TRADING IN CHAOS: ANALYSIS OF ACTIVE MANAGEMENT IN A FRACTAL MARKET Prince ...

294 Pages·2017·4.96 MB·English

by  Prince Kwasi Sarpong

TRADING IN CHAOS: ANALYSIS OF ACTIVE
MANAGEMENT IN A FRACTAL MARKET

by
Prince Kwasi Sarpong
212561506

A thesis submitted in the fulfilment of the requirements for the degree
of
Doctor of Philosophy in Finance

School of Accounting, Economics and Finance
University of KwaZulu-Natal

Supervisors
Dr Mabutho Sibanda
Prof Merle Holden
January 2017
DECLARATION
I, Prince Kwasi Sarpong, declare that:
i. The research reported in this dissertation, except where otherwise indicated, is my
original research.
ii. This dissertation has not been submitted for any degree or examination at any other
university.
iii. This dissertation does not contain other persons’ data, pictures, graphs or other
information, unless specifically acknowledged as being sourced from other persons.
iv. This dissertation does not contain other persons’ writing, unless specifically
acknowledged as being sourced from other researchers.
v. This dissertation does not contain text, graphics or tables copied and pasted from the
internet, unless specifically acknowledged, and the sources being detailed in the
dissertation and in the references sections.

Student’s signature……………………………
I | P age
DEDICATION

This dissertation is dedicated to my family in appreciation of their support and patience.

II | P age
ACKNOWLEDGEMENTS

I thank God for His protection and guidance throughout the period of my study. My sincere
gratitude goes to Professor Mabutho Sibanda and Professor Merle Holden for their support and
direction.
ABSTRACT

Many Nobel Laureates and thousands of academic papers have espoused the concept that risk
is compensated by return. However, the low volatility anomaly - the phenomenon where low-
risk stocks display markedly higher returns than the market portfolio on a risk-adjusted basis
and vice versa - contradicts this basic finance principle of risk-return trade-off and is possibly
one of the greatest anomalies in finance. Among the explanations for this anomaly are, the
behavioural bias of overconfidence, agency problems and the type of manager compensation.
This study investigates and confirms the low volatility anomaly on the Johannesburg Stock
Exchange (JSE) using the risk-adjusted return measure of the Sharpe ratio. According to the
Efficient Market Hypothesis, this is not expected to happen and consequently offers no
explanation for this phenomenon. This study applies the Fractal Market Hypothesis (FMH)
formalised within the framework of Chaos Theory, to explain the existence of the low volatility
anomaly on the JSE.
Building upon the Fractal Market Hypothesis to provide evidence on the behaviour of returns
time series of selected indices of the JSE, the BDS test is applied to test for non-random chaotic
dynamics and further applies the rescaled range analysis to ascertain mean reversion,
persistence or randomness on the JSE. The BDS test confirms that all the indices considered in
this study are not independent and identically distributed. Applying the re-scaled range
analysis, the FTSE/JSE Top 40 and the FTSE/JSE All Share Index appear relatively efficient
and riskier than the FTSE/JSE Small Cap Index, which exhibits significant persistence and
appears to be less risky and less efficient contrary to the popular assertion that small cap indices
are riskier than large cap indices.
The study further analyses the three fundamentals of the FMH namely, the impact of
information, the role of liquidity and time horizon on the top 40 and small cap indices.
Information is not uniformly distributed among the two indices as the FTSE/JSE Top 40 index
receives more publications form sources such as newspapers, online publications and journals
as well as JSE issued news and historical company news. The FTSE/JSE Top 40 also receives
more analyst coverage than the FTSE/JSE Small Cap Index. Using the absolute and normalised
volume of trade as a proxy for liquidity, the FTSE/JSE Top 40 index exhibits a relatively higher
level of liquidity than the FTSE/JSE Small Cap index. The study finds that domestic equity
fund managers in South Africa hold in their portfolios, a disproportionately greater percentage
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of FTSE/JSE Top 40 companies relative to other companies on the JSE and concludes that
these managers contribute to the low volatility anomaly on the JSE. The study further concludes
that in line with the FMH, lack of information and the illiquidity of the FTSE/JSE Small Cap
attracts long-term investors who become the dominant class of investors on the index and are
compensated for taking on the risk of illiquidity in the form of illiquidity premium and low
volatility. The highly liquid FTSE/JSE Top 40, which has relatively high availability of
information on the other hand attracts different classes of investors with differing horizons who
take opposite sides of each trade as different classes of investors interpret the same set of
information differently. The high liquidity and information leads to high volatility as investors
continually adjust their holdings with the emergence of new information. The high volatility
and subsequent underperformance of the FTSE/JSE Top 40 therefore is a cost of efficiency and
liquidity (liquidity discount).
Studies on the FMH are generally focused on market crashes. This study provides a novel
approach by using the FMH to explain the low-volatility anomaly. This synthesis of the FMH
and the low volatility anomaly provides an alternative technique of evaluating risk and also
provides insights into the efficiency of financial markets and contributes to the literature on the
FMH as well as the low volatility anomaly.

