Multifactor Asset Pricing Model Incorporating Coskewness and Cokurtosis: the Evidence from Asian Mutual Funds

MULTIFACTOR ASSET PRICING MODEL INCORPORATING COSKEWNESS AND COKURTOSIS: THE EVIDENCE FROM ASIAN MUTUAL FUNDS

MR. NATHEE NAKTNASUKANJN

A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF BUSINESS ADMINISTRATION (D.B.A.) MAJOR FINANCE THE JOINT DOCTORAL PROGRAM IN BUSINESS ADMINISTRATION (JDBA) FACULTY OF COMMERCE AND ACCOUNTANCY THAMMASAT UNIVERSITY ACADEMIC YEAR 2014 COPYRIGHT OF THAMMASAT UNIVERSITY MULTIFACTOR ASSET PRICING MODEL INCORPORATING COSKEWNESS AND COKURTOSIS: THE EVIDENCE FROM ASIAN MUTUAL FUNDS

MR. NATHEE NAKTNASUKANJN

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Dissertation Title MULTIFACTOR ASSET PRICING MODEL INCORPORATING COSKEWNESS AND COKURTOSIS: THE EVIDENCE FROM ASIAN MUTUAL FUNDS Author Mr. Nathee Naktnasukanjn Degree Doctor of Business Administration (D.B.A.) Major Field/Faculty/University Major Finance Faculty of Commerce and Accountancy Thammasat University Dissertation Advisor Prof. Pornchai Chunhachinda, Ph.D. Dissertation Co-Advisor Chaiyuth Padungsaksawasdi, Ph.D. Academic Years 2014

ABSTRACT

This dissertation adds cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model to be six-factor model to evaluate the equity mutual fund performance both unconditionally and conditionally, and between up and down market of three selected countries in Asia—China, Singapore, and Thailand as representatives of fast growing Asian countries. To my knowledge, this is the first research to incorporate both coskewness and cokurtosis risk factors into Carhart (1997) four-factor model, to become a six-factor model, to explain the equity mutual fund returns. Fund-by-fund investigation is also performed in order to examine whether there is any individual equity mutual fund that can outperform, or beat the market, by using first-moment, second-moment, lower partial-moment, and higher- moment measures.

Keywords: Multifactor, Higher Moment, Asset Pricing, Coskewness, Cokurtosis, Mutual Fund

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ACKNOWLEDGEMENTS

I thank my dissertation advisor, Ajahn Professor Dr. Pornchai Chunhachinda, and my dissertation co-advisor, Ajahn Dr. Chaiyuth Padungsaksawasdi, for their advices and recommendations on my dissertation. I thank Ajahn Associate Professor Dr. Tatre Jantarakolica for his kind help on Stata programming. I thank my dissertation committee chair, Ajahn Associate Professor Dr. Kulpatra Sirodom, and members, Ajahn Associate Professor Dr. Kamphol Panyagometh and Ajahn Assistant Professor Nattawut Jenwittayaroj, for their comments on my dissertation. I thank JDBA officers for their assistance on my dissertation defending process. And I thank my spouse and children on their understanding and patience during the development of my dissertation.

Mr. Nathee Naktnasukanjn

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TABLE OF CONTENTS

Page ABSTRACT (1)

ACKNOWLEDGEMENTS (2)

LIST OF TABLES (6)

CHAPTER 1 INTRODUCTION 1

1.1 Motivation 1 1.2 Background 3 1.3 Objective and Contribution 6 1.4 Structure of Dissertation 7

CHAPTER 2 SIX-FACTOR MODEL IN EXPLAINING MUTUAL FUND PORTFOLIO RETURN 9

2.1 Introduction 9 2.2 Review of Literature 11 2.3 Theoretical Background 14 2.3.1 Utility Function 14 2.3.2 The Multifactor Model 16 2.3.3 The Four-Factor plus Higher-Moment CAPM Risk Factor Model 19 2.4 Data and Methodology 21 2.5 Findings and Results 24 2.5.1 Summary Statistics 24 2.5.2 Performance and characteristics of decile portfolio constructed on the basis of Coskewness and Cokurtosis 25 2.5.3 Alphas and Betas of Coskewness and Cokurtosis portfolio 27

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2.5.4 Measure of Mutual Funds Performance using Higher Moment six-factor model 30 2.6 Conclusion 33

CHAPTER 3 SIX-FACTOR MODEL IN EXPLAINING MUTUAL FUND PORTFOLIO RETURN IN DIFFERENT MARKET CONDITIONS 59

3.1 Introduction 59 3.2 Review of Literature 62 3.3 Data and Methodology 66 3.3.1 Up- and down-market condition 67 3.3.2 Conditional performance evaluation 68 3.3.3 Bootstrap evaluation of fund alphas 69 3.4 Findings and Results 70 3.4.1 Measure of Mutual Funds performance by different market conditions 70 3.4.2 Measure of Mutual Funds performance by conditional model and bootstrap technique 74 3.5 Conclusion 75

CHAPTER 4 INDIVIDUAL MUTUAL FUND PERFORMANCE MEASUREMENT USING HIGHER MOMENT APPROACH 97

4.1 Introduction 97 4.2 Review of Literature 98 4.3 Data and Methodology 101 4.3.1 First-Moment Measure 101 4.3.2 Second-Moment Measure 102 4.3.3 Lower-Partial-Moment Measures 103 4.3.3.1 Reward-to-Target Absolute Semi-Deviation Ratio 103 4.3.3.2 Downside Deviation-based Sharpe Ratio 104

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4.3.4 Higher-Moment Measures 104 4.3.4.1 Adjusted for Skewness Return-to-Risk Ratio 104 4.3.4.2 Omega 106 4.4 Findings and Results 108 4.4.1 First-Moment Measure 108 4.4.2 Second-Moment Measure 109 4.4.3 Lower-Partial-Moment Measures 111 4.4.4 Higher-Moment Measures 112 4.5 Conclusion 115

REFERENCES 131

BIOGRAPHY 139

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LIST OF TABLES

Tables Page 2.1 Summary Statistics of Risk Factors 35 2.2 Cross Correlations of Risk Factors 37 2.3 Performance and Characteristics of Decile Portfolios Constructed on the Basis of Coskewness 39 2.4 Performance and Characteristics of Decile Portfolios Constructed on the Basis of Cokurtosis 41 2.5 Alphas and Betas of Equally-Weighted Coskewness Portfolios using CAPM, Fama-French three-factor model, and Carhart four-factor model 43 2.6 Alphas and Betas of Equally-Weighted Cokurtosis Portfolios using CAPM, Fama-French three-factor model, and Carhart four-factor model 47 2.7 Summary Statistics of Mutual Funds 51 2.8 Measures of Mutual Fund Performance using CAPM, Carhart four-factor model, and Higher moment (with Coskewness and Cokurtosis Risk Factors) six-factor model 52 3.1 Summary Statistics of Mutual Funds by Positive and Negative Excess Market Return 71 3.2 Measures of Mutual Fund Performance using higher moment (with Coskewness and Cokurtosis Risk Factors) six-factor model comparing positive and negative return 81 3.3 Measures of Mutual Fund Performance using higher moment (with Coskewness and Cokurtosis Risk Factors) six-factor model comparing different excess market return periods of China 88 3.4 Measures of Performance using Conditional and Unconditional Six-Factor Model 92 3.5 Measures of Performance using Unconditional Six-Factor Model and Bootstrap 95

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4.1 Descriptive Statistics of Total Return of Equity Mutual Funds and Stock Market Indexes 117 4.2 Test of Difference between Total Return of Equity Mutual Funds and Stock Market Indexes 118 4.3 Sharpe Ratio of Average of Monthly Total Return of Stock Market Indexes and Equity Mutual Funds 119 4.4 Test of Difference between Sharpe Ratio of Equity Mutual Funds and Stock Market Indexes 120 4.5 The Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio Equity Mutual Funds and Stock Market Indexes 121 4.6 The Downside Deviation-Based Sharpe Ratio (DDSR) of Equity Mutual Funds and Stock Market Indexes 122 4.7 Test of Difference between Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio of Mutual Funds and Stock Market Indexes 123 4.8 Test of Difference between Downside Deviation-Based Sharpe Ratio (DDSR) of Equity Mutual Funds and Stock Market Indexes 124 4.9 Skewness and Kurtosis Test of Mutual Funds 125 4.10 The Adjusted-for-Skewness Sharpe Ratio (ASSR) of Equity Mutual Funds and Stock Market Indexes 126 4.11 Test of Difference between Adjusted-for-Skewness Sharpe Ratio (ASSR) of Equity Mutual Funds and Stock Market Indexes 127 4.12 Omega (Index) Ratio of Equity Mutual Funds and Stock Market Indexes 128 4.13 Test of Difference between Modified Omega (Index) of Equity Mutual Funds 129 4.14 Comparison of All Measures of the Mutual Funds 130

CHAPTER 1 INTRODUCTION

1.1 Motivation

Capital Asset Pricing Model (CAPM) for pricing securities has been successful in communicating ideas related to the link between risk and return, and is still widely used both in academic research and professional analyses. However, CAPM assumes that returns are normally distributed and the variance of returns is an adequate measure of risk, while in fact the return distributions of portfolios are not symmetrical and thus the higher moment should also be incorporated into portfolio performance measurement (Chunhachinda et al., 1994, 1997; Prakash et al., 2003). Classical CAPM is extended to incorporate the effect of skewness and kurtosis on the asset valuation and it is found that systematic skewness (coskewness) and systematic kurtosis (cokurtosis) are important. Moreno and Rodriguez (2009) add coskewness risk factor (CSK) as a new factor into Carhart (1997) four-factor model, and become five-factor model. Coskewness is the component of an asset’s skewness related to the market portfolio’s skewness. An asset with negative coskewness is an asset that adds negative skewness to the portfolio and thus increasing the probability of obtaining undesirable extreme values in the left tail of the distribution of the portfolio’s return, when incorporated into a portfolio. The coskewness risk factor is constructed in the same way that the Fama and French (1993) risk factors are constructed. This dissertation continues from their research paper, adding cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model, and become six-factor model. Cokurtosis is the component of an asset’s kurtosis related to the market portfolio’s kurtosis. An asset with high cokurtosis is an asset that adds large kurtosis to the portfolio and thus increasing the probability of obtaining extreme values of the portfolio’s return, when incorporated into a portfolio. To my knowledge, this is the first research to incorporate both coskewness and cokurtosis risk factors 2 into Carhart (1997) four-factor model, to become a six-factor model, to explain the equity mutual fund returns. Some research papers have tested higher-order pricing models for U.S. stock data (Fang and Lai, 1997; Harvey and Siddique, 2000; Dittmar, 2002), U.K. stock data (Kostakis et al., 2012), emerging markets stock return (Hwang and Satchell, 1999), commodity contracts (Christie-David and Chaudry, 2001), and U.S. equity mutual funds (Moreno and Rodriguez, 2009; Heaney, Land, and Treepongkaruna, 2012), but there has been little research on mutual funds in growing Asian countries. This dissertation uses the six-factor model to evaluate the equity mutual fund performance of three selected countries in Asia—China, Singapore, and Thailand as representatives of fast growing Asian countries. Even they locate in same area and similar in their major citizen’s race, but they are different in fund size, activities and years of development and we could see whether they have same or different results. The literature discussing the value of fund management mostly focuses on unconditional return performance and found that on average, fund generally underperforms stock-based market benchmarks (Jensen, 1968; Henrikssen, 1984; Grinblatt and Titman, 1989, 1993; Elton et al., 1992; Brown et al., 1992; Malkiel, 1995; Gruber, 1996; Carhart, 1997; Edelen, 1999; Wermers, 2000). Recent literatures found that stock-based mutual fund performance measures are higher in recessions than in non-recessionary periods (Wermers, 2000; Moskowitz, 2000; Glode, 2011; Kosowski, 2011). Mutual funds appear to generate additional alpha during recessions, even though the returns on the market during recessions are negative. Traditional unconditional performance measures may understate the value added by mutual fund managers in recessions. This dissertation uses the six-factor model to evaluate the equity mutual fund performance both unconditionally and conditionally between up and down market of Asian countries. If an investor wants to invest in a mutual fund with professional investment management, he/she should expect a higher performance compared to the market; otherwise a passively-managed low-expense index fund should be purchased. An investor should be able to make this decision by simply comparing the total return (which also includes any dividends) of the mutual fund with the total return of the 3 market, or index. However, this simple and direct comparison between total returns does not take the risk of the portfolio into account. It may be more fair and appropriate to compare a return-to-risk ratio, e.g. the Sharpe ratio, between a mutual fund and the market, rather than just the total return alone, as an investor wants to construct a portfolio which maximizes the expected return while reducing risk, or the variance of the portfolio (Markowitz, 1952). But because the return distributions of portfolios are not symmetrical, thus the higher moment should also be incorporated into portfolio performance measurement. This might be done by factoring skewness and/or kurtosis into the Sharpe ratio to make it a better measure as the traditional measures of risk (i.e. variance or standard deviation) do not fully capture the ―true risk‖ as the probability of loss of the distribution of portfolio returns. As a mutual fund consists of assets like a portfolio, fund-by-fund investigation should be performed in order to examine whether there is any individual mutual fund that can outperform, or beat the market, by using higher-moment measures.

