensions to the initial work of Sharpe appeared in the
historical literature of finance. As an immediate response Lintner (1965) attempted to
give an alternative and transparent proof to the separation theorem of Fisher (1930)
which is also extended to Tobin (discussed in the previous section) in the light of
Sharpe (1964) discussed in section 2.2.3 of this chapter. The separation theorem is
defined as ―an investor makes choices on the basis of net present value of the
projected returns and not on his level of risk tolerance‖. 4
Following these extensions of Tobin‘s classic work, Lintner (1965) concentrated on
the set of risk assets held in risk averters‘ portfolios which gave identical approach to
the initial work of Sharpe. It is important to emphasize that the Sharpe and Lintner
asset pricing models, like the Markowitz and Tobin portfolio models, present one-
period analyses. The one-period return defined in this way is just a linear
transformation of the units in which terminal wealth is measured; an investor's utility
function can be defined in terms of one- period return just as well as in terms of
terminal wealth. Note that the one-period return involves no compounding; it is just
the ratio of the change in terminal wealth to initial wealth, even though the horizon
period may be very long.
Lintner considers an extension of the asset pricing model to the case where investors
disagree on the expected returns and standard deviations provided by portfolios. The
results are essentially the same as those derived under the assumption of homogenous
expectations.
4 www.investorwords.com/7441/portfolio. (last accessed 09/06/2011)
23
Recall that as previously mentioned, the emergence of CAPM is a collective
contribution of several Scholars. It is interesting to note that Lintner (1965) extended
the original version of Sharpe‘s work in several ways. However, the work of Sharpe
(1964) and work of Lintner (1965) share some similarities. Both have paid attention to
the selection of optimal portfolios for an individual investor. Therefore, it is observed
that the first section of the Lintner‘s paper parallels with first half of Sharpe‘s (1964).
Most of the models that appeared in both papers were also similar. Lintner (1965)
further introduced the option of short selling to the investor which was not addressed
by Sharpe in his deriving of the models.
Although short sales are excluded by assumption in most of the
writings on portfolio optimization, this restrictive assumption is
arbitrary for some purposes at least, and we therefore broaden the
analysis in this paper to include short sales whenever they are
permitted. (Lintner 1965 : 19 ).
He widened his work under two conditions; first, the optimum Portfolio Selection
when short sales are permitted and the second condition are the short sales that are not
permitted in selecting the optimum portfolio.5 In finalizing the study Lintner made the
following conclusions in equilibrium: (1) the same combination of risky assets will be
optimal for every investor (2) the investment amount invested in each risky asset will
be equivalent to the ratio of the aggregate market value of risky asset (3) each
investment amount in the individual risky assets must therefore be a positive amount.
2.3.3 Fisher Black
In 1972, Fisher Black examined the validity of the assumptions made by Sharpe
(1964) and Lintner (1965) in deriving the model. He gave two restrictions to the early
assumptions of the model in exploring the nature of capital market equilibrium. He
assumed that there is no riskless asset and that no riskless borrowing or lending is
allowed. Black (1972) stated that the assumption of availability of riskless borrowing
5 Short selling is a technique used by investors who try to profit from the falling price of the stock.
24
and lending is not realistic since restrictions on short selling are at least as stringent as
restrictions on borrowing. The relaxation of the assumptions of the model gave much
empirical sound background for the model. This study is identified as the first
extension to the initial work of Sharpe and Lintner.
In deriving the CAPM Sharpe (1964) and Lintner (1965) assumed that
there was a riskless asset in the investment opportunity set, and the
first significant extension of their work was by Black (1972) who
showed that the assumption of a riskless asset could be dispensed with.
(Ross 1977: 177).
By imposing restrictions on the assumption he confirmed that the expected return on
any risky asset is a linear function of its β, just as previous work of Sharpe (1964) and
Lintner (1965) were without any restrictions.
In summary, all theorists express optimal portfolios using the vector of (expected
mean) returns and variance. Initially Markowitz examines risky assets with E-V
efficient set, whereas Tobin employs a riskless asset in order to derive a liner
opportunity locus and finally Black utilized two fund separation theorem to construct
zero beta CAPM.
The work of Black presented the model more meaningfully and compressively than
the previous studies of Sharpe (1964) and Lintner (1965). The deriving process of the
model was completed with the work of Black and the name of the model became
popular as the SLB model in honor of Sharpe (1964), Lintner (1965) and Black
(1972).
25
Table 2.1: Characteristics of the Models
Characteristics Sharpe
(1964)
Lintner
(1965)
Black
(1972)
Single Period/Multi Period Single Single Single
Allows Short Sales No Yes Yes
Allows Leverage Disallowed Allowed Disallowed
Mean-variance objective function yes yes Yes
Market itself is efficient No Yes Yes
Market /Consumption-oriented Market Market Market
Discrete time/Continuous time Discrete Discrete Discrete
Source: Adopted from Table 2 of French (2003)
Table 2.1 summarizes the main characteristics of the key studies that contributed
towards the development of CAPM. The models of Sharpe (1964), Lintner (1965) and
Black (1972) have much in common. All are single- period discrete -time models and
market-focused, as opposed to consumption-focused. The most fundamental
similarities are that each rest on the foundations of Markowitz (1952) and Tobin
(1958) built upon the utility of wealth literature that assumes agents are risk-averters
with convex loci of constant expected utility of wealth represented as indifference
curves in the mean variance plane.
In contrasts, Sharpe (1964) explicitly disallowed the short sales in the model. Sharpe
(1964: 437) reports that a combination (of asset i plus an efficient combination of
asset g ) in which asset i does not appear at all must be represented by some negative
value of α not expressly allowing the overt negative holding of asset i.
But rather as a device which allows us to interpret point g’ in such a fashion without
any actual short sales having occurred. Lintner (1965: 19) has included short sales in
computing returns on a stock in his study, while Black has not addressed the concept
of short sales.
26
Another aspect which diverges each study is leverage. Sharpe (1964) disallows
leverage (borrowings) via his non negativity constraints on all assets, including the
risk free asset, he discussed the possibility Sharpe (1964: 433) if the investor can
borrow this is equivalent to disinvesting in risk free asset. Lintner (1965: 15) allows
for borrowings while Black (1972: 452) has not allowed borrowing.
2.3.4 The CAPM as it stands today
As previously explained, the CAPM proposes a theory to explain market equilibrium
under risky conditions. The model states that under certain assumptions the expected
return on any capital asset for a single period will satisfy:
fmifi RRERRE )()( (2.11)
where iR is the return on asset i for the period and is equal to the change in the price
of the asset, plus any dividends, interest, or other distributions, divided by the price of
the asset at the start of period, mR is the return on market portfolio of all assets taken
together; Rf is the return on a riskless asset for the period; βi is the market sensitivity
of asset i and is equal to the slope of the regression line relating iR and mR The
market sensitivity βi of asset i is defined algebraically by:
)var(/),cov( mmii RRR (2.12)
What is stated in equation 2.8 as the βi (beta value) of a specific share indicates its
marginal contribution to the risk of the entire market portfolio of risky securities.
Shares with a beta coefficient greater than 1 have an above-average effect on the risk
of the aggregate portfolio, whereas shares with a beta coefficient of less than 1 have a
lower than average effect on the risk of the aggregate portfolio. According to the
CAPM, the risk premium in an efficient capital market and thus, the expected return
on an asset will vary in direct proportion to the beta value. These relations are
generated by equilibrium price formation for efficient capital markets.
27
Risk Factors of the Model
It decomposes a portfolio‘s risk into systematic and specific risk. Systematic risk is
the risk of holding market portfolio. As the market moves each individual asset is
more or less affected to the extent that any asset that participates in such general
market moves entails a systematic risk. Specific risk is the risk which is unique to
individual asset. It represents the component of an asset‘s return which is uncorrelated
with general market moves. As stated in CAPM the marketplace compensates
investors for taking systematic risk, but not taking specific risk. This is because the
specific risk can be diversified. The categorization of risk into two components was
first developed by Harry Markowitz in 1950s as discussed in Section 2.2.2 in the
previous section. Sharpe (1964) identifies two components of risk as systematic and
unsystematic risk;
Moreover, such points may be scattered throughout the feasible region,
with no consistent relationship between their expected return and total
risk. However, there will be a consistent relationship between their
expected returns and what might best be called systematic risk. (Sharpe
1964: 436).
Assumptions of the Model
The assumptions that are generally used in deriving equation (2.8) are as follows: (a)
all investors have the same opinions about the possibilities of various end-of-period
values for all assets. They have a common joint probability distribution for the return
on the available asset. (b) The common probability distribution describing the
possible returns on the available assets is joint normal. (c) Investors choose portfolios
that maximize their expected end-of-period utility of wealth and all investors are risk
averse.6 (d) An investor may take a long or short position of any size in any asset,
6 This assumption© places the analysis within the framework of Markowitz one-period mean –standard
deviation portfolio model.
28
including the riskless asset. Any investor may borrow or lend any amount he wants at
the riskless rate of interest.
Emergence of this model (CAPM) took the world of finance by storm. This
remarkable finding of the model filled the long waited void in the field of finance. As
stated in the previous section, the concept of asset pricing and valuation initiated from
the 1930s. However, CAPM has received wider acceptance from the academics and
professionals who used the model in making investment decisions in the stock
markets. The model is still used as a valid model in determining stock returns of the
common stocks in the capital markets. The CAPM attempts to capture the pricing of
capital asset under condition of market equilibrium which indicates that in
equilibrium total asset holdings of all investors must equal the total supply of assets.
2.3.5 Capital Market Line (CML) and the CAPM
A useful representation of CML is shown in Figure 2.4, the horizontal axes of the
graph represent the expected return and the vertical line represents the risk. The area
shown in a curly bracket is the pure interest rate. In equilibrium capital market prices
adjusted so that the rational investor can attain any desired point along a capital
market line. She/he may obtain a higher expected rate of return on his security only by
accepting additional risk. In effect, the market presents him with two prices. First, the
price of time or the pure interest rate as shown in Figure 2.4 and the second is price
of risk that is the additional expected return per unit of risk borne.
29
Figure 2.4: Capital Market Line
pure Interest Rate
0
Expected Rate of Return
Capital Market Line Risk
Source: Figure 1 of Sharpe (1964)
The line which measures the relationship between systematic risk and expected return
in financial markets is usually named as the Security Market Line (SML). This is a
very important concept in finance because it is a useful tool in determining whether an
asset being included in a portfolio offers a reasonable return for risk. The decision
criteria in SML is that if security‘s risk vs expected returns is plotted above SML it is
undervalued stock because the investor can get greater return for inherent risk. A
security plotted below the SML is overvalued because the investor would be
accepting less return for the amount of risk assumed. The SML is essentially a graph
which represents the results derived from the CAPM. Thus, the equation for the SML
is fmifi RRERRE )()~
( which is exactly same as CAPM. The x-axis
represents the risk (beta) and the y-axis represents the expected return. The market
risk premium is determined by the slope of the SML.
30
2.4 Major issues of the model and empirical tests
The previous section discussed the deriving of the model citing the major contribution
for the CAPM from prominent scholars during 1960s and 1970s. Since then several
empirical studies have been conducted in various stock markets in the world
preserving the fundamental aspects of the original CAPM. The purpose of this section
is to explore those studies in the context of the current study. Apart from that, the
major issues discovered from these studies will also be explored in the context of the
practical application of the model.
2.4.1 The Asset Returns in CAPM
Under the CAPM, a return to an asset is determined by three guidelines. First, all asset
must have an expected return at least equal to the risk-free asset (except negative beta
stocks). The rational is that any risky asset must be expected to return at least as
much as one without risk or there is no incentive for anyone for holding risky assets.
The second guideline is that there is no expected return for taking unsystematic risk
since it can be easily avoided by diversification. Diversification simple does not
affect the economies of the asset held by the investors. Therefore, there is no
compensation inherent in the model for accepting this needless risk by choosing to
hold asset in isolation. Finally, assets that are subject to systematic risk are expected
to yield a return greater than risk-free rate. This premium should be incremental to the
risk-free rate by an amount proportional to the amount of this risk (beta) present in the
assets. This risk cannot be diversified away and must be borne by the investor if the
assets are to be financed and employed productively. The higher the systematic risk,
the higher the average long-term returns must be for holder to be willing to accept the
risk.
2.4.2 Econometric Problem of the Model
Miller and Scholes (1972) and several other studies provide an analysis of the
econometric problems inherent in the early empirical tests of the CAPM. Many of
these issues are important to discuss in the context of the study as they are very much
common to capital market based research. First, the distributions of asset returns are
31
likely somewhat skewed due to the limited liability of financial asset returns,
irrespective of the firm size. The assets pricing models discussed in this study assume
that stock returns are normally distributed in all the sample companies. This
assumption is further confirmed by Fama and French (1996) and concludes that
return distributions are very close to normal and the assumption of normality is
reasonable7.
Miller and Scholes (1972) demonstrate that the most damaging problem in the early
tests of the CAPM is the error-in-variables problem. The error-in-variable problem
exists because the risk beta estimated in the first-pass time-series regressions are
estimated with some degree of error. However, researchers have used various
methods to counter this problem. For example Kothari, Shanken and Sloan (1995),
Kandel, Shmuel et al.(1995) and others shows that beta is alive if annual returns are
used. Much has been written by Cooper and Ejarque (2001) and others about what
constitutes a good index they argued that ideally, an index is transparent, unbiased,
rules based, investable and above all, representative of a given market.8 Other
evidences reports that this issue can be minimized if more than one market portfolio is
available to a country and apply them for the model as market proxies.
2.4.3 The CAPM and the Real World Market
In the real world portfolio theory of Markowitz (1952) and the CAPM of SLB have
become widely accepted tools in making investment decisions in the practitioner
community. Many investment professionals believe that the distinction between firm-
specific and systematic risk are comfortable with the use of beta to measure the
systematic risk in making investment decisions. Douglas (1969) found two drawbacks
that hinders the validity of the CAPM and he is the first to cast doubt on the empirical
7 Basic Book, New York.
8 Christopherson, Jon A., David R. Carino and Wayne E. Ferson. 2009. Portfolio Performance
Measurement and Benchmarking. McGraw Hill.
32
validity of the model. First, contradiction to the prediction of the theory that
unsystematic risk did seem to explain average returns. Second, the estimated security
market line was too shallow; it was greater than the risk free rate, implying that
defensive stocks β < 1 tended to have positive alphas, while aggressive stocks β > 1
tended to have negative alphas.
Four years later Miller and Scholes (1972) published a paper demonstrating
formidable statistical problems that hinder a straightforward test similar to Douglas.
They estimated the potential error that may have resulted from each step of Douglas‘s
procedure and were able to rationalize his findings. However, Miller and Scholes‘s
explanation does not by itself provide positive evidence that the CAPM is valid. Later
studies, most notably Black, Jensen and Scholes (1972) and Fama and MacBeth
(1973) used procedures designed to address the various econometric problems. The
most important of these was to test the CAPM using logically constructed portfolios
to diminish the statistical noise resulting from firm specific risk. These efforts were
also not sufficient to establish the validity of the CAPM.
While all these accumulated evidence against the CAPM remained largely within the
ivory towers of academia, Roll‘s (1977) study titled as ―A Critique of Capital Asset
Pricing Tests‖ shook the practitioner world as well. Roll argued that since the true
market portfolio can never be observed, the CAPM is necessary untreatable. The
publicity of the new classic Roll‘s critique resulted in popular articles such as ―Is Beta
Dead‖? that effectively showed the permeation of portfolio theory through the world
of finance. This is quite ironic since, although Roll is absolutely correct on theoretical
grounds, some tests suggest that the error introduced by using a broad market index as
proxy for the true, unobserved market portfolio is perhaps the lesser of the problems
involved in testing the CAPM.
2.4.4 Empirical studies of the CAPM and Different versions of CAPM
The capital asset pricing model (CAPM) of Sharpe (1964), Lintner (1965) and Black
(1966) has played a central role in finance theory and financial practice. According to
available evidence among the assets pricing models, CAPM is the most reliable model
to estimate the cost of equity capital. Graham and Harvey (2001) report that the
33
CAPM is the most popular model to estimate the cost of equity capital. Even though
CAPM a is popular model, its application issues such as the time varying nature of
beta addressed by researchers (Henry, Olekalns and Shields 2004; Henry, Olekalns
and Lakshman 2007; Henry 2009) is very dominant. Apart from that the applicability
of past returns for the projection of future returns and difficulty to determine the
market proxy in the real world the researchers were encouraged to find new versions
of CAPM that have emerged in the finance literature. Numerous studies show (see
Fama and French 1992; Jagannathan and Wang 1996; Strong and Xu 1997; Lettau
and Ludvigson 2001) that the standard CAPM using the stock market index as a proxy
for the market portfolio performing poorly in explaining cross-sectional stock returns
in both emerging and developed markets.
The recent studies by Harvey and Siddique (2000) and Dittmar (2002) highlight the
superior performance of the three-moment CAPM. The three moment CAPM assume
that any rational investor chooses its portfolio using only the first three moments of
securities return distribution and four-moment CAPM (KCAPM) relative to the
standard CAPM in US stock returns. Dittmar finds that the best performance is by a
conditional version of the four-moment CAPM. Incorporating a proxy for human
capital in the market portfolio as in Jagannathan and Wang (1996) plays a critical role
in the superior performance of the four-moment CAPM. Dittmar (2002) also finds
that the conditional four-moment CAPM performs well relative to the Fama and
French (1993), model even though the factors in the four moments CAPM are
motivated from the theory.
2.4.5 Empirical Contradiction of the CAPM
A large number of studies have previously been conducted by various researchers on
CAPM, apart from the above mentioned studies. A prominent study of Nicolaas
(1999) investigated the nature of the time-variation in betas which indicates that beta
is not constant through time. In this study they focus on the validity of CAPM when
the beta is time varying. The beta was estimated using different methods of
regressions such as recursive regressions, rolling regressions and Kalman Filter. They
conclude that beta is not constant through time. They mainly argued that beta of any
34
security should be changed when the capital structure of the firm varies from time to
time. The main implication of this work was that CAPM does not give proper results
under this condition. Nicolas‘s findings empirically invalidated the CAPM on
empirical ground.
Another extensive work of Davis (1997) presents a method for solving the multiform
stochastic growth model Brock by (2001) whose asset pricing model forms an
intertemporal general equilibrium theory of capital asset pricing. A number of issues
in financial economics can be addressed with the solution to this dynamic model.
They have found that the market portfolio is a mean-variance efficient in a dynamic
context.
Bossaerts, Fine and Ledyard (2002) examined the CAPM in thin experimental
financial markets. This study was based on the Chicago market. Their argument was
in support of CAPM and the finding was that the CAPM principles appear at work
even when markets are thin. In testing the original CAPM, Ho-Chan and Huang
(2000) suggests to allow the beta risk coming from two different regimes namely, a
high-risk regime and low-risk regime. He finds that two regime assumptions are
accepted and CAPM is consistent with the data in the low risk state but is inconsistent
with the data high risk state. This was further investigated by Huang (2003) who
concluded that betas are unstable over time and the data may be consistent with
CAPM in one regime, but inconsistent in the other regime.
A study conducted by Gonzalez (2001) tested the CAPM performance in Venezuela
market for the period 1992-1998 and concluded that CAPM cannot be used to predict
assets returns in the Venezuela market. They have found that CAPM assumptions do
not apply in the Venezuela and invalidate the CAPM in predicting the cross sectional
variation of stock returns in the Venezuela market. However, they have found two
important results: first, the model appears to be linear and second, there are other
factors that influence Stock returns. They recommended the extension of the CAPM
and to design other multifactor linear models that takes into consideration other
economy-related variables.
35
In the time being the credibility of CAPM gradually declined due to the subsequent
contradictory findings of the studies stated above. Roll in 1977 found devastating
findings to the CAPM and highly criticized the validity of CAPM beta. Roll‘s
argument is comprehensively explained in the next section.
2.4.6 Roll’s Critique of Tests of the CAPM
Richard Roll in 1977 and 1978 wrote papers in which he criticized (1) empirical
testing of the CAPM (2) the use of beta as a risk measure and (3) measures of
portfolio performance employing the security market line as a benchmark. The three
parts of the paper were later published separately. Here only part 1 will be discussed,
as part 2 and 3 are essentially the same arguments. Roll‘s critique of test of the CAPM
can be divided into two parts. First, he claims that the results of tests like those of BJS
and FM (will be discussed in details subsequently) are tautological. That is, it is
probable that one would obtain results no matter how stocks were priced in relation to
risk in the real world. If that is true we have learned little or nothing about the
structure of stock prices from these tests, and CAPM has never really been tested.
Therefore, the current study attempts to test the CAPM under high and low volatile
situations, in both Sri Lankan and US markets. This is a novel work that separately
tests the model during crisis and non crisis periods of both stock markets. Testing the
Model under crisis situation is particularly important because when there is an
economic crisis the market fundamentals such as inflation, interest rates, money
supply, exchange rates etc. will change dramatically. In the history of capital markets
in the world, crises have occurred from time to time in different degrees in both
developed and emerging markets.
A large number of studies have attempted to discover a better fit model than CAPM
by introducing new variables. Section 2.4 deals with the post CAPM development and
the reliability of post CAPM findings in the better prediction of variation of stock
returns.
36
2.5 Post CAPM and Pre-FF3F Development of Literature
It was evident from the previous discussions that the popular CAPM which was
developed in 1960s was the widely accepted model among professionals and others.
However, its acceptance was short lived as researchers found other factors, in addition
to the market beta of the CAPM in determining the average stock returns in the capital
markets. These factors are known as the CAPM anomalies in the finance literature.
Post CAPM developments in the literature clearly damage the popularity of the
CAPM and researchers started to investigate other characteristics of the stock returns
in 1970s and 1980s. This section presents a detailed analysis of anomalies until the
discovery of FF3F in 1990s.
2.5.1 January effect
This study will not be complete without testing the January effect in addition to the
CAPM and FF3F. Because January effect has close links with these two models, both
FF3F and January effect are considered as CAPM anomalies. It is also interesting and
timely important to fill the void in the literature to test the presence of January effect
in the six portfolios formed as big and small in these two markets. Another important
fact is that these two markets are in two streams; namely emerging market (CSE) and
developed markets (US). Therefore, the findings of the test can be generalized
separately for these two markets, giving due recognition to each model. In addition,
research evidences has revealed that small firms generate higher returns than big firms
during January in most of the market in the world. Currently researchers are interested
in emerging markets and they have started to look for more focused studies such as
stock market anomalies.
The anomaly of January effect historically emerged with the landmark discovery of
of Keim (1983) who has conducted a study on monthly seasonality by using data on
shares traded on NYSE and AMEX for the period from 1963 to 1979 and reported
that significantly higher returns are observed for the Month of January than other
months. And also they found that over 50% of returns have occurred during the first
week of January. His study has also documented that the January effect is extensively
higher for small firms and firms with low stock prices. This study will immensely
37
reshape the study of Keim (1983) as it applies six small and big portfolios for testing
the January effect in the US market. These tests guarantee that this is a comprehensive
study compared to the previous studies of this nature.
This study attempts to further investigate modalities of these phenomena by testing
the January effect for Small Low (SL), Small Medium (SM), Small High (SH), Big
Low (BL), Big Medium (BM) and Big High (BH) portfolios.9 Thus, the results will
give widespread information about the firms in these portfolios for concerned parties
like fund managers. The FF3F will be tested along with the January returns, taking
weekly data for long period particularly in the US (from 1964 -2008). This
empirically extended work also attempts to measure the responses of FF3F to January
effect. The outcome of the test very widely describes the return patterns of small and
big portfolios in January and the responses of stock prices to factors such as tax lost
selling hypothesis.
It is considered that an anomaly inconsistent with the concept of market efficiency in
financial market is the January effect. The January or turn of the year effect refers to
unusually high returns earned by the common stocks of small firms, beginning on the
last trading day of December and continuing in to January, with the effect becoming
less pronounced as the month progresses. The researchers who investigated on capital
market seasonality have discovered higher returns in January compared to other
months in several markets, particularly in U.S markets.
Early Evidence on January effect
The January effect first mentioned by Wachtel (1942) is more particular for small
capitalization companies. A more formal investigation is due to Rozeff and Kinney
(1976). In addition, Gultekin and Gultekin (1983) provide evidence in support of the
January effect for the U.S. and other industrialized countries. More recently,
Aggrawal and Tandon (1994) investigated monthly anomalies in eighteen countries,
9 These will be discussed in detail in Chapter 3.
38
other than the U.S. Some of the important studies are Rozeff and Kinney (1976), Roll
(1983) and Lakonishok and Smidt (1984) who reported on the January effect in
corporate bond market. Wilson and Jones (1990) found the January effect to be
prevalent in the commercial paper market.
Previous studies in international finance indicate that the January effect extends to the
market for the U.S dollar. Angrist and Stanley (1991) notes higher returns in January
of every year for the period of 1980 through 1989, except in 1986 and 1987.
Reinganum (1983) documented the presence of January effect in the market for the
U.S dollar over a longer sample period of 1975-1990, and during strong dollar sub-
periods of 1981 through June, 1985 and 1989. They also found higher returns in
January for each of the years 1977, 1979, 1988 and 1989. The other popular studies of
(Keim 1983; Roll 1983) have found that a significant portion of the size premium to
small firms occurs in January. Brown and Donald (1983) examined the monthly
seasonal patterns of all the industrial firms listed on the Australian Stock Exchange
for the period from 1958 to 1979 and found high average returns in December and
January.
The January effect is one of the mostly debated anomalies in finance literature and it
is recognized as the most common anomaly among other calendar anomalies such as
day of week effect, holiday effect etc.
Main Causes of January Effect
Another explanation is that the January effect is caused by portfolio managers
engaging in window dressing at year end. Selling of losing and risky stocks and
holding instead cash blue chip stocks to mark yearend portfolios appear more
conservative. The other motive of portfolio managers is locking in their bonuses
which are typically based on the rate of returns achieved during the year as at the
beginning of the year portfolio managers utilize the allocated funds. If portfolios
produce satisfactory returns, during the year many managers will be inclined to lock
in order to secure their annual bonuses by reducing the risk profile of their portfolios.
As a new financial year begins in January the cycle starts all over again as managers
39
move funds back into stocks. These evidences will also be dominant factors for the
January effect in most of the markets.
In this study the existence of January effect in the Sri Lankan market and US market
will be examined. Here the test is carried out with the portfolios formed as big and
small. This approach is different from other previous studies in several ways; (1 )
testing of January effect for six portfolios formed as big and small based on size and
book-to-market ratio (2) use of weekly excess returns for the cross sectional
regressions and (3) most recent data is applied in both markets. Thus, the main
objective of this extended work is to re-investigate the January effect in US market by
applying the Fama and French portfolios and extend the work to Sri Lankan emerging
market to uncover January effect in the Colombo Stock Exchange. Hence, this
research further extends its analysis to examine the existence of the January effect
during the period from 1964 to 2008 in the US market. The methods used in this study
are methodologically different from the previous studies such as Drew, Naughton and
Veeraraghavan (2003) who added a dummy variable, which takes a value of 1 in
January, in the three factor model and this study tests the effect by running separate
regression tests for January months‘ data. By doing so, a comparison can be made
between January and other period (months) in the three factor model.
2.5.2 Size effect
The size effect was one of the first discovered anomalies of the CAPM and it is well
documented in historical academic literature. The size effect literature became
dominant in the field of finance in 1980s. The main investigators include, Banz
(1981) Keim (1983) and Reinganum (1982). These studies find that small market
capitalization stocks tend to outperform large capitalization stocks after adjusting for
market risk factors. In the landmark paper Chan and Hsieh (1985) examine the
behavior of size effect in the context of Ross‘ 1976 APT model using Chen, Roll and
Ross (1986) risk factors.
Several researchers have given numerous reasons for the anomalous behavior of
stock prices due to size effect. Roll (1983) conjectures that the size effect may be a
statistical artifact of improperly measured risk. In an important study of Scholes and
40
Williams (1977) it is stated that non-synchronous trading of securities imparts a
downward bias to the estimated beta when the underline security trades infrequently.
Similarly, a study undertaken by Dimson (1979) suggests that trading infrequency
biases beta estimates and predicts a downwards bias for infrequently traded shares and
an upward bias for frequently traded shares. Closely following the work of Scholes
and Williams (1977) Reinganum (1982) and Dimson (1979), interesting findings were
emerged by Keim (1983). First, there is no distinguishable relation between the OLS
estimates of beta and firm size measured by market value of equity. Second, although
the Scholes and Williams beta estimates for smaller firms that are generally larger
than the corresponding OLS estimates, there is still is no distinct ordering of beta in
line with the firm size. Third, the Dimson beta estimate for the portfolio of smallest
firms is significantly higher than the largest firm portfolio beta and there is a near
monotone declining relation between firm size and Dimson beta.
The above evidences suggest that the size anomaly impairs the credibility of the
CAPM. Even though CAPM was well accepted in 1960s, its reliability gradually
declined in 1980s with the findings of the size effect in stock returns. Apart from
these studies in late 1980s, researcher looked for the other risk factors that determine
the stock price.
2.5.3 Momentum effect
There are significant volumes of studies about the anomaly of momentum effect in the
historical fiancé literature. Many investment advisors and other researchers believe
that momentum strategies yield significant profit for the investors. The momentum
effect first investigated by Jegadeesh and Titman (1993) examined a variety of
momentum strategies. They demonstrate that buying the well performing portfolios of
NYSE and AMEX stocks and selling the low performing portfolios produce
significant positive abnormal returns. In a subsequent study, Jegadeesh and Titman
(2001) further investigated the work of 1993 and conducted various explanations to
their previous study. Interestingly they found similar results in 2001 even after eight
years from their original work and confirm that the momentum profits are not purely
due to the data snooping. Conrad and Kaul (1998) argues that momentum profits arise
41
because of cross-sectional differences in expected returns, rather than time series
return pattern. Hong and Stein (1999), present behavioral models which suggest that
the post holding period returns of momentum portfolio should be negative. The
reliability of the CAPM further inspired the work of Jegadeesh and Titman who
unearthed the momentum effect.
2.5.4 The Black, Jesnsen and Scholes Test (1972)
The study of Black, Jensen, and Scholes (BJS) does not directly test the prediction
that the market portfolio is on the efficient set like in CAPM and portfolio theory.
They concentrate instead, on the security market line. It is a well known fact that if
the market portfolio is efficient, it follows automatically that a liner positive sloped
the relationship exists between betas and expected rate of return. If investors can
borrow and lend at a risk-free rate, it also follows that a zero stock or portfolio can be
expected to produce a return equal to the risk-free rate. The empirical test of BJS is
designed to test these properties of the security market line. BJS restrict their initial
sample to all stocks traded on the NYSE during the period 1926 through 1965. They
start their study with the exchange (NYSE) throughout this period, using as a market
index an equally weighed portfolio of all stocks on the NYSE. Nest they rank the
stocks on the basis of beta and formed 10 portfolios with 10 percent of the stocks with
the highest betas into portfolio 1 and so on.
Then, they compute the rates of return to each of the portfolios in each of the 12
months of 1931. At the end of this year, they again compute the betas for every stock
on the exchange for the period 1927 through 1931 and they reform the 10 portfolios.
BJS repeat this process each year, 1931 through 1965, obtaining a series of monthly
rates of return for each of the 10 portfolios. They now attempt to estimate the
expected rates of return and beta factors for each of the portfolios by taking sample
estimates from the rates of return.
The sample estimates of the expected value are of course the arithmetic mean of
return. This is the unbiased estimator of the expected rate of return at the beginning of
each of portfolio returns to their market index, while they take sample estimates for
the overall period 1931 through 1965.
