Tryphena Ow -Thesis

1

Tryphena Ow, An Examination of the Market Timing Ability of Mutual Funds using

Quarterly Trades

ACKNOWLEDGEMENTS

The journey to complete my thesis was both trying and fulfilling, I would not have

made it this far without the love and support from my family, lecturers and friends.

First and foremost, I would like to express my immense gratitude to my supervisor,

Professor Dominic Gasbarro. His tireless guidance, constructive suggestions and advice had

inspired me to strive for the best. Without his inexhaustible patience and guidance, this thesis

would not have been possible to accomplish. Under his abounding guidance, I have also

acquired new skills and insights, not only in academic studies but vigour in life.

Next, this valuable opportunity I have today, I owe to Professor Andrew Taggart. I am

very grateful to be awarded the Vice Chancellor’s SG50 Honours Scholarship. This award

has granted me a valuable opportunity to further my education abroad.

In addition, I would like to sincerely thank Mr Stephen Klomp for his hospitality and

kind guidance during my stay in Perth. I would also like to thank my lecturers, Dr Amy

Huang, Miss Thanesvary Subraamanniam and Miss Michelle Gander for their patience and

guidance throughout my units.

Last but not least, to my cherished family, I am deeply thankful and appreciative of

their boundless love, unwavering support and encouragement throughout this journey.

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ABSTRACT

Past research primarily focus on evaluating market timing abilities using the returns

and stockholdings of mutual funds. We examine the market timing abilities of fund managers

using the trade proportions of mutual funds. These are statistically significant trade

proportions that encompass beta, sentiment beta and momentum. Trade proportions provide

insights on the direction that the fund manager was pursuing. Market and systemic risk

indicators are important for our study as they reflect the overall performance of the market

and the economy. We compare between the values of these indicators and the values of our

statistically significant trade proportions to evaluate if these values are highly correlated

during various market cycles. Using correlation and regression analysis, we examine the

relation between the trade proportions (dependent variable), the market and systemic risk

indicators (independent variables). We have also taken into consideration of certain

conditions that might affect the adjustments of these trade proportions and conducted some

preliminary and robust tests. In general, we expect that prior to a bull (bear) market, fund

managers will adjust their portfolios towards positive (negative) trade proportions.

Furthermore, majority of past studies had evaluated market timing abilities only during

recession periods therefore our study period between 1991 and 2012 has incorporated both

recession and boom periods to avoid biasness in results. However, similar to previous

findings, these trade proportions did not demonstrate superior market timing abilities.

Although no significant market timing abilities were exhibited, momentum trade proportions

displayed the most significant correlation and regression results. We observed an inverse

relationship between the positive momentum trade proportions and the momentum index.

This is consistent with fund managers having pursued a contrarian strategy.

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CONTENTS

ACKNOWLEGDEMENTS 1

ABSTRACT 2

CONTENTS 3-7

FIGURES 8

GRAPHS 9

TABLES 10

1 INTRODUCTION 13-18

1.1 Introduction 13-18

2 LITERATURE REVIEW 19-60

2.1 Introduction 19

2.2 Overview of Literature 19-21

2.3 Characteristics of Mutual Funds 21-22

2.4 Mutual Fund Performance- Market Timing 22-23

2.4.1 Timing using Convex Relationship between Fund Returns and

Market Returns

23-25

2.4.2 Stationary Beta versus Non-Stationary Beta in Bull and Bear Markets 25-34

2.4.3 Evaluating Market Timing Abilities simultaneously with Security

Section Abilities

34-37

2.4.4 Free from Beta Estimates 37-39

2.4.5 Portfolio Performance Measures without Benchmarks 39-41

2.4.6 Volatility Timing 41-42

2.4.7 Downside of Returns Chasing Behaviour 43-44

2.4.8 Persistence in Fund Performance 44-46

2.4.9 Business Cycles and Predictability Skills 46-47

2.4.10 Stockholdings versus Trades 47-53

2.4.10.1 Market Timing Abilities 48-51

2.4.10.2 Stock Selection Abilities 51-54

2.4.11 Downside of Risk Shifting Behaviour 54-55

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2.4.12 Successful Market Timing Abilities 56-57

2.5 Overview of Contrarian Strategies 57-58

2.5.1 Identifying Contrarian Strategies in Mutual Fund Trades 59

2.6 Conclusion of Literature Review and Motivation of Present Study 59-60

3 METHODOLOGY 61-79

3.1 Introduction 61

3.2 Overview of Methodology 61-63

3.3 Data Description 63

3.3.1 Bull and Bear Markets 63-64

3.3.2 Recession and Boom Periods 64-66

3.3.3 Four States of Bull and Bear Markets 66-68

3.4 Trades 68

3.4.1 Identifying Market Timing Trades 68

3.4.1.1 Formula for Identifying Market Timing Trades 68-69

3.4.2 Identifying Sentiment Beta Timing Trades 69

3.4.3 Identifying Momentum (Contrarian) Trades 69-70

3.5 Importance of Indices 70-71

3.5.1 Description of Indices 72-74

3.5.1.1 The S&P 500 Index 72

3.5.1.2 The Baker & Wurgler’s Sentiment Index 72

3.5.1.3 The S&P 500 Momentum Index 73

3.5.1.4 The S&P 500 Quality Index 73

3.5.1.5 The S&P 500 Growth Index 73-74

3.5.1.6 The S&P 500 Low Volatility Index 74

3.5.1.7 The S&P 500 High Beta Index 74

3.5.2 Systemic Risk Measures 74-77

3.5.2.1 Brief Description of Systemic Risk Measures (19 Elements) 75-77

3.6 Sources of Data and Availability 78

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3.7 Trades’ Correlation with Indices 78-79

3.8 Conclusion of Methodology 79

4 RESULTS AND DISCUSSION 80-133

4.1 Introduction 80

4.2 Overview of Results and Discussion 80-83

4.2.1 Market Indicators 81

4.2.2 Systemic Risk Indicators 81-82

4.2.3 Overview of Analysis (Schematic Diagram) 82-83

4.3 Fund Quarters, Significant Fund Quarters and Proportions 83-85

4.3.1 Descriptive Statistics of Significant Fund Quarters and Proportions 86-87

4.4 Descriptive Statistics of Market and Systemic Risk Indicators 87-91

4.4.1 Descriptive Statistics (In Months) 87-90

4.4.2 Descriptive Statistics (In Quarters) 90-91

4.5 Performance of Market Indicators 92-99

4.6 Correlation Testing 99

4.6.1 Correlation Testing between Market Indicators (Main Market

Indicators and Sub-Market Indicators)

100-102

4.6.2 Correlation Testing between Systemic Risk Indicators 102

4.6.2.1 Brief Description of the Selected Systemic Risk Indicators 102-107

4.7 Final Selection of Market and Systemic Risk Indicators 107-109

4.8 Correlation and Regression Analysis between Trade Proportions

(DV) and Indicators (IV)

109-111

4.9 Overall Test for Correlation and Regression Analysis 111-117

4.10 Preliminary Test 117-129

4.10.1 Market Beta Trade Proportions 118-121

4.10.1.1 Market Index 118-119

4.10.1.2 Market “Return” Indicator 119-121

4.10.2 Sentiment Beta Trade Proportions 121-124

4.10.2.1 Sentiment Index 121-122

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4.10.2.2 Sentiment “Return” Indicator 122-124

4.10.3 Momentum Trade Proportions 125-128

4.10.3.1 Momentum Index 125-127

4.10.3.2 Momentum “Return” Indicator 127-129

4.11 Summary Table of Significant Results based on Overall Analysis

and Preliminary Tests

130

4.12 Conclusion of Results and Discussion 131-133

5 ROBUST TESTING 134-164

5.1 Introduction 134

5.2 Overview of Robust Testing 134-137

5.3 Beta Trade Proportions and the Market “Return” Indicator 137-140

5.3.1 Test (1): Magnitude of Change 137-138

5.3.2 Test (2): Changes in Standard Deviation 138-139

5.3.3 Test (3): Changes in Signs 139

5.3.4 Test (4): Persistence in Index 139-140

5.4 Beta Trade Proportions and the Market Index 142-143

5.4.2 Test (4): Persistence in Index 142

5.5 Sentiment Beta and the Sentiment “Return” Indicator 143-146

5.5.1 Test (3): Changes in Signs 143


5.6 Sentiment Beta and the Sentiment Index 146-147

5.6.1 Test (3): Changes in Signs 145-146


5.7 Momentum Trade Proportions and the Momentum “Return”

Indicator

148-149


5.8 Momentum Trade Proportions and the Momentum Index 149-151


5.9 Multiple Regression Analysis 151-160

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5.9.1 Market Beta 151-54

5.9.1.1 Positive Market Beta Proportions with the Market “Return”

Indicator

151-153

5.9.1.2 Positive Market Beta Proportions with the Market Index 153-154

5.8.2 Sentiment Beta 154-157

5.9.2.1 Positive Sentiment Beta Proportions with the Sentiment “Return”

Indicator

154-156

5.9.2.2 Positive Sentiment Beta Proportions with the Sentiment Index

Indicator

156-157

5.9.3 Momentum Trades 157-160

5.9.3.1 Positive Momentum Proportions with the Momentum “Return”

Indicator

157-159

5.9.3.2 Positive Momentum Proportions with the Momentum Index 159-160

5.10 Summary Table of Significant Results based on Robust and

Multiple Regression Tests

161

5.11 Conclusion of Robust Testing 162-164

6 CONCLUSION 165-79

6.1 Introduction 165

6.2 Overview of Conclusion 165-167

6.3 Significant Research Findings 167-168

6.4 Limitations of the Research 168

6.6 Areas of Future Research 169-170

6.6 Summary of Study 170-171

REFERENCES 169-179

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FIGURES

Figure 1.1: Schematic Diagram: Overview of Methodology 18

Figure 2.1: The Characteristic Line of a Fund that Outguess the Market (Treynor

and Mazuy, 1966)

23

Figure 3.1: Schematic Diagram: Overview of Methodology

62

Figure 4.1: Trades, Market Indicators and Systemic Risk Indicators

83

Figure 4.2: Final Selection of Indicators for Analysis

108

Figure 4.3: Statistically Significant Trades and their Respective Indicators

109

Figure 5.1: Types of Robust Test Conducted

136

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GRAPHS

Graph 4.1: Price Fluctuations of the Market Index, June 1991 to September 2012 92

Graph 4.2: Price Fluctuations of Market “Return” Indicator, July 1991 to

September 2012 93

Graph 4.3: Changes in the Sentiment Index Values, June 1991 to March 2011 95

Graph 4.4: Changes in the Values of the Sentiment “Return” Indicator, July 1991

to March 2011 96

Graph 4.5: Changes in the Momentum Index Values, September 2006 to

September 2012 97

Graph 4.6: Changes in the Values of the Momentum “Return” Indicator, October

2006 to September 2012

98

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TABLES

Table 3.1: Bull and Bear Market Durations throughout the Trading Period

between July 1991 and October 2012

63

Table 3.2: Recession and Boom Durations throughout the Trading Period

between July 1991 and October 2012

65

Table 3.3: Data Sources, Availability and Types of Data

78

Table 4.1: Trades- Number of Fund Quarters, Significant Fund Quarters and

Proportions

85

Table 4.2: Descriptive Statistics of Statistically Significant Fund Quarters and

Proportions

86-87

Table 4.3: Descriptive Statistics of Market and Systemic Risk Indicators

(Presented in Months)

89-90

Table 4.4: Descriptive Statistics of Market and Systemic Risk Indicators

(Presented in Quarters)

91

Table 4.5: Correlation of Market Indicators: 73 Monthly and 25 Quarterly

Observations, September 2006 – September 2012

101-102

Table 4.6: Correlation between Systemic Risk Indicators: 247 Monthly

Observations and 83 Quarterly Observations, June 1991 to

December 2011

104-105

Table 4.7: Significant (at 0.01 Level) Results of Positive and Negative

Correlations between the Selected Systemic Risk Indicators: 83

Quarterly Observations, June 1991 to December 2011

106-107

Table 4.8: Overall Correlation and Regression between Trade Proportions and

Indicators

115-117

Table 4.9: Individual Correlation and Regression Analysis between Market

Beta Trades (Proportions) and the Market Index – June 1991 to

September 2012

118-119

Table 4.10: Individual Correlation and Regression Analysis between Market

Beta Trades (Proportions) and the Market “Return” Indicator – July

1991 to September 2012

120-121

Table 4.11: Individual Correlation and Regression Analysis between Sentiment

Beta Trades (Proportions) and the Sentiment Index– June 1991 to

March 2011

122

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Table 4.12: Individual Correlation and Regression Analysis between Sentiment

Beta Trades (Proportions) and the Sentiment “Return” Indicator–

July 1991 to March 2011

124

Table 4.13: Individual Correlation and Regression Analysis between

Momentum Trades (Proportions) and the Momentum Index –

September 2006 to September 2012

127

Table 4.14: Individual Correlation and Regression Analysis between

Momentum Trades (Proportions) and the Momentum “Return”

Indicator – October 2006 to September 2012

129

Table 4.15: Significant Results based on Overall Analysis and Preliminary Tests

130

Table 5.1: Number of Quarters in relation to Market “Returns”- July 1991 to

September 2012

138

Table 5.2: Empirical Rule for Normally Distributed Data

139

Table 5.3: Robust Testing between Proportions of Beta Trades based and the

Market “Return” Indicator

141

Table 5.4: Robust Testing between Proportions of Beta Trades and the Market

Index

143

Table 5.5: Robust Testing between Proportions of Sentiment Beta Trades and

the Sentiment “Return” Indicator

145-146

Table 5.6: Robust Testing between Proportions of Sentiment Beta Trades and

Sentiment Index

147

Table 5.7: Robust Testing between Proportions of Momentum Trades and the

Momentum “Return” Indicator

149

Table 5.8: Robust Testing between Proportions of Momentum Trades and the

Momentum Index

150

Table 5.9: Robust Testing for Proportions of Beta Trades with the Market

“Return” Indicator and 11 Systemic Risk Indicator

152-153

Table 5.10: Robust Testing for Proportions of Beta Trades with the Market

Index and 11 Systemic Risk Indicator

154

Table 5.11: Robust Testing for Proportions of Sentiment Beta Trades with the

Sentiment “Return” Indicator and 11 Systemic Risk Indicator

155-156

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Table 5.12: Robust Testing for Proportions of Sentiment Beta Trades with the

Sentiment Index and 11 Systemic Risk Indicator

157

Table 5.13: Robust Testing for Proportions of Momentum Trades with the

Momentum “Return” Indicator and 11 Systemic Risk Indicator

158-159

Table 5.14: Robust Testing for Proportions of Momentum Trades with the

Sentiment Index and 11 Systemic Risk Indicator

160

Table 5.15: Significant Results based on Robust and Multiple Regression Tests

161

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CHAPTER 1

INTRODUCTION

1.1 Introduction

The performance measures for market timing abilities of fund managers has been a

predominant topic. Market timing is the ability of fund managers to tilt their portfolios in

accordance to the anticipated market trends to exploit returns. Common market trends are the

bullish and bearish markets. During bullish markets, fund managers can take advantage of the

market by buying high beta stocks and selling low beta stocks. In contrast, during bearish

markets, fund managers can take advantage of the market by buying low beta stocks and

selling high beta stocks.

In relation to predictability skills, fund managers can monitor the performance of the

market with the assistance of market indicators as they reflect the market movements. If the

index level of the S&P 500 market index consistently increases (decreases), we can anticipate

a bullish (bearish) market. However, market timing can also be a form of risk as the cost of

adjusting a portfolio may not be justified for the gains in return. Furthermore, portfolio tiling

may not necessarily suggest that fund managers are taking advantage of fluctuating

investment opportunities but a signal of ill motivated trades from mediocre abilities of fund

managers or agency issues (Huang, Sialm and Zhang, 2011). There is also a possibility of

mistiming which exposes funds to underperformance by selling (buying) stocks with high

(low) betas before a bullish (bearish) market period.

Early studies identified market timing abilities by evaluating the returns of mutual

funds. Treynor and Mazuy (1966) studied the returns of mutual funds on their historical

success of forecasting variations in the stock market. They reported that the fund returns and

the market returns had a convex relationship. Successful market timers would increase their

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exposure to the market during bullish markets and decrease their exposure during bearish

markets. However, they did not consider how the systematic risk which is measured by beta

could vary in bullish and bearish markets. Subsequently, researchers incorporated the use of a

non-stationarity beta to evaluate market timing abilities of fund managers (Fabozzi and

Francis, 1979; Kim and Zumwalt, 1979; Miller and Gressis, 1980; Chen, 1982). A non-

stationary beta gives allowance for the increase in risk exposure. However, there were still no

significant evidence of market timing abilities.

Attention has been shifted to the evaluation of the performance of stockholdings and

trades to examine the predictive abilities of fund managers. Jiang, Yao and Yu (2007) found

positive market timing abilities when quarterly portfolio holdings were applied to a single

index model. However, Elton Gruber and Blake (2012) re-examined their study and argued

that using quarterly portfolio holdings may have resulted in an inaccurate conclusion of

market timing abilities as a vast number of trades were not captured in their analysis. In

addition, when monthly portfolio holdings were applied to a two index model, market timing

abilities were non-existence.

Comparing the use between stockholdings and trades, Chen, Jegadeesh and Wermers

(2000) reported that active stock trades represents a stronger opinion of a manager as

compared to a “passive” stockholding. Although no evidence of predictive abilities, Chen,

Jegadeesh and Wermers (2000) and Baker, Litov, Wachter and Wurgler (2010) found that

trade buys outperformed the trades they sell.

Using a different approach, researchers have also evaluated market timing abilities

simultaneously with stock selection abilities. Similar studies by Chang and Lewellen (1984)

and Chen and Stockum (1986) evaluated market timing and stock selection skills at the same

time using mutual fund returns. Chang and Lewellen (1984) proposed that there is a

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possibility that fund managers might exploit returns by engaging in effective “macro” market

timing activities as well as careful “micro” security selection efforts. However, there were no

evidence of market timing abilities. Following the same method, Kacperczyk, Niewerburgh

and Veldkamp (2014) also evaluated market timing and stock selection abilities

simultaneously. However they took into consideration of the changing economic trends like

the boom and recession periods. They conditioned the state of the economy and developed a

new method where more weightage is given to a fund manager’s market timing success

during recession periods and stock picking success during boom periods. Studying mutual

fund holdings, they found market timing abilities in both recession and boom periods.

We contribute to the literature in several ways. First, we examine the market timing

abilities of fund managers by evaluating their statistically significant trade proportions that

encompass beta, sentiment beta and momentum. Second, we investigate if fund manager

adjust their portfolios between positive and negative trade proportions in accordance to the

various market cycles. Unlike past researchers, we study the proportions of these trades as

they provide insights on the direction that a fund manager was pursuing. We expect a higher

proportion of positive trades when the market is bullish or in an expansion phase. In contrast,

we expect a higher proportion of negative trades when the market is bearish or undergoing a

recession period. Third, we show that although momentum trade proportions had the least

number of quarter observations, they exhibited the most significant results from our

correlation and regression analyses. We observed that positive momentum trade proportions

exhibited an inverse relationship with the momentum index during bullish market periods.

Although results were inconsistent to our expectations, an inverse relationship suggests that

the fund manager may have pursed a contrarian strategy.

To identify trades that are engaged in market timing in any calendar quarter, we

conducted correlation and regression analyses between the trade proportions and their related

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market indicators. We apply these measures to mutual fund trade proportions from 1991 to

2012. We conduct an overall correlation and regression test between the trade proportions

and their respective indicators to appreciate the general direction of their relationship. Next,

we consider how bullish and bearish markets will affect the adjustments of trade proportions.

We expect that during bullish market periods, the positive trade proportions would exhibit a

direct relationship with the market indicators. Similarly, during bearish market periods, we

expect negative trade proportions to exhibit a direct relationship with the market indicators.

Finally, various robust tests were also conducted to investigate if fund managers were

selective with the adjustments of their portfolio proportions based on market persistence,

turning points of the market and we study how big and small changes in the market returns

will affect their portfolio adjustment decisions.

We observe the following results from the correlation and regression analyses. Based

on the results of overall correlation and regression analysis, we observe that the positive

sentiment and positive momentum trade proportions exhibited significant results. However,

both trade proportions had an inverse relationship with their respective indicators. There were

no significant results from the beta trade proportions. Second, when bullish and bearish

market conditions are considered, the most number of significant results were exhibited from

the sentiment and momentum trade proportions. We observe an inverse relationship between

these trade proportions and their respective indicators. Third, based on the results from the

robust tests, the most number of significant results were also from the sentiment and

momentum trade proportions. Likewise, inverse relationships were exhibited between these

trade proportions and their respective indicators. Overall, despite momentum trade

proportions having the least number of quarter observations, they displayed the most number

of significant relationships. It is plausible that these fund managers have adopted a contrarian

strategy. Similar to previous findings, there we no evidence of market timing abilities.

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We consider some limitations of the study. Although the use of quarterly data

observations provides more time allowance for fund managers to form market expectations

and make right decisions in portfolio adjustments, these observations may not be able to

capture sufficient information of fund managers with higher trading frequencies. It is also

possible that the total number of quarter observations might have affected our results.

Therefore, we suggest some areas of future research. We consider evaluating a longer time

period that incorporates all four recession periods in future studies as research have shown

that predictability skills are best displayed during recession periods. We also suggest

evaluating market timing and stock selection skills simultaneously with regards to the

changes in the economic conditions using the trade proportions of mutual funds.

This paper is organized in the following manner. In Section 2.0, we discuss the

literature review. In Section 3.0, we discuss the data and provide an overview of the

methodology. In Section 4.0, we discuss and present our findings. In Section 5.0, we conduct

various robust tests. In Section 6.0, we conclude our study. An overview of our study’s

methodology is provided (Refer to Figure 1.1).

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Figure 1.1 Schematic Diagram: Overview of Methodology

The figure below illustrates the overview of our methodology. Trade betas that encompass beta,

sentiment beta and momentum are provided by Cullen et al. (2015). Quarterly data observations of

trade proportions are used for the analysis.

Indices

Trade Betas

(Proportions)

(1991-2012)

Trades associated with

Market Beta


Sentiment Beta


Momentum

S&P500 Market Index

Baker & Wurgler’s Sentiment Index

S&P 500 Momentum Index

S&P 500 Quality Index

S&P 500 Growth Index

S&P 500 Low Volatility Index

S&P 500 High Beta Index

Systemic risk

measures

Market Trends

-Bull and Bear Markets

-Recession and Boom Periods

-Further break down of Bull and Bear Markets

with the consideration of Volatility

Quarterly

Convert Data

Correlated

Check with

Daily

Monthly

Quarterly

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CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter describes the background and presents the literature review for this

study. In section 2.2, we discuss the background of our study and review the literature on the

key areas which are the market timing abilities of mutual funds managers, the evolution

performance measures which involves the use of stationarity and non-stationarity beta and the

examination of stockholdings and trades of mutual funds. We also identify the purpose of our

research and provide an overview of our methodology. Our sample comprises mainly of

statistically significant trade betas that encompass beta, sentiment beta and momentum of US

equity mutual funds over the period 1991 to 2012 and the data are provided by Cullen et al.

(2015).

2.2 Overview of Literature

Millions of people have invested in a once obscure financial instrument, the mutual

fund. Investors have constantly compared the advantages between active trading and passive

trading strategies of mutual funds. Over the years, the evaluation of mutual fund

performance has been vital to ensure optimal investment allocation as well as the

development of a mutual fund manager’s reward structure. Nevertheless, performance

measures have been consistently challenged and subsequently refined. Measures of a mutual

fund’s performance includes stock selection, market and industry timing abilities. Stock

selection and market timing abilities are the most popular measures of performance where

stock selection is the ability to select undervalued securities and market timing is the ability

to adjust security holdings to anticipate the movements of the market.

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Determining the market timing abilities of mutual fund managers have been the focal

point of research. Managers with market timing abilities can attempt to exploit returns using

two common strategies. They can either move in and out of the market or conduct a tactical

asset allocation between low and high beta stocks using predictive methods by monitoring the

performance of indicators like the S&P 500 Market Index to detect any changes in the market

trends. The early stages of determining market timing abilities was derived using a quadratic

term in the capital asset pricing model (CAPM). Subsequently, researchers had focused on

the stationarity and non-stationarity of beta in the bull and bear market. The increase

(decrease) of a non-stationarity fund’s beta allows the fund’s equity holdings to rebalance in

the anticipation of the expected bull (bear) market.

In order to avoid these benchmark issues, recent studies have concentrated on mutual

fund holdings and mutual fund trades. The intuition is that a fund with successful market

timing skills will hold more stocks that possess high beta in bull markets and conversely hold

predominately lower beta in bear markets. Similarly, a fund will purchase high beta stocks

and sell low beta stocks when the market is expected to rise and purchase low beta stocks and

sell high beta stocks when the market is expected to fall.

We contribute to the literature in several ways. First, we examine market timing

abilities of fund managers by evaluating the statistically significant trades that encompass

beta, sentiment beta and momentum. Trade proportions are used as they provide insights on

the direction that the fund manager is pursuing. Second, we consider both upmarket and

downmarket periods in our study. Third, using a new approach, we investigate if fund

managers make technical adjustments to their portfolios according to different market trends

based on market indices. During the bullish periods, we expect a higher proportions of

positive trades in a fund’s portfolio. On the other hand, during bearish markets, we expect a

higher proportions of negative trades in a fund’s portfolio. Market timing is significant when

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we observe a positive significant relationship between the market indices and the statistically

significant trade proportions.

This paper is organized in the following manner: in Section 2.0, we discuss the

literature of our research. Section 3.0, we provide and discuss the data and overview of the

methodology. In Section 4.0 we discuss the results of our research. Section 5.0, we conduct

various robust test. Finally in Section 5, we conclude the study and discuss about the

limitations of our study and suggest areas of future research.

2.3 Characteristics of Mutual Funds

Generally, in comparison to larger investment companies, individual investors lack of

substantial wealth to invest in large variety of stocks, bonds and securities. Consequently,

these individual investors turned into risk averse investors. Russell (2007) explained that

individual investors usually lack of professional knowledge and experience to make the best

decisions for their portfolios. Also, due to time management issues and complicated

paperwork, investors often struggle to keep up to their portfolios.

By offering diversification and simplicity for individual investors, mutual funds are a

good solution to these problems as they are a collection form of investments (Russell, 2007).

These funds are open-end investment companies and they pool funds of individual investors

offering them professional management by investing in a variety of securities or other assets

(Russell (2007); Bodie, Kane and Marcus (2014)). Instead of owning individual stocks or

bonds, mutual fund investors owns a portion of shares in a mutual fund and these shares

represent a portion of the holdings of the funds (Investopedia, 2016). The common types of

mutual funds are the money market funds, equity funds, bond funds, hedge funds and index

funds (Bodie, Kane and Marcus, 2014).

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Commonly used by sophisticated investors due to their numerous advantages, mutual

funds are also well known for their professional management of money (Investopedia, 2016).

As investors may lack time or expertise to manage their own portfolio, these funds offer

convenience and cost efficiency as they allow investors to have an inexpensive way to make

and monitor their investments (Investopedia, 2016). Bodie, Kane and Marcus (2004)

explained that as mutual funds includes a wide range of securities, this reduces portfolio risk

as any loss in a particular security can be minimised by the gains of others (Investopedia,

2016).

Mutual funds also offer lower transaction costs as they are usually purchased and sold

in large volumes of securities in bulk (Bodie, Kane and Marcus, 2004). Compared to

individual investors, these large scale investors are usually given a discounted trading cost.

Additionally, mutual funds are valuable for their liquidity advantages. Although they are a

collective form of investments, they allow shares to be converted into cash at any point of

time of request like an individual stock (Bodie, Kane and Marcus, 2004).

2.4 Mutual Fund Performance – Market Timing

In our study, market timing is the ability of a fund manager to adjust his or her

portfolio composition between high volatile stock and low volatile stocks based on using

predictive methods such as technical indicators like the market index. The market index

reflects the overall performance of the market and suggesting periods of bullish or bearish

market trends.

Fund managers that possess market timing abilities can generate superior returns by

adjusting their portfolios in accordance to the anticipated market trend. During bullish

(bearish) market periods, fund manager can adjust their portfolios towards high (low) volatile

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stocks. In other words, during bullish (bearish) periods, fund manager can exploit returns by

buying high (low) beta stocks and selling low (high) beta stocks.

2.4.1 Timing using Convex Relationship between Fund Returns and Market Returns

There has been an ongoing debate on the best performance measure for market timing

abilities of fund managers. Traditional performance measures like the Capital Asset Pricing

Model (CAPM) have reported that the relationship between the fund returns and market

returns are linear. Conversely, the study by Treynor and Mazuy (1966) showed that the

relationship between the fund returns and market returns are actually convex. Treynor and

Mazuy (1966) evaluated market timing abilities of mutual funds based on their historical

success in predicting major fluctuations in the stock market. They concluded that successful

market timers would increase their exposure to the market when a bullish period is

anticipated and reduce exposure to the market when a bearish period is anticipated. This

action causes the characteristic line of the portfolio to surpass the market as the portfolio

asset structure can be constantly adjusted (Figure 2.1).

Figure 2.1: The Characteristic Line of a Fund that Outguess the Market (Treynor and Mazuy,

1966)

Volatility

Volatility

Fund Returns

Market Returns

Characteristic Line

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Using the basis of the CAPM, Eq. (1), Treynor and Mazuy (1966) developed a least

square regression technique performance focusing on the squared relation between fund

returns and market returns. A curvature line was identified by fitting in the characteristic line

data of 57 open-end mutual funds using their yearly data observations of returns during the

period between 1953 and 1963, Eq. (2):

𝑅𝑖𝑡 = 𝑅𝑓 + 𝛽𝑖(𝑅𝑚𝑡 − 𝑅𝑓𝑡) (1)

𝑅𝑖𝑡 − 𝑅𝑓𝑡 = 𝑎𝑖 + 𝛽𝑖(𝑅𝑚𝑡 − 𝑅𝑓𝑡) + 𝛾𝑖(𝑅𝑚 − 𝑅𝑓𝑡)2

+ ℯ𝑖𝑡 , (2)

where, 𝑅𝑖𝑡 denotes return on assets of the selected fund at time t, 𝑅𝑓𝑡 denotes risk free return

rate at time t, 𝑅𝑚𝑡 is the return on the market at time t, 𝑎𝑖 denotes a selectivity ability,

𝛾𝑖 denotes the parameter measuring the market timing performance, if 𝛾𝑖 > 0, it implies the

existence of a timing ability. The difference between the equation of the CAPM model and

the Treynor and Mazuy model is the addition of 𝛾𝑖(𝑅𝑚 − 𝑅𝑓𝑡)2 as this changes the linear

relationship between the fund returns and market returns into a quadratic equation.

Treynor and Mazuy used yearly data observations of returns as they believed that

even for smaller funds, the frequency of portfolio changes which will alter their fund’s

volatility will not happen more than once a year. However, only one out of 57 funds exhibited

a curve characteristic line. This suggest that on average, mutual funds were not successful at

outguessing the market. Treynor and Mazuy (1966) concluded that any excess returns

generated were not from the success of timing abilities but from the abilities of fund

managers in identifying under-priced industries and companies.

Supporting the study of Treynor and Mazuy (1966), Williamson (1972) stated that the

relationship between the fund returns and the market returns would be convex instead of

linear. Based on the characteristic line graph, when the line is curved upwards at the upper

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right and lower left end, this suggest that mutual funds had performed well in bearish markets

and performed even better during bullish markets.

Williamson (1972) attempted to identify market timing abilities by reviewing the

available published data of 180 mutual funds during the period between 1961 and 1970.