1.2 Background

A mutual fund is a type of professionally-managed collective investment vehicle that pools money from many investors to purchase securities (U.S. Securities and Exchange Commission, 2011). They are ―mutual‖ because the investors own all of the assets in the fund, and are responsible for all of its operating costs. The funds are organized by a fund-management company that undertakes the legal registration of the fund, nominates a board of directors for the fund, and arranges for the distribution and sale of fund shares to the public. The board of directors of the fund contracts with an investment advisor to manage the assets and to handle ongoing operational details such as marketing, administration, reporting and compliance. Mutual fund assets are owned by the fund investors, who can normally redeem their shares instantly at their net asset value (NAV). Compared to direct investments in individual stocks and bonds, mutual funds offer the advantages of liquidity and diversification at a relatively low cost for investors. The first mutual fund was established in Europe by a Dutch merchant in 1774. The first mutual fund outside the Netherlands was the Foreign and Colonial Government Trust, established in London 4 in 1868. Mutual funds were introduced into the U.S. in the 1890s and became popular during the 1920s until the stock market crashed in 1929 (Rouwenhorst, 2004). When confidence in the stock market returned in the 1950s, the U.S. mutual fund industry began to grow again, with growth continuing into the 1980s and 1990s. At the end of 2010, there were over 15,000 mutual funds of all types in the U.S. with combined assets of $13.1 trillion while the worldwide mutual fund assets were $24.7 trillion (including U.S.) on the same date. Mutual funds in the U.S. accounted for 23% of household financial assets. Their role in retirement planning is significant; roughly half of assets in 401(k) plans (a type of tax-deferred retirement account) and individual retirement accounts are invested in mutual funds. Stock or equity mutual funds invest in common stocks. At the end of 2010, stock funds accounted for 48% of the assets in all U.S. mutual funds (Investment Company Institute, 2011). Equity investment in emerging markets has grown rapidly in the 1990s, much of it flowing through mutual funds. The mutual fund industry in Asia remains small when compared to highly developed financial markets such as the US and Europe. The large fund management industries in the region are Japan, Singapore, Korea, China, Malaysia, Thailand and Indonesia. In the rest of the countries in Asia, the mutual fund industry is either negligible or non-existent. By the end of 2011, there are 358 equity mutual funds in China, 127 in Singapore and 197 in Thailand. The significantly increase in mutual fund industry in China, Singapore and Thailand is the reason why we select them as representative for Asian mutual fund industry in our study. A fund is considered to have investment ability if it generates returns that exceed the benchmark before costs and fees. A fund that outperforms the benchmark on an after-cost basis is considered to add value for investors. Fund managers believe they have the ability to better estimate the true securities’ risks and returns, to spot any mispriced securities, and to time the market, thus generating excess returns for the fund. Therefore they frequently adjust their fund portfolios seeking opportunities to beat the market. Academics have debated whether mutual fund managers who trade stocks actually add value since the studies of Sharpe (1966) and Jensen (1968). The majority of studies concluded that managed funds on average underperform index funds. The value-weighted portfolio of funds that invest primarily in U.S. equities is 5 close to the market portfolio, and estimated before expenses, their alpha relative to common benchmarks is close to zero (Fama and French, 2009). Many studies suggest that more than half of the mutual funds have negative alphas, good performance does not persist, funds just have enough investment ability to cover their fees and trading costs, and they do not add value for investors after costs. Thus, investors are better off, on average, buying a low-expense index fund. There have been two major approaches to test the performance of fund, or fund manager: (1) returns-based performance evaluation and (2) portfolio-holding- based performance evaluation (Wermers, 2011). Most returns-based models use the four-factor model of Carhart (1997) to determine if the alpha is statistically significantly greater than zero and large enough to compensate for the costs of the fund and add value to the investor. Carhart (1997) constructed a four-factor model using Fama and French’s (1993) three-factor model (market, book-to-market ratio, and size) plus an additional factor capturing Jegadeesh and Titman’s (1993) one-year momentum anomaly. However, this model still cannot explain all financial anomalies in cross-sectional patterns. On another branch, classical CAPM is extended to incorporate the effect of skewness and kurtosis on the asset valuation and it is found that systematic skewness (coskewness) and systematic kurtosis (cokurtosis) are important (Fang and Lai, 1997; Hwang and Satchell, 1999; Harvey and Siddique, 2000; Christie-David and Chaudry, 2001; Dittmar, 2002; Moreno and Radriguez, 2009; Kostakis et al., 2012; Heaney, Land, and Treepongkaruna, 2012). The literature on mutual fund performance can be divided into two broad categories—those that use unconditional performance and those that use conditional performance measures. Within both of these categories, funds can be examined for their ability to time the market and their ability to choose mispriced stocks accurately. Unconditional or traditional performance measures do not allow for market or economic conditions in determining whether a fund has performed abnormally well. Conditional performance measures look at the state of the economy in trying to determine whether a fund’s performance is abnormally strong or just in line with the expectations given the state of economy. The prevailing consensus is that unconditionally, mutual funds deliver negative risk-adjusted returns where returns are measured after fees and expenses. However, depending on the state of the economy, 6 mutual funds have been found to perform better although still not well enough to justify the fees that investors pay to mutual fund managers. Another recent branch of literature examines whether mutual funds deliver stronger returns when the economy is in recessions, when investors require these funds to perform well and are in fact paying for that skill. Investors are willing to pay a premium for assets with payoffs negatively correlated with consumption. As consumption tends to be low in recessions (Rubinstein, 1976; Harrison and Kreps, 1979; Breeden, 1979, 1986; Grossman and Shiller, 1981), investors are willing to accept lower average fund performance if funds perform well in recessionary times when investors care most about performance. Thus, unconditional mutual fund performance measures may underestimate the value of mutual funds to investors when investor wealth or income is low and when investor marginal utility of wealth is high, such as during recessions. This implies that investors are willing to trade some overall performance, or average returns, for good performance in particular economic states of nature (Kosowski, 2011).

1.3 Objective and Contribution

The objective of this dissertation is to use coskewness and cokurtosis risk factors incorporating with the four-factor model—become six-factor model, to evaluate the equity mutual fund performance of Asian countries both unconditionally and conditionally between up and down markets. The performance evaluations are also performed both in portfolio, and each individual fund. The performance evaluation of individual funds are by using first-moment measure, second-moment measure, lower-partial-moment measure, and higher-moment measures, to determine whether any equity mutual funds significantly outperformed by using different types of measure. The three Asian countries are China, Singapore, and Thailand. These countries are selected as representative of Asia since they have fast growing economies and mutual fund businesses in Asia. The contributions of this dissertation to the literatures are: 1) to introduce six-factor model to show empirical evidence for the importance of coskewness and cokurtosis risk factors in performance evaluation of equity mutual funds, 2) to show 7 empirical evidence for the importance of coskewness and cokurtosis risk factors in performance evaluation of equity mutual funds for emerging countries in Asia, 3) to show empirical evidence for the significant difference in performance of equity mutual funds for emerging countries in Asia between up and down market periods, and 4) to show empirical evidence whether there is any individual equity mutual funds in emerging countries in Asia that can significantly outperformed the market by higher-moment measures.

1.4 Structure of Dissertation

Chapter 2 of this dissertation studies the adding of coskewness and cokurtosis risk factors into the Carhart (1997) four-factor model—become six-factor model, to see whether coskewness and cokurtosis risk factors help explain the cross- section of returns of mutual funds for three Asian countries—China, Singapore, and Thailand. Chapter 3 of this dissertation uses the six-factor model to compare fund performance between up and down markets, whether they are significantly different, and whether the difference between fund performance and stock market index performance are significantly different between the two periods. Whether equity mutual funds perform better when the market is down than when market is up, and whether equity mutual funds perform better than the stock market index (or beat the market) when the market is performing poorly. This dissertation defines two stages of market conditions in two ways. First, this study uses positive market excess return— up market and negative market excess return—down market, as defined in Pettengill et al. (1995). And second, this study uses regime breakpoints using Bai and Perron (1998, 2003) techniques. Chapter 4 of this dissertation tests individual equity mutual fund performance by various measures whether it can beat the market and whether those mutual fund performance measures can be substituted one for another as choices of calculation. The study begins with direct and simple single-dimensional comparisons of total return, and then moves to multi-dimensional comparisons of return-to-risk ratios in a second-moment framework, lower-partial-moment and higher-moment 8 frameworks to determine whether any equity mutual funds significantly outperformed, or beat the market. Then the rank of each measure is compared to see whether they are similar and can be substituted for each other, or if they are significantly different from each another due to the calculation methodology. 9

CHAPTER 2 SIX-FACTOR MODEL IN EXPLAINING MUTUAL FUND PORTFOLIO RETURN

2.1 Introduction

Classical CAPM is extended to incorporate the effect of skewness and kurtosis on the asset valuation and it is found that systematic skewness (coskewness) and systematic kurtosis (cokurtosis) are important. Moreno and Rodriguez (2009) add coskewness risk factor as a new factor into Carhart (1997) four-factor model, and become five-factor model. The coskewness risk factor is constructed in the same way that the Fama and French (1993) risk factors are constructed. This research continues from their research paper, adding cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model, and become six-factor model. Incorporating cokurtosis alongside coskewness could provide a more complete modeling of tail risk in the return distribution. Although a number of papers have tested higher-order pricing models for U.S. stock data (Fang and Lai, 1997; Harvey and Siddique, 2000; Dittmar, 2002), U.K. stock data (Kostakis et al., 2012), emerging markets stock return (Hwang and Satchell, 1999; Chiao, Hung and Srivastava, 2003), commodity contracts (Christie- David and Chaudry, 2001), and U.S. equity mutual funds (Moreno and Radriguez, 2009; Heaney, Land, and Treepongkaruna, 2012), but there has been little research on mutual funds in growing Asian countries. This research tests coskewness and cokurtosis with the four-factor model on mutual fund performance evaluation for three Asian countries—China, Singapore, and Thailand. These countries are selected as representative of Asia since they have fast growing economies and mutual fund businesses in Asia, and they are different in the market size and development level even the major citizen’s race are the same. Moreno and Rodriguez (2009) construct coskewness risk factor and incorporate it into four-factor Carhart (1997) model and become five-factor model. Following that approach, cokurtosis risk factors is constructed and incorporated into 10 five-factor model as additional variable. This study is to test whether coskewness and cokurtosis risk factors can increase the explanatory power of the cross-sectional of total return distribution of equity mutual fund. An asset with a negative coskewness is an asset that adds negative skewness, decreasing the probability of obtaining extreme values in the right tail of the distribution, when incorporated into a portfolio. An asset with positive coskewness is an asset that adds positive skewness, increasing the probability of obtaining extreme values in the right tails of the distribution, when incorporated into a portfolio. An investor would prefer a positive coskewness because this represents a higher probability of extreme positive returns in the security over market returns. Because investors dislike negative coskewness assets and prefer positive coskewness assets, the coskewness risk factor is constructed in the way that it equals to the return of the most negative coskewness (S-) minus the return of the most positive coskewness (S+). The return spread (S--S+) of the portfolios of the month t+1 (post- rank return) is the coskewness risk factors CSK. Cokurtosis is the component of an asset’s kurtosis related to the market portfolio’s kurtosis. An asset with high cokurtosis is an asset that adds large kurtosis to the portfolio and thus increasing the probability of obtaining undesirable infrequent extreme values of the portfolio’s return, when incorporated into a portfolio. Cokurtosis is interpreted in the same direction as beta. Because investors dislike large cokurtosis assets and prefer small cokurtosis assets, the cokurtosis risk factor is constructed in the way that it equals to the return of the most positive cokurtosis (K+) portfolio minus the return of the most negative cokurtosis (K-) portfolio. This is similar to coskewness risk factor but in the opposite direction. The return spread (K+- K-) of the portfolios of the month t+1 (post-rank return) is the cokurtosis risk factors CKT. Then the coskewness and cokurtosis risk factors are added into the Carhart (1997) four-factor model, and it becomes a six-factor model which is being used to test the equity mutual fund performance in this study. The remainder of this chapter is organized in four sections: the review of literature in section 2, the theoretical background in section 3, the data and methodology in section 4, the findings and results in section 5, and conclusion in section 6. 11

2.2 Review of Literature

After Markowitz’s (1952) work on diversification and modern portfolio theory was published, the Capital Asset Pricing Model (CAPM) for pricing securities was introduced by Sharpe (1964), Lintner (1965), Mossin (1966), and Black (1972). The prediction of CAPM is that the expected excess return on an asset is equals to the beta of the asset times the expected excess return on the market portfolio. The beta is the covariance of the asset’s return with the return on the market portfolio, divided by the variance of the market return. This model has been successful in explaining ideas of the link between risk and return, and is still widely used both in academic research and professional analyses. However, CAPM has theoretical and empirical limitations. CAPM assumes that returns are normally distributed and the variance of returns is an adequate measure of risk. But the mean-variance model is appropriate only if the investor’s utility is quadratic or the joint distribution of returns is normal. The higher moments cannot be neglected unless there is a reason to believe that the asset returns are normally distributed or the utility function is quadratic (Arditti, 1967, 1971; Rubinstein, 1973).