42
2.5.5 Fama–Macbeth Study (1974)
Fama and MacBeth (1974) also direct their attention to the properties of the security
market line. Their study, however, fundamentally differs from that of BJS in that they
attempt to predict the future rates of return of portfolios on the basis of risk variables
estimated in previous periods. Fama and MacBeth examine the time varying nature of
CAPM beta.
Their procedure and database is the same as that of BJS. They also use the same index
of the market portfolio, an equally weighted portfolio of all stocks on the NYSE. They
begin by computing the beta factor for every stock that was listed on the NYSE in the
period 1926 through 1929. They then rank the stocks by beta and form 20 portfolios
in the same procedure as BJS. Thereafter, they estimate the beta of each portfolio by
relating monthly returns to their market index in the period 1930 to 1934. At the end
of 1934 they have an estimate of beta factor for each of the portfolios and they use
these betas to predict the portfolio returns in the subsequent months of the period
1935 through 1938. For each of the months they relate the monthly returns on the
portfolios to the betas to obtain monthly estimates of the market line.
To determine whether the security market line exhibits any evidence of nonlinearity,
FM now add on an additional term to the relationship, the square of the beta factor.
The relationship is now three-dimensional with the returns to the portfolios on one
axis and with beta and square on the other two.
The CAPM also predicts that beta or systematic risk is the only determinant of
expected security returns. Residual variance is unimportant in determining the price
and expected rate of return of a stock as portfolio investors can diversify it away. FM
tested this prediction of CAPM by including a residual variance term in the
relationship. The 20 portfolios are equally weighted and include a large number of
stocks, so the residual variance for each portfolio should be relatively small.
However, to determine whether the residual variance of a stock affects its price and
therefore, its parent portfolio‘s expected rate of return, FM included in the
relationship is the average residual variance of the stocks in each portfolio.
43
At the end of this period, they calculate fresh estimates of the beta coefficients for the
portfolios by repeating the entire process. That is, they estimate stock betas in the
period 1930 through 1933. They then form portfolios and estimate portfolio betas in
the period 1934 through 1938. The sample estimate of the expected value is the
arithmetic mean rate of return. This is the unbiased estimator of the expected rate of
return at the beginning of each individual month. They estimate the beta of each
portfolio by relating the portfolio returns to their market index while they take
estimates for the overall period 1931 through 1965.
2.6 Emergence of Fama and French three factor model
The short comings and some methodological issues documented on the CAPM and
other anomalies led to the emergence of the FF3F historically. As explained in the
above section, several papers have severely criticized the single factor as the whole
determinant of average return of stock prices. Roll‘s Critique is one of prominent
shortcomings of the CAPM that has emerged historically. The period 1980s was the
crucial time for the CAPM, as it was the period with the most significant CAPM
anomalies uncovered by researchers.
Fama and French (1992) introduced two other factors; namely market equity and
book-equity to market equity (size and BE/ME) that can explain the cross section of
stock returns, in addition to the CAPM. They found that the three factors of the model
explain 95% of the variation of stock returns, while it was only 70% of explanatory
power along with the CAPM beta. Furthermore, advancing their findings in 1992
Fama and French (1993) confirm that portfolios constructed to mimic risk factors
related to size and BE/ME add substantially to the variation of stock returns
explained by a market portfolio. As their model comprises of three factors it was
popularly known as ―Three Factor Model.‖ These risk factors will be discussed in
detail comprehensively in Section 3.3 in Chapter 3.
The rest of this section is organized into five subsections. The first subsection
highlights the properties of the FF3F in the real market place. The second explains the
salient features of the risk factors of the FF3F. The empirical studies that use the FF3F
44
are examined in the third which is the Subsection 2.6.3. The fourth examines the
differences and the similarities of the CAPM and the FF3F. The last subsection briefs
on other multi factor models, with special focus on Arbitrage Pricing Model (APT).
2.6.1 Properties of the FF3F
As explained above, in addition to the CAPM, beta the FF3F comprises of two other
factors—size and BE/ME. The size factor compares the weighted average market
value of the stock in a portfolio to the weighted average market value of stocks in the
markets. The BE/ME factor compares the amount of value exposure in relation to the
market. Value stocks are companies that yield low earnings growth rates, high
dividends, and high book value. The FF3F measures the performance of high BE/ME
stocks against low BE/ME stocks.
2.6.2 Risk Proxies of the model
In this subsection the discussion is focused on the risk proxies of the FF3F. Here only
SMB and HML are explained as the market factor is common to the CAPM and
FF3F. Construction of the factors and the steps involved in the process will be
discussed in Chapter 3. Here, more attention is given to the theoretical and the
practical aspect of the two risk factors of the model.
In practice SMB factor represent size premium and SMB stands for Small minus Big.
This is designed to measure the additional returns the investors have historically
received by investing in stocks in companies with relatively small market
capitalization stocks. A positive SMB in a period indicates that small cap stock
outperformed large cap stock in that period.10
The other factor is HML which stands for High minus low constructed to measure the
value premium provided to investors for investing in companies with high-book-to
market value. A positive HML in a period indicates that value stocks outperformed
growth stock in that period. A negative HML in a given period indicates the growth
10 Period may be daily, weekly or monthly data.
45
stocks outperformed. In recent years the value strategy has generated considerable
interest among the fund managers. Value firms appear to earn much higher long-term
returns than those with low BE/ME firms.
2.6.3 Empirical studies of the model.
Alternative assets pricing models, another response to the poor performance of the
CAPM, has been the development of empirical factor models such as Fama and
French (1993) or Carhart (1997) where the factors capture different anomalies such as
size and book-to-market ratio. However, these models affected by the problem that
the factors are not motivated from theory.
Fama and French (1993) introduced a three-factor model in which factors include the
return on a broad stock index, the excess return on a portfolio of small stocks over a
portfolio of large stocks, and the excess return on a portfolio of high book-to-market
stocks over a portfolio of low book –to- market stocks. Carhart (1997) augmented the
model to include a portfolio of stocks with high returns over the past few months.
These models broadly capture the performance of stock portfolios grouped according
to these characteristics, with the partial exception of the smallest value stocks. The
interpretation of this evidence has received much attention by Simpson and
Ramchander (2008) in the literature and continues to be a subject of ample debate.
On the one hand, researchers argue that ME and BE/ME are company-specific
factors–which means that the risk associated with them might be eliminated through
diversification–rather than pervasive risk factors or state variables, and therefore the
observed significance of the FF3F factors is indicative of irrational investor behavior
or market inefficiencies (see for example Lakonishok, Shleifer and Vishny 1994; La
Porta 1996). Still others, such as Kothari, Shanken and Sloan and MacKinlay
(MacKinlay 1995), cite several reasons, (including sample selection biases, data
mining, beta estimation, and trading frictions), in downplaying the economic
importance of the FF3F factors.
2.6.4 CAPM and FF3F similarities and Differences
It is considered that CAPM has at least one strong advantage from the analysis‘s point
of view. The derivation of CAPM necessarily brings the reader through a discussion
46
of efficient sets of investments. The CAPM mainly describe the pricing of asset in
equilibrium. In the CAPM the expected return is expressed as a function of risk or
beta. The model bases on the idea that all risk affect the stock prices. Only systematic
risk is considered in determining the prices. Conversely, Fama and French argue that
size (SMB) and book-to-market ratio (HML) capture the cross sectional differences of
expected returns. Both models use risk factors as the predictors of the model. The
only difference of the FF3F is that it applies two more company fundamental factors,
in addition to the market factor. However, researchers and professionals still use
CAPM widely than FF3F in different occasions in practice.
2.6.5 CAPM, FF3F and Multi-Risk Factor Models
The asset pricing theory has been expanded to multiple sources of risk in important
studies by Ross (1976), Sharpe (1982), Merton (1973) and Long (1974). The intuition
of these models is that assets have exposures to various types of risk such as inflation
risk, business-cycle risk, interest rate risk, exchange rate risk, and default risk
regression are sometimes called factor loadings, risk sensitivities or risk exposures.
The models which attempt to capture these risk factors are known as multi-risk factor
models. However, the multi factor models maintain the basic idea of the CAPM
which suggests that the higher the exposure, the greater the expected return on the
asset. Some important studies on multifactor asset pricing formulations which tried to
explain average returns with average risk loadings are Roll and Ross (1980) and
Chen, Roll and Ross (1986). However, these studies assume that risk is constant, risk
premiums are constant and expected returns are constant.
Ferson and Harvey (1993) examined a model which uses multiple factors, but allows
all the parameters of the model shift through time. Ferson and Harvey in their study
titled ―The Risk and Predictability of International Asset Returns‖ extended the
dynamic factor model to an international setting. In ―predictable Risk and Returns in
Emerging Markets,‖ Harvey explores a similar formulation in emerging capital
markets.
Among the multi factor models, the Arbitrage Pricing Theory (APT) due to Ross
(1976) is very popular among researchers as it provides many advantages to them.
47
One important advantage of the APT is that it can handle multiple factors, while the
CAPM ignores them totally and as does the FF3F to some extent. The multi factor
model is probably more reflective of reality than single factor models. One cannot
actually build an optimal portfolio along with the APT. It is essential to list out the
factors and estimate the returns for exposure to risk for each factor. Some advocates
of the APT have said one should just estimate expected returns empirically. Sharpe
(1998) argues that is very dangerous because historic average returns can differ
monumentally from expected returns in empirical investigations. To address this issue
a factor model is needed to reduce the dimensions, whether it is a three- factor model
or a five-factor model or a 14 asset-class factor model, which is what we tend to use
in application. The APT says that if returns are generated by a factor model, then
without making any strong assumptions in addition to the model which is strong to
begin with, one cannot assign numeric values to the expected returns associated with
the factors. The CAPM goes further, putting some discipline and consistency into the
process of assigning expected returns.
There are many ways to build APT models. The arbitrary nature of the APT leaves
enormous room for creativity in implementation than CAPM and FF3F. Two equally
well-informed scholars working independently will not come up with similar
implications. In addition, structural models postulate some relationships between
specific variables. The variables can be macroeconomics, fundamental or market
related. All types of variables can be used in one model without any complication.
Practitioners tend to prefer the structural models, since these models allow them to
connect the factors with specific variables and therefore link their investment
experience and intuition to the model.
Finally, academics build APT models very frequently to test various hypotheses about
market efficiency, the efficacy of the CAPM, etc. and tend to prefer the purely
statistical models, since they can avoid putting their prejudgments into the model.
48
2.7 Economic Crises and Stock Market Crashes
Stock markets are considered as the first hit element of economic crises in any
economy. Due to the uncertainty created by the crisis environment there is a high
volatility in the stock markets in which crisis is directly affected. In a volatile
environment in the market the stock returns also show highly fluctuating patterns.
This irregular behavior in the returns directly affects the future predictions of stock
returns made with the pricing models.
Therefore, it is essentially beneficial to review the crises that have occurred in the
recent past in the main context of this analytical study. Apparently there is a close
relationship between the asset pricing volatility and the stock market crises. Thus, it is
vital to incorporate the previous literature relating to the market crises in the world,
with special focus on the US stock market and emerging stock markets. The rest of
the section deals with the explanation of the nature of the economic market crises and
the stock market crash. This section also describes the link between stock market
volatility and economic crises.
2.7.1 General overview of Economic Crisis and Stock Market Crashes
A stock market crash is a sudden dramatic decline of stock prices across a significant
cross section of a stock market. Crashes are driven by panic, as much as by
underlying economic factors. They often follow speculative stock market bubbles.
Stock market crashes are in fact a social phenomena, where external economic events
combines with crowd behavior and psychology in a positive feedback loop, where
selling by some market participants drives more market participants to sell. Generally
speaking, crashes usually occur under the following conditions.
A prolonged period of rising stock prices and excessive economic optimism, a market
where price to Earnings ratios exceed long-term averages, with the extensive use of
margin debt and leverage by market participants. There is no numerically specific
definition of a crash, but the term commonly applies to steep double-digit percentage
losses in a stock market index over a period of several days. Crashes are often
distinguished from bear markets by panic selling and abrupt, dramatic price declines.
49
Bear markets are period of decline stock market prices that are measured in month or
years. While crashes are often associated with bear markets, they do not necessarily
go hand in hand. The crash of 1987, for example, did not lead to a bear market.
Likewise, the Japanese Nikkei bear market of the 1990s occurred over several years
without any notable crashes. The term crisis is applied broadly to a variety of
situations in which some institutions or assets suddenly lose a large part of their value.
There are namely 4 types of crisis: first, banking crisis; secondly speculative bubbles
and crashes; thirdly international financial crisis; and fourthly wider economic crisis.
In the 19th
and early 20th
centuries, many financial crises were associated with
banking panics and many recessions coincided with these panics. Other situations that
are often called financial crisis include stock market crashes and the bursting of other
financial bubbles, currency crises and sovereign defaults.
Sort list of major financial crises:
1910- Shanghai rubber stock market crisis
1930s- The Great Depression - the largest and most important economic depression in
the 20th
century.
1973-oil crisis-oil prices soared, causing the 1973-1974 stock market crash.
1980s-Latin American debt crisis-beginning in Mexico
1987-Black Monday (1987)-the largest one-day percentage decline in stock market
history
1989-91-United States Savings and Loan crisis
1990s - Japanese asset pricing collapsed
1992-93-Black Wednesday speculative attacks on currencies in the European
Exchange Rate Mechanism
50
1994-95- 1994 economic crisis in Mexico –speculative attack and default on Mexican
debt
1997-98-1997 Asian Financial Crisis – devaluations and banking crisis across Asia
1999-2002- Argentine economic crisis- originated with the declining of GDP
2008- up to date- Subprime Mortgage Crisis in US.
Many economists have offered theories about how financial crises develop and how
they could be prevented. There is little consensus, however, and financial crises are
still a regular occurrence around the world.
2.7.2 Information effect on Crisis
Galbraith (2009) and Palma (1998) argue that the stock market was inherently
unstable and anything could have shattered the public‘s confidence. One of the major
causes of the crisis is the asymmetric information. The major barrier to the financial
system to perform its role is the asymmetric information, the fact that one party to a
financial contract does not have the same information as the other party, which results
in moral hazard and adverse selection problems.
Mishkin (1998), Mishkin and Schmidt-Hebbel (2001) defines a financial crisis to be a
non liner disruption to financial markets in which the asymmetric information
problems of adverse selection and morel hazard become much worse. Under these
conditions financial markets are no longer able to channel funds efficiently to those
who have the most productive investment opportunities. In most financial crises, the
key factor that causes asymmetric information problems to worsen and launch a
financial crisis is a deterioration of balance sheets, particularly those in the financial
sector. Presence of asymmetric information in a stock market directly affects the
pricing patterns of the stocks in the market. These differences in the behavioral
patterns of the stock prices in the stock market will largely influence the volatility of
stock prices traded in the stock exchange.
51
Thus, the predictions made with the assets pricing models such as CAPM and FF3F
will become invalid under a high volatile situation induced by the asymmetric
information in the market place. On the other hand, the assumptions made during the
construction of the above models will no longer be valid under market crisis situation.
For example, the CAPM applies in the markets with the assumption that an asset with
zero beta yields the risk free rate. But during high volatile situation there will be
higher standard deviation of stock returns which create high risky environment in the
stock market. If it is true there cannot be zero beta stocks in the market. Therefore, to
come to a universally valid conclusion, the models should be tested separately for
high and low volatile periods in the market. In other worlds the sample periods should
be taken as crisis and non crisis periods in the stock markets.
2.7.3 Historical Empirical Evidence of Market Crisis
The crisis literature has mostly focused on currency crisis and the U.S. stock market
crash of 1987, and examined issues related to the causes of crisis, price changes
surrounding the crisis, international market linkages, contagion, and changes in
benefits to international diversification. The U.S. stock market crash of October 1987
inspired several studies on assets pricing. Fama and French (1989) Roll (1989) seek
to explain the crash in term of shifts in fundamental factors, such as downward
revisions in expectations about global economic activity, or higher equilibrium
required returns. In contrast, Seyhun (1990) concludes, based on the behavior of
corporate insiders, that investor overreaction was an important part of the crash. His
evidence showed that, while the crash was a surprise to insiders, they bought stocks in
record numbers immediately after the crash, especially those stocks which had
declined the most, and these stocks had large positive returns in 1988. Van Norden
(1996) uses regime-switching regressions to conclude that the degree of prior market
overreactions explain subsequent U.S. stock market crashes for the period 1926-89.
The U.S. stock market crash inspired several studies on the international links
between stock markets. In early literature, Solnik (1974) showed that international
investments are beneficial for U.S. investors since correlations between U.S. and non-
U.S. markets are low. Bennett and Kelleher (1988) find that the transmission of stock
52
price volatility between markets was greater than normal during the crash, and that
periods of high daily volatility are associated with high correlations between markets.
Neumark, Tinsley and Tosini (1991) show that correlations between stock market
prices of different countries increase during times of extreme volatility and become
small or close to zero during more normal periods and suggest that transactions costs
may explain this pattern of asymmetric correlations.
There is a large array of literature on international currency crisis. One strand of this
literature seeks to develop early warning signals of exchange rate crisis. Masson
(1999) reviewed the results of selected studies on currency crisis and identified 103
crisis indicators. A second strand of the currency literature examines the issue of
currency contagion. The current study attempts to examine the behavior of the
portfolios sorted by market capitalization and BE/ME under the most recent crisis
periods. However, this study will not focus on the indicators of most recent market
crisis. It focuses on the stock price behavior and validity of the CAPM and FF3F as a
result of crisis indicators mentioned above.
2.7.4 Evidences on Volatility, Crisis and other Events
It is worthwhile to study some historical tests on the volatility of stock markets as the
stock market volatility and crises are occurring at the same time in the market place
in most of the situations. Historically, statistical literature on changes of variance
started with Hsu, Miller and Wichern (1974) who unearth this formulation as an
alternative to the Pareto distribution model stock returns. There are many works
aimed at identifying the point of change in a data set of independent random variables
(Hinkley 1971; Smith 1975; Menzefricke 1981).
Booth and Smith (1992) used the Bayes ratio to decide whether a series presents a
single change of variance at an unknown point. For example (1977; Hsu 1979; Hsu
1982) studied the detection of the variance shift at an unknown point in a sequence of
independent observations, focusing on the detection of points of change one at a time
because of the computational burden involved in looking for several points change
simultaneously. Worsley (1986) used maximum likelihood methods to test a change
in a mean for a sequence of independent exponential family random variables, to
53
estimate the change point and to give confidence regions. His work focused on
finding one change point at a time.
For autocorrelated, observations Hsu, Miller et al. (1974) studied an autoregressive
model of order one, having a sudden variance change at an unknown point. Abraham
and Abraham and Wei (1984) used a Baufays and Rasson (1985) and estimated the
variances and the points of change of maximum likelihood. Tsay (1988) discussed
autoregressive moving average models, allowing for outliers and variance changes
and proposed a scheme for finding the point of variance change of maximum
likelihood. According to Dayong, David and Marco (2005) several factors can be
attributed for the volatility change of stock markets. First, the prevailing regulation
rules are important for the volatility change. They further conclude that tight
regulation in the market leads to the decline of the volatility in the market. Secondly,
liquidity and the economic environments equally influence the volatility change in the
stock markets.
The link between volatility and crisis is a currently growing phenomenon in the area
of financial economic and in the contemporary business dialogue in the world.
Apparently it seems that there is a positive relationship between volatility and world
prominent crisis in the world economies. Some argue that social, political and
economic events cause the volatility in the stock markets. According to Aggarwal,
Inclan and Ricardo (1995) the high volatility of emerging markets is marked by
frequent sudden changes in variance. The periods with high volatility are found to be
associated with important events in each country, rather than global events. The
October 1987 crisis is the only global event in the past decade that significantly
increased volatility in several markets. Aggarwal‘s argument was re-confirmed by
Bekaert and Campbell (1997a) and (1997), who concludes that on average the
proportion of variance attributable to world factors is quite small for emerging
markets. Bailey and Chung (1995) find that important political events tend to be
associated with sudden change in volatility.
54
2.7.5 Main Causes of Volatility of Stock Returns
Various economic and firm specific factors are driving forces of stock market crisis.
There is also reason to believe that stock return volatility is related to the level of
economic activity prevailing in the economy. For example, if firms have large fixed
costs, net profits will fall faster than revenues if demand falls. This often called
operating leverage. Stock market volatility is related to the general health of the
economy. One interpretation of this evidence is that it is caused by financial leverage.
Stock prices are a leading indicator, so stock prices fall before and during recessions.
Thus, leverage increases during recessions, causing an increase in the volatility of
levered stocks. Apart from these factors there can be other factors such as systematic
(global oil pieces changes, inflation shocks etc.) and unsystematic (company specific
and sector specific factors) factors that influence the stock market volatility. Thus,
there is a close relationship between stock market volatility and economic crisis.
2.8 Patterns and gaps in the empirical literature
This section attempts to organize the empirical literature looked into so far in this
chapter in a bid to identify any gaps therein. This analysis involves looking into the
vast empirical literature which uses the CAPM and the FF3F, as well as empirical
literature on stock market crisis. Chapter 1 outlined that the present study is focused
on the testing of CAPM and FF3F under a market turmoil condition; therefore, the
present section is important to prove the originality of this thesis. This analysis of
literature is not meant to be exhaustive or representative. Instead, the attempted here
is to establish broad trends and patters in the literature using a very small sample of
papers.
Figure 2.5 demonstrates the analysis of the selected empirical studies on CAPM,
FF3F and crisis literature using a Venn diagram. This enables a clear identification of
interactions across these three strands of the literature. Obviously the interactions are
identified in the overlapping section in the diagram. The figure attempts to categorize
a sample of 42 studies selected randomly, but in way that both developed and
55
emerging market studies are included. The bold fonts represent the studies of
developed markets.
56
Figure 2.5: Analysis of empirical literature involving asset pricing and stock market crises. The
Bold fonts identify the developed market
Crisis Literature
CAPMFF3F
5 6 7 32 10 11
12 13 14
25 26 29
31 36
35 15 16
20 22 24
28 30 3334 27
1 2 3 8 9
17 18 19
38 23
1. Grout (2006)
2. Abdelghany (2005)
3. Lean (2007)
4. Fama (1989)
5. Groenewold (1999)
6. Gonzalez (2001)
7. Devis (1997)
8. Bartholdy (2005)
9. Bartholdy (2003)
10. Mackenzie (2000)
11. Bossaerts (2002)
12. Fletcher (2005)
13. Bossaerts (2002)
14. Gencay (2005)
15. Fuerst (2006)
16. Tai (2003)
17. Mullins (1982)
18. Chou (2010)
19. Carhart (1997)
20. Norden (1996)
21. Roll (1989)
22. Nimal (1997)
23. Fama and French (1996)
24. Fama and French (1992)
25. Ross (1977)
26. Keim (1986)
27. Fama (1993)
28. Fama (1995)
29. Jagannathan (1996)
30. Jensen (1997)
31. Nicolaas (1979)
32. Pereiro (2006)
33. Drew (2003)
34. Charitou (2004)
35. Iqbal (2007)
36. Samarakoon (1997)
37. Sehhum (1990)
38. Wai (2005)
39. Solnik (1974)
40. Bennett (1988)
41. Porter (2003)
42. Stiglitz (1990)
4 21 41
40 39 37
20 42
Current Study
57
In Figure 2.5 out of the 42 studies 26 are from developed markets, while the balance
(16 studies) is from emerging markets. 24 studies test the CAPM, out of which 15 are
for developed markets. Similarly 21 studies are about FF3F, out of which 8 are for
developed markets. The overlapping area (except the area of crisis literature) shows
10 studies focused on both models and 7 studies are in developed markets. The
studies available on crisis periods in stock markets are 8 and out of that 4 are related
to the developed markets. Among the previous studies reviewed by the investigator in
the context of this chapter, there were some studies that investigated both CAPM and
FF3F which is shown in the overlapping area of the diagrams that represent CAPM
and FF3F.
It can be noticed that a significant volume of empirical studies have been conducted
on the CAPM and the FF3, but none of these address the issue of the impact of stock
market crisis on the models. It is interesting to note that no single study on CAPM and
FF3F is found under the crisis setting in the empirical studies previously undertaken
by the researchers. The shaded area in Figure 2.5 is the literature gap identified in the
analysis in this section. The current study aims to fill this gap and straddles all three
study areas in the figure as pointed out by the arrow.
2.9 Summary and Conclusion
This chapter attempted to review and incorporate some important theories and
concepts that led to the emergence of so called (CAPM, FF3F) asset pricing models.
Among the literature that preceded the CAPM, the contribution made by Tobin (1958)
and Markowitz (1952) is pivotal for the development/emergence of the CAPM. The
CAPM itself is the outcome of the work of three eminent scholars—Sharpe (1964),
Lintner (1965), and Black (1972). However, as discussed in the chapter later on some
empirical studies started questioning the validity of the model in the 1970s when the
various CAPM anomalies were identified. The anomalies such as January effect, size
effect and momentum effect featured prominently in the 1980s. The chapter also
shows that questions about the validity of the CAPM have led to the emergence of
FF3F due to Fama and French (1993). A large volume of empirical work is available
for the CAPM and for the FF3F in developed and emerging markets. It is also
58
understood in the review of crisis literature that the world economic crises and stock
market crashes had a significant impact on the predictions made by these two models.
The analysis of empirical literature on CAPM, FF3F and stock market crises revealed
a gap which this work purports to fill.
59
Chapter 3
Data and Methodology
3.1 Introduction
Conducting stock market research in developing country contexts poses particular
challenges that researchers do not have to face in developed country contexts. As
illustrated in the previous chapters, a key contribution of this research is the way it
overcomes these challenges. The present chapter discusses, in detail, aspects of the
data and the methodology which provided useful solutions to these challenges.
The main focus of this work is using the popular CAPM and FF3F asset pricing
models in the Sri Lankan context. Therefore, any discussion of methodology would
have to discuss these models. In addition, the application of the FF3F to the CSE
makes it necessary to manually create multiple portfolios using price information of
stocks traded in the CSE. This is a long and arduous process as some of the data are
not in digital form or unavailable. Thus, much of the manual data processing backed
by innovative programming skills was necessary to make this possible. This chapter
elaborates on this process in detail.
Another key methodological distinction of this work is how it segmented the final
outcome of the applications of the models into crisis and non-crisis periods. This was
achieved by objectively identifying volatility thresholds and then defining periods
where volatility was high and low. The former was defined as crisis periods; the latter
as non-crisis periods. This distinction was made using Cumulative Sums of Squares
(CSS) method for the detection of changes in variance due to Inclan and Tiao (1994).
This chapter devotes much time for the application of the CSS test for the Sri Lankan
and the US market data as this information is critical to achieve the main aim of this
research.
The rest of this chapter is organized as follow. This section is followed by Section 3.2
which discusses the CAPM and issues related to its implementation. Section 3.3
derives the FF3F and examines various methodological issues of the model. Section
60
3.4 introduces the data used in this study. The penultimate section introduces the
mechanics of implementing Inclan and Tiao (1994) methods to identify the crisis
periods in Sri Lanka and the US. The final section summarizes the chapter and
provides some concluding remarks.
3.2 The Capital Assets Pricing Model (CAPM)
As explained in Chapter 2, the CAPM can be used to model the theoretical
relationship between risks and expected return of individual stocks or a portfolio of
stocks. The present work primarily uses it on a number of portfolios created for the
purpose of testing the FF3F. As both CAPM and FF3F have been applied to the same
portfolios within this work it can be used to compare predictive capacities of these
two models. As such it is important to understand the version of CAPM used herein.
This study applies the original CAPM developed by Sharpe, Linter and Black for the
six portfolios constructed here (Sharpe 1964; Lintner 1965; Black 1972). Application
of CAPM for the portfolios is consistent with researchers such as Blume (1970)Friend
and Blume (1973) and Black, Jensen and Scholes (1972) .The model used in this work
is:
fmpffp RRERRRE )( (3.1)
where, Rp, Rf and Rm are return on the portfolio, the risk free return and the market
return. In addition, βp is the systematic risk given by 2, mmp RRCov and E(.) is the
expectations operation.
The standard method of implementing (3.1) and estimating βp therein is to regress
historical returns of a portfolio in excess of the risk free rate (Rp-Rf) against the excess
return on the market (Rm-Rf). Therefore, to implement CAPM for the various
portfolios from Sri Lanka and the US, this thesis estimates the equation:
tptftmpptftp RRRR ,,,,, (3.2)
61
Where Rf,t for each country is approximated by the respective three month weekly
treasury bill rate and Rm,t is approximated by weekly returns in the CSE and the
NYSE. In addition, αp is the intercept and εp,t is the residual term of this model which
is assumed to have properties necessary to estimate the model using ordinary least
square (OLS) method.
This research organizes the results of OLS estimation of (3.2) according to whether
the portfolios consist of firms with high capitalization (big portfolio) or firms with
low capitalization (small portfolio) and whether the data relates to a crisis period or
not. Furthermore the result, particularly the estimated βp‘s is used herein to illustrate
the relative safety of the portfolios. In addition, the model estimates can be used to
construct a performance index (PI) for each of the portfolios considered here
introduced by Sharpe (1966). Chapters 4 and 5 present the results of this empirical
work for Sri Lanka and the US respectively.
The applicability or the relevance of the CAPM is tested here using statistical
significance of βp. This is done by using the following hypothesis test where Ho: β = 0
against H1: β ≠ 0.
3.3 The Fama and French 3 Factor (FF3F) Model
As explained in Chapter 2 FF3F is developed by Fama and French (1992) to capture
the factors that are not captured (size and BE/ME) by the CAPM. Thus, FF3F states
that the expected return on a risky portfolio in excess of the risk free rate is explained
by three factors: (i) the excess return on the market portfolio (MKT), (ii) the
difference between the return on a portfolio covering small-size stocks and the return
on a portfolio covering large-size stocks, commonly referred to as SMB (small minus
big); and (iii) the difference between the return on a portfolio of high BE/ME stocks
and the return on a portfolio of low BE/ME stocks, commonly referred to as HML
(high minus low). Thus, according to FF3F the expected excess return on a
portfolio p can be written as:
)()()( HMLEhSMBEsMKTRRE pptpfP (3.3)
62
The time series implementation of the above model is (Fama and French 1996: 56):
tptptptpptftp HMLhSMBsMKTRR ,,, (3.4)
Where αp, βp, ps and ph are the estimated coefficients and tp, is an error term
satisfying all the conditions necessary for the OLS estimation of the equation. Notice
that the model in (3.2) is nested within (3.4). This nested nature of the two models
mean that the condition sp=hp=0 if satisfied for (3.4) would imply that the CAPM
specification fits the data better than the FF3F specification. Thus a main hypothesis
tested using the FF3F estimation in this work is H0: sp=hp=0 against H1: sp≠0 or hp≠0.
Apart from the main test of FF3F this study additionally tests two things; first, the
explanatory power of SMB and HML in the model for the crisis and non crisis
periods. The second is the testing sensitivity of the model to January seasonal effect.
3.4 Data preparation
The previous two sections, while introducing the empirical models used in this work,
also highlighted the important part played by the weekly returns data on the six
portfolios. The formation of these portfolios from scratch, i.e. from weekly stock
prices of constituent listed companies, is a key contribution of this work. The present
section, therefore, outlines the important steps in the formation of these weekly
portfolio returns. The processes involved in the formation of portfolios are identical
for Sri Lanka and the US. The only difference being that for Sri Lanka the process,
including all the steps, had to be mostly manually implemented. In the rest of this
section the portfolio preparation is organized in two subsections: one explaining the
generic data preparation steps and the other looking into the peculiarities encountered
in the case of Sri Lanka arising primarily out of the manual nature of the work. In
addition, the section also looks at the creation of two new variables (factors) from the
six portfolios. These two variables are factors to be used in the implementation of the
FF3F.