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TABLE OF CONTENTS

DECLARATION ........................................................................................................................ I
DEDICATION ........................................................................................................................... II
ACKNOWLEDGEMENTS ..................................................................................................... III
ABSTRACT ............................................................................................................................. IV
TABLE OF CONTENTS ......................................................................................................... VI
LIST OF FIGURES ................................................................................................................. 11
LIST OF TABLES ................................................................................................................... 14
CHAPTER ONE ........................................................................................................................ 1
INTRODUCTION AND OVERVIEW ..................................................................................... 1
1.1 Introduction ................................................................................................................................... 1
1.2 Context of the Study ..................................................................................................................... 3
1.3 Statement of the Problem .............................................................................................................. 4
1.4 Aim ............................................................................................................................................... 5
1.5 Research Objectives ...................................................................................................................... 5
1.6 Research Questions ....................................................................................................................... 5
1.7 Scope of the Study ........................................................................................................................ 5
1.8 Significance of the Study .............................................................................................................. 7
1.9 Structure of the Thesis .................................................................................................................. 7
1.10 Summary ................................................................................................................................... 10
CHAPTER TWO ..................................................................................................................... 11
CLASSICAL FINANCE ......................................................................................................... 11
2.1 Introduction ................................................................................................................................. 11
2.2 Classical Finance Theories.......................................................................................................... 11
2.3 Historical Background ................................................................................................................ 13
2.4 Mean Variance Theory and Capital Asset Pricing Model (CAPM)............................................ 17
2.5 Random Walk Hypothesis .......................................................................................................... 22
2.6 Efficient Market Hypothesis (EMH) ........................................................................................... 23
2.7 Arbitrage Pricing Theory (APT) and the Multi Factor Models .................................................. 28
2.8 The Fama-French Three-Factor Model ....................................................................................... 29
2.9 Low Volatility Anomaly ............................................................................................................. 34
2.10 Efficiently Inefficient Market ................................................................................................... 42
2.11 Joint Hypothesis Problem ......................................................................................................... 44
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2.12 Summary ................................................................................................................................... 44
CHAPTER THREE ................................................................................................................. 45
CHAOS THEORY AND FRACTAL MARKET HYPOTHESIS .......................................... 45
3.1 Introduction ................................................................................................................................. 45
3.2 Shortcomings of Classical Finance ............................................................................................. 46
3.3 CHAOS THEORY ...................................................................................................................... 52
3.4 Fractal Market Hypothesis (FMH) .............................................................................................. 52
3.5 Summary ..................................................................................................................................... 57
CHAPTER FOUR .................................................................................................................... 58
FINANCIAL CRISES ............................................................................................................. 58
4.1 Why Financial Crises Keep Recurring ........................................................................................ 58
4.2 Financial Instability Hypothesis (FIH) ....................................................................................... 60
4.3 Categories of Financial Crises .................................................................................................... 61
4.3.1 Quantitative Definition of Financial Crises ......................................................................... 61
4.3.2 Financial Crises by Event .................................................................................................... 62
4.4 SOME NOTEWORTHY FINANCIAL CRISES ....................................................................... 63
4.4.1 Tulip Mania .......................................................................................................................... 64
4.4.2 The South Sea Bubble .......................................................................................................... 66
4.4.3 The Mississippi Bubble ........................................................................................................ 68
4.4.4 The Panic of 1837 ................................................................................................................ 70
4.4.5 The Rich Man’s Panic of 1907 ............................................................................................ 70
4.4.6 The Great Depression........................................................................................................... 71
4.4.7 The Latin American Debt Crisis .......................................................................................... 73
4.4.8 The Asian Financial Crisis ................................................................................................... 74
4.4.9 Russian Crisis of 1998 ......................................................................................................... 75
4.4.10 The Dot Com Bubble ......................................................................................................... 76
4.4.11 The Great Recession .......................................................................................................... 78
4.5 Summary ..................................................................................................................................... 81
CHAPTER FIVE ..................................................................................................................... 82
BEHAVIOURAL FINANCE .................................................................................................. 82
5.1 Introduction ................................................................................................................................. 82
5.2 What Is Behavioural Finance? .................................................................................................... 84
5.3 A History of Behavioural Finance .............................................................................................. 86
5.4 Risk and Uncertainty ................................................................................................................... 88
5.5 Investor Biases and Heuristics .................................................................................................... 90
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5.5.1 Overconfidence Bias ............................................................................................................ 91