However, similar to Treynor and Mazuy (1966), on average, no mutual funds were able to

outperform the market. Moreover, four out of 180 funds displayed significant unsuccessful

forecasting. Against expectations, these funds were more volatile during bearish market and

less volatile during bullish markets.

2.4.2 Stationary Beta versus Non-Stationary Beta in Bull and Bear Markets

Jensen (1968) believed that the performance of risky investment portfolios is the

ability of a portfolio manager to earn superior returns through successful predictions of future

security prices. These returns should be higher than the returns expected by the portfolio

manager for the level of risk associated with their portfolios. This belief is based on the

concept that on average, the riskier the asset is, the higher the returns will be. Portfolio

managers will be compensated for taking on additional risk. If the asset’s actual returns are

above the expected returns of the asset, a positive alpha is established.

On the contrary to earlier studies that evaluated forecasting abilities of portfolio

managers using relative performance measures, Jensen (1968) has provided an absolute

measure of performance. Absolute performance measure is a measure that is compared

against a certain standard. The Jensen’s equation determines the superior returns obtained

when deviated from the benchmark, Eq. (3):

𝛼𝑖 = [𝑒(𝑟𝑖𝑡) − 𝑟𝐹𝑡] − 𝛽𝑖(𝑒(𝑟𝑚𝑡) − 𝑟𝑓𝑡), (3)

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where, 𝑟𝑖𝑡 denotes the return of fund 𝑖 at time t, 𝛼𝑖 denotes the abnormal returns of the fund

(an idea of forecasting abilities), 𝛽𝑖 denotes the systematic risk of the fund 𝑖, 𝑟𝑚𝑡 denotes the

return of the market at time t and 𝑟𝑓𝑡 denotes the risk free rate at time t. The value of alpha

could either positive or negative. Having a positive alpha would imply superior forecasting

abilities and in contrast, having a negative alpha would imply either poor selection choices or

the existence of high expenses.

Given that the predictability skills of a portfolio manager not only involves the skills

to predict price movements of individual securities and the general behaviour of future

security prices, the Jensen (1968) model also considers the abilities of a fund manager to

forecast the market behaviour. Henceforth, the Jensen (1968) model not only evaluates the

portfolio manager’s ability to predict how much a security or portfolio is expected to earn

given the level of systemic risk (measured by beta) but also measures the ability of a portfolio

manager to forecast the market’s behaviour. However, this is based on the assumption that

the portfolio manager tries to maintain the given level of risk in his or her portfolio.

Jensen (1968) investigated the existence of predictability skills by analysing 115 open

ended mutual funds using their yearly data observation of returns during the period between

1945 and 1964. Based on the results, on average, mutual funds were not able to predict

security prices to outguess the market henceforth underperforming buy and hold strategies.

They were also unsuccessful in their trading activities to recoup brokerage expenses. We

consider some limitations of this study. The assumption that the portfolio manager attempts

to maintain the same level of risk may have caused inaccurate results. As mutual funds are

being actively managed, it is reasonable to expect changes in the level of risk due to the

buying and selling decisions of portfolio managers.

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Subsequently, there has been attention drawn to the stability of the systematic risk

measured by beta in bull and bear market conditions. The systematic risk of mutual funds in

different market conditions is an important factor in evaluating the market timing abilities of

a fund manager. If there is different beta for different market conditions, using a stationary

beta for the entire period can result in different conclusion of a fund manager’s abilities.

During market changes, when a stationary beta is used for the entire time period there is no

consideration for the additional risk exposure. If a fund manager correctly adjusts the fund’s

beta in an anticipation of a bull market, the beta in a bull market would be greater than the

estimation of beta for both bull and bear market period. One of the limitations from Jensen

(1968) study was the use a stationary beta for the entire period of the study as the fund

managers attempted to on average, maintain the given level of risk in their portfolio.

Taking into consideration a non-stationary beta, Fabozzi and Francis (1979)

investigated if the beta of mutual funds varies in bullish and bearish markets. A statistical

model was developed by Fabozzi and Francis (1979) to examine if the systemic risk of

mutual funds was altered during different market conditions. The monthly data observations

of returns of 85 mutual funds were tested between the period from 1965 and 1971. In order to

examine if the systematic risk (beta) are different in various market conditions, this equation

has taken into consideration of beta shifting, Eq. (3):

𝑅𝑖 = 𝐴1𝑖 + 𝐴2𝑖𝐷𝑡 + 𝛽1𝑖𝑅𝑚𝑡 + 𝛽2𝑖𝐷𝑡𝑅𝑚𝑡 + ℯ𝑖𝑡, (4)

where, 𝑅𝑖 denotes the excess returns of fund i, 𝑅𝑚𝑡 denotes the excess returns on the market

𝐷𝑡 denotes a dummy variable which is unity if the tth period is a bull market and zero

otherwise, The coefficients of the dummy variable, 𝐴2𝑖 and 𝐵2𝑖, measure the differential

effects of bull market conditions on the alpha, 𝐴1𝑖 and beta, 𝐵1𝑖 respectively and ℯ𝑖𝑡 is the

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random error term. This equation allows the shifting of alpha and beta and is designed to

determine if the regression coefficients are significantly different in bull and bear markets.

Fabozzi and Francis (1979) reported that there were three definitions of bull and bear

markets for this study. First, defined by a well-established textbook (Cohen, Zingbarg and

Zeikel, 1973), certain months were designated as bull and bear markets in accordance to

market trends. Second, when market returns positive, the market is known to be bullish.

When market returns are negative, the market is known to be bearish. Third, without the

consideration of market trends, months with market returns higher (lower) than one half of

the standard deviation of market returns over the sample period are designated as bull (bear)

markets.

While betas of individual securities may be stable despite changes in market trends

like the bull and bear markets, Fabozzi and Francis (1979) argued that there is a possibility

for a non-stationary beta to occur even if the fund manager did not attempt to adjust the

portfolio risk. They considered how the individual securities’ betas may be intertemporally

unstable. Also, changes in the relative market value weights of individual securities will alter

the portfolio’s beta, which is the weighted average beta regardless if the betas of individual

securities were not altered. Therefore, a benchmark is created to determine if the number of

funds that shifted in beta were a result of a planned changed in risk exposure. For comparison

purpose, 85 random portfolios were created as benchmarks. Each stock of the 85 random

portfolios were given equal weightage.

Despite considering a non-stationary beta, results suggest that regardless of different

market conditions, on average, mutual funds did not respond differently. Similar to previous

studies, mutual fund managers were not able to outguess the market to earn higher risk-

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adjusted returns for shareholders. Fund managers did not alter their fund’s beta to benefit

from the different market conditions.

Fabozzi and Francis (1979) revealed three reasons why fund managers were not

observed to increase their funds’ beta during bearish to bullish market periods or decrease

their funds’ beta during bullish to bearish periods. One, there were random beta coefficients

from a significant number of New York Stock Exchange (NYSE) stocks and the portfolio

managers might have overvalued or undervalued the beta. Two, there is a possibility that the

portfolio manager was unable to foresee changes in market conditions hence was unable to

shift the fund’s beta during bullish markets. Three, although fund managers may have

correctly anticipated the right change in direction of the market, the cost of altering a fund’s

beta may not be justifiable for the gains in return.

An extension to the Fabozzi and Francis (1979) study, Kim and Zumwalt (1979)

investigated if there were variations of returns of securities and portfolios in up (bull) and

down (bear) markets. This process has the effect of separating the total variation of the

security or portfolio returns into two components, variations when the market is up and

variations when the market is down. Kim and Zumwalt (1979) pointed out that although the

beta of mutual funds are not significantly different in up and down market periods, the

variations of returns of mutual funds may be different. If investors are presumed to be risk-

averse, they would expect to receive a premium for bearing additional risk from the “down”

market and expected to pay a premium for the returns they would receive from the “up”

market.

For the development of the study, two assumptions were employed. The first

assumption was that each security may react differently in up and down markets. If securities

do respond differently, beta coefficients may be determined for both up and down markets

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and investigated for statistically significant differences. There were three measures to

determine what establishes an “up” or “down” market. An “up” market are months with rate

of returns on the market portfolios that exceed the 1) average market return, 2) the risk free

rate or 3) zero. Otherwise, the market is defined as a “down” market. The single index model

was modified to examine both up and down betas, Eq. (5):

𝑅𝑖𝑡 =∝𝑖+ 𝛽𝑖+𝑅𝑚𝑡

+ + 𝛽𝑖−𝑅𝑚𝑡

− + ℯ𝑖𝑡, (5)

where, 𝑅𝑖𝑡 denotes the excess return of fund i , ∝𝑖 denotes the actual return of fund i minus

the expected return of fund i, 𝑅𝑚𝑡 denotes the excess return on the market, ℯ𝑖𝑡 is the random

error term, 𝛽𝑖+is determined from the months when the returns comes from the “up” market

and 𝛽𝑖− is determined when the returns come from the “down” market. As the number of

securities in the portfolio increases, the unsystematic risk also known as firm-specific risk

would be diversified away. The variance of portfolio equation would be written as, Eq. (6):

𝜎𝑝2 = (𝛽𝑝

+)2𝜎𝑝2

𝑝+ + (𝛽𝑝−)2𝜎𝑝

2𝑝− , (6)

where, 𝜎𝑝2 is the variance of the portfolio. The formula is separated into (𝛽𝑝

+)2𝜎𝑝2

𝑝+ being the

variations from the bull market and (𝛽𝑝−)2𝜎𝑝

2𝑝− being the variations from the bear market.

The second assumption was that investors had a preference for greater up side

variation of returns and a preference for a smaller downside variation of returns. This

suggests that an investor has a preference that is positively related to the upside variations

and negatively related to the downside variations. Kim and Zumwalt (1979) believed that

investors require a risk premium on the downside portion of variation and a negative risk

premium on the upside portion of the variation. Expressed in Eq. (7):

𝐸(𝑅𝑝) = 𝑅𝑓 + 𝜆1 𝛽𝑝+ + 𝜆2 𝛽𝑝

− (7)

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where, 𝜆1 𝛽𝑝+ denotes the negative coefficient and 𝜆2 𝛽𝑝

− denotes the positive coefficient. The

two beta model of equation 7 was tested to determine if the expected negative value for 𝜆1

and positive value for 𝜆2 was confirmed.

Kim and Zumwalt (1979) developed the two beta model to incorporate the responses

of beta during “up” and “down” market periods. The variations of returns in both market

periods were investigated using the monthly data observations of returns from a sample of

322 securities between the periods from 1962 to 1976. This model allows the separation of

the total systemic risk into two components, risk from upside variations markets which are

considered to be favourable and risk from bearish markets which are considered to be

unfavourable.

Results reflected that out of 322 securities, 34 exhibited significantly different up and

down market betas. In comparison to the Fabozzi and Francis (1979) study, more securities

displayed statistically significant differences between “up” market and “down” market betas

than would occur randomly. The signs of the regression coefficients were also correct and

statistically significant, suggesting that investors do receive a risk premium for tolerating

downside risk. Consistent to Kim and Zumwalt’s expectations, the negative premium was

associated to the beta of the “up” market. This suggests that the measurement of downside

variation of returns is more appropriate when measured by the “down” market beta rather

than the conventional single beta in the market model.

Miller and Gressis (1980) created a new measure based on the traditional CAPM

which allows and statistically estimates the extent of non-stationarity in the relationships

between the fund returns and market returns. This measure allows a precise estimation of

alpha and beta in the presence of non-stationarity beta. Miller and Gressis (1980) revealed

that if non-stationarity is significant in a risk return relationship but is ignored, this can result

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in misleading information as the estimates of alphas and betas are calculated based on a

stationary beta which is the weighted averages of the actual values. When mutual funds are

actively managed, the level of systemic risk would fluctuate as a result of the buying and

selling decisions of their managers. Hence beta, the measure of systematic risk should not be

ignored as this might result in biased results. It is also reasonable to expect non-stationary

risk return relationships in some mutual funds as well-managed funds would take advantage

of the market by altering their betas in accordance to the general market movements.

Miller and Gressis’s (1980) approach is based on the traditional CAPM which allows

and statistically gauge the extent of non-stationarity in relationships between the returns of

funds and the returns from the market. In order to obtain a more precise estimate of beta and

alpha, time can be segmented into intervals during which the betas are stationary. A

partitioning algorithm and partition selection procedure is conducted on the sample of 28

mutual funds using the weekly data observations of returns between the periods from 1973 to

1974. Unlike previous researchers that evaluated the performance of mutual funds using

yearly or monthly data observations of returns (Jensen, 1986; Fabozzi and Francis, 1979;

Kim and Zumwalt, 1979), Miller and Gressis (1980) used weekly data observations of returns

as they believed that it is a more appropriate measure in detecting shifts between the risk and

returns of mutual funds.

The presence of a non-stationary beta would suggest either changes in the distribution

of risk in the economy or changes in the mutual fund portfolio composition. Investors are

interested in such changes as they attempt to take advantage of these deviations to earn

superior returns. Based on the results, only one out of 28 funds exhibited stationary betas and

the rest had betas that varied over the periods. Based on correlation and regression analysis

results of the information gathered from the partition regression, a mixture of results were

exhibited between the betas and the market returns. There were some evidence of weak

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positive relationships and some weak negative relationships between the betas and market

returns. Similarly, there were also weak negative relationships and weak positive

relationships between the alphas and betas. However, there were no statistically significant

relationships of either type.

Following up on the studies that incorporated the use of non-stationary beta, Chen

(1982) re-examined the relationship between the risk and returns of mutual funds in in bull

and bear market conditions. Chen (1982) evaluates the study of Kim and Zumwalt (1979) as

their procedure of valuing “up” and “down” market betas may have led to in inaccurate

results in the risk analysis of “up” and “down” markets.

Chen (1982) revealed that the study by Kim and Zumwalt (1979) gave inconsistent

results due to multicollinearity issues which resulted in large sampling variances of estimates

of the “up” and “down” market betas. Also, the model did not take into consideration that the

beta coefficient would change over time. Chen (1982) used a time-varying beta coefficient

approach to resolve these issues. It is revealed that the two beta model used for the test of the

trade-off between the risk and returns in “up” and “down” market is constant regardless of a

stable or non-stable beta coefficient. The two beta model from the Kim and Zumwalt’s study

was modified to be, Eq. (8):

𝐸(𝑅𝑝𝑡) = 𝑅𝑓 + 𝛽𝑝+𝐸(𝑅𝑚𝑡 − 𝑅𝑓)

++ 𝛽𝑝

−𝐸(𝑅𝑚𝑡 − 𝑅𝑓)−

+ ℯ𝑖𝑡 (8)

where, 𝐸(𝑅𝑝𝑡) denotes the expected return of the portfolio, 𝑅𝑓 denotes the risk free rate of

interest, 𝛽𝑝+ denotes the bull market beta, 𝛽𝑝

− denotes the bear market beta and ℯ𝑖𝑡 denotes the

random error term.

The sample of 360 mutual funds’ monthly data observations of returns were tested

between the periods from 1965 to 1977. Similar to Kim and Zumwalt’s (1979) results, Chen

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(1982) concluded that investors do require a premium for taking on risk from the downside

market and investors pay a premium for the returns they receive from the “up” market. The

results of the time varying beta approach method have supported the Kim and Zumwalt’s

findings that the breakdown of total systemic risk into risk due to upside deviation of returns

and risk due to the response of a bear market still appeared to be correct even with a non-

stationary beta. Irrespective of a stationary or non-stationary beta, investors do request

compensation for undertaking the risk from the variation of returns from the bear market

which was viewed as unfavourable and pay a premium for the upside variation of returns

which was viewed as favourable.

Both studies by Chen (1982) and Kim and Zumwalt (1979) revealed that an

appropriate measure of downside risk (bear market) would be the “down” market beta instead

of a stationary beta. It is not appropriate to consider the use of a stationary beta as a

measurement of the market as the market cycle changes over time. A stationary beta does not

give any allowance for the increase in risk exposure.

2.4.3 Evaluating Market Timing Abilities simultaneously with Security Selection

Abilities

Past research have investigated the market timing abilities of fund managers

individually. Using a different approach, Chang and Lewellen (1984) evaluated market

timing abilities of fund managers simultaneously with security selection abilities. They

believed that portfolio managers might be able to exploit returns by engaging in effective

“macro” market timing activities as well as cautious “micro” security selection efforts. That

is the ability to modify the total risk composition of their portfolios in the anticipation of the

general movements of the market. This study considers the fact that a non-stationary beta

would be a more appropriate measure of mutual fund performance. Based on the studies by

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Fabozzi and Francis (1979), Kim and Zumwalt (1979), Miller and Gressis (1980) and Chen

(1982), they found some evidence that mutual fund portfolios do not have a constant risk

position over time. They also concluded that skills of market timing may well be a

measurement of a fund manager’s decision process.

Chang and Lewellen (1984) conducted a parametric statistical procedure that allowed

a joint test for the presence of either security selection or superior market timing skills in

managed portfolio to investigate the performance of 67 mutual funds using their monthly data

observations of returns between the periods from 1971 to 1979. Majority of research have

evaluated the performance of mutual funds based on the single market model equation, Eq.

(9):

𝑍𝑝(𝑡) − 𝑅(𝑡) = 𝑎𝑝 + 𝛽𝑝[𝑍𝑚(𝑡) − 𝑅(𝑡)] + 𝜖(𝑡), (9)

where, 𝑍𝑝(𝑡) denotes the observed rate of return on the portfolio p during the period, 𝑅(𝑡)

denotes the simultaneous rate of return on a riskless asset, 𝑍𝑚(𝑡) denotes the return on the

fully diversified “market” portfolio of all risky assets during t and 𝜖(𝑡) denotes the random

error term with it being a value of 0. 𝛽𝑝 is assumed to be stationary over time. When alpha

has a positive value, this indicates superior return performance based on security selection

efforts. However, this model only evaluates stock selection abilities and does not take into

consideration that the level of systemic risk (𝛽𝑝) might change over time.

The equation was later modified by Henriksson and Merton (1981) to a least square

regression which evaluates the stock selectivity and market timing abilities of mutual fund

abilities separately. It was also modified to capture an “up-market beta” and a “down-market

beta.” The modified equation was, Eq. (10):

𝑍𝑝(𝑡) − 𝑅(𝑡) = 𝛼∗ + 𝛽1∗𝑋1(𝑡) + 𝛽2

∗𝑋2(𝑡) + 𝜖𝑝∗ (𝑡), (10)

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where, 𝑋1(𝑡) and 𝑋2(𝑡) =𝑍𝑚(𝑡) − 𝑅(𝑡), 𝛽1∗ denotes the “up-market beta” of a managed

portfolio and 𝛽2∗ denotes the “down market beta”. The contributions of returns have been

separated into two components, α represents the returns due to security selection ability and

𝛽 is used to measure the portfolio’s market-timing skill. When there is no existence of market

timing abilities, the value of beta would be zero.

While this was a joint test that considered both market timing and stock selection

abilities of fund managers, results suggest that on average, neither skilful market timing nor

clever security selection abilities were evident. Overall, mutual funds were unable to outguess

the market. It seemed that passive strategies still have an upper hand in mutual fund

investments.

Similar to Chang and Lewellen (1984), Chen and Stockum (986) also investigated the

market timing and stock selection abilities of fund managers simultaneously. Traditional

performance measures like the Sharpe ratio assumed that that the systematic risk level of a

fund is a fixed coefficient rather than a decision variable. However, this results in inaccurate

performance measures as the risk of the portfolio varies over time. Following which, studies

have incorporated the use of a non-stationary beta. However, they did not consider that the

mutual fund’s beta could also be non-stationary when fund managers are not engaged in

timing decisions (Fabozzi and Francis, 1979; Kim and Zumwalt, 1979; Miller and Gressis,

1980; Chen, 1982). Hence, the presence of a non-stationary beta does not necessary represent

the existence of market timing abilities.

Chen and Stockum (1986) presented a generalized varying parameter model to

examine the performance of mutual funds by allowing for both timing decisions of funds and

random behaviour of fund’s systematic risk levels. Although the generalized varying

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parameter model is similar to the Treynor and Mazuy model, this model allows the beta of

mutual funds to be a decision variable instead of a fixed coefficient, Eq. (11):

𝑅𝑖𝑡 = 𝑎𝑖 + 𝑅𝑚𝛽− + 𝜆𝑖𝑅𝑚𝑖

2 + 𝜔𝑖𝑡 (11)

where, 𝜔𝑖𝑡 equals (𝜇𝑖𝑡 + 𝜖𝑖𝑡𝑅𝑚𝑡). 𝑅𝑖𝑡 denotes mutual fund i’s return at time t, 𝑅𝑚 denotes the

market return at time t, 𝜇𝑖𝑡 denotes random shock, β denotes target systemic risk, 𝑎𝑖 measures

the selectivity component and 𝜆𝑖𝑅𝑚𝑖2 measures changes due to market timing. A portfolio

beta might still be non-stationary even if fund managers are not actively managing their

portfolios by adjusting the portfolio beta in accordance to the market. This is because a

portfolio beta might respond differently to various market cycles.

Chen and Stockum (1986) examined 43 mutual funds using their quarterly data

observations of returns between the periods from 1975 to 1982. Unlike prior studies that used

monthly or yearly data observations of returns, Chen and Stockum (1986) stated that the use

of quarterly data observations gives fund managers an extended period of time to form

market expectations and adjust their portfolios accordingly. Throughout this sample period,

there were two bull and two bear market periods. By incorporating both cycles of the

markets, it will help to reduce biasness in this study.

Based on the results, 30% of funds showed selectivity, 19% were random betas and

14% showed significant but negative market timing performance. Although there were some

significant selectivity abilities, results suggest that similar to previous findings, mutual funds

did not reflect any market timing abilities regardless individually or as a group.

2.4.4 Free from Beta Estimates

On the contrary to prior research, Ferri, Oberhelman and Roenfeldt (1984) examined

the market timing abilities of mutual funds without the use of beta estimates. This method

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focuses on the composition of assets in a fund’s portfolio and investigates alterations in the

composition prior to variations in the broad level of stock market prices. The main objective

of this method is to examine whether a fund manager’s decision to gradually increase or

decrease the fund’s commitment to common stocks. The expectations of fund managers are

reflected on the decisions that they made and simultaneously shifts the portfolio’s market-

related volatility.

A fund manager is successful at market timing when their decisions and expectations

are consistent with the later movements of the market. For instance, a fund manager who

anticipates a bearish market will lower the portfolio’s volatility by decreasing the percentage

of assets in a portfolio that are invested in stocks. Market timing skills are exhibited if the

later market is bearish. Likewise, successful market timing is exhibited when a fund manager

increases the portfolio assets invested in stocks in the expectations of an increase in market

prices and the later market is bullish.

Ferri, Oberhelman and Roenfeldt (1984) examined the quarterly changes in the

mutual fund’s stock holdings of 69 mutual funds between the periods from 1975 to 1980.

These types of mutual funds have aggressive management with a preference of being

completely invested by stocks. Therefore, any alterations in these funds are considered as an

attempt to forecast or time the market movements. Additionally, two subgroups of

stockholdings were also examined, those preceding extensive fluctuations in stock prices and

those when managerial reallocations of portfolios are not impacted by shareholder’s

contributions or withdrawal from funds.

Market timing abilities are evaluated by examining the increases and decreases in a

fund’s relative commitment to stocks measured by the ratio of net purchases or sales of

common stocks (NETPS) to total assets. If the NETPS has a positive value, the fund has

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purchased more stock than it sold, increasing its exposure to market risk. A t test was

conducted to compare the mean levels of NETPS for a fund quarter before an increase in the

stock index with the mean NETPS for the fund quarter before a decrease in the stock index.

Ferri, Oberhelman and Roenfeldt (1984) hypothesized that the NETPS is classified as an

upmarket decision if the stock index increases during the subsequent months and the NETPS

is classified as downmarket decision if the stock index decreases during the subsequent

months. The null hypothesis is rejected if the average NETPS for the upmarket is

significantly larger than the average NETPS for the down market. However, the test of means

could be inaccurate as there is a possibility that a fund made merely a few large mistakes as

the test results are reliant on the extent of the deviations in stock holdings. Therefore, a

frequency test is also conducted as it only examines the direction of changes in stock

holdings prior to the movements in the stock index and eliminates the limitations of the test

of means. A correct decision can either be classified as a positive NETPS before a bullish

market or a negative NETPS before a bearish market.

Based on the results, although a few funds displayed some market timing abilities, on

average, there were no significant market timing abilities exhibited. In sum, although this

study offers an alternative way of examining market timing abilities which is a method that is

free from the estimates of beta, there were no new evidence that fund managers possess

market timing abilities.

2.4.5 Portfolio Performance Measures without Benchmarks

Past researchers have evaluated performance measures of mutual funds by comparing

the returns of managed portfolios to the returns of a benchmark portfolio. However, this

could be a bias measure of market timing abilities as results are dependent on the choice of

benchmark selected. Often, information regarding the portfolio composition of funds are not

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utilised. Grinblatt and Titman (1993) believed that by making use of information about the

portfolio composition, the method of comparing returns to a benchmark portfolio can be

eliminated.

This method is adapted by the Event Study Measure where the performance of mutual

funds are evaluated by calculating the differences between the returns of assets during the

portfolio period known as “the event period” and returns of a later date known as “the

comparison period”. This is the belief that the assets held in a well-managed portfolio (event

period) would have higher returns compared to periods when assets are not included in any

portfolios (comparison period). This method uses later period returns compared to earlier

period returns as they have taken into account that some portfolio managers are likely to pick

their assets based on their past returns. However, this might be a bias assumption as it forces

the researcher to ignore assets that lacked returns in the comparison periods.

Grinblatt and Titman (1993) developed a new measure that is not subjected to

survivorship biases. It is based on the assumption that from the standpoint of uninformed

investors, the direction of expected asset returns is constant over time. This implies that the

portfolio holdings of an uninformed investor does not have any form of relationship with the

future returns. Unlike a well-informed manager who is able to predict when certain assets

will exhibit higher or lower than average returns, the direction of the expected asset returns

will vary over time. The manager can take advantage of these changing expected returns by

tilting his or her portfolio weights towards assets that have increased in expected returns and

tilt away from assets that have decreased in expected returns.

Grinblatt and Titman (1993) examined 155 mutual funds quarterly changes in

stockholdings from the period between 1974 and 1984. Concluding results showed that on

average, mutual fund portfolios exhibited positive abnormal investment performances and

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that the strongest performance was computed from the aggressive growth category of funds

which earned significantly positive risk adjusted returns. In relation to the study by Ferri,

Oberhelman and Roenfeldt (1984), any movements in these funds are considered as an

attempt to forecast or time the market movements. Although no market timing abilities were

present, this article emphasized that superior performance can be predicted without the use of

a benchmark when portfolio holdings were examined.

2.4.6 Volatility Timing

Previous studies have examined the market timing abilities of mutual fund managers

exclusively by comparing the returns between their funds and the market (Treynor and

Mazuy, 1966; Jensen, 1968; Fabozzi and Francis, 1979; Kim and Zumwalt, 1979; Miller and

Gressis, 1980; Chen, 1982). The main theory behind these studies often investigate if fund

managers have taken advantage of superior information by adjusting their funds towards

more (less) volatile stocks in the anticipation of bull (bear).

Often, fund managers encounter difficulties in predicting market returns. Using a new

perspective, Busse (1999) investigated the funds’ ability to time market volatility. He

examined if funds change market exposure in relation to market volatility changes and

highlighted that volatility timing is a significant influence in the returns of mutual funds as it

leads to higher risk-adjusted returns.

Attention has been shifted to market volatility for two reason. First, unlike market

returns which are hard to predict, market volatility is predictable because it is persistent. High

volatility is usually followed by high volatility and low volatility is usually followed by low

volatility. Second, majority of performance measures are risk adjusted. These measures affect

the cash flows of funds and how funds manage risk has repercussions for manager

compensation. However, it is uncertain that a fund manager can increase risk adjusted

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performance or investor utility by timing market volatility. Therefore, Busse (1999)

investigates if funds respond to changes in market volatility and how these strategies will

affect the performance of funds.

Busse (1999) motivated volatility timing in the perspective of a fund manager,

assuming that fund managers attempt to time market exposure in the best interest of the fund

shareholder. Busse (1999) analysed the daily data observation of returns of 230 domestic

equity funds between 1985 and 1995 with a daily single factor volatility timing model to

study how managers respond to publicly available information. This single factor volatility

timing model is modified from the four index model by adding in terms to capture the effects

of volatility timing. Unlike previous researchers that analysed monthly return data (Fabozzi

and Francis, 1979, Kim and Zumwalt, 1979; Chen 1982; Chang and Lewellen, 1984), the use

of daily returns’ data allows a more efficient estimate of time variations in systematic risk

considering that monthly returns’ data might not be able to capture the day to day activities of

active mutual funds.

A conditional analysis was conducted to provide detailed explanations of mutual fund

risk and the reasons for its changes. It also allows the evaluator to differentiate between

passive effects and the effects by public information usage. Furthermore, it also helps to

differentiate among active managers of different abilities and as such lead to better asset

allocation decisions.

Based on the results, Busse (1999) found a strong inverse relationship between the

funds’ systemic risk levels and conditional market volatility. When conditional market

volatility is higher than average, systemic risk levels are lower. When conditional market

volatility is high, funds that reduce systemic risk earned higher risk-adjusted returns. This

demonstrates that mutual funds have taken advantage of the superior information by

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increasing their market exposure when there is low market volatility and decreasing their

market exposure when market volatility is high.

2.4.7 Downside of Returns Chasing Behaviour

Over the years, researchers have focused on exploiting mutual fund returns. A

contrasting article by Karceski (2002) developed an agency model to express that such return

chasing behaviour of fund managers will lead to beta being under-priced to the degree that is

predicted by the standard CAPM. Based on Karceski’s (2002) model, he revealed that the

goals of fund managers and the behaviour of return chasing fund managers will influence

fund management to adjust their portfolios towards high beta stocks. Based on the theory of

supply and demand, this will lead to a high demand of high beta stocks which lead to an

increase in prices and in turn lower the expected returns. The model is supported by three

verifiable facts. First, investors tend to buy funds that have recently displayed extraordinary

returns. Second, fund managers chase returns through time. During the transition period from

the bear to the bull market, there is a tendency of larger cash inflows into the equity mutual

fund industry. Third, during bullish market periods, high beta stocks outperforms low beta

stocks.

Karceski (2002) believed that active fund managers focus on outperforming peers

during the transition phase between bearish and bullish markets as returns are usually larger.

The rewards from the bullish market are usually higher than the rewards from the bearish

market as cash inflows are usually minimised after a “down” market. Mutual fund investors

would tilt their portfolios towards high beta stocks during an upward market in anticipation

that it will lead to a larger cash inflow as high beta stocks typically outperform in bull

markets. However, this return chasing behaviour by mutual fund managers will lead to

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CAPM’s beta to be either under-priced or overpriced than the expected amount, resulting in a

reduction of beta risk premium in equilibrium. In an equilibrium world, the demand for high

beta stocks prior the bull market will push their price higher and expected returns lower.

Karceski (2002)’s model predict that these actions will cause expected returns to fall.

The model investigates the monthly holdings of mutual funds from the period between 1984

and 1996. Consistent to Karceski (2002) expectations, results reflected that fund investors

appeared to be inexperienced as they tend to increase their equity funds stake after the market

goes up and pick funds based on their past performance despite justified warnings by

disclaimers to the contrary. Based on the agency model created, the behaviour of mutual fund

managers chasing returns across funds cause them to tilt towards high beta stocks resulting in

a flatter security market line and as a result reduces the expected returns premium for high

beta stocks. The total stock portfolio was over weighted with aggressive growth funds (high

beta stocks) compared to income equity funds (low beta stocks).