63
3.4.1 The generic description of portfolio creation
This subsection identifies the steps that were followed when preparing the weekly
returns of the six portfolios. The steps discussed here are commonly followed for the
case of Sri Lanka, as well as for the US. Here we identify two sets of procedures. The
first deals with the selection of stocks to various portfolios. The second set of
procedures deal with calculating weekly returns for these portfolios.
Procedure 1
Step 1.1: Obtain market capitalization data for all listed stocks in the respective
market for a selected year.
Step 1.2: Sort the stocks according to market capitalization and groups them into
categories of small and big capitalizations. This is done by first sorting and then
dividing the companies at the median capitalization value. The resulting two groups
are as at end of June, which is when the year end financial statements can be expected
to be available to the public.
Step 1.3: Calculate BE/ME ratio for all companies for the year. The data, especially
for the calculation of the book value, can be obtained from the annual published
financial statements. The book value is calculated as book value of shareholders
equity, plus balance sheet differed taxes and investment tax credit (if available),
minus book value of preferred stocks. And the market value is taken as at the date of
publication of annual reports. Screen out all negative BE/ME companies before
moving on to the next step (Fama and French 1996: 58).
Step 1.4: Sort each of the big and small portfolios into three sub portfolios according
to the BE/ME ratios. The subgroups are based on the 30th
and 70th
percentile of the
stock market. This yields six size-BE/ME portfolios, identified using the acronyms
SL, SM, SH, BL, BM, and BH. For instance SL stands for ―[S]mall capitalized stocks
with [L]ow BE/ME ratio‖.
64
Step 1.5: Repeat Steps 1.1 through Step 1.4 for all years.
The above stated Procedure 1 generates a database of stocks to be represented each
year for all of the six portfolios. After accomplishing this it is necessary to calculate
the weekly returns for these portfolios by following Procedure 2.
Procedure 2
Step 2.1: Select a year.
Step 2.2: Select one of the portfolios in the selected year and obtained weekly price
data for them (portfolios) during the selected year (Step 2.1)
Step 2.3: Calculate weekly stock returns from the price data.
Step 2.4: Calculate value weighted return for the selected portfolio (Step 2.2) for the
selected year (Step 2.1).
Step 2.5: Compute the weekly return series for the selected year (Step 2.1) for all of
the six portfolios by repeating Step 2.2 through Step 2.4.
Step 2.6: Repeat Step 2.1 through Step 2.5 and generate the weekly return series for
the six portfolios for the remaining years.
3.4.2 The formation of the FF3F portfolios: the Sri Lankan peculiarities
While the steps outlined in the previous subsection was adhered to in both stock
markets studied here, the research had to manually implement all eleven steps for the
Sri Lankan case; for the US the weekly data for the six portfolios was available to
download. This subsection outlines the peculiarities encountered while implementing
the above steps for the CSE in Sri Lanka. The documentation of these peculiarities is
important not only for future research in Sri Lanka, but also for other emerging
markets in the world, as most of the material covered here and highlighted as
problematic for research in the CSE, are also commonly found in the wider realm of
global emerging markets.
65
Steps 1.1 and 1.2 were straight forward to implement as market capitalization data
that was available from the CD of data library issued by the CSE (hereinafter CSE
database). However, there were some complications arising from new listings, de-
listings, and re-listing of companies. This is probably more problematic in the CSE
because these dynamics and changes in market composition are large, relative to the
size of the market. The resulting year-on-year change in the total number of
companies in the CSE is quite large. Additionally, this is also reflected in the
composition of the portfolios. For instance, a company what was small-cap in one
year could appear in the big-cap category in the next year.
Step 1.3 where the BE/ME ratios were calculated for all the companies was
particularly challenging because the book equity or the book value is not given in
digital form in the CSE database. Instead, the relevant information has to be manually
extracted from the Handbook of Listed Companies published by the CSE and used to
calculate the BE values. The researcher used the handbook for 2008 to obtain
necessary data. The book values were calculated manually for all the companies in the
CSE for 10 years. This task was made even more difficult by inconsistencies,
omissions, errors, etc. in reporting in the handbook. Specific issues included
unreported capital structure, inaccuracy of reserve recognition and unclear reporting
of differed taxes and preferred dividends. These issues were solved by referring to
company annual reports.
The next problem in implementing Step 1.3 for Sri Lanka was matching the book
equity (BE) with the corresponding market equity (ME) to calculate BE/ME ratios for
the companies. This was a problem because the two came from two sources: book
equity as explained earlier came from the Handbook, whereas the market equity came
from the CSE database. This meant that the company codes/names were either
differently written across the sources or not available at all. For instance, the company
name ―ACME‖ in the CSE database appeared as ―ACME PRINTING &
PACKAGING LTD‖ in the Handbook. Thus, matching the book equity of a company
for the particular year with the corresponding market equity could not be achieved
easily using the available packages; for example, MS Excel. And the alternative of
doing this manually for hundreds of companies for 10 years was not feasible and was
66
highly prone to human errors. Therefore, a Visual Basic (VB) program attached in
Appendix C was used for this purpose. The program basically aligned the ME values
and BE values for all companies in a given year. After repeating it for all years it
yielded the companies to be included in each of the six portfolios for each of the ten
year.
The calculation of portfolio returns as a value weighted average of weekly company
returns in the portfolios and the case of CSE was difficult for two reasons. Firstly, the
CSE database had only monthly and daily prices at the company level, but not weekly
prices. Thus the researcher had to either prepare weekly data out of the daily data or
look for another source where the weekly data was available. The calculation from
daily data was difficult to achieve because of the issue of holidays (Sri Lanka had a
notoriously high number of public holidays in some years exceeding 33). Thus,
investigator opted to download the company level weekly price data from the
Metastock data base maintained by a UK based firm (http://www.equis.com/).
Ultimately weekly data was obtained spending about seven days (it took 3-5 minutes
to download data of one company for a year) to download data of nearly 240
companies from 1999 to 2008.
3.4.3 The creation or generation of data for additional risk factors
The FF3F‘s main contention is that in addition to the market factor, there are other
risk factors that determine pricing. The model as applied here looks at two such
factors acronymed SMB (Small Minus Big) and HML (High Minus Low). This
research used the method commonly used in the literature to calculate these from the
six portfolio return series calculated in Subsection 3.4.2. For instance, SMB is the
difference, each week, between the average of the returns on the three small stock
portfolios and the average of the returns on the three big-stock portfolios.
SMB = 1/3 (SL + SM + SH) – 1/3 (BL + BM + BH) (3.5)
HML is the difference between the average returns of the returns on the two high-
BE/ME portfolios and the average of the returns on the two low-BE/ME portfolios.
HML = 1/2 (SL + BL) – 1/2 (SH + BH) (3.6)
67
3.5 The Data
This section presents the time series plots and the time series properties of the weekly
data used in this work. The various steps involved in the preparation of this data were
explained in the previous section. Understanding time series properties of the data is
an essential first step before venturing to run regressions based on this data. This is
done firstly by examining the time series plots of the main series which reveals certain
properties that can be picked up visually. The plots for the six portfolios and the
market in each of the countries are included here. However, as such visual
explorations are not sufficient, the section attempts to examine basic distributional
properties of the data used here, including the portfolios as well as the factors
examined here. In addition, the section also analyses rudimentary statistics to
construct a basic understanding of interlinks among the key portfolios used here.
3.5.1 Sri Lankan stock market data
As previously mentioned, this research uses weekly price data for companies listed in
the CSE, annual book equity values for the same companies, weekly returns based on
the aggregate market index (ASPI) in the CSE and weekly data for 90 day treasury
bill rate from the CBSL, to calculate weekly data for six portfolios in line with the
FF3F. CBSL securities are known to have very low, even zero, default risk which
makes it a very good proxy for the risk free rate. For instance it is rated to be even
lower than the default risk of BRIC countries. 11
The six portfolio returns for Sri Lanka were generated for a ten year period starting
from the first week of 1999 to the last week of 2008. Section 3.4 described this
process in detail. Excess returns on the portfolios are then calculated as the
continuously compounded return in excess of the chosen proxy for the unobservable
riskless return which for the purpose of this study was the continuously compounded
return to a T-Bill position held for one week. The resulting excess return series for the
six portfolio are plotted in Figure 3.1. For clarity and comparison purposes the ASPI
11 Conference for University Lecturers -14 May 2011 Central Bank of Sri Lanka.
68
weekly market excess return series is also plotted there. The six FF3F portfolios are
identified in the figure as SL, SM, SH, BL, BM, and BH and the weekly market
returns as MKT. This is slightly different to the way the portfolio acronyms were first
introduced in Subsection 3.4.1, namely in the first encounter the acronyms were used
to denote portfolio returns and not excess returns.
Figure 3.1 illustrates that the FF3F portfolios for the CSE, as well as MKT, are all
stationary about the value of zero. As seen in these plots, the excess returns data
exhibit volatility clustering; large (small) shocks, of either sign tend to follow large
(small) shocks. This phenomenon in returns is associated with time varying
conditional variance first identified by Engle (1982). There is visual evidence that
periods of high volatility are not common across all portfolios. It is possible that this
is a phenomenon found only in developing country stock markets in anticipation
69
Figure 3.1: Weekly time series plots of excess return of the six portfolios and the market for the
CSE. Though only the bottom panel identifies the first week of each year in its horizontal axis the
axis can be used for other panels as well.
-1.5-1.0-0.50.00.51.01.52.0
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
SL
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
SM
-2.0-1.00.01.02.03.04.05.06.0
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
SH
-2.0-1.00.01.02.03.04.05.0
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
BL
-1.5-1.0-0.50.00.51.01.52.02.5
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
BM
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
BH
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
MK
T
70
of results in the next subsection for the US, these results are starkly different.
However, at least for the three small portfolios (SL, SM, and SH) there is some
correspondence in the periods where high volatility periods occur.
Though the visual method of examining data is a useful first step to understand the
data, it is not generally considered adequate for the purpose. That is why it is
important to look at summary statistics relating to the distributional properties of the
return series. These are tabulated in Table 3.1 which also includes statistics for the
FF3F factors used here. All of these data correspond to the period from the first week
in 1999 to the last week in 2008.
Table 3.1: Descriptive Statistics for the weekly data from the CSE (1999-2008).
variable Mean SE Mean St. Dev Skewness Kurtosis
SL 0.003 0.013 0.292 0.39 5.97
SM 0.010 0.013 0.281 0,26 5.12
SH 0.122 0.029 0.648 2.75 12.71
BL 0.045 0.022 0.488 3.46 20.23
BM 0.006 0.012 0.277 0.77 10.26
BH -0.010 0.018 0.400 1.76 13.26
MKT 0.001 0.001 0.036 0.66 6.53
SMB 6.98 0.685 14.8 0.74 1.01
HML -22.7 1.96 42.5 -1.26 -0.26
The means returns for all portfolios given in Table 3.1 are close to the value of zero.
In fact, based on the value of standard error of the mean (third column of the table) it
is clear that the means of these portfolio returns are not significantly different from
zero. This corroborates the information in Figure 3.1 which illustrates that the returns
do not consistently deviate from zero. This is evidence that the time series are
stationary. The two factors SMB and HML, on the other hand display means that are
significantly different from zero.
The standard deviations of the returns are close to zero in all the portfolios including
the market portfolio (fourth column in Table 3.1). However, much higher standard
deviations are reported for SMB and HML. Since these are two are based on extreme
71
portfolios representing high cap and low cap investment positions the standard
deviation is higher for SMB and HML due to grouping effect. But MKT represents
the entire market portfolio and due to off-setting effect the standard deviation for
MKT is lower in comparison. SMB and HML represent company fundamentals which
may also account for the large standard deviation of these factors. Market portfolio is
an index which represents the returns of all the stocks. The mean values represent the
average return of the portfolios and the standard deviation is the degree of the
riskiness of the portfolios. Interestingly the theoretical positive relationship between
the return (approximated by the means) and the risk (approximated by the standard
deviation) is upheld for the CSE portfolios. For example, the correlation coefficient
between the SE and the Mean of the 7 portfolios is 0.7752, which is significant at the
level of 5 percent level.
The skewness measures are all greater than zero except for HML. Positive skewness
means that the returns have right skewed distribution and most values are
concentrated on left of the mean, with extreme values to the right. It is possible that
the shifting of the series caused by the deduction of Rf,t may have a role in these
skewness figure. In addition to skewnes, the majority of portfolios also report kurtosis
values above 3 which confirm that these return portfolio returns have distributions
with fatter tails than the normal distribution. The skewness and kurtosis statistics in
combination confirm that the FF3F portfolios for the CSE are all not normally
distributed.
3.5.2 The US stock market data
This subsection describes the data from the US by plotting them and analyzing their
distributional properties similar to what was achieved for the Sri Lankan case in the
previous subsection. The weekly data for the period, starting the first week in 1985 to
the last week in 2007, are used here. Figure 3.2 plots the weekly portfolio returns for
the US. The time series plots confirm the presence of volatility clustering in the US
data. However in this figure, unlike in Figure 3.1, high and low volatility clusters are
synchronized across the portfolios. For instance, the high volatility episode noted for
72
Figure 3.2: Weekly time series plots of excess return of the six portfolios and the market for the
US. Though only the bottom panel identifies the first week of each year in its horizontal axis the
axis can be used for other panels as well.
-30
-20
-10
0
10
20
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007
SL
-20
-15
-10
-5
0
5
10
19851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007
SM
-20
-15
-10
-5
0
5
10
19851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007
SH
-15
-10
-5
0
5
10
19851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007
BL
-15
-10
-5
0
5
10
19851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007
BM
-15
-10
-5
0
5
10
15
19851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007
BH
-15
-10
-5
0
5
10
15
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007
MK
T
73
Table 3.2: Descriptive Statistics for the US stock market (1985-2007)
variable Mean SE Mean St. Dev Skewness Kurtosis
SL 0.073 0.079 2.74 -1.09 7.74
SM 0.182 0.058 2.01 -1.34 9.18
SH 0.201 0.056 1.96 -1.39 9.30
BL 0.155 0.064 2.24 -0.58 3.47
BM 0.161 0.056 1.97 -0.63 3.13
BH 0.167 0.055 1.91 -0.58 3.01
MKT 0.150 0.059 2.07 -0.82 5.23
SMB -0.009 0.0372 1.28 -0.42 5.74
HML 0.069 0.034 1.20 -0.54 5.86
MKT during 1999/2000 period is also seen in the rest of the portfolios. In fact even
the occasional outlier in the series seems to synchronize. It is tempting to identify this
as a developing country phenomenon as such synchronicity was not observed in the
figures for Sri Lanka. However, more research needs to be done before one comes to
such a conclusion. The rest of this subsection supplements this visual information
with distributions properties of the portfolios and the factors which will give more
insight into the characteristics and the properties of the portfolios. This information is
presented in Table 3.2.
The above table summarizes the descriptive statistics related to the US market data.
All the portfolios have yielded positive mean return for the period 1985 to 2007,
except SMB. Standard deviation of the portfolios represents the degree of risk in the
portfolio return. The portfolios SL, SM, BL can be considered as risky portfolios
(standard is higher) out of six portfolios. The skewness is negative for all the
portfolios which indicate that all the values are in the right side of the mean value.
None of the portfolio has zero or close to zero values for the skewness. All the values
of the kurtosis are also more than three. These results confirm that the assumption of
the normality is not true for the portfolios.
74
3.5.3 Interlinks among the six portfolios and the market portfolio
The discussion about the time series plots in Figure 3.1 and Figure 3.2 alluded to a
key distinction between the plots for Sri Lanka and the US: that the former had less
interlinks among its portfolios, compared to the latter. Here the matter is taken up for
discussion again but using a more formal measure of association; namely, the
correlation coefficients. Table 3.3 summarizes the correlation matrix of portfolios and
the market series for Sri Lanka in Panel A and for the US in Panel B.
Table 3.3 formalizes the pair-wise association among the portfolios. There is a clear
distinction between Panel A which summarizes Sri Lankan portfolios and Panel B
which summarizes the US. The main distinction that can be easily picked is that more
correlation coefficients, in fact all of them, are significant in the US than in Sri Lanka.
This confirms the tentative results of the time series plots which asserted that
cross-portfolio associations are less synchronous in Sri Lanka. Not only are the
correlations significant in Panel B, but they are quite high ranging from 0.675 to
0.973.
Ten out of the twenty-one (10/21) correlation coefficients are significantly different
from zero at 5 percent level in Panel A. It is interesting that while 3/3 correlation
coefficients are significant for the three small portfolios (SL, SM, and SH), only 1/3
are significant for the case of the big portfolios (BL, BM, and BH). Interestingly there
are 5/21 correlation coefficients in Sri Lanka that are negative. However, they are not
significantly different from zero. Another notable feature of the Sri Lankan market is
that SM, SH, BL, BM and BH are all negatively (albeit insignificantly) correlated
with the market portfolio. Several reasons can be attributable for this behavior. The
negative correlation of small and big portfolios with market suggests that the investors
react opposite to the movement of market portfolio. In other words, when the market
goes up, the portfolio returns go down significantly. Also, the company specific
factors may have positive correlation with these portfolios than market due to this
behavior.
75
Table 3.3: Pair-wise correlations for FF3F portfolios and the market
Panel A: Sri Lanka (1999-2008)
SL SM SH BL BM BH MKT
SL 1.000
SM 0.953* 1.000
SH 0.706* 0.786* 1.000
BL 0.572* 0.655* 0.828* 1.000
BM 0.953* 0.100* 0.787* 0.655* 1.000
BH 0.052 0.074 0.052 0.063 0.074 1.000
MKT 0.006 -0.006 -0.005 -0.004 -0.006 -0.026 1.000
Panel B: The US (1985-2007)
SL SM SH BL BM BH MKT
SL 1.000
SM 0.940* 1.000
SH 0.897* 0.969* 1.000
BL 0.795* 0.772* 0.732* 1.000
BM 0.722* 0.794* 0.783* 0.867* 1.000
BH 0.675* 0.756* 0.778* 0.785* 0.914* 1.000
MKT 0.854* 0.852* 0.822* 0.973* 0.923* 0.851* 1.000
*Significant at the 5 percent level
3.6 Crisis identification and Inclan and Tiao (1994)
Inclan and Tiao (1994) introduce and refine a test for the detection of multiple
changes in volatility of a time series. The test is identified as ICSS because it uses
Iterated Cumulative Sum of Squares method which is applied here for the CSE and
NYSE return series. This method is better than the other methods discussed in Section
2.7.4 of this thesis, as it can objectively identify the volatility breaks. The method
used data to reveal crisis periods without human intervention, which makes it an
objective approach. The most important merits of this method is that it can detect
change points systematically at given segment of a series and can use all the
information in the series to indicate the point of variance change. Though the test is
suitable for series with more than 200 observations it is not a problem for this study.
Thus as examined in Chapter 2, the changes in volatility in these series that were
76
identified using the ICSS, can be mapped onto changes from crisis periods to non-
crisis periods and vice versa.
This section is organized in three subsections. Section 3.2.1 presents the centered
cumulative sum squares function, Dk, and outlines the how ICSS uses it iteratively to
identify multiple volatility breaks. The remaining two subsections illustrate the result
from using ICSS on the CSE and NYSE return series.
3.6.1 Iterated Cumulative sum of squares (ICSS) Algorithm
The ICSS algorithm according to Inclan and Tiao (1994) compares well against
alternative approaches available in the literature to detect changes in volatility. Inclan
and Tiao (1994) make this comparison using monte carlo simulation methods which
revealed that ICSS algorithm was the best for analyzing long time series with
potentially multiple change points of variance in a series. Inclan and Tiao (1994: 913)
define a long time series as on with 200 or more observations. These conditions are
satisfied for the weekly return processes that are studied here. In other words, they are
long time series with potentially multiple volatility breaks.
The present research, for reasons stated above uses the ICSS to detect structural shifts
in volatility in weekly market returns series from the CSE and the NYSE. The ICSS
mainly asserts that the variable Dk is more sensitive to the changes in volatility than
the alternatives available. Here Dk is defined as
,,...,1 , TkT
k
C
CD
T
k
k (3.7)
0with 0 TDD where
k
t
tmk RC1
2
, and Rm,t is the market return series at week t.
CT is the sum of all returns in the series and K is defined as the value of the series that
maximum Dk is attained. Thus, the ICSS tracks the changes in Dk to detect changes in
volatility. The algorithm involves several iterative steps that are followed in this
research. These steps given below closely follow the explanation by Inclan and Tiao
(1994: 916). Here the notation 21 : ttR represents 2111 ,2,1,, ,...,,, tmtmtmtm RRRR , t1>t2
77
and notation 21 : ttRDk represents the range over which cumulative sum of squares
are sought.
Step 1. Let t1 = 1,
Step 2. Calculate TtRDk :1 . Let TtRk :* 1 be the point at which
TtRDkk :max 1 is obtained and let
TtRDtTTtM kTkt :2/1(max):( 111 1
If *:1 DTtM , where D* is the critical value, consider that there is a change point
at TtRk :* 1 and proceed to Step 2a. Critical value is D*.05 = 1.358. This was
visually tested.
Step 2a. Let t2= TtRk :* 1 . Evaluate 21 : ttRDk ; that is the centered cumulative
sum of squares are applied only to the beginning of the series up to t2. If
*: 21 DttM , then there will be a new point of change and repeat Step 2a until
*: 21 DttM , When this occurs it can be concluded that there is no evidence of
change in 21,....ttt and therefore the first point of change is 2tk first .
Step 2b. A similar search starting from the first change point found in step 1 , towards
the end of the series. Define a new value for t1: let .1]):[( 1
*
1 TtRkt Evaluate
TtRDk :1 , and repeat Step 2b until *:1 DTtM . Let 11 tK last
Step 2c. If ,arg elfirst KK then there is just one change point. The algorithm steps
there. If ,arg elfirst KK keep both values as possible change points and repeat steps 1
and 2 on the middle part of the series; that is 11 firstKt and T=Klast. Each time that
steps 1 and 2 are repeated then result can be one or two more points. Call NT the
number of change points found so far.
78
Step 3. If there are two or more possible change points, make sure they are in
increasing order. Let cp be the vector of all the possible change points, found so far.
Define the two extreme values 00 cp and .1 TcpNT Check each possible change
point by calculating .,....1 ]),:1[( 11 Tjjk NjcpcpRD If
*,):1( 11 Dcpcpm jj then keep the point; otherwise eliminate it. The retained
points constitute the multiple volatility change points in the Rm,t series.
3.6.2 The ICSS and the periods of crisis in the CSE
When the ICSS algorithm was applied to the CSE returns it revealed several structural
changes in the volatility of the series. The aim of this subsection is to flag the
importance of these breaks and how they could be used to discern information about
crisis periods that the CSE would have experienced. Here an interesting attempt at
linking the ―objectively‖ identified crisis periods with historical crises occurrence in
the country will be attempted. For the most part this effort resulted in plausible
matches between ICSS crisis periods and country level historical crisis. Thus, the
mainpurpose of the ICSS algorithm would probably be that it allowed the
determination of exact start and end weeks of a more vaguely understood crisis
periods.
Figure 3.3 illustrates the identified crisis periods using shaded areas. The plot of the
CSE return series in Panel (a) illustrates the volatility clustering in the CSE return
series.12
It is also clear from Panel (a) that the shaded areas roughly coincide with the
more volatile periods signified by more pronounced lateral movement of the return
series. This is a consolation, as it shows that the ICSS algorithm is generating accurate
results that can be verified visually. However Panel (a) is also evidence that beyond
the approximate/rough identification of crisis periods, the visual examination of return
series is not very useful. For instance, one cannot objectively identify an exact start
and end week of a give crisis period using visual methods. This is why an algorithm
12 This phenomenon was discussed in Chapter 2.
79
such as the ICSS is indispensable to bring in objectivity into this important step of this
research.
In Panel (b) a graph of approximate variances of the return series is presented. For the
purpose of generating this graph the variance for any given week is calculated as the
variance of the returns of the weekly returns in the preceding quarter. This is why it is
described here as a moving variance. Though the calculation of such a moving
variance is not required by the ICSS algorithm, this moving variance is useful to
illustrate the validity of the ICSS identified crisis periods. For instance in the case of
the CSE weekly returns, the ICSS identified crisis periods clearly coincides with the
high volatility of periods in Panel (b) of Figure 3.3. This is corroborated by Panel (c)
80
Figure 3.3: The application of Inclan and Tao (1994) to the CSE return series. The periods of
high volatility thus identified are shaded in all three panels capturing different manifestations of
the CSE return series: (a) the CSE return series, (b) the quarterly moving variance of the return
series, and (c) the cumulative sum of squared return series.
-30%
-20%
-10%
0%
10%
20%
30%
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
(a) CSE return ser(a) CSE return series
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
(a) CSE return ser(b) CSE volatility series
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
(a) CSE return ser(c) CSE cumulative sum of squred returns
81
which graphs cumulative sum of squares of the returns which is defined as Ck in
equation (3.7). The cumulative squared returns are also an indication of the level of
volatility and Panel (c) clearly illustrates that the sharp increases in Ck coincide with
the crisis periods in the CSE.
Table 3.4 summarizes the crisis volatility break indentified in CSE and compares their
timing with the local and global economic changes. During the past periods CSE
performance was badly affected by the war and this resulted in the fluctuation of stock
prices rapidly from time as the political uncertainty that prevailed in the country
during the last decades hindered the development of the market. In addition to the
global stock market crises, these factors can also be attributed for the high volatility in
CSE during the past periods.
Table 3.4: Volatility breaks and crisis periods in the CSE
Breakpoints Timing Local/Global events
to from
128 139 2001
This is the period the Sri Lankan government held General
Election which led to a change of government. Impact of market
crash of 2000 in the US may also have affected the local market.
This impact, in combination of the resumption with hostilities
contributed to the negative GDP growth in 2001. During this
period The Cease Fire Agreement (CFA) between the GoSL and
the LTTE also came into effect.
207 253 2003/2004
This is the period Tsunami hit the Sri Lankan economy and it
badly affect the Sri Lankan stock market. In addition, the impact
of 2000-2003 crash in the US may also be reflected in the high
volatility in the CSE.
326 331 2005/2006
The resumption of the Eelam War IV coincides with this period.
This period covers the period immediately after the 2005
presidential election which heralded much change in economic
policy in the country under Mahinda Chinthana.
459 463 2008 This period represents the Current global market crisis. This crisis
badly affected the garment industry in the country.
82
According to CSE and the Central Bank of Sri Lanka (CBSL), the market is highly
exposed to the global economy in several ways; particularly in terms of foreign direct
investments (FDI) and international trades. The ICSS procedure confirmed this
phenomenon by identifying several breakpoints in the CSE in line with the global
prominent market crises. Interestingly, in these results most of these breakpoints of
the market portfolio represent economic crisis periods that were experienced from
time to time in the world.
The volatility periods that are identified in this test satisfy the requirement of
volatility series for the asset pricing test. It identified 70 observations for the assets
pricing, a test which is approximately 1/5 of the total series of CSE. In the return
series in 3.1(a), after selecting the crisis periods other balance period of the series
from the full sample were identified as non-crisis period. In non-crisis series returns
fluctuate around zero.
3.6.3 ICSS and periods of crisis in the NYSE
Table 3.5: Volatility Breaks and Market Crashes- NYSE
Breakpoints Timing Global Crises
To From
84
105
89
106 1987
1987- Black Monday the largest one day percentage decline in
the market history
144
155
250
147
249
267
1989-1991 This period is associated with the Gulf War and United states
Savings and Loan crises
367
644
720
797
643
712
756
798
1999-2000 The market crash of 2000 which was the greatest curtailment of
assets values in American history
805
874
872
895
2001-2002
2001-2002 Argentine crisis during this crisis periods investors
shifted funds to US market from Argentine market
914
929
916
951 2003
Nasdaq 2000-2003 crash in the US that suffered a devastating
bear market
1155 1200 2007 Early periods of 2008 crisis
83
The NYSE return series, with 1200 weekly observations, is also subjected to the ICSS
algorithm to identify the crisis periods therein. Figure 3.4 illustrates the results, with
the shaded areas highlighting the crisis periods, similar to Figure 3.3. The 27 volatility
breakpoints in the NYSE series were used to separate out the crisis periods from the
non-crisis periods. The figure is interesting as most of the volatility periods of US
market also represent the world prominent crisis periods during the period 1985 to
2007. Table 3.5 shows the breakpoints derived from the volatility test of the US
market with the corresponding variances; for example the variance relating to 84th
breakpoint is 0.58 as shown in the table.
84
Figure 3.4: The application of ICSS to the NYSE returns series. The periods of high volatility are
shaded in the panels capturing different manifestations of the NYSE return series: (a) the NYSE
return series, (b) the quarterly moving variance of the return series, and (c) the cumulative sum
of squared return series.
-15%
-10%
-5%
0%
5%
10%
15%
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007
(a) NYSE return series
0
5
10
15
20
25
30
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007
(b) NYSE volatility series
0
0.1
0.2
0.3
0.4
0.5
0.6
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007
(c) NYSE cumulative sum of squares series
85
3.6.4 Descriptive statistics for crisis and non-crisis periods
Subsections 3.6.2 and 3.6.3 divided both markets studied here into two periods, as
crisis and non-crisis periods. As various econometric models will be fitted to the data
thus divided in the forthcoming chapters, it is appropriate that the data from these
periods (for both countries) be examined for their distributional characteristics and
other properties. The tools used for the purpose is similar (summary statistics and
correlations) to those used in Subsections 3.5.1 and 3.5.2 to examine the full data set,
including both crisis and non-crisis periods. It is obvious that the properties of the
data are different under high and low volatile conditions in the market.
Table 3.6: Descriptive statistics for the CSE.
Panel A: Crisis Period.
variable Mean SE Mean StDev Skewness Kurtosis
SL -0.014 0.027 0.314 -0.72 2.89
SM -0.002 0.024 0.276 -0.68 5.18
SH 0.234 0.105 1.19 5.71 47.00
BL 0.038 0.034 0.393 3.71 28.72
BM -0.010 0.022 0.254 3.72 16.26
BH -0.022 0.050 0.566 0.12 9.11
MKT 0.016 0.004 0.047 1.67 4.12
SMB 8.90 1.41 15.93 1.22 -0.53
HML -0.27 0.062 1.25 0.62 9.59
Panel B: Non Crisis Period
Variable Mean SE Mean StDev Skewness Kurtosis
SL 0.003 0.014 0.298 0.56 5.93
SM 0.007 0.014 0.287 0.38 5.27
SH 0.120 0.032 0.649 2.99 14.55
BL 0.039 0.024 0.482 3.51 21.37
BM 0.007 0.014 0.291 0.85 9.43
BH -0.011 0.018 0.364 0.90 6.44
MKT -0.008 0.001 0.030 0.15 5.43
SMB 6.69 0.735 14.74 0.75 1.33
HML -21.95 2.091 41.83 -1.28 -0.20
86
Table 3.6 reports the distributional properties of the portfolios and the FF3F factors
for the CSE in two panels: Panel A looks at the crisis periods and Panel B the
non-crisis periods. As shown in Panel A, the mean return is not significantly different
from zero for the all six portfolios. Only MKT is statistically significant in that panel,
but that too is not economically significant. Overall the portfolio returns during crisis
periods oscillate around the value of zero. Four out of six portfolios report negative
means, but as noted above these are not statistically significant. The portfolio average
returns and SE in Panel A has a positive relationship illustrated by the correlation
coefficient of 0.8519.
Statistics in Panel B of Table 3.6 show that in the non-crisis period only BH portfolio
yields negative mean return. However, again none of the means are statistically
significant. Generally most of the portfolios on average yield a lower return during
crisis than during non-crisis: the average for portfolio return during crisis is 0.0342
and for non-crisis 0.0224. This makes sense, as high risk crisis periods need to
compensate the investor with a higher return. The risk return relations implied in
Panel B seem to be weaker than that in Panel A. The correlation coefficient for non-
crisis period is 0.8251, which is comparatively lower than that of Panel A reported in
the previous paragraph. The standard deviation is relatively similar in both periods.