5.5.2 Anchoring and Adjustment Bias .......................................................................................... 93
5.5.3 Cognitive Dissonance Bias .................................................................................................. 94
5.5.4 Availability Bias .................................................................................................................. 96
5.5.5 Representativeness Bias ....................................................................................................... 96
5.5.6 The Affect Heuristic............................................................................................................. 97
5.5.7 The Prospect Theory ............................................................................................................ 99
5.5.8 Framing .............................................................................................................................. 100
5.5.9 Herding .............................................................................................................................. 101
5.5.10 Endowment Bias .............................................................................................................. 104
5.5.11 Hindsight Bias .................................................................................................................. 105
5.5.12 Reputation Mining ........................................................................................................... 106
5.5.13 Regret Aversion Bias ....................................................................................................... 107
5.6 The Argument for Heuristics .................................................................................................... 108
5.7 All Models Are Wrong ............................................................................................................. 112
5.8 Summary: Let A Hundred Flowers Bloom ............................................................................... 114
CHAPTER SIX ...................................................................................................................... 116
THE ASSET MANAGEMENT INDUSTRY ....................................................................... 116
6.1 Introduction ............................................................................................................................... 116
6.2 An Overview of Portfolio Management .................................................................................... 119
6.3 Active versus Passive Portfolio Management ........................................................................... 120
6.4 Major Product Segments ........................................................................................................... 128
6.4.1 Mutual Funds ..................................................................................................................... 128
6.4.2 Exchange Traded Funds (ETFS) ........................................................................................ 131
6.4.3 Hedge Funds ...................................................................................................................... 133
6.4.4 Venture Capital (VC) And Private Equity (PE) ................................................................. 137
6.4.5 Insurance Companies ......................................................................................................... 142
6.4.6 Pension Funds .................................................................................................................... 144
6.4.7 Sovereign Wealth Funds (SWFs) ....................................................................................... 146
6.4.8 Real Estate ......................................................................................................................... 149
6.5 Systemically Important Financial Institutions (SIFIs) .............................................................. 152
6.6 The Future Of The Asset Management Industry....................................................................... 156
6.7 Summary ................................................................................................................................... 159
CHAPTER SEVEN ............................................................................................................... 160
THE JOHANNESBURG STOCK EXCHANGE (JSE) ........................................................ 160
7.1 Introduction ............................................................................................................................... 160
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7.2 JSE Sens ................................................................................................................................ 163
7.3 JSE Strate .............................................................................................................................. 163
7.4 Demutualization .................................................................................................................... 164
7.5 JSE TradElect ........................................................................................................................ 165
7.6 JSE Clear ............................................................................................................................... 165
7.7 The JSE and Market Efficiency ................................................................................................ 166
7.7 Spillover Effects of International Financial Markets on The JSE ............................................. 168
7.8 Summary ................................................................................................................................... 169
CHAPTER EIGHT ................................................................................................................ 170
DATA AND METHODOLOGY ........................................................................................... 170
8.1 Introduction ............................................................................................................................... 170
8.2 Data ........................................................................................................................................... 170
8.3 Statistical Analysis Techniques ................................................................................................ 173
8.3.1 Risk-Adjusted Returns ....................................................................................................... 173
8.3.2 The BDS Test ..................................................................................................................... 174
8.3.3 The Rescaled Range Analysis (The Hurst Exponent) ........................................................ 176
8.3.4 The Variance Ratio Test .................................................................................................... 178
8.3.5 Analysis of Portfolio Holdings .......................................................................................... 181
8.3.6 Analysts Coverage ............................................................................................................. 181
8.3.7 Frequency of Publication ................................................................................................... 182
8.3.8 Normalized Volume of Trade ............................................................................................ 182
8.4 Summary ................................................................................................................................... 182
CHAPTER NINE ................................................................................................................... 183
DATA ANALYSIS AND INTERPRETATION ................................................................... 183
9.1 Results and Discussion ............................................................................................................. 183
9.2 FTSE/JSE Small Cap Outperforms FTSE/JSE Top 40 Index ................................................... 184
9.2 BDS Test ................................................................................................................................... 190
9.3 Rescaled Range Analysis (Hurst Exponent) ............................................................................. 192
9.4 FTSE/JSE Top 40 More Volatile than FTSE/JSE Small Cap Index ......................................... 194
9.5 Variance Ratio Test ................................................................................................................... 194
9.6 Factors That May Contribute to The Low Volatility Anomaly on the JSE .............................. 199
9.6.1 Publication Frequency is Lower for Small Caps ................................................................ 199
9.6.2 The Number of Analysts Covering Small-Cap Equities is Smaller Than for Large-Cap .. 201
9.6.3 General Equity Funds Gravitate to Large Caps ................................................................. 202
9.6.4 Small Cap Index Exhibit Less Liquidity Than Large Cap Index ....................................... 205
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