Results reflected that equity mutual funds held a larger percentage of high beta stocks

compared to the overall equity market portfolio. Karceski (2002) predictions were right that

due to active fund managers tilting towards high beta stocks, this reduces the expected return

premium for high beta stocks and flattens the security market line. In some extreme cases,

this may lead to the returns of low beta stocks surpassing the equilibrium expected returns of

high beta stocks despite conventional risk measures such as beta or standard deviation and

performance in bear markets suggesting that high beta stocks should acquire a higher

expected return.

2.4.8 Persistence in Fund Performance

Bollen and Busse (2005) believed that superior information is built on the expectation

that some fund managers possess significant predictive abilities and if this ability persists, it

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allows vigilant investors to predict future performance based on past results. Bollen and

Busse (2005) examined the persistence in mutual fund performance emphasizing on short

term periods.

There are two types of decision making strategies, stock selection and market timing.

Stock selection refers to predicting returns of individual stocks and market timing refers to

predicting relative returns of broad asset classes. Majority of past studies found no significant

evidence that fund managers were able to achieve abnormal returns over long periods

regardless pursuing a stock selection or market timing strategies.

Bollen and Busse (2005) examined if mutual fund performance persist over a

relatively short period of three months. They reported that fund performance exists for a

relatively short amount of time due to the mutual fund industry being competitive by nature

or to managerial turnover. Having short measurement periods provides a more accurate way

of identifying top performers. Daily fund returns are examined with quarterly measurement

periods as Bollen and Busse (2005) argued that monthly fund returns will not be an efficient

estimation. Previous studies that used mostly monthly data of returns found insignificant

evidence that fund managers were able to generate positive abnormal returns from stock

selection abilities or market timing abilities over a long period of time. Also, using quarterly

measurement periods controls for cash flows as it allows mutual fund factor loadings to

gradually alter.

The parameters of stock selection and market timing models were estimated and stock

selection and market timing abilities were examined using the four factor model and two

timing models. Bollen and Busse (2005) allowed the coexistence of both types of abilities in

their measurement as previous studies have focus on either one of this abilities individually

without taking into consideration that some fund managers are stock pickers whereas some

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are market timers. By stereotyping them as one type of fund manager could result in

inaccurate results. There is a likelihood that fund managers may also switch strategies. They

studied the daily returns of 230 funds between 1985 and 1995. Funds are ranked every

quarter by their risk adjusted return measured over a three month period using market timing,

stock selection and mixed strategy models. Following which, the risk adjusted return of

deciles of funds over the subsequent three month period are measured.

While abnormal returns were reflected in the top decile of funds suggesting

persistence in mutual fund performance, Bollen and Busse (2005) argued that abnormal

returns cease to exist when funds are being evaluated over a longer time horizon. This reflects

that superior performance is short lived and only significant when they are evaluated

regularly. Taking into consideration of account transaction cost and taxes, superior returns

may be generated by passive strategies like the buy and hold strategy compared to a

performance chasing strategies even if short term performance is foreseeable.

2.4.9 Business Cycles and Predictability Skills

Avramov and Wermers (2006) reported that most investment profits are generated

from the predictability in manager skills. Based on prior research, most studies find that

passive strategies have consistently outperformed active strategies. However, an article

focusing on stock picking skills reported that active management achieved significant returns

when examined during recession periods in comparison to expansion periods (Moskowitz,

2000). This suggests that business cycle variables may be advantageous in identifying

actively managed mutual funds that outperform.

Avramov and Wermers (2006) designed optimal portfolios of no load, open-end US

domestic equity mutual funds in the presence of manager selectivity and benchmark timing

skills, mutual fund risk loadings and benchmark returns. They analysed both ex post out of

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sample performance and ex ante investment opportunity set delivered by predictability based

strategies. When an investor does not have any predictability skills, he or she will invest in

index funds. In comparison, investors that believed in the possibility of predicting fund risk

loadings and benchmark returns will invest in actively managed funds.

Avramov and Wermers (2006) analysed the optimal portfolio of 1301 open-end, no

load US domestic equity mutual funds which include index funds, sector funds, actively

managed funds and exchange traded funds. These mutual funds’ monthly database was over

the sample period between 1975 and 2002. Results reflected that incorporating predictability

skills makes actively managed funds more attractive and these funds generated larger Sharpe

ratios. Out of sample optimal portfolios that did not incorporate any predictability skills

produced negative alphas. By incorporating manager’s skills in predictability into long term

strategies, these strategies had outperformed their Fama-French and momentum benchmarks

by 2% to 4% per year by timing industries over business cycle and additional 3% to 6% per

year by choosing funds that outperform the industry benchmarks.

Avramov and Wermers (2006) found that predictability in manager skills are the

leading basis of investment profitability. Active management adds significant values in their

investment and industries are important in locating outperforming mutual fund. Also,

investment strategies that incorporated predictability manager selectivity and benchmark

timing skills consistently outperform. Predictability skill strategies performed best during

recessions but are also good during expansion. These skills are able to identify the best

performing funds during both expansion and recessions. Overall, active management of

mutual funds adds on significant values.

2.4.10 Stockholdings versus Trades

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Numerous of studies have concluded that on average, mutual funds are not able to

outguess the market. Actively managed funds have underperformed their benchmark

portfolios. Although there has been no significant evidence of successful fund possessing

market timing or stock selection abilities to surpass the market, investors have continued to

invest in actively managed funds in hopes of achieving abnormal returns. Articles have

shifted their attention on evaluating the performance of stockholdings and trades of mutual

funds. Majority of these studies have focused on evaluating stock selection abilities with the

use of stockholdings and trades. Regardless, we examine how stockholdings and trades will

result in different values of active trading strategies.

2.4.10.1 Market Timing Abilities

Early studies have evaluated the returns of mutual funds but find no significant

evidence of market timing abilities. Jiang, Yao and Yu (2007) reported that these return-

based test are exposed to “artificial timing” biasness. They proposed an alternative market

timing measurement using mutual fund holdings to investigate the active changes of fund

betas as these holdings are not subjected to artificial timing biasness.

Using holdings, Jiang, Yao and Yu (2007) estimated the beta of a fund as the

weighted average of the individual stocks’ betas from the portfolio holdings and directly

tested if the covariance between the fund betas at the initial holding period and the market

returns of the holding period is significant. In comparison to return based measures that relied

on ex post realised returns to estimate the adjustments of beta, these measurements based on

holdings used only ex ante information. Therefore, these measures do not suffer from any

biasness by subsequent trading activities in the course of a holding period or dynamic trading

effect. In addition these holding based measures have better statistical power.

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Jiang, Yao and Yu (2007) evaluated 2,294 actively managed equity mutual funds by

applying both return-based test and holdings-based test from the period between 1980 and

2002 using a single index model. Monthly observation data of returns of mutual funds are

used for the return based test and quarterly holdings of mutual funds are used for the holdings

based test. Jiang, Yao and Yu (2007) reflected that the results from the return based measures

exhibited similar results from majority of the research that on average, mutual funds have

slightly negative but insignificant market timing abilities. Whereas the results reflected from

holdings based measure suggested that on average, mutual funds have positive timing

abilities.

Implementing the alternative market timing measurement, Jiang, Yao and Yu (2007)

conducted the holding based test using active changes of fund beta and results suggested that

mutual funds time the market through active trading. While linking several fund

characteristics and market timing performances, they discovered market timing funds are

typically funds with high industry concentration, particularly those with a tilt towards small

cap stocks and with large fund size. Additionally, they stated that fund managers adjust fund

betas in accordance to macroeconomic variables such as price to earnings ratios and total

dividend yield. When macroeconomic variables are controlled, average market timing

abilities still appeared to be positive. This suggest that fund managers are not only utilising

information from the publicly accessible macroeconomic information but also private

information to time the market.

Following up on the study by Jiang, Yao and Yu (2007), Elton, Gruber and Blake

(2012) re-examined the existence of market timing abilities with the use of monthly portfolio

holdings instead of quarterly portfolio holdings. Elton, Gruber and Blake (2012) believed that

the use of monthly holdings data will capture a vast number of trades that are missed by

quarterly holdings data and provide a better estimation of timing trades. Unlike, Jiang, Yao

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and Yu that only investigated the market timing abilities of actively traded equities, Elton,

Gruber and Blake (2012) investigated a full range of securities like options, futures, preferred

stock, bonds and non-traded equity. They reported that these range of securities use

additional instruments to time and ignoring their presence will result in inaccurate results of

market timing decisions.

In the study by Jiang, Yao and Yu (2007) which found positive market timing

abilities, they estimated portfolio betas with the use of portfolio holdings and security betas

and investigated the effects of changing betas with a single index model. Elton, Gruber and

Blake (2012) investigated if similar results will be exhibited when a multi index model is

used. The multi index model recognises bonds as an individual vehicle for timing.

Furthermore, they also re-examined market timing abilities with the used the Fama-French

model both with unconditional and conditional betas and a model that studies the effect of

adjusting allocation across industries.

Elton, Gruber and Blake (2012) examined the monthly data of holdings between the

periods from 1994 to 2005. Based on the results, negative timing abilities were reflected.

Results from the Fama-French model suggest that timing decisions of fund managers led to a

decrease in performance regardless being measured using conditional or unconditional

sensitivities. Similarly, the sector allocation’s model also reflected negative timing measures.

Inconsistent to the results from the single index model, the results from the two index

model reflected a different conclusion. Elton, Gruber and Blake (2012) discovered that the

timing decisions of mutual funds did not result in superior returns. First, when the managers

change their exposure to the market, they do so by adjusting their exposure to small stocks or

higher growth stocks. Taking into account of this shifting procedure, timing results was

altered as such unlike the single index model which reflected positive timing abilities, the two

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index model exhibited negative timing abilities. Second, Elton, Gruber and Blake (2012)

reported that a large number of trades have been neglected with the use of quarterly holdings.

Third, the use of a wider range of securities may have impacted the results and that the major

contribution of negative timing abilities were from high technology stocks. Although no

market timing abilities were exhibited, Elton, Gruber and Blake (2012) showed that with

monthly holdings, timing ability can be measured more precisely as compared to using

quarterly or yearly data which misses a large number of trades.

While Jiang, Yao and Yu (2007) concluded that positive timing abilities are

significant, the study by Elton, Gruber and Blake (2012) questioned the credibility of their

results. Jiang, Yao and Yu (2007) assumes that the beta on the market of all securities that are

not traded equity is zero, as a result non-traded equity, bonds, futures, options, preferred

stocks and mutual funds are treated as identical instruments with each of them having a beta

on the market of zero. Elton, Gruber and Blake (2012) reported that 18.5% of trades by an

average fund manager were not captured when market timing measures were applied to

quarterly data holdings. In addition, even though Jiang, Yao and Yu (2007) found market

timing abilities using a single-index model, these findings did not hold up when a two-index

model was used.

2.4.10.2 Stock Selection Abilities

Chen, Jegadeesh and Wermers (2000) studied the value of active mutual fund

management by evaluating the stockholdings and trades of mutual funds. By examining both

stockholdings and trades, it resolves the issue of whether a stock truly signifies superior

information in regards to the stock’s value. They presumed that active stock trades represents

a stronger opinion of a manager in comparison to a passive decision of holding an existing

position in a stock as stockholdings may be prompted by reasons in relation to non-

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performance like transaction costs and capital gain taxes. Therefore, they expect any evidence

of stock selection abilities to exhibit from the examination of trades compared to holdings.

Chen, Jegadeesh and Wermers (2000) compared the returns from stock holdings and

trades by high turnover funds and the returns from stock holdings and trades by low turnover

funds of 2,424 mutual funds quarterly data from the period between 1975 and 1995 to study

the value of active mutual fund management.

Based on the results from the examination of stock holdings, Chen, Jegadeesh and

Wermers (2000) found no difference in the performance of stocks that are most widely held

by mutual funds and those that are least widely held. However, when examining mutual fund

trades, stocks buys significantly gave higher returns than stocks sold. They concluded that

examining trades would be a better choice for portfolio performance examining trades as it is

a more powerful metric to determine the existence of superior information.

Pinnuck (2003) examined the performance of Australian fund managers’ monthly

stock holdings as well as trades of mutual funds to investigate if they possess superior

information. Stockholdings allow a more accurate examination of performance as compared

to traditional performance measures that relied on the examination of mutual funds’ return.

The examination of mutual funds’ trades is motivated by the study of Chen, Jegadeesh and

Wermers (2000) as the study showed that trades of mutual funds are more likely to represent

a signal of private information compared to passive stockholdings.

Pinnuck (2003) evaluated the stockholdings and trades of 35 Australian active equity

fund managers using their monthly portfolio holdings data from the period between 1990 and

1997. Unlike previous studies that examine the performance of stocks held at calendar quarter

ends, Pinnuck (2003) examined month end portfolios as they argued that quarter end

portfolios may not fully represent a typical fund portfolio and in addition have reporting

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biases. Taking into consideration of the study by Chen, Jegadeesh and Wermers (2000) which

argued that studying trades of mutual funds would be a more powerful metric to determine

the existence of superior information. Pinnuck (2003) also investigated on the performance of

the stocks a fund manager trades, specifically stocks buys and stocks sold.

Based on the results, stocks held by fund managers on average, realised abnormal

returns. The results from the evaluation of individual trades showed that stocks that are

purchased by fund managers achieve abnormal returns but stocks sold did not exhibit any

abnormal returns. This suggests that fund managers do not possess superior information with

regards to bad news.

Pinnuck (2003) concluded that overall fund managers have the ability to select stocks

that realised positive abnormal returns. However, there were some limitations of this study.

Due to a limited time period, results may be time period specific. Also due to a small sample

size, results may be sample specific too. Trades exhibiting abnormal returns may result from

the consequences of price pressure rather than fundamental information. Survivorship

biasness which is the tendency for mutual funds with poor performance to be dropped by

mutual fund managers may have some impact on the resulted abnormal returns.

Baker, Litov, Wachter and Wurgler (2010) developed an alternative method of

identifying trading skills. They studied the nature of stock picking abilities and constructed

measures of trading skills built on how stocks are traded and held by fund managers perform

at subsequent corporate earnings announcement. It is the ability to buy stocks that are about

to enjoy high returns prior to their upcoming quarterly earnings announcements and sell

stocks prior to the suffering of low returns upon that announcement. This method enables a

more powerful approach to detect skilled trading and attempts to differentiate between the

winners from losers based on their trading activities. They believed that this approach will be

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more useful in detecting trading skills as it exploits segments of the returns at earning

announcements.

Baker et al. (2010) analysed the returns by fund holdings but focused mainly on the

trades of the funds measure mutual fund manager trading skills by using the sample of

quarterly data from several million funds from the period between 1980 and 2005. Results

show that the average fund buys performs better at future earnings announcements than

control stocks and that the fund sells perform worse. Mutual fund trades also forecasted

earnings surprises and this concludes that mutual fund managers are able to trade profitably

as they are able to predict earnings-related fundamentals. In sum, mutual fund trades have the

ability to forecast earnings fundamentals.

2.4.11 Downside of Risk Shifting Behaviour

Majority of the research focus on the benefits of risk shifting but Huang, Sialm and

Zhang (2011) aimed to fill the gaps of the performance consequences of risk shifting

behaviour. They reported that mutual funds alter their risk levels significantly over time and

that this risk shifting behaviour may be a result of ill motivated trades of unskilled or agency-

prone fund managers who trade for personal benefits to increase their personal compensation.

However, risk shifting can also be executed when a skilled fund manager trades to take

advantage of their stock selection and timing abilities.

Huang el at. (2011) investigated the performance consequences of risk shifting and

examined what stimulates this risk shifting behaviour. They reported that altering the risk

levels of mutual funds may not be harmful to investors for two reasons. First, as mutual funds

have the incentive to shift risk to take advantage of the competition for extra returns,

investors are not necessarily hurt by risk shifting. Second, risk shifting behaviour shows

one’s superior skill since it is associated to the activeness of the investment tactics of funds.

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When active managers change their portfolio composition to take advantage of their stock

selection or timing abilities this will result in a change of risk exposure as an unintentional

consequence. However if risk shifting funds indeed excel better than other funds, then this

risk shifting behaviour profits the investors.

When risk shifting is motivated by agency related issues, superior performance of

funds would not be expected. Likewise, fund managers lacking of skills and abilities are more

likely to alter risk levels and therefore worst performance of funds would be expected.

However, if risk shifting is executed by a skilled managers taking advantage of their market

or stock selection abilities, superior performance from funds are expected.

In order to investigate the risk shifting behaviour of mutual funds, Huang el at. (2011)

used the quarterly holdings of the sample of 2,979 equity funds over the period between 1980

and 2009. They measured the risk shifting behaviour of mutual funds by proposing a holdings

based measure to investigate the difference between the volatility of a fund’s current holdings

and its past realised volatility.

Results exhibited that funds that change risk tend to subsequently perform worse than

funds that maintained a stable risk level. Huang et al. (2011) described three reasons for risk

shifting. First, funds can alter risk levels by switching between equity holdings and cash

holdings. Second, based on equity holdings, fund managers can alter risk by changing their

exposure to systematic risk. Fund managers can switch between high beta stocks and low

beta stocks. Third, funds can alter risk by changing their exposure to certain industries or by

deviating from their benchmarks. Based on these reasons, Huang et al. (2011) reported that

inferior performance of funds are mostly caused by fund increasing idiosyncratic risk

exposure whereas funds that alter their risk between equity and cash holdings and between

systematic risk levels did not exhibit much reductions in fund performance. In addition, risk

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shifting can be costly for active mutual funds. Therefore, risk shifting does not necessarily

apply that skilled fund managers are taking advantage of changing investment opportunities.

Instead, risk shifting is more likely to be a signal of ill motivated trades either from inferior

ability of fund managers or agency issues.

2.4.12 Successful Market Timing Abilities

Kacperczyk, Nieuwerburgh and Veldkamp (2014) examined fund manager skills and

developed measures of market timing and stock picking. Similar to Chang and Lewellen

(1984) and Chen and Stockum (1986), they evaluated both market timing and stock selection

abilities simultaneously. Kacperczyk et al. (2014) proposed a new definition of fund

manager’s skill as the rational ability to pick stocks or time the market.

Past researchers find little market timing evidence as it is typically exhibited only in

recession periods. Therefore, unlike previous studies that isolate stock picking and market

timing abilities unconditional to the state of the economy, Kacperczyk et al. (2014) evaluated

market timing and stock selection abilities with regards to the changing of economic

conditions, taking into consideration for both booms and recession periods. They consider the

fact that the type of skills a fund manager exhibits might alter in accordance to the state of the

business cycles.

By conditioning the state of the economy, Kacperczyk et al. (2014) found surprising

results that managers have performed in both stock picking and market timing abilities. Those

who are stock picking during boom periods are also good at market timing during recessions.

Therefore, Kacperczyk et al. (2014) developed a new real time measure to detect a fund

manager’s skill where more weightage is given to a fund manager’s market timing success

during recession period and stock picking success during bloom period. This new measure

demonstrates persistence of up to one year and forecasts performance.

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In order to determine the skills of fund managers, Kacperczyk et al. (2014)

constructed estimates of stock picking and market timing for each firm to determine if these

skills differ significantly over the business cycle. The sample is built upon several data sets

giving a final sample of 3,477 distinct mutual funds monthly holdings between the periods

from 1980 to 2001. Kacperczyk et al. (2014) tested for stock picking abilities in the top 25%

of funds in expansion periods and tested for market timing abilities on the same 25% of funds

in recession periods and found significant stock picking and market timing abilities. They

also selected top 25% of funds in terms of their market timing abilities during recession

periods and showed that the same 25% of funds had significant stock picking abilities in

boom periods too.

This study showed that managers readjust their skills as circumstances change,

changing the nature of activities depending on the business cycle. There were also evidence

that on average, the same fund managers are able to stock pick in boom period and market

timing in recession as well as pick stocks well in expansions and also time the market well in

recessions. These results suggest a new way to measure a manager’s ability by giving more

weightage of a fund’s market timing in recessions and giving more weightage of a fund’s

stock picking in booms. This new method displays more persistence than individually testing

either market timing or stock picking individually. These fund managers have also

outperformed passive benchmarking.

2.5 Overview of Contrarian Strategies

Contrarian strategies go against market trends by purchasing assets that perform

poorly in the past (prior losers) and sell assets that had performed well (prior winners) (Lo

and MacKinlay, 1990). Lo and Mackinlay (1990) reported that profitability of contrarian

strategies are influence by the overreacting market as it is a strategy that takes advantage of

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the negative serial dependence in assets returns. A market overreacting is a situation whereby

investors overreact and drive up the prices of winners but eventually these winners became

losers. Likewise, investors drive down the pricing of loser by overreacting to the market but

eventually these losers became winners.

When “losers” are purchased and “winners” are sold, this will result in positive

expected profits as investors believed largely in a negative correlation that current winners

are likely to become future losers and current losers are likely to be future winners. Lo and

Mackinlay (1990) reported that over a long period, stocks tend to move in the same direction

but their speed may vary. An example would be the possibility that one stock could move in

an upwards direction while another stock could move in a downward direction during a

particular time frame. As a contrarian trader, he or she would sell the stock that moved in an

upwards direction and purchase the stock that moved in a downwards direction. If both stocks

return back to their mean, the contrarian would be able to profit from this action. Typically,

contrarian traders show signs of overconfidence and risk seeking behaviours (Menkhoff and

Schmidt, 2005).

Lo and Mackinlay (1990) examined if the profitability of contrarian investment

strategies can only arise due to a stock market overreacting. However, they concluded that an

overreacting market is the not the only source where a contrarian trader can profit. Contrarian

profits are also realised when some stocks are faster in reacting to information compared to

other stocks, or when the returns of some stocks lead the returns of others. An example given

by Lo and Mackinlay (1990) would be that if the price change of stock A leads to the price

change of stock B, a contrarian strategy may profit from subsequently buying stock B if stock

A increase and selling stock B when there is a decline in stock A. Lo and Mackinlay (1990)

concluded that a contrarian strategy profit does not only happen when a stock market

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overreacts and there is a possibility that both over and under reaction might lead to

profitability.

2.5.1 Identifying Contrarian Strategies in Mutual Fund Trades

Cullen, Gasbarro, Zumwalt and Monroe (2009) used mutual fund holdings and their

associated trading activities to examine if mutual funds rebalanced their portfolio towards a

contrarian strategy. Actual trading activities of mutual funds can result in a change of mutual

fund’s risk level which will change their expected returns. Cullen et al. (2009) also examined

if the performance of a mutual fund that is following a contrarian strategy is differentially

affected by risk changes.

Using a regression analysis on actual mutual fund trades, they were able to identify

mangers which adopted the contrarian trading strategy. Their performance was examined

using simple excess returns and contrarian trades were found on average to achieve abnormal

returns. They used 2,829 funds quarterly stock holdings from the period between 1991 and

2005.

Results reflected that excess returns were present when they are aware of the risk of

the stocks they select and reflected that 15% of the funds demonstrated contrarian trading

behaviour. Mutual funds that titled towards contrarian strategy and purchase high risk stocks

did not improve in their performance. But mutual funds that titled towards contrarian strategy

and purchase wining and low risk stocks enhance their performance. Cullen et al. (2009)

concluded that contrarian strategies will benefit by buying high risk stocks and selling low

risk stocks.

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2.6 Conclusion of Literature Review and Motivation of Present Study

Contemporary research tend to focus on stock holdings of mutual funds to assess the

performance of mutual funds rather than trades of these funds. Although, this approach

avoids criticisms on the appropriate benchmark selection it introduces problems associated

with holding periods, stock holdings and stock trading.

This research takes on a different approach to examine the market timing abilities of

mutual funds trades to examine how they make technical adjustments according to different

market trends. Unfortunately, the selection of holding periods is hampered by data

availability. Although monthly holding periods are available, the predominant data are

available on a quarterly basis. Hence, the present data will be examined using this holding

period. Also, this approach is in the favour of a recently developed method that allows each

fund to be statistically identified with preferential trades associated with beta, sentiment beta

and contrarian tiling.

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CHAPTER 3

METHODOLOGY

3.1 Introduction

This chapter presents the dataset and the methodology for this study. We presume that

fund managers that possess market timing abilities will tilt their portfolio in accordance to the

anticipated market movement to generate superior returns. In the interest of determining if

our expectation is true, we require the holdings or the asset composition of mutual funds and

explore how these holdings change with respect to the anticipated market movements.

3.2 Overview of Methodology

Conducive to examining how these holdings change with respect to the market

movements, we require the statistically significant trades pursued by these funds. The

statistically significant trades enables us to study how mutual fund managers make careful

investment decisions to buy or sell their stocks during different anticipated market

movements. However, these trade movements may not necessarily occur due to forecasted

market movements but may occur randomly. Hence, we employ the method presented in

Cullen et al. (2015) with the associated results to identify statistically significant trades that

encompass beta, sentiment beta and momentum (contrarian) strategies.

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Besides identifying the respective trades, it is important to analyse if these trades have

occurred prior to contemporaneously or post the relevant market movement. To facilitate

answering this question, we will examine market movements as revealed by the selected

indices. They are the S&P 500 Market Index, Baker and Wurgler’s Sentiment Index and S&P

500 Momentum Index. By understanding the trading movements of these indices, we are able

to determine if these statistically significant trades and their respective indices are moving in

the same direction as the anticipated market. In order to exploit returns, mutual fund

managers will be tilting their portfolios accordingly to various market trends which will be

reflected by the index values. The figure below (Refer to 3.1) presents the overview of our

methodology.

Figure 3.1 Schematic Diagram: Overview of Methodology

The figure below illustrates the overview of our methodology. Trade betas that encompass beta,

sentiment beta and momentum are provided by Cullen et al. (2015). Quarterly data observations of

trade proportions are used for the analysis.

Indices

Trade Betas

(Proportions)

(1991-2012)


Market Beta


Sentiment Beta


Momentum

Systemic risk

measures

Market Trends

-Bull and Bear Markets

-Recession and Boom Periods

-Further break down of Bull and Bear Markets

with the consideration of Volatility

Quarterly

Correlated

Check with

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3.3 Data Description

We obtain the statistically significant trade betas of US equity mutual funds from the

data provided by Cullen et al. (2015) for the period between July 1991 and October 2012.

The sample contains 62,676 fund quarters and 86 quarters. The trading period is characterised

by different market trends such as the bull and bear markets and recessions and booms

periods. In addition, the bull and bear market trends have been discovered to have a further

breakdown of four distinct states and it will be discussed in section 3.3.3.

3.3.1 Bull and Bear Markets

Table 3.1 reports the length and date specifications for each of the five periods during

our trading period. There might be some subjectivity on the start and end dates of bull and

bear market periods due to various sources. The trading period of our study is between July

1991 and October 2012.

Table 3.1: Bull and Bear Market Durations throughout the Trading Period between July 1991

and October 2012

Bull/Bear Start Date End Date Duration (Months)

Bull July 1991 January 2000 102

Bear January 2000 October 2002 33

S&P500 Market Index

Baker & Wurgler’s Sentiment Index

S&P 500 Momentum Index

S&P 500 Quality Index

S&P 500 Growth Index

S&P 500 Low Volatility Index

S&P 500 High Beta Index

Convert Data

Daily

Monthly

Quarterly

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Bull October 2002 October 2007 62

Bear October 2007 March 2009 16

Bull March 2009 October 2012 42

Source: Logan (2014)

During our trading period, there were three bull market periods and two bear market

periods. The existence of these diametrically different markets allows us to examine our

conjecture.

Our research is based on the study of Logan (2014), the bull (bear) market is defined

as having a maximum (minimum) 20% rise (fall) in the measurement from the closing low

(high) of the previous bear (bull) market to the bull (bear) market’s closing high (low).

Another determinant of the bull (bear) market would be the index rising (falling) 20% off the

bear (bull) market low (high). Generally, bull markets last for a longer period compared to

the bear markets. However, bear markets have a more significant declines (Logan, 2014).

Logan (2014) reported that the bull market comes to an end when prices are no longer

increasing any further to surpass the current bull market high. In addition, the beginning of a

bear market is often hinted by the movements of traders as they would start shifting gear and

adjusting their trading strategies in tune with the bear markets.

In general, bear markets are often associated with recession periods (Logan, 2014).

The bear market that occurred between October 2007 and March 2009 was associated to the

drastic economic contraction. Logan (2014) reported that the recession period was so severe

that it was labelled as the Great Recession.

The bear market will come to an end when a long term trend reversal has taken place

as it indicates the beginning of a bull market. With the power of the bull market, the market

has the ability to revert back to a sustainable upward trend (Logan, 2014).

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3.3.2 Recession and Boom Periods

As defined by the National Bureau of Economic Research (NBER), a recession period

occurs when the economic activity has a significant decline across the economy. This decline

usually last for a long duration, usually more than a few months. It is significantly reflective

in the real GDP. In contrast, a boom period occurs when the economic activity has

substantially increased across the economy. The boom and recession periods that occurred

during our trading period is presented in the table below (Refer to Table 3.2).

Table 3.2: Recession and Boom Durations throughout the Trading Period between July 1991

and October 2012

Recession/Boom Start Date End Date Duration (Months)

Boom March 1991

March 2001 107

Recession

March 2001 November 2001 8

Boom

November 2001 December 2007 73

Recession December 2007 June 2009 18

Boom

July 2009 July 2012 35

Source: Amadeo (2016)

The business cycle is constructed by expansions and contractions in the economy. The

bull and bear market periods are highly correlated to the economy as a bear market is

typically accompanied by an economic recession. Based on our trading periods, we are able

to identify similar time periods in both market trends.

During our trading period, the first boom period had occurred between July 1991 and

March 2001 (Logan, 2014; Amadeo, 2016). As stated by Logan (2014), boom periods are

typically linked to the bull market period. The market was trending upwards before the crash

of the Dotcom bubble. The Dotcom bubble was a crisis that befell due to a drastic increased

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in the equity markets which were built up by investments in internet-based companies

(Investopedia, 2016). These markets eventually collapsed due to overconfidence and pure

speculation of investors and resulted in a recession that began in March 2001 and lasted till

November 2001 (Johnson and Karlsson, 2016; Amadeo, 2016). The September 11 attack was

also another contributing factor to the first bear market. This attack was a terrorist encounter

which led to market chaos due to panic selling (Investopedia, 2016).

Subsequent to the recession period, the second boom period began in November 2001

and lasted till December 2007 (Johnson and Karlsson, 2016). This boom period was linked to

the bull market that was falsely created by the initial profits of the subprime mortgage crisis

and the US housing bubble. As a result of the built up of the subprime mortgage crisis, the

collapse of US housing bubble and the global financial crisis (GFC) the market eventually

crashed leading to the next recession period which occurred between December 2007 and

June 2009 (Johnson and Karlsson, 2016; Investopedia, 2016). The subprime mortgage crisis

was the default of the sudden drastic increase in high risk mortgages which were packaged

with high interest rates. The subprime mortgage crisis was also related to the burst of the

housing bubble, where lenders offer home loans to individuals with low credit ratings. This

eventually started the global financial crisis where dozens of banks went bankrupt and it led

to huge losses in the economy (Investopedia, 2016).

The recovery of the global final crisis led to the current boom period which began in

June 2009 and it currently still ongoing (Johnson and Karlsson, 2016; Amadeo, 2016).

However for our analysis, we consider the last boom period to be between June 2009 and

October 2012.

3.3.3 Four States of Bull and Bear Markets

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Past methodologies have identified business cycles into two distinct states, the bull

and bear markets. The bull market is a state where on average, the stock returns are higher. In

contrast, the bear market is a state where on average the stock returns are on lower.

