The effectiveness of a Technical Analysis strategy versus a Buy-and-hold strategy on the FTSE/JSE Top 40 Index shares of the JSE Ltd: The case of the Moving Average Convergence Divergence Indicator by Anton Wouter Du Plessis MINOR DISSERTATION submitted in partial fulfilment of the requirements for the degree MAGISTER COMMERCII in FINANCIAL MANAGEMENT in the FACULTY OF ECONOMIC AND FINANCIAL SCIENCES at the UNIVERSITY OF JOHANNESBURG SUPERVISOR: Prof. R J Eiselen CO-SUPERVISOR: Prof. G Els OCTOBER 2012
Transcript
The effectiveness of a Technical Analysis strategy versus a Buy-and-hold strategy on the FTSE/JSE Top 40 Index shares of the JSE Ltd: The case of the Moving
Average Convergence Divergence Indicator
by
Anton Wouter Du Plessis
MINOR DISSERTATION
submitted in partial fulfilment of the requirements for the degree
MAGISTER COMMERCII
in
FINANCIAL MANAGEMENT
in the
FACULTY OF ECONOMIC AND FINANCIAL SCIENCES
at the
UNIVERSITY OF JOHANNESBURG
SUPERVISOR: Prof. R J Eiselen
CO-SUPERVISOR: Prof. G Els
OCTOBER 2012
II
Abstract This study compares two main investment strategies on the JSE Ltd for 2001 to 2010 on the FTSE/JSE Top 40 Index shares. The one strategy is the Fundamental Analysis strategy (Buy-and-hold) and the other is the Technical Analysis (MACD). It was found that within the limitations of this study, the Buy-and-hold investment strategy is more effective than the MACD investment strategy.
Key words
Fundamental Analysis, Technical Analysis, Moving Averages, Moving Average Convergence Divergence (MACD), Buy-and-hold, value investing, JSE Ltd, FTSE/JSE Top 40 Index, share market, charts, Dow Theory, trends.
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DECLARATION OF ORIGINAL WORK
I, Anton du Plessis, declare that this minor dissertation is my own unaided work. Any
assistance that I have received has been duly acknowledged in the dissertation. It is
submitted in partial fulfilment of the requirements for the degree of Master of
Commerce at the University of Johannesburg. It has not been submitted before for
any degree or examination at this or any other University.
___________________ __________________
Signature Date
IV
Acknowledgements Sometimes in life people inspire you without even knowing it. I would like to first of all thank my niece Antoinette Du Plessis for being an everyday inspiration to me. The way you live your life every day inspires me to achieve more.
I would also like to thank Prof. Reitte Eiselen for all her patience in helping me through this project. I know it has not been easy with me overseas for some of the time and her in the hospital for some of the time. Also thank you to Prof. Els for helping out at times.
I would like to thank my wife and family for putting up with me through what must have seemed like a never-ending journey.
Thank you.
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TABLE OF CONTENTS Chapter 1
Introduction and background to the study
1.1 Introduction 1 1.2 Problem statement 5 1.3 Research question 5 1.4 Purpose of the study 6 1.5 Scope of the study 6 1.6 Proposed research methodology and analysis 9 1.7 Limitations of the study 9 1.8 Perceived significance of the study 10 1.9 Chapter outline 12
Chapter 2 Literature review
2.1 Introduction 13 2.1.1 Background 13
2.2 Types of investors 14 2.3 Fundamental Analysis 15
2.3.1 - Definition 15 2.3.2 - Factors determining the intrinsic value of a company 17 2.3.3 - Fundamental Analysis strategies 18
2.5 Dow Theory 21 2.5.1 - Introduction 21 2.5.2 - Six assumptions of the Dow Theory 21
2.5.2.1 The averages discount everything 21 2.5.2.2 The market is made up of three trends 21 2.5.2.3 Primary trends have three phases 22 2.5.2.4 The averages must confirm each other 22 2.5.2.5 The volume confirms the trend 23 2.5.2.6 A trend remains intact until it gives a definite reversal signal 23
2.8 The MACD 29 2.8.1 - Introduction 29 2.8.2 - Working of the MACD’s signal 30 2.8.3 - False signals 32 2.8.4 - Variations 33 2.8.5 - Example calculations of MACD 33 2.8.6 - Challenges of the MACD 36
2.9 The Fundamental / Technical Analysis debate 36 2.10 Chapter summary 37
CHAPTER 3 Research methodology
3.1 Introduction 38 3.2 Research question and objectives 38 3.3 Scope of the research study 39 3.4 Research design and strategy 39 3.5 Sampling strategy 40 3.6 Data collection method 41 3.7 Data to be collected 41 3.8 Data analysis 41
3.8.1 - Applying signals to the data 42 3.8.2 - Dividend addition data analysis 44 3.8.3 - Transactional history 45
3.8.3.1 Buy-and-hold from day 1 (BH0) 45 3.8.3.2 Buy-and-hold from first MACD signal (BH1) 46 3.8.3.3 MACD strategy (MACD) 48
3.8.4 - Control sheet 49 3.8.5 - T-tests performed on investment methods 53
3.9 Validity and reliability of data 58 3.9.1 - Validity of measurement 58 3.9.2 - Reliability 58 3.10 Ethical considerations 58 3.11 Limitations 59 3.12 Chapter summary 61
Chapter 4 Results and discussion
4.1 Introduction 62 4.2 Description of the sample 62
VII
4.3 Results 63 4.4 Conclusion of the chapter 89
Chapter 5 Findings, conclusions and recommendations
5.1 Introduction 90 5.2 Reason for undertaking the research 90 5.3 Summary of the findings 91 5.4 Discussion of the findings 95 5.5 Contribution of the study 97 5.6 Limitations 98 5.7 Recommendations for further research 98
List of references 100
Appendices
Appendix 1: Data analysis 0% transaction cost 104
Appendix 2: Data analysis 0.4% transaction cost 115
Appendix 3: Data analysis 0.5% transaction cost 126
Appendix 4: Data analysis 0.6% transaction cost 137
Appendix 5: Data analysis 0.7% transaction cost 148
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LIST OF TABLES Table Description Page
Table 1.1 FTSE/JSE Top 40 Index equities as at 1 January 2011 7 Table 1.2 Summary of chapters and content 12 Table 2.1 Anglo Gold: Worked MACD sample data 33 Table 3.1 Sample of applying signals to the data per share 42 Table 3.2 Sample of dividend addition data analysis 44 Table 3.3 Sample of data for Buy-and-hold from day 1 45 Table 3.4 Sample of data for Buy-and-hold from first MACD signal 46 Table 3.5 Sample of data for MACD 48 Table 3.6 Sample of data analysis per share 50 Table 3.7 Sample of result set per year 52 Table 3.8 T-test per year assuming 0% transaction cost 53 Table 3.9 Calculation of eta2 57 Table 4.1 Summary of results for each year and the ten-year period at 0% transaction
cost 63
Table 4.2 Summary of results for each year and the ten-year period at 0.4% transaction cost
64
Table 4.3 Summary of results for each year and the ten-year period at 0.5% transaction cost
64
Table 4.4 Summary of results for each year and the ten-year period at 0.6% transaction cost
65
Table 4.5 Summary of results for each year and the ten-year period at 0.7% transaction cost
65
Table 4.6 Ranking of investment strategies per year for 0% transaction cost. 66 Table 4.7 Ranking of investment strategies per year for 0.4% transaction cost. 66 Table 4.8 Ranking of investment strategies per year for 0.5% transaction cost. 67 Table 4.9 Ranking of investment strategies per year for 0.6% transaction cost. 67 Table 4.10 Ranking of investment strategies per year for 0.7% transaction cost. 68 Table 4.11 Results for the ten years separately at 0% transaction cost 69 Table 4.12 Results for the whole ten years at 0% transaction cost 69 Table 4.13 Ranking number per year at 0% transaction cost 70 Table 4.14 Ranking percentage per year at 0% transaction cost 71 Table 4.15 T-test results for 0% transaction cost. (p-values) 71 Table 4.16 Eta-squared results for 0% transaction cost. 72 Table 4.17 Results for the ten years separately at 0.4% transaction cost 73 Table 4.18 Results for the whole ten years at 0.4% transaction cost 73 Table 4.19 Ranking number per year at 0.4% transaction cost 74 Table 4.20 Ranking percentage per year at 0.4% transaction cost 74 Table 4.21 T-test results for 0.4% transaction cost. (p-values) 75 Table 4.22 Eta-squared results for 0.4% transaction cost. 75 Table 4.23 Results for the ten years separately at 0.5% transaction cost 77 Table 4.24 Results for the whole ten years at 0.5% transaction cost 77 Table 4.25 Ranking number per year at 0.5% transaction cost 78 Table 4.26 Ranking percentage per year at 0.5% transaction cost 78 Table 4.27 T-test results for 0.5% transaction cost. (p-values) 79
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Table Description Page
Table 4.28 Eta-squared results for 0.5% transaction cost. 79 Table 4.29 Results for the ten years separately at 0.6% transaction cost 81 Table 4.30 Results for the whole ten years at 0.6% transaction cost 81 Table 4.31 Ranking number per year at 0.6% transaction cost 82 Table 4.32 Ranking percentage per year at 0.6% transaction cost 82 Table 4.33 T-test results for 0.6% transaction cost. (p-values) 83 Table 4.34 Eta-squared results for 0.6% transaction cost. 83 Table 4.35 Results for the ten years separately at 0.7% transaction cost 85 Table 4.36 Results for the whole ten years at 0.7% transaction cost 85 Table 4.37 Ranking number per year at 0.7% transaction cost 86 Table 4.38 Ranking percentage per year at 0.7% transaction cost 86 Table 4.39 T-test results for 0.7% transaction cost. (p-values) 87 Table 4.40 Eta-squared results for 0.7% transaction cost. 87 Table 4.41 Linking the results to the objectives of the study. 89 Table 5.1 Annual ranking number for BH0, BH1 and MACD 91 Table 5.2 Annual ranking percentage for BH0, BH1 and MACD 91 Table 5.3 Ten-year ranking number for BH0, BH1 and MACD 92 Table 5.4 Ten-year ranking percentage for BH0, BH1 and MACD 92 Table 5.5 Returns for BH0, BH1 and MACD for the ten-year period 93 Table 5.6 Returns for BH0, BH1 and MACD for each of the ten years 94 Table 5.7 MACD ranking per transaction cost 95
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LIST OF FIGURES Figure Description Page
Figure 1.1 MACD chart 3 Figure 2.1 Graphical representation of chapter 2 13 Figure 2.2 Line chart example 25 Figure 2.3 Bar and volume charts example 26 Figure 2.4 MACD chart 32 Figure 2.5 Graphical representation of data from Table 2.1 35 Figure 3.1 Graphical representation of data analysis 47 Figure 4.1 Ranking for each year of the ten-year period at 0% transaction cost per
investment strategy 70
Figure 4.2 Graphical representation of eta2 for 0% transaction cost 72 Figure 4.3 Ranking for each year of the ten-year period at 0.4% transaction cost per
method 74
Figure 4.4 Graphical representation of eta2 for 0.4% transaction cost 76 Figure 4.5 Ranking for each year of the ten-year period at 0.5% transaction cost per
method 78
Figure 4.6 Graphical representation of eta2 for 0.5% transaction cost 80 Figure 4.7 Ranking for each year of the ten-year period 0.6% transaction cost per
method 82
Figure 4.8 Graphical representation of eta2 for 0.6% transaction cost 84 Figure 4.9 Ranking for each year of the ten-year period at 0.7% transaction cost per
method 86
Figure 4.10 Graphical representation of eta2 for 0.7% transaction cost 88 Figure 5.1 Percentage Returns for Buy-and-hold and MACD 93 Figure 5.2 MACD first rankings per transaction cost 96
Figure 5.3 Buy-and-hold first rankings per transaction cost 96
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Chapter 1
Introduction and background to the study
1.1 Introduction
Any person investing money in shares wants to make money. When investing in
shares investors can increase their wealth in one of two ways: the share can be sold
for more than it was bought and/or dividends can be paid out. In terms of buying
shares and selling them at a higher price, it is critical to buy and to sell at the right
time in order to maximise profits. There are two schools of thought regarding the
buying and selling of shares, namely Fundamental- and Technical Analysis.