However, HML has very high standard deviation during non-crisis periods. This can
be mainly attributed to the degree of exposure of this factor to crises. This also
suggests that HML is not sensitive to the crisis periods when compared with the non-
crisis periods.
Table 3.6 reports skewness and kurtosis measures for the variables from the CSE
separated according to whether they cover crisis periods or non-crisis periods. They
indicate that the distributions are not normal.
87
Table 3.7: Descriptive statistics for the US
Panel A: Crisis Period.
variable Mean SE Mean St. Dev Skewness Kurtosis
SL -0.003 0.158 3.18 -1.63 9.95
SM 0.067 0.114 2.31 -1.82 11.57
SH 0.053 0.107 2.16 -1.73 10.50
BL 0.180 0.132 2.67 -0.70 3.07
BM 0.062 0.114 2.30 -0.54 2.45
BH 0.068 0.105 2.12 -0.48 1.82
MKT 0.118 0.121 2.45 -1.00 5.02
SMB -0.065 0.079 1.59 -0.72 6.17
HML -0.027 0.062 1.25 1.08 9.59
Panel B: Non-Crisis Period.
Variable Mean SE Mean St. Dev Skewness Kurtosis
SL 0.125 0.102 2.53 -0.45 3.66
SM 0.264 0.070 1.74 -0.95 6.97
SH 0.320 0.072 1.78 -1.26 10.6
BL 0.155 0.084 2.10 -0.41 2.77
BM 0.231 0.073 1.81 -0.66 3.62
BH 0.223 0.075 1.85 -0.63 4.28
MKT 0.172 0.077 1.91 -0.55 4.31
SMB 0.033 0.045 1.12 0.26 0.74
HML 0.131 0.051 1.27 0.2 3.08
Table 3.7 summarizes the statistics of the US data series for the crisis and non-crisis
periods. In Panel A which includes the statistics for crisis periods in the US, the mean
returns for the portfolios are positive for all the portfolios except SL and out of FF3F
factors only HML shows a negative return. None of the portfolio means are
significantly different from zero.
Panel B shows that for the non-crisis periods the portfolios, as well as the factors,
have positive means, though they are not significant. On average the means of
portfolio returns during non-crisis (0.0778) is higher than in the crisis period (0.2128).
Surprisingly the theoretical risk and return relationship seems to be violated here:
mean return and standard deviation are not changing in the same direction.
88
The reported skewness values are negative for portfolios in both panels and some are
close to zero. The kurtosis values are ranging between 0.74 and 6.97, here also some
values are close to 3. These results indicate that the US portfolios are partially
normally distributed.
3.6.5 The correlation analysis of the crisis and non-crisis periods
Interlinks between portfolios examined in Subsection 3.5.3 was useful to understand
the distinctions between Sri Lankan and the US markets. However, since that
discussion the data had been separated into two on the basis of crisis/non-crisis. It is
appropriate that the discussion of the portfolio interlinkages extend to issue of
whether the links in question are sensitive to the crisis/non-crisis distinction. This
section looks at the prosperities and the behavior of the portfolios using pair-wise
correlation analysis.
89
Table 3.8: Pair-wise correlations of portfolios for the crisis and non-crisis periods in the CSE
Panel A: Crisis Period
SL SM SH BL BM BH MKT
SL 1.000
SM 0.512* 1.000
SH 0.350* 0.004 1.000
BL 0.101 0.271* -0.052 1.000
BM 0.575* 0.621* 0.196 0.233 1.000
BH -0.014 0.027 -0.027 0.090 0.035 1.000
MKT 0.188 0.194 0.279* 0.078 0.147 0.234 1.000
Panel B: Non Crisis Period
SL SM SH BL BM BH MKT
SL 1.000
SM 0.336* 1.000
SH -0.040 0.005 1.000
BL 0.060 0.010 0.008 1.000
BM 0.344* 0.210* 0.031 -0.014 1.000
BH -0.008 0.010 -0.030 0.033 0.034 1.000
MKT -0.003 0.053 -0.019 -0.026 0.011 0.075 1.000
* critical value for the correlation coefficient is calculated as n1 .
Table 3.8 presents the pair wise correlation for the crisis period (Panel A) and
non-crisis period (Panel B) for CSE. Panel A shows that during crisis periods 6/21
correlation coefficients are significant. This falls to 3/21 in Panel B. If one compares
the correlation coefficients across the panels (ignoring whether they are significant), it
is clear that correlation figure in the Panel A are generally higher than the
corresponding figures in Panel B (Correlations are high for 18/21 cases in Panel A). It
can be concluded that crisis periods seem to be generating conditions that promote
interlinks in the market. This is consistent with the work of others in the literature
which show that correlations can increase during crisis settings (see Longin and
Solnik 2001; Ang and Bekaert 2002).
90
Table 3.9: Pair-wise correlations of portfolios for the crisis and non-crisis periods in the US
Panel A: Crisis Periods
SL SM SH BL BM BH MKT
SL 1.000
SM 0.964* 1.000
SH 0.933* 0.977* 1.000
BL 0.784* 0.783* 0.753* 1.000
BM 0.719* 0.766* 0.756* 0.914* 1.000
BH 0.672* 0.720* 0.732* 0.847* 0.926* 1.000
MKT 0.851* 0.854* 0.828* 0.980* 0.941* 0.877* 1.000
Panel B: Non crisis Periods
SL SM SH BL BM BH MKT
SL 1.000
SM 0.915* 1.000
SH 0.856* 0.958* 1.000
BL 0.792* 0.760* 0.705* 1.000
BM 0.694* 0.801* 0.783* 0.821* 1.000
BH 0.645* 0.767* 0.794* 0.720* 0.896* 1.000
MKT 0.844* 0.841* 0.802* 0.970* 0.895* 0.809* 1.000
* critical value for the correlation coefficient is calculated as n1 .
Table 3.9 summarizes the inter-portfolio correlation for crisis and non-crisis periods
in the US market. It is interesting to see that all portfolios are highly correlated with
other portfolios in both periods. This usual behavior of the portfolios seen in
developed markets. In a scenario like this the investors will not be able to get the
diversification benefits as all the portfolios move in the same direction under different
conditions in the economy. However, during crisis periods (Panel A) inter-portfolio
correlation is higher than non-crisis periods. If a comparison is made between Panel A
and Panel B, out of 21 correlation pairs, 17 pairs show higher values in Panel A, than
corresponding values in Panel B. This suggests that inter-portfolio correlation
increases when the market becomes highly volatile in a crisis setting.
91
3.7 Summary and Conclusion
Chapter 3 discusses the methodology of this research, placing much emphasis on the
formation of the portfolios used here. The key models used here, the CAPM and the
FF3F, were explained with additional notes on their empirical formulation. Since the
testing of crisis sensitively of these models is a major contribution of this thesis (see
Chapter 1) it was necessary to clearly explain how the crisis periods were identified
for the purpose. This chapter, therefore, explained in detail the ICSS algorithm due to
Incan and Tiao which is used here to identify the crises. The crisis periods are
identified in both the CSE and NYSE data. Usefully the identified crisis periods could
be given historical explanations in most cases for both countries. The chapter also
provides, with some discussion, summary statistics for the data used in this paper.
This discussion is organized by the country and by whether crises were observed for
the period.
92
Chapter 4
Test of Pricing Models and Anomalies in Colombo Stock
Exchange
4.1 Introduction
Since the end of war in May 2009, Sri Lanka has been attracting global attention for
both good and bad reasons. The attention Sri Lanka received from international
investors is one of the positive outcomes of ending 26 years of civil conflict. In fact
much local publicity has been given for CSE intermittently registering best
performing global market status based on the total market return percentage which is
higher than anywhere in the world. This paves the path to bring in arguably the most
important chapter of this thesis that scrutinizes the performance of asset pricing
models in the CSE.
Here the methodology and the CSE data prepared and described in Chapter 3 is used
to examine the validity of the CAPM, the FF3F and the January effect for Sri Lanka:
a key, if not the main objective of this work. It must be reemphasized that a massive
amount of work at the level of data preparation and portfolio construction has already
been done even before data analysis. In addition, the analysis investigates the crisis
sensitivity of these results by implementing the CAPM and the FF3F for crisis periods
and non-crisis periods separately. Chapter 3 discusses the modalities of using the
ICSS algorithm due to Inclan and Tiao (1994) to separate crisis and non-crisis periods
in Sri Lanka.
The rest of the chapter is organized as follows. Section 4.2 explains the main features
of global emerging stock markets. Section 4.3 introduces the reader to the Sri Lankan
context, drawing special attention to the investment climate and the CSE. Section 4.5
discusses the CAPM results for Sri Lanka, followed by the FF3F results for Sri Lanka
in Section 4.5. The next section deals with the January effect for the country. Section
4.8 concludes the chapter.
93
4.2 Main Features of Emerging stock markets
In the 1980s and first half of 1990s, the emerging markets became popular among
investors. Generally these markets were highly volatile and more risky, but yield more
returns to investors. More fund managers and brokerage firms came into these
markets to operate their businesses and despite the risk of the market pensions, funds
were invested in these markets during that period. In the arena of investment in stock
markets, new avenues of investment were generated with the liberalization of world
emerging markets and it resulted to attract more local and foreign investors to these
markets. However, the popularity of these markets was eroded with the sudden Asian
crisis that originated from Thailand in 1997. A large number of investors were
withdrawn from the worst affected markets. Countries such as Korea, Thailand and
Indonesia were badly affected by the 1997 Asian crisis.
The most dominant feature of emerging market is the ‗country effect‘ which means
that these markets are more susceptible to country specific factors unlike developed
markets.
During the past two decades globally the recognition of emerging markets has
increased rapidly. These markets have shown phenomenal growth in terms of market
capitalization. More specifically, market capitalization has increased 32 times
between 1980 and 2000. Growth in stock market liquidity as measured by trading
value has been even more striking; it has increased by more than 170 times during the
past 20 years.
4.3 Investing in Sri Lanka and the CSE
This section provides a detailed description about Sri Lanka in a bid to provide a
reasonable grounding for the reader about the country. It provides a general country
description including a socio-economic description, as well as a more focused
description about the history, operations and current status of the CSE.
94
4.3.1 Sri Lanka: the economy in general
Sri Lanka is a South Asian island nation situated at the southern tip of India and
surrounded by the Indian Ocean. Though the economy of the country was for 26 years
overshadowed by the civil war between the Government of Sri Lanka (GoSL) and the
Tiger separatists (LTTE), there was an element of resilience in the economy which
saw economic growth averaging at about 5 percent level during this period (see). At
the turn of the last century the economy of the country under the British colonialist
was characterized by the significance of the plantations. About this time, tea had
replaced coffee as the main crop in this sector and later, since its introduction in 1905.
Additionally, rubber had also been an important contributor to the plantation sector.
Plantation history, while being important to paint the evolution of the modern
economic history of the country in general, is also important in tracing the history of
the stock market in the country.
Figure 4.1: Percentage contribution by each sector to the economy of Sri Lanka (left axis) and the
GDP growth rate (right axis). The data is from 1950 to 2009.
-2
0
2
4
6
8
10
0
10
20
30
40
50
60
70
19
50
19
53
19
56
19
59
19
62
19
65
19
68
19
71
19
74
19
77
19
80
19
83
19
86
19
89
19
92
19
95
19
98
20
01
20
04
20
07
20
10
GDP growth Agri Industry Service
Source: Central Bank of Sri Lanka Annual Reports (various years).
95
Since independence in 1948, however, the contribution of the agricultural sector
(including the plantations sector) to the GDP of the country has gradually declined.
These trends are mapped in Figure 4.1 which illustrates the evolution of the economy
gradually being dominated by the services sector. Nevertheless, much of the labor
force of the country is still engaged in agriculture. In 2009 for instance agriculture
accounts for 33 percent of the total employment in the country. In the mean time the
service sector accounts for 41 percent and the industrial sector 26 percent of total
employment (CIA World Fact Book). Figure 4.1 also visually illustrates the structural
shift in 1977 characterized by the liberalization of the trade account. This regime shift
consolidates the services sector in the country which includes wholesale and retail
trade, tourism, transport, telecom, financial services. All these areas are earmarked for
exponential growth in the post-war era.
Sri Lanka now classified by the World Bank as a lower middle income country,
currently enjoys a per capita GDP of USD 2053 (CBSL, 2009). The per capita income
of the country is 3700$. The poverty rate of the people living in Sri Lanka is 22% of
the total population. The human development index is 0.740 and Sri Lanka is ranked
97 out of 177 countries and 73% enjoy basic amenities such as electricity. (Website:
International Center for Ethnic Studies). Sri Lanka's 91% literacy rate in local
languages and life expectancy of 75 years rank is well above those of India,
Bangladesh, and Pakistan. The English language ability and usage was relatively high
in past deacdes, but has declined significantly since the 1970s.
The economic situation in Sri Lanka faltered in 2009 due to the global credit crisis. In
2009 GDP grew by 3.5%, down significantly from 6% growth in 2008. Exports fell
by about 13.5%. In 2008, trade and current accounts recorded large deficits due to
high oil and commodity prices, and an unsuccessful effort by the government to
defend the Sri Lankan rupee that drained Sri Lanka‘s exchange reserves, forcing it to
turn to the International Monetary Fund (IMF) in early 2009 for assistance. Sri Lanka
depends on a strong global economy for investment and expansion of its export base,
and the global slowdown has proved to be detrimental to Sri Lankan growth. It hopes
to diversify export products and destinations to make use of the Indo-Lanka and
96
Pakistan-Sri Lanka Free Trade Agreements and other regional and bilateral
preferential trading agreements.
4.3.2 An overview of the Colombo Stock Exchange
The commencement of Share trading in Sri Lanka is linked with the plantation
industry in the British colonial period. After the ―coffee blight‖ the British Planters
required funds to replace the coffee plantations in Sri Lanka with tea plantations. This
led to the setting up of the Colombo Share Brokers Association which commenced
trading of shares in limited liability companies in 1896. In 1985, the Colombo Stock
Exchange (CSE) was set up as a company which took over these operations from the
Colombo Shares Brokers Association.
The CSE is one of the smallest stock markets in terms of turnover, the capitalization
and the number of trades. Currently the number of companies listed in the CSE is 242.
The number of investors in the market is around 130,000. However, among these the
number of active investors who trade frequently is less than 40,000. The stocks in the
CSE are classified into 20 sectors as plantation, banking and finance, manufacturing,
tourism, etc. A full list and the number of companies in each sector at the time of
writing are given in the appendix.
The performance of the market is mainly measured with the values of All Share Price
Index (ASPI) which can be described as a crude measure of the macroeconomic
environment of the country. A plot of the ASPI during the 10 years covered in this
research is given in the top panel of Figure 4.2. The vertical axis of the graph is
measured in 100s. For example in the first week in 1999, the starting point of the
figure, the ASPI was at 583. As such the graph starts at 5.83 in an axis given in 100s.
It is obvious that the ASPI had moved approximately horizontally during the years
1999 to 2001 and had trended upward thereafter. The shaded area of the graph shows
the crisis periods identified in Chapter 3 (see Figure 3.3). The post 2001 movement of
the ASPI in both directions can be linked to important socio-political events in Sri
Lanka. For instance, the change of government in 2001, the signing of the CFA in
2002, the tsunami of 2004, the election of President Rajapakse in 2005, resumption of
Eelam War IV in 2006, are all important events. The high interest rate regime in 2008
97
and 2009, as well as the global financial crisis, had caused the ASPI to dip in this
period. Nevertheless, the CSE has continued to attract much attention from the
investors due to the post-war peaceful environment in the country.
The movement of the ASPI also affected the four-fold investor group trading in stocks
of the 242 listed companies (in he 20 sectors) available in the CSE. The four
categories of investors are local companies, local individuals, foreign companies, and
foreign individuals. The bottom panel of Figure 4.2 illustrates the way these investor
groups contribute to market capitalization. Comparing the top and bottom graphs, one
can identify a clear pattern: that foreign participation rate generally reflects the level
of the ASPI. In other words, the higher degree of foreign involvement in the market,
will lead for higher ASPI. This is in fact a generally accepted phenomenon of the
CSE, probably reflecting the relationship between the confidence of the investors
(captured by the foreign participation level) and the market performance.
In addition to the above improvements, technological improvements and restructured
trading process has tremendously contributed to the better performance of the CSE.
The Central Depository System (CDS) introduced in 1991 became fully operational in
June 1992. The CSE has always attempted to bring in the latest technological
innovations to Sri Lanka. The small size of the market probably makes this relatively
easy for the case of Sri Lanka. The branch network of the CSE is another strategic
move of the CSE to attract more local participants to the market. Currently CSE has
opened five branches in the Inland covering important provinces. Out of branch
network, the recently opened branch in the Jaffna peninsula, (war-tone area for 26
years) will be a good opportunity for the people deprived of opportunity for investing
in CSE. These branches conduct awareness campaigns regularly for school children
and the general public, in addition to providing other advisor services. The main
objective of CES from these initiate is to increase the participation of local individuals
into the market.
98
Figure 4.2: All Share Price Index (ASPI) and identified crisis periods for the CSE (top graph)
and the investor composition of the CSE (bottom graph). Axis in the top graph is in 100s and the
bottom one in percentages. Also top graph is derived from weekly data while the bottom one is
from annual data. Thus to make comparative sense from the two graphs they are horizontally
aligned in so that year references in the bottom graph falls between the year references in the top
graph.
0%10%20%30%
40%50%60%70%80%90%
100%
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Local Companies Local Individuals
Foreign Individuals Foreign Companies
0
5
10
15
20
25
30
35
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008ts
un
am
i
Pre
s.E
lecti
on
Eela
mW
ar
IV
LT
TE
fir
st a
ir r
aid
CF
A
4.3.3 Impact of Recent Global Crisis on the CSE
The current financial crisis has affected the CSE according to the top panel of Figure
4.2. However, events that showed the downward trend quickly reversed after the end
of civil war in May 2009, a period which is not shown in the graph. In fact, the ASPI
has gone into all time high levels after the time period in the graph. For instance in
mid-2010, when this thesis was being finalized, the ASPI was nudging the 5000 level
(see the CSE website at http://www.cse.lk). So it gives a general perception that the
99
crisis had less economic impact (in terms of the lost jobs etc.) as in some of the other
countries, due to the country having minimal interaction with financial institutions
severely hit by the global crisis. Certain sectors in the economy with strong links with
the external sector, like the apparel sector, have been more affected by the crisis than
others. However, overall the Sri Lankan economy has been resilient to the present
crisis. This has made local stock brokers very optimistic about the market. They base
this argument on the fact that foreign interest in the CSE is still intact. The
significance of foreign markets as an indicator of the performance of the CSE was
examined earlier using Figure 4.2. Generally the stock brokers would start worrying if
foreign investors and fund managers start pulling out from Sri Lanka as their profit
margin decline due to such behavior of foreign investors. However, it is not likely
with post-war euphoria in CSE.
The Sri Lankan situation examined in this section is important to understand and
appreciate the empirical results detailed in the next few sections. This empirical work
begins with the application of the CAPM to the weekly FF3F portfolios for the CSE
compiled in Chapter 3.
4.4 Test of the CAPM using the FF3F portfolios
This section presents the results of fitting the CAPM to the 6 size-BE/ME portfolios.
This is done using the time series regression of equation 3.2 explained in Chapter 3.
The present work also tests whether these results from fitting the CAPM are sensitive
to crises in the CSE. This is achieved by applying the model to crisis and non-crisis
data separately. Section 3.6 described how the data was separated for this purpose.
The estimation results are organized in Table 4.1 in three panels. Panel A, Panel B
and Panel C in the table present the results for the full period, crisis period and the
non-crisis period respectively.
100
Table 4.1: Test of CAPM in the CSE
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1999 to 2008 the CSE stocks are allocated in an independent sort to two groups (small or big) based on
their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated in
an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios namely SL, SM, SH, BL, BM, and BH. Rmt is the excess weekly return of ASPI in CSE.
Regression: tptftmpptftp RRRR ,,,,,
Panel A: Full Sample Period
Dependent
Variables αp βp α(t) β(t) R
2 adj
SL 0.014 0.338 0.86 0.77 0.201
SM 0.007 0.657 0.56 1.85 0.330
SH 0.139 3.001 3.77* 2.99* 0.218
BL 0.381 -1.431 2.64* -0.37 0.200
BM 0.004 0.263 0.31 0.75 0.201
BH -0.011 0.804 -0.59 1.61 0.311
Panel B: Crisis Period
Dependent
Variables
αp βp α(t) β(t) R2 adj
SL 0.001 0.691 0.03 1.58 0.235
SM -0.004 0.773 -0.14 1.63 0.237
SH 0.211 5.671 1.26 2.39* 0.477
BL 0.127 0.895 1.31 0.65 0.206
BM -0.018 0.457 -0.70 1.23 0.221
BH -0.045 1.431 -0.861 1.35 0.354
Panel C: Non Crisis Period
Dependent
Variables
αp βp α(t) β(t) R2 adj
SL 0.014 -0.033 0.82 -0.05 0.201
SM 0.009 0.564 0.63 1.06 0.202
SH 0.116 -0.450 3.57* -0.37 0.200
BL 0.419 -3.271 2.47* -0.52 0.200
BM 0.007 0.457 -0.70 1.23 0.221
BH -0.173 1.741 -0.653 1.51 0.305
*significant at the 5 percent level
The CAPM equation 3.2, which is also identified as the security market line (SML) in
Chapter 2, estimates three important coefficients: the intercept, the slope term and the
standard error.13
The intercept is defined as the average risk-free rate for the period
being studied (see Chapter 2). Theoretically therefore, the estimated intercepts should
be equal across portfolios in a given panel. However, this condition is not seen in
13 The standard error is calculated using HAC robust statistics.
101
most cases in the results presented here. In the above three panels (A, B and C) 4/18
intercepts are significant at the 5 percent level across three periods. All of the
significant values are positive. Out of the remaining 14/18 intercept terms, 5/18 are
negative which are theoretically wrong; for example Scholes and Williams (1977) .
However, the implications about none of these negative values are significant.
The estimated αp values can be compared vis-à-vis the risk free rates of the market. If
the market risk free rate is approximated by the average 3 month TB rate, which is
12.28 percent for the relevant period, then it becomes obvious that the estimated
intercept of the SML curve does not accurately approximate the risk-free rate of the
economy. This result is consistent with the results presented by Gonzalez (2001: 337)
for the case of the Caracas Stock Exchange, Venezuela. The calculated average
intercepts for full sample in crisis and non-crisis periods are 0.059, 0.003 and 0.065
respectively. Their proximity to the value of zero further confirms the above
conclusion.
The main coefficient in the equation 3.2 depicting the CAPM is the beta factor that
measures the systematic risk component of the portfolios (see Chapter 2). Panels A, B
and C in Table 4.1 reveal that only 2/18 beta coefficients are significant at the 5
percent level. Both these are significant betas for SH portfolios: one in the full sample
period and the other in the crisis periods. This result clearly rejects the CAPM as a
valid model for capturing the variation of portfolio returns in the CSE. It can be
interpreted as evidence that systematic risk factors such as inflation, GDP growth,
global oil prices, etc. that are not significantly influencing the fluctuation of stock
prices in the CSE.
The main reason for the rejection of the CAPM may be the inadequacy of market
index (ASPI) to capture the overall market risk. For the model to work properly it is
important that the ASPI (proxy used for market portfolio) represent the entire asset set
in the economy, including the human capital of the country. The ASPI is a value
weighted index that captures the pricing behavior of listed companies of CSE and it
does not represent all assets available for the Sri Lankan investor. This issue was
clearly stated by Roll (1977) that the inappropriate proxies immensely led to the
102
incorrect predictions of the CAPM. He further argues that relationship between
expected returns and beta of the CAPM is just the minimum variance condition that
holds in any efficient portfolio applied to the market portfolio. If we can find a proxy
that is on the minimum variance frontier, CAPM can be used to describe differences
in expected retunes. However, in the absence of proxy which satisfies the above
condition, researches use market index as the proxy for market beta. Despite this
limitation ASPI is widely applied in CSE as the market proxy by the researchers and
professionals in the absence of alternative proxy for it in CSE.
The values of adjusted R2 as a measure of the total variance explained by the models
is not close to 1 in the results. If the model explains the variation of the stock return it
should be close to 1. Though the estimated beta is significant for SH in two occasions
as discussed earlier, even in these situations the R2 is low. Previous work, not
necessarily in the area of CAPM involving the CSE, also report low R2 values (see
Nimal 1997; Samarakoon 1997; Guneratne 2001). In conclusion, the above results
suggest that the relationship between the market and the portfolio returns is weak in
the CSE which is consistent with the findings of others in the emerging market
contexts (see Kargin 2002; Huang 2003; Salomons and Grootveld 2003) as well as in
developed market contexts (Cohen, Maier, Schwartz and Whitcomb 1986; Fama and
French 1992; Groenewold and Fraser 1997).
4.5 Test Results for the FF3F
This section uses the portfolio data constructed for the CSE in Chapter 3 to estimate
the multi factor regression in equation 3.4. The results are tabulated in Table 4.2
according to whether the full period, crisis period or the non-crisis period is being
used for the regression. But first the table presents some descriptive statistics for the
six portfolios in Panel A. The table is organized in two main columns. Each separated
according to the BE/ME categorization. The format of the table is heavily influenced
by Fama and French (1996: 59). The header rows of Table 4.2 explain what each
column stands for and the explanation is relevant for the entire table, including all
panels.
103
Table 4.2: The FF3F results for the CSE based on weekly data (1wk 1999 to 52wk 2008).
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1999 to 2008 the CSE stocks are allocated in an independent sort to two groups (small or big) based on
their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated in
an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios namely SL, SM, SH, BL, BM, and BH. MKT, SMB and HML are as discussed in Chapter 3.
Book to market equity (BE/ME) portfolio
Low Medium High Low Medium High
Size
Panel A: Descriptive Statistics (Annual Averages)
BE/ME ratio The number of firms in portfolios
Small 0.013 0.010 0.041 33 45 34
Big 0.368 0.011 0.042 34 47 35
Regression: tptptptpptftp HMLhSMBsMKTRR ,,,
Panel B: Test for FF3F Full Sample Period
αp α(t)
Small 0.013 0.010 0.041 0.79 0.78 3.93*
Big 0.368 0.011 0.042 2.30* 0.81 1.80
βp β(t)
Small 0.206 0.518 2.78 0.49 1.57 2.79*
Big -0.477 0.115 1.11 -0.12 0.35 1.95
sp s(t)
Small 0.019 0.018 0.021 7.33* 9.06* 3.38*
Big -0.133 0.018 -0.002 -5.55* 8.92* -0.57
hp h(t)
Small 0.005 0.005 0.007 6.40* 8.11* 3.44*
Big -0.041 0.005 0.009 -4.92* 8.22* 7.69*
R2 adj RMSE
Small 0.305 0.356 0.237 0.301 0.261 0.79
Big 0.256 0.340 0.68 0.825 0.261 0.45
Panel C: Test for FF3F Crisis Period (Volatile)
αp α(t)
Small 0.019 0.025 0.293 0.68 0.73 1.50
Big 0.207 0.005 0.004 1.73 0.26 0.06
Β β( t)
Small 0.429 0.463 4.781 1.26 1.09 2.01*
Big 0.345 0.174 0.455 0.24 0.64 0.53
sp s(t)
Small 0.037 0.032 0.099 7.61* 5.25* 2.87*
Big 0.019 0.034 -0.008 0.93 8.55* -0.70
hp h(t)
Small 0.012 0.011 0.033 7.23* 5.21* 2.82*
Big 0.008 0.011 0.006 1.18 8.31* 1.56
R2 adj RMSE
Small 0.68 0.52 0.380 0.180 0.231 .681
Big 0.21 0.73 0.701 0.802 0.150 0.47
104
Table 4.2: (continued)
Book to market equity (BE/ME) portfolio
Low Medium High Low Medium High
Size
Panel D: Test for FF3F Non Crisis Period (Non Volatile)
αp α (t)
Small 0.011 0.008 0.131 0.60 0.52 3.61*
Big 0.391 0.011 0.053 2.11* 0.76 2.10*
βp β (t)
Small -0.228 0.374 -0.572 -0.35 0.76 -0.48
Big -1.711 -0.059 2.161 -0.28 -0.12 2.60*
sp s(t)
Small 0.017 0.017 0.014 6.06* 7.95* 2.60*
Big -0.148 0.016 -0.002 -5.47* 7.45* -0.41
hp h(t)
Small 0.005 0.005 0.004 5.10* 6.86* 2.63*
Big -0.046 0.005 0.009 -4.88* 6.71* 7.64*
R2 adj RMSE
Small 0.286 0.341 0.318 0.351 0.266 0.647
Big 0.270 0.422 0.689 0.712 0.274 0.449
*significant at 5 percent level
Panel A reports the annual averages of the BE/ME values and average of annual
number of firms in each portfolios. Such statistics had been used by Fama and French
(1993: Table 1). The average BE/ME values reported here show that small, medium,
and high categorization is in fact correctly done. The number of firms implies that the
firms had been on average divided in order that a similar numbers fall into all 6 size-
BE/ME portfolios. These statistics based on annual averages are different in certain
ways to the statistics presented in, for example, Chapter 3. The main difference being
that in contrast to the ones presented here, the statistics in the Chapter 3 mostly
illustrate the distributional characteristics of the weekly returns.
The rest of Table 4.2 presents the regression results for the three periods that are
organized in three panels in Table 4.2: Panel B, Panel C and Panel D respectively. All
panels are vertically separated into two parts similar to the format used by Fama and
French (1996: 59). In each of Panel B to Panel D in Table 4.2 the left hand side
reports the estimated coefficients of the equation 3.4, as well as the R2 values of the
regressions for each of the portfolios. The right hand side, reports the corresponding t-
105
values of the coefficients listed in the left hand side, as well as the Root Mean Square
Error (RMSE) of each regression.
The discussion on the estimates results are organized by the estimated coefficients.
For instance, firstly, the discussion is about the constant term, α, in all three panels:
Panel B, Panel C and Panel D. The estimates of α are all positive. Though all these 18
coefficients are positive, only five (two in Panel B and three in Panel D) are
statistically significant at the 5 percent level. Even among these 5, only three seem
economically significant. Fama and French (1996: 57) suggest that if FF3F describes
the expected returns, the regression intercepts, α, should not be significantly different
from zero. On the basis of this assertion it seems that the FF3F fits the completely
crisis periods better than the non-crisis periods. Referring back to the issue of positive
α’s which are statistically significant; it could mean that the FF3F factors are
consistently under predicting the portfolio returns.
An interesting pattern in the estimated α’s is observed across the three periods: α’s
are large (not necessarily significantly) for big size, low BE/ME portfolios (BL) and
small size, high BE/ME portfolios (SH). In all other cases the intercepts are close to
zero. The results derived from the test here are different from Drew, Naughton and
Veeraraghavan (2003) who found that none of the six alphas is significantly different
from zero. However, partially consistent with the findings of Wai and Gordon (2005)
who found that out of nine portfolios only four alphas are significant at the 5 percent
level. The average values for α’s of six portfolios for three periods (full sample, crisis
and non-crisis) are, 0.080, 0.092 and 0.100 respectively. It shows a slight increase in
alpha during non-crisis period.
Next, let‘s consider the estimated slope coefficients for MKT factor, β‘s, in Table 4.2.