Jiang and Fang (2015) suggested two other states in the business cycles. Besides

focusing on the average number of stock returns, the volatility factor in stock returns also

plays a key role in identifying states in the business cycles as stock returns have displayed

different characteristics in the volatility. Jiang and Fang (2015) used the Markov switching

model to identify all possible states in the business cycles which do not only consider the

mean in stock returns but also the volatility factor in the US stock market. This model allows

flexibility for measuring changes in the mean and volatility of stock returns and it is capable

of categorising states that defines high volatility and low volatility (Jiang and Fang, 2015).

Additionally, it determines the optimal number of states in the stock market by comparing

models with various number of states (Jiang and Fang, 2015). The data used for identifying

states in the business cycle was the S&P 500 stock returns.

From the results, four different states had been established. According to Jiang and

Fang (2015) the first state reflects that has very low average return and high volatility and

thus termed as the “extreme bear market” in the US stock market. The cause of this state is

highly related to stock market crashes. Based on our trading period (April 1991 to July 2012),

the “extreme bear market” had occurred during the global financial crisis between December

2007 and June 2009 (Investopedia, 2016).

The second state indicates a state with on average, negative returns and it is known as

the “general bear market” in the US stock market (Jiang and Fang, 2015). According to our

trading periods, the general bear market had occurred during the Dotcom bubble between

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March 2001 and November 2001, which subsequently took place during the subprime crisis

between December 2007 and June 2009 (Investopedia, 2016).

As specified by Jiang and Fang (2015), the third and fourth state reveals states with on

average, high returns in which they are associated to the bull market. However these states

varies in the volatility factors as state three has a higher level of risk amount compared to

state four (Jiang and Fang, 2015). State three is titled as “the volatile bull market” whereas

state four is termed as the “steady bull market” (Jiang and Fang, 2015). Observing our trading

period, these states had occurred prior to the Dotcom bubble burst, during the built up of the

global financial crisis and the aftermath of the global financial crisis (Investopedia, 2016).

Jiang and Fang (2015) has enabled us to have a more precise classification of the bull and

bear market.

3.4 Trades

We have provided a brief exposition of the method presented by Cullen et al. (2015)

to identify trades that encompass beta, sentiment beta and momentum (contrarian) trading

strategies but recommend the Cullen et al. (2015) paper and Cullen, Gasbarro, Monroe and

Zumwalt (2009) for a more complete explanation. To facilitate the intuition of the method we

present the formula used to identify such trades in the subsequent sections.

3.4.1 Identifying Market Timing Trades

Cullen et al. (2015) calculated the market betas of each stock held by mutual funds

using their stock returns. The market betas are used to rank the stocks held by each mutual

funds. For each quarter, the beta ranked stocks are allocated to twenty equal value buckets

and the weighted average of each bucket is calculated. For the regression, the dependent

variable is the values of stocks in each bucket in a fund’s portfolio that are traded during a

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quarter and the independent variable are the buckets’ betas. If trades are identified to be

related to the betas, they will exhibit positive (buy) or negative (sell) coefficient values.

3.4.1.1 Formula for Identifying Market Timing Trades

The equation below (Refer to the next page) is used to identify market timing trades.

The trade value is equivalent to the value of stocks in each bucket in a fund’s portfolio that

are traded during a quarter. Using the trade value we are able to identify the beta coefficients

of the bucket, Eq. (1):

𝑇𝑟𝑎𝑑𝑒𝑉𝑎𝑙𝑢𝑒𝑗 = 𝛼 + 𝛽𝐵𝑢𝑐𝑘𝑒𝑡_𝐵𝑒𝑡𝑎𝑗 + 𝜀𝑗, (1)

where,

𝑇𝑟𝑎𝑑𝑒𝑣𝑎𝑙𝑢𝑒𝑗 ≡ ∑ 𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖𝑡𝑟𝑎𝑑𝑒𝑑;

𝑛

𝑡=1

𝐵𝑢𝑐𝑘𝑒𝑡𝐵𝑒𝑡𝑎𝑗≡ ∑(𝐵𝑒𝑡𝑎𝑖

𝑛

𝑡=1

×𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖ℎ𝑒𝑙𝑑

∑ 𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖ℎ𝑒𝑙𝑑𝑛𝑖=1

);

𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖𝑡𝑟𝑎𝑑𝑒𝑑 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 𝑡𝑟𝑎𝑑𝑒𝑑 𝑑𝑢𝑟𝑖𝑛𝑔 𝑞𝑢𝑎𝑟𝑡𝑒𝑟 𝑡;

𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖ℎ𝑒𝑙𝑑 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 ℎ𝑒𝑙𝑑 𝑎𝑡 𝑡ℎ𝑒 𝑠𝑡𝑎𝑟𝑡 𝑜𝑓 𝑞𝑢𝑎𝑟𝑡𝑒𝑟 𝑡;

𝐵𝑒𝑡𝑎𝑖 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝐵𝑒𝑡𝑎 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 𝑖𝑛 𝑞𝑢𝑎𝑟𝑡𝑒𝑟 𝑡 + 1; 𝑎𝑛𝑑

𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘𝑠 𝑖𝑛 𝑏𝑢𝑐𝑘𝑒𝑡 𝑗.

3.4.2 Identifying Sentiment Beta timing Trades

The same method is used to identify sentiment beta trades. However, instead of

calculating market betas, sentiment betas are calculated. If trades are identified to be related

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to the sentiment betas, they will exhibit positive or negative coefficient values. Stocks that

exhibit positive sentiment betas are related to high sentiment and stocks that exhibit negative

sentiment betas are related to low sentiment.

3.4.3 Identifying Momentum (Contrarian) Trades

Unlike identifying market beta and sentiment beta that require market or sentiment

betas of each stock held by mutual funds using stock returns, identifying momentum

(contrarian) trades require the excess returns of each stock held by a fund over the quarter

prior to the start of each trading period, Eq.(2):

𝐵𝑢𝑐𝑘𝑒𝑡𝐵𝑒𝑡𝑎𝑗≡ ∑(𝑆𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑜𝑟 𝑝𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒𝑖

𝑛

𝑡=1

×𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖ℎ𝑒𝑙𝑑

∑ 𝑉𝑎𝑙𝑢𝑒𝑠𝑡𝑜𝑐𝑘𝑖ℎ𝑒𝑙𝑑𝑛𝑖=1

); (2)

Excess returns are calculated by subtracting the value weighted market return from

the stock return. These returns are ranked and assigned to each fund’ stocks to “prior

performance buckets”. A regression analysis is conducted to determine the trading strategy

for each fund and to test the association between the proportions traded and stock prior

performance. A significant positive (negative) coefficient would reflect that the fund has

made momentum (contrarian) trades.

Momentum traders follow a strategy where they believe that when an investor’s

sentiment is low, the market is going towards a downwards trend. Momentum strategies

believes in the persistence of performance in securities and rebalance their portfolios towards

superior performing stocks. In contrast, contrarian traders follow a strategy whereby they

believe that when an investor’s sentiment is low, the market is going towards an upwards

trend and when an investor’s sentiment is high, the market is moving towards a declining

trend. They would rebalance their portfolio towards underperforming stocks. As such, these

traders buy low sentiment beta stocks when an investor’s sentiment is high and buy high

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sentiment beta stocks when an investor’s sentiment is low. These traders believe in market

reversal and they are betting against the current market trend (Investopedia, 2016).

3.5 Importance of Indices

Having the ability to predict certain market trends may be advantageous to the mutual

fund managers to gain profits and adjust their portfolio strategies in their favour. Logan

(2014) revealed that as the market environment is greatly influenced by individual stocks,

stocks tend to move in the same direction as the index. Hence, by monitoring the broad

market movements this allows us to predict and determine the direction and the strength of

these market trends. We examine if fund managers made technical adjustments to their

portfolios in accordance to different market trends.

Based on our literature review, several indices were selected to explore if these trades

that are associated to beta, sentiment beta and contrarian tilting are correlated to certain

indices. Having monitor the value changes in the indices, we are able to analyse their changes

in accordance to the different market trends. This helps us to see if our trade betas have

similar trading activities as the indices.

There are different indices to represent different sections of the market. These indices

reflects changes in their value and we are able to examine if their increase and decrease in

values are correlated to certain market trends. (Logan, 2014). Having examine a wide range

of indices gives us a thorough, robust and non-biased examination. It is also very important to

select indices which are potential market trend predictors. This research is concentrated on

the US stock market as such the choices of indices that we have selected are the S&P500

Market Index, the Baker and Wurgler’s Sentiment Index, the S&P 500 Momentum Index

(Contrarian Index), the S&P500 Quality Index, the S&P500 Growth Index and the S&P500

Low Volatility Index, S&P High Beta Index.

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Besides focusing on the selected market indices, we consider an article by Giglio,

Kelly and Pruitt (2016) that investigated how systemic risk and the financial markets affects

the economy. Systemic risk increases the risk in the real economy, by analysing measures of

systemic risk it can also be useful in predicting market trends. Giglio et al. (2016) examined

19 different measures of systematic risk and constructed a systemic risk index which was

successful in predicting future macroeconomic shocks.

3.5.1 Description of Indices

In general, most of our indices are selected from Standard and Poor (S&P) index

provider as it is globally recognised for its various benchmark indices.

3.5.1.1 The S&P 500 Index

The S&P 500 index is an indicator of the US stock market. It contains 500 of the

largest stocks in the US and it is regarded as the most reliable estimation of large-cap US

equities. It measures the performance of the overall market and it is a good benchmark for

determining the overall health of the US stock market. This index is important for our

research as we are studying trades that encompass market betas (Standard & Poor’s, 2016).

3.5.1.2 The Baker and Wurgler’s Sentiment Index

The Baker and Wurgler’s Sentiment index is a reflector of an investor’s sentiment

which is built on an investor’s sentiment survey (Bormann, 2013). Sentiment index is the

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belief of investors about the future cash flows and risk of investment but it is not verified by

any facts. As an investor sentiment cannot be directly measured, it is considered by various

factors. These factors are the investors’ surveys, investors’ mood and retail investor trades.

Also, mutual fund flows, trading volumes, dividend premiums and macroeconomic

conditions. (Baker and Wurgler, 2007).

As sentiment reveals the strategies of market participants, it is an important concept in

market analysis. When a sentiment value increases too quickly, it is often viewed as a

contrary signal and this can help to identify potential market trends reversal. Typically,

market participants have the tendency to be excessively bullish at a market top and

exceedingly bearish at a market bottom (Logan, 2014).

3.5.1.3 The S&P 500 Momentum Index

The S&P 500 index is developed to measure the performance of securities in the S&P

500 universe that exhibit persistence in their relative performance (Standard & Poor’s, 2016).

Chen and Vincent (2016) revealed that the use of momentum predictors and

investment sentiment predictors are very important for evaluating an investor’s extreme

optimism and pessimism in forecasting the bear stock market. The investor sentiment index is

an important tool as it is a contrarian indicator for the bear and bull stock market (Chen and

Vincent 2016). Using a single predictor model, Chen and Vincent found that momentum

variables have produced substantial predictive coefficients. This reflects that investor may be

following a strategy whereby a bull (bear) market follows a high (low) value of the previous

market trend.

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With the combination of market momentum, investor sentiment and economic

fundamentals such as the money supply, investors are more capable in achieving abnormal

returns. The market momentum index serves as a trend following indicator whereas the

investor sentiment index serves as a contrarian indicator (Chen and Vincent 2016).

3.5.1.4 The S&P 500 Quality Index

The S&P500 Quality index is an indicator of all high quality stocks and we used it to

monitor the stocks by their quality score. The quality score is tabulated based on return on

equity, accruals ratio and financial leverage ratio (Standard & Poor’s, 2016).

3.5.1.5 The S&P 500 Growth Index

The S&P Growth Index measures growth stocks. It is a good reflection of all growth

stocks based on three factors: sales growth, the ratio of earning change to price and

momentum. As growth stocks are measured based on momentum, this may be useful for

identifying market trends in our contrarian trade betas (Standard & Poor’s, 2016).

3.5.1.6 The S&P 500 Low Volatility Index

The S&P Low Volatility index is constructed to measure the performance of the least

volatile stocks amongst their respective benchmark index (Standard & Poor’s, 2016).

3.5.1.7 S&P 500 High Beta Index

The S&P 500 High Beta index measures the performance of 100 constituents in the

S&P 500 that are most sensitive to deviations in market returns. This index is designed for

investors that are creating a directional bet on current markets or commencing a bullish

strategy (Standard & Poor’s, 2016).

3.5.2 Systemic Risk Measures

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Quarterly Trades

Besides monitoring the market with the use of indices, a recent paper by Giglio, Kelly

and Pruitt (2016) analysed how the built up of systemic risk in the financial system affects the

real economic activity. Giglio et al. (2016) proposed using systematic risk measures to help

with the prediction of recession periods and developed a systemic risk index to signal future

macroeconomic shocks. Adrian and Brunnermeier (2011) stated that by monitoring the

increase in systemic risk, this can help to capture the potential spreading of financial distress

across institutions.

During a financial down turn, financial institutions have huge losses and this threatens

the entire financial system. This situation results in the rise of systemic risk which can impair

the financial system and create issues with the credit supply to the real economy.

As defined by Investopedia (2016), systemic risk is the likelihood that an event at the

company level could initiate severe instability or lead to the failure of the whole industry and

the economy. Systemic risk has made a huge contribution to the recent global financial crisis

which occurred from 2007 to 2009. For instance, an event at the company level would be

financial institutions like banks which are very large relative to their respective industries and

they represent a huge part of the economy. A good example would be the collapse of the

Lehman Brothers which generated problems for the financial system and eventually the

economy (Investopedia, 2016). By drawing the attention on these events, many hope that it

would serve as an early warning sign for future financial crisis based on their systemic risk

fluctuations.

Giglio et al. (2016) examined 19 proposed measures of systemic risk in the US. First,

they examined each individual risk measure to understand how much information capacity it

can provide about future macroeconomic shocks. Next, they considered the combination of

all measures to form a systematic risk index to enhance its forecasting power.

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Quarterly Trades

3.5.2.1 Brief Description of Systemic Risk Measures (19 Elements)

The Absorption ratio is useful in detecting market changes in the US stock market as

drawdowns are reflected by spikes in the absorption ratio. A high absorption ratio indicates

that the financial market is moderately compressed. This signifies that the market is more

crumbly as shocks spread quickly and broadly. A low absorption ratio indicates that the

market is less compacted and this implies that it is less vulnerable to shocks. The Delta

Absorption Ratio captures shifts in short-term absorption ratio relative to long-term

absorption ratio. The Delta Absorption Ratio also serves as an early signal of asset

depreciation and financial turbulence (Kritzman et al., 2010).

AIM is a measurement of systemic risk as it captures a weighted average of the stock

level illiquidity (Amihud, 2002). Chen, Chou and Yen (2015) reported that the illiquidity

measure proposed by Amihud (2002) had been successful in predicting recessions. Based on

NBER, recession periods have proven that liquidity tends to fall prior to recession and rises

after a recession period ends.

CoVar and ∆CoVar is the value at risk (VaR) of the whole financial system

conditional on institution that are in distress. ∆ CoVar is the difference between CoVar

conditional on distress of an institution and the CoVar condition on the normal state of the

institution. ∆ CoVar captures the marginal contribution of a specific institution to the overall

systematic risk. This measure allows us to gauge the risk spill overs from institutions to

institutions across the financial system (Adrian and Brunnermeier, 2011).

Acharya, Pedersen, Philippon and Richardson (2010) proposed the risk measurement,

MES which captures the shock exposure of each individual firm as compared to the total

system. Brownlees and Engle (2011) proposed MES-BE which employed dynamic volatility

models to estimate the components of MES.

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Quarterly Trades

CATFIN developed by Allen, Bali and Tang (2012) is a measurement of systematic

risk focusing on the increase in the collective level of bank risk exposure as it is significantly

useful in detecting economic declines. Having a high level of CATFIN indicates the

prediction of a decline in bank lending activities and it is correlated to the state of health of

banks, CDS spreads and financial ratio. Having a decline in bank lending activities is a good

signal that a recession period is approaching.

Giglio et al. (2016) proposed using Book Leverage and Market Leverage ratios. Book

Leverage is the ratio of debts over assets and Market Leverage is the ratio of debt over

market equity. These ratios are capable in capturing potential instability and shocks when

large intermediaries have more debt than equity.

Billio et al. (2012) proposed the Dynamic Causality Index (DCI) as this index aims to

determine the degree of how much a set of financial institutions are connected. Diebold and

Yilmaz (2009) proposed the international spill over measure. They have formulated and

examined precise measures of return spill overs and volatility spill overs. Giglio et al. (2016)

also constructed the volatility index which measures the volatility of financial institutions

which are computed by measuring the within-month standard deviation of daily returns.

Additionally, Giglio et al. (2016) proposed the size concentration index which captures

potential instability due to the threat of default of the largest firms.

Kritzman and Li (2010) considered Turbulence as a factor of measuring systemic risk

as financial turbulence is a situation where the asset prices are behaving differently compared

to their historical behaviour and extreme price movements are reflected. The TED Spread is

the difference between three-month LIBOR and three-month T-bill interest rates. Default

Yield Spread is the difference between yields on BAA and AAA corporate bonds.

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Gilchrist and Zakrajsek (2012) proposed the GZ spread which is another measure of

credit spread created from individual unsecured corporate bonds, where the yield of each

bond is compared to the yield of a synthetic treasury bond with the same cash flows to obtain

an exact degree of its credit spread. The individual credit spreads are then averaged across all

maturities and all firms to obtain an index, GZ.

Finally, Giglio et al. (2016) accumulated all of the information of the systematic

measures with a factor model for the conditional quantiles of macroeconomic activity. There

were two ways of incorporating all the information of the systemic risk measures. First, using

the principal components quantile regression (PCQR), this two-step procedure first removes

principal components from the panel of systemic risk measures then uses these factors in a

predictive quantile regression. Second, using a partial quantile regression (PQR) which is an

adaption of the partial least squares to the quantile setting. However the PQR model is

preferred as it is a more accurate at predicting macroeconomic shocks.

3.6 Sources of Data and Availability

Due to a limited time frame, we were unable to get a complete range of data for

certain indices that met the requirements of our trading period. The table below (Refer to

Table 3.3) summarises our data collection.

Table 3.3 Data Sources, Availability and Types of Data

Index Source Data availability Daily/Monthly Data

S&P 500 Market

Index

Yahoo Finance 01/07/1991-

01/10/2012

Monthly

Baker and Wurgler’s

Sentiment Index

Jeffrey Wurgler’s

website

01/07/1991-

01/10/2012

Monthly

S&P 500 Low

Volatility Index

S&P Website 01/09/2006-

1/10/2012

Daily

S&P 500 Quality S&P Website 01/09/2006- Daily

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Index 1/10/2012

S&P 500 Growth

Index

S&P Website 01/09/2006-

1/10/2012

Daily

S&P 500

Momentum Index

S&P Website 01/09/2006-

1/10/2012

Daily

S&P 500 High Beta

Index

S&P Website 01/09/2006-

1/10/2012

Daily

Systemic risk

measures (Giglio et

al.,2016)

Sethpruitt Website* 01/07/1991-

01/10/2012

Monthly

* Data can be download from www. Sethpruitt.net/GKPwebdata.zip.

3.7 Trades’ Correlation with Indices

We determine if the trades that encompass beta, sentiment beta and momentum

(contrarian) are correlated to the final selection of indicators. Using the software “Statistical

Packages for the Social Sciences” (SPSS), we develop a correlation matrix to understand if

the trades have a significantly positive correlation to their respective indices. We expect these

statistically significant trades to be moving in the same directions as their respective indices

during various market trends. In addition, a simple regression analysis was conducted to

evaluate if these statistically significant trades can be explained by the movements of their

related indices.

As the statistically significant trade betas are in the form of quarterly data

observations, it is necessary to convert all daily or monthly data of the indices into quarterly

data observations. The respective dates of the quarters in a year are as follows: 1st of January,

1st of April, 1st of July and lastly 1st of October.

3.8 Conclusion of Methodology

We believe that mutual fund managers with market timing abilities will tilt their

portfolio accordingly to the anticipated market movements in hopes of generating abnormal

returns. These market movements are caused by various market trends which influence the

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market to be either trending upwards or downwards. We examine the trades of mutual funds

that encompass beta, sentiment beta and momentum to understand their trading movements.

However, these trading movements may occur out of pure randomness. In order to

determine if they are purchased and sold in the direction of the anticipated market movements

by mutual fund managers with market timing abilities, we address this issue with the help of

the relevant indices. These indices offered assistance in exploring the trading movements of

mutual funds as we would like to examine if these trades are moving in the same direction as

the indices during various market trends.

Studying how mutual funds trade in the anticipation of various market trends enable

us to have a better understanding of market timing abilities. Ultimately, investors seek to

have additional returns on top of their expected returns. If these trades have a significant

positive correlation with their respective indices, it can be concluded these trades are adjusted

in accordance to the overall market. The next chapter presents the results of the correlation

matrix and regression analysis.

CHAPTER 4

RESULTS AND DISCUSSION

4.1 Introduction

This chapter shows the analyses and results of our test. We conducted some

correlation and regression analyses between the statistically significant trades, the market and

systemic risk indicators. Trade proportions were used for the analysis as proportions provide

insights on the direction that the fund manager was pursuing. First, we run an overall

correlation and regression analysis without any specifications to get a general idea of the

relationship between these trade proportions and their respective indicators. Second, we

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consider how bullish and bearish trends affects the adjustments of trade proportions. Third,

we examine if quarters with higher proportions of positive (negative) trade proportions

suggest a bullish (bearish) market. We find that the most number of significant results were

exhibited from the sentiment and momentum trade proportions. However, both sentiment

beta and momentum trade proportions exhibited an inverse relationship with their respective

indicators.

4.2 Overview of Results and Discussion

The focal point of our research is to examine if mutual fund managers possess market

timing abilities. Fund managers with successful market timing abilities can take advantage of

the market by adjust their portfolios in accordance to the anticipated market trend to exploit

returns. Common market trends are the bull and bear market trends and the recession and

boom market trends. In general, bear market periods are highly correlated to recession

periods (Logan, 2014). We observed similar periods between the bull and boom market

trends as well as the bear and recession market trends. Therefore, for analysis purpose, we

will be focusing on the bull and bear market trends. During a bull market, mutual fund

managers can take advantage of the market by tilting their portfolios towards positive trade

proportions. On the contrary, mutual fund managers can take advantage of the market by

tilting their portfolios towards negative trade proportions when bearish markets are

anticipated.

4.2.1 Market Indicators

Market indicators also known as market indices are important as they represent the

overall performance of the market thus tracking changes in the market over time. An index is

the total value produced by the combination of several stocks or investment vehicles. It is

expressed against a base value from a specific date. Indices are often used as benchmarks for

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investors to gauge the state of the economy and achieve an overall perspective of the bull and

bear market periods. Two common indices are the S&P 500 Market Index and the Baker and

Wurgler’s Sentiment Index. The S&P 500 Market Index is an index of 500 stocks reflecting

the performance of US equities. The Baker and Wurgler’s Sentiment Index reveals the

strategies of market participants. This index is based on the beliefs of investors about future

cash flows and the risk of an investment. A sudden spike in sentiment values is often viewed

as contrary signal of market trend reversals.

4.2.2 Systemic Risk Indicators

Systemic risk indicators also known as systemic risk measures have been developed

to serve as a warning signal for upcoming recession periods. Systemic risk is the risk that an

event at the company level could cause the entire economy to collapse. It was a major

contributor of the global financial crisis that occurred in 2008. When there is an accumulation

of systemic risk in the financial division, this intensifies the risk in the economy (Giglio,

Kelly and Pruitt, 2016). Such increases are correlated to the increases in the left tail of the

economic activities.

Market and systemic risk indicators are important for our study as they reflect the

overall performance of the market and economy. We require these indicators to examine the

market timing abilities of the statistically significant trade proportions that encompass beta,

sentiment beta and momentum. During bull market period, the values of stocks and

investment vehicles are high, this contributes to an increase in the total index value. We

expect mutual fund managers to tilt their portfolios towards positive trade proportions to take

advantage of the bull market. On the contrary, during a bear market period, the values of

stocks and investment vehicles are low, this contributes to a decrease in the total index value.

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We expect mutual fund managers to tilt their portfolios towards negative trade proportions to

take advantage of the bear market.

4.2.3 Overview of Analysis (Schematic Diagram)

Figure 4.1 provides a schematic diagram of how the analysis will proceed. As can be

observed, statistically identified trades will be examined in relation to market indicators and

systemic risk indicators. Notably trades pursued by fund managers will be examined from the

perspective of portfolio tilts based on beta, sentiment beta and momentum.

Figure 4.1: Trades, Market Indicators and Systemic Risk Indicators

The figure below illustrates the overall process of our research analysis. There are two different types of indicators used to

examine the market timing abilities of mutual fund managers based on the statistically significant trades: 1) Market

indicators 2) Systemic Risk indicators. Market indicators are indices that represent the overall performance of the US stock

market. Systemic risk indicators gauge the overall performance of the economy. *Indicators that are directly related to

the statistically significant trades that encompass beta, sentiment beta and momentum.

Trades

Market Indicators

Systemic Risk Indicators

*Market Index

Absorption Ratio

*Market “Return”

Delta Absorption Ratio

*Sentiment Index AIM

*Sentiment “Return”

CoVar

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*Momentum Index Delta CoVar

*Momentum “Return”

CATFIN

Low Volatility Index

Market Leverage

Quality Index

Book Leverage

Growth Index

Real Volatility

High Beta Index

Turbulence

PQR

Note: Brief Description of Systemic Risk Indicators-Absorption Ratio/Delta Absorption Ratio: Useful in detecting market

changes in the US Stock Market; AIM: Measures illiquidity which is useful for predicting recessions; CoVar/ Delta CoVar:

Value at risk of the whole financial system conditional on institutions that are in distress; CATFIN: Measures increase in the

level of bank risk exposure, useful for detecting economic declines; Book Leverage/Market Leverage: Capable in capturing

potential instability and shocks ;Real Volatility: Volatility of financial institutions; Turbulence: Reflects situations where

asset prices are behaving differently relative to their historical behaviour (extreme price movements); PQR(Partial Quantile Regression): Measures macroeconomic activity and gives strong forecasting power of shocks.

4.3 Fund Quarters, Significant Fund Quarters and Proportions

Table 4.1 presents the number of fund quarters, significant fund quarters and the

percentage of significant positive and negative trade proportions. Our sample contains 62,676

fund quarters and 86 quarters. Panel A presents the number of fund quarters between 1991

and 2001. Panel B presents the total number of statistically significantly positive and negative

beta, sentiment beta and momentum fund quarters in both values and percentages. Panel C

presents the proportions of statistically positive fund quarters (negative proportions equals

one minus positive proportions). Referring to Table 4.1, columns that are highlighted in blue

are bullish market periods and columns that are not highlighted are bearish periods.

There were three bull and two bear market periods between 1991 and 2012.

Unavoidably as bear market periods are highly correlated to recession periods, there were

also three boom periods and two recession periods. Between our trading periods, we observed

more bullish market periods therefore emphasis is given to the positive trade proportions of

the statistically significant mutual funds as we expect a higher proportion of positive trades.

During bullish periods, mutual fund managers can take advantage of the market by tilting

their portfolios towards positive trade proportions.

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To assist with the examination of market timing abilities, correlation and regression

tests will be conducted using the trade proportions of the statistically significant trades. Trade

beta proportions provide some insights on the behaviour of the mutual fund managers.

Quarters with a higher proportions of positive trades suggest a bullish market. In contrast,

quarters with a higher proportions of negative trades suggest a bearish market. Trade

proportions are calculated by dividing the number of positive trades over the total number of

positive and negative trades per quarter.

We observe from Panel A of Table 4.1 that fund quarters have substantially increased

over the years. Consistent to our expectations, as presented in Panel B of Table 4.1, there

were a higher number of significant positive beta and sentiment beta fund quarters exhibited

in each period. In contrast, we observe a higher number of significant negative momentum

fund quarters in each period. Similar to Panel B, Panel C of Table 4.1 exhibited a higher

proportion of statistically significant positive beta and sentiment beta fund quarters.

However, we observe a higher proportion of statistically significant negative momentum fund

quarters. Based on these observations, it is plausible that the mutual fund managers may have

chosen to pursue a contrarian strategy. Although we presumed that during bearish market

periods, there would be a higher proportion of negative fund quarters, we observe no

significant changes in the proportions of fund quarters between bullish and bearish periods.

86

Tryphena Ow, An Examination of the Market Timing Ability of Mutual Funds using Quarterly Trades

Table 4.1. Trades- Number of Fund Quarters, Significant Fund Quarters and Proportions

The number of observations of significant, non-significant fund quarters and proportions are provided below. We obtained the trade betas of US equity mutual funds from the data provided by

Cullen et al. (2015) for the period between June 1991 and September 2012. These fund quarters encompass beta, sentiment beta and momentum strategies and they are based on quarterly

data observations. Panel A presents the total number of fund quarters, Panel B presents the number of statistically significant positive and negative fund quarters and Panel C presents the

proportions of statistically significant positive fund quarters (one minus positive proportions equals negative proportions). The total number of fund quarters equals 62,676. Highlighted in

blue: Bull Market periods. Not highlighted: Bear Market Periods. Bear market periods are highly associated to Recession Periods.

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 1991-

2012

Panel A. Fund quarters

Total Fund Quarts 803 1,134 1,178 920 844 857 1,111 1,584 1,858 2,755 2,410 2,732 2,731 2,636 4,880 5,864 5,271 3,903 4,920 3,480 5,990 4,815 62,676

Panel B. Significant Fund quarters

Beta 13,836

Positive (Value) 119 145 112 91 86 65 118 177 281 521 415 388 387 316 464 584 445 365 1073 498 649 598 7,895

(%) 14.8 12.8 9.5 9.9 10.2 7.6 10.6 11.2 15.1 18.9 17.2 14.2 14.2 12.0 9.5 10.0 8.4 9.4 21.8 14.3 10.8 12.4 12.6

Negative (Value) 61 128 93 73 75 54 100 174 128 348 289 341 273 245 357 440 378 404 515 308 686 471 5,941

(%) 7.6 11.3 7.9 7.9 8.9 6.3 9.0 11.0 6.9 12.6 12.0 12.5 10.0 9.3 7.3 7.5 7.2 10.4 10.5 8.9 11.5 9.8 9.5

Sentiment Beta 10,810

Positive (Value) 117 158 146 98 64 94 171 202 259 529 440 395 364 316 515 599 429 335 679 237 159 6,306

(%) 14.6 13.9 12.4 10.7 7.6 11.0 15.4 12.8 13.9 19.2 18.3 14.5 13.3 12.0 10.6 10.2 8.1 8.6 13.8 6.8 2.7 10.1

Negative (Value) 55 123 103 70 104 84 97 125 171 403 274 356 258 241 328 417 376 341 324 183 71 4,504

(%) 6.8 10.8 8.7 7.6 12.3 9.8 8.7 7.9 9.2 14.6 11.4 13.0 9.4 9.1 6.7 7.1 7.1 8.7 6.6 5.3 1.2 7.2

Momentum 19,438

Positive (Value) 180 190 237 138 106 128 130 281 226 379 367 514 435 357 578 905 733 779 926 504 810 522 9,425

(%) 22.4 16.8 20.1 15.0 12.6 14.9 11.7 17.7 12.2 13.8 15.2 18.8 15.9 13.5 11.8 15.4 13.9 20.0 18.8 14.5 13.5 10.8 15.0

Negative (Value) 99 177 160 131 160 134 166 246 320 524 374 373 388 405 806 965 990 616 599 518 1040 822 10,013

(%) 12.3 15.6 13.6 14.2 19.0 15.6 14.9 15.5 17.2 19.0 15.5 13.7 14.2 15.4 16.5 16.5 18.8 15.8 12.2 14.9 17.4 17.1 16.0

Panel C. Statistically Significant Fund Quarters ( Proportions )

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

1991-

2012

Beta

Positive (%) 66.1 53.1 54.6 55.5 53.4 54.6 54.1 50.4 68.7 60.0 58.9 53.2 58.6 56.3 56.5 57.0 54.1 47.5 67.6 61.8 48.6 55.9 57.1

Sentiment

Positive (%) 68.0 56.2 58.6 58.3 38.1 52.8 63.8 61.8 60.2 56.8 61.6 52.6 58.5 56.7 61.1 59.0 53.3 49.6 67.7 56.4 69.1 58.3

Momentum

Positive (%) 64.5 51.8 59.7 51.3 39.8 48.9 43.9 53.3 41.4 42.0 49.5 57.9 52.9 46.9 41.8 48.4 42.5 55.8 60.7 49.3 43.8 38.8 48.4

Number of Fund Quarters, Significant Fund Quarters and Fund Quarters Proportions

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4.3.1 Descriptive Statistics of Significant Fund Quarters and Proportions

Table 4.2 presents the descriptive statistics of the statistically significant fund quarters

and proportions. Panel A presents the descriptive statistics of positive and negative

statistically significant fund quarters. Panel B presents the descriptive statistics of positive

and negative fund quarter proportions. The mean and median values helps to determine if the

data are normally distributed or skewed. Skewed data occurs when the median and mean

values are significantly different.