Classical CAPM is extended to incorporate the effect of skewness on the asset valuation and it is found that systematic skewness is important. Investors with decreasing marginal utility of wealth and non-increasing absolute risk aversion prefer positive skewness (Rubinstein, 1973; Kraus and Litzenberger, 1976). The three- moment CAPM implies that coskewness is important—a stock with a negative coskewness with the market will earn a higher risk premium. A model incorporating coskewness helps explain the expected returns by the increment of coefficient of determination in cross-sectional regression (Harvey and Siddique, 2000). The price of coskewness risk is empirically large, especially at times when market skewness is negative (Smith, 2007). In addition, coskewness and cokurtosis are priced in the cross-section of industry-sorted stock portfolio (Dittmar, 2002). Cokurtosis is a statistical measure that calculates the degree of peak of a variable's probability distribution in relation to another variable's peakedness. Cokurtosis is calculated using 12 a security's historic price data as the first variable, and the market's historic price data as the second. Ceteris paribus, a higher cokurtosis means that the first variable has a fatter probability distribution. This provides an estimation of the security's risk in relation to the market. In finance, cokurtosis can be used as a supplement to the covariance calculation of risk estimation. Risk-adverse investor should prefer a lower cokurtosis as the security's returns would not be much different from the market's returns. Many patterns emerge from empirical studies which are not explained by CAPM. These include expected returns and earnings-to-price ratios having a positive relationship (Basu, 1977); companies with smaller equity market capital having higher stock returns than larger firms (Banz, 1981); the positive relationship between the level of debt and stock returns (Bhandari, 1988); and the book-to-market ratio considered as an explanatory variable in stock returns (Chan et al., 1991; Fama and French, 1992). Fama and French (1993) construct a three-factor model to explain stock returns: market (classical CAPM), book-to-market ratio, and size. This model summarizes earlier results of Banz (1981), Huberman and Kandel (1987), Chan and Chen (1991). Fama and French interpret their three-factor model as evidence for a distress premium—small stocks with high book-to-market ratios are firms that have performed poorly and are vulnerable to financial distress (Chan and Chen, 1991), thus commanding a risk premium. Carhart (1997) constructs a four-factor model using Fama and French’s (1993) three-factor model plus an additional factor capturing Jegadeesh and Titman’s (1993) one-year momentum anomaly—that, at three months to one-year horizons, stocks that have outperformed (winners) or underperformed (losers) in the past may continue to do so in the future. The four-factor model is consistent with a model of market equilibrium with four risk factors. It might be explained as a performance attribution model, where the coefficients and premiums on the factor-mimicking portfolios indicate the proportion of mean return attributable to four strategies: high versus low beta stocks, small versus large market capitalization stocks, value versus growth stocks, and one-year return momentum versus contrarian stocks. However, this model still cannot explain all financial anomalies in cross-sectional patterns. 13

The impact of systematic skewness (coskewness) and systematic kurtosis (cokurtosis) on asset pricing using four-moment CAPM on U.S. stocks are examined by Fang and Lai (1997) and it is discovered that the expected excess rate of return is related to the systematic variance (covariance), systematic skewness (coskewness), and also systematic kurtosis (cokurtosis). The cokurtosis is considered in the same way as the systematic market risk (covariance), i.e. greater returns are required for portfolios with larger covariance risk (beta) and cokurtosis risk. The higher the covariance and cokurtosis, the higher the expected return. But investors have a preference for positive skewness in their portfolios and thus require a higher expected return on assets when the portfolio is negatively skewed. The higher the coskewness, the lower the expected return. Investors are compensated with a higher expected return for bearing the covariance and the cokurtosis risks. Investors forego the expected excess return for the benefit of increasing positive coskewness. In the mean- variance framework, the coskewness and cokurtosis are not priced. In the three- moment framework, the cokurtosis is not priced. There is more evidence supporting the return explanation of the four-moment CAPM in emerging markets (Hwang and Satchell, 1999; Chiao, Hung and Srivastava, 2003) and future markets (Christie-David and Chaudry, 2001). They find that coskewness and cokurtosis are significant, and cokurtosis has even more explanatory power than coskewness in pricing securities. Moreno and Rodriguez (2009) evaluated U.S. equity mutual fund performance using standard CAPM and the Carhart (1997) four-factor model plus the coskewness factor and find that the coskewness factor is statistically significant even when factors based on size, book-to-market value, and momentum are included. Incorporating a coskewness factor as an additional variable increases the explanatory power of the model in both the unconditional and conditional frameworks. The average fund performance changes when coskewness is taken into account. Thus, failure to consider systematic skewness could bias the risk-adjusted returns obtained by mutual funds. But in contrary, some researches find that the price of coskewness risk help explain but not greatly matter in the pricing of unconditional portfolio of stocks e.g. Friend and Westerfield (1980), Poti and Wang (2009). Heaney, Land, and Treepongkaruna (2012) investigate whether coskewness and cokurtosis are priced in U.S. stocks during 1963-2010 using Fama and Macbeth (1973) method and find 14 evidence of priced coskewness and cokurtosis factors but they are subsumed by Fama and French (1992, 1993) size and book-to-market factors. The importance of higher moment risk factor is still unclear and so far there is still no evidence in Asian mutual fund industry.

2.3 Theoretical Background

2.3.1 Utility Function

The desirable properties for an investor’s utility function (Arrow, 1971) are (1) positive marginal utility for wealth (the first derivative of the utility function of wealth should be positive), i.e. non-satiety with respect to wealth—an increase of wealth always increases the utility; (2) decreasing marginal utility for wealth (the second derivative of the utility function of wealth should be negative), i.e. risk aversion—the speculator is not a gambler, as he always will give more utility to a certain gain than to a random result with the same expected return, and he invests despite the underlying risks and requires compensation; and (3) non-increasing absolute risk aversion, i.e. risky assets are not inferior goods. The first two conditions are consistent with the mean-variance preference. The possibilities of the first derivative of the utility function ( ) are ( ) , ( ) , or ( ) . When marginal utility is positive, ( ) . Then the possibilities of the second derivative are ( ) , ( ) , or ( ) . When marginal utility is positive and decreasing, ( ) , which is called hyper-absolute risk aversion (HARA) (Arrow, 1971).

( ) The Arrow-Pratt absolute risk aversion coefficient ( ) ( ) measures the actual dollar amount an individual chooses to hold in risky assets, given a certain wealth level W. There are three types of absolute risk aversion: ( ) (increasing absolute risk aversion (IARA)—holding fewer dollars in risky assets as wealth increases); ( ) (constant absolute risk aversion (CARA)—holding the same dollar amount in risky assets as wealth increases); and ( ) (decreasing 15 absolute risk aversion (DARA)—holding a larger dollar amount in risky assets as wealth increases).

( ) The Arrow-Pratt relative risk aversion coefficient ( ) ( )

( ) measures the percentage of wealth an individual chooses to hold in risky assets, given a certain wealth level W. There are three types of relative risk aversion:

( ) (increasing relative risk aversion (IRRA)—holding a smaller percentage of wealth in risky assets as wealth increases); ( ) (constant relative risk aversion (CRRA)—holding the same percentage of wealth in risky assets as wealth increases), and ( ) (decreasing relative risk aversion (DRRA)—holding a larger percentage of wealth in risky assets as wealth increases). Individuals should display decreasing absolute risk aversion (DARA) and increasing relative risk aversion (IRRA) with respect to wealth—holding a larger dollar amount but smaller percentage of wealth in risky assets as wealth increases (Arrow, 1965). The reasoning for DARA is that wealthy individuals are less risk averse than poorer ones with regard to the same risk. Thus, DARA is necessary if risky assets are to be considered ―normal goods‖; that is, the rise in wealth leads to an increase in demand for them (whereas increasing absolute risk aversion (IARA) implies they are ―inferior goods‖). The reasoning for hypothesizing IRRA is that as wealth increases and the magnitude of the risk increases, the willingness to accept the risk should decline. IRRA implies that the wealth elasticity of demand for risky assets is less than one. Experimental and empirical evidence is mostly consistent with DARA. The decreasing absolute risk aversion (DARA) condition implies preference for positive skewness (Arditti, 1967). The quadratic utility cannot be an adequate description of investor preferences (Campbell and Viceira, 2002). The utility functions which posses DARA and IRRA are the power utility function and the logarithmic utility function, for example (Roy and Wagenvoort, 1996): ( ) ( ) ( ) ( ) ( ) ( ) where a and c are constant.

One of the popular alternatives in the literature is the constant relative risk aversion (CRRA) power utility function. This function embeds aversion to negative skewness and excess kurtosis as long as the RRA coefficient greater than 1. Preference for positive skewness is embedded in any differentiable, monotonic and concave utility functions with ( ) ; this behavior is called prudence (Kimball (1990). Aversion to excess kurtosis is accommodated in the case where ( ) ; this behavior is called temperance (Kimball, 1992; Gollier and Pratt, 1996).

2.3.2 The Multifactor Model

Start from the standard CAPM model:

, - (2.1)

where is the return on asset in time t, is the return on risk-free asset in time t, is the return of the market in time t and represent the residual. In order to study the joint roles of market , size, E/P, leverage, and book- to-market equity in the cross-section of average stock returns, Fama and French (1992a) used the cross-section regressions of stock returns of Fama and MacBeth (1973). They found that (the slope in the regression of a stock’s return on a market return) provides little information about average returns but Size, E/P, leverage, and book-to-market equity have explanatory power. In combinations, size (ME) and book- to-market equity (BE/ME) absorb the apparent roles of leverage and E/P in average returns. The final conclusion is that two variables, size and book-to-market equity, can explain the cross-section of average returns on NYSE, Amex and NASDAQ stocks for the 1963 to 1990 period. Fama and French (1992b) used six portfolios formed from sorts of stocks on ME and BE/ME. In June of each year t, all stocks are ranked by size (price times shares outstanding). The median size is used to split stocks into two groups—small and big (S and B). Stocks are also broken down into three book-to-market equity groups based on the breakpoints for the bottom 30% (low), middle 40% (medium), and top 30% (high) of the ranked values of BE/ME. The decision to sort firms into three groups based on BE/ME and two groups based on ME followed the evidence in Fama and French (1992a) that book-to-market equity has a stronger role in average 17 stock return than size. Six portfolios are constructed from the intersections of the two ME and the three BE/ME groups—S/L, S/M, S/H, B/L, B/M, B/H. Monthly value- weighted returns on the six portfolios are calculated from July of year t to June of t+1, and the portfolios are re-formed in June of t+1. Portfolio SMB (Small minus Big) mimics the risk factor in returns related to size, and is the difference—each month—between the simple average of the returns of the three small-stock portfolios (S/L, S/M, S/H) and the simple average of the returns on the three big-stock portfolios (B/L, B/M, B/H). Thus SMB is the difference between the returns on small-stock and big-stock portfolios with about the same weighted-average book-to-market equity. This difference is free from the influence of BE/ME, focusing instead on the different return behaviors of small and big stocks. Portfolio HML (High minus Low) mimics the risk factor in returns related to book-to-market equity. HML is the difference each month between the average of the returns of the two high BE/ME portfolios (S/H and B/H) and the average of the returns of the two low BE/ME portfolios (S/L and B/L). The two components of HML are returns of high BE/ME and low BE/ME portfolios with about the same weighted- average size. This difference is free from the size factor in returns, focusing instead on the different return behaviors of high BE/ME and low BE/ME firms. The proxy for the market factor in stock returns is the excess market return, , where is the return on the value-weighted portfolio of the stocks in the six Size-BE/ME portfolios, and is the one-month Treasury bill rate. The returns to be explained are the excess returns on 25 portfolios, formed using size and book-to-market equity as dependent variables in time-series regressions. The 25 Size-BE/ME portfolios are formed like the six Size-BE/ME portfolios. In June of each year t, stocks are sorted by size and by book-to-market equity independently. For the size sort, ME is measured at the end of June. For the book-to-market sort, ME is market equity at the end of December of year t-1, and BE is book common equity for the fiscal year ending in calendar year t-1. The 25 portfolios are constructed from the intersections of the size and BE/ME quintiles and value-weighted monthly returns of the portfolios from July of year t to June of year t+1 are calculated. The monthly excess returns on these 25 portfolios are the dependent variables for stocks in the time-series regression. 18

Fama and French (1993) expanded the set of asset returns to include U.S. government bonds and corporate bonds, using the time-series regression approach of Black, Jensen and Scholes (1972). Monthly returns of stocks and bonds are regressed using the returns of a market portfolio of stocks mimicking portfolios for size, book- to-market equity (BE/ME), and term-structure risk factors in returns. They found that the portfolio constructed to mimic risk factors related to size and BE/ME captured strong common variations in returns for stock. The intercepts from three-factor regressions that included the excess market return and the mimicked return for size and BE/ME factors are close to zero, which means they are good at explaining the cross-section of average stock returns. The Fama and French (1993) three-factor model is:

, - (2.2)

where , , and represents the market, size, book-to- market value factors. SMB (Small minus Big) is the difference between the equal weighted average of the returns on the three small-stock portfolios and the three big-stock portfolios. HML (High book-to-market minus Low book-to-market) is the difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio of low book-to-market stocks. Using Fama and French’s (1993) three-factor model plus an additional factor capturing Jegadeesh and Titman’s (1993) one-year momentum anomaly—that, at three months to one-year horizons, stocks that have outperformed (winners) or underperformed (losers) in the past may continue to do so in the future, Carhart (1997) constructed a four-factor model. The four-factor model is consistent with a model of market with four risk factors. It is a performance attribution model, where the coefficients and premiums on the factor-mimicking portfolios indicate the proportion of mean return attributable to four strategies: high versus low beta stocks, small versus large market capitalization stocks, value versus growth stocks, and one- year return momentum versus contrarian stocks.

Performance relative to four-factor model is estimated as:

, - (2.3)

where represents the momentum factor. WML (Winner minus Loser) is the difference between the return on a portfolio of high momentum (most positive return in the past eleven months) and the return on a portfolio of low momentum stocks (most negative return in the past eleven months). WML is constructed as the equal-weighted average of firms with the highest 30% eleven-month returns lagged one month minus the equal-weighted average of firms with the lowest 30% eleven-month returns lagged one month. The portfolios included all stocks and are re-formed monthly. Mutual funds are sorted on January 1 each year into decile portfolios based on their previous calendar year’s return. The portfolios are equally weighted monthly so the weights are readjusted whenever a fund disappeared. Funds with the highest past one-year return comprised Decile 1 and funds with the lowest past one-year return comprise Decile 10. The portfolios are held until the following January and then rebalanced again.