In the one school of thought, Fundamental Analysis (Marx, Mpofu, Van der Venter,
Nortje, 2006), the expected value of the shares of a company is determined based
on its historical growth, dividends paid out and its predicted future cash flows.
Although there are various Fundamental Analysis strategies, the Buy-and-hold
strategy is the most commonly used (Busetti, 2009). A Buy-and-hold investment
strategy is a fundamental investment strategy in which shares are bought and then
held for a long period, regardless of the market's fluctuations. The Buy-and-hold
approach to investing in shares rests upon the assumption that in the very long term
(over the course of, say, 10 or 20 years) share prices will go up, but the average
investor does not know what will happen to the share price the next day. The logic
behind the Buy-and-hold strategy is that in a capitalist society the economy will keep
expanding. This will result in profits that will keep on growing and both share prices
and share dividends increasing. The basic notion is that irrespective of short-term
fluctuations that may be due to business cycles or rising inflation, in the long term
these will be smoothed out and the market as a whole will rise.
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In the other school of thought referred to as Technical Analysis (Marx, et al., 2006),
the expected value of the shares of a company is based purely on the share price
history. In Technical Analysis it is believed that all the required information about a
share is reflected in its price, that is, that the strong form of the Efficient Market
Hypothesis (EMH) holds. Technical Analysis therefore involves the study of historical
prices in order to predict future price movements. It assumes that the information
contained in historical prices is correctly incorporated in current prices (Ellinger,
1971). Whether technical trading rules can generate excess returns has long been a
controversial issue especially in view of the fact that transactions costs are incurred
in buying and selling shares. A number of studies have suggested that market
indicators alone cannot improve the prediction of the future prices (Neftci, 1991;
Hudson et al., 1996; Mills, 1997). However, there are also studies that support
technical trading rules such as Treynor and Ferguson (1985) and Brock et al. (1992).
The nature of share price movements that underpins Technical Analysis is that they
are volatile due to the fact that there are many different factors that have an effect on
share prices. When Technical Analysis is used, this problem is addressed by
analysing the moving averages of the shares rather than the share prices. The
moving averages contain the trend of the share prices. Moving averages are the
average of a share price for a certain period of time (t – k) recalculated on a daily
basis (t) and for the same historical length in days (k). These moving averages can
also be calculated for other periods of time, for example hourly, monthly, yearly etc.
Moving averages help to smooth out volatility to a certain degree depending on the
number of days (k) used in the calculation of the moving average. This smoothed-out
version of the share price history provides a better indication of the longer term
direction of the share price movement.
Technical strategies commonly used by investors include the Directional Movement
Index (DMI), moving averages (on their own), the Average Directional Index (ADX),
Stochastics, the Relative Strength Index (RSI) and candle sticks (Marx, et al., 2006).
Whereas most of these Technical Analysis strategies utilise the moving average of
the share prices, some even use more than one moving average. One of the
indicators using more than one moving average that technical analysts employ is the
Moving Average Convergence Divergence (MACD) indicator: two moving averages
3
of a price history are used. The one moving average is over a shorter term (shorter
number of days) and the other over a longer term (longer term of days). The
operation on this indicator is as follows: when the shorter-term moving average
moves above the longer-term moving average it is a “buy” signal and when the
shorter-term moving average moves below the longer-term average it is a “sell”
signal. The rationale for this sell and buy signals is that the short-term movement in
price indicates that the current price is falling faster than the long-term movement.
The opposite is true for a buy signal (Appel, 1979). Figure 1.1 shows a graphical
representation of an example of the MACD indicator.
Figure 1.1: MACD Chart
Source: Graphical presentation of sample data generated using ShareMagic PRO
software (version 8.9.0, 2011)
From the above, it is evident that the length of time an investment is held plays a role
in terms of the strategy that the investor adopts. Long-term investments are often
associated with Fundamental Analysis while short-term investments are often
associated with Technical Analysis. The International Financial Reporting Standards
(IFRS) also have a definition of this concept that is aligned with investing. Short term
is defined as twelve months or less and long term as any time longer than twelve
months (The South Africa Institute of Chartered Accountants, 2009). This definition is
logical if one considers the definition of fundamental versus Technical Analysis. In
Buy Sell
Buy
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Fundamental Analysis one will use the financial statements of a company as the
main source of information and this will only be issued once a year. Thus it would
make sense that a long-term investment would at least span more than a year as
one would need the next set of financial statements to make an assessment of an
investment. In a Buy-and-hold or long-term strategy the investment is normally held
for many years; as long as the fundamental indicators used to acquire the
investment are still satisfying the investor. In Technical Analysis, the buy and sell
signals come from changes in share prices which are more volatile and short term.
Short-term strategies employed by Technical Analysis investors involve constant
buying and selling of shares due to the fact that these techniques attempt to use the
short-term volatility to predict the short-term future price movements.
Based on the preceding discussion, it is evident that both schools of thought
(fundamental and technical) have their proponents as well as their opponents, as
both have been shown to provide accurate as well as inaccurate predictions of share
price movements. An individual investor is left with a dilemma in terms of which of
these two schools of thought is more effective in realising a profit on an investment.
The aim of this study is to investigate if investors can use Technical Analysis to help
them make investment decisions for themselves. In particular, this study is aimed at
exploring differences and similarities between the fundamental and technical
investment strategies for investors that actively invest on the JSE Ltd. This will be
explored for one type of Fundamental Analysis (Buy-and-hold) and one type of
Technical Analysis (MACD). Investors can invest passively through some third party
that will make investment decisions for them or they can invest actively and make
their own investment decisions. This study is not aimed at passive investors i.e.
investors that let advisors make their investment decisions. Differences and
similarities in adopting the Buy-and-hold and the MACD strategies when investing in
shares will be investigated and evidence regarding the returns of trading using these
strategies will be highlighted.
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1.2 Problem statement
The central problem of this study is formulated against the framework presented in
the preceding introduction and rationale.
The research problem to be investigated in this study is that active share investors
need to decide which strategy they should use to arrive at a decision of when to buy
and when to sell the shares in which they have decided to invest. Should they follow
the Fundamental Analysis route by considering the financial statements of a
company, should they consider the actual share price movement, or should they use
a combination of the two strategies?
1.3 Research question
In an attempt to address the research problem, the research question to be
addressed in this study is limited to a specific fundamental strategy, namely the Buy-
and-hold strategy and to a specific Technical Analysis strategy, namely the MACD
strategy. The study is furthermore limited to a ten-year period namely 2001 to 2010.
It is also limited to the FTSE/JSE Top 40 Index shares on the JSE Ltd.
The research question is thus:
Which one of the MACD or the Buy-and-hold strategies on the FTSE/JSE Top 40
Index shares of the JSE Ltd over the period 2001 to 2010 is more effective?
Sub-questions are:
To what extent do transaction cost (i.e. costs incurred when buying and selling
shares) have an effect on the effectiveness of the MACD in comparison with the
Buy-and-hold strategy?