We observe from Panel A of Table 4.2 that the mean and median values of the

statistically significant beta, sentiment beta and momentum fund quarters are not significantly

different. These implies that the fund quarters are normally distributed. Similarly, we observe

from Panel B that the proportions of fund quarters are normally distributed.

Table 4.2. Descriptive Statistics of Statistically Significant Fund Quarters and

Proportions

The descriptive statistics of statistically significant fund quarters and proportions are provided below. We

obtained the trade betas of US equity mutual funds from the data provided by Cullen et al. (2015) for the

period between June 1991 and September 2012. These fund quarters are based on quarterly data

observations. Panel A describes the statistically significant fund quarters of beta, sentiment beta and

momentum tilting. Panel B presents the proportions of beta, sentiment beta and momentum tilting fund

quarters. The total number of funds quarters equals 62,676.

Panel A: Significant Fund Quarters

Start Period End Period No. of Fund Quarters Mean Median

Beta Jun-91 Sep-12 13,836

Positive

7,895 359.0 376.0

Negative

5,941 270.0 281.0

Sentiment Beta Jun-91 Mar-11 10,810

Positive

6,306 300.3 259.0

Negative

4,504 214.5 183.0

Momentum Tilting Jun-91 Sep-12 19,438

Positive

9,425 428.4 373.0

Negative

10,013 455.1 381.0

(Panel B continues on next page)

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Panel B. Proportion of Significant Fund quarters

Start Period End Period No. of Fund Quarters Mean Median

Beta Jun-91 Sep-12

Positive (%)

7,895 56.7 55.7

Negative (%)

5,941 43.3 44.3

Sentiment Jun-91 Mar-11

Positive (%) 6,306 58.1 58.5

Negative (%)

4,504 41.9 41.5

Momentum Jun-91 Sep-12

Positive (%)

9,425 49.3 49.1

Negative (%) 10,013 50.7 50.9

4.4 Descriptive Statistics of Market and Systemic Risk Indicators

4.4.1 Descriptive Statistics (In Months)

Table 4.3 and Table 4.4 presents the descriptive statistics of market and systemic risk

indicators we have considered for our analysis. We have considered 10 market indicators and

11 systemic risk indicators as they represent different components of the overall market and

the economy. Although the statistically significant trade betas are in calendar quarters, we

have presented the values of market and systemic risk indicators in both months (Table 4.3)

and quarters (Table 4.4) in order to examine if there are any substantial differences in their

mean and median values. This is to ensure that despite having a limited number of fund

quarter observations, results will not be affected.

Panel A of Table 4.3 and Table 4.4 presents the descriptive statistics of market

indicators that are related to the statistically significant trade proportions that encompass beta,

sentiment beta and momentum. Hereby known as “Main Market Indicators”, they are the

Market Index, Sentiment Index and Momentum Index. We have also constructed the “return”

indicators to avoid spurious issues. Typically market indices have constant increases or

decreases in their index values. Creating the “return” indicators allows us to standardise and

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compare changes against the base values. “Returns” are calculated based on their respective

indices values in quarters, Eq. (1):

"Returns" = (𝐼𝑛𝑑𝑒𝑥 𝑉𝑎𝑙𝑢𝑒

𝑡1

𝐼𝑛𝑑𝑒𝑥 𝑉𝑎𝑙𝑢𝑒𝑡0− 1) ∗

360

4∗ 100 (1)

These indicators are the Market “Return”, Sentiment “Return” and Momentum “Return”

indicators. We expect “return” indicators to detect more changes in the index values.

Panel B of Table 4.3 and Table 4.4 presents the descriptive statistics of indicators that

are not directly related to the statistically significant trade proportions. However they provide

insights on the performance of other components of the market. Hereby known as “Sub-

Market Indicators”, they are the S&P Quality Index, S&P Growth Index, the S&P Low

Volatility Index and the S&P High Beta Index.

Panel C of Table 4.3 and Table 4.4 presents the descriptive statistics of systemic risk

indicators. These indicators help to predict macroeconomic outcomes. Recession indicators

are the Absorption ratio, Delta Absorption ratio, AIM and CATFIN. Indicators that signal

distress in financial institutions are CoVar, Delta CoVar and Real Volatility. Economic

instability or shocks indicators are the Book Leverage, Market Leverage and Real Volatility

and Partial Quantile Regression (PQR). Turbulence is an indicator that reflects shifts in asset

prices relative to their historical prices.

We observe from Panel A, Panel B and Panel C of Table 4.3, the momentum index,

the momentum “return” and the sub-market indicators have significantly lesser quarter

observations (over 70 quarters) compared to main market and systemic risk indicators (over

200 quarters). This was due to limited data availability as these indicators were recently

created in 2006.

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Focusing on the mean and median values, we observe from Panel A of Table 4.3 that

all but the market “return”, sentiment “return” and momentum “return” indicators had similar

values. This suggests that the index values are normally distributed. As “return” indicators

measure changes in the index, skewed data is expected. Market “return”, sentiment “return”

and momentum “return” indicators have mean values that are lesser than the median, this

implies that “return” values are negatively skewed to the left. As these indicators measure

changes, it is reasonable to have skewed data as changes in the index values can range from

small to large values.

We observe from Panel B of Table 4.3 that all sub-market indicators have normally

distributed index values. We also observe from Panel C of Table 4.3 that all of the systemic

risk indicators have normally distributed values except for the Turbulence indicator with a

mean value significantly larger than the median. This suggest that the values of the

turbulence indicator is positively skewed to the right. As the turbulence indicator reflects

shifts in asset prices relative to their historical prices. It is likely to have skewed data as

changes could range from very small to very large changes.

Table 4.3. Descriptive Statistics of Market and Systemic Risk Indicators (Presented in

Months)

The descriptive statistics of the market and systemic risk indicators are provided below. For market

indicators, information is downloaded from Yahoo Finance, S&P website and Baker and Wurgler

website. For systemic risk indicators, information is downloaded from the Sethpruit website.

Quarterly data are presented in months. Panel A presents the descriptive statistics of the indices that

are directly related to the statistically significant trades also known as “Main Market Indicators”.

Panel B presents the descriptive statistics of the indices that are not directly related to the statistically

significant trades also known as “Sub-Market Indicators”. Panel C presents the descriptive statistics of

Systemic Risk Indicators.

Panel A: Main Market Indicators No. of Quarts Mean Median

Market Index (Jun 1991 - Sep 2012) 256 998.27 1103.00

Market “Return” (Jul 1991- Sep 2012) (% p.q) 255 7.21 12.18

Sentiment Index (Jun 1991 - Sep 2012) 256 0.30 0.26

Sentiment “Return” (Jul 1991- Sep 2012) 255 0.15 -0.15

Momentum Index (Sep 2006- Sep 2012) 73 377.29 391.99

Momentum “Return” (Oct 2006- Sep 2012) (%p.q) 72 1.48 6.44

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(Panel B and C continues on the next page)

Panel B: Sub-Market Indicators (Sep 2006 - Sep 2012)

Quality Index 73 528.51 532.16

Growth Index 73 624.27 649.12

Low Volatility Index 73 3675.11 3723.20

High Beta Index 73 5191.28 4950.06

Panel C: Systemic Risk Indicators (Jun 1991 - Dec 2011)

Absorption Ratio (ABR) 247 0.66 0.67

Delta Absorption Ratio (DABR) 247 0.08 0.08

AIM 247 0.01 0.01

CATFIN (CF) 247 0.05 0.04

CoVar (Co) 247 0.02 0.02

Delta CoVar (DCo) 247 0.01 0.01

Real Volatility (RV) 247 0.02 0.02

Book Leverage (BL) 247 0.93 0.93

Market Leverage (ML) 247 7.20 6.56

Turbulence (TURB) 247 26.38 15.34

PQR 247 -0.01 -0.01 Recession Indicators: ABR, DAR, AIM, CF; Signal of Distress Financial Institutions: Co, DCo, Real Vol;

Economic instability or shocks: BL, ML, Real Vol, PQR (Partial Quantile Regression); Shift in asset prices

relative to history price: TURB.

4.4.2 Descriptive Statistics (In Quarters)

Similar observations were reflected from Table 4.4. The number of quarters from the

momentum index, momentum “return” and sub-market indicators have lesser quarters

compared to the rest of the indicators.

We observe from Panel A, Panel B and Panel C of Table 4.4 that “returns” indicators

have values that are negatively skewed to the left and the Turbulence indicator is positively

skewed to the right. These indicators focus on reflecting changes in the index values therefore

exhibiting skewed values are expected.

Based on the descriptive statistics of Table 4.3 and Table 4.4, we can conclude that

having lesser quarter observations will not affect the reliability and validity of our results.

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Table 4.4. Descriptive Statistics of Market and Systemic Risk Indicators (Presented in

Quarters)

The descriptive statistics of the market and systemic risk indicators are provided below. For market

indicators, information is downloaded from Yahoo Finance, S&P website and Baker and Wurgler

website. For systemic risk indicators, information is downloaded from the Sethpruit website.

Quarterly data are presented in quarters. Panel A presents the descriptive statistics of the indices that

are directly related to the statistically significant trades also known as “Main Market Indicators”.

Panel B presents the descriptive statistics of the indices that are not directly related to the statistically

significant trades also known as “Sub-Market Indicators”. Panel C presents the descriptive statistics of

Systemic Risk Indicators.

Panel A: Main Market Indicators No. of Quarts Mean Median

Market Index (Jun 1991 - Sep 2012) 86 995.19 1094.86

Market “Return” (Jul 1991- Sep 2012) (% p.q) 85 7.45 9.68

Sentiment Index (Jun 1991 - Sep 2012) 86 0.32 0.30

Sentiment “Return” (Jul 1991-Sep 2012) 85 0.65 -0.08

Momentum Index (Sep 2006 - Sep 2012) 25 374.98 391.14

Momentum “Return” (Oct 2006-Sep 2012) (%p.q) 24 4.85 9.73

Panel B: S&P Sub-Market Indicators (Period: Sep 2006 - Sep 2012)

Quality Index 25 524.97 537.90

Growth Index 25 620.65 642.17

Low Volatility Index 25 3662.86 3704.60

High Beta Index 25 5156.52 4850.51

Panel C: Systemic Risk Indicators (Jun 1991 - Dec 2011)

Absorption Ratio (ABR) 83 0.66 0.67

Delta Absorption Ratio (DABR) 83 0.08 0.09

AIM 83 0.01 0.01

CATFIN (CF) 83 0.05 0.04

CoVar (Co) 83 0.02 0.02

Delta CoVar (DCo) 83 0.01 0.01

Book Leverage (BL) 83 0.93 0.93

Market Leverage (ML) 83 7.20 6.46

Real Volatility (RV) 83 0.02 0.02

Turbulence (TURB) 83 28.73 14.54

PQR 83 -0.01 -0.01 Recession Indicators: ABR, DAR, AIM, CF; Signal of Distress Financial Institutions: Co, DCo, Real Vol;

Economic instability or shocks: BL, ML, Real Vol, PQR (Partial Quantile Regression); Shift in asset prices

relative to history price: TURB.

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4.5 Performance of Market Indicators

Studying the performance of market indicators allows us to understand how the

market behaves during bullish and bearish markets. Between June 1991 and September 2012,

there were three bull and two bull market periods.

The three periods of bull markets are as follows, July 1991 to January 2000, October

2002 to October 2007 and March 2009 to October 2012. The two periods of bear markets are

as follows, January 2000 to October 2002 and October 2007 to March 2009.

Amadeo (2016) reported that bear periods are highly correlated to recession periods as

an economic decline usually leads to a widespread of falling securities prices. During bear

and recession periods, we expect to see plunges in the values of the main market indicators.

In contrast, during bull and boom periods, we expect to see increasing index values of the

main market indicators. Graph 4.1 to 4.6 reflects changes in index values during bull and bear

market periods.

Graph 4.1: Price fluctuations of the Market Index, June 1991 to September 2012

The graph below presents the values of the market index based on quarterly opening prices. The

market index is a reflector of 500 stocks in the US equity market. Index values are presented in

quarters.

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Graph 4.1 reflects the overall performance of the US stock market during our trading

period (June 1991 to September 2012). There were two significant declines in the market

index values. The first significant decline occurred between September 2000 and March 2003

which coincides with the first bear market that occurred between January 2000 and October

2002. Likewise, the second significant decline which began from June 2008 to March 2009

coincides with the second bear market period between October 2007 and March 2009. Rapid

declines in the performance of the market usually occurs after a prolonged bull market

period. During July 1991 to January 2000 the market was in a bullish state as such the market

index was consistently increasing in values, reflecting good performance from the US stock

market. The performance of stocks tends to be the strongest during bullish periods as growth

is accelerating and interest rates are low which are attractive to investors. In contrast, during

bear market periods the performance of stocks will drastically decline as investors will

typically switch to bonds and cash investments.

Graph 4.2: Price fluctuations of Market “Return” Indicator, July 1991 to September

2012

The graph below presents the standardized changes in the market index. The values of the market

“return” indicator are calculated from the market index. Values are calculated quarterly and presented

in quarters (percentages).

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Based on Graph 4.2, the market “return” indicator has fluctuated drastically during the

trading period. As the market index only reflects “surface” changes which has consecutive

positive values, the market “return” indicator is a better standard for reflecting specifically

how much changes there were in each quarter or how much has the index increased or

decreased in values. There was a significant decline in market returns between December

1997 and September 1998 followed by a significant increase in market returns between

September 1998 and December 1999. This could be a warning signal for an upcoming

bearish market. The first bear period occurred between January 2000 and October 2002.

When the market is bullish, it usually goes through a peak period and the economy is running

at full steam. Employment levels are at peak level with high GDP output and high inflation

levels. However, such economy progress will be stalled and contracted as wages and prices of

goods are inflexible to change. This will result in a market crash and involuntarily leads to a

bear market period.

The recovery of a bear period usually results in a sharp rise in market prices with an

accelerating growth rate. This is because the base values of opening prices usually drops to a

new low. Also to help with economy recovery, credit conditions are usually less strict to ease

monetary policies in order to create a healthy environment for rapid margin expansion and

profit growth.

Similarly, we observe a significant decline in market returns between March 2008 and

December 2008, followed by a drastic increase in market returns between December 2008

and December 2009 and another decline between December 2009 and September 2010. This

changes could be associated to the occurrence of the second bear market period that happened

between October 2007 and March 2009.

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Graph 4.3: Changes in the Sentiment Index Values, June 1991 to March 2011

The graph below presents the values of the sentiment index. Investor sentiment reflects the strategies

of market participants. When there is a sudden increase in sentiment values, it is viewed as a contrary

sign for market trend reversals. Sentiment index values are presented in quarters.

Based on Graph 4.3, we observe a rapid increase in sentiment values between

December 1999 and March 2001. It is possible that this rapid increase was a warning for the

upcoming recession period between March 2001 and November 2001. Such rapid increase

are usually signals of market trend reversal. As expected, when the recession period began in

March 2001, the values of the sentiment index fell rapidly between March 2001 and

September 2002 before returning to average index values. When an investor’s sentiment is

low, we expect investors to tilt their portfolios towards negative sentiment beta trade

proportions. Although the recession period ended in September 2002, the sentiment index

values only began to increase after November 2002. As the recovery of an economic

downturn usually takes a longer time period, the gap between September 2002 and November

2002 could be a transition phase to recovery. However, we observe that during the second

recession period there were no significant changes in the sentiment index values.

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Graph 4.4: Changes in the values of the Sentiment “Return” Indicator, July 1991 to

March 2011

The graph below presents the standardized changes in the sentiment index. The values of the

sentiment “return” indicators are calculated from the sentiment index. Values are calculated quarterly

and presented in quarters.

Graph 4.4 presents the standardized changes of the sentiment index. Although the

sentiment index has frequent positive and negative index values, it is plausible that the

sentiment “return” would be a better reflector of sentiment changes. The sentiment index

specifically reflects the differences in the index values in each quarter.

Compared to the sentiment index (Graph 4.3), there were two distinct series of returns

fluctuations. We observe that between September 1998 and June 1999, the sentiment returns

had fallen drastically but increased significantly between June 1999 and December 1999.

Such changes could suggest an upcoming economy downturn. We observe that the sentiment

returns reverted to average values between December 1999 and June 2000. It is plausible that

this changes are related to the first recession period between March 2001 and November

2001.

We also observe that between September 1998 and June 1999, sentiment returns had

significantly increase before falling back to average return values between December 2008

and June 2009. This fluctuation of returns could also be associated with the second recession

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period between December 2007 and June 2009. When there is a bullish market, an investor’s

sentiment is usually low. In contrast when there is a bearish market, an investor’s sentiment is

usually high.

Graph 4.5: Changes in the Momentum Index Values, September 2006 to September

2012

The graph below presents the values of the momentum index. The momentum index represents the

persistence in stock performance prior to their history performance. Momentum index values are

presented in quarters.

The momentum index reflects the overall persistence in the performance of S&P

funds compared to their relative performance. The momentum index is considered a “return”

indicator as it measures changes to the prior performance. During bullish (bearish) markets,

the investor buy (sell) “winners” and sell (buy) “losers” as they believe that the performance

of these funds will continue to excel.

We observe from Graph 4.5, the values of the momentum index did not display any

significant changes during our trading period besides a drastic drop in index values between

June 2008 and December 2009. However compared to the other market indicators, the

momentum index had only six years of quarterly data observations. Throughout September

2006 to September 2012, there was only one bear market period which occurred between

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October 2007 and March 2009. The slight decrease in the values of the momentum index

could be associated to the bear market. During bullish market, we expect persistence of

positive proportion trades to be high. In contrast, during bearish market, we expect the

persistence of negative proportion trades to be high.

Graph 4.6: Changes in the values of the Momentum “Return” Indicator, October 2006

to September 2012

The graph below presents the standardized changes in the momentum index. The values of the

momentum “return” indicators are calculated from the momentum index. Values are calculated

quarterly and presented in quarters (percentages).

Although the momentum index is already considered as a “return” indicator, we

created the momentum “return” indicator to examine if the momentum index can detect more

changes.

Similar to the momentum index (Graph 4.5), we observed from Graph 4.6 that there

was a significant decline in the values of the momentum “return” indicator between

September 2008 and March 2009. Likewise, this rapid decline could be associated with the

bear market period. Unlike the momentum index, the “return” indicator also reflects a rapid

increase in returns value between March 2009 and September 2009. This suggests the

recovery of the bear market period and the transition to a bullish market. During bullish

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market, we expect momentum “returns” to be high. In contrast, during bearish market, we

expect the “momentum” returns to be low.

4.6 Correlation Testing

Correlation testing is important for our study as it measures the degree to which two

variables move in relation to each other. The main variables in our study are the statistically

significant trade proportions (dependent variable) and the market and systemic risk indicators

(independent variables). There are three types of correlation analysis, Pearson Correlation,

Kendall Correlation and Spearman Correlation.

Based on Lee and Peters (2015), the Pearson correlation measures the degree of the

relationship between linear related variables and these variables are assumed to be normally

distributed. The Kendall correlation is a non-parametric test that measures the strength

between two variables and also test similarities in the ordering of data when it is ranked by

qualities. The Spearman correlation is also a non-parametric test that is used to measure the

degree of association between two variables. The difference between the Pearson correlation

and the Spearman correlation is that the Spearman Correlation measures non-linear

relationships and variables are measured on a scale that is at least ordinal. A high correlation

value ranges from ±0.5 to ±1.0, medium correlation ranges from ±0.3 to ±0.5 and a low

correlation ranges from ±0.1 to ±0.3. Having a positive (negative) high correlation value

implies that when one variable moves, the other variable moves in lockstep in the same

(opposite) direction. Also, the significant levels (p-values) of the correlation results are

important to determine if the correlation between the variables are not the results of chance or

random sampling error.

In this study, we will be using the Pearson correlation analysis as most of our data

observations are normally distributed.

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4.6.1 Correlation Testing between Market Indicators (Main Market Indicators and

Sub-Market Indicators)

Considering a wide range of market indicators allow us to have a comprehensive

study of the market movements and they reflect bullish and bearish market trends. We study

the relationship between these indicators to determine if they are moving in the same

direction therefore reflecting similar market performances. If these market indicators are

highly correlated, we are able to conclude that they are moving in accordance during changes

in market trends. Emphasis is given to the main market indicators which are the Market

Index, Sentiment Index and Momentum Index as they are directly related to the statistically

significant trades that encompass beta, sentiment beta and momentum.

A correlation test would also be conducted between the main market indicators and

the sub-market indicators which are the Quality Index, Growth Index, Low Volatility Index,

and High Beta Index. This is to ensure that these indicators are all moving in accordance to

the market hence reflecting similar behaviour of market trends and performances.

Correlation analysis will not be conducted between the “return” indicators as they do

not reflect the overall performance of the market but reflect the quarterly period changes in

their respective indicators.

Table 4.5 presents the two correlation results, firstly between the main market

indicators and secondly between the main market indicators and sub-market indicators.

Results are presented in months and quarters to ensure that despite lesser number of fund

quarters, results will not be affected. Panel A presents the results of the correlation test

between the main market indicators in months. Panel B presents the results of the correlation

test between the main market and sub-market indicators in months. Panel C presents the

results of the correlation test between the main market indicators in quarters. Panel D

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presents the results of the correlation test between the main market and sub-market indicators

in quarters.

We observe from Panel A of Table 4.5, the correlation results between the main

market indicators displayed significantly high correlation results. The correlation results

between the market index and momentum index has the highest correlation value of 0.965.

This suggests that the main market indicators are all moving in the same direction implying

similar market performances.

We observe from Panel B of Table 4.5, the correlation results between the main

market indicators and the sub-market indicators exhibited significantly high correlation

results. Between these indicators, the correlation between the momentum index and the

growth index had the highest correlation value of 0.954. This suggests that despite reflecting

the performance of different components of the market, all indicators are moving in the same

direction.

Similarly, we observe from Panel C and Panel D of Table 4.5, all main market

indicators are highly correlated between each other and all main-market indicators are highly

correlated to the sub-market indicators. This suggests that despite lesser number of

observations, results will not decrease in validity.

Table 4.5. Correlation of Market Indicators: 73 Monthly and 25 Quarterly

Observations, September 2006 – September 2012

The correlation analysis results between the market indicators (main market indicators and sub-market indicators) are

provided below. Main market indicators are the market, sentiment and momentum index. Sub-market indicators are the low

volatility, quality, high beta and growth index. Panel A presents the correlation results between the main market indicators

(in months). Panel B presents the correlation results between the main market Indicators and the sub-market Indicators (in

months). Panel A presents the correlation results between the main market indicators (in quarters). Panel B presents the

correlation results between the main market Indicators and the sub-market Indicators (in quarters).

Panel A: Correlation of Main Market Indicators (Monthly)

Market Index Sentiment Index Momentum Index

Market Index 1 0.856*** 0.965***

Sentiment Index

1 0.803***

Momentum Index

1

(Panel B, C and D continues in the next page)

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Panel B: Correlation of Main Market Indices and Sub-Market Indicators (Monthly)

Low volatility Index Quality Index High Beta Index Growth Index

Market Index 0.883*** 0.848*** 0.894*** 0.917***

Sentiment Index 0.738*** 0.614*** 0.833*** 0.710***

Momentum Index 0.911*** 0.901*** 0.785*** 0.954***

Panel C: Correlation of Main Indicators (Quarterly)

Market Index Sentiment Index Momentum Index

Market Index 1 0.853*** 0.972***

Sentiment Index

1 0.799***

Momentum Index

1

Panel D: Correlation of Main Market Indicators and Sub-Market Indicators (Quarterly)

Low volatility Index Quality Index High Beta Index Growth Index

Market Index 0.893*** 0.858*** 0.883*** 0.92***

Sentiment Index 0.744*** 0.618*** 0.843*** 0.703***

Momentum Index 0.927*** 0.910*** 0.782*** 0.956***

*** Significant at the 0.01 level

** Significant at the 0.05 level

* Significant at the 0.10 level

4.6.2 Correlation Testing between Systemic Risk Indicators

We have considered all 19 systemic risk indicators and selected 11 indicators that are

most insightful in measuring risk in the real economy. Fluctuations in systemic risk signals

changes in the economy and impacts the probability of an economic downturn. Systemic risk

indicators are useful in reflecting recession market trends. When there are changes in the

values of these systemic risk indicators, it serves as a warning for upcoming economic

changes.

4.6.2.1 Brief Description of the Selected Systemic Risk Indicators

We have selected the Absorption ratio, Delta Absorption ratio, AIM, CoVar, Delta

CoVar, Book Leverage, Market Leverage, Real Volatility, CATFIN, Turbulence and the PQR

indicators.

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Primary recession indicators are the Absorption ratio, Delta Absorption ratio, AIM

and the CATFIN. The Absorption ratio is useful in detecting US market changes. When there

is a high absorption ratio, it implies that the market is vulnerable. The Delta Absorption ratio

measures “changes”, it captures shifts in short term absorption ratio relative to the long term

absorption ratio. AIM reflects the illiquidity in an economy. It has been successful in

predicting recession as liquidity tends to fall before a recession. CATFIN reflects the level of

risk a bank is expose to, this ratio is very useful in detecting economic declines.

Indicators that monitor the performance of financial institutions are the CoVar, Delta

CoVar and Real Volatility indicators. CoVar is the value at risk of a distress financial

institution. Delta CoVar captures how much a particular institution has contributed to the

overall systemic risk. Real Volatility measures the volatility of financial institutions.

Primary economic instability indicators are the Book Leverage, Market Leverage and

the PQR indicators. Book and Market Leverage are useful in capturing instability and shocks.

The PQR indicator gives strong forecasting power of macroeconomic shocks in the economy.

Lastly, Turbulence ratio captures the shift in asset prices relative to their historical price.

When asset prices display extreme changes, this signals an economic downturn.

A correlation test was conducted between these 11 systemic risk indicators to identify

which indicators are highly and lowly correlated, in both positive and negative values.

Selecting these indicators gives us a broader understanding of how highly correlated or

negatively correlated trades can affect the trading movements of the statistically significant

trades.

Table 4.6 presents the results of the correlations analysis between 11 of the systemic

risk indicators in months and quarters. Panel A presents the results of the correlation analysis

in months. Panel B presents the results of the correlation analysis in quarters. Similar to the

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correlation test between the market indicators, conducting the correlation test using monthly

and quarterly data observations ensures the validity of our results.

We observe from Panel A and Panel B of Table 4.6 that most of the systemic risk

indicators displayed high correlations values that are significant at the 0.01 level. Comparing

the results of Panel A and Panel B, we did not observe any significant differences in the

values of the correlation analysis. Therefore, having a lesser number of data observations will

not affect the reliability of our results.

Table 4.6. Correlation between Systemic Risk Indicators: 247 Monthly Observations

and 83 Quarterly Observations, June 1991 to December 2011 The results of the correlation analysis between the 11 of the systemic risk indicators are provided below. Panel A presents

the results of the correlation analysis between the 11 of the systemic risk Indicators (in months). Panel B presents the results

of the correlation analysis between the 11 of the systemic risk indicators (in quarters). Primary Recession Indicators: ABR,

DABR, AIM, CF; Signal of Distress Financial Institutions: Co, DCo, Real Vol; Economic instability or shocks: BL, ML,

PQR; Shift in asset prices relative to history price: TURB. The data covers the period between 1991 and 2011.

Panel A: Monthly Observations

ABR DABR AIM Co DCo BL ML RV TURB CF PQR

ABR 1 -0.40*** -0.20*** 0.78*** 0.81*** 0.30*** 0.45*** 0.46*** 0.29*** 0.44*** -0.32***

DABR

1 0.21*** -0.33*** -0.33*** -0.06 -0.08 0.06 -0.03 0.06 0.00

AIM

1 -0.10 -0.13** 0.00 -0.16** 0.03 -0.03 0.01 -0.02

Co

1 0.96*** 0.20*** 0.56*** 0.65*** 0.33*** 0.62*** -0.47***

DCo

1 0.12 0.66*** 0.57*** 0.29*** 0.55*** -0.37***

BL

1 0.06 0.16** 0.20*** 0.15** -0.21***

ML

1 0.42*** 0.31*** 0.48*** -0.30***

RV

1 0.72*** 0.31*** -0.71***

TURB

1 0.76*** -0.71***

CF

1 -0.64***

PQR

1

Panel B: Quarterly Observations


ABR 1 -0.34*** -0.25*** 0.77*** 0.80*** 0.32*** 0.53*** 0.47*** 0.30*** 0.45*** -0.34***

DABR

1 0.26** -0.31*** -0.31*** -0.01 -0.08 0.09 0.00 0.07 -0.07

AIM

1 -0.15 -0.17 -0.01 -0.14 -0.03 -0.04 -0.03 0.03

Co

1 0.96*** 0.22** 0.57*** 0.60*** 0.26** 0.56*** -0.45***

DCo

1 0.15 0.67*** 0.52*** 0.21 0.56*** -0.37***

BL

1 0.06 0.19 0.20 0.21 -0.14

ML

1 0.39*** 0.23*** 0.46*** -0.28***

RV

1 0.79*** 0.84*** -0.62***

TURB

1 0.84*** -0.37***

CF

1 -0.52***

PQR 1

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ABR: Absorption Ratio, DABR: Delta Absorption Ratio, Co: CoVar; Dco: Delta CoVar, BL: Book Leverage,

ML: Market Leverage, CF: CATFIN, TURB: Turbulence PQR: Partial Quantile Regression




In order to have an optimal analysis process, we are interested in correlation values of

indicators that that are significant at the 0.01 level and they being replaced by correlation

symbols and presented in Table 4.7, Panel A.

Panel A presents the level of correlation between the systemic risk indicators that

have exhibited correlation results that are significant at the 0.01 level and they are presented

in these symbols: 𝐶𝐻±, 𝐶𝑀± and 𝐶𝐿±. High correlation value is denoted by 𝐶𝐻±, Medium

correlation value is denoted by 𝐶𝑀±and Low correlation value is denoted by 𝐶𝐿±. A high

correlation value ranges from ±0.6-1.0, a medium correlation value ranges from ±0.3-0.6 and

a low correlation value ranges from ±0.1-0.3. Panel B presents the highest positive and

negative correlated values and the lowest positive and negative correlated values of the

systemic risk indicators (in bold).