In the three panels 5/18 beta values are negative, but none of these negative ones are
significant at the 5 percent level. From the remaining positive beta values, only three
are statistically significant; all of these are for high BE/ME portfolios (2 small and 1
big). It is interesting that the average of all beta values, irrespective of whether
significant or not for small portfolios (SL, SM, and SH) in Panel B, is 1.16. When this
is compared with the average figure of 0.24 for the big portfolios (BL, BM, and BH)
106
in Panel B, it suggests that the small portfolios are more risky than big ones. This
gives a rational signal to the portfolio managers when they are rebalancing their
portfolios among risk averse and aggressive investors. Similarly, small portfolios are
a better choice for aggressive investors, while big portfolios are better choice for risk
adverse investors. The comparison is similar in Panel C with an average beta of small
portfolios (SL, SM, SH) of 1.89, compared against the average for big portfolios of
0.32. In Panel D, however, the average beta of small portfolios is -0.14 and for the big
portfolios it is 0.13. The average overall betas in the three panels are 0.708, 1.107, and
-0.005 overall for crisis and non-crisis periods and this clearly indicate that the beta
and hence the risk in crisis period is higher.
The estimated coefficient of the SMB factor, sp, is discussed here. In Panel B, C, and
D for instance 14/18 of the sp coefficients are significant at the 5 percent level. In
short, it suggests that size factor can explain the differences in average returns across
stocks in 14 portfolios out of 18. Only two of these values are negative, this means
that when the size factor increase on weekly basis the corresponding return of
portfolio decreases by the value of slope coefficient. Moreover, the slopes on SMB
for stocks are related to size (see Chapter 2). In relation to what is discussed in the
previous paragraph, it is clear that for the CSE data the SMB factor is more important
than MKT factor. In other words this suggests that SMB, the mimicking returns for
the size factor, is able to capture the shared variation in portfolio returns that is missed
by the market (MKT). The average sp for the nine small portfolios in the three panels
is 0.091. In contrast, the average for the big portfolios is –0.062. This suggests that
small portfolios are more sensitive to the SMB than big portfolios. A compression
across Panel B, Panel C and Panel D demonstrates that BH portfolio is not significant
and yields a negative slope for all the periods.
The third factor, the HML, is a proxy for capturing the effect of BE/ME in the model.
Interestingly in panels B, C and D 16/18 hp coefficients are significant at the 5 percent
level. The weekly returns from portfolio BL is negatively related to the HML as per
panels B and D. It suggests that the HML is capable of capturing shared variation in
stock returns of the CSE. The average of HML coefficients (six portfolios) in crisis
and non-crisis periods are 0.0135 and -0.003 respectively. It reveals that in crisis
107
periods all the six portfolios on average negatively related to the FF3F factors, while
it has positive for non-crisis periods.
Thus, the two factors SMB and HML are able to capture the variations of portfolio
returns that are missed by the MKT factor in the CSE. This finding is consistent with
other findings in the historical literature (Fama and French 1993: 21; Wai and Gordon
2005: 703). In the analysis of their findings, Fama and French (1993) conclude that
adding SMB and HML to the regressions collapse the β‘s for stocks toward 1.0 (low β
move up and high β move down). However, this pattern is not prominently seen in the
current results in CSE. They also conclude that this behavior is due to the correlation
between market and SMB and HML.
The strong performance of the SMB and HML factors in explaining the returns of the
CSE portfolios is clear. The reported adjusted R2 can be used to statistically establish
this assertion. The low value of reported R2 is a common occurrence in the literature
in Sri Lanka (see Section 4.4). The present research is particularly interested in
whether the addition of the SMB and HML variables to the single factor model in
equation (3.2) improves the model‘s goodness of fit. In other words, the research
attempts to answer the question whether the FF3F is a better representation of the
CSE portfolios than the CAPM. It is evident that the adjusted R2 had monotonically
increased from CAPM (in Table 4.1) to FF3F (in Table 4.2). The average adjusted R2
of the CAPM regressions is 0.2511; the average for the FF3F is 0.4289. This result
confirms that the FF3F is more powerful than CAPM in explaining the variation of
portfolio returns.
The adjusted R2 values in Table 4.2 can be looked at according to the period of
study—full sample, crisis, and non-crisis. For instance, the average of the adjusted R2
in the six portfolios during crisis period is 0.53. This figure is much higher than in the
other two periods: for the full sample it is 0.3623; for the non-crisis period 0.3876.
Earlier in this section, in discussing the estimated constant term of the model, it was
asserted that the intercepts being close to zero implied that the FF3F variables had
useful explanatory power. The evidence based on the adjusted R2 also supports this.
108
In view of the objectives of this research, it is important to sum up this section by
contrasting the FF3F‘s performance in crisis periods vis-à-vis its performance in the
non-crisis periods. Some differences can be found between Panel C and Panel D in
Table 4.2 that reports the FF3F results for crisis and non-crisis periods in Sri Lanka.
For example, it is significant to take into consideration the behavior of the MKT
factor during crisis period and non-crisis period. All market betas are positive in crisis
period and higher than the corresponding betas of non-crisis period. This suggests that
due to the high volatility in the market the size-BE/ME portfolios are exposed to more
risky situation in a crisis setting. However, there is no significant difference in pricing
the portfolios during crisis and non crisis periods with the SMB factor and the HML
factor (both have similar number of significant coefficients in Panels C and D). The
R2 values reported in Table 4.2 confirm an improvement in R
2 value during crisis
period. The results also confirm a positive relation between size, book-to-market and
average return during crisis period in all the portfolios. However, some negative
relation between average rerun and size and book-to-market is found in non-crisis
periods.
4.6 Test for Explanatory Power of SMB and HML
The results of Sections 4.3 and 4.4 can be interpreted as a comparison of the
explanatory power of the CAPM which is a single factor model and the FF3F which is
a multi factor model. This comparison entailed a limited analysis of the relative
explanatory powers of the FF3F risk factors—MKT which approximate the market
factor, SMB which approximates the size factor and HML which approximates the
BE/ME factor. The present section extends this work further to establish the
comparative strength of the factors within the CSE context.
The present chapter re-estimates a modified version of the FF3F equation 3.2 (in p.60)
in a bid to separate out the impact of SMB and the impact of HML on the 6 size-
BE/ME portfolios. In order to test which of the two variables, SMB (size) and HML
(BE/ME) is more effective in explaining the variation of stock return, the FF3F
equation is constrained by imposing restrictions h = 0, sp=0. This procedure is free
109
from omitted variable bias because the correlation test suggests that the omitted
variables are not positively correlated with the existing variables.
tptptpptftp SMBsMKTRR ,,, (4.1)
and (2) sp = 0 is used to highlight the impact of HML without the impact of SMB
which yields
tptptpptftp HMLhMKTRR ,,, . (4.2)
All notations are as explained for equation 3.2. This approach was used by others
previously to test the power of the FF3F factors (Groenewold and Fraser 1997). It is
important to measure the power of factors separately for the factors because when all
the three factors are put together in the model, the significance of one factor may
offset with other factor/factors. The risk profiles captured by these factors individually
can be used by investors to rebalance their portfolios from time to time. The test
results for full sample and sub-periods are presented in Table 4.3. It presents the
results fitting the models in equations 4.1 and 4.2 to the CSE data. The
presentation/format of the table adheres to the format used by Charitou and
Constantinidis (2004: 31).
To explain the presentation of the table the first row of results can be used as an
example. It presents estimated results of equation 4.1 for the SL portfolio. The results
are useful to identify the explanatory power of the SMB in the case of this portfolio.
Notice that as the coefficient hp is not estimated in this instance hp and h(t) columns
are left empty. The first row is followed by the estimated coefficients and the t-values
for equation 4.1 for the remaining portfolios. Thus, the top half of Panel A present
results for equation 4.1 only. The rest of Panel A, the bottom half, presents the results
of estimating equation 4.2 for the 6 portfolios. Adhering to this format will be
followed in the rest of this thesis and the reminder of Table 4.3, Panel B and Panel C,
repeat the same estimates for crisis and non-crisis periods.
110
Table 4.3: A test of explanatory power of SMB and HML (1wk 1999 to 52wk 2008).
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1999 to 2008 the CSE stocks are allocated in an independent sort to two groups (small or big) based on
their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated in
an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios, namely, SL, SM, SH, BL, BM, and BH. MKT, SMB and HML are as discussed in Chapter 3.
In order to test which of the two variables SMB (size) and HML (BE/ME) is more powerful the
variation of stock return, the FF3F equation constrained by imposing restrictions hp = 0, and sp = 0.
Regressions: tptptpptftp SMBsMKTRR ,,,
tptptpptftp HMLhMKTRR ,,,
Panel A: Full Sample Period
Exp.
Var.
Dep.
Var.
αp βp sp hp α(t) β(t) s(t) h(t) R2 adj
MKT SL -0.012 0.394 0.001 - -0.720 0.912 3.55* - 0.423
and SM -0.015 0.706 0.003 - -1.110 2.01* 3.82* - 0.233
SMB SH 0.130 3.021 0.001 - 3.17* 3.01* 0.548 - 0.215
BL 0.556 -1.79 -0.024 - 3.49* -0.461 -2.55* - 0.209
BM -0.015 0.303 0.002 - -1.107 0.870 3.25* - 0.319
BH 0.023 0.733 -0.004 - 1.16 1.49 -4.01* - 0.034
MKT SL 0.006 -0.360 - -0.003 0.360 0.822 - -0.844 0.199
and SM 0.003 0.668 - 0.001 0.257 1.881 - -0.512 0.203
HML SH 0.156 2.950 - 0.007 3.71* 2.93* - 0.843 0.216
BL 0.418 -1.512 - 0.001 2.53* -0.392 - 0.651 0.203
BM 0.004 0.262 - 0.000 0.290 0.740 - 0.037 0.197
BH 0.032 0.671 - 0.001 1.59 1.37 - 4.48* 0.042
Panel B: Crisis Period
Exp.
Var.
Dep.
Var.
αp βp sp
hp α(t) β(t) s(t) h(t) R2 adj
MKT SL -0.003 0.878 0.003 - -0.920 1.980 1.773 - 0.251
and SM -0.021 0.865 0.016 - -0.540 1.763 0.795 - 0.217
SMB SH 0.762 2.454 0.060 - 0.768 2.452
*
0.57 - 0.354
BL 0.170 0.659 -0.004 - 1.479 0.466 -0.690 - 0.216
BM -0.042 0.589 0.002 - -1.376 1.559 1.457 - 0.223
BH 0.013 0.089 -0.005 - 0.19 0.101 -1.27 - 0.003
MKT SL -0.001 0.704 - -0.000 -0.045 1.530 - -0.102 0.206
and SM 0.078 0.699 - 0.003 0.193 1.412 - -0.595 0.212
HML SH 0.239 5.514 - 0.008 1.173 2.22* - 0.243 0.235
BL 0.196 0.489 - 0.002 1.650 -0.341 - 0.316 0,208
BM -0.126 0.423 - 0.001 -
.0.390
1.089 - 0.323 0.206
BH 0.027 -0.013 - 0.002 0.36 -0.01 - 1.42 0.004
111
Table 4.3 (continued)
Panel C: Non Crisis Period
Exp.
Var.
Dep.
Var.
αp βp sp hp α(t) β(t) s(t) h(t) R2 adj
MKT SL -0.012 0.125 0.004 - -0.613 3.31*
*
- 0.221
and SM -0.015 0.480 0.003 - -1.022 0.926 3.89* - 0.434
SMB SH 0.109 -0.474 0.060 - 3.05* -0.391 0.493 - 0.204
BL 0.605 -2.648 -0.027 - 3.27* -0.423 -2.43* - 0.210
BM -0.012 0.046 0.003 - -0.811 0.097 3.08* - 0.218
BH 0.050 2.881 -0.005 - 1.89 3.27* -3.58* - 0.041
MKT SL 0.005 -0.496 - -0.000 0.248 -0.079 - -1.963 0.202
and SM 0.026 0.552 - -0.000 0.172 1.043 - -0.853 0.200
HML SH 0.127 -0.431 - 0.004 3.46* -0.364 - 0.636 0.203
BL 0.442 -3.235 - 0.010 2.31* -0.518 - 0.255 0.204
BM 0.005 0.112 - -0.000 0.716
0
0.835 - 0.862 0.204
BH 0.060 2.881 - 0.002 2.24* 3.24* - 3.98* 0.055
*significant at the 5 percent level
Let us now look at the top half of Panel A in Table 4.3. Here 2/6 of the estimated
intercept terms for equation 4.1 are significant at the 5 percent level. Out of six SMB
coefficients, 5 are significant at 5 percent level, out of which 2 are negative. However,
the coefficient of MKT is significant only for two portfolios and there are no negative
coefficients within the significant portfolios which indicate a positive relationship
between market risk and portfolio returns. The results indicate that SMB factor has a
significant influence on the variation of excess returns of small size-BE/ME portfolios
than market factors during the full sample period.
The same method is used for testing the explanatory power of HML. The results of
estimating equation 4.2 are given in the bottom half of Panel A. Out of six HML
portfolios, only one portfolio is significant in this occasion. Thus, explanatory power
of the model declines in replacing SMB with HML. Similarly, out of six market
factors, only one is significant at 5 percent level. Here only BH portfolio is significant
for HML and others are not significant. Finally, it can be concluded that SMB is more
powerful than HML in explaining stock returns for the entire sample period.
Panel B in Table 4.3 summarizes the regression estimates of equations 4.1 and 4.2 for
the crisis period. The power of both SMB and HML has dramatically declined in this
112
period when compared to Panel A. None of size-BE/ME portfolio is significant in
both estimates (SMB and HML). For the market factor only SH is significant, which
is in the second half of the panel A. This result confirms that neither SMB nor HML
factors are significant in explaining the variation in stock returns during crisis periods
in CSE. The last panel reports the estimated results of equation 4.1 and 4.2 for the
non-crisis period. In this case also SMB is more powerful than HML; out of six
portfolios 5 are significant at the 5 percent level as shown in the first six rows of
Panel C. Finally for the non- crisis series shown in Panel C, out of six portfolios five
are significant. Conversely, only one is insignificant for SMB and in case for the
HML factor only BH is significant. In this case SMB is more powerful than HML.
The adjusted R2 value improves the estimates of equation 4.1 which captures SMB
and MKT as explanatory variable. The average adjusted R2 for SMB is 0.314 and for
the HML is 0.289. This means that on average 31% portfolio returns are explained by
SMB and 28% by HML in CSE. In summary, in the Sri Lankan market, SMB is
powerful than HML as the proxies in capturing the variation of portfolio returns. This
result confirms that size factor is more dominant in the Sri Lankan stock market
during the estimation period. During crisis periods the explanatory power of the SMB
and HML decline significantly.
The above results may be attributable to several reasons that prevail in the economy in
a situation where an economy is exposed to a crisis. Generally in a crisis situation
macro economic factors deteriorate at an exponential rate. In a bad economic
environment high inflation, high interest rates, changes in money supply, fluctuation
of exchange rates, etc. are unavoidable. All of these affect the performance of firms in
the country. These factors directly affect the performance of firm‘s fundamental
variables. High inflation leads to high cost of production and due to this firm are not
in a position to set competitive prices in the market for their products. High interest
rate creates more credit risk for the firms, leading to loosing of confidence in
investors and other stakeholders. These consequences directly affect the performance
of firm fundamentals. The factors estimated here are based on company fundamentals.
Among the two variables examined here HML is more fundamentally based than
SMB, because it is mostly based on accounting variables such as accounting
113
treatments for deferred taxies and treatment for capital and revenue reserves.
Therefore, economic interpretation to the above results can be generalized as
deterioration of firm fundamentals (BE/ME in this study) due to the fluctuation of
macroeconomic variables in crisis and non-crisis periods.
4.7 Market anomalies and the January Effect in the CSE
The results of estimating the CAPM and the FF3F reveal that the returns for the CSE
portfolios are more responsive to the market anomalies (SMB, and HML) than to the
market factor (MKT). Further, in the previous section it was observed that the way
market anomalies operate is sensitive to crises: the estimated SMB and HML are
notably different in crisis period than in non-crisis period. The above sensitivity of the
results to primarily a time-bound phenomenon, led this research to look into the most
widely discussed time-bound anomaly in the literature: the January effect. The present
section seeks to measure whether the results presented so far demonstrate any
sensitivity to the January effect.
Chapter 2 examines time periods in the finance literature where the January effect as
an anomaly has been documented. For instance, Keim (1983) and Roll (1983)
document that a significant portion of the size premium to small firms occurs in
January. In this backdrop, it would be interesting to examine whether the anomalies in
the Sri Lankan stock market also change their behavior in January. The present
section achieves this by closely following the methodology of Wai and Gordon (2005:
714) who examined market anomalies in three Asian emerging markets (Hong Kong,
Singapore and Taiwan).
4.7.1 Preliminary evidence of January effect in the CSE
To start with, it is appropriate that some preliminary tests for the presence of January
effect in the CSE be conducted. This is done by examining whether the return, in the
month of January in the CSE is different to returns in other months. This comparison
is performed for all return processed used in the study, including those for the six
size-BE/ME portfolios and the market. To be more specific, the returns in the month
of January for the ten years examined here are extracted and compared against the
114
non-January returns. For additional analysis the returns for January first week are also
separated.
Some statistics regarding the above data are presented in Table 4.4. The table offers a
column each for returns from January months, January first weeks, and non-January
months. All information is presented for the full sample. The small number of
observations in Sri Lanka prevents the analysis from being extended to look at the
crisis sensitivity.
Table 4.4: Mean excess returns for the CSE portfolios. The average values represent the mean
value of seven portfolios for the intended period, which is the total return for all the seven
portfolios.
Variable January 1wk January Non-January
SL 0.101 0.308 0.007
SM 0.043 0.193 0.005
SH 0.198 0.173 0.138
BL 0.253 -0.127 0.391
BM 0.036 0.080 0.001
BH 0.072 0.851 -0.012
MKT 0.005 0.016 0.001
Average 0.117 0.246 0.088
The means of excess returns for portfolios reported in Table 4.4 are mostly positive
(19/21 means are positive). The two means that are negative are for big sized
portfolios (BL in Panel B and BH in Panel C). Similar results are reported by Keim
(1983) which showed that big firms have negative average excess returns. The
average values present in the panels (A, B and C) represents the average of the six
portfolios in each panel. Out of three panels, the highest average yield is in Panel B
(first week in January) and the second is in Panel A (January months). It is clear that
January returns are higher than non-January returns. This suggests that the January
effect exists in the CSE.
Table 4.4 is further analyzed to ascertain whether the January effect has a
significantly influence on the performance of small and big portfolios. A close look
115
into the Table 4.4 revealed that the average return of small portfolios recorded highest
in 1st week of January (0.224), and the lowest is reported in non-January (0.05).
Similarly, the highest mean return for big portfolios (0.268) is in 1st week of January.
These numbers reveal that big portfolios have performed better in January than small
portfolios. This result is contradictory with the findings of Keim (1983) and Roll
(1983) who show that small firms yield a higher premium than the big firms.
4.7.2 The CSE, January effect and the FF3F
The previous subsection, by establishing that returns from the CSE are different
across January and non-January months, builds a case for a more formal examination
of January effect in the applications of the FF3F for the CSE. Table 4.5 presents the
result of fitting equation 3.4 to excess returns from the six portfolios from the CSE for
January months (Panel A) and for non-January months (Panel B). As the CSE data is
available for only 10 years, the January month estimations are done with 40 (4×10)
observations. However, one might question why the researcher did not use January
dummies and interactions and condition on all 10 years of data other than splitting
data in to January. But, the investigator wanted to observe the behavior of all three
factors of the model, for the January months only. This purpose will not be served in
applying the dummy variable.
According to the results, the market factor (MKT) is not significant in explaining
January return and non-January returns in CSE. In both panels (A and B) none of size-
BE/ME portfolio is significant for MKT factors. This is not surprising as MKT was
not significant in the results presented in Sections 4.4 and 4.5 which included both
January and non-January data. Another interesting finding is that all the coefficients
for the market factor are negative in January (Panel A). However, with non-January
data all β coefficients are positive. However, as noted above, none of these are
significant at the 5 percent level.
Table 4.5 also attempts to distinguish whether there are noticeable January impacts on
the way SMB and HML affect the pricing of portfolios. The number of instances
where the SMB factor is significant has not shown much difference in January and
non-January months. Out of six coefficients of SMB, only two are significant with
116
January data and this goes up to three with non-January data. Both factors are
significant for more portfolios in non-January months than in January months. It
seems that the significance of factors SMB and HML for the full sample (see Table
4.2) are mostly the result of the impact of non-January data. Another pattern that is
noticeable in Table 4.5 is that all small portfolios have significant coefficients for both
SMB and HML.
Earlier it was argued that the SMB and HML factors were mostly significant in
explaining the variation of stock returns (see Table 4.2 and Table 4.3). However,
when the data is differentiated as January and non-January, the explanatory power of
these factors seems to decrease. Though Table 4.4 illustrates that the portfolio returns
in January months is higher than in non-January months, the FF3F is not able to
capture this increase. In practical sense several reasons can be attributed for FF3F not
being an accurate description of the market activity in months of the CSE during
January months. The argument of tax-loss selling in explaining the January effect
does not apply to the Sri Lankan stock market where there are no capital gains taxes
in place according to the prevailing tax law (Inland Revenue Act. 2007/2008).
However, a partial effect may come from foreign investors who hold large portfolios
in the CSE and are subject to capital gains taxation under the national tax codes in
their countries.
Another reason is that the portfolio management in Sri Lanka is still in an infant stage
as the financial system in the country is still in a developing stage. This leads to
infrequent portfolio rebalancing in the market. A more powerful explanation for the
non existence of January effect in Sri Lankan market can be attributed to timing in
disclosure of financial statements. The Companies registered at the Sri Lankan market
have to disclose their cumulative financial statements quarterly throughout the year.
The financial year in Sri Lanka is March through April. The results of this study is
consistent with the previous studies of Guneratne (2001). This study examined the
two phenomena in the financial knowledge base known as the January effect and
monthly seasonality for the period 1985 to 1998 and confirmed that January effect is
not significant for the case of Sri Lanka.
117
Table 4.5: Testing of responses of FF3F to the January effect 1999 to 2008 in CSE
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1999 to 2008, the CSE stocks are allocated in an independent sort to two groups (small or big) based
on their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated
in an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios, namely, SL, SM, SH, BL, BM, and BH. MKT, SMB and HML as discussed in Chapter 3.
Weekly returns of January months are collected for all the portfolios and include 40 (4wk×10yrs)
observations. The data for non-January months are taken from 1999 February to 2008 December,
excluding those in the 40 observations from the January months of course. Panel A presents the results
of January months and Panel B represents the results of non-January months.
Regression: tptptptpptftp HMLhSMBsMKTRR ,,,
Book to market equity (BE/ME) portfolio
Low Medium High Low Medium High
Size
Panel A: January Months (1999–2008)
αp α(t)
Small 0.037 -0.002 0.420 0.240* -0.041 2.09*
Big 0.432 0.023 0.063 1.041 0.420 1.010
βp β (t)
Small -3.130 -0.871 -2.510 -0.860 -0.672 -0.530
Big -4.091 -0.223 -0.513 -0.422 -0.174 -0.351
sp s(t)
Small 0.042 0.036 0.040 1.852 4.430* 1.360
Big -0.029 0.035 -0.004 -0.480 4.151* -0.050
hp h(t)
Small 0.100 0.009 0.019 1.400 3.55* 1.960
Big -0.003 0.010 0.010 -0.200 3.72* 3.43*
R2 adj s(e)
Small 0.344 0.621 0.350 0.740 0.268 0.960
Big 0.202 0.551 0.940 1.993 0.272 0.301
Panel B: Non January Months (1999-2008)
αp α(t)
Small 0.0100 0.013 0.124 0.690 0.970 3.77*
Big 0.041 0.008 0.031 1.543 0.599 1.46
βp β (t)
Small 0.472 0.613 0.110 1.353 1.820 0.142
Big 0.052 0.147 0.712 0.080 0.440 1.392
sp s(t)
Small 0.017 0.015 0.014 8.14* 7.36* 2.85*
Big -0.004 0.016 0.001 -1.053 7.80* 0.320
hp h(t)
Small 0.005 0.005 0.004 7.37* 6.80* 2.60*
Big -0.001 0.005 0.002 -1.274 7.05* 2.02*
R2 adj s(e)
Small 0.332 0.314 0.401 0.269 0.260 0.608
Big 0.603 0.318 0.661 0.500 0.256 0.395
*significant at the 5 percent level
118
4.8 Summary and Conclusion
This chapter empirically tests the CAPM and the FF3F and rejects CAPM in favor of
FF3F for the case of the CSE data. The market factor is not significant in the majority
of the portfolios when considering the full sample, crisis periods or non-crisis period.
In contrast the FF3F better fits the CSE data. The additional two factors—SMB and
HML—of the FF3F seem to be able to predict the excess returns of the six size-
BE/ME portfolios better than the market factor. In the FF3F or the three factor model,
only SMB and HML are significant in the majority of portfolios. This leads to the
conclusion that the market factor is insignificant in pricing stocks in the CSE. In
addition, while the well documented anomaly of January effect is also observed in the
CSE data, the FF3F is not able to capture this effect adequately.
119
Chapter 5
Testing of Asset Pricing Models for the US
5.1 Introduction
This chapter presents the results of fitting the CAPM and the FF3F to the weekly
stock market data from the US. This makes it possible to compare the behavior of
these models with the CSE and US data, which is one of the stated objectives of this
thesis. Further, this exercise is in itself an important addition to the literature as
weekly US stock returns has so far not been used with these models.
Chapter 1 asserts that a large numbers of studies empirically test the CAPM with the
FF3F using data from developed markets. This assertion was substantiated in Chapter
2, where some of the results of these studies were examined. This examination
revealed that none of the developed country studies had tested the hypothesis that
these models behave differently under market crisis situations. Looking at this is
particularly important in the case of the US because the most catastrophic of crises—
in terms of their global spread and the losses inflicted—originated from the US, for
instance the global crises in 1987 and in 2008. Methodology described in Chapter 3
which was used with Sri Lankan data in Chapter 4 is reapplied in the present chapter
for the testing of the CAPM, the FF3F and the January effect using the US data.
The rest of the chapter is structured as follows. Section 5.2 briefly examines economy
and the stock market of the US in the context of crisis experiences. This is important
to contextualize the empirical work in the current chapter. Section 5.3 summarizes the
results of fitting the CAPM and the FF3F to the weekly US data. The additional
assessment conducted to measure the explanatory power of the SMB and HML
factors are discussed in Section 5.4. The January effect, which is a pervasive anomaly
in the US market and its relevance to the six FF3F portfolios, is explored in Section
5.5 followed by some concluding remarks in Section 5.6.
120
5.2 The US Economy
This section provides a cursory look at the US economy. This is important because it
helps to understand the stock market activity in the US, which is the primary focus of
the present chapter. For instance, according to the CAPM and the FF3F a key
determinant of stock price movement is the return on the market portfolio which is
impacted by the overall performance of the economy. This section reviews the recent
macroeconomic and financial indicators that are considered to be the key macro
variables that influence stock market performance. The economic indicators directly
influence the fluctuation of market portfolio of any country. However, it is
noteworthy highlighting the behavior of the economic variables in the US because the
performance of the US economy is a key factor for the performance of the markets of
rest of the world as it is the largest economy in the world.
Table 5.1 tabulates annual values of five variables which summarize the recent
performance of the US economy. The data presented in the table covers the period
from 1980 to 2009, which includes the period examined in this thesis. Table shows
that nominal GDP has increased throughout this period. In 1980 the GDP was $2,788
bn which had increased many times over to $14,119 bn by 2009. However, the growth
in real GDP, which is also reported in the table, offers a different perspective and
shows that the US growth has not increased during this period. It is evident that
growth has oscillated around the period average of 2.7% during 1980-2009. The
growth figures also reveal declining economic performance in the last few years of
1980‘s and also post-2008. These patterns will be referred to later in this section.
The per capita disposable personal income reported in Table 5.1 adjusts the above
data for population growth. Interestingly it has increased steadily over the period from
1980 to 2009. These increases are in real terms as the reported per capita incomes in
2005 are for constant prices. Declining inflation reflected reported by the GDP
deflator during this period and no doubt helped the growth of disposable income. The
GDP deflator also reveals that early 1980‘s was inflationary for the US economy,
compared to the period after that.
121
Table 5.1: Macro Variables of US Economy
GDP
($ bn)
GDP
Growth
Per capita
disposable
personal
income
(2005
constant
prices)
GDP
Deflator
Net gov
lending or
net
borrowing
(-) $ bn
1980 2,788 -0.3 18,863 9.1 (75.7)
1981 3,127 2.5 19,173 9.4 (73.5)
1982 3,253 -1.9 19,406 6.1 (161.3)
1983 3,535 4.5 19,868 4.0 (201.8)
1984 3,931 7.2 21,105 3.8 (190.4)
1985 4,218 4.1 21,571 3.0 (215.5)
1986 4,460 3.5 22,083 2.2 (238.5)
1987 4,736 3.2 22,246 2.9 (208.4)
1988 5,100 4.1 22,997 3.4 (186.7)
1989 5,482 3.6 23,385 3.8 (181.7)
1990 5,801 1.9 23,568 3.9 (251.8)
1991 5,992 -0.2 23,453 3.5 (301.3)
1992 6,342 3.4 23,958 2.4 (373.1)
1993 6,667 2.9 24,044 2.2 (338.3)
1994 7,085 4.1 24,517 2.1 (262.3)
1995 7,415 2.5 24,951 2.1 (244.5)
1996 7,839 3.7 25,475 1.9 (179.7)
1997 8,332 4.5 26,061 1.8 (73.8)
1998 8,794 4.4 27,299 1.1 27.0
1999 9,354 4.8 27,805 1.5 64.4
2000 9,952 4.1 28,899 2.2 146.6
2001 10,286 1.1 29,299 2.3 (65.1)
2002 10,642 1.8 29,976 1.6 (422.4)
2003 11,142 2.5 30,442 2.2 (553.3)
2004 11,868 3.6 31,193 2.8 (531.1)
2005 12,638 3.1 31,318 3.3 (418.3)
2006 13,399 2.7 32,271 3.3 (291.6)
2007 14,062 1.9 32,693 2.9 (408.1)
2008 14,369 0 32,946 2.2 (912.3)
2009 14,119 -2.6 32,847 0.9 (1,592.7)
Source: Bureau of Economic Analysis US Department of Commerce
122
The last economic indicator shown in the Table 5.1 is the net borrowings of the
economy which reveals that apart from a brief period in late 1990‘s, the US has been
a net borrower throughout the period examined here. The biggest ever deficit of
$1,593 bn was recorded in 2009 attributed to the impact of the event that followed
after 2008.
The relevance of macroeconomic analysis is multifaceted in this study. First, the stock
markets are key contributors of the economic growth as it facilitates the capital
investment need in the economy. For example, if people have per capita income in
excess of consumption, they can invest it and can gain returns in future. The stock
market facilitates the general public to get the ownership of the companies by
purchasing shares. On the other hand, the companies can gather long term capital
requirement without much difficulty if the country has a potential investor base. This
simple example very clearly suggests that the performance of the companies is based
on the prevailing macro economy of the country. Second, the variables presented in
Table 5.1 are identified as major determinants of the performance of the US market.
The market factor is key variable in this study which determines the performance of
the model significantly.
Moreover, the corporate profit is also based on the soundness of variables such as
GDP, per capita income and inflation etc. The key variables, SMB and HML of FF3F
represent the profitability of the companies largely. Therefore, capital market based
research demands substantive analysis of macro economy of the country to obtain
sound background for the analysis of the findings.
In view of the subject covered in this thesis it is important to specially look at the
financial sector of the US economy. Table 5.2 tabulates six variables that are useful
for such a discussion. The performance of capital markets are influenced by these
financial factors. For example, there is a close relationship between long term interest
rates and the share prices in investors‘ standpoint. The strength of exchange rate is
also important to attract international investors. It is one of the key determinants of
the international risk component of the capital market.