Under what conditions will either the MACD or the Buy-and-hold strategy yield
higher returns?
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1.4 Purpose of the study
This study aims to investigate the effectiveness of using one of the technical
strategies as a trading indicator in comparison with a fundamental strategy on the
equities making up the FTSE/JSE Top 40 Index over the ten-year period 2001 to
2010.
In this study only one technical indicator, namely the MACD will be used and one
fundamental strategy (Buy-and-hold). In other words, for a strategy of constant
buying and selling in comparison with a simple buy and hold strategy, which method
is the most effective? For the primary focus of this study, the Buy-and-hold strategy
will indicate buying a share at the beginning of a year and selling it at the end of the
year, and buying it at the beginning of the ten-year period and selling it at the end of
the ten-year period. This will be compared to the returns of the MACD strategy at the
end of each year and at the end of the ten-year period.
1.5 Scope of the study
Only shares in the FTSE/JSE Top 40 share index with a ten-year history will be
considered in the study to ensure comparability of results for all equities over the
whole ten years. A list of the FTSE/JSE Top 40 Index as at 31 December 2010 will
be obtained directly from the JSE Ltd. The FTSE/JSE Top 40 Index actually consists
of 42 shares. The JSE Ltd rebalances the index from time to time and this results in
there sometimes being either more than 40 shares or at other times fewer than 40
shares in the index. The FTSE/JSE Top 40 Index is rebalanced every quarter by the
JSE Ltd in order to ensure that the shares of the index are representative of the
whole market. For this study the index as at 31 December 2010 is used. For the ten-
year period under review there are a total of 32 shares that also have ten years’
worth of data.
Another reason the FTSE/JSE Top 40 Index was selected is the fact that they
represent the market. This implies that the whole market does not have to be tested
to arrive at a conclusion and that the other shares on the JSE Ltd contribute a small
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segment of the market. The actual number of shares tested in the end will be fewer
than the 42 shares making up the index. The reason for this is that a history of ten
years will be needed for this study. The companies not tested do not have a price
history of ten years. The main reason for this is that the companies that are not
considered were not listed for the entire ten-year period.
A period of ten years has been selected for this study in order to access various
market cycles. In the last ten years the market has been through economic cycles
such as the dot.com. and the 2008 financial crises as well as the boom periods in
2002 and 2007.
The list of shares on the FTSE/JSE Top 40 Index will be inspected and only the
shares with an available ten-year history will be used, i.e. from 1 January 2000 to 31
December 2010. As shown in Table 1.1, there are 32 shares on the FTSE/JSE Top
40 Index that satisfy the criteria and these will be used for this study. Table 1.1
shows the shares that form part of the FTSE/JSE Top 40 Index and have a ten-year
history.
Table 1.1: FTSE/JSE Top 40 Index equities as at 1 January 2011
Share Code
Share Name Date Listed Tested in
study
1 ABL African Bank Invest 01 January 1998 Yes 2 ACL ArcelorMittal South Africa Ltd 01 January 1989 Yes 3 AGL Anglo American 24 May 1999 Yes 4 AMS Anglo Platinum 01 January 1977 Yes 5 ANG Anglogold Ashanti 01 January 1944 Yes 6 APN Aspen Pharmacare Holdings 01 January 1987 Yes 7 ARI African Rainbow Minerals Ltd 01 January 1988 Yes 8 ASA Absa Group 03 December 1986 Yes 9 BIL BHP Billiton 01 January 1997 Yes 10 BVT Bidvest Group 01 January 1954 Yes 11 CFR Compagnie Financiere Richemont AG 01 January 1988 Yes 12 CSO Capital Shopping Centres Group Plc 24 June 1999 Yes 13 EXX Exxaro Resources 26 November 2001 No 14 FSR Firstrand Limited 28 May 1998 Yes 15 GFI Gold Fields 01 January 1998 Yes 16 GRT Growthpoint Prop Ltd 01 November 1987 Yes 17 HAR Harmony 01 January 1951 Yes 18 IMP Impala Platinum Hlds 01 January 1973 Yes 19 INL Investec Ltd 28 November 1986 Yes 20 INP Investec PLC 22 July 2002 No
8
Share Code
Share Name Date Listed Tested in
study
21 KIO Kumba Iron Ore 02 November 2006 No 22 LON Lonmin PLC 01 January 1969 Yes 23 MND Mondi Ltd 03 July 2007 No 24 MNP Mondi Plc 03 July 2007 No 25 MSM Massmart Holdings 04 July 2000 No 26 MTN MTN Group 01 January 1995 Yes 27 NED Nedbank Group 01 January 1969 Yes 28 NPN Naspers 12 September 1994 Yes 29 OML Old Mutual 12 July 1999 Yes 30 PIK Pick N Pay Stores 01 January 1968 Yes 31 REI Reinet Investments 21 October 2008 No 32 REM Remgro 26 September 2000 No 33 RMH RMB Holdings 01 January 1992 Yes 34 SAB SABMiller 08 March 1897 Yes 35 SBK Standard Bank Group 01 January 1970 Yes 36 SHF Steinhoff International Holdings 23 September 1998 Yes 37 SHP Shoprite 01 January 1936 Yes 38 SLM Sanlam 30 November 1998 Yes 39 SOL Sasol 01 January 1979 Yes 40 TBS Tiger Brands 01 January 1944 Yes 41 TRU Truworths International 11 May 1998 Yes 42 VOD Vodacom Group 18 May 2008 No
Source: (Magoli, 2011) JSE Ltd, 28 April 2011
The MACD has various signals that could be used for buy and sell signals but only
the 9-day signal line will be used in this study, as this is how Appel designed the
indicator originally (Appel, 1979). In this study only the crossing of the 9-day signal
line with the MACD will be considered. The variables used in this study are the same
as the inventor of the indicator (Appel, 1979) set them. These settings were derived
by trial and error (Appel, 1979), aligning them to the US market at the time. These
settings have remained the standard since then, but can be changed to get custom
results for specific shares.
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1.6 Proposed research methodology and analysis
This study is quantitative. Historical data is used from a secondary source. The daily
share price data for the FTSE/JSE Top 40 Index shares included in the study will be
obtained from the JSE Ltd for the 10 years under review. This data will then be
processed in Microsoft Excel to determine the MACD signals. After the MACD
signals have been determined, different simulated portfolios will be created taking
into account transaction cost for each buy and sell signal as well as dividend income.
Transaction cost for this study will be set at 0%, 0.4%, 0.5%, 0.6% and 0.7%. In the
South African market the transaction cost available to the general public range from
0.4% to 0.7% as on 31 December 2010.These portfolios will then be compared to
determine which one of the MACD and Buy-and-hold strategies is more effective.
For each of the years (2001 to 2010) and for the ten-year period, correlations
between the returns of the MACD and the Buy-and-hold will be determined.
Dependant t-tests will be used to determine whether there is a significant difference
between the average return of the Buy-and-hold and the MACD. In addition, the
effect size, i.e. the practical significance of the differences between the two statistics
will be determined.
1.7 Limitations of the study
The study will only consider the FTSE/JSE Top 40 Index equities as these form the
bulk of the market from both values and trading volume points of view. Since this
study is of a limited scope it would not be efficient to test the whole market. The
FTSE/JSE Top 40 Index equities are selected for the index based on their market
capitalisation (total market value of the shares based on their latest share price and
number of shares issued). This will ensure liquidity in the market in terms of this
study. The FTSE/JSE Top 40 Index shares are the most frequently traded shares on
the market (anon., 2011). For the purpose of this study the assumption will be made
that there will be a market for the shares when they need to be bought or sold. The
limitation here is that the actual equity market will not necessarily behave this way. If
all equities were considered, the potential shortage of supply of shares to the market
would also have to be considered. A further limitation of the study is that only when
10
to buy and when to sell a specific share will be considered. Which shares to buy or
sell will not form part of the scope of the study.
Although the ten-year (2001 to 2010) period selected reflects different market cycles,
the results of the analysis in this study cannot necessarily be applied to other
periods.
1.8 Perceived significance of the study
This study should inform investors who actively manage their own investment of
shares on the JSE Ltd. It will point to the effectiveness of using a Technical Analysis
approach, specifically the MACD indicator as opposed to using a Fundamental
Analysis, specifically the Buy-and-hold strategy. It should not only inform individual
investors but also corporate investors and fund managers who make investment
decisions on behalf of others as to which method is more effective.
More sophisticated investors can make profits by selling short and buying long.
Buying long (the Buy-and-hold strategy in particular) is what most investors are
familiar with. Buying long is when shares are bought at a low price and sold at a high
price. In this scenario, profits are made in a bull or rising market. Short selling will be
selling shares one does not currently own (by borrowing them) and buying them
back later. Here profits are made in a bear or falling market as shares are bought
back at a lower price than when they were sold. For the purpose of this study only
long positions will be considered and not short selling (the MACD strategy in
particular). Long positions are based on the premise that investors actually own the
shares.
The FTSE/JSE Top 40 Index shares are selected for this study for two reasons.
Firstly, the shares are tradable. This means there is a large enough market to buy
and sell shares, that is, there are no supply and demand problems. The bulk of the
value (volume multiplied by price) of shares traded daily on the JSE Ltd consists of
the FTSE/JSE Top 40 Index shares. This implies that the results of this study will be
applicable for a wide range of users: asset managers who manage large portfolios
will be able to apply the MACD or the Buy-and-hold strategy to their trading on the
FTSE/JSE Top 40 Index. The FTSE/JSE Top 40 Index shares have the liquidity to
11
provide buy and sell opportunities. In contrast, small independent investors will be
able to apply the MACD just as well to less liquid shares on the main board of the
JSE Ltd, in other words, listed shares that do not form part of the FTSE/JSE Top 40
Index, as small investors will trade in smaller quantities. The second reason is
closely linked to the first and that is that the market is also active. Shares in the
FTSE/JSE Top 40 Index are actively being traded and are not in a stale market
where shares do not sell.