We observe from Panel B of Table 4.7, the lowest negative correlation was between

the Absorption Ratio and AIM indicators with a correlation value of -0.25. The highest

negative correlation was between Real Volatility and PQR indicators with a correlation value

of -0.62. The lowest positive correlation was between Market Leverage and Turbulence

indicators with a correlation value of 0.23. The highest positive correlation was between

CoVar and Delta CoVar indicators with a correlation value of 0.96.

Between these indicators, the Absorption ratio and AIM are both recession indicators.

As the Absorption ratio and Delta Absorption ratio are similar measures of upcoming

recession periods, we have decided to select the Delta Absorption ratio for the final analysis

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as the Delta Absorption ratio captures the changes between the short term and long term

absorption ratios therefore avoids spurious issues. Similarly as CoVar, Delta CoVar and Real

Volatility indicators tracks the performance of financial institutions, we have selected the

Delta CoVar indicator to avoid spurious issues as we expect Delta CoVar indicator reflects

the differences in CoVar conditional on a distress institution and a normal state of the

institution. The Market Leverage and PQR indicators are measures of economic instability.

We have selected the PQR indicator as it is the accumulated information of the systemic risk

measures. It is a better indicator as it gives a stronger forecasting power of macroeconomic

shocks.

Therefore, the final selection of systemic risk indicators are the Delta Absorption

Ratio, Delta CoVar, PQR and Turbulence indicators.

Table 4.7. Significant (at 0.01 Level) results of Positive and Negative Correlations

between the Selected Systemic Risk Indicators: 83 Quarterly Observations, June 1991 to

December 2011

The results of the correlation analysis between 11 of the systemic risk indicators that are significant at

the 0.01 level are provided below. Panel A presents the symbols of the level of correlation between 11

of the systemic risk Indicators based on quarterly data observations. 𝐶𝐻+: Positive High Correlation,

𝐶𝐻− : Negative High Correlation; 𝐶𝑀+ : Positive Medium Correlation, 𝐶𝑀− : Negative Medium

Correlation, 𝐶𝐿+ : Positive Low Correlation, 𝐶𝐿− : Negative Low Correlation

Panel B presents the values of highly positively correlated, highly negatively correlated, lowly

positively correlated and lowly negatively correlated results, all results are significant at the 0.01

level. Highest and lowest results are in bold.

Recession Indicators: ABR, DABR, AIM, CF; Signal of Distress Financial Institutions: Co, DCo,

RV; Economic instability or shocks: BL, ML, PQR; Shift in asset prices relative to history price:

TURB. The data cover the period 1991 – 2011.

Panel A: Level of Correlation


ABR 1 𝐶𝐿− 𝐶𝐿− 𝐶𝐻+ 𝐶𝐻+ 𝐶𝑀+ 𝐶𝐻+ 𝐶𝑀+ 𝐶𝑀+ 𝐶𝑀+ 𝐶𝑀−

DABR

1 𝐶𝑀− 𝐶𝑀−

AIM

1

Co

1 𝐶𝐻+ 𝐶𝐻+ 𝐶𝐻+ 𝐶𝐻+ 𝐶𝑀−

DCo

1 𝐶𝐻+ 𝐶𝐻+ 𝐶𝐻+ 𝐶𝑀−

BL

1

(Table continues in the next page)

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ML

1 𝐶𝑀+ 𝐶𝐿+ 𝐶𝑀+ 𝐶𝐿−

RV

1 𝐶𝐻+ 𝐶𝐻+ 𝐶𝐻−

TURB

1 𝐶𝐻+ 𝐶𝑀−

CF

1 𝐶𝐻−

PQR 1

Panel B:Values of All Highest and Lowest significant correlations at 0.01 Level (Best results in

Bold)


ABR 1 -0.34 -0.25 0.77 0.80

0.53

DABR

1

AIM

1

Co

1 0.96 0.57 0.60 0.56

DCo

1 0.67 0.52 0.56

BL

1

ML

1

0.23 -0.28

RV

1 0.79 0.84 -0.62

TURB

1 0.84

CF

1 -0.52

PQR 1

ABR: Absorption Ratio, DABR: Delta Absorption Ratio, Co: CoVar; Dco: Delta CoVar; BL: Book Leverage,

ML: Market Leverage, CF: CATFIN, TURB: Turbulence PQR: Partial Quantile Regression




4.7 Final Selection of Market and Systemic Risk Indicators

The analyses have shown that we can parsimoniously reduce the number of indices

without loss of information while permitting an assessment of the trade preferences

undertaken by the fund managers. Based on the preceding analyses, we will retain six market

indicators and four systemic risk indicators. The figure below (Refer to Figure 4.2)

summarizes the approach.

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Figure 4.2. Final selection of Indicators for Analysis

The figure below illustrates the final selection of indicators for our research analysis. There are two

types of indicators: 1) Market indicators 2) Systemic Risk indicators. There are six market indicators

and four systemic risk indicators for our analysis.

Trades

Market Indicators


Market Return

Delta Absorption Ratio

Market Index Delta CoVar

Sentiment Return Turbulence

Sentiment Index PQR

Momentum Return

Momentum Index

Delta Absorption Ratio: Useful in detecting market changes in the US Stock Market; Delta CoVar:

Value at risk of the whole financial system conditional on institutions that are in distress; Turbulence:

Reflects situations where asset prices are behaving differently relative to their historical behaviour

(extreme price movements); PQR (Partial Quantile Regression): Measures macroeconomic activity,

strong forecasting power of shocks.

The statistically significant trade proportions of beta, sentiment and momentum will

analysed using a two-step procedure, a correlation analysis and a regression analysis. These

trade proportions will be tested with their respective indicators (Refer to Figure 4.3).

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Figure 4.3. Statistically Significant Trades and their Respective Indicators

The figure below illustrates the statistically significant trades and their respective indicators. Market

beta trades are related to the market “return” and market index indicators. Sentiment beta trades are

related to the sentiment index and the sentiment “return” indicator. Momentum trades are related to

the momentum index and the momentum “return” indicator. All statistically significant trades are

tested with the Systemic Risk indicators. Correlation and regression testing are based on positive and

negative trade proportions.

Trades

Market Beta Trades

Proportions

Sentiment Beta Trades

Proportions

Momentum Trades

Proportions

Market Return

Sentiment Return

Momentum Index

Market Index

Sentiment Index

Momentum Index




4.8 Correlation and Regression Analysis between Trade Proportions (DV) and

Indicators (IV)

Correlation and regression analyses will be conducted between the statistically

significant trade proportions and their respective indicators. Running a correlation and

regression test allows us to examine if these mutual fund managers were capable of adjusting

their portfolios according to the forecasted market trends by comparing them to market and

systemic indicators which reflects the performance of the market. A correlation test helps us

to understand the association between two variables. The variables for our research are the

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trade proportions, the market and systemic risk indicators. The dependent variables are the

trade proportions and the independent variables are the related market and systemic risk

indicators.

A regression analysis develops an equation that allows the value of one variable to be

used to predict the other, ŷ= βₒ+β₁X1+εi. As we are running the regression analysis

individually for each type of trade proportion, a simple regression will be conducted. In this

study, the predictor variables (x) are the market and systemic risk indicators and the

outcomes (y) are the trade proportions (beta, sentiment beta and momentum). We are

interested to know if these statistically significant trades can be explained by the movements

and changes of the market and systemic risk indicators. The regression equation (ŷ= βₒ+β₁X1+

ε) where ε is the sampling error, X is the independent variable, βₒ is the intercept and β₁

represents an estimate of the change in the dependent variable corresponding to one unit

change in the independent variable. The significance of the beta coefficient plays an

important role. If the beta coefficient is not statistically significant, no statistical significance

can be explained or interpreted from that predictor. A significant beta can either be in a

positive or negative value. Having a positive (negative) beta implies that for every 1 unit

increase (decrease) in the x variable, the y variable will be increase (decrease) by the

unstandardized beta coefficient value. The adjusted R2 is also an important component in the

regression analysis as it represents if the model is a good predictor in the analysis.

Although correlation and regression testing are both very important for our study,

regression results tells us if the movements of the trade proportions by the mutual fund

managers can be explained by the changes in index values. Market timing abilities allows

mutual fund managers to take advantage of the market and tilt their portfolios accordingly.

Therefore, the values of the market and systemic risk indicators can provide some

information on the adjustments of trade proportions during different market trends. Although

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the trade proportions may be correlated to the values of the indicators, it does explain if the

adjustment of trade proportions are influenced by the increases or decreases in the indicators’

values. A correlation analysis simply states the relationship and strength between trade

proportions and the values of these indicators without explaining the functional relationship.

However, a regression analysis provides a deeper understanding by explaining the slope and

intercepts of our variables.

4.9 Overall Test for Correlation and Regression Analysis

The first part of our analysis is to conduct an overall correlation and regression

analysis between our variables. The positive and negative trade proportions are our dependent

variables. The market and systemic risk indicators are our independent variables. This overall

analysis does not consider the possibility that the mutual fund managers may be selective of

positive or negative trade proportions based on different market trends or index behaviours.

This gives us a general idea of the relationship between statistically significant trade

proportions, the market and systemic risk indicators.

Table 4.8 presents the correlation and regression results between the statistically

significant trades, the market and systemic risk indicators. Positive trade proportions are

presented in Table 4.8. Emphasis is given to positive trade proportions as more bullish market

periods are observed during our trading period therefore we expect a higher proportion of

positive trade proportions. Trade proportions are preferred for the analysis as they provide

insights on the direction that the mutual fund manager is pursuing. Positive (negative) trade

proportions are calculated by dividing the number of positive (negative) trades over the total

number of positive and negative trades per quarter.

Panel A presents the results of the correlation and regression analysis between

positive trade proportions and their respective market indicators. Panel B presents the results

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of the correlation and regression analysis between the positive trade proportions and the final

selection of systemic risk indicators.

The correlation results interpret if the trade proportions and their respective indicators

co vary and also describes the strength of their relationship. These information explains if the

trade proportions of mutual fund managers are moving in the same direction as the values of

the indicators. Having a high correlation value (±0.6 to ±1.0) implies that during periods

when the values of the indices have increased, mutual fund managers would tilt their

portfolios towards positive trade proportions. An increase in the index value suggests that the

market is performing well.

The regression results are based on the beta coefficient values, the significance of the

beta coefficient values and the adjusted R2 value (%). The positive and negative signs of the

beta coefficient tells us the direction of slope of the regression line. We are able to determine

for 1 unit of increase or decrease in values of the indicators, the trade proportions will move

in the same direction based on the beta coefficient. The beta coefficient is important as it

describes whether the slope of the line is positive or negative which explains the relationship

between our variables. The significant level of the beta coefficient is important too as it

interprets if the result is not a random occurrence. Lastly, the adjusted R2 value indicates how

reliable the model is to predict if the trade beta proportions are explained by the values of the

indicators. The higher the R2 value is, the better the model is as it has a better line of fit.

However adjusted R2 values are typically low in values. It is possible to have a negative R2

value if the model is too complex for the sample size. A negative R2 value can occur when

the model contains terms that are not beneficial in predicting the response or that the

independent variables have too little predictive values.

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As we are dealing with simple regression analysis, the correlation values do not affect

the results of regression analyses. Multicollinearity occurs when two or more independent

variables in a multiple regression model are closely correlated to one another which will lead

to misleading results.

We observe from Panel A of Table 4.8 that despite positive proportion of momentum

trades having the least number of quarter observations, they exhibited the most significant

results. Positive momentum trade proportions have only 25 quarter observations compared to

the positive beta and sentiment beta trade proportions with over 80 quarter observations.

The positive momentum trade proportions are highly negatively correlated to the

momentum index with a value of -0.521, significant at the 0.01 level. This is an inverse

relationship which suggest the possibility that mutual fund managers may have pursued a

contrarian strategy. The beta coefficient between the positive momentum trade proportions

and the momentum index is -0.001, significant at the 0.01 level. Having a beta coefficient of -

0.001 implies that for every 1 unit decrease in the momentum index, the positive momentum

trade proportions will decrease by 0.001. The adjusted R2 value tells us that 24% of the

positive trade proportions can be explained by the momentum index.

The positive momentum trade proportions are also highly negatively correlated to the

momentum “return” indicator with a value of -0.445, significant at the 0.01 level. This

suggests that although the momentum “return” indicator was expected to display a better

correlation result as it measures standardized changes, the momentum index might be a better

alternative. A possible reason could be the result of a pseudo return, as the momentum index

is presumably a “return” indicator. The beta coefficient between the positive momentum

trade proportions and the momentum “return” indicator is -0.001, significant at the 0.05 level.

Having a beta coefficient of -0.001 implies that for every 1 unit decrease in the momentum

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“return” indicator, the positive momentum trade proportions will decrease by 0.001. The

adjusted R2 value tells us that 16.2% of the positive trade proportions can be explained by the

momentum “return” indicator.

The positive sentiment beta trade proportions are highly negatively correlated to the

sentiment “return” indicator with a value of -0.238, significant at the 0.05 level. We expected

that when sentiment “returns” are high, there would be higher proportions of positive

sentiment trade proportions. However, results suggest an inverse relationship between these

variables. The beta coefficient between the positive sentiment trade proportions and the

sentiment “return” index is -0.003, significant at the 0.05 level. Having a beta coefficient of -

0.003 implies that for every 1 unit decrease in the momentum index, the positive momentum

trade proportions will decrease by 0.003. The adjusted R2 value tells us that 4.5% of the

positive sentiment trade proportions can be explained by the sentiment “return” indicator.

We observe from Panel B of Table 4.8, positive beta trade proportions are moderately

negatively correlated to the Delta Absorption ratio indicator with a value of -0.310,

significant at the 0.01 level. This suggests an inverse relationship between the positive beta

trade proportions and the Delta Absorption ratio. We expect a higher proportion of negative

beta trades when the Absorption ratio is high as it signals an upcoming recession period.

Similar to the Delta Absorption ratio, when “changes” are high, we expect a higher

proportion of negative beta trade proportions. The beta coefficient between the positive

sentiment trade proportions and the sentiment “return” index is -0.184, however is not

significant. The adjusted R2 value tells us that 8.5% of the positive beta trade proportions can

be explained by the Delta Absorption ratio.

Similarly, the positive sentiment beta trade proportions are lowly negatively

correlated to the Delta Absorption ratio with a value of -0.262 significant at the 0.05 level.

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This suggests an inverse relationship between the positive beta trade proportions and the

Delta Absorption ratio. When “changes” are high, we expect a higher proportion of negative

sentiment beta trades. The beta coefficient between the positive sentiment trade proportions

and the Delta Absorption ratio is -0.300, however is not significant. The adjusted R2 value

tells us that 5.7% of the positive sentiment beta trade proportions can be explained by the

Delta Absorption indicator.

The positive momentum trade proportions are lowly negatively correlated to the Delta

CoVar indicator with a value of -0.231 significant at the 0.05 level. This suggests an inverse

relationship between the positive momentum trade proportions and the Delta CoVar

indicator. The beta coefficient between the positive momentum trade proportions and the

Delta CoVar indicator is -1.448, however is not significant. The adjusted R2 value tells us that

4.2% of the positive momentum trade proportions can be explained by the Delta CoVar

indicator.

We also observe that although the positive momentum trade proportions were not

significantly correlated to the PQR indicator, the beta coefficient between the positive

momentum trade proportions and the PQR indicator was 0.051, significant at the 0.05 level

with an adjusted R2 value of -1.0%.

Table 4.8. Overall Correlation and Regression between Trade proportions and

Indicators

The results of the correlation and regression analysis between the positive trade proportions and respective

indicators are presented below. Panel A: Results of positive trade proportions of beta, sentiment beta and

momentum trades and their respective market indicators. Panel B: Results of positive trade proportions of

beta, sentiment beta and momentum trades and systemic risk indicators. Results of negative trade

correlations are the opposite of positive trade correlations. Correlation and simple regression test are

conducted individually.

Regression testing (ŷ= βₒ+β₁X1+εi): X variables are the market and systemic risk indicators and y variables

are the trade proportions of beta, sentiment beta and momentum trades.

Two regression equations for positive beta trade proportions: positive market beta proportions= βₒ + β₁ (Market Index) +εi; positive market beta proportions= βₒ + β₁ (Market “Return”) +εi.

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Two regression equations for positive sentiment beta trade proportions: positive sentiment beta

proportions= βₒ + β₁ (Sentiment Index) +εi; positive sentiment beta proportions= βₒ + β₁ (Sentiment “Return”) +εi.

Two regression equations for positive momentum trade proportions: positive momentum trade

proportions= βₒ + β₁ (Momentum Index) +εi.; positive momentum beta proportions= βₒ + β₁ (Momentum “Return”) +εi.

Period (Market Indictors): Beta proportions and Market Index (Jun 1991-Sep 2012), Beta proportions and

Market “Return: Indicator (Jul 1991- Sep 2012), Sentiment Beta proportions and Sentiment Index (Jun

1991 to March 2011), Sentiment Beta proportions and Sentiment “Return” (Jul 1991 to March 2011),

Momentum proportions and Momentum Index (Sep 2006 to Sep 2012), Momentum proportions and

Momentum “Return” (Oct 2006 to Sep 2012).

Period (Systemic Risk Indicators): Beta proportions and Systemic Risk Indicator (Jun 1991- Dec 2011),

Sentiment beta proportions and Systemic Risk Indicator (Jun 1991- Mar 2011), Momentum proportions

and Systemic Risk Indicators (Sep 2006 –Dec 2011).

Panel A: Market Indicators and Positive Trade Proportions

Trades No. of Quarts Index Correlation Regression

β Sig Adj R² (%)

Beta

Positive 85 Market Index 0.190 ~0.000 0.864 -1.2

85 Market Return 0.162 0.001 0.138 1.5

Sentiment

Positive 80 Sentiment Index -0.029 -0.005 0.799 1.2

79 Sentiment Return -0.238** -0.003 0.034 4.5

Momentum

Positive 25 Momentum Index -0.521*** -0.001 0.008 24.0

Momentum Return -0.445** -0.001 0.029 16.2

Panel B: Systemic Risk Indicators and Positive Trades Proportions Trades No. of Quarts Index Correlation Regression

β Sig Adj R²(%)

Beta

Positive 83 Delta ABR -0.310*** -0.184 0.409 8.5

Delta Co -0.124 0.345 0.965 0.3

Turbulence -0.180 0.000 0.614 2.0

PQR 0.062 -0.963 0.653 -0.8

Sentiment

Positive 83 Delta ABR -0.262** -0.300 0.279 5.7

Delta Co -0.166 -0.384 0.698 1.5

Turbulence -0.117 -~0.000 0.976 0.1

PQR 0.006 -0.955 0.720 -1.3

Momentum

Positive 83 Delta ABR -0.033 -0.118 0.626 -1.1

Delta Co -0.231** -1.448 0.864 4.2

Turbulence 0.085 0.000 0.420 -0.5

PQR 0.051 0.543 0.021 -1.0

ABR: Absorption Ratio, Co: Covariance, TURB: Turbulence, PQR: Partial Quantile Regression

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4.10 Preliminary Test

Preliminary testing is essential as we consider alternative conditions that might affect

the trading movements of the statistically significant trades. This tests gives us a profound

examination of the existence of market timing abilities.

The first test examines the market timing abilities of mutual fund managers during

bullish and bearish market periods. During a bullish (bearish) market period, we expect

mutual fund managers with market timing abilities to adjust their portfolios towards positive

(negative) trade proportions to take advantage of the market. We compare the portfolio

adjustments of the statistically significant trades with the values of their respective indicators.

The second test examines the market timing abilities of fund managers based on the

proportions of their statistically significant trades. We expect that during periods with higher

proportion of positive (negative) trades, managers have anticipated an upcoming bull market

period therefore shifted their portfolios towards positive (negative) trade proportions. We

compare the portfolio adjustments of the statistically significant trades with the values of

their respective indicators.

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4.10.1 Market Beta Trade Proportions

4.10.1.1 Market Index

Table 4.9 presents the correlation and regression analysis between the positive and

negative beta trade proportions and the market index. Panel A presents the results between

the positive beta trade proportions and Panel B presents the results between the negative beta

trade proportions.

We observe from Panel A and B of Table 4.9 that the proportion of positive beta

trades are higher than the proportions of negative beta trades. This is consistent to our

expectations that due to more bullish periods between 1991 and 2012, we would expect a

higher proportion of positive beta trades.

We observe from Panel A that there were no significant correlation or regression

results from both tests. However, we observe from Panel B of Table 4.9 that the analysis

between the negative proportions of trade betas and the market index during bearish market

periods exhibited a reasonably high percentage of adjusted R2 value. Although there were no

significant correlation or regression results, the negative beta trade proportions are negatively

correlated to the market index. This suggest an inverse relationship. Likewise, although the

beta coefficient is not significant, the adjusted R2 of this model was 26.6%. This suggests that

26.6% of the negative beta trade proportions can be explained by the market index.

Table 4.9. Individual Correlation and Regression Analysis between Market Beta Trades

(Proportions) and the Market Index – June 1991 to September 2012

The different types of test based on the trade proportions are illustrated below. There are two types of

test: Market trend- Bull and Bear Market; Proportions of trades- Higher proportions in positive beta

trades and higher proportions of negative beta trades. Panel A presents the results of the correlation

and regression analysis between the positive beta trade proportions and the Market Index. Panel B

presents the results of the correlation and regression analysis between the negative trade proportions

and the Market Index. All regression analysis are conducted individually. Regression equation: (ŷ=

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βₒ+β₁X1+εi); Dependent Variables: Positive and Negative Beta Trade Proportions; Independent

Variable: Market Index

Panel A: Market Index and Positive Beta Trades

Types of Test No. of Quarts Correlation Regression

β Sig Adj R²(%)

Market Trend

Bull Period 75 0.08 ~0.000 0.905 -2.1

Proportions

Higher prop of Positive Beta per

quart. 60 0.01 ~0.000 0.946 -2.5

Panel B: Market Index and Negative Beta Trades


β Sig Adj R²(%)

Market Trend

Bear Period 17 -0.129 0.000 0.285 26.6

Proportions

Higher prop of Negative Beta per

quart. 24 -0.059 -~0.000 0.797 -3.8




4.10.1.2 Market “Return” Indicator


negative trade beta proportions and the market “return” indicator. Panel A presents the results

between the positive beta trade proportions and Panel B presents the results between the

negative beta trade proportions.

Similar to Table 4.9, we observe from Panel A and B of Table 4.10 that the

proportions of positive beta trades are higher than the proportions of negative beta trades.

This is consistent to our expectations that due to more bullish periods, we would expect a

higher number of positive beta trade proportions.

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As the “returns” indicators avoids spurious issues, we expected more significant

results from the market “return” indicator however the only significant correlation and

regression results exhibited was between the negative beta trade proportions and the market

“return” indicator. Previously, Panel B of Table 4.9 suggests that during bearish markets, the

negative beta trade proportions were negatively correlated to the market index but however

the correlation value was not significant. Consistent results were reflected from Panel B of

Table 4.10 that between the negative beta trade proportions and the market “return” indicator,

we observe an inverse relationship with a high correlation value of -0.549 and it is significant

at the 0.05 level.

We also observed that the beta coefficient between the negative beta trade proportions

and the market “return” indicator is -0.002 and it is significant at the 0.05 level. Having a beta

coefficient of -0.002 implies that for every 1 unit decrease in the market “return” indicator,

the negative beta trade proportions will decrease by 0.002.The adjusted R2 value tells us that

26.6% of the negative beta trade proportions can be explained by the market “return”

indicator during bearish market periods.

Table 4.10. Individual Correlation and Regression Analysis between Market Beta

Trades (Proportions) and the Market “Return” Indicator – July 1991 to September

2012


test: Market trend- Bull and Bear Market; Proportions of trades- Higher proportions in positive beta

trades and higher proportions in negative beta trades. Panel A presents results of the correlation and

regression analysis between the positive beta trade proportions and the Market “Return” indicator.

Panel B presents the results of the correlation and regression analysis between the negative trade

proportions and the Market “Return” indictor. All regression analysis are conducted individually.

Regression equation: (ŷ= βₒ+β₁X1+εi); Dependent Variables: Positive and Negative Beta Trade

Proportions; Independent Variable: Market “Return” Indicator

Panel A: Market “Return” Indicator and Positive Beta Trades


β Sig Adj R²(%)

Market Trend

Bull Period 75 0.019 ~0.000 0.905 -2.1

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Proportions

Higher prop of Positive Beta per

quart. 60 0.100 0.000 0.453 -2.5

(Panel B continues on the next page)

Panel B: Market “Return” Indicator and Negative Beta Trades


β Sig Adj R²(%)

Market Trend

Bear Period 17 -0.549** -0.002 0.016 26.6

Proportions

Higher prop of Negative Beta per

quart. 24 -0.222 0.000 0.310 -3.8




4.10.2 Sentiment Beta Trade Proportions

4.10.2.1 Sentiment Index


negative trade sentiment beta proportions and the sentiment index. Panel A presents the

results between the positive sentiment beta trade proportions and Panel B presents the results

between the negative sentiment beta trade proportions.

We observe from Panel A and B of Table 4.11 that the proportion of positive

sentiment beta trades are higher than the proportions of negative sentiment beta trades. This

is consistent to our expectations that due to more bullish periods, we would expect a higher

proportions of positive sentiment beta trades. However, there were no significant correlation

or regression results.

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Table 4.11. Individual Correlation and Regression Analysis between Sentiment Beta Trades

(Proportions) and the Sentiment Index– June 1991 to March 2011


test: Market trend- Bull and Bear Market; Proportions of trades- Higher proportions in positive

sentiment beta trades and higher proportions in negative sentiment beta trades. Panel A presents the

results of the correlation and regression analysis between the positive sentiment beta trade proportions

and the Sentiment Index. Panel B presents the results of the correlation and regression analysis

between the negative sentiment beta trade proportions and the Sentiment Index. All regression

analysis are conducted individually. Regression equation: (ŷ= βₒ+β₁X1+εi); Dependent Variables:

Positive and Negative Trade Proportions; Independent Variable: Sentiment Index

Panel A: Sentiment Index and Positive Sentiment Beta Trades


β Sig Adj R²(%)

Market Trend

Bull Period 70 -0.051 -0.012 0.672 -1.2

Proportions

Higher prop of Positive Sen Beta

per quart. 55 0.03 0.004 0.827 -1.8

Panel B: Sentiment Index and Negative Sentiment Beta Trades


β Sig Adj R²(%)

Market Trend

Bear Period 17 -0.139 -0.013 0.594 -4.6

Proportions

Higher prop of Negative Sen Beta

per quart. 25 -0.197 -0.018 0.346 -0.3




4.10.2.2 Sentiment “Return” Indicator


negative sentiment beta trade proportions and the sentiment “return” indicator. Panel A

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presents the results between the positive sentiment beta trade proportions and Panel B

presents the results between the negative sentiment beta trade proportions.


proportions of positive sentiment beta trades are higher than the proportions of negative

sentiment beta trades. This is consistent to our expectations that due to more bullish periods,

we would expect a higher proportion of positive sentiment beta trades.

The results from Table 4.12 are consistent to our expectations that “return” indicators

would reflect more significant results as they capture standardized changes in each quarter

period. We observe from Panel A of Table 4.12 that the positive sentiment beta proportions

are lowly negatively correlated to the sentiment “return” indicator during bullish periods.

Although we expect that during bullish markets, there would be a higher proportion of

positive sentiment beta trades due to higher returns, results suggest an inverse relationship.

The correlation value was -0.299 with a significant level of 0.05. The beta coefficient

between the positive sentiment beta trade proportions and the sentiment “return” indicator is -

0.003 and it is significant at the 0.05 level. Having a beta coefficient of -0.003 implies that

for every 1 unit decrease in the sentiment “return” indicator, the positive sentiment beta trade

proportions will decrease by 0.003.The adjusted R2 value tells us that 7.6% of the positive

sentiment beta trade proportions can be explained by the sentiment “return” indicator during

bullish market periods.

We observe from Panel B of Table 4.12 that there is a highly positive correlation

between the negative sentiment trade proportions and the sentiment “return” indicator when

there is a higher proportion of negative sentiment trade proportions. This is consistent to our

expectations that during periods with higher proportion of negative sentiment trade

proportions, fund managers have anticipated a bearish market therefore shifted their

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portfolios towards negative sentiment trade proportions. When the sentiment index reflects

poor market performance, there implies lower sentiment “returns”, therefore we expect fund

managers to tilt towards negative sentiment beta trade proportions. The correlation between

the negative sentiment beta trade proportions and the sentiment “return” indicator exhibited a

high correlation value of 0.698 and it is significant at the 0.01 level. The beta coefficient

between the negative sentiment beta trade proportions and the sentiment “return” indicator is

0.003 but however is not significant. The adjusted R2 value tells us that 46.5 % of the

negative sentiment beta trade proportions can be explained by the sentiment “return”

indicator.

Table 4.12. Individual Correlation and Regression Analysis between Sentiment Beta Trades

(Proportions) and the Sentiment “Return” Indicator– Jul 1991 to March 2011

The different types of test based on the trade proportions are illustrated below. There are two

types of test: Market trend- Bull and Bear Market; Proportions of trades- Higher proportions in

positive sentiment beta trades and higher proportions in negative sentiment beta trades. Panel A

presents the results of the correlation and regression analysis between the positive sentiment beta

trade proportions and the Sentiment “Return” Indicator. Panel B presents the results of the correlation

and regression analysis between the negative sentiment beta trade proportions and the Sentiment

“Return” Indicator. All regression analysis are conducted individually. Regression equation: (ŷ=

βₒ+β₁X1+εi); Dependent Variables: Positive and Negative Trade Proportions; Independent Variable:

Sentiment “Return” Indicator

Panel A: Sentiment “Return” Indicator and Positive Sentiment Beta Trades


β Sig Adj R²(%)

Market Trend

Bull Period 69 -0.299** -0.003 0.013 7.6

Proportions

Higher prop of Positive Sen Beta

per quart. 54 0.123 0.001 0.377 -0.4

Panel B: Sentiment “Return” Indicator and Negative Sentiment Beta Trades


β Sig Adj R²(%)

Market Trend

Bear Period 17 -0.264 -0.003 0.305 0.8

Proportions

Higher prop of Negative Sen Beta 25 0.698*** 0.003 0.000 46.5

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per quart.




4.10.3 Momentum Trade Proportions

4.10.3.1 Momentum Index


negative momentum trade proportions and the momentum index. Panel A presents the results

between the positive momentum trade proportions and Panel B presents the results between

the negative momentum trade proportions.

We observe from Panel A and B of Table 4.13 that the proportions of positive

momentum trades are lower than the proportions of negative momentum trades. This is

inconsistent to our expectations that due to more bullish periods, we would expect a higher

proportion of positive momentum trades. We consider how these mutual fund managers may

have pursued a contrarian strategy as mutual fund managers would buy funds that were past

“losers” and sell funds that were past “winners” based on their relative performance.

We observe from Panel A of Table 4.13 that the positive momentum trade proportions

are highly negatively correlated to the momentum index during bullish periods. Although we

expect that during bullish markets, there would be a higher proportion of positive momentum

trades due to the persistence in past “winners”, results suggest an inverse relationship. The

correlation value was -0.521 with a significant level of 0.01. The beta coefficient between the

positive momentum trade proportions and the momentum index is – 0.001 and it is significant

at the 0.01 level. Having a beta coefficient of -0.001 implies that for every 1 unit decrease in

the momentum index, the positive momentum trade proportions will decrease by 0.001.The

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adjusted R2 value tells us that 24.0% of the positive momentum trade proportions can be

explained by the momentum index during bullish market periods.