2.3.3 The Four-Factor plus Higher-Moment CAPM Risk Factor Model

Coskewness is the component of an asset’s skewness related to the market portfolio’s skewness. An asset with negative coskewness is an asset that adds negative skewness to the portfolio and thus increasing the probability of obtaining undesirable extreme values in the left tail of the distribution of the portfolio’s return, when incorporated into a portfolio. Coskewness risk factor is constructed in the same way that Fama and French’s (1993) SMB and HML. Monero and Rodriguez’s (2009) coskewness risk factor (CSK) is constructed by the return spread of the two portfolios, the most negative coskewness minus the most positive coskewness (S--S+). The coskewness measures for each asset are computed and ranked to form two portfolios: one contain the 30% of the assets that have the most negative coskewness (S-), the other one contains the 30% of the assets that have the most positive coskewness (S+). 20

To estimate the degree of coskewness for each stock at a given month t, a rolling window of 60 monthly excess returns for each stock i, is used, and the CAPM regression: , - to extract the residual

is employed. These residuals are net of covariance (beta) risk but still incorporate coskewness and cokurtosis risk, and thus the study can get a measure of standardized coskewness of each stock’s returns with the market returns over the period t-60 to t using the formulas:

, - (2.4)

√ [ ] , -

where is the residual previously extracted from the CAPM regression, and is the deviation of the excess market return in month t from the average value over the corresponding window of observations t-60 to t. The stocks then form two portfolios: one containing the 30% of stocks that have the most negative coskewness (S-) and another containing the 30% of stocks that have the most positive coskewness (S+). Because investors dislike negative coskewness assets and prefer positive coskewness assets, the coskewness risk factor is constructed in the way that it equals to the return of the most negative coskewness minus the return of the most positive coskewness. The return spread of the portfolios (S--S+) of the month t+1 (post-rank return) is the coskewness risk factors CSK. When a coskewness risk factor CSK is included in the four-factor model, it is the four-factor plus higher-moment CAPM risk factor model which becomes a five-factor model:

[ ]

(2.5) This dissertation extends the Monero and Rodriguez’s (2009) five-factor model by including another higher-moment risk factor, cokurtosis, into the equation to become six-factor model. The cokurtosis, which is the component of an asset’s kurtosis related to the market portfolio’s kurtosis, this research defines it as CKT risk factor as it is constructed by the return spread of the two portfolios, the most positive cokurtosis minus the most negative cokurtosis (K+-K-). 21

To estimate the degree of coskewness and cokurtosis for each stock at a given month t, a rolling window of 60 monthly excess returns for each stock i,

is used, and the CAPM regression: , - to extract the residual is employed. These residuals are net of covariance (beta) risk but still incorporate coskewness and cokurtosis risk and thus the study can get a measure of standardized cokurtosis of each stock’s returns with the market returns over the period t-60 to t using the formulas:

, - (2.6)

√ [ ] , - The cokurtosis risk factor is constructed in the same way as coskewness risk factor, i.e. form two portfolios: one containing the 30% of stocks that have the most negative cokurtosis (K-) and another containing the 30% of stocks that have the most positive cokurtosis (K+). But unlike coskewness and like beta risk factors, it equals to the return of the most positive cokurtosis portfolio (K+) minus the return of the most negative cokurtosis (K-). The return spread of the portfolios (K+-K-) of the month t+1 (post-rank return) is the cokurtosis risk factors CKT. When coskewness and cokurtosis risk factors are included in the four- factor model, it becomes a six-factor model.

[ ]

(2.7)

2.4 Data and Methodology

The database in this chapter consists of monthly total returns of mutual funds, with a focus on equity funds, and total returns of stock market indexes of China, Singapore and Thailand for twelve years between January 2000 and December 2011, obtained from the Bloomberg database. The data of total returns collected includes both active and inactive funds. By collecting both active and inactive fund total returns, the data is free from survivorship bias. The data to form SMB, HML, WML, CSK, CKT risk factors is retrieved from Thomson Reuters Datastream, which also includes both listed and delisted equities to be free from survivorship bias. 22

Data on the one-month risk-free rate are from The People’s bank of China, Monetary Authority of Singapore and The Thai Bond Market Association. Data on the monthly four-factors from the Carhart (1997) model, namely the Market Risk Premium, the SMB (Small Minus Big) factor, the HML (High Minus Low) factor, and the WML (Winner Minus Looser) factor are all created following Fama and French’s (1993) and Carhart’s (1997) methodology as explained in Kenneth R. French’s website. (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). To construct the SMB and HML factors, the stocks are sorted into two market capitalization and three book-to-market equity (B/M) groups at the end of each June. The Small and Big breakpoints are the 30th and 70th percentiles of the rank of the market capital of the stocks. SMB is the equal-weight average of the returns on the small-stock portfolio minus the average of the returns on the big-stock portfolio. HML is the equal-weight average of the returns for the high B/M portfolio minus the average of the returns for the low B/M portfolios. The sort on lagged momentum to construct WML is similar, but the momentum portfolios are formed monthly. The lagged momentum return of portfolio at the end of month t is a stock's cumulative return for month t–12 to month t–1. The momentum breakpoints are the 30th and 70th percentiles of the lagged momentum returns of the stock of the market. WML is the equal-weight average of the returns for the winner portfolio minus the average of the returns for the loser portfolio.

Rm - Rf for July of year t to June of t+1 includes all stocks for which there is market equity data for June of t. SMB and HML for July of year t to June of t+1 includes all stocks for which there is market equity data for December of t–1 and June of t, and book equity data for t–1. The portfolios used to construct WML each month include stocks with prior return data. To be included in a portfolio for month t that is formed at the end of the month t–1, the stocks must have their prices for the end of month t–13 and a return for t–2. The risk free rate data are from 1-month government bond rate from the People’s Bank of China, the Monetary Authority of Singapore and The Thai Bond Market Association.

Si and Ki values for each stock each month are estimated by equation 2.4 and 2.6, and sorted to construct decile portfolios. Portfolio 1 contains the stocks with 23

the lowest Si values, and portfolio 10 contains the stocks with the highest Si values.

This process is repeated using Ki values with portfolio 1 containing the stocks with the lowest Ki values and portfolio 10 containing the stocks with the highest Ki values. Then for each portfolio, the equally-weighted post-ranking (month t+1) returns in excess of the risk-free rate are calculated. Portfolios are rebalanced on a monthly basis. The descriptive statistics of the performance and characteristics of each decile portfolio constructed on the basis of coskewness and cokurtosis are recorded. The abnormal time-series performance of the portfolios P1-P10 that are constructed on the basis of Si and Ki measures are estimated, using: 1) Standard CAPM model in equation 2.1

, - 2) Three-factor Fama and French (1993) model in equation 2.2

, - 3) Four-factor Carhart (1997) model in equation 2.3

, - This is to test whether the risk-adjusted time-series performance of portfolios constructed on the basis of stocks’ coskewness and cokurtosis estimated values are significantly different from zero. In order to test the mutual fund performance, the mutual funds performances are formed in 10 portfolios. Mutual funds are sorted on into decile portfolios based on their previous twelve-month’s excess return. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. The performances of the portfolios P1- P10 are estimated, using: 1) Standard CAPM model in equation 2.1

, - 2) Standard CAPM model plus coskewness and cokurtosis risk factors

[ ] (2.8) 3) Four-factor Carhart (1997) model in equation 2.3

, - 24

4) Higher moment six-factor model in equation 2.5

[ ]

2.5 Findings and Results

2.5.1 Summary Statistics

Table 2.1 presents summary statistics on the risk factors. The mean, median, and standard deviation are in monthly percentage. Also the monthly maximum, minimum, skewness and excess kurtosis are shown. The market factor is the excess return on the market portfolio, SMB is the factor-mimicking portfolio for size, HML is the factor-mimicking portfolio for book-to-market, WML is the factor- mimicking portfolio for one-month return momentum, CSK is the factor-mimicking portfolio for coskewness, and CKT is the factor-mimicking portfolio for cokurtosis. Monthly equity returns from Thomson Reuters Datastream from January 2000 to December 2011 are used to compute the coskewness and cokurtosis factors. The mean of risk premium for Market, SMB, and HML are all positive for all countries but the mean of WML risk premium in China is negative. The mean of CSK risk premium is positive for China at 1.47%, but negative for Singapore at -.32%, and Thailand at -.1%. The mean of CKT are negative for all countries i.e. -.08% for China, -.6% for Singapore and -.12% for Thailand, but the median of CKT is positive for China at.31%, and the mean is also very close to zero. [Table 2.1 is here] To analyze the potential impact of the factors when they are added to the models, the correlation coefficient among them is calculated as shown in Table 2.2. Observe that these correlations are generally small to medium, ranging from -.69 to .62 in China, -.74 to .36 in Singapore and -.24 to .66 in Thailand. The highest correlation in China is between CSK and WML, in Singapore is between CKT and Market, and in Thailand is between CSK and Market. This might has some impact to the result of the coefficient calculation of CSK and CKT. [Table 2.2 is here] 25

2.5.2 Performance and characteristics of decile portfolio constructed on the basis of Coskewness and Cokurtosis

Table 2.3 reports the characteristics of decile coskewness portfolios during the period January 2000 to December 2011. All equities are sorted at month t in ascending order to their coskewness values estimated (S) via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the equities with the lowest (most negative) estimated S and P10 with the highest (most positive) S. The excess returns of these portfolios are calculated at month t+1 (i.e. post ranking returns). For China, the average of S value for portfolio 1 is -.08 and the numbers get increased for portfolio 2 up until portfolio 10 at .63. And it’s only portfolio 1 that show negative sign of S while all other portfolios from 2 to 10 are all positive. For Singapore, the average of S value for portfolio 1 is -1.13 and the numbers keep increasing up to portfolio 10 at .73. There are 7 out of 10 portfolios that show negative S while there are only 3 positive portfolios. For Thailand, the average of S value for portfolio 1 is -.59 and the numbers keep increasing up to .77 at portfolio 10. There are 5 portfolios that show negative S, same number of positive portfolios.

P1-P10 is the spread between portfolio 1 and portfolio 10. Portfolios are rebalanced on a monthly basis. EW returns is the average monthly returns of equally weighted portfolios. The values of t-test of the null hypothesis of no difference in means between portfolios P1 and P10 are reported. The p-value of Mann-Whitney non-parametric test is also report in the last column as robustness test of the t-test. For China, average S of P1-P10 is -.7 and this is significantly difference from zero. The difference of EW returns between P1 and P10 is 2.05% but this is not significantly different from zero as t-test value is only 1.18 and Mann-Whitney p-value is greater than .10. But excluding portfolio 9 and 10, the EW returns is highest at portfolio 1 and keeps decreasing quite monotonically to portfolio 8. This show trend on decreasing of return with the increment of S, even it’s not statistically significant but 2.7% per month difference between portfolio 1 and portfolio 8 is economically significant. For 26

Singapore, average S of P1-P10 is -1.85 and significant while the difference of EW returns between P1 and P10 is -.68% but this is not significantly different from zero. The EW returns is increasing monotonically from portfolio 1 to 5 and drop from 6 to 8 and up again from 8 to 9 and drop on portfolio 10. For Thailand, average S of P1- P10 is -1.36 and significant while the difference of EW returns between P1 and P10 is .52% but this is not significantly different from zero. The EW returns are similar in portfolios 3 to 5, 6 to 7 and 9 to 10, and are not in monotonic. This result shows that the return of portfolios that hold the least of coskewness equities is not statistically significantly different from the return of portfolios that hold the most of coskewness equities for Singapore and Thailand. Only China show some trend in decreasing of return from portfolio 1 to portfolio 8 while S keep increasing, even not statistically significant but economically significant. [Table 2.3 is here] Table 2.4 reports the characteristics of decile cokurtosis portfolios. All equities are sorted at month t in ascending order to their cokurtosis values estimated (K) via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the equities with the lowest estimated K while P10 is with the highest. The excess returns of the portfolios are calculated at month t+1. For China, the average of K value for portfolio 1 is 4.7 and the numbers get increased for portfolio 2 until portfolio 10 at 9.5. The difference of average K of P10- P1 is 4.8 and this is not significantly difference from zero. The EW returns is 2.34% at portfolio 1 and keep decreasing to portfolio 5 and go up again. The difference of EW returns between P10 and P1 is .6% but this is not significantly different from zero as t-test value is only .33 and p-value for Mann-Whitney non-parametric test is more than .10. For Singapore, the average of K value for portfolio 1 is -137 and the numbers keep increasing to portfolio 10 at 732. There are 3 out of 10 portfolios that show negative K in portfolios 1, 2 and 3. The average K of P10-P1 is 869 but not significantly different from zero while the difference of EW returns between P10 and P1 is -.69% but again this is not significantly different from zero. The EW returns is decreasing quite monotonically from portfolio 1 to 9. For Thailand, the average of K value for portfolio 10 is 21 and it’s the only portfolio that has positive value of K. The average K value of portfolio 1 is minimal at -152. The average K of P10-P1 is 173 27 and not significant while the difference of EW returns between P1 and P10 is -.31% and also not significantly different from zero. The EW returns are fluctuate up and down, and not in monotonic. This result shows that the return of portfolios that hold the most of cokurtosis equities is not significantly different from the return of portfolios that hold the least of cokurtosis equities. Looking at the value of K among the three countries, China has very low value around 5 to 10, and they are not much different in their value from portfolio 1 to portfolio 10. K value of Singapore has ranging from -140 to 700, and Thailand ranging from -150 to 20. It might be the high variance among their portfolios that make them insignificantly different from each other. [Table 2.4 is here]

2.5.3 Alphas and Betas of Coskewness and Cokurtosis portfolio

Table 2.5 reports the abnormal performance of the 10 equally-weighted coskewness portfolios using CAPM model, Fama-French three-factor model, and Carhart four-factor model. All equities are sorted at month t in ascending order according to their coskewness (S) values estimated via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the shares with the lowest coskewness and P10 with the highest coskewness. Portfolios are rebalanced on a monthly basis. For China, the r-square of CAPM ranging from .39 to .79 and the adjusted r-square increased to .65 - .79 when another two risk factors, SMB and HML, are added into the equation. The portfolios with low coskewness tend to have higher improvement in r-square rather than the portfolios with high coskewness. The coefficient of market premium is always significant at 1% level. Coefficients of Market and SMB are significant for all portfolios but the coefficient of HML is only significant for just one portfolio. When momentum risk factor, WML, is added into the equation, the adjusted r-square is slightly increased to .70-.79. Coefficients of SMB and WML are significant for almost all portfolios but the coefficient of HML is still only significant for just one portfolio. For all three models, the alpha is highest at portfolio 1 where the S value is lowest and the alpha values get decreasing quite monotonically to portfolio 10. 28