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1.9 Chapter outline
Table 1.2: Summary of chapters and content
CHAPTER CONTENT
Chapter 1: Orientation and motivation of the study
In the first chapter the study is introduced. The background to the study which resulted in the research problem is explained.
Chapter 2: Literature review
In the second chapter a critical review of the current literature on the research problem is presented.
Chapter 3: Research methodology
The research design and methodology used in the study are explained in the third chapter. The chapter commences with a discussion of the issues of research design and the methods for collecting and measuring the data. Techniques to ensure the validity and reliability of the data are also considered.
Chapter 4: Results and discussion
The results of the study are presented in the fourth chapter. The data is presented and interpreted in various statistical formats like graphs and tables, etc.
Chapter 5: Findings, conclusions and recommendations
Conclusions are drawn on the basis of the results of the study. Limitations and recommendations for further study are also addressed.
Source: Author’s deductions
13
Chapter 2
Literature review
2.1 Introduction
To address the research question of:
Which one of the MACD or the Buy-and-hold strategies on the FTSE/JSE Top 40
Index shares of the JSE Ltd over the period 2001 to 2010 is more effective?
Sub-questions are:
To what extent do transaction cost (i.e. costs incurred when buying and selling
shares) have an effect on the effectiveness of the MACD in comparison with the
Buy-and-hold strategy?
Under what conditions will either the MACD or the Buy-and-hold strategy yield
higher returns?
The literature review will assist to explain and highlight the research problem and the
rationale for the research question.
2.1.1 Background
Figure 2.1: Graphical representation of chapter 2
14
This section (2.1) serves as an overview of how chapter 2 is organised.
Investors can be divided into active or passive investors as discussed in 2.2. Active
investors have a range of options to use in deciding which shares to buy. The first
option is to buy haphazardly; here there is no information that back up the
investment decision. Investors here will buy shares because they simply like a
company or on a whim or advice from others. This method is not considered in this
study at all. In other words, it is assumed that the investor has made the decision on
which shares to buy or sell. The only issue is when to buy or sell.
The next method used to decide which shares to buy is Fundamental Analysis (2.3).
Here investors look at the performance of the company in question considering
issues such as dividends, financial statements, ratios, company growth and news
about the company. Because these indicators do not change on a daily basis it is
also seen as a Buy-and-hold strategy. The main reason for this is that new
information will only be available when the company releases its next set of financial
statements. The next way of deciding which shares to buy is the use of Technical
Analysis (2.4). Here only the share price and volume traded are used in various
ways to make the buy or sell decision. The practice of Technical Analysis is
underpinned by the Dow Theory (see 2.5). In 1897 Charles Dow was the first person
to popularise a form of Technical Analysis based mainly on moving averages.
Technical Analysis considers share price and volume traded to be discussed in 2.6.
This information can be used in various ways (see 2.7). Next, the MACD (2.8) will be
discussed. The MACD uses a combination of charts, moving averages and
momentum indicators. In section 2.9 the argument for and against both Technical
Analysis and Buy-and-hold is discussed.
2.2 Types of investors
Active investors are investors who manage their own investment portfolios and make
their own decisions as to when to buy, sell and hold their specific investments. For
the purpose of this study only active investors will be considered.
Passive investors are investors who invest money over a longer period of time. They
generally hand their funds over to a third party who will make investment decisions
for them. The third party usually uses an active strategy but the individual is blind to
15
it. The most common corporate investors in SA are those who manage pension and
provident funds. The individual merely hands over a certain amount of money each
month to the asset managers of these entities who decide in which investments or
assets to invest. These corporate investors are heavily regulated by law in South
Africa. Another type of passive investment that an individual can use is to buy unit
trusts. In this case the individuals have, to a limited extent, input in their investments.
They can choose the type of unit trust and when they want to sell their unit trust, but
the investment company still ultimately decides which specific shares or other
investments to hold and when to buy and sell.
Private active investors, that is, those who buy and sell individual shares, are the
focus of this study. It focuses on individuals who invest their own money directly in
the share market. They do not invest in the market via investment advisors or
externally-managed investment vehicles.
The study is also focussed on corporate investors, i.e. the institutions or investment
vehicle managers who invest in individual shares on behalf of individuals or
corporate entities. They typically invest other people’s money and normally have
access to large sums of money as compared to private investors. The regulations
are in terms of how secure the investments need to be as well as how balanced they
need to be. Although corporate investors who have to invest in shares can also use
Technical Analysis when they make buy and sell decisions they have an additional
limitation. For example, if the corporate investor, like a provident fund, has a
significant holding in a listed company or wants a significant holding in a listed
company, he cannot merely buy or sell at will as this may artificially drive the price of
the holding up or down. This happens because of the laws of supply and demand
and the fact that some corporate investors have very large sums of money to invest.
2.3 Fundamental Analysis
2.3.1 Definition
Fundamental Analysis is where investors consider a company in detail to make the
decision whether to buy or sell a share. They mainly consider information from
financial statements and the news. Based on this information they assess their
16
version of the company’s worth which is referred to as the intrinsic value of a
company.
Intrinsic value is the actual value of a company based on an underlying perception
of its true value including all aspects of the company, both tangible and
intangible factors. This value may or may not be the same as the current market
value of the company. An investor who bases his/her decisions on the intrinsic value
of a company is referred to as a value investor. Value investors use a variety of
analytical techniques in order to estimate the intrinsic value of shares in the hope of
finding investments where the true value of the investment exceeds its
current market value. For example, value investors who follow Fundamental Analysis
look at both qualitative (news of the company, business model, governance, target
market factors etc.) and quantitative factors, for example ratios, financial statement
analysis of a business, taxes and growth prospects, to see if the business is
currently out of favour with the market and is really worth much more than its current
valuation or vice versa. In Fundamental Analysis theory all shares have what is
referred to as intrinsic value. The intrinsic value will give the investor a price at
which the share will be “cheap” or “expensive”. If the share is then bought at the
price that is considered to be “cheap” it will be held for a long time and short-term
volatility will be ignored. The intrinsic value can be calculated by doing a careful
analysis of the present conditions of a share and also taking into consideration the
future prospects thereof. The Fundamental Analysis theory then holds that if a share
is considered to be “cheap”, the market will, over time, correct itself and trade at the
correct market price. This is how the fundamentalist will make his/her profit. The
main components of Fundamental Analysis theory are company earnings and
dividend payouts. A major drawback of this theory is that predicting future earnings
and dividends becomes an inexact science and, some claim, even guessing. The
theory uses future earnings and payouts, and discounts these to the present value.
The issue here is that if some of the companies on the stock exchanges around the
world are analysed for their performance during booms, there is no correlation
between share prices and market prices (Malkiel, 2003:29). Share price is the listed
active price for the share and market price is the value of the share as valued by an
analyst after considering the factors listed above.
17
2.3.2 Factors determining the intrinsic value of a company
The factors determining the intrinsic value of a company, using Fundamental
Analysis include (Cottle, Murray and Block,1988):
Level of earnings and profitability (this refers to the profitability of one company
in relation to others in the same industry or market);
Dividends paid or the capacity to pay these dividends (actual disbursements to
shareholders or the ability to pay disbursements);
The trend of earnings growth (have the earnings declined, been sustained or
grown over time?) ;
The stability and predictability of the qualitative and quantitative projections
which refer to the information used by an analyst;
The volatility of the share price;
Potential growth of the company; and
The management of the company.
The above-mentioned factors determine the value and a discount rate is then used
to calculate the intrinsic value. The discount rate is taking into account the time value
of money at a required rate of return by the investor.
Fundamental investors are seen as business valuators and not stock market
valuators. This implies that these investors analyse a business and arrive at an
intrinsic value per share. If the value they have calculated is below the current
market value they will buy the share and if the price of the share is above their
calculated market value they will sell. They only use the share price to give them buy
and sell signals but do not use the price information itself to give the signals
(Graham, 2006). In other words, they will use Fundamental Analysis to decide which
shares to buy but, when it comes to actually buying the share they may look only at
share prices to determine the time of purchase.
In Fundamental Analysis, investors look at indicators such as: asset values, return
on assets, profit margins, liquidity, cash flows from operations, book to market ratio
and leverage. These indicators help them decide if they should buy or sell a share.
Because the inputs into these analyses are greatly dependant on information
18
gathered from financial statements they do not change at a rate as fast as daily
share prices change (Piotroski, 2002).
A growth strategy is also a factor that can be used in a value-investment strategy.
From a valuation perspective, value shares are inherently more conducive to
financial statement analysis than growth (i.e. glamour) shares. Growth share
valuations are typically based on long-term forecasts of sales and the resultant cash
flows, with most growth investors heavily relying on non-financial information. And
most of the predictability in growth share returns appears to be momentum driven
(Asness, 1997). Momentum refers to the rate at which share prices change. In
contrast, the valuation of value shares focuses on recent changes in company
fundamentals (e.g., financial leverage, liquidity, profitability and cash flow adequacy).
The assessment of these characteristics is most readily accomplished through a
careful study of historical financial statements.
One approach to separate winners from losers is through the identification of a
company’s intrinsic value. The strategy presented by Frankel and Lee (1998)
requires investors to purchase shares whose prices appear to be lagging
fundamental values. Undervaluation is identified by using analysts’ earnings
forecasts in conjunction with an accounting-based valuation model (e.g., residual
income model) and the strategy is successful at generating significant positive
returns over a three-year investment window.