123
Table 5.2: Financial Indicators of US Economy
Central
Governm
ent total
debt
($ mn)
Long
term
interest
rates %
Share
Price
Index
Share
Returns
Annual
Inflation
(CPI) %
Exchange
Rate
(SDR/
USD)
1980 716,500 11.46 9.80 - 13.50 0.77
1981 795,400 13.91 10.60 8% 10.30 0.85
1982 930,700 13.00 9.90 -7% 6.10 0.91
1983 1,141,700 11.11 13.30 34% 3.20 0.94
1984 1,300,900 12.44 13.30 0% 4.30 0.97
1985 1,508,100 10.62 15.60 17% 3.50 0.97
1986 1,742,900 7.68 19.60 26% 1.90 0.85
1987 1,894,400 8.38 23.30 19% 3.70 0.77
1988 2,055,400 8.85 21.60 -7% 4.10 0.74
1989 2,165,800 8.50 25.90 20% 4.80 0.78
1990 2,426,100 8.55 26.40 2% 5.40 0.74
1991 2,760,200 7.86 29.70 13% 4.20 0.73
1992 3,064,200 7.01 33.00 11% 3.00 0.71
1993 3,297,400 5.87 35.90 9% 3.00 0.72
1994 3,483,700 7.08 36.60 2% 2.60 0.70
1995 3,654,200 6.58 41.90 14% 2.80 0.66
1996 3,778,400 6.44 51.50 23% 2.90 0.69
1997 3,814,800 6.35 65.70 28% 2.30 0.73
1998 3,760,400 5.26 79.20 21% 1.60 0.74
1999 3,665,600 5.64 89.10 13% 2.20 0.73
2000 3,395,489 6.03 92.60 4% 3.40 0.76
2001 3,339,674 5.02 87.10 -6% 2.80 0.79
2002 3,553,420 4.61 75.90 -13% 1.60 0.77
2003 3,924,300 4.02 74.10 -2% 2.30 0.71
2004 4,307,420 4.27 90.00 21% 2.70 0.68
2005 4,605,970 4.29 100.00 11% 3.40 0.68
2006 4,848,260 4.79 113.70 14% 3.20 0.68
2007 5,054,930 4.63 131.30 15% 2.90 0.65
2008 5,820,460 3.67 109.40 -17% 3.80 0.63
2009 7,561,736 3.26 82.90 -24% (0.40) 0.65
Source: Organization for Economic Co-operation and Development
Table 5.2 unveils six financial indicators of the US for the 1980-2009 periods. Among
these six the volume of government debt has dramatically increased during the past
124
three decades. The other financial indicators shown in Table 5.2 are also directly
affecting the capital market operation. Among them long term interest rates and
inflation go in hand with stock prices. At a glance that pattern is aptly demonstrated in
the values shown in the table as well. Theoretically the share prices and interest rates
have negative relationship, whereas share price and inflation has positive relationship.
Figure 5.1: Some economic and financial variables for the US. The perforated line
graphs should be read off the right axis; the solid graphs off the left axis. As the
horizontal time scale is common to both panels only it is spelt out only in the bottom
panel.
-4%
-2%
0%
2%
4%
6%
8%
-10%
0%
10%
20%
30%
40%
Gov. Debt (Left) GDP Growth (Right)
Panel A
0%
2%
4%
6%
8%
10%
12%
14%
16%
-30%
-20%
-10%
0%
10%
20%
30%
40%
Share returns (Left) Interest Rate (Right)
Panel B
Panel A and Panel B of Figure 5.1 highlight relations between some of the variables
from Table 5.1 and 5.2. These graphical methods are useful to expose links between
series of data. For instance, Figure 5.1.A looks at the annual percentage changes of
125
government debt and GDP growth rates of the US market for the period from 1981 to
2009. The growth of government debt has decreased during 1980s and 1990s
gradually and again it has started to increase dramatically since the beginning of
2000s. A towering trend of government debt is seen since the beginning of 2007. This
can be interpreted as the reflection of bail-out packages gained by the government to
overcome the 2008 crisis. On the other hand, the GDP growth rates highly fluctuated
during this period. It has gradually declined up to 2007 and after that dramatically
declined up to -2% in 2009. This can be identified as the decline of the total
productivity of the economy due to the recent economic turmoil.
Furthermore, Figure 5.1.B displays movements of the annual returns from share
markets and annual long term interest rates. The line which represents the left hand
side axis shows the share returns, while the line falling from right hand side axis
represents the interest rates. At a glance one can notice that these two variables
furnish a pattern of inverse relationship throughout the period. The reason for this
pattern may be that as the long term interest rate comes down investors shift from
bonds to common stocks as the prices of shares go up in the market due to demand
and supply mechanism. However, it shows a dramatic decline of both long term
interest rates and share prices at the beginning and the during the 2008 economic
crisis of the US.
Figure 5.1 demonstrates that the 2008 crisis is more severe than other crises that have
occurred in the US during the recent past. For example during the 1987 crisis there
was no big fluctuation of government debt and GDP growth as shown in Panel A in
the figure. However, Figure 5.1.B shows a dramatic decrease in long term interest
rates over the period of 1980 and 2009, whereas the share prices reflect a constant
trend with high volatility annually.
As previously stated the major concern of this study is the substantiation of asset
pricing models in crisis situations in the world. The analysis conducted above
demonstrated that the economic and financial variables in the US were sensitive to
crises in the country. Therefore, it is deemed that a discussion about the impact of
crises on the US stock markets is useful here.
126
Still more than 50% of global stock market share14
is held by US market. Therefore,
US market is a very important determinant in shaping the stock pricing behavior of
global stock markets. The evidences in the previous paragraphs revealed that stock
prices are considerably driven by macroeconomic factors which impact the US
market. Among the market crises that have occurred in the history of capital markets
the 1987 and the recent 2008 crises have most profoundly influenced the performance
of US market. Therefore, it is worthwhile to explain at this point about these two
crises.
Impact of 1987 Crisis on US Market
In the above analysis it is noticed that the 1987 crash has a direct link to the economic
variables and financial variables. In addition to what is discussed in the above
paragraphs, higher export earnings due to the devaluation of dollar have resulted in a
favorable balance sheet for companies. The company fundamentals have shown
favorable values for attracting more investments. These facts induced the demand for
the stocks of the companies that led to stock price hike. It is illustrated in Figure 5.1.B
which shows a sharp increase of stock price at the beginning of 1988. The subsequent
government intervention created the crash (taxes, falling interest rates etc.) in the
market. This evidence reveals that the both company level fundamental factors and
macro economic factors have influenced the crisis.
In the first half of 1987, the US dollar experienced a steep decline in value relative to
other world currencies. This made US goods and services less expensive and resulted
in increased exports. The increase in exports provided US companies with a strong
outlook on earnings and the stock market took off. There has been a great deal of
corporate restructuring in the years proceeding 1987 for American companies which
have been promising strong future earnings growth. International investors have also
taken notice of the improvements in the US market outlook.
14 Global share of equity investment April 2005 Standard and Poor‘s 2005 p.12.
127
Many of the explanations for the 1987 stock market crash and the volatility associated
with it are peculiar to financial institutions in the United States, and some to the
NYSE in particular. Mitchell and Netter (1989) argue that tax legislation introduced
in the week before on October 19, 1987, contributed to the crash. Others have argued
that the effect of computerized trading linking stock, options, and futures markets,
(sometimes called index arbitrage or portfolio insurance) on the 1987 crisis. As
described by Roll (1988, 1989), the important fact that the 1987 crash was
simultaneous and similar around the world challenges all explanations are distinctive
to a specific country; even a country as large as the U.S.
Repercussions of the Crisis of 2008
According to the prevailing evidences, the 2008 crash is considered as the biggest
crash that occurred after the great depression in 1929. The major cause for this
financial crisis is the reckless providing of loans by financial institutions, particularly
to the housing sector without proper supervision, and the resulting eventual
bankruptcy of such financial institutions. In other words, this is a turmoil caused by
the grant of loans to ―bad creditors‖ assuming them as good creditors.
A collapse of the US sub-prime mortgage market and the reversal of the housing
boom had ripple effects around the world. Furthermore, other weaknesses in the
global financial system have surfaced during this period. Some financial products and
instruments have become so complex and twisted, that as things start to unravel, trust
in the whole system started to fail. The extent of the problems has been so severe that
some of the world‘s largest financial institutions have collapsed. Others have been
bought out by their competition at low prices and in other cases, the governments of
the wealthiest nations in the world have resorted to extensive bail-out and rescue
packages for the remaining large banks and financial institutions.
September 16, 2008, saw the failures of large financial institutions in the United
States, which rapidly evolved into a global crisis resulting in a number of bank
failures in Europe and sharp reductions in the value of equities and commodities
worldwide. In United States 15 banks failed in 2008, while several others were
rescued through government intervention or acquisitions by other banks. The US
128
financial market crisis is due to heavy leveraging on instruments of property markets
by investment banks. Since early 2007, there had been speculation of a possible
recession starting in early or late 2008 in some countries. The US and the UK are
clearly in financial trouble.
This section explains the behavior of US stock market and the impact of market crises
on its performance. Here considerable attention is paid to explain the previous US
market crisis. It is important because this research directly tests the CAPM and FF3F
in a crisis setting. The next section explains the regression results of tests for CAPM
and FF3F.
5.3 Tests for the CAPM and the FF3F
This section presents the results of fitting the models in equations 3.2 and 3.4 using
the weekly US data. Here also the models are fitted for crisis and non-crisis periods
identified in Chapter 3 using the ICSS test (see p.76 of this work).
5.3.1 The CAPM test results in the US
The estimation results of the regression tests for US are organized in three panels in
Table 5.3 which present the results for the full period, crisis period and the non-crisis
period. Therefore the table contains results for 18 regressions. In the three panels (A,
B and C) 6/18 intercept terms are significant at the 5 percent level. Out of the
significant intercepts two are negative. Both of these are from Table 5.3.A which
represents the full sample period. Out of the remaining 12/18 insignificant intercept
terms 8/18 are negative.
The estimated α values of portfolios represent the risk free rate of the US financial
market. For example, if the market risk free rate is approximated by the average 3
month TB rate which for the relevant period is 14.5 percent (Kenneth R. French
database), then it becomes obvious that the estimated intercept of the SML curve do
not accurately approximate the risk-free rate of the US economy. The estimated real α
is far below the TB rate of the economy. This suggests that the alpha value derived
from the CAPM cannot capture the real risk-free rate of the economy.
129
Table 5.3: Test of CAPM in the US market
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1985 to 2007 the NYSE stocks are allocated in an independent sort to two groups (small or big) based
on their market capitalization (stock price into outstanding shares). Thereafter all stocks are allocated in
an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios namely SL, SM, SH, BL, BM, and BH. Rmt is the excess weekly return of NYSE.
Regression: tptftmpptftp RRRR ,,,,,
Panel A: Full Sample Period
Dependent
Variables αp βp α(t) β(t) R
2 adj
SL -0.096 1.130 -2.34* 56.80* 0.720
SM 0.057 0.820 1.900 56.20* 0.720
SH 0.084 0.770 2.60* 49.90* 0.670
BL -0.003 1.050 -0.220* 146.3* 0.940
BM 0.030 0.870 1.370 83.0* 0.850
BH 0.049 0.780 1.680 56.00* 0.720
Panel B: Crisis Period
Dependent
Variables
αp βp α(t) β(t) R2 adj
SL -0.133 1.100 -1.610 32.70* 0.720
SM -0.027 0.804 -0.460 33.17* 0.720
SH -0.032 0.730 -0.540 29.80* 0.680
BL 0.054 1.060 2.060* 98.70* 0.950
BM 0.041 0.881 -1.070 56.23* 0.880
BH 0.020 0.758 -0.410 36.70* 0.760
Panel C: Non Crisis Period
Dependent
Variables
αp βp α(t) β(t) R2 adj
SL -0.067 1.110 -1.230 38.90* 0.711
SM 0.132 0.766 3.480* 38.50* 0.707
SH 0.191 0.749 4.430* 33.20* 0.642
BL -0.028 1.060 -1.380* 99.43* 0.941
BM 0.085 0.846 2.620* 49.60* 0.800
BH 0.087 0.044 1.980 34.10* 0.654
*significant at the 5 percent level
The other important coefficient in the equation 3.2 is β which represents the
systematic risk component of the portfolios. Panels A, B and C in Table 5.3 reveal
that all the 18 beta coefficients are significant at the 5 percent level. This result
confirms that the CAPM is still valid in estimating stock returns in the U.S market,
irrespective of whether the data represents crisis periods or not. In a broader sense,
this result implies that the market proxy (NYSE) is a good indicator in predicting
cross sectional average stock returns of the US market even in market crisis periods.
No significant different is found in the results for crisis and non crisis periods. This
130
can be attributed to several factors. First the US is a developed market. Second, most
of the underlying assumptions of the CAPM are valid for the developed market which
was not the case with the CSE. In the developed markets, generally information goes
to the investors without much delay as a result the investors react to information
promptly in choosing stocks into their investment portfolios.
The values of adjusted R2 as a measure of the total variance explained by the models
are close to 1 in most of the cases. Out of 18 adjusted R2 values 14 are above 0.70.
This suggests that the model explains the variation of stock returns in US market.
Based on these results the CAPM is recommended as a valid model in predicting
stock return during market crisis periods and non crisis periods in the NYSE. No
significant differences are found in the predictability of the model between crisis and
non crisis periods.
Even though CAPM is valid in prediction stock returns in the US market, the common
issues such as usability of beta and market proxy issue in the CAPM still prevail in
the application of CAPM in the real world situation. However, its soundness in
application in developed markets is more reliable than the emerging markets.
5.3.2 Testing Results of Three Factor Model
This subsection applies the portfolio data constructed for the US market in Chapter 3
to estimate the multi factor FF3F regression in equation 3.4 using weekly US data.
The results are presented in Table 5.4 according to whether the full period, crisis
period or the non-crisis period is being used for the regression.
The estimated alphas in Table 5.4 yield both positive and negative values. Here, out
of 18 coefficients 8 are negative and 10 are statistically significant at 5 percent level.
As previously explained in Chapter 4, Fama and French (1996: 57) suggest that if
FF3F completely describes the expected returns, the regression intercepts, α, should
not be significantly different from zero. Interestingly in US market all α’s are close to
zero which suggests that the FF3F can completely explain the expected returns of
portfolios. The positive α’s which are statistically significant mean that the FF3F
131
Table 5.4: The FF3F results for the US based on weekly data (1wk 1985 to 52wk 2007).
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1985 to 2007 the US stocks are allocated in an independent sort to two groups (small or big) based on
their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated in
an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios namely SL, SM, SH, BL, BM, and BH. MKT, SMB and HML as discussed in Chapter 3.
Book to market equity (BE/ME) portfolio
Low Medium High Low Medium High
Size
Regression: tptptptpptftp HMLhSMBsMKTRR ,,,
Panel A: Test for FF3F Full Sample Period
αp α(t)
Small -0.071 0.016 0.0123 -4.73* -1.540 1.430
Big 0.033 -0.026 -0.049 3.33* -1.720 -3.36*
βp β(t)
Small 1.080 0.951 0.989 126.1* 158.4* 199.9*
Big 0.949 1.020 1.040 162.4* 117.1* 124.2*
sp s(t)
Small 0.999 0.791 0.814 82.80* 150.4* 117.6*
Big -0.226 -0.125 -0.041 -27.50* -10.20* -3.55*
hp h(t)
Small -0.132 0.419 0.687 -8.680* 37.20* 78.20*
Big -0.338 0.471 0.841 3.330* 30.29* 56.00*
R2 adj RMSE
Small 0.960 0.970 0.970 0.510 0.370 0.290
Big 0.970 0.920 0.930 0.350 0.520 0.500
Panel B: Test for FF3F Crisis Period (Volatile)
αp α(t)
Small -0.071 0.015 0.007 -2.83* 0.890 0.510
Big 0.043 -0.056 0.036 2.35* -2.22* -1.420
βp β(t)
Small 1.103 0.968 0.989 76.10* 95.16* 110*
Big 0.954 1.04 1.063 88.70* 71.50* 72.60*
sp s(t)
Small 0.981 0.782 0.779 56.8* 64.5* 75.10*
Big -0.242 -0.140 -0.057 -19.0* -8.05* -3.32*
hp h(t)
Small -0.067 0.427 0.707 -2.30* 20.70* 38.90*
Big -0.323 0.489 0.902 -14.8* 16.42* 30.20*
R2 adj RMSE
Small 0.971 0.970 0.970 0.500 0.350 0.310
Big 0.985 0.956 0.940 0.370 0.511 0.510
132
Table 5.4: (continued)
Book to market equity (BE/ME) portfolio
Low Medium High Low Medium High
Size
Panel C: Test for FF3F Non Crisis Period (Non Volatile)
αp α (t)
Small 0.086 0.024 -0.029 -3.77* 1.500 2.420*
Big 0.041 -0.000 -0.074 2.86* 0.040 -3.34*
βp β (t)
Small 1.100 0.920 0.994 80.80* 93.40* 138.0*
Big 0.956 0.998 1.060 111.0* 71.60* 80.6*
sp s(t)
Small 1.060 0.770 0.842 51.0* 51.20* 76.70*
Big -0.214 -0.115 0.007 16.30* -5.42* 0.400
hp h(t)
Small -0.112 0.421 0.698 -5.30* 27.50* 62.60*
Big -0.328 0.474 0.860 -24.60* 21.96* 41.90*
R2 adj RMSE
Small 0.950 0.940 0.970 0.550 0.400 0.290
Big 0.970 0.900 0.910 0.340 0.590 -0.530
*significant at 5 percent level
factors are consistently under predicting the portfolio returns. Here, out of significant
alphas 4 are positive. The average values for α’s of six portfolios for the three
periods—full sample, crisis and non-crisis are -0.0141, -0.0043 and 0.008
respectively. It shows a slight increase in alpha during non-crisis periods.
This provides a unique opportunity for comparing these results with those of Fama
and French (1996: 59) which involved 25 portfolios and monthly data for the period
1963-1993. In their work 16/25 alphas are close to zero and 13/25 are negative. These
earlier results can be compared with Table 5.4.A in the present study. The rest of the
results in Table 5.4 cannot be compared against Fama and French (1996) as the latter
does not separate the crisis periods as is done here. Out of the six estimated alphas in
Table 5.4.A three are significant, which is 1/2 of the total estimated alphas. Compared
to this out of the 25 estimated alphas in Fama and French (1996), 4 are significant
which is approximately 1/6 of total estimated alphas.
Among the three risk factors in the FF3F the most important variable is the estimated
slope coefficients for MKT factor, β‘s, in Table 5.4. In the three panels, all beta values
are positive and all are significant at 5 percent level. The finding of the current study
133
is consistent with the Fama and French (1996) in their results all beta coefficients (25)
are positive and significant at 5% level and similarly in the current findings all beta
values are significant for all 6 portfolios in the full sample period. On the other hand
it is interesting that the average of all beta values for small portfolios (SL, SM, and
SH) in Panel A is 1.0. When this is compared with the average figure of the big
portfolios (BL, BM, and BH) in Panel A no difference in beta value is found. It
suggests the risk is similar in the US portfolios, irrespective of small and big
portfolios. The average betas for crisis and non-crisis periods are also concentrated on
1.0. There is no difference in beta in crisis and non-crisis periods. This implies that no
investor can get the benefit of diversification in US market among small and big
portfolios.
The estimated coefficient of the SMB factor, sp, is discussed here. In panels A, B and
C all the 18 (3x6) portfolios are significant at 5 percent level. It is also interesting to
note that 7 negative coefficients are found out of 18 coefficients. The specialty of this
finding is that these 7 coefficients are related to the big firms. Interestingly, Fama and
French (1996 : 59 ) obtained almost similar findings for big portfolios with monthly
data; that is all 6 big portfolios yield negative loadings in their findings. However, in
the current study, in full sample periods all 3 portfolios have negative loadings on
SMB. This indicates that the SMB is negatively related to the changes in the big
portfolios in the US market. Further, this means that when the size factor increase on
weekly basis, the corresponding return of portfolio decreases by the value of slope
coefficient. The average sp for the nine small portfolios in the three panels is 0868. In
contrast the average for the big portfolios is –0.128. This suggests that small
portfolios are more sensitive to the SMB than big portfolios.
The last factor in the FF3F is the HML, is a proxy for capturing the effect of BE/ME
in the model. Here also in panels A, B and C all the hp coefficients are significant at 5
percent level. One interesting finding here is that SL and BL (in all factors) yield
negative coefficients except BL in HML. However, Fama and French (1996 : 59 )
yield negative loadings for HML for all 5 low small and big portfolios in current
study it is out of 2 low portfolios (full sample) only 1 yield negative loading. All
HML loadings are significant in Fama and French‘s study and similarly in the current
134
study also all six HML loadings are significant in full sample period. The average of
HML coefficients (six portfolios) in crisis and non-crisis periods are 0.355 and 0.335
respectively. It reveals that in crisis periods all the six portfolios on average are
slightly higher than in non-crisis period.
The results presented above indicate that the FF3F performs well in the US market.
All the three factors are equally important in determining the stock returns in the US
market. The reported adjusted R2 can be used to statistically establish this assertion.
The high value of reported R2 is a common occurrence in developed markets.
It is evident that the adjusted R2 had monotonically increased from CAPM (in Table
5.3) to FF3F (in Table 5.4). The average (in all three panels) adjusted R2 of the CAPM
regressions is 0.765 and the average for the FF3F is 0.952. This result confirms that
the FF3F is more powerful than CAPM in explaining the variation of portfolio returns
in the US market. The adjusted R2 values in Table 5.4 can be looked at according to
the period of study—full sample, crisis, and non-crisis. For instance, the average of
the adjusted R2 in the six portfolios during crisis period is 0.965. This figure is much
higher than in the other two periods: for the full sample it is 0.953; for the non-crisis
period 0.940. Earlier in this section, in discussing the estimated constant term of the
model, it was asserted that the intercepts being close to zero implied that the FF3F
variables had useful explanatory power. The evidence based on the adjusted R2 also
supports this.
The results demonstrate that these factors are able to capture the shared variation in
stock returns that are missed by the market portfolio (CAPM) in US market. All
2R are very high and ranging from 92% to 97%. That indicates the high sensitivity of
the model. These findings predominantly demonstrate that the three factor model
works very significantly in US Market during 1985-2007.
5.4 Test for Explanatory Power of SMB and HML
This section estimates the equation 4.1 and 4.2 in (see p.109) for the US market to
measure the explanatory power of SMB and HML in the FF3F for US market. This is
important to identify the individual explanatory power of the factors in the FF3F. The
135
discussion will be made here in line with the same section in Chapter 4 so as to
facilitate the comparison of the results of both countries.
In the top half of Table 5.5.A, 3 of the 6 estimated intercept terms for equation 4.1 are
significant at the 5 percent level. Moreover, all of the SMB coefficients are significant
at 5 percent level; all of these are positive. The coefficient of MKT is also significant
at 5 percent level for all the portfolios. None of the reported values are negative which
indicates that the portfolio returns and MKT has a positive relationship in the US
market. The results indicate that SMB factor has a significant influence on the
variation of excess returns of small and big portfolios in US market
The same method is used (in Panel A) for the testing the explanatory power of HML.
The results of estimating equation 4.2 are given in the bottom half of Table 5.5.A. Out
of six HML portfolios all are significant in this occasion, of which two are negatively
related. The t-values in this case are lower than SMB, which indicates that the
explanatory power of the model declines in replacing SMB with HML. Similarly, all
the MKT coefficients are significant. Finally it can be concluded that SMB is more
powerful than HML in explaining stock returns for the entire sample period.
136
Table 5.5: A test of explanatory power of SMB and HML (1wk 1985 to 52wk 2007).
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1985 to 2007 the NYSE stocks are allocated in an independent sort to two groups (small or big) based
on their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated
in an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios namely SL, SM, SH, BL, BM, and BH. MKT, SMB and HML are as discussed in Chapter 3.
In order to test which of the two variables SMB (size) and HML (BE/ME) is more powerful the
variation of stock return, the FF3F equation constrained by imposing restrictions hp = 0, and sp = 0.
Regressions: tptptpptftp SMBsMKTRR ,,,
tptptpptftp HMLhMKTRR ,,,
Panel A: Full Sample Period
Exp.
Var.
Dep.
Var.
αp βp sp hp α(t) β(t) s(t) h(t) R2 adj
MKT SL -0.086 1.120 1.020 - -5.60* 152.* 8.60* - 0.960
and SM 0.064 0.820 0.690 - 4.03* 106* 55.6* - 0.920
SMB SH 0.900 0.770 0.650 - 4.30* 75.9* 40.0 - 0.860
BL -0.004 1.050 -0.148 - -0.34 157* -13.7* - 0.950
BM 0.027 0.870 -0.233 - 1.370 90.5* -14.9* - 0.870
BH 0.046 0.780 -0.235 - 1.680 58.8* -10.9* - 0.740
MKT SL -0.038 0.970 - 0.501 -0.980 44.2 - -13.2 0.760
and SM 0.042 0.860 - 0.127 1.410 50.1* - 4.28* 0.720
HML SH 0.039 0.890 - 0.386 1.280
*
51.9* - 12.9* 0.710
BL 0.026 0.970 - -0.255 2.03* 131* - -20.0* 0.960
BM -0.030 1.030 - 0.518 -1.910 115* - 33.3* 0.920
BH -0.056 1.050 - 0.850 -3.44* 125* - 59.3* 0.920
Panel B: Crisis Period
Exp.
Var.
Dep.
Var.
αp βp sp
hp α(t) β(t) s(t) h(t) R2 adj
MKT SL -0.071 1.120 0.997 - -2.81* 109* 62.9* - 0.974
and SM 0.014 0.819 0.680 - 0.590 79.3* 42.8* - 0.950
SMB SH 0.006 0.744 0.629 - 0.200 54.2* 29.8* - 0.900
BL 0.044 1.060 -0.165 - 1.92 112.* -11.4* - 0.960
BM -0.057 0.876 -0.256 - -0.175 65.6* -12.5* - 0.910
BH -0.037 0.752 -0.272 - -0.820 40.2* -9.49* - 0.800
MKT SL -0.123 0.848 - -0.751 -1.64 20.5* - -9.30* 0.770
and SM -0.025 0.765 - 0.115 -0.44 23.5* - -1.81* 0.730
HML SH -0.034 0.782 - 0.151 -0.58 23.9* - 2.37* 0.680
BL 0.056 1.010 - -0.154 2.20 72.4* - -5.64* 0.962
BM -0.490 1.080 - 0.586 2.20 72.3* - 20.0* 0.942
BH 0.033 1.080 - 0.942 -1.28 76.5* - 34.1* 0.930
137
Table 5.5: (continued)
Panel C: Non Crisis Period
Exp.
Var.
Dep.
Var.
αp βp sp hp α(t) β(t) s(t) h(t) R2 adj
MKT SL -0.108 1.14 1.09 - -4.73* 95.3* 53.9* - 0.949
and SM 0.108 0.780 0.646 - 4.47* 61.7* 30.0* - 0.881
SMB SH 0.167 0.763 0.636 - 5.21* 45.5* 22.3* - 0.802
BL 0.024 1.06 -0.117 - -1.21* 102* -6.69* - 0.945
BM 0.095 0.840 -0.255 - 3.11 52.6* -9.40* - 0.825
BH 0.096 0.780 -0.245 - 2.26 34.9* -6.47* - 0.676
MKT SL 0.014 0.975 - -0.435 0.270 31.7* - -9.40* 0.747
and SM 0.097 0.827 - 0.187 2.58* 37.1* - 5.59* 0.721
HML SH 0.108 0.892 - 0.442 2.78* 38.8* - 12.7* 0.716
BL 0.020 0.981 - -0.262 1.22* 97.2* - -17.2* 0.960
BM -0.009 1.01 - 0.509 -0.420 72.3* - 24.1* 0.897
BH -0.073 1.06 - 0.858 -0.07* 82.0* - 43.8* 0.916
*significant at the 5 percent level
Table 5.5.B summarizes the regression estimates of equations 4.1 and 4.2 for crisis
period in the US market which were identified using the ICSS algorithm. As shown in
the first half of the Panel B, all the six SMB coefficients are significant at 5 percent
level. Similarly, HML is significant for all the six portfolios as presented in the
second half of the Panel B. The final panel reports the estimated results of equation
4.1 and 4.2 for the non-crisis period. In this case also all the coefficients of both SMB
and HML are significant.
The adjusted R2 value improves in the estimates of equation 4.1 which captures SMB
and MKT as explanatory variable. The average adjusted R2 for SMB is 0.881and for
the HML it is 0.831. This means that on average 88% portfolio returns are explained
by SMB and 83% by HML in the US. In summary, in the US market SMB is
powerful than HML as the proxies in capturing the variation of portfolio returns. If
the R2 values of SMB and HML are compared in crisis and non-crisis periods the
explanatory power of these two models increase in crisis period. The R2 for SMB for
crisis period is 0.915 and it is for non-crisis period 0.846. Similarly for the HML R2
for crisis period is 0.835 and it is 0.826 for non-crisis period.
138
This results very clearly demonstrates that the explanatory power of the SMB and
HML increases in crisis period. This result confirms that size factor is more powerful
in explaining portfolio returns in the US market. Nevertheless, the findings are
inconsistent with prior US results of Fama and French (1992) which shows that the
book-to-market effect (HML) is more powerful than size (SMB) in explaining
average returns. It follows that Fama and French‘s (1992) findings are reconfirmed by
the present study. These evidences imply that all factors in the FF3F cannot
universally capture all market anomalies. Their relevance differ across markets and
the samples considered.
5.5 Test Results of January effect US Market
This section summarizes the test results of January effect relating to US market for the
period of 1964 -2008 and to have further insight into January effect, the January first
week‘s mean excess returns is also calculated. The availability of long series of data
in the US market influenced the investigator to investigate long period from 1885 to
2007. Thus, the sample period for the analysis in this section is expanded to 1964
simply because this is the period where the emergence of asset pricing models taken
place (such as CAPM, Gordon Model) in the field of finance. In addition, the large
sample analysis done here is an important contribution to the literature on January
effect in the US as the existing works mostly concentrate on recent data. This section
further examines the responses of the FF3F to January effect and test the existence of
January effect for the portfolios other than single stocks.
5.5.1 Preliminary evidence of January effect US Market
This section attempts to describe the behavior of the return of portfolios between
January and non-January months. For this purpose the US return series of portfolios is
divided into three sub-sections as January, non-January and 1st week of January. By
doing so, the returns of each portfolio can be measured separately for each period. At
a glance it is very obviously seen that all portfolios yield positive returns in all the
three sub-sample period.
139
Table 5.6: Percentage return of January & Non January 1964-2008. The average values in the
last row represent the mean value of seven portfolios for the intended period which is the total
return for all the seven portfolios.
Portfolio January Non January January 1st week
SL 0.758 0.130 1.090
SM 0.817 0.231 1.240
SH 1.080 0.246 1.640
BL 0.228 0.188 0.090
BM 0.318 0.202 0.686
BH 0.611 0.224 1.090
Average 0.635 0.203 0.972
A close look into Table 5.6 demonstrates that the January returns are higher than
non-January returns: January month average returns is 0.635, whereas for non-January
month it is 0.203. The average for January 1st week, 0.972, indicates that most of the
month‘s returns in fact accrued in the first week. This analysis further confirms the
existence of January effect in U.S market for the six FF3F portfolios.