Similar to result in table 3, the return of portfolio that holds low coskewness equities is higher than the portfolio that holds high coskewness equities. This might means that coskewness could be a factor to evaluate the asset value and should be incorporated in the asset pricing model. For Singapore, the r-square of CAPM ranging from .28 to .66 and the adjusted r-square increased to .48 - .73 when another two risk factors, SMB and HML, are added into the equation. Coefficients of Market risk factor are significant for all portfolios, and coefficient of SMB are significant for almost all portfolios but the coefficient of HML is only significant for just two portfolios. When momentum risk factor, WML, is added into the equation, the adjusted r-square is slightly increased to .58 - .73. Coefficients of SMB and WML are significant for most of portfolios but the coefficients of HML are still only significant for just two portfolios. Unlike China, the alphas in Singapore do not have strong trend pattern. For Thailand, the r-square of CAPM ranging from .33 to .83 and the adjusted r-square is slightly increased to .34 - .83 when another two risk factors, SMB and HML, are added into the equation. Same as China and Singapore, the coefficient of market premium is always significant at 1% level. But unlike China and Singapore, coefficients of SMB are significant for only two portfolios while the coefficients of HML are significant for five portfolios. When momentum risk factor, WML, is added into the equation, the adjusted r-square is unchanged. Coefficients of HML are significant for five portfolios, coefficients of SMB are significant for only two portfolios, and the coefficients of WML are significant for just portfolio 3. Similar to Singapore but unlike China, the alphas do not have strong trend pattern in Thailand. This might means that coskewness could be a good factor to evaluate the asset value in China but not for Singapore and Thailand. [Table 2.5 is here] Table 2.6 reports the abnormal performance of the ten equally-weighted cokurtosis portfolios using CAPM model, Fama-French three-factor model, and Carhart four-factor model. All equities are sorted at month t in ascending order according to their cokurtosis (K) values estimated via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the shares with the lowest cokurtosis and P10 with the highest cokurtosis. Portfolios are 29 rebalanced on a monthly basis. For China, the r-square of CAPM ranging from .47 to .70 and the adjusted r-square increased to .64 - .74 when another two risk factors, SMB and HML, are added into the equation. Coefficients of Market and SMB are significant for all portfolios but the coefficient of HML is not significant for any portfolio. When momentum risk factor, WML, is added into the equation, the adjusted r-square is slightly increased to .69 - .77. Coefficients of Market and SMB are significant for all portfolios, coefficients of WML are significant for almost all portfolios but the coefficient of HML is still not significant for any portfolio. The alphas do not change much from portfolio 1 to 10 and thus show no trend pattern. For Singapore, the r-square of CAPM ranging from .05 to .75 and the adjusted r-square increased to .06 - .82 when another two risk factors, SMB and HML, are added into the equation. Coefficients of Market risk factor are significant for all portfolios, and coefficient of SMB are significant for almost all portfolios but the coefficient of HML is only significant for just two portfolios. When momentum risk factor, WML, is added into the equation, the adjusted r-square is still the same range. Coefficients of SMB are significant for most of portfolios, coefficients of WML are significant for four portfolios, but the coefficients of HML are still only significant for just two portfolios. The alphas are low in portfolio 1 and getting higher up to portfolio 8 for three factor and four factor models, showing some trend pattern. For Thailand, the r-square of CAPM ranging from .63 to .77 and the adjusted r-square is slightly increased to .65 - .76 when another two risk factors, SMB and HML, are added into the equation. Coefficients of Market risk factor are significant for all portfolio, coefficients of SMB are significant for only two portfolios while the coefficients of HML are significant for four portfolios. When momentum risk factor, WML, is added into the equation, the adjusted r-square is unchanged. Coefficients of Market are significant for all portfolios, coefficients of HML are significant for four portfolios, coefficients of SMB are significant for only two portfolios, and the coefficients of WML are significant for just one portfolio. Same as China, the alphas do not show strong trend pattern. Only three-factor and four-factor models in Singapore show trend in alpha from small to large, but not in China and Thailand. This might means that cokurtosis might be a good factor to evaluate the asset value and should be incorporated in the 30 asset pricing model for Singapore. Having some sign of significance contribution of coskewness and cokurtosis in asset pricing model in some countries, the research continues to apply this higher moment risk factors to mutual fund evaluation. [Table 2.6 is here]

2.5.4 Measure of Mutual Funds Performance using Higher Moment six-factor model

Now that the coskewness and cokurtosis are used to form portfolios of equities, and evaluated by the three classical models i.e. CAPM, three-factor model, and four-factor model. The results seem to show some trend in alpha on some countries. The coskewness and cokurtosis are used to form risk factors and be incorporated into the asset pricing models to evaluate the performance of mutual fund. As mutual funds are formed by equities into portfolios, the concepts of coskewness and cokurtosis portfolios could be applied to the mutual fund performance evaluation. Table 2.7 reports summary statistics for all mutual funds categorized by country: China, Singapore, and Thailand during January 2000 to December 2011. For each category, mean of total return (%), median of total return (%), mean of standard deviation (%), mean of skewness, mean of excess kurtosis, and total number of funds in each category are reported. There are 363, 157 and 216 equity mutual funds in China, Singapore, and Thailand stock market. The mean of return is -.19% for China, .28% for Singapore and 1.18% for Thailand. The median of return is -.21% for China, .21% for Singapore and 1.27% for Thailand. The mean of skewness is -.05 for China, -.31 for Singapore and -.48 for Thailand. This statistics show that the returns of mutual fund in all three countries are negatively skewed, similar to mutual fund in US (see Monero and Rodriguez, 2009). The mean of excess kurtosis is .45 in China, 3.4 in Singapore and 2.3 in Thailand. This statistics show that the return of mutual funds in China is mildly platykurtic distributions and the return of mutual fund in Singapore and Thailand are leptokurtic distributions. These results show that the skewness and kurtosis of funds do exist and should not be ignored. [Table 2.7 is here] 31

Table 2.8 reports the abnormal performance of the equity mutual fund portfolios using CAPM model, Carhart four-factor model, and Higher Moment six- factor model. Mutual funds are sorted into decile portfolios based on their previous twelve-month’s excess return. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. For China, the r-squares of CAPM are ranging from .80 to .92. The adjusted r-squares are slightly increased to .80 - .93 when higher moment risk factors, CSK and CKT, are added into the standard CAPM equation as additional explanatory variables. The alphas are negative at portfolio 1 and increase monotonically to portfolio 10. There is no any portfolio that has alpha statistically significantly different from zero. The coefficient of market premium is always significant at 1% level. There is one portfolio that coefficient of CSK is significant at 10% level while the coefficient of CKT are all insignificant. When another three risk factors, SMB, HML and WML, are added into the standard CAPM equation, the adjusted r-squares are increased to .83 - .93 and there are eight out of ten portfolios that have alpha significantly different from zero. When higher moment risk factors, CSK and CKT, are added into the four-factor equation as additional explanatory variables, the adjusted r-squares are slightly increased to .83 - .94. Coefficients of HML and WML are significant for almost all portfolios, but the coefficient of SMB is significant for only one portfolio. The coefficients of higher moment risk factor CSK and CKT are close to zero and show no significant on any portfolio. For Singapore, the r-squares of CAPM are ranging from .48 to .76. The adjusted r-squares increased to .57 - .85 when higher moment risk factors, CSK and CKT, are added into the standard CAPM equation as additional explanatory variables. The coefficient of market premium is always significant at 1% level. The alphas are mostly negative at portfolio 1 and increase monotonically to portfolio 10, and there is no any portfolio that has alpha statistically significantly different from zero. There are eight portfolios that coefficient of CSK are significant while there is one portfolio that the coefficient of CKT is significant. 32

When another three risk factors, SMB, HML and WML, are added into the standard CAPM equation, the adjusted r-squares are slightly increased to .51 - .75 and there is no portfolio that has significant alpha. When higher moment risk factors, CSK and CKT, are added into the equation as additional explanatory variables, the adjusted r-squares increased to .56 - .85. Coefficients of WML are significant for three portfolios while coefficient of SMB and HML are not significant for any portfolio. The coefficients of higher moment risk factor CSK show significant alpha for all ten portfolios. The coefficients of higher moment risk factor CKT show significant only on portfolio 10. For Thailand, the r-squares of CAPM are ranging very high from .92 to .96. The adjusted r-squares are slightly increased to .92 - .98 when higher moment risk factors, CSK and CKT, are added into the standard CAPM equation as additional explanatory variables. The coefficient of market premium is always significant at 1% level. The alphas are negative at portfolio 1 and increase quite monotonically to portfolio 10, and there is one portfolio that has alpha statistically significantly different from zero. There is only one portfolio that coefficient of CSK is significant, and also there is one portfolio that the coefficient of CKT is significant. When another three risk factors, SMB, HML and WML, are added into the standard CAPM equation, the adjusted r-squares remain unchanged and there is no any portfolio that show significant alpha. When higher moment risk factors, CSK and CKT, are added into the equation as additional explanatory variables, the adjusted r- square is slightly increased to .93 - .98. Coefficients of SMB, HML and WML are significant for four, two and seven portfolios respectively. The coefficients of higher moment risk factor CSK show significant alpha on two portfolios. The coefficients of higher moment risk factor CKT show significant on one portfolio. Investors should demand higher returns due to higher risk of coskewness, so the adjusted alpha of funds that incorporate negative (positive) coskewness assets should be lower (higher). The result of Singapore and Thailand where the average of the funds’ coskewness are negative confirm this result as the adjusted alphas of most portfolios move to the left after coskewness and cokurtosis are incorporated in. This result is the same as in US (see Monero and Rodriguez, 2009). This confirms the 33 importance of higher moments on the asset pricing model even they are not very strong in every markets. [Table 2.8 is here]

2.6 Conclusion

Recent asset pricing studies, especially in US, show that coskewness is important both in equities and mutual fund, this study shows that coskewness and cokurtosis risk factors show some significance in some countries in Asia. Looking at the equities, the ten portfolios sorted by coskewness of equities show some monotonically trend on the equally weighted return, even not statistically significantly but economically significantly different in China at 2.7% per month. But this pattern is not clearly found in Singapore and Thailand. The return of portfolio that hold different degree of coskewness equities does not yield statistically significant equally weighted return in Singapore and Thailand even the value of coskewness between portfolio 1 and 10 are statistically significantly different. The ten portfolios sorted by cokurtosis of equities show no statistically significantly different between both value of cokurtosis and their corresponding equally weighted return of the portfolio in all three countries. The cokurtosis values are much smaller in China compare to the other two countries, showing that the cokurtosis variation in China is very low. The return of portfolio that hold different degree of coskewness equities does not yield statistically significant equally weighted return in all three countries. Looking at the mutual fund, the study of mutual fund performance in China, Singapore, and Thailand using Higher Moment six-factor model, shows good support for the pricing of coskewness in Singapore, and weak support in Thailand. There are some little sign of mild support for the pricing of cokurtosis in Singapore and Thailand too, even very limited. But for all three countries, adding coskewness and cokurtosis risk factors in both CAPM and four-factor model, show some increment in the explanatory power of the models.

The skewness of the equity mutual fund in China is very low, and thus the return of the portfolio may not be impacted by the higher moment. Also the sample size of equity mutual funds in China is quite few in the early years of the data set, which could impact to the reliability of the result. The r-square of market risk factor is very high in Thailand showing that all equity mutual funds follow the index closely, more than equity mutual funds of other two countries. For Singapore, the negatively skewed distribution of return and well-developed of the equity market may result in the pricing of higher moment risk factors. Perhaps it could be that mutual funds in Singapore manage the coskewness into their portfolios like Moreno and Rodriguez (2009) found in the US mutual fund performance evaluation while mutual fund in China and Thailand are not. Asset management in Asian market could be more effective if apply and manage the coskewness and cokurtosis in their portfolios as they have shown their importance in the developed market.

Table 2.1 Summary Statistics of Risk Factors

This table reports summary statistics of the risk factors. The mean, median, and std. dev. are represented in percentages. The MKT factor is the excess return on the market portfolio, SMB is the factor-mimicking portfolio for size, HML is the factor- mimicking portfolio for book-to-market, WML is the factor-mimicking portfolio for one-month return momentum, CSK is the factor-mimicking portfolio for coskewness, and CKT is the factor-mimicking portfolio for cokurtosis.

Panel A: China MKT SMB HML WML CSK CKT Mean total return (%) 0.71 2.00 1.42 -0.51 1.47 -0.08 Median total return (%) 0.63 0.94 1.05 -0.79 1.86 0.31 Maximum 26.92 134.0 38.49 34.12 24.93 12.72 Minimum -23.01 -15.77 -6.04 -16.53 -12.36 -16.90 Standard Deviation 9.29 13.32 4.37 5.38 5.91 5.33 Skewness 0.15 7.23 4.55 1.94 0.50 -0.50 Excess Kurtosis 0.45 70.88 37.21 12.65 2.65 0.92

Panel B: Singapore MKT SMB HML WML CSK CKT Mean total return (%) 0.44 1.78 1.49 0.72 -0.32 -0.60 Median total return (%) 0.74 -0.02 1.27 1.17 -1.06 -0.54 Maximum 26.90 99.23 13.51 61.20 22.88 22.77 Minimum -23.82 -32.79 -4.88 -36.49 -8.86 -33.74 Standard Deviation 6.11 11.55 3.09 8.68 4.80 7.47 Skewness -0.14 4.65 0.93 1.68 2.12 -0.78 Excess Kurtosis 4.09 37.39 1.98 20.86 8.22 4.90

Panel C: Thailand MKT SMB HML WML CSK CKT Mean total return (%) 1.46 4.28 1.86 0.67 -0.10 -0.12 Median total return (%) 1.51 1.53 1.48 0.39 -0.34 -0.18 Maximum 23.48 96.53 15.69 20.97 8.19 5.11 Minimum -30.38 -14.67 -10.11 -8.68 -9.57 -4.83 Standard Deviation 7.41 14.46 3.80 3.64 3.26 1.74 Skewness -0.39 3.58 0.69 1.63 0.12 0.08 Excess Kurtosis 2.18 16.86 1.87 8.13 0.49 0.70 37