2.3.3 Fundamental Analysis strategies
Value investors have various systems they use when deciding when and if to invest
in a company. The systems are usually a combination of the indicators mentioned
above set against certain targets set by the investor. This leads to there being many
systems due to the fact that investors can get indicators from various aspects in the
financial statement data. Because of the cycles of available data being relatively far
apart and not that variable from year to year, these fundamental strategies are
referred to as Buy-and-hold strategies (Piotroski, 2002).
19
2.4 Technical Analysis
2.4.1 Definition
In contrast to Fundamental Analysis, Technical Analysis can also be adopted as an
investment strategy. The share price history is used to predict the future movements
of a share price. In Technical Analysis it is believed that all information required
about a share is reflected in its price. Phil Roth, Chief Technical market analyst of
Miller, Tabak & Co. LLC made the comment that, “The biggest mistake that a
fundamental analyst makes is thinking that a stock and a company are the same
thing. The biggest mistake a technician makes is thinking that a stock and a
company are different.” This implies that if investors only use one of either
Fundamental or Technical Analysis they run the risk of missing important information
about the shares they are investing in.
There are various Technical Analysis methods and indicators. Technical Analysis is
an attempt to exploit recurring and predictable patterns in share prices to estimate or
determine abnormal trading profits. Abnormal profits are profits that are above
average returns obtained in the share market.
Technical Analysis is based on human behaviour, but it is not a study in psychology.
This implies that when a share price changes, i.e. increases or decreases the
behaviour of the majority of investors can be predicted. If investors react the same
way to the same types of events again and again, it is reflected in the ebb and flow
of the share price. If one charts this activity over time, patterns in price action
emerge. Some of these patterns comprise of standard Technical Analysis, while
others emerge based on the investor’s observations and calculations. Historical data
is required to test theories and fine-tune parameter decisions (Khan, 2006).
The market often reacts in the same way after certain events. For example, if prices
are rising and then start to trade in a small range (a small range is when the lowest
and highest prices do not vary much from each other for a period of time), the
characteristics (shape and size) of the range can be used to determine how far the
market will move once the pattern is ended. This is not just a guess, but a highly
likely condition (reaction by humans) based on thousands of similar occurrences in
20
the past. The more historical data the investor has available, the more likely it is that
the investor will make a correct buy or sell decision.
An advantage of using historical data in making these decisions is that it gives the
trader perspective. A sharp price increase in one share in a day may be seen as a
bullish sign until it is viewed as part of the longer history of price movements.
A criticism against Technical Analysis is that it may be regarded as a self-fulfilling
prophecy. If, for example, a technical indicator gives a signal that a share price is
about to rise, technical investors may all buy this share resulting in a rise in price
(based on supply and demand). Another criticism is that past performance cannot
predict the future. The “random walk” theory of markets proposes that price
fluctuations are random and therefore nothing can predict them (Malkiel, 2003). In
contrast, technical analysts argue that prices are not random.
Mark Twain said that, “History does not repeat itself. But it does rhyme.” (Eayrs,
1971). No matter how much today’s market may look like a previous market, one
cannot be a hundred percent sure that it will continue to react in the same way. With
so many variables that can affect the market, the difference between having 80%
and 90% of shares reacting similarly probably does not matter to a bottom-line
decision of buy, sell or hold. It might affect the course or amount of the rally, but not
the decision to buy or sell.
2.4.2 Underlying assumptions of Technical Analysis
In order to achieve profits above the market average, technicians (technical analysts)
or “chartists” as they are referred to, make a number of assumptions according to
Marx, et al. (2006):
Market value (share price times shares issued) is determined solely by supply
and demand;
Supply and demand are governed by numerous factors both rational and
irrational. However, the market continually and automatically weighs all these
factors and their value is reflected in the share price;
Disregarding minor fluctuations in the market, share prices tend to move in
trends which persist for a certain length of time; and
21
Changes in trends are caused by shifts in supply and demand. These shifts
will be detected in the action of the market at some time, irrespective of why
they occur.
2.5 Dow Theory
2.5.1 Introduction
Technical Analysis strategies have their root in the Dow Theory. In 1897, Charles
Dow developed two broad market averages: the “Industrial Average” that included 12
blue-chip shares and the “Rail Average” comprising of 20 railroad companies. These
are now known as the Dow Jones Industrial Average and the Dow Jones
Transportation Average. The Dow Theory resulted from a series of articles published
by Charles Dow in The Wall Street journal between 1900 and 1902. As noted before,
the Dow Theory is the common ancestor of most principles of modern Technical
Analysis (Achelis, 2000).
The theory itself originally focused on using general stock market trends as a
barometer for general business conditions. It was not originally intended to forecast
share prices. However, subsequent work has focused almost exclusively on this use
of the theory. Underlying the theory, six assumptions are made:
2.5.2 Six assumptions of the Dow Theory
2.5.2.1 The averages discount everything
The price of an individual share reflects everything that is known about the share. As
new information arrives, market participants quickly disseminate the information and
the price adjusts accordingly.
2.5.2.2 The market is made up of three trends
At any given time in the stock market, three forces are in effect: the primary trend,
secondary trends and minor trends. The primary trend may either be a bullish (rising)
market or a bearish (falling) market. The primary trend usually lasts more than a year
but may also last several years.
22
Secondary trends are intermediate, corrective reactions to the primary trend. These
reactions typically last from one to three months. Secondary trends therefore
typically comprise of a number of minor trends within the primary trend.
Minor trends are short-term movements typically lasting from one day to three
weeks. The Dow Theory holds that since share prices over the short-term are
subject to some degree of manipulation (primary and secondary trends are not),
minor trends are unimportant and can even be misleading. This is one of the reasons
why moving averages are used to flatten out the minor fluctuations.
2.5.2.3 Primary trends have three phases
The first phase of the Dow Theory is that it is made up of aggressive buying by
informed investors (large corporates) in anticipation of economic recovery and long-
term growth. The general feeling during this phase is one of “gloom and doom” and
“disgust”. Informed investors, realising that a turnaround is inevitable, aggressively
buy from these distressed sellers. This is also known as accumulation.
The second phase is characterised by increased corporate earnings and improved
economic conditions. Investors will begin to accumulate shares as conditions
improve. This phase is also known as expansion.
The third phase is characterised by record corporate earnings and peak economic
conditions. The general public (individual investors) now feels comfortable
participating in the stock market, fully convinced that the stock market is headed for
the moon. They now buy even more shares, creating a buying frenzy. It is during this
phase that those few investors who did the aggressive buying during the first phase
begin to liquidate their holding in anticipation of a downturn. This phase is also
known as distribution (Achelis, 2000).
2.5.2.4 The averages must confirm each other
Major trends and their sub-trends must confirm each other. For example the original
Dow had an index for Industrials and a sub-set for Transports that formed part of
Industrials. The Industrials and Transports must confirm each other in order for a
valid change of trend to occur. Both averages must extend beyond their previous
secondary peak (or trough) in order for a change in trend to be confirmed. In other
23
words, if the Transport index was rising and the Industrials falling, they would not be
confirming each other.
2.5.2.5 The volume confirms the trend
The Dow Theory focuses primarily on price action. Volume is only used to confirm
uncertain situations. Volume should expand in the direction of the primary trend. If
the primary trend is down, volume should decrease as the market declines. If the
primary trend is up, volume should increase as the market advances.
2.5.2.6 A trend remains intact until it gives a definite reversal signal
An up-trend is defined by a series of higher highs and higher lows. In other words:
even with some variability it is obvious that the market goes higher and higher or
lower and lower. In order for an up-trend to reverse, prices must have at least one
lower high and one lower low (the reverse is true of a down trend). When a reversal
in the primary trend is signalled by both the Industrials and Transports, the odds of
the new trend continuing are high. However, the longer a trend continues, the odds
of the trend remaining intact become progressively smaller (Achelis, 2000).
2.6 Components of Technical Analysis
All Technical Analysis is performed using the following input gathered at any time
interval required by the investor. (Although the period interval can range from
minutes, hours, days up to years, the period in this study will be a day, i.e. t is
measured in days). In this study the following will be obtained on a daily basis:
Time: date/time;
Price: Opening price for the period(t)
Closing price for the period(t)
Highest price within the period(t)
Lowest price within the period(t); and
Volume: shares traded within the period(t).
Of these variables, price is the most important. Investors measure profits and losses
in price differences between buys and sells. Volume includes such concepts as
accumulation and distribution, market breadth and trade count. Time (date) includes
24
cycles, seasonality and relationships between patterns and trends from a duration
point of view (Graham, 2006).
What a company earns has a direct impact on its share value. Technical Analysis
does not consider earnings, financial statements and news directly. Rather, it
assumes that all that information (both tangible and intangible) is contained in the
current share price. Another way of looking at it is that price is the sum total to date
of actions of everyone participating in the share market.
2.7 Technical Analysis strategies
There are various strategies or methods to use when applying Technical Analysis.
2.7.1 Chart patterns
Charts are the simplest but considered to be the most objective way of looking at
share prices by considering the actual graphs to identify certain pre-determined
shapes in the graphs (Covel, 2006). In other words, charts are a purely visual tool to
evaluate a share by the investor. Depending on identified shapes (according to the
instinct and beliefs of the investor) investors make estimates as to the direction the
market will take. Some of these shapes include support and resistance lines,
“rectangles”, “triangles”, “flags”, etc. Identifying and using these shapes in Technical
Analysis is not covered in this study. While many technical trading rules are based
on patterns in share prices, there is a lack of convincing explanations of how and
why these patterns arise, and why trading rules based on Technical Analysis are
profitable.