The January effects identified above are more emphatically highlighted in Figure 5.2
which identifies the composition of mean returns that represents January, non-January
and January 1st week mean returns. It is prominently seen that there is a higher mean
returns in January 1st week for all the portfolios, except for big small which represent
least returns for the January 1st week. This gives a message to the investors that if they
hold their portfolio for long time horizon they end with lower returns. If they sell
their portfolios every January and rearrange their portfolios they get more returns than
other months. This pattern is visible for both small and big portfolios. This suggests
that any portfolio in combination with SH and BH yield more returns to investors.
Figure 5.2 reveals an interesting and useful pattern in the behavior of the mean return
across portfolios. The mean return for high HML (BE/ME) portfolios is higher than
medium HML (BE/ME) medium portfolios which in turn yields a higher return than
low HML (BE/ME) portfolios. This pattern is visible for both small and big
portfolios. This suggests that any portfolio in combination with SH and BH yield
more returns to investors.
140
Figure 5.2: January and non-January mean returns of the FF3F portfolios for the US Market
(1964-2008).
0
0.5
1
1.5
2
SL SM SH BL BM BH
January Non January January 1st week
Mea
n R
etu
rn
5.5.2 Response of the FF3F to the January effects in the US
The above section revealed that the average return for the months of January is much
higher than that of other months. It would be interesting to apply FF3F model for the
weekly returns of January. It will importantly, measure the applicability and validity
of the FF3F under the condition of high return in the market.
Table 5.7 demonstrates that all the slope coefficients are positive for both small and
big portfolios in the US market. However, only small high (SH) and big low (BL)
portfolios are statistically significant at 5% level. The parameter for market portfolio
is highly significant in all small and big portfolios. SMB (size) portfolio is also
significant for both small and big portfolios but negative relationship is observed for
big portfolios.
The result for HML is somewhat different from SMB. Here all portfolios are
statistically significant but negative relation is reported for small low and big low
portfolios. The possible reason for this anomalous behavior is that a small company is
more likely to reinvest its earnings back into the company. Causing the retained
earnings to grow faster and increasing the value of the common stock.
141
Table 5.7: Testing of responses of FF3F to the January effect 1964 to 2008 in US Market
Rf,t is the three month treasury bill rate observed at each week. At end of June each year t, for the period
1964 to 2008 the US stocks are allocated in an independent sort to two groups (small or big) based on
their market capitalization (stock price into outstanding shares). Thereafter, all stocks are allocated in
an independent sort to three BE/ME groups based on the 30th
and 70th
percentile. This yields six
portfolios namely SL, SM, SH, BL, BM, and BH. MKT, SMB and HML are as discussed in Chapter 3.
Weekly returns of January months are collected for all the portfolios and include 176 the (4wk×44yrs)
observations. The data for non-January months are taken from 1964 February to 2008 December,
excluding those in the 176 observations from the January months of course.
Regression: tptptptpptftp HMLhSMBsMKTRR ,,,
Book to market equity (BE/ME) portfolio
Low Medium High Low Medium High
Size
Panel A: January Months (January 1964 –January 2008)
αp α(t)
Small 0.08 0.041 0.190 1.50 1.15 6.30*
Big 0.25 0.023 0.088 4.07* 0.400 1.79
βp β (t)
Small 1.06 0.964 0.978 44.9* 60.70* 73.4*
Big 0.912 1.03 1.02 33.6* 39.50* 46.9*
sp s(t)
Small 0.99 0.806 0.821 26.70* 32.2* 39.1*
Big -0.186 -0.198 -0.001 4.36* -4.82* -0.06
hp h(t)
Small -0.198 0.028 0.657 -4.73* 13.3* 27.7*
Big -0.349 0.432 0.771 -7.25* 9.31* 19.9*
R2 adj s(e)
Small 0.940 0.960 0.970 0.655 0.440 0.369
Big 0.890 0.890 0.920 0.752 0.226 0.600
Panel B: Non January Months (1964-2008)
αp α(t) Small 0.067 0.137 0.129 6.58* 17.8* 20.75*
Big 0.146 0.103 0.084 18.7* 9.09* 8.03*
βp β (t)
Small 1.09 0.957 0.998 186* 216* 277*
Big 0.971 0.992 1.07 217* 152* 179*
sp s(t)
Small 0.999 0.804 0.824 111* 7.36* 2.85*
Big -0.206 -0.134 -0.030 -30.1* -13.48* -3.36*
hp h(t)
Small -0.168 0.361 0.640 -15.7* 44.8* 98.2*
Big 0.361 0.365 0.829 -44.3* 30.6* 75.4*
R2 adj s(e)
Small 0.969 0.969 0.979 0.471 0.354 0.286
Big 0.974 0.926 0.938 0.359 0.523 0.483
*significant at the 5 percent level
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However, a large company is more likely to use its earnings in ways that generally do
not increase the value of its common stock. Paying dividends to preferred
stockholders is one example. Since large companies are retaining a smaller percentage
of their earnings than the small firms, the common stock is returning less to its
owners. The results suggest that the FF3F works well in January. All the three factors
are significant for all six portfolios except small big portfolio. Based on this result it
can be concluded that the FF3F can be applied to capture the cross sectional variation
of stock returns for the monthly seasonal data in the US market.
5.6 Summary and Conclusion
This chapter summarized the results of application of single factor (CAPM) and
multifactor (FF3F) models of asset pricing for the US data. Based on the results, the
validity of the CAPM cannot be rejected for the US. This model is applicable even in
market crisis situation in the market without any issue. On the other hand, it is
observed that explanatory power of the CAPM increases in the crisis period.
The FF3F is also able to capture the variation of stock returns in the US market. The
regression test conducted to measure the explanatory power generated interesting
results. It demonstrates that the explanatory power of both SMB and HML increase
during crisis periods. Also if the two factors are individually considered the SMB
factor is more powerful than HML in the US market. Based on the results the January
effect is seen in the US market and FF3F model is sensitive to the January effect. Its
explanatory power further improves in January months.
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Chapter 6
A Comparative Analysis of the Impact of Market Anomalies
in Sri Lanka and in the US
6.1 Introduction
The previous two chapters examined the behavior of asset pricing models with special
reference to anomalies in relation to data from Sri Lanka and the US. An important
objective of this thesis is to identify whether the findings about the Sri Lankan
markets demonstrated any peculiarities vis-à-vis other more advanced countries. This
objective is achieved by focusing on the US for comparative purposes. This
comparison, which is the main objective of the present chapter, provides a new
perspective on how these models (CAPM and FF3F) operate in developing countries
with emerging markets.
Historically the CAPM and FF3F Models have been developed under some set of
assumptions that are discussed in detail in Chapter 2 and Chapter 3. It is identified
that the validity of these assumptions and theories differ from market to market,
depending on the prevailing economic background of the country. These differences
pose various practical problems in application of the models in emerging markets
which has led academics to question the validity of the assumptions in an emerging
market context (see Chapter 2). The countries in which these markets operate are also
different in various ways; not only in terms of economic and financial environment,
but also in political environment. Therefore, this comparison will be useful for the
investors concerned with investment opportunities and others involved in policy
initiatives. In addition, this comparison will provide more academic value to the
present study by making an invaluable contribution to the existing knowledge in
financial economics.
The rest of the sections of this chapter are organized as follows. Section 6.2
summarizes the general economic outlook of US economy and Sri Lankan economy.
It is important to the understand macroeconomic environment of both countries before
144
making a detail comparison of the findings. Section 6.3 explains the comparison of
risk and rewards of the Sri Lankan market and US market. The empirical comparison
of findings is carried out in section 6.4. Section 6.5 summarizes all the empirical tests
of the two markets. Section 6.6 concludes the chapter.
6.2 The current economic trends
The comparison envisaged in this chapter warrants an appreciation of economic
analysis in the economy of Sri Lanka vis-à-vis that of the US. The economies of Sri
Lanka and of the US were briefly examined in Section 4.3 and Section 5.2
respectively. The present section, using that material, compares/contrasts the two
economies in a manner that lends to a more holistic appreciation of the work
presented in the rest of this chapter. The focus here is mostly on the recent trends and
the future potential of these economies as such matters have a particular bearing on
the stock market performance.
6.2.1 Sri Lankan and the US economies: a recent snap shot
As previously discussed in early chapters, this study is based on two markets which
belong to two categories of markets; namely, emerging and developed markets.
Therefore, the main features of these economies and their relative position in the
world significant. This kind of analysis is important because, according to MSCI
classification stock markets are categorized in this manner based on the soundness of
the economy prevailing. Understanding the latest macro economic variables is
important as this research generalizes the findings country wise and it suggests some
policy measures for both markets.
Table 6.1 collates the most recent economic data (some of which were presented in
Section 4.3 and Section 5.2 ) for the two countries, along with the respective world
ranking. The table presents data on the Sri Lankan (SL) economy and US economy
are arranged in five columns. The columns two and three present the absolute values
of the respective indicator whereas columns four and five establish the relative
position of each indicator, or the respective country ranking according to the CIA
factbook.
145
Table 6.1: Comparison of Key Economic Indicators.
Category Absolute value Relative Position in world
SL US SL US
GDP (PPP) $ 96 bn $ 14 tn 69 2
GDP Growth 3.5% -2.6% 54 157
GDP Per capita
(PPP) $ 4,500 $ 46,000 150 11
GDP (by sector)
agri: 12.6%
ind: 29.7%
ser: 57.7%
agri: 1.2%
ind: 21.9%
ser: 76.9%
- -
Labor Force 7.6 mn 154.2 mn 58 4
Unemployment 5.9% 9.3% 54 110
Population Below
Poverty Line 23% 12% - -
Gini Index (2007) 49 45 27 42
Investment – Gross
Fixed (% of GDP) 22.7% 12.3% 64 145
Inflation Rate 3.4% -0.3% 109 20
Value of Publicly
traded Shares $ 8.1 mn
$ 11.74 tn
(2008) 84 1
Current Acc. Bal. $ -1.69 mn $ -419 mn 146 190
FDI received $ 3 bn $ 2.4 tn 115 1
Interest Rate 7.5% 0.5% 35 134
€ per currency 0.0061 0.7338 - - Note: All figures in the table are as at 2009 unless stated otherwise.
Source: CIA World Factbook and the Central Bank of Sri Lanka
Table 6.1 reveals salient features of these economies that may impact the performance
of their stock markets. It is fascinating to note that some indicators/variables place Sri
Lanka above the US, even though its economy is minute (in terms of PPP adjusted
GDP) compared to the US economy. The indicators such as GDP growth,
unemployment, Current Account Balance, growth rate, Investment rate, etc. ranks Sri
Lanka higher than the US. However, the absolute values of economic indicators in the
US are many times larger than those in SL. Shear size and the might of the economy
accounts for this unassailable number one position of the US economy. To put things
in perspective for the comparison envisaged here, the US is in the top position in
publicly traded shares in the world, whereas Sri Lanka is ranked 84th
.
Conversely, another perspective of this comparison is that, after all 2008 was a very
unusual year for the US market. It will be one of reasons for ranking some variables
146
in better position for Sri Lankan market. A comparison with decade or quarter century
averages will have a different picture. However, Table 6.1 very well demonstrates the
current picture of the key economic variables in both counties.
Moreover, there are some limited similarities across the countries such as the
prominence of the contribution of the service sector. In both countries the industrial
sector takes the second place and agricultural contribution is the least. The similarities
of the sectoral GDP, however, end with these ranking as actual numbers are
substantially different. For instance in the US agriculture contributes a mere 1.2
percent, where as the Sri Lankan economy still substantially depends on agriculture.
In fact when one looks at sectoral employment the reliance on agriculture in Sri Lanka
is much more: the agricultural employment figure for the country (not shown in Table
6.1) is 32.7 percent in 2010.
As shown in the table the interest rate is another important indicator which heavily
influences the performance of financial sector of the economy. It is much higher in SL
(7.5 percent), compared to 0.5 percent for the US. Low interest rates have a thriving
impact on the financial sector; particularly capital market investments. However, the
higher interest rates in SL without doubt have hindered the development of the
investment climate during the past decades. In addition, the exchange rate of US in
2009 was €0.7338/$, whereas in Sri Lanka the rate is €0.0061/Rs. This implies that
the US can gain comparative advantage in foreign trades many times than SL.
Having established the above comparative analysis on the two countries some
important projections can be made on these two countries. This section principally
attempts to brief the current economic status of Sri Lankan economy and US economy
in the light of the main implications of this study. The SL economy dramatically
changed in 1977 with Colombo dumping statist and import substitution policies for
more market and export-oriented policies, including encouragement of foreign
investment. This created an atmosphere where the country is more sensitive to the
fluctuation of macroeconomic factors taking place locally and globally. However, the
country could not get the full dividend of these policy changes for the development of
the country due to the civil war that prevailed in the country for nearly three decades.
147
Sri Lanka suffered through a vicious civil war from 1983 to 2009 that crippled the
country‘s development. Regardless of the war, Sri Lanka saw GDP growth average
nearly 5% in the last 10 years. Government spending on development and fighting the
LTTE drove the GDP growth to around 6-7% per year in 2006-2008. Growth was
3.5% in 2009, still high despite the world recession. Taking the advantage of the
peaceful environment in the country, now the government has forecasted an economic
growth of 8% in the year 2010. In order to achieve the targeted growth massive
infrastructure development projects are being undertaken by the government.
Among the upcoming projects top priority is given for the reconstruction and
development projects in the north and east. Opening of new ventures in the war -tone
area creates more room for the expansion of the Sri Lankan capital markets. Also,
funding these projects will be difficult, as the government is already faced with high
debt interest payments, a bloated civil service, and high budget deficits. Therefore, the
government needs to seek help from private sector investors. The only effective way
to attract private investors for the development of country is the capital market. There
is also positive sign of the market booming during post war atmosphere. The Sri
Lankan stock market gained over 100% (ASPI) in 2009, one of the best performing
markets in the world. Official foreign reserves improved to more than $5 billion by
November 2009, providing over 6 months of imports cover.15
However, as stated previously in Chapter 4, the 2008-2009 global financial crisis and
recession exposed Sri Lanka's economic vulnerabilities and nearly caused a balance of
payments crisis, which was alleviated by a $2.6 billion IMF standby agreement in
July 2009. But the end of the civil war and the IMF loan restored investors'
confidence and CSE started to perform better than before.
In the same way, the current behaviour of US economy has acquired a new tempo
after the 2008 financial turmoil. The global economic downturn, the sub-prime
mortgage crisis, investment bank failures, falling home prices, and tight credit pushed
15 CIA World Factbook.
148
the US into a recession by mid-2008. To help stabilize financial markets, the US
Congress established a $700 billion Troubled Asset Relief Program (TARP) in
October 2008. The government used some of these funds to purchase equity in US
banks and other industrial corporations. The US Congress has also passed the
American Recovery and Reinvestment Act. President Obama signed the Act into law
on 17 February 2009.
The economic stimulus contained in the Act totals $787bn, or around 5.5% of the
GDP. Through one-third in tax cuts and two-thirds in increased spending, it is
designed to provide support to the economy over several years, to help ease what
economists expect to be one of the longest and deepest recessions in the post-war
period. Most forecasters expect the package to add around one percentage point to
growth in 2009 and 2010. But it will also push the budget deficit over 9.5% in 2009
and 8% in 2010. This year has got off to a positive start, with data showing a
substantial increase in GDP growth in the fourth quarter of 2009.
The President set out his economic policy plans for the year in his State of the Union
Address in January 2009 - emphasising jobs, financial regulation, and the deficit16
. He
emphasised that increased support for jobs would be a priority in the government
future plans. Due to this crisis the investors‘ confidence decreases in any form of
investment, including capital market. This creates volatility in the stock market. This
ultimately resulted in the accuracy of the predictions of stock markets with the pricing
models.
6.2.2 The stock markets: The key performance indicators
This subsection presents some performance indicators from the Sri Lankan and the
US stock markets and uses them to compare the two markets. Five such indicators are
described here: (1) the number of listed companies, (2) total value of share trading, (3)
price earnings ratio (P/E) and dividend yield, (4) market price indices, and (5) market
16 CIA World FactBook.
149
capitalization. These indicators are widely used by practitioners and professionals in
measuring the stock market performance. For example, if the number of listed
companies in the market increases, it is often interpreted as an indicator of expansion
of the operational activities of the market.
Table 6.2: Important Performance Indicators of Sri Lankan Market and US Market
Indicators 1997-99 2000-02 2003-05 2006-08
SL US SL US SL US SL US
No. listed
companies 239 2774 238 2411 242 2290 236 2180
Value of share
trading ($bn) 0.26 1155 0.21 10619 0.81 11811 1.01 28180
P/E Ratio 9.4 27.5 8.3 25.2 11.4 NA 10.3 NA
Dividend Yield % 4.3 1.4 5.9 1.2 3.0 NA 3.6 NA
Price Index 624 6193 627 6060 1497 7148 2255 40401
Market Cap ($bn) 1.79 10198 1.36 10525 4.03 12556 6.54 13427
Source: World Federation of Exchanges
As discussed the in previous chapters the CAPM and FF3F attempts to capture the
market and company fundamental factors for the fluctuation of stock returns.
Therefore, this section discusses other company fundamental factors and their
performance that are very much relevant for the current study. For example the
number of listed companies is a key determinant of the size of the market.
Table 6.2 provides statistics of the above five items for the cases of Sri Lanka and the
US. The data collected from the World Federation of Exchanges (WFE) are presented
in three year averages to provide a panoramic view of what happened in these markets
from 1997 to 2008. It seems in case of CSE that there is no big variation in the
number of firms listed throughout the period from 1997 to 2008; it varies from 236 to
242. In the US the number of listed firms is more than 10 times larger than the CSE.
It appears that there is an increasing trend in the total value of share trading in the
CSE during the period. During the period 2006-08 it has increased up to $1.01 billion.
Similarly, the total value of share trading has increased in the US dramatically during
150
the period same period. It has increased from $1155 billion to $28180 billion during
the periods 1987-2008. This indicates that stock market operations have significantly
increased during these periods in both markets. Conversely, there is no significant
improvement in price earnings ratio and dividend yield during the period in both
countries. The major market portfolios (ASPI and NYSE) show a significant
improvement during the period.
Among the above indicators P/E ratio and the dividend yield are important indicators
of stock market performance. P/E ratio measures the price paid for a share relative to
the annual net income or profit earned by the firm per share. This is considered as the
one of oldest and most frequently used method for valuation and security analysis. In
general a high P/E ratio suggests that investors are expecting higher earnings growth
in the future compared to firms with lower P/E. Thus, as shown in the table, investors
who concentrate on the US market expect more earnings growth in the future when
compared to SL. The data on dividend yield also ratifies this picture.
The above discussions revealed that the performance of the two markets has
significantly improved during the recent past. This is important as this study covers
such a dynamic periods in the two markets. The above analysis will be an ancillary
evidence of the study to determine how the behavior of the model significantly
changes in a dynamic market environment.
6.3 Risk and rewards comparison using summary statistics and
pair-wise correlations
Table 3.6 and Table 3.7 in Chapter 3 provide summary statistics for the six portfolios
constructed for the testing of the FF3F in the CSE and the US respectively. The mean
return of Table 3.6.A represents return for the investors who hold these portfolios for
the 10 year period 1999-2008. During this period all the mean return is positive,
excluding big high portfolios. The standard deviation represents the variability of
mean returns of portfolios. More variability means more risky portfolios; it seems that
there is a positive relationship between the mean return and standard deviation in
moderate number of the portfolios in Sri Lankan market.
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Table 3.7 presents the descriptive statistics for the portfolios formed as big and small
in the US market. The results illustrate that the mean returns for the investment
portfolio are positive in all six portfolios and three risk proxies. The statistics in the
US market is also comparable with the results of the Sri Lankan market. At this
juncture in the US market there is a close relationship between mean return and
standard deviation of portfolios. In other words, risk and returns relationship is very
outstandingly visible in the US market, than what is shown in the CSE.
It seems that there is a higher mean return in the Sri Lankan market compared to the
US market. This is largely due to the high risk atmosphere of emerging Sri Lankan
stock market. As previously explicated under the review of previous research in
Chapter 2 the emerging markets are more risky and as a result the investors get more
returns than developed markets. For this reason the emerging markets are more
popular among investors. These markets have now become cash cows for the
international investors. The summary statistics of portfolios reported at this point
unfailing with most of the previous findings of the related studies. Finally it makes
obvious that the investors gain more abnormal returns in emerging markets, than in
developed markets.
The result of the correlation analysis is presented in Table 3.8 for the Sri Lankan
market during full sample periods and other two sub-periods. According to the results
in the CSE only few pair wise combinations are significant at 5% level. The big and
small portfolios are positively correlated with market factor during crisis periods,
whereas its correlation with other portfolios is negative in full sample period and non-
crisis period.
On the other hand, the results shown in Table 3.9 are absolutely different in the US
market. Based on the outcome of the analysis the pair wise correlation gained among
the portfolios are greatly considerable in all the sample periods, including the crisis
period in the US market. There is a high positive correlation among portfolios in the
US market. As portfolio returns are highly correlated to each other, no diversification
benefit is gained from the US market. Conversely, in Sri Lankan market portfolios
152
are not highly correlated. Hence, this offers investors an opportunity to diversify some
of their risks.
6.4 Market wise comparison of major findings
This section, the most important one in this chapter, offers a comparative angle to
view the key findings of earlier chapters. This chapter examines the soundness of
CAPM and FF3F and compares their comparability with the Sri Lankan data and with
the US data. This comparison is significant as it can, in most cases, be generalized and
looked upon as a comparison of the behavior of asset pricing models across emerging
and developed markets.
6.4.1 Analysis of the Results of the CAPM in CSE and US
As a precursor to the FF3F model, this research examines the soundness of the CAPM
in predicting stock returns for the six portfolios constructed for the testing of the
FF3F. This is an advancement of the techniques used in the literature for the reason
that the early tests on the CAPM are mostly based on individual stocks and time
varying nature of CAPM beta. For example, Groenewold and Fraser (1999)
investigated the time varying behavior of the CAPM beta and concluded that beta is
time varying and non-stationary. In the current study it is established that beta varies
significantly across portfolios. Test result for CAPM in Sri Lankan market is reported
in Table 4.1 in Chapter 4. Based on these results the CAPM is redundant in Sri
Lankan market with the exclusion of small high (SH) portfolios which shows
significant pricing of market factor (ASPI) in all the sample periods, including crisis
period.
In the case of the US, in contrast, the CAPM works very prominently including in
crisis periods (see Table 5.3 in p.129). Market factor is more dominant in the US
market and it is shown that beta is highly significant in all the portfolios. The R2 is
above 65 percent in every period for every portfolio six portfolios. But in case of the
CSE, the value of R2 is low and it is not much higher than 25 percent in majority of
the portfolios. This suggests that the portfolios of stocks in Sri Lankan market are
riskless and proportionately exposed to market risk, when compared with the US
153
market. This indicates that other firm specific factors (unsystematic risk) are more
prominent in the market in pricing stocks in CSE. The results also re-confirm that the
CAPM is illogical in emerging markets as suggested by the current empirical
evidences available in finance literature.
Figure 6.1: Relationship between CAPM betas and excess return of portfolios. The
solid line represents the returns of portfolios in the CSE and the US; the perforated
line the estimated beta values. The square bullets () represent values for the US. The
horizontal axis is common to all panels and can be read off Panel C.
154
Figure 6.1 shows the relationship between beta and mean return among portfolios in
the Sri Lankan market and the US market. Each graph has four lines representing beta
and mean return for the two markets. Panels A, B and C in the table stand for the
different sample periods. The figure shows that beta for the CSE fluctuate much
across the six portfolios in all three panels. The beta for small high (SH) portfolio is
high in the CSE during full sample period and crisis period, but is close to zero in
non-crisis period. It implies that SH portfolios become more risky in the CSE during
crisis periods. According to the evidence in the figure, higher risk in SH is not always
rewarded by the higher returns which contradicts the notion of positive risk-return
relationship.
Interestingly it seems that there is no significant deviation in mean excess return in the
two markets even though the two has beta values that deviate much. However, it
seems exceptionally different behavior in small portfolios that is the beta and return
moves positively in these portfolios. This result is consistent with Ho-Chan and
Huang (2000) who suggests that CAPM is constant with the data in the low-risk, but
inconsistent with the data in the high risk occasions. The analysis conducted here
uncovers important findings that the theory of risk and return works well in the US
market, but it is not seen in the CSE.
In summary, it shows that the portfolio return in the US market varies in relation to
the changes in beta. But in the Sri Lankan market the portfolio return is not followed
by variation in beta. In the Sri Lankan market there is a big variation in beta across six
portfolios. On the other hand, the irregular behavior of the risk and return is a major
barrier for the investors to forecast their future risk and return trade off in the CSE.
6.4.2 Comparison of the results of the FF3F
This sub-section attempts to accomplish a cross comparison of the findings related to
Sri Lankan and US markets based on the FF3F. This comparative analysis relies on
the results of multi factor regression tests of the FF3F that are summarized in Table
4.2 in Chapter 4 and in Table 5.4 in Chapter 5 for the CSE and the US respectively.
The CSE results in the Table 4.2 shows that the FF3F does not work effectively in the
Sri Lankan market. It can also be seen that the market factor is not significant in
155
almost all the periods, including non-crisis periods. The exceptions are SH and BH
portfolios. These results are more pronounced when the model is applied to the full
sample and to the crisis period. Table 4.2 very clearly shows that the market factor is
significant only for the small high (SH) portfolios and big high (BH) portfolios in
both periods.
When evidences on other two fundamental factors of the FF3F are considered in CSE,
it shows that SMB and HML are significant in the majority of portfolios and in all the
sample periods as shown in Table 4.2. These results substantiate that only SMB and
HML factors can capture the variation of stock returns in the Sri Lankan Market,
while market portfolio is not a significant factor in determining the stock return in the
Sri Lankan Market.
These results are evident of the semi strong form of efficiency as discovered by
Eugene Fama in his PhD thesis. Semi-strong efficiency implies that share prices
adjust to publicly available new information very rapidly. Both SMB and HML
factors of the FF3F are constructed based on publicly available information. These
results may be due to the fact of the semi-strong features of the Sri Lankan market.
Another point is that transaction cost is very much higher in the Sri Lanka compared
to the US. Due to high transaction cost Sri Lankan market is operationally inefficient.
In the Sri Lanka market majority of the investors are small investors as illustrated in
Figure 4.2. The high tractions cost limits their trading and ultimately the liquidity
position of the investors. But, in the US market the investors are very big investors
and the transaction cost of the US is lower relative to SL. This might affect the
performance of CAPM and FF3F. Moreover brokerage fees and SEC fees is about 3%
in Sri Lanka, compared to which the feeds in developed countries such as the US is
low. Also, high liquid firms (frequently trading) are liable to pay less brokerage fee
therefore; their cost of capital is lower resulting in higher returns for the stocks.
The results of the test of three factor model for the US market are presented in Table
5.4. As shown in the results, the Fama and French Model works well in the US market
in all the sample periods of crisis period. All the parameters of all three factors are
156
statistically significant at 5% level. These results suggest that the US market has
efficient market features as the market factor is significant.
Figure 6.2: Multi factor beta of small and big portfolios. The perforated lines plot the estimated
beta values. The square bullets () represent values for the US. The horizontal axis is common to
all panels and can be read off Panel C.
-1
0
1
2
3
Mult
i F
acto
r B
eta
Panel A : Full Sample Period
-2
0
2
4
Mult
i F
acto
r B
eta
Panel B : Crisis Period
0
2
4
6
SL SM SH BL BM BH
Mult
i F
acto
r B
eta
Panel C : Non - crisis Period
CSE US
Figure 6.2 shows the fluctuating pattern of multi factor betas of the six portfolios of
CSE and US markets during three periods. It is very prominently seen in all three
panels (A, B and C) that the multi factor beta for the US market is constant through
time across portfolios. In other words, there is no high variability in market risk (multi
157
factor beta) among big and small portfolios in the US market. However, the market
beta for CSE portfolios shows a high fluctuation across portfolios. It shows that multi
factor beta of big low portfolios is relatively lower in all the sample periods in the
CSE as shown in all three panels. Throughout crisis situation Small High portfolios
has a declining beta, while the other two periods (panels A and C) demonstrate an
increasing trend.
This kind of behavior of beta suggests that the market risk of the CSE can be
minimized by diversification of portfolios in combination with small and big
portfolios. This result clashes with the finance theory of risk and return. The theory
says that the market risk (systematic risk) cannot be diversified away by way of
diversification. However, it seems there is a constant beta among portfolios in US
market. This result is consistent with the theory and shows that in US market
systematic risk is common to all portfolios. Thus, it can be concluded that irrespective
of crisis periods, the portfolio diversification theory works well in the US market but
it does not work properly in the Sri Lankan market.
6.4.3 Comparison of explanatory power of SMB and HML
For the purpose of examining the individual power of the SMB and HML factors in
the FF3F model, a break up analysis is conducted for each time period for both
markets. Table 4.3 presented in Chapter 4 shows the test results for the CSE. It
explains that SMB is more powerful in explaining the variation of stock returns than
HML in the CSE. It can be seen prominently during full sample periods and non-crisis
periods. Both factors are significant in full sample period and non-crisis periods in the
table. During the crisis periods none of the factors are significant in the Sri Lankan
market.
In the US market, both factors (SMB and HML) are equally influential in explaining
stock returns. There is no significant difference in the explanatory power of SMB and
HML in crisis period, when contrasted with the other two periods. In addition, the R2
values are higher in the three factor model (MKT, SMB and HML) in the US.
However, it declines when two factors are applied in the model. This suggests that the
market factor is more powerful than SMB and HML in the US market. The analysis of
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R2 resulting from regression equations (4.1 and 4.2) describes this phenomenon
succinctly.
Table 6.3: Measuring Explanatory Power of SMB and HML
Full Sample Crisis period Non-crisis
CSE
SMB-Average R2
0.2388 0.2106 0.2213
HML-Average R2
0.1766 0.1726 0.1780
US
SMB-Average R2
0.8833 0.9156 0.8463
HML-Average R2 0.8316 0.8356 0.8261
Table 6.3 summarizes the estimated R2 values for equations 4.1 and 4.2. The R
2 values
present in the table are averages of all six portfolios. It shows that the R2 for the SMB
is greater than HML in the Sri Lankan market in all the three periods. It indicates that
the SMB is more sensitive than HML in explaining portfolio returns of the US. For
the US also the average R2 value for SMB is higher than HML for all three periods. In
US SMB is more powerful as similar to the CSE. In the US market it seems that the
explanatory power of SMB has greatly increased during crisis period than other
periods. The R2 is 0.9156 which is the highest in the table among others.
It follows that the explanatory power of SMB is more in both markets, while in the
US this effect is even more pronounced during a crisis period. These findings imply
that the significance of factors in the FF3F vary time to time with the changes in the
general market condition in the economy. Thus, the investment decisions should not
be influenced by one period test of the FF3F, but it is sensible to test the model with
different categories of data series. One interesting conclusion here is the SMB is more
sensitive in the model in both markets indicating the size factor is more dominant in
explanting portfolio returns by way of the FF3F model.
In addition to the analysis in Table 6.3 a closer examination of the behavior of the
SMB is shown in Figure 6.3. The figure shows that SMB loadings in the CSE are
close to zero in all most all the portfolios. Conversely, in case of the US the SMB
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loadings for small portfolios significantly deviate from zero and have positive
loadings whereas in the big portfolios are close to zero and have negative loadings.
The movement of SMB among portfolios is similar across all the three sample periods
as shown in Panels A, B and C. This suggests that the explanatory power of SMB is
not sensitive to the economic crisis. On the other hand, the negative loadings of SMB
on BL, BM and BH suggest that the size factor has a negative impact on the
movement of portfolio returns.