Table 2.2 Cross Correlations of Risk Factors

This table reports the contemporaneous correlations between the risk factors included in the model. The MKT factor is the excess return on the market portfolio, SMB is the factor-mimicking portfolio for size, HML is the factor-mimicking portfolio for book- to-market, WML is the factor-mimicking portfolio for one-month return momentum, CSK is the factor-mimicking portfolio for coskewness, CKT is the factor-mimicking portfolio for cokurtosis. The p-values are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China MKT SMB HML WML CSK CKT MKT 1 SMB -0.03 1 (0.68) HML 0.24*** 0.62*** 1 (0.00) (0.00) WML 0.05 0.32*** 0.50*** 1 (0.59) (0.00) (0.00) CSK -0.07 0.62*** 0.20* -0.69*** 1 (0.53) (0.00) (0.06) (0.00) CKT 0.10 -0.25** 0.02 0.41*** -0.47*** 1 (0.38) (0.02) (0.83) (0.00) (0.00)

Panel B: Singapore MKT SMB HML WML CSK CKT MKT 1 SMB 0.05 1 (0.55) HML -0.20** 0.36*** 1 (0.02) (0.00) WML -0.28*** 0.02 0.18** 1 (0.00) (0.83) (0.04) CSK 0.07 -0.28** -0.24** -0.57*** 1 (0.50) (0.01) (0.03) (0.00) CKT -0.74*** -0.31*** -0.10 0.17 -0.17 1 (0.00) (0.00) (0.37) (0.12) (0.12)

Panel C: Thailand MKT SMB HML WML CSK CKT MKT 1 SMB -0.20** 1 (0.02) HML -0.24** 0.29*** 1 (0.01) (0.00) WML 0.20** 0.26*** -0.01 1 (0.02) (0.00) (0.87) CSK 0.66*** -0.16 -0.16 -0.03 1 (0.00) (0.15) (0.15) (0.81) CKT 0.02 -0.06 0.00 -0.14 0.03 1 (0.83) (0.60) (0.99) (0.21) (0.81) 39

Table 2.3 Performance and Characteristics of Decile Portfolios Constructed on the Basis of Coskewness

This table reports the characteristics of decile coskewness portfolios during the period January 2000 to December 2011. All equities are sorted at month t in ascending order to their coskewness values estimated (S) via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the equities with the lowest and P10 with the highest S. The excess returns of the portfolios are calculated at month t+1. P1-P10 is the spread between portfolio 1 and 10. Portfolios are rebalanced on a monthly basis. EW returns is the average monthly returns of equally weighted portfolios. The values for t-test and Mann-Whitney (MW) of the null hypothesis of no difference in means between portfolios P1 and P10 are reported in the last two columns. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P1- t- MW P10 test p- value Avg -.08 .11 .16 .19 .23 .26 .30 .35 .43 .63 -.70 -17.1 S *** EW 3.93 2.53 2.34 2.26 1.67 1.93 1.67 1.20 1.34 1.88 2.05 1.18 .68 returns (%)

Panel B: Singapore P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P1- t- MW P10 test p- value Avg -1.13 -1.08 -.98 -.53 -.34 -.23 -.10 .02 .19 .73 -1.85 -46.9 S *** EW .27 .23 1.30 1.45 1.56 .94 .55 .37 1.19 .95 -.68 -.86 .13 returns (%)

Panel C: Thailand P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P1- t- MW P10 test p- value Avg -.59 -.33 -.23 -.15 -.08 .00 .09 .20 .36 .77 -1.36 -16.4 S *** EW 1.55 .66 .79 .79 .77 .92 .96 1.28 1.00 1.03 .52 .70 .39 returns (%) 41

Table 2.4 Performance and Characteristics of Decile Portfolios Constructed on the Basis of Cokurtosis

This table reports the characteristics of decile cokurtosis portfolios during the period January 2000 to December 2011. All equities are sorted at month t in ascending order to their coskurtosis values estimated (K) via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the equities with the lowest and P10 with the highest K. The excess returns of the portfolios are calculated at month t+1. P10-P1 is the spread between portfolio 10 and 1. Portfolios are rebalanced on a monthly basis. EW returns is the average monthly returns of equally-weighted portfolios. The values for t-test and Mann-Whitney (MW) of the null hypothesis of no difference in means between portfolios P10 and P1 are reported in the last two columns. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P10 t- MW -P1 test p- value Avg 4.7 6.8 7.0 7.2 7.4 7.5 7.6 7.8 8.0 9.5 4.8 .85 K EW 2.34 2.09 2.41 2.15 1.56 1.71 1.89 1.78 1.86 2.94 .60 .33 .61 returns (%)

Panel B: Singapore P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P10 t- MW -P1 test p- value Avg -137 -70 -69 182 549 605 667 708 716 732 869 1.38 K EW 1.43 .73 .96 .99 1.05 1.35 .98 .54 .03 .74 -.69 -.70 .85 returns (%)

Panel C: Thailand P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P10 t- MW -P1 test p- value Avg -152 -133 -122 -112 -104 -97 -84 -68 -41 21 173 1.11 K EW 1.31 .81 .92 1.21 1.45 .61 .79 .93 .74 .99 -.31 -.36 .94 returns (%)

Table 2.5

Alphas and Betas of Equally-Weighted Coskewness Portfolios using CAPM, Fama- French three-factor model, and Carhart four-factor model

This table reports the abnormal performance of the 10 equally-weighted coskewness portfolios. All equities are sorted at month t in ascending order according to their coskewness (S) values estimated via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the shares with the lowest coskewness and P10 with the highest coskewness. Portfolios are rebalanced on a monthly basis. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Capital Asset Pricing Model 2.74** 1.19 .93 .85 .32 .50 .20 -.21 -.04 .54 (2.55) (1.28) (1.02) (.98) (.39) (.62) (.26) (-.33) (-.07) (1.06) .73*** .82*** .86*** .86*** .83*** .87*** .90*** .86*** .85*** .82*** (7.4) (9.6) (10.4) (10.8) (11.3) (11.8) (12.7) (14.5) (15.7) (17.6) .39 .53 .56 .58 .61 .63 .66 .72 .75 .79 Fama-French Three Factors Model .82 -.36 -.82 -.35 -.88 -.63 -.66 -.90 -.35 .42 (1.01) (-.41) (-1.00) (-.41) (-1.12) (-.78) (-.83) (-1.35) (-.57) (.76) .98*** .95*** .98*** .96*** .92*** .96*** .98*** .92*** .92*** .87*** (12.9) (11.6) (12.8) (11.9) (12.4) (12.7) (13.2) (14.7) (16.2) (17.0) 1.03*** .62*** .63*** .48*** .44*** .43*** .37*** .29*** .27*** .15** (9.67) (5.39) (5.87) (4.28) (4.28) (4.06) (3.58) (3.30) (3.33) (2.13) .00 .34 .49* .26 .32 .29 .14 .13 -.17 -.14 (.00) (1.26) (1.93) (.96) (1.3) (1.15) (.57) (.63) (-.89) (-.85)

.71 .65 .70 .66 .68 .69 .70 .75 .77 .79 Carhart Four Factors Model .28 -.93 -1.21 -.78 -1.32* -.97 -1.00 -1.10 -.50 .50 (.38) (-1.19) (-1.54) (-.97) (-1.8) (-1.25) (-1.30) (-1.64) (-.83) (.91) .92*** .89*** .94*** .92*** .87*** .92*** .95*** .90*** .91*** .87*** (13.8) (12.3) (12.9) (12.1) (12.8) (12.7) (13.2) (14.5) (15.9) (16.9) .74*** .31** .42*** .25** .21* .24** .19 .19* .18* .20** (6.72) (2.62) (3.54) (2.02) (1.85) (2.06) (1.63) (1.84) (1.97) (2.35) -.01 .33 .48** .25 .31 .28 .13 .13 -.17 -.14 (-.05) (1.37) (2.01) (.99) (1.38) (1.18) (.57) (.62) (-.92) (-.84) -.82*** -.86*** -.59*** -.66*** -.67*** -.52*** -.52*** -.29* -.23* .13 (-5.00) (-4.86) (-3.29) (-3.55) (-4.00) (-2.92) (-2.94) (-1.91) (-1.69) (1.02)

.78 .73 .74 .70 .73 .72 .73 .76 .78 .79

Panel B: Singapore P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Capital Asset Pricing Model -.29 -.24 .70 .84 .85 .44 .00 -.21 .56 .65* (-.66) (-.61) (1.35) (1.58) (1.62) (.87) (.01) (-.45) (1.46) (1.66) .68*** .57*** .72*** .74*** .86*** .60*** .66*** .70*** .76*** .36*** (9.9) (9.2) (8.9) (8.9) (10.5) (7.6) (8.7) (9.4) (12.7) (5.8) .54 .50 .49 .48 .57 .41 .47 .51 .66 .28 Fama-French Three Factors Model -.42 -.23 .24 .11 .29 -.31 -.69 -1.01** -.05 .16 (-.86) (-.53) (.46) (.23) (.59) (-.65) (-1.52) (-2.23) (-.14) (.43) .68*** .57*** .73*** .75*** .87*** .62*** .67*** .72*** .78*** .36*** (9.9) (9.2) (9.8) (10.9) (12.3) (9.0) (10.2) (11.1) (14.5) (6.9) -.05 -.08 .26*** .34*** .32*** .23*** .23*** .18*** .11* .23*** (-.66) (-1.21) (3.40) (4.68) (4.40) (3.27) (3.43) (2.66) (1.96) (4.23) .15 .09 -.02 .07 -.03 .23 .19 .33** .30** .05 (.89) (.60) (-.09) (.43) (-.18) (1.29) (1.14) (2.00) (2.15) (.38)

.53 .50 .57 .65 .68 .56 .61 .63 .73 .48 Carhart Four Factors Model -.19 -.01 .32 .12 .28 -.40 -.80* -1.11** -.08 .13 (-.48) (-.04) (.63) (.25) (.57) (-.86) (-1.81) (-2.54) (-.22) (.36) .57*** .47*** .69*** .75*** .87*** .66*** .72*** .77*** .79*** .37*** (9.9) (9.3) (9.0) (10.4) (11.7) (9.5) (10.9) (11.8) (14.2) (6.8) .07 .03 .30*** .34*** .32*** .19** .18*** .13* .09 .22*** (1.15) (.64) (3.82) (4.51) (4.13) (2.55) (2.64) (1.87) (1.59) (3.83) .14 .08 -.02 .07 -.03 .24 .20 .34** .30** .05 (.96) (.62) (-.13) (.43) (-.18) (1.38) (1.24) (2.13) (2.17) (.39) -.26*** -.25*** -.09* -.01 .01 .11** .12*** .12*** .04 .02 (-6.70) (-7.37) (-1.82) (-.19) (.21) (2.30) (2.67) (2.65) (1.00) (.69)

.70 .70 .58 .65 .68 .58 .63 .66 .73 .48

Panel C: Thailand P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Capital Asset Pricing Model .83* -.22 -.07 .01 -.07 .05 .24 .64** .43 .77*** (1.81) (-.61) (-.20) (.04) (-.26) (.18) (.77) (2.10) (1.32) (3.00) .66*** .81*** .79*** .71*** .77*** .78*** .65*** .58*** .52*** .23*** (10.2) (15.5) (15.8) (14.7) (19.9) (17.3) (15.0) (13.3) (11.4) (6.45) .55 .74 .75 .72 .83 .78 .73 .68 .61 .33 Fama-French Three Factors Model .16 -.47 -.34 -.54 -.40 -.20 -.04 .26 -.03 .52* (.31) (-1.11) (-.84) (-1.47) (-1.29) (-.57) (-.12) (.77) (-.09) (1.79) .72*** .83*** .82*** .76*** .79*** .80*** .69*** .61*** .56*** .26*** (10.8) (14.9) (15.4) (15.6) (19.7) (16.8) (15.0) (13.6) (11.9) (6.7) .03 .03 .04 .06* .02 .01 .05* .03 .03 .01 (.78) (.87) (1.25) (1.97) (.82) (.31) (1.91) (1.25) (.95) (.66) .43** .10 .09 .26** .19* .18 .07 .20* .28** .15 (2.60) (.76) (.68) (2.19) (1.93) (1.50) (.59) (1.76) (2.39) (1.59)

.59 .74 .75 .75 .83 .78 .74 .69 .63 .34 Carhart Four Factors Model .11 -.46 -.39 -.56 -.42 -.24 -.04 .26 -.04 .52* (.23) (-1.09) (-.98) (-1.51) (-1.37) (-.67) (-.13) (.76) (-.12) (1.78) .74*** .83*** .86*** .77*** .82*** .83*** .69*** .61*** .57*** .26*** (10.5) (13.7) (15.2) (14.6) (18.7) (16.2) (13.8) (12.5) (11.1) (6.1) .08 .02 .10** .08* .04 .05 .05 .03 .04 .01 (1.38) (.50) (2.19) (1.90) (1.33) (1.21) (1.43) (.86) (.96) (.43) .41** .11 .07 .26** .18* .16 .07 .20* .28** .15 (2.52) (.77) (.55) (2.12) (1.84) (1.40) (.58) (1.75) (2.34) (1.58) -.22 .03 -.27* -.09 -.12 -.19 -.01 .01 -.05 .01 (-1.18) (.18) (-1.85) (-.69) (-1.07) (-1.44) (-.08) (.06) (-.40) (.08)

.59 .74 .76 .74 .83 .79 .73 .69 .63 .33

Table 2.6

Alphas and Betas of Equally-Weighted Cokurtosis Portfolios using CAPM, Fama- French three-factor model, and Carhart four-factor model

This table reports the abnormal performance of the ten equally-weighted cokurtosis portfolios. All equities are sorted at month t in ascending order according to their cokurtosis (K) values estimated via a rolling window of 60 monthly observations and they are classified into ten portfolios. P1 is the decile portfolio of the shares with the lowest cokurtosis and P10 with the highest cokurtosis. Portfolios are rebalanced on a monthly basis. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Capital Asset Pricing Model 1.17 .71 .98 .72 .22 .31 .50 .39 .48 1.52* (1.27) (.87) (1.21) (.89) (.30) (.40) (.65) (.56) (.73) (1.71) .72*** .84*** .87*** .88*** .82*** .85*** .85*** .86*** .85*** .87*** (8.6) (11.3) (11.7) (11.8) (11.9) (11.9) (12.1) (13.4) (14.1) (10.7) .47 .60 .62 .62 .63 .63 .64 .68 .70 .58 Fama-French Three Factors Model -.25 -.20 -.32 -.34 -.88 -.81 -.52 -.52 -.37 .52 (-.30) (-.25) (-.42) (-.43) (-1.20) (-1.04) (-.68) (-.73) (-.55) (.63) .88*** .97*** .99*** .98*** .91*** .93*** .92*** .91*** .89*** 1.04*** (11.3) (13.2) (14.0) (13.3) (13.3) (12.8) (12.8) (13.8) (14.1) (13.5) .68*** .52*** .55*** .49*** .45*** .42*** .38*** .32*** .27*** .63*** (6.25) (4.98) (5.55) (4.68) (4.63) (4.08) (3.73) (3.46) (3.00) (5.87) .12 -.05 .24 .13 .24 .30 .27 .26 .31 -.17 (.47) (-.22) (1.00) (.53) (1.05) (1.25) (1.14) (1.19) (1.45) (-.64)