From Panel A of Table 4.13, we observe that there is a highly negative correlation

between the positive momentum trade proportions and the momentum index when there is a

higher proportion of positive momentum trades. This is inconsistent to our expectations that

during periods with higher positive momentum trade proportions, fund managers have

anticipated a bullish market therefore shifted their portfolios towards positive momentum

trade proportions. When the values of the indicators are reflecting good market performance,

this implies a higher persistence on positive momentum trades, therefore a higher proportion

of positive momentum trades. The correlation between the positive momentum trade

proportions and the momentum index exhibited a high correlation value of 0.638 and it is

significant at the 0.05 level. The beta coefficient between the positive momentum trade

proportions and the momentum index is -0.001 and it is significant at the 0.05 level. Having a

beta coefficient of -0.001 implies that for every 1 unit decrease in the momentum index, the

positive momentum trade proportions will decrease by 0.001. The adjusted R2 value tells us

that 35.5 % of the positive momentum trade proportions can be explained by the momentum

index.

We also observe from Panel B of Table 4.13 that there is a high positive correlation

between the negative momentum trade proportions and the momentum index when there is a

higher proportion of negative momentum trades. This is consistent to our expectations that

during periods with higher negative momentum trade proportions, fund managers have

anticipated a bearish market therefore shifted their portfolios towards negative momentum

trade proportions. However, the correlation value, 0.546 was not significant. The beta

coefficient between the negative momentum trade proportions and the momentum index is

0.001 and it is significant at the 0.10 level. Having a beta coefficient of 0.001 implies that for

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every 1 unit increase in the momentum index, the negative momentum trade proportions will

increase by 0.001. The adjusted R2 value tells us that 22.8 % of the negative momentum trade

proportions can be explained by the momentum index.

Table 4.13. Individual Correlation and Regression Analysis between Momentum Trades

(Proportions) and the Momentum Index – September 2006 to September 2012


types of test: Market trend- Bull and Bear Market; Proportions of trades- Higher proportions

in positive momentum trades and higher proportions in negative momentum trades. Panel A

presents the results of the correlation and regression analysis between the positive momentum

trade proportions and the Momentum Index. Panel B presents the results of the correlation

and regression analysis between the negative trade proportions and the market index. All

regression analysis are conducted individually. Regression equation: (ŷ= βₒ+β₁X1+εi);

Dependent Variables: Positive and Negative Trade Proportions; Independent Variable:

Momentum Index

Panel A: Momentum Index and Positive Momentum Beta Trades


β Sig Adj R²(%)

Market Trend

Bull Period 25 -0.521*** -0.001 0.008 24.0

Proportions

Higher prop of Positive Mom

Trades per quart. 13 -0.638** -0.001 0.019 35.3

Panel B: Momentum Index and Negative Momentum Beta Trades


β Sig Adj R²(%)

Market Trend

Bear Period 7 0.597 0.000 0.157 22.7

Proportions

Higher prop of Negative Mom

Trades per quart. 12 0.546 0.001 0.066 22.8




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4.10.3.2 Momentum “Return” Indicator


negative momentum trade proportions and the momentum “return” indicator. Panel A

presents the results between the positive momentum trade proportions and Panel B presents

the results between the negative momentum trade proportions.


proportion of positive momentum trades are lower than the proportion of negative momentum

trades. This is inconsistent to our expectations that due to more bullish periods, we would

expect a higher proportion of positive momentum trades. Although we expect the “return”

indicator to exhibit more significant results based on Table 4.14, the momentum index had

more significant correlation results. This reason may be cause by a pseudo return as the

momentum index is already considered as “return” indicator.

We observe from Panel B of Table 4.14 that the negative momentum trade

proportions are highly positively correlated to the momentum “return” indicator during

bearish periods. This is consistent to our expectations that during bearish periods, there would

be a higher proportion of negative momentum trades as the “returns” would be low. The

correlation value was -0.841 with a significant level of 0.01. The beta coefficient between the

negative momentum trade proportions and the momentum “return” indicator is 0.001 and it is

significant at the 0.05 level. Having a beta coefficient of 0.001 implies that for every 1 unit

increase in the momentum “return” indicator, the positive momentum beta proportions will

increase by 0.001.The adjusted R2 value tells us that 65.0% of the negative momentum trade

proportions can be explained by the momentum “return” indicator. However, the credibility

of these results are questionable as there were only 7 quarters.

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Table 4.14. Individual Correlation and Regression Analysis between Momentum Trades

(Proportions) and the Momentum “Return” Indicator – October 2006 to September 2012


types of test: Market trend- Bull and Bear Market; Proportions of trades- Higher proportions in

positive momentum trades and higher proportions in negative momentum trades. Panel A

presents the results of the correlation and regression analysis between the positive momentum

trade proportions and the Momentum “Return” Indicator. Panel B presents the results of the

correlation and regression analysis between the negative trade proportions and the market index.

All regression analysis are conducted individually. Regression equation: (ŷ= βₒ+β₁X1+εi);

Dependent Variables: Positive and Negative Trade Proportions; Independent Variable:


Panel A: Momentum “Return” Indicator and Positive Momentum Beta Trades


β Sig Adj R²(%)

Market Trend

Bull Period 20 -0.238 -0.001 0.313 0.4

Proportions

Higher prop of Positive

Mom Trades per quart. 13 -0.454 -0.001 0.119 13.4

Panel B: Momentum “Return” Indicator and Negative Momentum Beta Trades


β Sig Adj R²(%)

Market Trend

Bear Period 7 0.841** 0.001 0.018 65.0

Proportions

Higher prop of Negative

Mom Trades per quart. 11 -0.011 ~-0.000 0.974 -11.1 *** Significant at the 0.01 level



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4.11 Summary Table of Significant Results based on Overall Analysis and Preliminary

Tests

Table 4.15. Significant Results based on Overall Analysis and Preliminary Tests

The table below summarises which types of trade proportions and their respective market and

systemic risk indicators have produced significant correlation and regression results. √ represents

significant results, × represents no significant results exhibited.

Types of Test

Types of

Trades

Positive Negative Types of

Indicators

Correlation Regression

Overall Sentiment √ √

Sentiment

"Return" √ √

Momentum √ √ Momentum Index √ √

Momentum √ √

Momentum

"Return" √ √

Beta √ √ Delta ABR* √ ×

Sentiment √ √ Delta ABR* √ ×

Momentum √ √ Delta CoVar √ ×

Bull Market Sentiment √

Sentiment

"Return" √ √

Momentum √ Momentum Index √ √

Bear Market Beta

√ Market Index √ √

Beta

√ Market "Return" √ √

Momentum √

Momentum

"Return" √ √

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Higher Pos Prop. Momentum √

Momentum Index √ √

Higher Neg

Prop. Sentiment

√

Sentiment

"Return" √ √


* ABR: Absorption Ratio

4.12 Conclusion of Results and Discussion

By examining the proportions of statistically significant trades that encompass beta,

sentiment beta and momentum, we identify fund managers that adjust their portfolios

between positive and negative trade proportions in accordance to the market performance.

We refer this portfolio tilting action as the ability to time to the market. We evaluate trade

proportions as they provide insights on the direction that the mutual fund manager is

pursuing. Typically, when the market is performing well, we expect more positive trade

proportions in each quarter. In contrast, when the market is performing poorly, we expect

more negative trade proportions in each quarter.


performance of the market and the economy. Market indicators are very important as they

reflect bearish and bullish market periods. Based on the index values, mutual fund managers

can shift their portfolios accordingly to take advantage of the market. We also created

“return” indicators to measure standardize changes in the index values in each quarter, this

helps to prevent spurious issues. After the recent global financial crisis, systemic risk

indicators were created to detect upcoming recession periods. We examined if these

statistically significant trades proportions have a direct relationship with these index values

during different market trends.

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We conducted an overall correlation and regression analysis to investigate in general,

if there were any significant relationship between the statistically significant trade

proportions and their respective indicators. Beta trade proportions were examined with the

values of the market index, market “return” indicator and the systemic risk indicators.

Sentiment beta trade proportions were examined with the values of the sentiment index,

sentiment “return” indicator and the systemic risk indicators. Momentum trade proportions

were examined with the values of the momentum index, momentum “return” indicator and

the systemic risk indicators.

Our results showed that only positive sentiment trade proportions and positive

momentum trade proportions displayed significant correlation and regression results between

their respective indicators. However, these positive trade proportions exhibited an inverse

relationship. This suggests the possibility of a contrarian strategy.

Preliminary tests were also conducted with the consideration of bullish and bearish

market trends as well as periods with higher proportions of positive or negative trade

proportions. These test are conducted to investigate if mutual fund managers are selective in

adjusting their portfolios based on certain conditions.

For bullish market trends, we observe significant correlation and regression results

between the positive sentiment trade proportions and the sentiment “return” indicator.

However, an inverse relationship was exhibited. The positive momentum trade proportions

also displayed significant correlation and regression results when evaluated against the

momentum index. Similarly, an inverse relationship was exhibited. For bearish market

trends, the negative beta exhibited significant correlation and regression results when

compared to the market index and the market “return” indicator. These results suggest an

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inverse relationship. Results were also significant between negative momentum trade

proportions and the momentum “return” indicator with a positively high correlation value.

For periods with higher proportions of positive proportion trades, we expect that fund

managers had anticipated a bullish market therefore shifted their portfolios towards positive

trades. However, there was only one significant results between the positive momentum trade

proportion and the momentum index however, it was an inverse relationship. For the periods

with higher proportions of negative proportion trades, we expect that fund managers had

anticipated a bearish market therefore shifted their portfolios towards negative trades. The

analysis between the negative sentiment trade proportions and the sentiment “return”

indicator displayed a significant correlation and regression results with a high positive

correlation value. Although the analysis between the negative momentum trade proportions

and the momentum index displayed a high correlation value, it is not significant.

Based on these analyses, we observe mostly inverse relationship patterns between

these trade proportions and their respective indicators variables. However, beta trade

proportions did not reflect any substantial correlation or regression results. Similarly, the

results between the trade proportions and the systemic risk indicators were not constructive.

Some possible reasons could be that the variations of the dependent variables, statistically

significant trade proportions and the independent variables, market and systemic risk

indicators were not very high. We also consider how using statistically significant trade

proportions might have affected our results. Lastly, using proportions might lead to herding

behaviour providing inaccurate analyses.

We consider the possibility that these mutual fund managers were unable to select

turning points of bullish and bearish market periods. Therefore, we proceed to conduct robust

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testing to identify if these managers are capable of identifying large or small market shocks

and market persistence.

CHAPTER 5

ROBUST TESTING

5.1 Introduction

This chapter shows the analyses and results of my robust tests. We conducted various

robust test; Magnitude of Change, Changes in Standard Deviation, Changes in Signs and

Persistence. We also conducted a multiple regression analysis to simultaneously test all

independent variables in our analysis to examine if one or more variables will affect the

predictability value of our dependent variable. Similar to the results of the preliminary tests,

sentiment beta and momentum trade proportions exhibited the most number of significant

results. However, both sentiment beta and momentum trade proportions exhibited an inverse

relationship with their respective indicators.

5.2 Overview of Robust Testing

In the previous chapter, we conducted an overall correlation and regression analysis

between the statistically significant trade proportions, market and systemic risk indicators. An

overall test does not take into consideration that these mutual fund managers may be selective

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in adjusting their portfolios according to different situations of the market. This analysis

provides some general insights on the possibility of any form of direct or inverse relationship

between these statistically significant trade proportions, the market and systemic risk

indicators.

After conducting an overall analysis, we ran some preliminary tests between these

statistically trade proportions and their respective indicators. First, we consider if mutual fund

managers are capable of predicting bullish and bearish market trends. Second we examine if

there were any form of relationship between positive (negative) trade proportions and their

respective indicators when we isolated periods with higher proportions of positive (negative)

trade proportions. We expect that periods with high proportions of positive (negative) trades

are influence by good (poor) market performance which are reflected by the values of the

indicators. Based on the results, we observe an inverse relationships between positive

momentum trade proportions the momentum index. It is plausible that these mutual fund

managers are pursuing a contrarian strategy. We investigate further by conducting a few

robust tests between the trade proportions and their respective market indicators.

Robust testing is essential as it subjects the constructs to rigorous statistical testing,

thus ensuring the reliability of the results obtained. It is possible that fund managers may not

be able to isolate turning points in the market’s economic or financial behaviour but identify

or be sensitized to large market shocks, market persistence. We have considered four types of

robust test; Magnitude of change, Changes in Standard Deviation, Changes in Sign and

Persistence. We will examine these in turn.

Figure 5.1 provides a schematic diagram on the types of robust tests that we have

considered. The diagram presents which type of robust test will be conducted on the related

statistically significant trade proportions that encompass beta, sentiment beta and momentum.

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Figure 5.1: Types of Robust Test Conducted

The figure below illustrates the overall process of robust testing. There are four types of robust tests.

(1) Magnitude of Change (2) Changes in Standard Deviation (3) Changes in Signs (4) Persistence.

Test (1) and (2) are mainly for “return” indicators. Beta trade proportions: Test (1), (2), (3) and (4);

Sentiment beta trade proportions: Test (3) and (4); Momentum trade proportions: Test (4)

Robust Test

Magnitude of

Change

(1)

Changes in

Standard Deviations

(2)

Changes in Signs

(3)

Persistence

(4)

Beta Trade

proportions

Beta Trade

Proportions

Beta Trade

proportions

Beta Trade

proportions

Market “Return”

Indicator

Market “Return”

Indicator

Market “Return”

Indicator

Market “Return”

Indicator

Sentiment beta

proportions

Sentiment beta

proportions

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-Sentiment

“Return” indicator

-Sentiment

“Return” Indicator

-Sentiment Index

-Sentiment Index

Momentum

Proportions

-Momentum


-Momentum Index

While these statistically significant trades proportions that encompass beta, sentiment

beta and momentum are directly related to the market index, sentiment index and momentum

index, emphasis is given to the market “return”, sentiment “return” and momentum “return”

indicators. We expect more significant results to be exhibited from these “return: indicators

as they are constructed to detect standardized changes in the index values against the base

values and this avoids spurious issues.

5.3 Beta Trade Proportions and the Market “Return” Indicator

5.3.1 Test (1): Magnitude of Change

The magnitude of change test allows us to identify if mutual fund managers had

successful trade-offs. We examine if they are capable of selecting either large or small

changes based on the market “returns” to adjust their portfolios to take advantage of the

market. Big changes are market returns that are above 5%, 10%, 15%, 20%, 25% and 30%

and small changes are market returns that are lower than -5%, -10%, -15%, -20%, -25% and -

30%.

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Table 5.1 presents the number of quarter observations based on their returns. This

provides some understanding on the direction that these mutual fund managers were

pursuing. We expect that during periods with higher returns, mutual fund managers will be

tilting their portfolios towards positive beta trade proportions. Similarly we expect that during

periods with lower returns, mutual fund managers will be tilting their portfolios towards

negative beta trade proportions. High returns are related to bullish market periods and low

returns are related to bearish market periods.

Table 5.1. Number of quarters in relation to Market “Returns”- July 1991 to September

2012

Column 2 presents the number of quarters that have market return above 5%, 10%, 15%. 20%. 25%

and 30%. Column 4 presents the number of quarters that have market returns less than -5%, -10%, -

15%, -20%, -25% and -30%.

Returns Above No. of Quarts Returns Below No. if Quarts Total No. of Quarts

30% 19 -30% 12 31

25% 22 -25% 13 35

20% 30 -20% 13 43

15% 38 -15% 15 53

10% 41 -10% 22 63

5% 53 -5% 23 76

We observe from Table 5.1 that between 1991 and 2012, most market “returns” were

more than 5%. There were 53 quarter observations that reflected market returns that were

above 5%. However, 5% change may not be significant enough to detect the market timing

abilities of the mutual fund managers.

Logan (2014) reported that that a bull market period occurs when the index is rising

20% off the bear market low and a bear market period occurs when the index is falling 20%

off the bull market. Therefore, we expect mutual fund managers to display market timing

abilities during quarters with returns higher than 20% and returns lower than -20%.

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5.3.2 Test (2): Changes in standard deviation

Similar to the test of magnitude of changes, we evaluate how confident fund managers

are in picking changes. We examine market returns that are above the mean plus half a

standard deviation and market returns that are below the mean minus half a standard

deviation. We expect mutual fund managers to tilt their portfolios towards positive beta trade

proportions when returns are above the mean plus half a standard deviation and we expect

mutual fund managers to tilt their portfolios towards negative beta trade proportions when

returns are below the mean plus half a standard deviation. There is a 38% chance that the

mutual fund managers will select positive trade proportions when returns are above the mean

and a 38% chance that the mutual fund managers will select negative trade proportions when

returns are below the mean.

Table 5.2. Empirical Rule for Normally Distributed Data

Distance from mean Values within distance

𝜇 ± 0.5𝜎 38%

𝜇 ± 1𝜎 68%

𝜇 ± 2𝜎 95%

𝜇 ± 3𝜎 99.7%

Source: Black et al. (2016)

5.3.3 Test (3): Changes in Signs

We examine if mutual fund managers are capable of selecting turning points in the

values of the market “return” indicator. We expect successful market timers to tilt their

portfolios towards positive trade proportions when market “returns” transit from negative to

positive value from the previous quarter. This could be a signal of a bull market period.

Similarly, we expect successful market timers to tilt their portfolios towards negative trade

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proportions when market “returns” transit from positive to negative values from the previous

quarter. This could be a signal of a bear market period.

5.3.4 Test (4): Persistence in Index

We examine if mutual fund managers exhibit market timing abilities based on market

persistence. We expect mutual fund managers to tilt their portfolios towards positive beta

trade proportions when the market “returns” displays consecutive increases in values.

Similarly, we expect mutual fund managers to tilt their portfolios towards negative beta trade

proportions when the market “returns” displays consecutive decreases in values. Market

persistence is similar to momentum strategies with the belief that past “winners” are still

“winners” and past “losers” are still “losers”. We also observed the market “return” indicator

has exhibited more than three quarters of consecutive decreases in “returns”.

Table 5.3 presents the correlation and regression results of the robust test that we have

conducted between the proportions of negative, positive beta trades and the market “return”

indicator. Panel A presents the results from the magnitude of change test. Panel B presents

the results from the changes in standard deviation test. Panel C presents the results from the

changes in signs test. Panel D presents the results from the market persistence test.

We observe from Panel A (Magnitude of Changes) and Panel B (Changes in Standard

Deviation) of Table 5.3 that there were no significant correlation or regression results.

From Panel C (Changes in Signs) of Table 5.3, we observe significant results

between the negative beta trade proportions and the market “return” indicator. Although there

were no significant correlations, the correlation value of -0.346 suggests an inverse

relationship. This is inconsistent to our expectations that mutual fund managers will tilt their

portfolios towards negative trade proportions when the “return” values transit from a positive

“return” to a negative “return”, a possible signal of a bearish market. The beta coefficient

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between the negative beta trade proportions and the market “return” index is -0.001,

significant at the 0.10 level. Having a beta coefficient of -0.001 implies that for every 1 unit

decrease in the market “return” indicator, the negative beta trade proportions will decrease by

0.001. The adjusted R2 value tells us that 8.6% of the negative beta trade proportions can be

explained by the market “return” indicator.

We observe from Panel D (Persistence) of Table 5.3 that the negative beta trade

proportions exhibited significant regression results when the market displayed consecutive

decreases in “returns”. Although there were no significant correlation results, the value -

0.274 suggests an inverse relationship. The beta coefficient between the negative beta trade

proportions and the market “return” index is -0.001, significant at the 0.10 level. Having a

beta coefficient of -0.001 implies that for every 1 unit decrease in the market “return”

indicator, the negative beta trade proportions will decrease by 0.001. The adjusted R2 value

tells us that 5.5% of the negative beta trade proportions can be explained by the market

“return” indicator.

Table 5.3. Robust Testing between Proportions of Beta Trades based and the Market “Return” Indicator

The different types of test conducted between the positive and negative proportion of trade betas and the market

“return” indicator are illustrated below. There are four types of robust test: Magnitude of change based on

market “returns”; Changes in standard deviation of market “returns”- Market “return” > Mean+0.5SD and

Market “return” < Mean-0.5SD; Changes in sign based on the positive or negative index value per quarter;

Persistence in positive or negative signs of values in the index per quarter. Panel A presents the correlation and

regression results of the magnitude of changes test. Panel B presents the correlation and regression results of the

changes in standard deviation test. Panel C presents the correlation and regression results of the changes in signs

test. Panel D presents the correlation and regression results of the persistence test. There were only three or

more consecutive decrease in the values of the market “return” indicator, there were no three or more

consecutive increases. Simple regression analysis are conducted. (ŷ=βₒ+β₁X1+εi). DV: positive or negative trade

proportions; IV: Market “Return” Indicator.


β Sig Adj R²(%)

Panel A: Magnitude of Change (Jul 1991 - Sep 2012)

Market Return > 30% 15 -0.192 -0.001 0.494 -3.7

Market Return < -30% 9 -0.455 -0.002 0.219 9.3

Market Return > 25% 22 -0.241 -0.001 0.281 1.1

Market Return < -25% 10 -0.427 -0.002 0.218 8.0

Market Return >20% 29 -0.125 -0.001 0.520 -2.1

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Market Return < -20% 12 -0.458 -0.002 0.135 13.0

Panel B: Changes in Standard Deviation (Jul 1991 – Sep 2012)

Return> Mean+0.5SD 24 -0.249 -0.001 0.241 1.9

Return< Mean-0.5SD 61 -0.186 -0.001 0.150 1.8

Panel C: Changes in Sign (Sep 1991 - Sep 2012)

Positive 57 -0.059 0.000 0.664 -1.5

Negative 28 -0.346 -0.001 0.071 8.6

Panel D: Persistence (Jul 1991 - Sep 2012)

Increase in Index 37 -0.119 0.000 0.483 -1.4

Decrease in Index 48 -0.274 -0.001 0.059 5.5

Decrease > 3 consecutive quarts. 17 -0.343 -0.002 0.178 5.9




5.4 Beta Trade Proportions and the Market Index


Replicating the analysis between beta trade proportions and the market “return”, we

examine if mutual fund managers exhibit market timing abilities based on persistence in the

values of the market index. We expect mutual fund managers to tilt their portfolios towards

positive beta trade proportions when the market index displays consecutive increases in

values. Similarly, we expect mutual fund managers to tilt their portfolios towards negative

beta trade proportions when the market index displays consecutive decreases in values. We

also observe that the market index has exhibited more than three quarters of consecutive

increases in index values.

Table 5.4 presents the correlation and regression results of the market persistence test.

We observe from Table 5.4, that there were some significant regression results between the

negative trade proportions and the market index when the market index displayed consecutive

decreases in their index values. Although, there were no significant correlation results, the

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value 0.331 suggests a direct relationship consistent to our expectations. However, the beta

coefficient between the negative beta trade proportions and the market index is 0.000,

significant at the 0.01 level. The adjusted R2 value tells us that 7.5% of the negative beta

trade proportions can be explained by the market index.

Table 5.4. Robust Testing between Proportions of Beta Trades and the Market Index

The results of the regression and correlation test between the proportion of positive and negative trade

betas and the market index is illustrated below. There is one robust testing: Persistence in increase or

decreases in the values of the market index. There were only three or more consecutive increases in

the values of the market index, there were no three or more consecutive decreases. Simple regression

analysis are conducted. (ŷ=βₒ+β₁X1+εi). DV: positive or negative trade proportions; IV: Market Index.

Type of Test No. of Quarts Correlation Regression

β Sig Adj R²(%)

Persistence (Jun 1991 - Sep 2012) Increase in Index 57 0.214 ~0.000 0.110 2.8

Increase > 3 consecutive quarts. 40 0.178 ~0.000 0.272 0.6

Decrease in Index 28 0.331 0.000 0.085 7.5




5.5 Sentiment Beta Trade Proportions and the Sentiment “Return” Indicator

As the “returns” of the sentiment index are not “real” returns, Test 1 and Test 2 are

not required.

5.5.1 Test (3): Changes in Sign

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Quarterly Trades

We examine if mutual fund managers are capable of selecting turning points in the

values of the sentiment “return” indicator. We expect successful market timers to tilt their

portfolios towards positive sentiment beta trade proportions when sentiment “returns” transit

from negative to a positive value from the previous quarter. It is plausible that the investor’s

sentiment has increased when the market is performing well. Similarly, we expect successful

market timers to tilt their portfolios towards negative sentiment trade proportions when

sentiment “returns” transit from positive to negative values from the previous quarter. It is

likely that the investor’s sentiment has decreased when the market is performing poorly.


We examine if mutual fund managers exhibit market timing abilities based on

sentiment persistence. We expect mutual fund managers to tilt their portfolios towards

positive sentiment beta trade proportions when the sentiment “returns” displays consecutive

increases in values. When returns are “high”, it suggest that an investor’s sentiment is high.

An investor’s sentiment is usually high when the market is performing well. Similarly, we

expect mutual fund managers to tilt their portfolios towards negative sentiment beta trade

proportions when the sentiment “returns” displays consecutive decreases in values. When

“returns” are low, it suggest that an investor’s sentiment is low. An investor’s sentiment is

usually low when the market is performing badly. We also observed the sentiment “return”

indicator has exhibited more than three quarters of consecutive decreases in “returns”.


conducted between the proportions of negative, positive sentiment beta trades and the

sentiment “return” indicator. Panel A presents the results from the changes in signs test. Panel

B presents the results from the market persistence test.

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We observe from Panel A (Changes in Signs) of Table 5.5 that there were some

significant results between the positive sentiment beta trade proportions and the sentiment

“return” indicator. The correlation value of -0.428 is significant at the 0.01 level, this

suggests an inverse relationship. This result is inconsistent to our expectations that mutual

fund managers will tilt their portfolios towards positive trade proportions when the “return”

values transit from a positive “return” to a negative “return”, a possible signal of a bullish

market. The beta coefficient between the sentiment beta trade proportions and the sentiment

“return” index is -0.005, significant at the 0.01 level. Having a beta coefficient of -0.005

implies that for every 1 unit decrease in the sentiment “return” indicator, the positive

sentiment beta trade proportions will decrease by 0.005. The adjusted R2 value tells us that

16.1% of the positive sentiment beta trade proportions can be explained by the sentiment


We observe from Panel D (Persistence) of Table 5.5 that the positive sentiment beta

trade proportions exhibited some significant regression results when the sentiment index

displayed consecutive increase in “returns”. The correlation value of -0.423 significant at the

0.05 level suggests an inverse relationship. This is inconsistent to our expectations that

mutual fund managers will tilt their portfolios towards positive trade proportions when the

“return” values consecutively increase in each quarter which suggest that the market is

performing well. The beta coefficient between the sentiment beta trade proportions and the

sentiment “return” index is -0.005, significant at the 0.05 level. Having a beta coefficient of -

0.005 implies that for every 1 unit decrease in the sentiment “return” indicator, the positive

sentiment beta trade proportions will decrease by 0.005. The adjusted R2 value tells us that

15.4% of the positive sentiment beta trade proportions can be explained by the sentiment


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Table 5.5. Robust Testing between Proportions of Sentiment Beta Trades and the Sentiment


The different types of test conducted between the positive and negative sentiment beta trades and the

sentiment “return” indicator are illustrated below. There are two types of robust test: Changes in sign

based on the positive or negative index value per quarter; Persistence in positive or negative signs of

values in the index per quarter. Panel A presents the correlation and regression results of the changes

in signs test. Panel B presents the correlation and regression results of the persistence test. There were

only three or more consecutive decreases in the values of the sentiment return indicator, there were no

three or more consecutive increases. Simple regression analysis are conducted. (ŷ=βₒ+β₁X1+εi). DV:

positive or negative sentiment trade proportions; IV: Sentiment “Return” Indicator.


β Sig Adj R²(%)

Panel A: Changes in Sign (Sep 1991 - Mar 2011)

Positive 39 -0.428*** -0.005 0.007 16.1

Negative 40 -0.026 0.000 0.875 -2.6

(Panel B continues in the next page)

Panel B: Persistence (Jul 1991 - Mar 2012)

Increase in Index 35 -0.423** -0.005 0.011 15.4

Decrease in Index 43 0.078 0.001 0.621 -1.8

Decrease > 3 consecutive quarts. 17 0.045 0.001 0.865 -6.5




5.6 Sentiment beta and the Sentiment index

5.6.1 Test (3): Changes in Sign

Replicating the analysis between sentiment beta trade proportions and the sentiment

“return” indicator, we examine if mutual fund managers exhibit market timing abilities if they

are able to select turning points in the values of the sentiment index. We expect successful

market timers to tilt their portfolios towards positive sentiment beta trade proportions when

the values of the sentiment index transit from negative to positive values from the previous

quarter. This could be a signal of a bull market period. Similarly, we expect successful

market timers to tilt their portfolios towards negative sentiment beta trade proportions when

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the values of the sentiment index transit from positive to negative values from the previous

quarter. This could be a signal of a bear market period. Sentiment values are usually high

during a bullish market period and low during a bearish market period.


Similarly, we replicate the analysis between sentiment beta trade proportions and the

sentiment “return” indicator, we examine if mutual fund managers exhibit market timing

abilities based on sentiment persistence. We expect mutual fund managers to tilt their

portfolios towards positive sentiment beta trade proportions when the sentiment index

displays consecutive increases in values. When an investor’ sentiment is high, this suggest

that the market is performing well. Similarly, we expect mutual fund managers to tilt their

portfolios towards negative sentiment beta trade proportions when the sentiment index

displays consecutive decreases in values. When an investor’ sentiment is low, this suggest

that the market is performing poorly. We also observe that the sentiment index has exhibited

more than three quarters of consecutive increases as well as decreases in their index values.


conducted between the proportions of negative, positive sentiment beta trades and the

sentiment index. Panel A presents the results from the changes in signs test. Panel B presents

the results from the sentiment persistence test. However, there were significant correlation or

regression results.

Table 5.6. Robust Testing between Proportions of Sentiment Beta Trades and Sentiment

Index

The different types of test conducted between the positive and negative proportion of sentiment beta

trades and the Sentiment index are illustrated below. There are two types of robust test: Changes in

sign based on the positive and negative values of the sentiment index per quarter; Persistence in

positive and negative signs of values in the index per quarter. Panel A presents the correlation and

regression results of changes in signs test. Panel B presents the correlation and regression results of

persistence test. All regression analysis are conducted individually. There were three or more

consecutive increases and decreases in the values of the sentiment index. Simple regression analysis

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are conducted. (ŷ=βₒ+β₁X1+εi). DV: positive or negative sentiment trade proportions; IV: Sentiment

Index.

Types of Test No. of Quarts Correlation Regression(ŷ=βₒ+β₁X1+εi)

β Sig Adj R²(%)

Panel A: Changes in Sign (Jun 1991 to Dec 2011)

Positive 60 0.037 0.008 0.778 -1.6

Negative 20 0.092 0.039 0.700 -4.7

Panel B: Persistence (Jul 1991 to Dec 2011)

Increase in Index 44 -0.147 -0.028 0.340 -0.2

Increase > 3 consecutive quarters 32 -0.017 -0.003 0.925 -3.3

Decrease in Index 35 -0.115 -0.019 0.509 -1.7

Decrease > 3 consecutive quarters 24 -0.275 -0.046 0.194 3.4




5.7 Momentum Trade Proportions and the Momentum “Return” Indicator

There were only 25 quarter observations of momentum trade proportions. The limited

number of observations prevented us undertaking Test (1), (2) and (3).


We examine if mutual fund managers exhibit market timing abilities based on

momentum persistence. As the momentum index is designed to measure the performance of

funds that exhibited persistence in their relative performance, we expect this persistence test

to be exhibited significant results as the “returns” of the momentum index is already

measuring persistence. We expect mutual fund managers to tilt their portfolios towards

positive momentum proportions when the momentum “returns” displays consecutive

increases in values. This is the belief that past “winners” are still “winner” and past “losers”

are still “losers”. Similarly, we expect mutual fund managers to tilt their portfolios towards

negative momentum proportions when the momentum “returns” displays consecutive

decreases in values.