Figure 6.3: Analysis of SMB Loading. The perforated lines with circular bullets (Ο) plot the
estimated SMB values for CSE. The solid line with square bullets () represent SMB values for
the US. The horizontal axis is common to all panels and can be read off Panel C.
-0.5
0
0.5
1
1.5
SM
B
Panel A: Full Sample Period
-0.5
0
0.5
1
1.5
SM
B
Panel B: Crisis Period
-0.5
0
0.5
1
1.5
SL SM SH BL BM BH
SM
B
Panel C: Non-Crisis Period
SMB Loading -CSE SMB Loading-US
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Figure 6.4: Analysis of HML Loading. The perforated lines with circular bullets (Ο) plot the
estimated HML values for CSE. The solid line with square bullets () represent HML values for
the US. The horizontal axis is common to all panels and can be read off Panel C.
-0.5
0
0.5
1
HM
L
Panel A: Full Sample Period
-0.5
0
0.5
1
HM
L
Panel B: Crisis Period
-0.5
0
0.5
1
SL SM SH BL BM BH
HM
L
Panel C: Non-Crisis Period
HML Loading-CSE HML Loading-US
Similarly, Figure 6.4 depicts the relationship between HML and portfolio returns of
the CSE and the US for the full sample, crisis and non-crisis periods. There is a
considerable variation in HML loading in the US while it is more stable in the case of
the CSE. In other words, the impact of HML changes with the portfolios in the US
market, but it is not the case in the CSE. It seems an increasing trend of HML from
BL portfolio to BH portfolios in the US market in all the periods. Interestingly BL
shows negative loading on HML which suggests that BE/ME factor is negatively
related to the movement of portfolio returns in BL portfolios during crisis and non-
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crisis periods. However, in case of CSE, BE/ME factor is equally influencing for the
fluctuation of portfolio returns across all the sample periods.
In summary, Figure 6.1, Figure 6.2, Figure 6.3 and Figure 6.4 explain the inter-links
of the estimated coefficients of the CAPM and FF3F for all the sample periods in both
markets. When this evidence is perused collectively, it reveals a peculiar pattern of
how the various factors—MKT (β), SMB (s) and HML (h)—play out in the two
markets. In case of CSE β fluctuates much across portfolios in the CAPM and the
FF3F. However, SMB and HML loadings are mostly constant across the portfolios in
the CSE.
Conversely, in case of US, CAPM beta and FF3F beta are mostly constant across the
portfolios in all the periods, whereas SMB and HML loadings are highly fluctuating
among the portfolios in all the periods. This gives an important message to the
portfolio managers and investors about the behavior of the risk in the market. The
concept of systematic risk and unsystematic risk is very specifically shown in the US
market. But, it is not applicable to the CSE as the beta factor is highly fluctuating
across portfolios. If that concept is applicable, betas must be constant among the
portfolios. In case of the CSE however, SMB and HML can be identified as common
risk factors for all small and big portfolios. Thus, due attention must be paid to these
recommendations by the investors when they are picking up stocks into their
portfolios.
6.4.4 Differences and Similarities of January effect in both markets.
Table 6.4 reports the average of portfolio returns for the three sub-sample series;
namely January, 1st week of January and Non-January for the CSE and the US. The
average returns represent the average of the six portfolios in each period. It
demonstrates that the mean return of portfolios is substantively higher in January
when compared with the other Non-January periods in both markets. The average
mean return for the first week of January is even greater than other weeks of the same
months.
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Table 6.4: January Seasonality of CSE and US
January
1st week of
January Non-January
Average Mean Return-CSE 0.117 0.246 0.088
Average Mean Return-US 0.635 0.972 0.203
This apparently suggests that the January effect is valid in both markets. However, for
a valid conclusion for the January effect more analysis should be undertaken. As
explained in previous explanations several factors are attributable to this behavior in
the markets. Researchers have found that the turn of year effect significantly
influences the higher return in January. The tax loss selling hypothesis can be one
more reason for the anomalous return in January however; it is not applicable to CSE
due to the fact that capital gain tax rule does not exist in Sri Lanka.
Table 6.5: Sensitivity of FF3F to January Effect
MKT SMB HML R2
CSE
January -1.889 0.020 0.024 0.501
Non-January 0.351 0.009 0.0033 0.4381
US
January 0.994 0.372 0.2235 0.9283
Non-January 1.013 0.3761 0.398 0.9591
As an additional investigation to the work volume of FF3F the sensitivity of FF3F is
examined. Table 6.5 summarizes the regression results of FF3F with January and
Non-January data series for both markets. The values reported in the table contain the
average of the regression coefficients of the FF3F model and the average R2 of each
of the test presented in Chapter 4 and Chapter 5. If coefficients are closely examined
in the CSE it seems the SMB and HML coefficients of the CSE are close to zero.
However; in the US the coefficients are different from zero largely. When the R2 takes
into consideration in case of CSE, the explanatory power of the FF3F is more
powerful in January as exhibit in the value of R2. Similarly, in case of US average
mean return is much higher in January than other months (0.63) and for the 1st week
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of January it further increased to 0.972. However, based on the values in Table 5.7 in
Chapter 5 it is found that FF3F in the US is highly sensitive to the January effect.
6.5 Summary of the findings
Table 6.6 presents the major findings of this study for the CSE and the US. However,
no detail discussions will be done as the findings of the tests are discussed
comprehensively in the relevant chapters. As shown in the first column in Table 6.6
the study has focused on six empirical tests in both markets including CAPM and
FF3F tests. The √ mark indicates the gravity of explanatory power and the fitness of
the test. As the number of √ marks in a cell increases the gravity of explanatory power
and the soundness of the results also increase.
It seems that the predictive power of all most all tests is very low in the CSE when
compared to the US in all the tests. However, the FF3F outperforms the CAPM in
CSE and in US both CAPM and FF3F work satisfactorily. It is interesting to note that
the explanatory power of the SMB and HML decreases in the CSE during crisis
period and for the US market their power increases in crisis period when compared to
other periods.
The test results of the FF3F with January weekly data yields moderately similar
results to the other periods. However, for the CSE the explanatory power of the SMB
and HML has declined and no significant dissimilarity is found in the US market.
The mean return of 1st week of January is significantly higher in both markets.
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Table 6.6: Gravity of major findings
Empirical Tests
CSE US
Full
Sample
Crisis Non-
Crisis
Full
Sample
Crisis Non-
Crisis
CAPM
CAPM-Beta √ √ √ √ √√ √ √√ √ √√√
FF3F
Multifactor Beta √ √ √ √√ √ √√ √ √ √ √
SMB √√√ √√ √ √ √ √√ √ √√√ √ √ √
HML √ √ √ √ √ √ √ √ √ √√ √√√ √ √√
Power of SMB &
HML
SMB √ √ √ √ √ √ √ √√√ √√ √
HML √ √ √ √ √ √ √√ √√ √
Jan. Effect (FF3F)
Multifactor Beta √ N/A N/A √√√ N/A N/A
SMB √ √ N/A N/A √√ √ N/A N/A
HML √ √ N/A N/A √√ √ N/A N/A
Non-Jan (FF3F )
Multifactor Beta √ N/A N/A √√√ N/A N/A
SMB √ √ N/A N/A √√ √ N/A N/A
HML √ √ N/A N/A √√ √ N/A N/A
Mean Return
January √ √ N/A N/A √√ N/A N/A
1st Week of January √ √ √ N/A N/A √√ √ N/A N/A
Non-January √ N/A N/A √ N/A N/A
Note: Number of √ indicates the power of Predictability
N/A: Not Applicable
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6.6 Conclusion
This chapter effectively established a comparison and a revision of the key findings of
Chapter 4 and 5 within the dichotomous framework of emerging/developed markets.
The main objective of this chapter is to encompass a cross comparison on the practical
modalities of the major findings of the key models of CAPM and FF3F. It is observed
that there are some similarities and dissimilarities of the behavior of the models in
these two markets. There are some considerable differences in the behavior of the
models in crisis and non-crisis settings, both in the CSE and the US markets. The
evidences also suggest that the asset pricing models work effectively in developed
markets and in emerging markets these models do not work effectively. Furthermore,
evidences revealed that the dynamic nature of the predictions of the models is affected
by the financial crisis in both in the CSE and in the US.
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Chapter 7
Summary of the Findings and Conclusion
7.1 Introduction
This important and final chapter summarizes the work presented in the previous
chapters of this thesis and discusses its implications for public policy on stock market
operations based on the country specific findings. It also highlights the contribution of
this research for the benefit of scholars in the field of asset pricing. This chapter also
examines whether the research questions stated in Chapter 1 are answered in the
findings of the various empirical tests of this study. The thesis concludes by proposing
areas for future research, giving due acknowledgement to the limitations stated at the
beginning of the research.
7.2 Summary of key findings
The foremost objective of this study is to investigate the validity of single factor
models and multi factor assets pricing models in predicting the variation of stock
returns in Sri Lankan and US market, with special focus on two prominent models
popularly known as the CAPM and the FF3F. The distinctive feature and the key
objective of this research is that it investigates the predictability of asset returns on
three different periods that are objectively identified as full sample period, stock
market crisis period (high volatile periods) and non-crisis period (low volatile). The
other supplementary extension of this research is the testing of the January effect with
the same portfolios constructed for the purpose of FF3F for both CSE and US
markets.
The outcome of the test revealed that the CAPM cannot be used to predict differences
in stock returns in the CSE effectively, whereas the findings confirm that the CAPM
is an applicable model in predicting the differences in stock returns in the US market.
The current study also finds one important result on the behavior of the CAPM in the
US market, which is the model that appears to be linear as evidence confirms. In other
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words, the high beta is followed by higher returns and vise versa in most of the
portfolios in the US market.
The empirical evidence also confirms that the FF3F model outperforms the CAPM in
the CSE. It is because out of three factors in the model only SMB and HML are
significant in most of the cases. Conversely, findings suggest that FF3F effectively
works in the US and it completely explains the differences of stock returns. The test
outcome of the model on crisis data reveals some significant differences in the
behavior of the models in the period market that are exposed to the economic crisis. It
is found in the empirical analysis that the FF3F model is sensitive to January effect.
Based on the findings it seems that the impact of the January effect is moderate in the
CSE, while it is quite significant in the US market.
7.3 Answers for research questions
In addition to the main and secondary objectives that are addressed in the previous
section, the study also has six specific research questions. It is important to identify
and whether and how the study has answered these questions. Answers for the six
questions are identified as ancillary objectives of the current study.
The first question aims to address whether size (SMB) and Book-to-Market (HML)
factors would hold and work well in the Sri Lankan market and in the US market
during market crisis periods. In case of the CSE, even though the FF3F cannot fully
explained the differences of stock returns in the CSE, both SMB and HML factors are
able to significantly explain the variation of portfolio returns in the CSE. The findings
suggest that SMB and HML are convincing fundamental factors in explanting stock
returns during market crisis periods and non-crisis periods in the US. Moreover, the
predictive power of these two factors declined during the crisis period, indicating that
the model is sensitive to the economic crisis and volatility in the stock markets of
these two countries.
The second research question is ―Does the FF3F model outperforms the CAPM in
Market crisis period and Non-crisis period?‖ The investigated results elaborate that
the FF3F can capture the variability of stock returns missed by the CAPM. The FF3F
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model outperforms the CAPM in the Sri Lankan market. Out of the three factors only
SMB and HML are able to capture the variation of stock returns in CSE. Here the
market factor (MKT) is not able to explain the stock returns as the majority of the
estimated MKT coefficients are not significant in each of the three sample periods. In
contrast, the FF3F is found to be more applicable to the case of the US. All the
coefficients representing the three factors in the FF3F model are highly significant in
all the sub periods in the US market. These results confirm that the FF3F is a valid
model in capturing the CAPM anomalies in the US market.
The third question which this study addresses is ―whether the size factor (SMB)
dominates BE/ME (HML) during crisis periods and normal periods or not‖. In order
to deal with this question separate tests are conducted with each factor, along with the
market factors for each market. The results of Sri Lankan market reveal that the SMB
(size) factor is more powerful in explaining stock returns in CSE, both in crisis and
non crisis periods. Interestingly the test result for the US market also shows a similar
result, the explanatory power of the SMB is more powerful than HML in most of the
portfolios. When the SMB factor is included into the model the R2 improves
significantly in the US market. In summary it confirms that size (SMB) effect is one
of the momentous anomalies in explanting the variation in stock prices in the CSE and
in the US.
The fourth question is whether the CAPM is a valid explanation of the differences in
stock returns during crisis and non crisis periods. This question was addressed by
testing whether the FF3F portfolio returns were explained by the CAPM. The result of
the test is not compatible between the two markets. In the Sri Lankan market it is
found that the beta factor is significant only for small number of portfolios (SH and
BH) which signals that the CAPM is not a valid indicator in predicting the returns of
the most of the portfolios formed as big and small portfolios. The results of the US
market on CAPM indicate that the model works favorably for the validation of
CAPM. It is because the beta factor is highly significant for all the portfolios in full
sample, both in crisis and non-crisis periods.
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The fifth question is ―Does January effect prevail during crisis periods and non crisis
periods in big and small portfolios?‖ This is an additionally conducted assessment to
measure the sensitivity of January months‘ high return on the predictive power of the
FF3F. It is generally known that January returns for stocks is higher than other
months due to several reasons such as January effect, new year effect etc. The results
reveal that the model is not sensitive to the January month‘s returns in the Sri Lankan
market. However, in US market higher mean return is reported in all the portfolios in
January that confirms the existence of January effect in the US. In the Sri Lankan
market a significant value of mean return not being reported in January indicates the
non-existence of January effect in the Sri Lankan market. The results of the FF3F
analysis with January weekly returns reveal that the FF3F is sensitive to the January
effect.
The final question is whether the answers to the above 1 to 4 questions are sensitive to
the market crisis. The findings of the study confirm that both the CAPM and the FF3F
are sensitive to market crises and significant differences in the models and the
variables within the models are discovered.
7.4 Country specific findings in the Sri Lankan market
The Sri Lankan stock market is minute by global standards and has received less
attention from the researchers. In view of filling this drawback, the investigator
conducted this research in the area of asset pricing, with special focus on CAPM and
FF3F Model in the CSE. It is also found that the results of the current research are
consistent with the handful of previous studies available on the market, whereas some
inconsistencies are found in some areas of the findings. However, most of the findings
of this research are exceptional to this study merely because the research approach is
very unique in this thesis. One of the major arguments of the research is to investigate
the validity/invalidity of the CAPM and the three factor model under crisis and non-
crisis periods in the CSE.
The impact of market crisis on CAPM measured by beta suggests that the systematic
risk does not significantly influence the explanation of future stock returns in the
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CSE. This finding strongly contradicts with the theoretical recommendation of the
original work of Sharpe (1964), Lintner (1965) and Black (1972), and with later
empirical studies which test the CAPM on developed markets. Section 2.4 (see page
30) outlines some of these works. These findings imply that the beta coefficient alone
cannot provide an efficient mechanism of examining and predicting excess stock
returns in CSE as an emerging market.
The results derived from the FF3F test reveal that the FF3F model outperforms the
CAPM in the Sri Lankan market both in crisis and non-crisis periods. It is found that
out of three factors, the market factor (MKT) is not significant for the majority of
portfolios, as well as for few SMB and HML slope coefficients. This is a common
finding for all the sample periods. However, when it is compared with the CAPM, the
inclusion of SMB and HML factors to the regression improves the quality and the
reliability of the model in terms of increased predictive power of R2 and their
significance at 5% level.
Another significant finding is that the average absolute pricing error (intercept) of the
CAPM is more extensive than the FF3F model. The statistics also further confirm that
the CAPM is dominated by the FF3F in the Sri Lankan stock market. Several factors
can be attributed for the invalidity of CAPM in the CSE. The most profound fact is
the invalidity of the assumptions in emerging markets such as the CSE. For example;
in CAPM it is assumed that there are no transactions cost or private information.
Therefore, diversified portfolio includes all traded investments held in proportion to
their market value. However, in emerging markets like the CSE transition cost is very
high and leakage of corporate information is a frequent occurrence.
The two models (CAPM and FF3F) tested in Chapter 4 and Chapter 5 demonstrates
the need for new models for the CSE in order to capture returns determinants of the
portfolios of assets. Further, most of the empirical work in finance is based on
efficient market assumption conducted in developed markets headed by the US and
the UK. Their appeal to the empirical modelers is perhaps that they are more likely to
be consistent with these fundamental assumptions. The flip side of this is that the
emerging market studies, including the Sri Lankan study conducted here, may find
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that these models are not able to fit the data precisely because the assumptions are not
held.
7.5 Country specific findings in the US Market
This section summarizes the important findings of chapter five which represents the
analysis of the findings of the US market. Among the important findings it is
discovered that the CAPM is a valid model in predicting the excess returns of
portfolios in the US market both in crisis and non-crisis period. The market factor
(MKT) is highly significant in all the periods. This discovery is unfailing with the
theory developed by Sharpe (1964), Lintner (1965) and Black (1972) and several
other empirical studies (cited in chapter 2) conducted in the US and other markets.
The extraordinary attribute of this research is the testing of the CAPM with the
portfolios opposed to individual stocks that reduce the dimensionality of the results.
In addition, these portfolios represent broad asset classes that follow popular
investment style in the US market.
Furthermore, the test results confirm that the FF3F model works effectively in the US
market during non-crisis period and crisis period. All the three risk factors of the
model are highly significant in each period. It is interesting to note that in the US
market similar to the Sri Lankan market, the SMB is more powerful than HML in
explaining portfolio returns of small and big portfolios. Moreover, interestingly the
pair wise correlation test reveals that the portfolio return of the US market is highly
correlated with each other. It implies that the diversification of portfolios in this
market does not persuade the desires of the investors which is the diminution of risk
by diversification. The computation of the correlation between each pair of stocks is
virtually impossible, therefore this portfolio approach is recommended for measuring
the correlation effect of the stocks in the market.
The summary statistics shown in Chapter 5 demonstrate that the mean return of the
portfolios is remarkably higher in January than in other months in almost all the
portfolios. In addition, summary statistics show a positive relationship between mean
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return and standard deviation of small and big portfolios suggesting the validity of the
risk and return relationship in the US market.
Nevertheless, there is no guarantee that a characteristic that has been proven
significant in specific market and during specific time periods could be a competent
indicator in different markets or time periods. Thus, investors should not expect these
research results to work perfectly in the real world investment decision making.
Rather, they should use these findings as a guide for their own investment strategies
and prepare to live with the results, whatever they may turn out to be in different
markets from time to time.
7.6 Contribution of this thesis
This thesis has made a significant contribution to scholarship in asset pricing and its
anomalies, and as well as contribution to the policy and practice related to the Sri
Lankan stock market and the US market. It has systematically developed an argument
on unique attributes of the CAPM and the FF3F in crisis and non-crisis environments
in the market.
The most significant contribution of this study is the validation of the CAPM and the
FF3F in capturing the variation of stock returns in the CSE and the US market. The
findings to this investigation reveal the important and unique behavior of the models
which can be identified as the contribution of this research to scholarship in finance.
It was revealed in the literature review that the testing of the CAPM for the portfolio
of assets has not been undertaken by the previous researchers in CSE. Breaking this
gap this study investigated the validity of the CAPM using FF3F portfolios in
predicting portfolio expected returns in the CSE. It is found that the CAPM is not
compelling in predicting the portfolio returns in the CSE. This can be identified as
one of major contributions to the body of knowledge in asset pricing in the CSE.
In addition, further investigation into the previous literature revealed that no study has
attempted to validate the CAPM in market crisis periods for the CSE. This is also
identified as one of major contributions of the thesis. For the separation of the crisis
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periods from the long series of data, the ICSS algorithm of Inclan and Tiao (1994)
was applied for the first time in order to identify volatility breaks in the markets. As
ICSS was applied for the first time, this can also be considered as one of noteworthy
contributions of this thesis. Here the ICSS can be recognized as an effective tool in
identifying market crisis periods in almost all the historical crises that coincide with
the breakpoints identified from this test. Empirical results confirm that the CAPM is
not applicable even in the market crisis periods in the CSE.
On the other hand, to the best of the researcher‘s knowledge, no early studies are
available on the FF3F in the CSE. Contributing to this literature gap this study
investigated the model in the CSE and found that the FF3F can better explain the
expected portfolio returns than what is seen in the CAPM. Similar to the CAPM, the
FF3F model is investigated on crisis periods. Based on the results some significant
differences in the behavior of the models during crisis periods are established.
The January effect is identified as a pervasive stock market anomaly and this study
examines its impact on portfolios of stocks. This is also one of significant
contributions of the current study for the CSE.
Further expanding the scope of the study, all the steps in the CSE are reproduced in
the US market as a benchmark for the comparison purposes of the findings. Unlike
the CSE, there is a large volume of studies on CAPM and FF3F based on the US
market. Importantly, the inventive empirical studies of these two models are also
based on the US market. However, the current study contributes to the US market in
three ways. Firstly, use of weekly data for the testing of both the CAPM and the
FF3F. Secondly validation of both CAPM and FF3F for the market crisis periods and
non-crisis periods in the US is also unique. Finally, measuring the impact of January
effect on the behavior of portfolios return and sensitivity of the FF3F for the January
effect in the US has not being done before.
7.7 Policy implications of the findings
The investigator anticipates that this research will contribute to the deliberations of
policy makers, scholars, investors, fund managers and industry experts. The findings
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of this research suggest that the different investment policies must be implemented by
the investors and fund managers separately for market crisis and non-crisis periods as
significant differences are found in the models.
Asset pricing models primarily concern the estimation of required rate of return or
cost of capital for a firm. In addition, the CAPM and the FF3F are the theoretical
representation of the behavior of financial markets and can be used as a tool for
estimating firms‘ cost of capital. Despite their limitations, financial managers heavily
relied on the estimations of these two models for decision making purposes. In the
CSE the FF3F can to some extent accurately estimate the cost of capital, whereas cost
of capital estimates with CAPM does not derive the real cost of capital. Thus, there is
a possibility of making incorrect capital budgeting decisions that hinders the firm
value largely. However, in the US market, both CAPM and FF3F will possibly draw
precise cost of capital for the firm. Conversely, Fama and French (1996) find that the
FF3F signals higher costs of equity for distressed industries than for strong industries,
largely because the distressed industries have higher loadings on HML. Thus, the
findings imply that the financial managers should ascertain the predictive power of
the models before they are applied for the corporate financial decision makings.
Furthermore, the explanatory returns on SMB and HML are not motivated by
prediction about state variables of concern on investors. For example, some studies
which focus on economic conditions are Chan and Hsieh (1985) and Fama and French
(1995). They found that small size firms and low book-to-market firms are risky,
while distressed firms are more prone to default during adverse economic conditions.
Therefore, they must provide relatively high risk premium during declining economic
conditions. In this research, it is found that small stocks yield higher risk premium
(more return for bearing more risk). Thus, these portfolios are favorable investment
for the investors who expect more returns with higher returns. The investment
advisory firms and other agencies should implement their policies accordingly.
The results of this study are multidimensional and significant differences in the
behavior of excess return of portfolios were found in every sub-period. The findings
175
suggest that a significant and consistent size and book-to-market effect prevails only
during expansive monetary policy periods, but not during restrictive periods.
This view supports findings of Fama and French (1995) and Chan and Hsieh (1985)
who examined the effects of Book-to-market and size in a general asset pricing model
using several markets, including the UK market. They conclude that Book-to-market
and size effects are international in character and strong under the general model and
against a variety of alternative macroeconomic and financial conditioning variables.
According to Reinganum (1983), the three-factor model is useful in applications and
he found that the size-adjusted average returns are higher for the NYSE stocks than
NASDAQ stocks. NYSE stocks have higher loadings on HML and it leads to higher
predicted returns. Carhart (1997) finds that the three factor model provides sharper
evaluations of the performance of mutual funds than the CAPM.
7.8 Suggested areas for future research
This thesis provides the basis for many avenues of future research. First, the largest
limitation of this research is probably the short sample period, especially in the Sri
Lankan market, due to the limitation of availability of the trading information in the
market. The possibility of examining a longer period would also provide the models
with more statistical power. Unlike in the Sri Lankan market, this can be executed
with some other market that has longer series of data.
The scope of this study is limited only for the three factor model and the January
effect as the CAPM anomalies in the Sri Lankan market and the US market applies
two set of data as crisis and non-crisis periods. In future, the researchers can examine
the validity of other anomalies such as E/P, C/P under crisis and non-crisis set of data
series. The sample countries can also be expanded with more emerging markets.
Examining other countries would be more desirable to provide support for the
conclusion of this thesis. It would also bring satisfactory results to the model if the
portfolio return is predicted in the Sri Lankan market with other economic variables
like inflation, oil prices, GDP growth, etc. This will enable to avoid the rejection of
the model resulting from adopting incorrect variables. Finally, this research has
176
examined simply the January effect of the portfolio that represented big and small
firms. As an extension to this, it is recommended to test other calendar anomalies with
the same portfolios.
7.9 Final remarks
This rare attempt at modeling emerging market stock returns revealed numerous
challenges at the level of data preparation and fitting models such as the CAPM and
the FF3F. Undoubtedly these challenges partly explain the lack of empirical works for
these markets. Even when one overcomes these challenges, as it done here, the
interpretation of the results needs to be done with extra care, as the assumptions that
underlie these models become very shaky when applied to emerging markets. These
challenges, therefore, highlight the need to revisit finance theories that can be
meaningfully used for the analysis of these markets. However, from a cost benefit
point of view, given the minuscule size of these markets, it is not clear whether such
an effort would attract the academics of developed countries.
177
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186
Appendix A: The companies in the CSE
New Listing and De-Listing of Companies 1999-2008
year Name of newly listed Companies Name of the De-Listed Companies
1999 Nations Trust Bank Ltd, Metropolitan
Resource Holdings Ltd, Ruhunu Hotels &
Travels Ltd, Namunukula Plantations Ltd
Carsons Marketing Ltd
Champs Developments Ltd
Electro Holiday Resorts Ltd
Ceylon Nutritional Foods Ltd
Siedles T.V. Indusry Ltd
Forbes Ceylon Ltd
Aitken Spence Hotels Ltd
2000 Asian Alliance Insurance Co Ltd, Talawakelle
Plantations Ltd, Malwatte Plantations Ltd,
Elpitiya Plantations Ltd
Lady Havelock Gardens Company Ltd
Elastomeric Engineering Company Ltd
Associated Rubber Products Ltd
2001 Watapota Investment Limited
Habarana Walk Inn Ltd
Walkers Tours Ltd
Ceylon Synthetic Textile Mills Ltd
2002 E-Channeling Ltd,
Touchwood Investment Ltd, Tess Agro Ltd
Collettes Ltd
Mikechris Industries Ltd
Korea Ceylon Footwear Manufacturing
Company Ltd
Kandy Textile Industries Ltd
Hayleys Photoprint Ltd
Haytech Marketing Ltd
Reckitt Benckiser (Lanka) Ltd
Coca-Cola Beverages (Sri Lanka) Ltd
Ocean View Ltd
2003 The Lanka Hospitals Corp. Ltd, Ceylon
Leather Products Ltd, Ceylon Hospitals Ltd,
Hemas Holdings Ltd.
Ceylon Strategic Holdings Ltd
2004 1) Nawaloka Hospitals Limited
2) Lanka IOC Ltd.
Asian Hotels Corporation Ltd, Metalix
Engineering Co. Ltd, Pugoda Textile Mills
Ltd, Veyangoda Textile Mills Ltd, Metal
Recyclers Colombo Ltd, Upali Enterprises
Ltd.
187
year Name of newly listed Companies Name of the De-Listed Companies
2005 Dialog Telekom Limited
Sierra Cables Limited
W.M.Mendis & Company Limited
Ceylon Holiday Resorts Limited
Habarana Lodge Limited
International Tourists & Hoteliers Ltd
Kandy Walk Inn Limited
Lake House Investments Limited
Bata Shoe Company of Ceylon Limited
Glaxo Wellcome Ceylon Limited
NDB Bank Limited
2006 Vallibel Power Erathna Ltd
Mercantile Leasing Ltd.
Lakdhanavi Ltd.
Metal Packaging Ltd.
Statcon Ltd.
2007 Samuel Sons &Company Ltd.
Ceylon Oxygen Ltd.
2008 Janashakthi Insurance Company PLC
Ceylinco Insurance PLC (Non Voting )
Millers
Associated Hotels PLC.
Source: CD of Data Library CSE.
188
Appendix B: Classification of Sectors of the CSE
Bank Finance and Insurance 33
Land and Property 21
Beverage Food Tobacco 18
Manufacturing 32
Chemical Pharms 9
Motors 7
Construction and Engineering 4
Oil Palms 5
Diversified 10
Plantations 18
Footwear Textile 4
Power and Energy 18
Health Care 6
Services 7
Hotel Travels 33
Storces Supplies 6
IT 1
Telecommunications 2
Investment Trust 6
Trading 11
Source: Colombo Stock Exchange
189
Appendix C: VB codes
Codes for Matching BE and ME values for all companies
Dim moApp As Excel.Application ' Excel File with New data
Dim moWB As Excel.Workbook
Dim mows As Excel.Worksheet
Dim DataMat(250, 7) As String 'create new 2D array
Dim xlApp As Excel.Application ' Excel file with Original data
Dim wb As Workbook
Dim ws As Worksheet
Private Sub Command1_Click()
'Load existing Excel file
Set xlApp = New Excel.Application
Set wb = xlApp.Workbooks.Open("D:\Sabaragamuwa-dean\SmallBig
portfolio.xls")
Set ws = wb.Worksheets(cmbYear.Text)
xlApp.Visible = True
ws.Activate
End Sub
Private Sub Command2_Click()
'Create New Excel File
Set mows = moWB.Worksheets.Add
mows.Name = cmbYear.Text
mows.Cells(1, 1).Value = "Company ID"
mows.Cells(1, 2).Value = "Company Name in Short"
mows.Cells(1, 3).Value = "Company Code1"
mows.Cells(1, 4).Value = "Price"
mows.Cells(1, 5).Value = "Company Name in Long"
mows.Cells(1, 6).Value = "Company Code2"
mows.Cells(1, 7).Value = "BEPS"
'Read existing Excel sheet and write to new sheet
For i = 1 To 250
If ws.Cells(i, 1) = "Big Portfolios" Then
i = i + 2
For j = 2 To 250
If (ws.Cells(i, 3) <> "") And (ws.Cells(i, 3) = ws.Cells(j, 6)) Then
For k = 0 To 3
190
p = i - 2
If k < 4 Then
DataMat(p, k) = ws.Cells(i, (k + 1))
End If
mows.Cells(i, (k + 1)).Value = DataMat(p, k)
Next
For k = 4 To 5
p = i - 2
If k < 6 Then
DataMat(p, k) = ws.Cells(j, k + 2)
End If
mows.Cells(i, (k + 2)).Value = DataMat(p, k)
Next
End If
Next j
Else
For j = 2 To 250
If (ws.Cells(i, 3) <> "") And (ws.Cells(i, 3) = ws.Cells(j, 6)) Then
For k = 0 To 3
p = i - 2
If k < 4 Then
DataMat(p, k) = ws.Cells(i, (k + 1))
End If
mows.Cells(i, (k + 1)).Value = DataMat(p, k)
Next
For k = 3 To 5
p = i - 2
If k < 6 Then
DataMat(p, k) = ws.Cells(j, k + 2)
End If
mows.Cells(i, (k + 2)).Value = DataMat(p, k)
Next
End If
Next j
191
End If
Next i
moApp.Visible = True
MsgBox ("Year " & cmbYear.Text & " completed")
wb.Close
xlApp.Application.Quit
Set wb = Nothing
Set xlApp = Nothing
End Sub
Private Sub Form_Load()
Set moApp = New Excel.Application
Set moWB = moApp.Workbooks.Add
End Sub