.64 .69 .73 .70 .71 .69 .69 .73 .74 .70 Carhart Four Factors Model -.70 -.72 -.76 -.74 -1.26* -1.13 -.81 -.77 -.51 .40 (-.91) (-1.03) (-1.09) (-.99) (-1.81) (-1.50) (-1.06) (-1.10) (-.75) (.48) .83*** .92*** .95*** .95*** .88*** .90*** .89*** .89*** .88*** 1.03*** (11.5) (14.0) (14.5) (13.5) (13.5) (12.8) (12.6) (13.7) (13.7) (13.2) .44*** .23** .32*** .27** .25** .25** .23* .19* .19* .57*** (3.69) (2.20) (2.96) (2.38) (2.32) (2.14) (1.96) (1.75) (1.82) (4.48) .11 -.07 .23 .12 .23 .30 .27 .26 .30 -.17 (.46) (-.30) (1.06) (.53) (1.08) (1.28) (1.15) (1.20) (1.44) (-.65) -.69*** -.79*** -.67*** -.60*** -.57*** -.48*** -.43** -.38** -.22 -.18 (-3.91) (-4.94) (-4.20) (-3.54) (3.57) (-2.79) (-2.46) (-2.41) (-1.39) (-.94)

.69 .76 .77 .74 .74 .72 .71 .74 .74 .70

Panel B: Singapore P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Capital Asset Pricing Model .56 -.02 .14 .21 .23 .55 .62* .43 -.02 -.60* (.99) (-.03) (.29) (.48) (.55) (1.39) (1.87) (1.61) (-.13) (1.88) 1.05*** .90*** .99*** .93*** .99*** .97*** .44*** .13*** .07** .17*** (11.7) (11.5) (13.6) (13.4) (15.2) (15.8) (8.44) (3.17) (2.29) (3.40) .62 .61 .69 .68 .74 .75 .46 .10 .05 .11 Fama-French Three Factors Model -.25 -.73 -.44 -.34 -.43 -.14 .15 .33 -.10 .04 (-.54) (-1.66) (-.99) (-.82) (-1.11) (-.39) (.47) (1.14) (-.47) (.12) 1.06*** .91*** 1.00*** .94*** 1.00*** .98*** .45*** .14*** .07** .19*** (15.7) (14.5) (15.6) (15.6) (18.0) (18.7) (10.1) (3.22) (2.44) (4.24) .44*** .34*** .24*** .25*** .19*** .13** .18*** -.02 -.05 .07 (6.22) (5.18) (3.56) (3.92) (3.38) (2.47) (3.88) (-.37) (-1.44) (1.56) .00 .06 .09 .07 .21 .31** .10 .09 .12 .31*** (.01) (.35) (.59) (.47) (1.49) (2.33) (.93) (.85) (1.49) (2.77)

.79 .75 .76 .76 .81 .82 .61 .08 .06 .31 Carhart Four Factors Model -.21 -.70 -.39 -.25 -.36 -.12 .09 .29 -.11 .02 (-.44) (-1.59) (-.86) (-.62) (-.94) (-.34) (.29) (.99) (-.55) (.08) 1.04*** .90*** .98*** .90*** .97*** .98*** .47*** .16*** .08** .19*** (14.8) (13.7) (14.6) (14.8) (17.1) (17.7) (10.6) (3.64) (2.58) (4.20) .46*** .35*** .27*** .29*** .23*** .15** .15*** -.04 -.05 .06 (6.26) (5.14) (3.86) (4.61) (3.89) (2.52) (3.17) (-.88) (-1.62) (1.33) .00 .05 .09 .06 .21 .31** .11 .09 .12 .31*** (-.01) (.34) (.57) (.43) (1.48) (2.31) (1.00) (.90) (1.51) (2.77) -.05 -.03 -.07 -.10** -.08* -.02 .07** .05* .02 .02 (-1.05) (-.68) (-1.47) (-2.51) (-2.05) (-.57) (2.21) (1.80) (.85) (.52)

.79 .75 .76 .76 .82 .81 .63 .11 .05 .31

Panel C: Thailand P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Capital Asset Pricing Model .55 .11 .24 .48 .74*** -.13 .09 .18 .07 .27 (1.60) (.29) (.68) (1.25) (2.71) (-.40) (.26) (.53) (.25) (.81) .69*** .63*** .61*** .66*** .64*** .67*** .64*** .68*** .61*** .66*** (14.2) (11.8) (12.2) (12.2) (16.5) (14.8) (12.6) (14.1) (15.8) (14.2) .71 .63 .64 .64 .77 .73 .66 .70 .75 .71 Fama-French Three Factors Model .20 -.41 -.14 -.17 .69** -.37 -.20 -.31 -.24 -.11 (.53) (-.99) (-.35) (-.42) (2.18) (-1.03) (-.49) (-.85) (-.80) (-.30) .71*** .68*** .65*** .73*** .65*** .69*** .67*** .72*** .64*** .70*** (14.2) (12.4) (12.3) (13.6) (15.5) (14.6) (12.5) (14.6) (15.8) (14.2) -.02 .06* .03 .10*** .01 .04 .04 .00 .02 .02 (-.60) (1.80) (.95) (3.24) (.46) (1.44) (1.25) (.10) (.75) (.83) .32** .23* .21 .20 .01 .07 .11 .38*** .19 .22* (2.61) (1.72) (1.59) (1.51) (.09) (.61) (.83) (3.11) (1.90) (1.83)

.72 .65 .65 .69 .76 .73 .66 .73 .76 .72 Carhart Four Factors Model .20 -.40 -.17 -.22 .65** -.40 -.18 -.36 -.25 -.14 (.53) (-.95) (-.41) (-.54) (2.07) (-1.11) (-.44) (-.98) (-.81) (-.37) .71*** .67*** .67*** .77*** .67*** .71*** .65*** .75*** .64*** .72*** (13.1) (11.3) (11.7) (13.3) (15.2) (13.9) (11.3) (14.3) (14.6) (13.5) -.02 .05 .06 .15*** .05 .07* .02 .05 .02 .05 (-.50) (1.04) (1.32) (3.43) (1.56) (1.73) (.46) (1.19) (.71) (1.25) .32** .24* .20 .19 .00 .06 .12 .37*** .19 .21* (2.59) (1.73) (1.52) (1.40) (-.04) (.53) (.88) (3.01) (1.86) (1.76) .01 .06 -.14 -.23 .20* -.13 .09 -.22 -.03 -.13 (.10) (.38) (-.92) (-1.54) (-1.77) (-1.00) (.64) (-1.63) (-.24) (-.95)

.72 .65 .65 .69 .77 .73 .66 .73 .76 .72

Table 2.7 Summary Statistics of Mutual Funds

This table reports summary statistics for all mutual funds categorized by country: China, Singapore, and Thailand during January 2000 to December 2011. For each category, reports mean of total return (%), median of total return (%), mean of standard deviation (%), mean of skewness, mean of excess kurtosis, and total number of funds.

China Singapore Thailand Average/All Mean of Return (%) -0.193 0.275 1.178 0.420 Median of Return (%) -0.207 0.206 1.268 0.422 Mean of Standard Deviation (%) 7.153 6.120 6.849 6.707 Median of Standard Deviation (%) 7.097 5.535 7.059 6.564 Mean of Skewness -0.050 -0.312 -0.482 -0.281 Median of Skewness -0.156 -0.467 -0.457 -0.360 Mean of excess Kurtosis 0.452 3.418 2.300 2.057 Median of excess Kurtosis 0.117 1.394 1.811 1.107 No. of Funds 363 157 216 736

Table 2.8

Measures of Mutual Fund Performance using CAPM, Carhart four-factor model, and Higher moment (with Coskewness and Cokurtosis Risk Factors) six-factor model

This table shows the OLS estimates of the different asset pricing models for equity mutual funds. Mutual funds are sorted on January 1 each year from 2001-2011 into decile portfolios based on their previous twelve-month’s excess return. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Excess -1.55 .19 .86 1.27 1.57 1.84 2.13 2.54 3.26 4.74 Return Capital Asset Pricing Model -.10 .07 .20 .19 .29 .27 .40 .27 .44 .59 (-.43) (.28) (.86) (.79) (1.12) (1.01) (1.38) (1.06) (1.54) (1.63) .67*** .73*** .74*** .76*** .72*** .74*** .71*** .71*** .73*** .68*** (30.6) (31.4) (32.5) (32.8) (29.2) (29.6) (25.8) (29.5) (26.6) (19.6) .91 .91 .92 .92 .90 .90 .88 .90 .88 .80 Capital Asset Pricing Model + Higher Moment -.21 -.00 .23 .31 .21 .28 .48 .40 .47 .78* (-.80) (-.00) (.88) (1.19) (.72) (.94) (1.42) (1.44) (1.45) (1.86) .67*** .73*** .75*** .77*** .73*** .75*** .72*** .72*** .73*** .68*** (28.5) (32.3) (31.6) (32.7) (28.0) (28.7) (24.0) (29.0) (25.2) (18.2) .06 .00 -.04 -.08 -.02 -.06 -.07 -.09* -.09 -.12 (1.31) (.06) (-.75) (-1.57) (-.42) (-1.21) (-1.14) (-1.78) (-1.57) (-1.56) -.01 -.04 -.06 -.03 -.05 .03 -.01 -.04 -.02 -.06 (-.23) (-.82) (-1.19) (-.58) (-.78) (.58) (-.12) (-.69) (-.25) (-.64)

.91 .93 .92 .93 .90 .91 .88 .91 .89 .80

Panel A: China (Continue) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Carhart Four Factors Model -.21 .26 .52** .56** .63** .66** .82*** .64** .93*** 1.03*** (-.86) (1.01) (2.07) (2.22) (2.30) (2.55) (2.73) (2.45) (3.23) (2.75) .67*** .75*** .76*** .78*** .75*** .78*** .74*** .73*** .76*** .70*** (27.9) (30.1) (31.0) (31.7) (28.0) (31.1) (25.3) (28.9) (27.2) (19.4) .01 .01 -.02 .01 .03 .10** .04 .03 .05 .06 (.19) (.37) (-.48) (.30) (.70) (2.28) (.82) (.76) (1.12) (1.05) -.01 -.25*** -.27*** -.22*** -.23** -.20** -.25** -.19** -.29*** -.16 (-.15) (-2.96) (-3.36) (-2.68) (-2.61) (-2.39) (-2.54) (-2.23) (-3.06) (-1.29) -.11* -.06 -.02 .13** .12* .28*** .19** .19*** .23*** .32*** (-1.83) (-.97) (-.29) (2.16) (1.77) (4.62) (2.60) (3.08) (3.31) (3.66)

.91 .92 .93 .93 .91 .92 .89 .91 .90 .83 Higher Moment Six Factors Model -.27 .20 .56** .63** .59** .60** .85** .69** .87*** 1.16*** (-.94) (.76) (2.07) (2.32) (1.99) (2.10) (2.48) (2.42) (2.67) (2.75) .67*** .75*** .77*** .79*** .75*** .79*** .74*** .74*** .76*** .70*** (25.4) (30.4) (30.4) (31.3) (27.1) (29.6) (23.1) (27.8) (25.2) (17.8) .02 .02 -.02 .01 -.00 .09* .03 .03 .05 .03 (.38) (.34) (-.49) (.22) (-.07) (1.89) (.43) (.62) (.97) (.46) -.03 -.24*** -.31*** -.24*** -.28*** -.24** -.28** -.21** -.30*** -.17 (-.29) (-2.80) (-3.57) (-2.77) (-2.95) (-2.60) (-2.54) (-2.28) (-2.88) (-1.30) -.12 -.02 .04 .17** .21** .30*** .24** .21*** .27*** .43*** (-1.56) (-.23) (.53) (2.33) (2.54) (3.76) (2.51) (2.64) (2.99) (3.68) -.01 .02 .05 .04 .12 .04 .07 .02 .04 .09 (-.12) (.24) (.66) (.54) (1.65) (.61) (.79) (.27) (.50) (.87) -.00 -.03 -.04 -.03 -.05 .01 -.01 -.05 -.03 -.09 (-.01) (-.49) (-.83) (-.62) (-.81) (.22) (-.21) (-.86) (-.43) (-1.08)

.91 .93 .93 .94 .92 .93 .89 .92 .90 .83

Panel B: Singapore P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Excess -2.45 -1.00 -.55 -.25 .03 .32 .61 .94 1.41 3.61 Return Capital Asset Pricing Model -.62 -.12 -.05 -.13 -.22 -.22 -.01 -.02 -.13 .31 (-1.64) (-.41) (-.17) (-.56) (-1.07) (-1.06) (-.02) (-.10) (-.56) (.84) .74*** .65*** .64*** .65*** .68*** .66*** .69*** .69*** .67*** .66*** (12.0) (14.2) (14.3) (17.8) (20.2) (19.7) (19.2) (19.3) (18.0) (11.0) .52 .60 .61 .71 .76 .75 .74 .74 .71 .48 Capital Asset Pricing Model + Higher Moment -.51 -.23 -.09 -.41* -.37* -.37* -.13 -.17 -.17 .02 (-1.61) (-.78) (-.28) (-1.84) (-1.69) (-1.70) (-.58) (-.73) (-.64) (.05) .64*** .63*** .65*** .67*** .66*** .69*** .70*** .74*** .71*** .58*** (8.7) (9.4) (8.6) (12.9) (13.2) (13.8) (13.5) (13.6) (11.9) (5.1) -.11* -.06 -.07 -.09* -.13*** -.20*** -.16*** -.20*** -.30*** -.46*** (-1.67) (-1.03) (-1.06) (-1.82) (-2.81) (-4.46) (-3.43) (-3.99) (-5.49) (-4.40) -.07 -.03 -.02 -.02 -.06 -.03 -.06 -.04 -.02 -.20** (-1.14) (-.55) (-.36) (-.52) (-1.32) (-.57) (-1.45) (-.84) (-.41) (-2.01)