In a study by Friesen, Weller & Dunham (2008), a model was provided that tried to
explain the success of certain trading rules that are based on patterns in past prices.
They indicated that confirmation (decisions confirmed by technical information) bias
was very important in predicting future trends. It has been shown to play a key role
also in other types of decision making, for example traders who acquire information
and trade on the basis that information tends to bias their interpretation of
subsequent information in the direction of their original view. This produces auto-
correlations and patterns of price movement that can predict future prices, such as
the ‘‘head-and-shoulders” and ‘‘double-top” patterns. ‘‘Head-and-shoulders” and
‘‘double-top” are terms given to certain patterns that reveal themselves to analysts
25
using charts. The model also predicted that sequential price jumps for a particular
share will be positively auto-correlated. In their study they found that jumps exhibit
statistically and economically significant positive auto-correlations.
2.7.1.1 Chart types
There are basically three types of charts used in Technical Analysis. The first is line
charts: this is the simplest chart and is just a continuous line connecting the closing
price of each day as shown in Figure 2.2. This is the type of chart used in this study.
The other two types of charts are bar charts and volume charts. Bar charts show the
opening price, the closing price, the high for the day and the low for the day (Busetti,
2009). Volume charts show the volume sold for the day as a bar chart (seen in
Figure 2.3).
Figure 2.2: Line chart example
Source: Line chart of sample data for Sasol for the period June 2010 to May 2011
obtained using ShareMagic PRO software (version 8.9.0, 2011)
26
Figure 2.3: Bar and volume charts example
Source: Bar and volume chart of sample data for Standard Bank for the period
December 2010 to May 2011 obtained using ShareMagic PRO software (version
8.9.0, 2011)
2.7.2 Trends
Technical analysts use trends in share prices to assess the general direction of price
movements. In this type of analysis, a simple trend line is imposed on top of the
closing price data to get an idea of the price direction. This line can be a simple
straight line or a line based on moving averages. Although this type of analysis is not
considered in this study, the MACD (to be discussed in 2.8) is based on various
moving averages (Covel, 2006). The issue of moving averages is henceforth
discussed.
2.7.2.1 Moving averages
In share price analysis it is common to use moving averages to predict price
movements. However, the nature of share price movements is that they are volatile
due to the fact that there are many different factors that have an effect on share
prices. Moving averages help to smooth out volatility to a certain degree depending
on the duration of days (k) used in the calculation of the moving average. Moving
averages are the average of share prices for a certain period (t – k) recalculated on a
daily basis (t) and for the same historical length in days (k). This smoothed-out
27
version of the share price history provides a better indication of the longer-term
direction of the share price movement (Albright, et al., 2009).
There are different ways of using moving averages in Technical Analysis. They can
be used on their own or in other indicators such as the MACD. One way of
determining the longer-term direction of a share price is to use Technical Analysis.
One indicator commonly used by technical analysts is the Moving Average
Convergence Divergence (MACD). In effect this technique uses two moving
averages of a price history, one over a shorter period and the other over a longer
period. The operation on this indicator is as follows: when the shorter-term moving
average moves above the longer-term moving average it is a “buy” signal. When the
shorter-term moving average moves below the longer-term average it is a “sell”
signal. The rationale and details of the MACD will be discussed in 2.8.
Other short-term strategies based on moving averages employed by Technical
Analysis investors are to use strategies involving constant buying and selling of
shares. The main aim of these strategies is to attempt to use the short-term volatility
to predict the short-term future price movements (Covel, 2006).
Other technical strategies based on the moving average principle commonly used by
investors include the Directional Movement Index (DMI), moving averages on their
own, the Average Directional Index (ADX), Stochastics, the Relative Strength Index
(RSI) and candle sticks. One of these strategies is the MACD. However, there is
conflicting evidence in the literature regarding the effectiveness of using technical
trading strategies. Whereas some researchers have found these to outperform the
simple Buy-and-hold strategy, others have found these strategies to be less effective
than the Buy-and-hold strategy.
2.7.3 Volume
Some technical analysts use volume to get an indication of market activity. Volume is
normally used separately from other technical analyses. A trader would use the
volume charts in combination with other graphs to confirm that the market (supply
and demand) actually supports the price information. For example, a good buy signal
will not be useful if there is not a supply of shares available to buy.
28
2.7.4 Technical indicators
Technical analysts also employ “technical indicators” as tools to give more exact
information about a share price. Here the information gathered is put into formulae
and the answers to these are used by the analysts to make a decision to buy or sell.
The following technical indicators will be described next: momentum and market
indicators as often used by technical analysts:
2.7.4.1 Momentum
Price momentum indicators measure the speed and force of the trend of the market.
The theory is that markets in motion tend to stay in motion and markets at rest tend
to stay at rest unless acted upon by an external force. The following indicators can
be used i.e. the MACD indicator (to be discussed in 2.8) and the Absolute Breadth
Index (ABI) as another momentum indicator. The ABI indicates how much activity,
volatility and change are taking place in an exchange while ignoring where the
direction prices are headed (Covel, 2006).
2.7.4.2 Market indicators
Market indicators help the investor to gauge changes in all securities within a specific
market. Market indicators are also used to analyse the local share market or
international markets.
The Relative Strength Index (RSI) is a popular market indicator referred to as an
oscillator. Oscillators are non-trending indicators i.e. the RSI is a price-following
oscillator that ranges from 0 to 100.
A popular way to analyse the RSI is to identify divergence in which the share is
reaching a new high and is failing to surpass its previous high. In a study done by
Newsome and Turner (2007) they examined the monthly returns of exchange traded
funds (ETFs) during the period of January 1999 to December 2005 to determine
whether employing a momentum/oscillator-based trading strategy (relative strength
index) could yield comparable returns to that of other investment strategies. The
sectors used were energy, healthcare, financials and technology. There was no
statistical difference in mean returns for either of the four sector ETFs and the hedge
fund indices. However, there was substantial economic difference in the hedge fund
29
index returns and those of the ETFs using the relative strength index (RSI) which
was higher.
Based on the RSI strategies, investors would not be able to replicate hedge fund
returns. A very popular non-trending indicator is Stochastics, which calculates the
position of the current time’s (t) closing price relative to a range established over a
time period specified by the user (Covel, 2006). The higher the close today relative
to the range, the more overbought the share. An overbought share is expected to
revert to its mean.
An article by Hwa (2007b) showed the importance of having a clear timing strategy
when trading in the stock market. Stochastics was found to be a powerful indicator to
identify bullish and bearish divergences (signals that warn of an impending trend
reversal). However, a different indicator or trend line analysis could increase the
reliability of divergence signals.
Another popular oscillator is the Average Directional Index (ADX) which measures
the strength of a trend rather than its direction. The higher the ADX, the stronger the
current trend of a share.
2.7.4.3 Other technical methods
There are also some other ways to use Technical Analysis. The Japanese have
developed what is known as “candle stick charts” that are a variation of the OHLC
charts (open, high, low and close). This type of chart is still popular in Japan. The
charts have patterns with names like “pregnant lady”, “hammer” and “hanging man”.
These patterns have the same type of interpretations as other chart patterns (Hwa,
2007a). There are also line studies where the technicians use Fibonacci
retracements to predict price movements. The Fibonacci retracement indicator is
used in an attempt to forecast potential support levels and price targets based on the
height of the overall move and any wave patterns (Elliott, 1997).
2.8 The MACD
2.8.1 Introduction
The MACD indicator was created by Gerald Appel in 1979 and is one of the most
popular indicators used in Technical Analysis. The MACD uses three exponential
30
moving averages (EMA), which are lagging indicators (i.e. considering previous
periods), to identify the continuation or reversal of a trend. As its name implies, the
MACD is all about the convergence and divergence of two moving averages (a slow
moving average calculated over a longer period of time and a fast moving average
calculated over a shorter period of time). Convergence occurs when the moving
averages move towards each other. Divergence occurs when the moving averages
move away from each other. Unlike other technical indicators the MACD has been
around for a long time and is widely used. It is easy to construct and understand.
2.8.2 Working of the MACD’s signal
The first part of the MACD’s signal is created by subtracting the slow-moving
average from the fast-moving average. In a standard setting the periods are 12 days
(for the fast indicator) and 26 days (for the longer indicator) for generating the first
indicator (the MACD). The 12 day and 26 day averages are used most often as they
give the best results in general, but the periods (12 or 26) can be changed per share
to give better custom-fitted results (Appel, 2003).
MACD = EMA (12-day closing prices) – EMA (26-day closing prices)
The second part of the indicator, called the signal line, is an EMA to smooth the first
part of the indicator as shown above. The standard setting for a signal line is 9 days.
The signal line is used to confirm the MACD crossovers.
Signal = EMA (9-day MACD)
The formula for the EMA is as follows:
( ) ( )
( )
( ) ( ) ( )
Where cpt is the closing price on day t and
( )
Where N is the number of days (9 for 9 day EMA)
Using the EMAs gives the most recent price information more weight than the older
data when calculating the moving averages. The weighted principle is more useful
2.1
2.2
2.3
31
than regular moving averages as the market will also give more weight to recent
information. The moving averages also smooth out the price movements. In other
words, they reduce the volatility. Because of the way it is calculated, the EMA will
follow the price movement more accurately than a simple moving average (SMA)
(Covel, 2006).
A buy signal is generated when the more volatile indicator (MACD) moves above the
less volatile one (signal). On the other hand, a sell signal is given when the MACD
indicator moves below the signal indicator.