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Table 5.7 presents the correlation and regression results of the persistence robust test

that we have conducted between the proportions of negative, positive momentum trades and

the momentum “return” indicator. We observe from Table 5.7 that despite no significant

correlation results between the negative momentum proportions and the momentum “return”

indicator when the momentum indicator displayed consecutive decreases in “returns”. The

correlation value, 0.571 suggests a direct relationship which is consistent to our expectations.

The beta coefficient between the negative beta trade proportions and the momentum “return”

index is 0.001, significant at the 0.10 level. Having a beta coefficient of 0.001 implies that for

every 1 unit increase in the momentum “return” indicator, the negative momentum trade

proportions will increase by 0.001. The adjusted R2 value tells us that 25.8% of the negative

beta trade proportions can be explained by the momentum “return” indicator.

Table 5.7. Robust Testing between Proportions of Momentum Trades and the


The robust test between the positive and negative proportions of trades and the momentum “return”

indicator are illustrated below. Table 5.7 presents the correlation and regression results of the

persistence test. There were no consecutive increases or decrease in momentum return indicator.

Simple regression analysis are conducted. (ŷ=βₒ+β₁X1+εi). DV: positive or negative momentum trade

proportions; IV: Momentum “Return” Indicator.


β Sig Adj R²(%)

Panel D: Persistence (Oct 2006 - Sep 2006)

Increase in Index 11 0.028 0.000 0.934 -11.0

Decrease in Index 12 0.571 0.001 0.053 25.8 *** Significant at the 0.01 level



5.8 Momentum Trade Proportions and the Momentum Index


Replicating the analysis between momentum trade proportions and the momentum

“return” indicator, we examine if mutual fund managers exhibit market timing abilities based

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on persistence in the values of the momentum index. We expect mutual fund managers to tilt

their portfolios towards positive momentum proportions when the momentum index displays

consecutive increases in values. Similarly, we expect mutual fund managers to tilt their

portfolios towards negative momentum proportions when the momentum index displays

consecutive decreases in values.

Table 5.8 presents the correlation and regression results of the persistence robust test

that we have conducted between the proportions of negative, positive momentum trades and

the momentum index. We observe from Table 5.8 that the positive momentum trade

proportions exhibited some significant regression results when the values of the momentum

index displayed consecutive increases in values. The correlation value of -0.552, significant

at the 0.05 level suggests an inverse relationship. Inconsistent to our expectations that mutual

fund managers will tilt their portfolios towards positive momentum trade proportions when

the index values consecutively increase in each quarter which suggest that the persistence

level is high implying that the market is performing well. The beta coefficient between the

momentum trade proportions and the momentum index is -0.001, significant at the 0.05 level.

Having a beta coefficient of -0.001 implies that for every 1 unit decrease in the momentum

index, the positive momentum trade proportions will decrease by 0.001. The adjusted R2

value tells us that 25.1% of the positive momentum trade proportions can be explained by the

momentum index.

Although the results from Table 5.8, suggest the possibility of a contrarian strategy,

based on the results of Table 5.7, there were no inverse relationships between the momentum

trade proportions and the momentum “return” indicator. However, results may be misleading

as the momentum index is already considered as a “return” indicator. Having a “return” on

“return” analysis may lead to inconsistent results due to pseudo returns.

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Table 5.8. Robust Testing between Proportions of Momentum Trades and the

Momentum Index

The robust test between the positive and negative proportions of trades and the momentum index are

illustrated below. Table 7 presents the correlation and regression results of the persistence test. There

were no consecutive increases or decrease in momentum return indicator. Simple regression analysis

are conducted. (ŷ=βₒ+β₁X1+εi). DV: Positive or negative momentum trade proportions; IV:

Momentum Index.

Types of Test No. of Quarts Correlation Regression (ŷ= βₒ+β₁X1+εi)

β Sig Adj R²(%)

Persistence (Sep 2006 - Sep 2012)

Increase in Index 15 -0.552** -0.001 0.033 25.1

Decrease in Index 9 -0.286 0.000 0.456 -5.0




5.9 Multiple Regression Analysis

In the previous chapter, we conducted simple regression analysis between the trade

proportions and their respective market and systemic indicators. However to our dismay, we

did not find any exceptional results. We considered an alternative analysis by conducting a

multiple regression analysis.

We consider how two or more independent variables will affect the predictability

value of the dependent variable. For example, we examine how the market index as well as

how each individual component of the systemic risk indicator will simultaneously affect the

regression results when run in a multiple regression model, unlike the simple regression

model which concentrates on how the market index or the Absorption ratio influences the

trade proportions of the market beta individually.

The multiple regression analysis is conducted using the stepwise method. Stepwise

linear regression is the best option as it regresses multiple independent variables while

concurrently removing variables that are not important. Multiple regression analysis are

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conducted on a step by step basis, each time excluding variables have the weakest correlation

leaving the best independent variable that best explain the distribution.

5.9.1 Market Beta

5.9.1.1 Positive Market Beta Proportions with the Market “Return” Indicator

The dependent variable of this multiple regression model is the positive proportions of

beta trades. The independent variables of this multiple regression model are the market

“return” indicator, and 11 of the systemic risk indicators. They are the Absorption Ratio,

Delta Absorption Ratio, AIM, CoVar, Delta CoVar, Book Leverage, Market Leverage, Real

Volatility, Turbulence, CATFIN and PQR indicators.

We have presented the stepwise regression results of positive beta proportions as the

results of the negative beta proportions are the same but in opposite signs. The emphasize is

on the positive beta trade proportions as there are more bullish market periods than bearish

market periods. We expect a higher proportion of positive beta trades.

We observe from Table 5.9 that the only variable that was included in the model was

the Delta Absorption Ratio. This implies that the Delta Absorption Ratio was the single best

predictor. With the predictor “Delta Absorption Ratio”, 8.1% of the variance was accounted

for. Based on the beta coefficient, Eq. (1):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐵𝑒𝑡𝑎 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 − 0.514 (𝐷𝐴𝐵𝑅) + 𝜀 (1)

The Tolerance value is based on the collinearity diagnostics. Multicollinearity occurs when

independent variables in a multiple regression model are closely correlated to each other

resulting in misleading results when a researcher is attempting to determine how well each

individual independent variable can predict the dependent variable in the regression model.

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When the tolerance value is lesser than 0.10, this indicates multicollinearity. In this case,

multicollinearity is not an issue.

Table 5.9. Robust Testing for Proportions of Beta Trades with Market “Return”

Indicator and 11 Systemic Risk Indicator

The stepwise multiple regression analysis conducted between the positive proportions of beta trades

(dependent variable) and the market “return” and 11 systemic risk indicators (independent variables)

are illustrated below. The 11 systemic risk indicators are the ABR, DABR, AIM, Co, DCo, BL, ML,

RV, Turb, CF and PQR. Multiple regression equation: (ŷ= βₒ+β₁X1+ β2X2+……….+ εi). There 12

independent variables in this analysis.

Positive Beta Proportions (85 quarters)

Included Excluded β Sig Adj R²(%) Tolerance

Market “Return”

x

ABR

x

DABR x

-0.514 0.005 8.1 1

AIM

x

Co

x

(Table continues in the next page)

DCo

x

BL

x

ML

x

RV

x

Turb

x

CF

x

PQR

x

ABR: Absorption Ratio; DABR: Delta Absorption Ratio; Co: CoVar; DCo: Delta CoVar; BL: Book

Leverage; ML: Market Leverage; CF: CATFIN; TURB: Turbulence; PQR: Partial Quantile

Regression

5.9.1.2 Positive Market Beta Proportions with Market Index


beta trades. The independent variables of this multiple regression model are the market index

and similarly 11 of the systemic risk indicators.

Similarly, we have presented the stepwise regression results of positive beta

proportions as the results of the negative beta proportions are the same but in opposite signs.

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The emphasize is on the positive beta trade proportions as there are more bullish market

periods than bearish market periods. We expect a higher proportion of positive beta trades.

We observe from Table 5.10 that the results exhibited were similar to Table 5.9 where

the only variable that was included in the model was the Delta Absorption Ratio. This implies

that the Delta Absorption Ratio was the single best predictor. With the predictor “Delta

Absorption Ratio”, 8.4% of the variance was accounted for. Based on the beta coefficient,

Eq. (2):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐵𝑒𝑡𝑎 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 − 0.527 (𝐷𝐴𝐵𝑅) + 𝜀 (2)



Table 5.10. Robust Testing for Proportions of Beta Trades with Market Index and 11

Systemic Risk Indicator

The stepwise multiple regression analysis conducted between the positive proportions of beta trades

(dependent variable) and the market index and 11 systemic risk indicators (independent variables) are

illustrated below. The 11 systemic risk indicators are the ABR, DABR, AIM, Co, DCo, BL, ML, RV,

Turb, CF and PQR. Multiple regression equation: (ŷ= βₒ+β₁X1+ β2X2+……….+ εi). There 12 independent

variables in this analysis

Positive Beta Proportions (86 Quarters)


Market Index

x

ABR

x

DABR x

-0.527 0.004 8.4 1

AIM

x

Co

x

DCo

x

BL

x

ML

x

RV

x

Turb

x

CF

x

PQR

x



Regression

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5.9.2 Sentiment Beta

5.9.2.1 Positive Sentiment Beta Proportions with Sentiment “Return” Indicator


beta trades. The independent variables of this multiple regression model are the sentiment

“return” indicator, and 11 of the systemic risk indicators.

We have presented the stepwise regression results of positive sentiment beta

proportions as the results of the negative sentiment beta proportions are the same but in

opposite signs. The emphasize is on the positive sentiment beta trade proportions as there are

more bullish market periods than bearish market periods. We expect a higher proportion of

positive sentiment beta trades.

We observe from Table 5.11 that unlike the regression test with beta trade proportions

being the dependent variable, there were two variables included in the model and there are

the sentiment “return” variable and the Delta CoVar indicator. Stepwise runs multiple

regression a number of times, each time removing the weakest correlated variable. The Delta

CoVar indicator is a better predictor. With the predictor “Delta CoVar”, 4.8% of the variance

was accounted for. With two predictors, “Delta CoVar and Sentiment Return indicator”, 8.4%

of the variance was accounted for. With beta coefficient of Delta CoVar being 4.967, Eq. (3):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑆𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡 𝐵𝑒𝑡𝑎 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 + 4.967(𝐷𝐶𝑜) + 𝜀 (3)

When the second independent variable, Delta CoVar was included, the sentiment return beta

coefficient was -0.002, Equation (4):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑆𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡 𝐵𝑒𝑡𝑎 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 + 4.581(𝐷𝐶𝑜) − 0.002 (𝑆𝑒𝑛 𝑅𝑒𝑡) + 𝜀 (4)

The Tolerance value is based on the collinearity diagnostics. Multicollinearity occurs when

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independent variables in a multiple regression model are closely correlated to each other

resulting in misleading results when a researcher is attempting to determine how well each

individual independent variable can predict the dependent variable in the regression model.

When both variables have tolerance values lesser than 0.10, this indicates multicollinearity.

In this case, multicollinearity is not an issue.

Table 5.11. Robust Testing for Proportions of Sentiment Beta Trades with Sentiment


The stepwise multiple regression analysis conducted between the positive proportions of sentiment

beta trades (dependent variable) and the sentiment “return” and 11 systemic risk indicators

(independent variables) are illustrated below. The 11 systemic risk indicators are the ABR, DABR,

AIM, Co, DCo, BL, ML, RV, Turb, CF and PQR. Multiple regression equation: (ŷ= βₒ+β₁X1+

β2X2+……….+ εi). There 12 independent variables in this analysis.

Positive Sentiment Beta Proportions (85 quarters)


Sentiment “Return” x

4.967 0.029 4.8 1

ABR

x

DABR

x

AIM

x

Co

x

DCo x

-0.002 0.048 8.4 0.992

BL

x

ML

x

RV

x

Turb

x

CF

x

PQR

x



Regression

5.9.2.2 Positive Sentiment Beta Proportions with Sentiment Index


sentiment beta trades. The independent variables of this multiple regression model are the

sentiment index and similarly 11 of the systemic risk indicators.

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Similarly, we have presented the stepwise regression results of positive sentiment beta

proportions as the results of the negative sentiment beta proportions are the same but in

opposite signs. The emphasize is on the positive sentiment beta trade proportions as there are

more bullish market periods than bearish market periods. We expect a higher proportion of

positive sentiment beta trades.

We observe from Table 5.12 that unlike sentiment “return” indicator analysis in Table

5.11, the only variable that was included in the model was the Delta Absorption Ratio. This

implies that the Delta Absorption Ratio was the single best predictor for both beta and

sentiment trade proportions. With the predictor “Delta Absorption Ratio”, 8.4% of the

variance was accounted for. With -0.507 beta coefficient, Eq. (5):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑆𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 − 0.507(𝐷𝐴𝐵𝑅) + 𝜀 (5)



Table 5.12. Robust Testing for Proportions of Sentiment Beta Trades with Sentiment


The stepwise multiple regression analysis conducted between the positive proportions of sentiment

beta trades (dependent variable) and the sentiment index and 11 systemic risk indicators (independent

variables) are illustrated below. The 11 systemic risk indicators are the ABR, DABR, AIM, Co, DCo,

BL, ML, RV, Turb, CF and PQR. Multiple regression equation: (ŷ= βₒ+β₁X1+ β2X2+……….+ εi). There

12 independent variables in this analysis

Positive Sentiment Beta Proportions (86 Quarters)


Sentiment Index

x

ABR

x

DABR x

-0.507 0.019 5.7 1

AIM

x

Co

x

DCo

x

BL

x

ML

x

RV

x

Turb

x

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CF

x

PQR

x



Regression

5.9.3 Momentum Trades

5.9.3.1 Positive Momentum Proportions with the Momentum “Return” Indicator


momentum trades. The independent variables of this multiple regression model are the

momentum “return” indicator and similarly 11 of the systemic risk indicators.

We have presented the stepwise regression results of positive momentum proportions

as the results of the negative momentum proportions are the same but in opposite signs.

Although we observe from previous analysis that the number of quarters of negative

momentum trade proportions are higher, positive momentum trade proportions are presented

to stay consistent.

Based on Table 5.13, we observe that the only variable that was included in the model

was the CoVar indicator. This implies that the CoVar indicator was the single best predictor

for positive momentum trade proportions. With the predictor “CoVar”, 24.1 % of the

variance was accounted for. Based on the beta coefficient, Equation (6):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 − 4.294(𝐶𝑜) + 𝜀 (6)



Table 5.13. Robust Testing for Proportions of Momentum Trades with Momentum


The stepwise multiple regression analysis conducted between the positive proportions of momentum

trades (dependent variable) and the momentum “return” indicator and 11 systemic risk indicators

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Quarterly Trades

(independent variables) are illustrated below. The 11 systemic risk indicators are the ABR, DABR,

AIM, Co, DCo, BL, ML, RV, Turb, CF and PQR. Multiple regression equation: (ŷ= βₒ+β₁X1+

β2X2+……….+ εi). There 12 independent variables in this analysis

Positive Momentum Proportions (24 Quarters)


Momentum “Return”

x

ABR

x

DABR

x

AIM

x

Co x

-4.294 0.009 24.1 1

DCo

x

BL

x

ML

x

RV

x

Turb

x

CF

x

PQR

x



Regression

5.9.3.2 Positive Momentum Proportions with Momentum Index


momentum trades. The independent variables of this multiple regression model are the

momentum index and similarly 11 of the systemic risk indicators.

Similarly, we have presented the stepwise regression results of positive momentum

proportions as the results of the negative momentum proportions are the same but in opposite

signs. Although we observe from previous analysis that the number of quarters of negative

momentum trade proportions are higher, positive momentum trade proportions are reflected

to keep consistency in presentation.

We observe from Table 5.14, we observe that similar to the momentum “return”

indicator, the only variable that was included in the model was the CoVar indicator. This

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Quarterly Trades

implies that the CoVar indicator was the single best predictor for negative momentum trade

proportions. With the predictor “CoVar”, 24.8 % of the variance was accounted for. Based on

the beta coefficient, Equation (7):

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑠 = 𝛽0 − 4.252(𝐶𝑜) + 𝜀 (7)



Table 5.14. Robust Testing for Proportions of Momentum Trades with Momentum


The stepwise multiple regression analysis conducted between the positive proportions of momentum

trades (dependent variable) and the momentum index and 11 systemic risk indicators (independent

variables) are illustrated below. The 11 systemic risk indicators are the ABR, DABR, AIM, Co, DCo,

BL, ML, RV, Turb, CF and PQR. Multiple regression equation: (ŷ= βₒ+β₁X1+ β2X2+……….+ εi). There

12 independent variables in this analysis

Negative Momentum Proportions (25 Quarters)


Momentum Index

x

ABR

x

DABR

x

AIM

x

Co x

-4.252 0.007 24.8 1

DCo

x

BL

x

ML

x

RV

x

Turb

x

CF

x

PQR

x



Regression

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5.10 Summary Table of Significant Results based on Robust and Multiple Regression

Tests

Table 5.15. Significant Results based on Robust and Multiple Regression tests

The table below summarises the significant results of the robust and multiple regression test. Panel A

presents the significant results of the robust test. Panel B represents the significant results of the

multiple regression test. √ represents significant results, × represents no significant results exhibited.

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5.11 Conclusion of Robust Testing

This chapter focus on market timing abilities of mutual fund managers through

various robust tests. Robust tests are conducted between the statistically significant trade

proportions that encompass beta, sentiment beta and momentum and their respective market

Panel A: Robust Test

Types of Test Types of

Trades

Positive Negative Types of

Indicators

Correlation Regression

Changes in Signs Beta √ Market "Ret" × √

Sentiment Beta √ Sentiment "Ret" √ √

Persistence Beta √ Market "Ret" × √

Beta √ Market Index × √

Sentiment Beta √ Sentiment "Ret" √ √

Momentum √ Momentum "Ret" × √


Panel B: Multiple Regression

Types of Trade

(DV)

Types of

Indicators (IV)

No. of

Excluded Var

No. of Included

Var

Included

Var(s)

Adjusted

R²(%)

Beta Market "Ret" 11 Systemic Risk 11 1 DABR 8.1

Market Index 11 Systemic Risk 11 1 DABR 8.4

Sentiment Beta Sentiment "Ret" 11 Systemic Risk 10 2 Sen "Ret"; Dco 4.8; 8.4

Sentiment Index 11 Systemic Risk 11 1 DABR 5.7

Momentum Momentum "Ret" 11 Systemic Risk 11 1 Co 24.1

Momentum Index 11 Systemic Risk 11 1 Co 24.8

Var: Variables; DV: Dependent Var; IV: Independent Var; DABR: Delta Absorption Ratio; Dco: Delta CoVar; Co: CoVar

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indicators. The adjustments of positive and negative trade proportions are dependent on the

forecast of the market. In the previous chapter, we examine the abilities of fund managers to

isolate turning points in the market’s economic and financial behaviour. Our results showed

that the sentiment and momentum trade proportions exhibited an inverse relationship with

their respective indicators. We investigate further on the significant relationship between

these variables by conducting various robust tests.

We consider several conditions that might influence the changes in the values of these

market indicators. These indicators reflect the performance of the market henceforth fund

managers can take advantage of the market by adjusting their portfolio accordingly. There are

four types of robust test, magnitude of changes, changes in standard deviation, change in

signs and market persistence.

The “magnitude of change” and the “changes in standard deviation” tests focus on the

“returns” of the market index. These test are conducted between the beta trade proportions

and the market “return” indicator. The “magnitude of change” test attempts to identify fund

managers that are capable of selecting big or small changes based on the market “returns”.

This test is conducted between the beta trade proportions and the market “return” indicator.

Similarly, the “changes in standard deviation” test attempts to identify fund managers that are

capable of selecting changes based on returns that 38% (half a standard deviation) above the

mean or 38% (half a standard deviation) below the mean. This test identifies how confident a

fund manager is at selecting changes. However, our results did not exhibit any significant

results between the beta trade proportions and the market “return” indicator.

The “changes in signs” test focus on the ability of mutual funds to select turning

points of the index based on the values of the indicators. When the values of the indicators

transit from positive (negative) to negative (positive) values, this could be a signal that

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market conditions are changing suggesting an upcoming bear (bull) market. We expect

mutual fund managers to adjust their portfolios towards negative (positive) trade proportions.

However, this test can only be conducted on indicators that are free from spurious issues.

We conducted the “changes in signs” test between these trade proportions and their

respective indicators: beta trade proportions and the market “return” indicator; the sentiment

beta trade proportions and the sentiment “return” indicator; the sentiment beta trade

proportions and the sentiment index. The only significant correlation and regression results

was exhibited between the positive sentiment beta trade proportions and the sentiment

“return” indicator. Results suggest an inverse relationship between these variables.

The “persistence” test identifies fund managers that adjust their portfolios according

to the persistence in index values. We examine how “persistence” of the values of the market

indicators and their respective trade proportions. Significant correlation and regression results

were present between the positive sentiment trade proportions and the sentiment “return”

indicator. Similar to the “changes in signs” test, results suggest an inverse relationship.

Significant correlation and regression results were also present between the positive

momentum trade proportions and the momentum index. Consistent to our findings, results

also suggest an inverse relationship.

Similar to previous findings, it is plausible based on the results of the correlation and

regression analysis that fund managers might have undertaken a contrarian strategy as most

correlation results reflected an inverse relationship between the trade proportions and the

market indicators. As these results were not consistent to our expectations, we investigate

further by conducting a multiple regression analysis.

Previously, simple regression analyses were conducted, concentrating on how one

independent variable (market indicators, “return” indicators and systemic risk indicators)

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might affect the dependent variable (trade proportions). By conducting a multiple regression

analysis, we consider how two or more independent variables, be it market or systemic risk

indicators might simultaneously affect the predictability value of the statistically significant

trade proportions. Although there were some significant regression results, the multiple

regression test did not reflect any new evidence on the existence of market timing abilities of

these statistically significant trade proportions.

Overall, based on these results, there were insufficient evidence to substantiate that

fund managers possess market timing abilities based on examination of their statistically

significant trade proportions. However, consistent results were displayed from the analyses

between the sentiment trade proportions, the momentum trade proportions and their

respective indicators. Both sentiment and momentum trade proportions exhibited an inverse

relationship with their respective indicators. Furthermore, contrary to our expectations,

despite momentum trade proportions having the least number of quarter observations, these

trade proportions produced the most number of significant results. Interestingly, we did not

find any significant results from the beta trade proportions. In the next chapter, we conclude

the findings, discuss the limitations of this study and also discuss suggestions for future

research.

CHAPTER 6

CONCLUSION

6.1 Introduction

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This chapter concludes our thesis. In this chapter, we provide an overview of our

study, identify the limitations and offer suggestions for future research.

6.2 Overview of Conclusion

The performance measures for market timing abilities of mutual fund managers have

been evolving over the years. In our study, we define market timing as the ability of fund

managers to adjust their portfolios in accordance to the anticipated market trends to take

advantage of the market. Common market trends are the bull, bear, recession and boom

periods.

Majority of the performance measures studied the returns and stockholdings of mutual

funds but on average, found no significant market timing abilities. Using a different

approach, Chen, Jegadeesh and Wermers (2000) evaluated market timing abilities using

mutual funds trades and argued that active stock trades represent a stronger opinion of a

manager as compared to “passive” stock holdings.

Similar to the study of Chen et al. (2000), we evaluated the market timing abilities of

fund managers using mutual fund trades. We obtained the statistically significant trade betas

of US equity mutual funds from the data provided by Cullen et al. (2015). There were 62,676

fund quarters and 86 quarters. These statistically significant trades encompass beta, sentiment

beta and momentum. Using a new approach, we evaluated these trades using proportions as

they provide some insights on the direction that the fund manager is pursuing in each quarter.

When the market is anticipated to be bullish or in expansion, we expect a higher proportion

of positive trades. When the market is anticipated to be bearish or undergoing a recession

period, we expect a higher proportion of negative trades. The act of adjusting between

positive and negative trade proportions in accordance to bullish and bearish markets is similar

to the study by Jiang, Yao and Yu (2007) which stated that a fund manager with market

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timing abilities would increase and decrease beta exposure according to macroeconomic

variables. Although risk shifting can be done when a skilled fun manager takes advantage of

their market timing abilities, Huang, Sialm and Zhang (2011) explained that risk shifting

could also be a signal of ill motivated trades either from inferior ability of fund managers or

agency issues.

Previously, Avamov and Wermers (2006) found that predictability skills are best

performed during recession periods but also present in expansion periods. Likewise for our

study, we have considered both “up” and “down” market trends. Our period of study was

between 1991 and 2012. There were three bull market periods and two bear market periods.

There were also three expansion periods and two recession periods. There were similar

numbers of “up” market trends and “down” market trends as bear market periods are highly

associated to recession periods. Therefore, our trade proportions were tested during volatile

conditions.


performance of the market. Market indicators signal periods of upcoming bullish and bearish

markets. Systemic risk indicators reflect the performance of the economy. After the recession

global financial crisis, systemic risk indicators were created to signal upcoming recession

periods. We considered how bullish and bearish market periods will influence the

adjustments of positive or negative trade proportions. We also conducted various robust tests

that identify if fund managers were capable of picking small or big changes, how confident

they are at picking changes, picking turning points of the market and how market persistence

affects their trading decisions. We conducted a series of correlation and regression tests

between these statistically significant trade proportions (dependent variable) and their

respective market and systemic risk indicators (independent variables). We observed if these

variables co vary and if so exhibit a direct or inverse relationship.

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6.3 Significant Research Findings

We observed from the results of the correlation and regression analysis, momentum

trade proportions displayed the most number of significant results despite having the least

number of quarters. However, results were inconsistent to our expectations that during bullish

periods, fund managers will adjust their portfolios towards positive trade proportions. Instead,

results suggest that these fund managers have adjusted their portfolios towards negative trade

proportions during bullish market periods. It is likely that these mutual fund managers were

pursuing a contrarian strategy. Lo and Mackinaly (1990) discussed that contrarian strategies

are strategies that go against market trends by purchasing assets that were past “losers” and

selling assets that were past “winners”. Cullen, Gasbarro, Zumwalt and Monroe (2009)

examined the trading activities of mutual funds to determine if they had adjusted their

portfolios towards stocks that were recent “winners” (momentum strategy) or recent “losers”

(contrarian strategy). They reported that a contrarian strategy is said to be profitable when the

market overreacts as fund managers that followed a momentum strategy will cause the prices

of “winners” to rapidly increase and eventually these “winners” will become losers.

It is plausible that market timing abilities were exhibited from these statistically

significant trade proportions when fund managers pursued a contrarian strategy. Our results

also suggest long term persistence in the market timing abilities of mutual funds. Previously,

Bollen and Busse (2005) studied the daily returns of 230 mutual funds between 1985 and

1995 and concluded that market timing abilities were only significant when evaluated in a

short term period but cease to exist when funds are evaluated over a longer time horizon.

6.4 Limitations of the Research

Our study focused on evaluating the market timing abilities of fund managers using

quarterly observations of the statistically significant trade proportions. Using quarterly data

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observations give fund managers more time allowance to form market expectations and

adjust their portfolios accordingly. However, it also imposed some limitations on this study.

As mutual fund managers may have higher trading frequencies, quarterly data observations

may not be able to capture sufficient information. We considered how daily, monthly or

weekly data will reflect the frequent trading activities of mutual funds.

We considered how the number of quarters might affect the results of our analysis. In

this study, there were 86 quarters available for our analysis. Although momentum trade

proportions displayed significant results with only 25 quarters, it is plausible that the

correlation and regression results between the beta and sentiment beta trade proportions and

their respective indicators were affected by the number of quarters. Furthermore, we observed

from the robust tests that there were less than 30 observations of quarters.

It is also possible that the use of only statistically significant trade proportions have

affected the results of our study. In this case, we used 5% significance level to select trades in

a specific direction. It would be useful to examine whether different significance levels result

in different findings. However, the use of ratios of may mitigate any differences.

We also considered if the use of trade proportions have biased our analysis process as

proportions are affected by the level of statistical significance. The lower the significance

level is, the more number of trades which will impact the proportions of positive and negative

trades. Proportions might be also be disadvantage due to a small denominator arising when

we increase the statistical significance.

6.5 Areas of Future Research

Former studies focused on evaluating market timing abilities in recession periods

only. On the other hand, similar to Avamov and Wemers (2006), we have considered both

recession and expansion periods in our analysis. During the study of Avamov and Wemers

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(2006) which was between 1975 and 2002, there were two recession periods. Similarly

between 1991 and 2012, there were also two recession periods. We considered how future

research may examine market timing abilities based on a longer time period which includes

all four recession periods and expansion periods.

Future research might also consider evaluating the market timing abilities of trade

proportions based on daily, weekly or monthly data observations to capture higher trading

frequencies of trading activities. Elton, Gruber and Blake (2012) reported that 18.5% of

trades by an average fund manager were not detected when market timing measures were

applied to quarterly data holdings. Additionally, this study was based on 5% statistically

significant trade proportions, future research might consider using 1% or 10% statistical

significance as the proportion analysis may reveal different results. For example, using 10%

(1%) significance level will increase (decrease) the number of significant trades.

Majority of the research evaluated market timing abilities of mutual fund managers

without considering the existence of stock selection abilities. Unlike majority of the research,

Chang and Lewellen (1984) believed that fund managers might exploit returns by engaging in

effective “macro” market timing activities along with cautious “micro” stock selection

efforts. They examined the monthly returns of 67 mutual funds and evaluated market timing

abilities of mutual funds while simultaneously evaluating stock selection abilities in mutual

funds. However, there were no evidence of market timing abilities. An additional study by

Chen and Stockum (1986) also investigated mutual fund’s selectivity and timing skills

simultaneously using the quarterly returns of 43 funds. Although stock selection ability was

present, there were still no market timing skills exhibited.

Using a different approach the study by Kacperczyk, Nieuwerburgh and Veldkamp

(2014) found market timing abilities while simultaneously investigating the stock selection

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abilities of mutual fund managers using equity mutual fund holdings. Their methodology

focused on skills of managers by giving more weightage of a fund’s market timing more in

recession periods and stock picking in booms. Future research may examine the trade

proportions of mutual funds instead of fund holdings, similarly by giving more weightage of

a fund’s market timing more in recession periods and stock picking in booms. Giving

considerations that the skills of fund managers might alter accordingly to different business

cycles.

We have also considered the study by Jiang and Fang (2015) that suggested two other

states in the business cycles besides the bull and bear markets. Based on the volatility factor

in stock returns, business cycles have been broken down into the “extreme bear market”, “the

general bear market”, “the volatile bull market” and the “steady bull market”. However, we

were unable to pursue this area of research as there were insufficient data to permit this

partitioning. Future research might consider incorporating all four states of the business cycle

in their studies.

6.6 Summary of Study

Using a new approach, our study focused on evaluating market timing abilities using

trade proportions. Trade proportions give us some insights on the direction that the fund

manager was pursuing. Our trading period between the year 1991 and 2012 had three bullish

markets and two bearish markets. We developed a method that studies how the values of the

market and systemic risk indicators which reflect different market trends might influence a

fund manager to adjust his or her portfolios. Using correlation and regression analysis, we

examined the relationships between these variables.

We found the most significant results between momentum trade proportions and the

momentum indicators. It is probable that these fund managers have undertaken a contrarian

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strategy as their positive momentum trade proportions had an inverse relationship with the

momentum index during bullish market periods. However, results were only significant from

the momentum trade proportions. Therefore, we are unable to conclude that fund managers

possess market timing abilities. Further research employing our approach with a longer

examination period, with an associated increase in observations, will provide supplementary

evidence on market timing abilities.

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