The MACD oscillates above and below the zero line (the zero line is where the
MACD = 0, i.e. EMA(12) = EMA(26)), known as the centre line. These crossovers
signal that the 12-day EMA has crossed the 26-day EMA, either in a positive or
negative direction. A positive MACD indicates that the 12-day EMA is above the 26-
day EMA. Positive values increase as the shorter EMA diverges further from the
longer EMA. This means upside momentum is increasing. A negative MACD
indicates that the 12-day EMA is below the 26-day EMA. Negative values increase
as the shorter EMA diverges further below the longer EMA. This means downside
momentum is increasing.
Centre line crossovers can last a few days or a few months. It all depends on the
strength of the trend. The MACD will remain positive as long as there is a sustained
uptrend. The MACD will remain negative when there is a sustained downtrend as
can be seen in Figure 2.4.
32
Figure 2.4: MACD Chart
Source: Graphical presentation of sample data generated using ShareMagic PRO
software (version 8.9.0, 2011)
From Figure 2.4, it is clear that there was a buy signal in mid-September 2010 and a
sell signal again in late November 2010. These signals are created every time the
solid line at the bottom crosses the zero line.
Due to the lagging feature of the MACD indicator, any buy or sell signals will be
generated shortly after the lowest share price value or the highest value. Standard
MACD works well when there are clear upward and downward trends in price
movement. However, in a sideways market with no clear upward or downward trends
MACD crossovers may lead to false signals.
2.8.3 False signals
Like any indicator, the MACD can generate false signals. A false positive, for
example, would be a bullish crossover followed by a sudden decline in a share. A
false negative would be a situation where there was no bullish crossover, yet the
share suddenly accelerated upwards.
Analysts use a variety of approaches to filter out false signals and confirm true ones.
As a lagging indicator, the MACD is often paired with a leading indicator, like the
Buy SellBuy Zero line
33
Relative Strength Index (RSI). Historical comparisons to similar shares as well as a
careful investigation of past price movements provide added information about how a
share tends to move.
2.8.4 Variations
As indicated above there are periods (12, 26 and 9) for the MACD. The reason for
this is that Appel tested various scenarios and found these periods to be most
effective at the time. Studies have been conducted to test the effectiveness of the
MACD when these settings are changed. Chong, Li & Yu (2009) tested the MACD
on the US, Japan, Germany and Hong Kong markets. They used 9-day and 14-day
signal lines as well as a zero-line crossing. For the zero-line crossing the two EMAs
were used and signals were created where they crossed each other. They found that
the MACD worked well in Germany and Hong Kong. The Hong Kong markets
returned double digits for all three trading rules. The zero-line crossing worked the
best in Germany, US and the UK. The 9-day signal worked the best in Japan and the
14-day signal worked the best in Hong Kong. The same study also showed that
markets have become more efficient over time as the profit margins for these
strategies have slowed down in recent times. To illustrate the MACD, an example is
provided in 2.8.5.
2.8.5 Example calculations of the MACD
Table 2.1 shows a grouping of data for Anglo Gold Limited on the JSE Ltd from 16
April 1996 to 18 July 1996. The share and period are used for illustrative purposes
only. The 12 day and 26 day EMAs are calculated using the formulae above. The 9-
day signal line is calculated and the results are plotted in figure 2.5.
Source: JSE Ltd Data obtained from Profile Media using ShareMagic Pro
Figure 2.5: Graphical representation of data from Table 2.1
Source: Sample data obtained using ShareMagic PRO software (version 8.9.0,
2011)
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
26/0
4/19
96
03/0
5/19
96
10/0
5/19
96
17/0
5/19
96
24/0
5/19
96
31/0
5/19
96
07/0
6/19
96
14/0
6/19
96
21/0
6/19
96
28/0
6/19
96
05/0
7/19
96
12/0
7/19
96
MACD
Signal
Cross over 1
Cross over 2
divergence
convergence
36
2.8.6 Transaction cost in Technical Analysis
One of the main challenges of using any technical trading system is transaction cost.
In very volatile markets these systems can create many buy and sell signals. All
these transactions will generate a substantial cost which in turn will undermine the
profits possible. In South Africa transaction cost can typically vary from 0.4% to
0.7%. This study will investigate the effect of transaction cost as well.
The MACD has some standard settings. But each share has its own behaviour, so
altering the settings based on a per share basis could possibly improve one’s results.
This study will only test the default settings of the MACD (Covel, 2006).
2.9 The Fundamental / Technical Analysis debate
As indicated in Chapter 1, the research problem centres around the debate of whether Technical Analysis is more effective or less effective than Fundamental Analysis.
Anti–Technical Analysis
Some investment specialists claim that Technical Analysis ignores the nature of
companies, their products, markets, financial structure, risks and their sensitivity to
economic, industry and stock market trends and that it is only popular because it
appears easy. It is said that if this worked everyone would be using it and if everyone
used it, it would stop working because of the regularities eliminated by everyone
using it (Busetti, 2009).
Pro–Technical Analysis
Technical Analysis is accepted as a viable analytical approach by most universities
and brokerage firms. Very few large investments are made without reviewing the
technical information. But even with its acceptance, very few people actually perform
Technical Analysis (Marx, et al., 2006).
Fundamental vs. Technical
Neely, Rapach, Tu & Zhou (2010) compared the ability of economic fundamentals
and technical trading rules to forecast the monthly U.S. equity premium for 1960–
37
2008. Both approaches provided statistically and economically significant forecasting
gains. They concluded that fundamental and Technical Analysis capture different
sources of equity premium fluctuations and the two approaches appear largely
complementary.
2.10 Chapter summary
In the literature consulted there appears to be contradicting conclusions on the
effectiveness of using a Technical Analysis investment approach versus the Buy-
and-hold approach. This study aims to provide a South African perspective for the
ten years under review, using the MACD approach in Technical Analysis.
38
CHAPTER 3
Research methodology
3.1 Introduction
In this chapter, the research methodology to be used in this study is described in
terms of the research problem.
Active share investors need to decide what strategy they should use to arrive at a
decision of when to buy and when to sell the shares they have decided to invest in.
Should they follow the Fundamental Analysis route by considering the financial
statements of a company or should they consider the actual share price movement
or should they use a combination of the two strategies?
3.2 Research question and objectives
In order to address the research problem the following research question is posed:
What is the effectiveness of a Technical Analysis strategy versus a fundamental
strategy?
In particular, what is the effectiveness of a specific Fundamental Analysis strategy,
namely the Buy-and-hold strategy and a specific technical strategy, namely the
Moving Average Convergence Divergence (MACD) Indicator on the FTSE/JSE Top
40 Index shares of the JSE Ltd over a ten-year period (2001 to 2010).
In order to address the research question, the following objectives are stated:
a) For each share, determine the return on the Buy-and-hold strategy and the
MACD per year and over a ten-year period (achieved in 3.8.4).
b) For each share determine the administrative costs on the Buy-and-hold
strategy per year and over a ten-year period (achieved in 3.8.3.1).
39
c) For each share determine the net return on the Buy-and-hold and the MACD
strategy per year and over a ten-year period (achieved in 3.8.4).
d) For each share determine the administrative costs on the MACD strategy per
year and over a ten-year period (achieved in 3.8.3.3).
e) For each share compare the effectiveness of the two strategies in terms of
administration cost (achieved in 3.8.4).
f) Compare the overall effectiveness of the two strategies in terms of
administrative costs (achieved in 3.8.4).
g) Calculate the magnitude of the differences in the means to observe if the
differences are statistically significant (achieved in 3.8.5).
3.3 Scope of the research study
Only shares in the FTSE/JSE Top 40 Index with a ten-year history will be considered
in the study to ensure comparability of results for all shares over the whole ten years.
A list of the FTSE/JSE Top 40 Index as at 1 January 2011 will be obtained directly
from the JSE Ltd. The FTSE/JSE Top 40 Index on the JSE Ltd actually consists of
42 shares. The JSE Ltd rebalances the index from time to time and that results in
there sometimes being either more than 40 shares or at other times fewer than 40
shares in the index. The FTSE/JSE Top 40 Index is rebalanced every quarter by the
JSE Ltd in order to ensure that the shares of the index are representative of the
whole market. For this study the index was considered as at 31 December 2010.
Thirty two (32) shares satisfied all the conditions. More information on the scope can
be obtained from 1.5.
3.4 Research design and strategy
The nature of the research question, namely a comparison of the effectiveness of the
two different strategies by analysing share prices, requires a quantitative research
strategy as it is considered to be the most appropriate. A quantitative research
strategy is aimed at numerical data or data that could usefully be quantified to help
answer the research question and to meet stated objectives (Saunders, et al., 2009).
Within the quantitative research paradigm, the strategy to be followed in this
research study is the statistical analysis of secondary data.
The advantages of utilising secondary data are (Saunders, et al., 2009):
40
It has fewer resource requirements. Using secondary data saves time and
money if the data is readily available;
It is an unobtrusive way of obtaining data;
Longitudinal studies are possible;
It can provide comparative data;
The accuracy of the data can be verified by others; and
If the data is obtained from a reputable source, it can be considered reliable.
The disadvantages are:
The data may not match the exact needs of the researcher to address the
research question;
Access may be difficult or may be obtained at a price; and
There is no control over the reliability of the data.
In this study the data was obtained from the JSE Ltd via Profile Data and the data
can thus be considered to be reliable since it is the source used by share investors in
South Africa. The data furthermore meets the requirements of the researcher.
The data is readily available and is downloaded at a minimal fee. Secondary data to
be utilised in this study are daily share prices over the period of ten years.
The study will be longitudinal, evaluating the results of the two strategies over ten
years. Because of the availability of the underlying data over the ten-year period, this
type of study is possible.
The research is deductive in nature since the relationship between the two
investment strategies is investigated and evaluated. In other words, the most
effective strategy is used to compare the two strategies.
3.5 Sampling strategy
The list of shares on the FTSE/JSE Top 40 Index will be inspected and only the
shares with an available 10 year history will be used, i.e. from 1 January 2001 to 31
December 2010. There are 32 shares on the FTSE/JSE Top 40 Index that satisfy the
criteria and these will be used for this study. The shares that meet this requirement
are tabulated in Chapter 1, Table 1.1.
41
3.6 Data collection method
The closing price data for the FTSE/JSE Top 40 Index shares to be analysed will be
downloaded from the JSE Ltd via a software package: ShareMagic PRO software
(version 8.9.0, 2011). ShareMagic Pro accumulates all listed company information
including Annual Financial Statements and all share information and distributes it on
demand to its subscribers. The data is in no way protected and is accessible to the
general public.
3.7 Data to be collected
The data will be downloaded from Profile Media using the ShareMagic PRO software
(version 8.9.0, 2011) and analysed using Microsoft Excel 2007. Profile Media is a
registered JSE Ltd user and obtains its data directly from the JSE Ltd. Other
registered JSE Ltd users use the data from Profile Media, both in electronic form and
in their various publications. The JSE Ltd therefore verifies that the data is correct.
For each share the following data will be extracted for each day the market was
open:
the date;
the opening price;
the closing price;
the highest price for the day;
the lowest price for the day;
the volume of shares traded; and
dividends, if any paid.
For this study only the date, closing price and dividend information will be used. This
should yield approximately (120 months x 22 working days per month) 2640 data
points per share.
3.8 Data analysis
The EMA (exponential moving averages) and the signal line (see 2.8) will be
determined using the formula capabilities of Excel. The data will be analysed on an
annual basis for each individual year from 2001 to 2010. The data will be analysed
for the Buy-and-hold strategy where the shares are bought on the first trading day
(BH0), and for the Buy-and-hold straregy where shares are bought on the first MACD
42
signal (BH1), then finally for the MACD strategy. Transaction cost will be calculated
for each of 0, 0.4%, 0.5%, 0.6% and 0.7%. These trancation costs are consistent
with the range of transaction cost charged by stock brokers to individual clients in
South Africa.
Different levels of data analyses will be applied in various stages. The different levels
of data analysis are summarised below. The section where these levels of analysis is
conducted is shown in brackets.
1. Applying signals to the data: moving averages will be calculated and will be
determined as explained in section 2.8, according to the buy and sell signals
for the MACD strategy (3.8.1).
2. Dividend addition data analysis: this level of analysis adds the dividend
payout data to ensure that the dividends are added to the value of the
investments if at that point in time any shares are owned (3.8.2).
3. Transaction history: the first two levels of analysis provide the buy and sell
signals for the MACD strategy as well as the dividend pay outs. In the
transaction history step the initial investment amount is subtracted from the
share value calculated in 1 and 2 for each of the three different strategies:
Buy-and-hold from day 1 (BH0), Buy-and-hold from the first MACD signal
(BH1) and the MACD strategy (3.8.3).
4. Control sheet: the next step of analysis is to accumulate all the results per
level of transaction cost and per year (3.8.4).
5. t-tests performed on investment methods: the last level of analysis is to test if
the different investment methods have significantly different means (3.8.5). In
addition, the correlations between each pair of the BH0, BH1 and MACD will
be determined.
3.8.1 Applying signals to the data
Calculations related to 1, 2 and 3 are illustrated below.
Applying signals to the data is done as follows:
Table 3.1: Sample of applying signals to the data per share
Date Close EMA (12-day) EMA (26-day) MACD Signal B/S Tx
Table 3.6 is a sample of data used in the example control sheet.
Share name: the share code for the share being analysed.
Transaction cost: this is the variable used for the transaction cost (0, 0.4, 0.5,
0.6 and 0.7%).
Initial capital: this is the initial amount used as a starting point. For most
stockbrokers there is a fixed transaction cost for smaller amounts invested,
only once one goes above on average R20 000, is the sliding scale used. To
be safe in this study, R100 000 was used. The results in the spreadsheets
were tested for higher amounts as well and the results as far as rankings and
percentage profits were exactly the same as for R100 000. This amount was
chosen for easy reference and to ensure that fixed transaction cost does not
play a role.
End value: this is the value of the investment after the period using the
selected strategy. Thus the initial R100 000 will now be worth this amount
after a year or ten years of applying a selected strategy. It is important to note
that for each year from 2001 until 2010 these strategies are applied with a
fresh R 100 000 at the beginning of the period. For the ten-year analysis the
R 100 000 will only be applied once.
% Change: this is the percentage change of the investment from the
beginning of the investment.
Rank: this ranks the different strategies per period (line) across the strategies
(BH0, BH1 and MACD).
The result set per variable set (change in transaction cost) will then be saved on a
combined sheet until all the variables (different transaction cost, shares, periods and
strategies) have been used. All these result sets for each of the 32 shares will then
be transferred to a new workbook and analysed per year as well as for the ten-year
period in total.
The result sets per year can be found in Appendix 1 to 5 and are constructed as
seen in Table 3.7.
52
Table 3.7: Sample of result set per year
Source: JSE Ltd Data obtained from Profile Media using ShareMagic Pro
Table 3.7 is a sample of data that shows an extract of the data as created per year for a specific level of transaction cost. The headings are the same as for table 3.6.
Table 4.12: Results for the whole ten years at 0% transaction cost
2001 to 2010 with 0% transaction cost
BH0 BH1 MACD
AVG End value
AVG % Change/Y
AVG Rank AVG End value
AVG % Change/Y
AVG Rank AVG End value
AVG % Change/Y
AVG Rank
10 Yrs 761 102.01 17.75% 1.75 719 902.89 17.24% 2.5 1 311 955.14 23.73% 1.75 Source: Research data
70
In Table 4.11 and 4.12 each of the 32 shares was assessed for each year (2001 to 2010) and for the ten-year period at a 0% transaction cost. For each share a value was obtained for the value of the investment at period end, the percentage change of the investment for each share and what the ranking of the method was (did each share rank 1, 2 or 3rd for BH0, BH1 or MACD). Next the averages were calculated per level of transaction cost and investment strategy (BH0, BH1 and MACD). In the tables these are represented by AVG End Value, AVG % change and AVG Rank.
Figure 4.1: Ranking for each year of the ten-year period at 0% transaction cost
per investment strategy
Source: Research data
Table 4.13: Ranking number per year at 0% transaction cost
Source: Research data
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Ran
k
BH0
BH1
MACD
BH0 BH1 MACD
Times first 150 89 81 Times second 142 127 52 Times third 28 104 187
71
Table 4.13 shows the annual results in ranking for the three investment methods at a 0% transaction cost level. Each column and row adds up to 320 (32 shares x 10 years).
Table 4.14: Ranking percentage per year at 0% transaction cost
Source: Research data
Table 4.14 shows the annual results in percentage for the three investment methods at a 0% transaction cost level.
Table 4.15: t-Test results for 0% transaction cost (p-values)
BH0 vs BH1 BH0 vs MACD BH1 vs MACD
2001 with 0% transaction cost 5.79E-04 5.99E-02 1.47E-01
2002 with 0% transaction cost 5.70E-06 2.45E-13 6.19E-14
2003 with 0% transaction cost 4.85E-13 1.65E-11 4.25E-09
2004 with 0% transaction cost 2.23E-06 2.72E-10 1.10E-10
2005 with 0% transaction cost 5.84E-08 3.49E-11 4.02E-13
2006 with 0% transaction cost 4.78E-17 1.24E-04 5.80E-07
2007 with 0% transaction cost 3.40E-09 6.75E-02 2.53E-01
2008 with 0% transaction cost 1.76E-11 2.06E-02 4.91E-01
2009 with 0% transaction cost 4.54E-01 9.35E-03 1.14E-01
2010 with 0% transaction cost 7.06E-01 2.04E-02 1.67E-02
Ten years with 0% transaction cost 2.15E-04 1.13E-02 6.40E-03
Table 4.15 displays the results of the T-tests done for the results between the different investment strategies for 0% transactions costs. The shaded cells in the table indicate instances where the means of the different strategies were not significantly different. The next set of results shows the effect of those cases.
BH0 BH1 MACD
% First 46.9% 27.8% 25.3% % Second 44.4% 39.7% 16.3% % Third 8.8% 32.5% 58.4%
72
Table 4.16: Eta-squared results for 0% transaction cost
BH0 vs BH1 BH0 vs MACD BH1 vs MACD
2001 with 0% transaction cost 0.003 0.034 0.018
2002 with 0% transaction cost 0.004 0.446 0.483
2003 with 0% transaction cost 0.074 0.505 0.377
2004 with 0% transaction cost 0.005 0.350 0.383
2005 with 0% transaction cost 0.031 0.532 0.653
2006 with 0% transaction cost 0.016 0.137 0.244
2007 with 0% transaction cost 0.004
2008 with 0% transaction cost 0.133 0.105
2009 with 0% transaction cost 0.043
2010 with 0% transaction cost 0.032 0.034
Ten years with 0% transaction cost 0.001 0.065 0.076
If the p-value in the t-test is less than 0.05 then there is a statistical significant
difference between the means of the two investment strategies. If the effect size
(eta2) falls above 0.14 then there is a large practical difference as well. There are
nine cases where eta2 is larger than 0.14 for 0% transaction cost.
Figure 4.2: Graphical representation of eta2 for 0% transaction cost
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Eta
2 v
alu
es
Moderate effect Small effect
Large effect
73
0.4% Transaction cost
Table 4.17: Results for the ten years separately at 0.4% transaction cost