.71 .72 .67 .82 .84 .85 .85 .85 .81 .57 56

Panel B: Singapore (Continue) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Carhart Four Factors Model -.51 -.06 -.03 -.17 -.32 -.26 -.11 -.13 -.25 .05 (-1.23) (-.18) (-.08) (-.68) (-1.37) (-1.13) (-.43) (-.55) (-1.03) (.11) .69*** .62*** .63*** .64*** .69*** .66*** .71*** .72*** .71*** .72*** (10.7) (12.8) (13.0) (16.4) (18.9) (18.6) (18.3) (19.3) (19.0) (11.6) .04 .02 .01 .01 .01 .01 .01 .00 .02 .02 (1.23) (.94) (.31) (.55) (.33) (.38) (.70) (.12) (1.02) (.50) -.08 -.05 -.01 .03 .06 .01 .03 .03 -.01 .08 (-.57) (-.49) (-.09) (.34) (.79) (.09) (.39) (.37) (-.19) (.59) -.09* -.04 -.02 -.02 -.01 .02 .03 .07*** .11*** .14*** (-1.97) (-1.16) (-.74) (-.71) (-.21) (.80) (1.07) (2.64) (4.16) (3.08)

.53 .60 .60 .70 .75 .74 .74 .75 .74 .51 Higher Moment Six Factors Model -.45 -.22 -.01 -.39 -.42* -.36 -.16 -.17 -.19 .07 (-1.38) (-.70) (-.04) (-1.57) (-1.76) (-1.50) (-.64) (-.66) (-.67) (.12) .56*** .60*** .59*** .65*** .64*** .66*** .72*** .77*** .75*** .55*** (7.1) (7.9) (6.7) (10.8) (11.2) (11.4) (11.8) (12.1) (11.0) (4.15) -.03 .01 -.06 .00 -.03 -.04 .03 .02 .04 -.09 (-.45) (.13) (-.87) (.05) (-.81) (-1.05) (.66) (.44) (.86) (-.93) .11 .06 .07 .03 .12 .07 -.01 -.06 -.08 .05 (.93) (.49) (.52) (.31) (1.38) (.78) (-.15) (-.59) (-.78) (.24) -.14*** -.08** -.06 -.06* -.04 -.02 -.00 .03 .05 .04 (-3.50) (-2.14) (-1.44) (-1.94) (-1.46) (-.64) (-.00) (1.18) (1.46) (.66) -.27*** -.14* -.17* -.15** -.18*** -.24*** -.15** -.15** -.23*** -.45*** (-3.32) (-1.84) (-1.89) (-2.43) (-3.01) (-4.04) (-2.37) (-2.37) (-3.26) (-3.34) -.11 -.04 -.08 -.03 -.07 -.06 -.04 -.02 .01 -.25** (-1.52) (-.52) (-.94) (-.58) (-1.42) (-1.03) (-.76) (-.39) (.22) (-2.10)

.74 .72 .67 .83 .85 .84 .85 .84 .81 .56

Panel C: Thailand P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Excess -.43 .78 1.15 1.36 1.49 1.62 1.76 1.93 2.21 3.38 Return Capital Asset Pricing Model -.13 -.24* -.18 .05 -.07 -.06 -.06 -.01 .05 .11 (-.88) (-1.72) (-1.32) (.35) (-.50) (-.43) (-.41) (-.08) (.33) (.65) .76*** .91*** .92*** .93*** .91*** .94*** .92*** .92*** .89*** .86*** (38.0) (49.7) (50.6) (50.9) (48.5) (53.2) (50.3) (45.8) (42.3) (37.6) .92 .95 .95 .95 .95 .96 .95 .94 .93 .92 Capital Asset Pricing Model + Higher Moment -.22 -.21** -.19* .00 -.08 -.07 -.12 .00 -.02 .05 (-1.24) (-2.04) (-1.86) (.01) (-.75) (-.65) (-1.03) (.01) (-.16) (.27) .77*** .91*** .91*** .92*** .92*** .93*** .91*** .90*** .89*** .85*** (23.5) (47.4) (48.6) (43.1) (45.1) (47.1) (42.1) (36.5) (32.9) (24.5) -.08 -.07* -.02 .00 .03 .01 -.01 .00 -.03 -.00 (-1.12) (-1.74) (-.45) (.01) (.69) (.18) (-.16) (.07) (-.54) (-.03) .22** .09 .04 .00 -.01 -.01 -.02 -.02 -.01 .03 (2.21) (1.46) (.67) (.05) (-.17) (-.18) (-.32) (-.28) (-.18) (.27)

.92 .98 .98 .98 .98 .98 .97 .97 .96 .93 58

Panel C: Thailand (Continue) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Carhart Four Factors Model .04 -.07 -.07 .15 -.06 -.04 -.06 -.02 .08 .10 (.24) (-.43) (-.46) (.93) (-.36) (-.27) (-.38) (-.10) (.42) (.50) .77*** .91*** .92*** .92*** .90*** .93*** .91*** .90*** .87*** .85*** (37.8) (46.8) (46.7) (46.7) (44.4) (48.8) (46.3) (42.3) (38.9) (34.5) .02* -.00 -.01 -.01 -.01 -.01 -.01 -.02 -.02 -.00 (1.83) (-.12) (-.54) (-.90) (-.72) (-.88) (-.98) (-1.50) (-1.40) (-.23) -.10** -.07* -.04 -.03 .00 .00 .01 .02 .00 -.01 (-2.53) (-1.77) (-.97) (-.80) (.11) (.02) (.25) (.52) (.07) (-.15) -.15*** -.07* -.02 .01 .03 .05 .07* .09** .10** .08* (-3.57) (-1.81) (-.55) (.27) (.82) (1.27) (1.73) (2.06) (2.25) (1.67)

.93 .95 .95 .95 .95 .96 .95 .94 .93 .92 Higher Moment Six Factors Model -.27 -.11 -.09 .13 -.01 -.01 -.09 .04 .05 .13 (-1.44) (-.99) (-.82) (1.02) (-.08) (-.12) (-.69) (.24) (.30) (.66) .82*** .92*** .89*** .91*** .90*** .92*** .89*** .87*** .85*** .80*** (24.4) (44.7) (42.8) (38.7) (40.0) (41.3) (37.2) (32.9) (29.8) (21.8) .07*** .02 -.01 -.00 -.01 -.01 -.02 -.03** -.04** -.05** (3.22) (1.42) (-.59) (-.08) (-1.07) (-.98) (-1.08) (-2.18) (-2.31) (-2.29) -.06 -.10*** -.06 -.10** -.04 -.03 -.01 .02 -.01 -.00 (-1.05) (-2.82) (-1.59) (-2.53) (-1.09) (-.71) (-.26) (.39) (-.10) (-.02) -.30*** -.09** .02 .02 .09** .07 .10** .18*** .21*** .27*** (-4.25) (-2.05) (.55) (.49) (2.04) (1.62) (2.15) (3.36) (3.64) (3.64) -.12* -.08** -.01 .00 .04 .02 .00 .03 -.00 .03 (-1.80) (-2.08) (-.36) (.07) (.96) (.39) (.11) (.52) (-.09) (.45) .17* .07 .04 .01 .01 .00 .00 .01 .03 .08 (1.81) (1.23) (.74) (.15) (.15) (.06) (.02) (.21) (.35) (.82)

.93 .98 .98 .98 .98 .98 .98 .97 .96 .94

CHAPTER 3 SIX-FACTOR MODEL IN EXPLAINING MUTUAL FUND PORTFOLIO RETURN IN DIFFERENT MARKET CONDITIONS

3.1 Introduction

The literature discussing the value of fund management mostly focuses on unconditional return performance and finds that, on average, fund generally underperforms stock-based market benchmarks (Jensen, 1968, Henrikssen, 1984, Grinblatt and Titman, 1989, 1993; Brown et al., 1992; Elton et al., 1992; Malkiel, 1995; Gruber, 1996; Carhart, 1997; Edelen, 1999; Wermers, 2000). Some funds appear to have a degree of selection ability rather than timing ability, but mutual funds collectively underperform the market (Change and Lewellen, 1984). Attempts at predicting which funds will do better than average appear to be no different than picking a mutual fund at random. Nevertheless, still more than $24 trillion were invested in these mutual funds worldwide at the end of 2010. Investors might be willing to pay a premium for assets with payoffs negatively correlated with consumption. As consumption tends to be low in recessions (Rubinstein, 1976; Harrison and Kreps, 1979; Breeden, 1979, 1986; Grossman and Shiller, 1981), investors might accept lower average fund performance if funds perform well in recessionary times when investors care most about performance. Thus, unconditional mutual fund performance measures may understate the value of mutual funds to investors when investor wealth or income is low and when investor marginal utility of wealth is high, such as during recessions. Since consumption is low when marginal utility is high, other things being equal, an asset faring poorly during recessionary times when an investor feels poor and is consuming little is less desirable than an asset faring poorly during expansionary times when an investor feels wealthy and is consuming a lot. This implies that investors are willing to trade average returns for good performance in particular economic states of nature (Kosowski, 2011). If there is no value-added benefit for holding mutual funds, why then are investors around the world still investing in them? 60

Conditional mutual fund performance moves with the business cycle when dividend yield is used to track the business cycle (see Lynch, Wachter and Boudry (2002)). Abnormal performance rises during peaks for growth fund. But for all other fund types, abnormal performance rises during downturns, regardless of which factor model is used. Stock-based mutual fund performance measures are higher in recession periods than in expansion periods (Wermers, 2000). During 1975 to 1994, U.S. mutual funds generated both gross and net returns approximately 6% higher (on an annualized basis) in recessionary periods compared to non-recessionary periods, despite the overall market returns were approximately +1% per month in non-recessionary periods and approximately -1.5% per month in recessionary periods (Moskowitz, 2000). The component of returns attributable to stock selection is 1% higher (on an annualized basis) in recessionary periods compared to non-recessionary periods. Mutual funds appear to generate additional alpha during recessions, even though the returns on the market during recessions are negative. A sample of U.S. mutual funds from 1980 to 2005 showed that funds that performed poorly unconditionally charged higher fees, but these higher fees possibly are justifiable because these funds performed significantly better during recessionary periods compared to non-recessionary periods (Glode, 2011). A multivariate conditional regime-switching performance methodology to examine the performance of U.S. domestic equity mutual funds in recessions and expansions during 1962 to 2005 find that traditional unconditional performance measures understated the value added by mutual fund managers in recessions (Kosowski, 2011). The alphas from single-factor CAPM, three-factor Fama-French (1993) and four-factor Carhart (1997) models during recessionary periods are higher than in expansionary periods using NBER business cycle dates. This chapter uses the four-factor Carhart (1997) model incorporating the higher-moment risk factor CAPM model (coskewness and cokurtosis risk factors), which then becomes a six-factor model. This six-factor model is used to compare fund performance between up and down markets, whether they are significantly different. And whether the difference between fund performance and stock market index performance are significantly different between the two periods (whether equity mutual funds perform better when the market is down than when market is up, and 61 whether equity mutual funds perform better than the stock market index (or beat the market) when the market is performing poorly). This study defines two stages of market conditions in two ways. First, this study uses positive market excess return condition for up market, and negative market excess return for down market, as defined in Pettengill et al. (1995). And second, this study uses regime breakpoints and lets the structural changes be determined by the data using Bai and Perron (1998, 2003) techniques. By using such methods, the performance of systematic higher moments are less sensitive to how bull and bear market states are defined. Traditional unconditional models can attribute abnormal performance to an investment strategy that is based on public information. It is possible to control common variations caused by public information by using instruments for the time- varying expectations. Following Ferson and Schadt (1996), this study applies conditional performance evaluation to ensure that a managed portfolio is not judged as having superior performance by using readily available public information. The task to distinguish between skilled fund managers and lucky ones is the core of investment performance evaluation. Classical statistical analysis addresses the question of whether an estimated performance measure like alpha is significantly different from zero. However, there are a large number of funds which makes time series asymptotic often unreliable. Many funds enter and leave a standard database during any sample period, raising issues of survivorship and selection biases. Fund returns tend to be non-normal and funds are heterogeneous in their volatility, autocorrelation, skewness and kurtosis. Following Kosowski et al. (2006), this study applies a bootstrap statistical technique to examine the performance of equity mutual funds because the cross-section of mutual funds has a complex non-normal distribution due to heterogeneous risk taking by funds and also non-normality in individual fund alpha distributions. The key advantage of the bootstrap method is that the statistic is directly calculated from re-sampling the error terms rather than relying on an assumed population generated from a normal distribution. This chapter studies mutual fund performance in three selected Asian countries—China, Singapore, and Thailand—during 2000 to 2011 to determine whether equity mutual funds perform differently during different economic conditions, i.e. expansionary and recessionary market periods. 62

The remainder of this chapter is organized in four sections: the review of literature in section 2, the data and methodology in section 3, the findings and results in section 4, and conclusion in section 5.

3.2 Review of Literature

The literature on mutual fund performance can be divided into two broad categories—those that use unconditional performance and those that use conditional performance measures. Within both of these categories, funds can be examined for their ability to time the market and their ability to choose mispriced stocks accurately. Unconditional or traditional performance measures do not allow for market or economic conditions in determining whether a fund has performed abnormally well. Conditional performance measures look at the state of the economy in trying to determine whether a fund’s performance is abnormally strong or just in line with the expectations given the state of economy. The prevailing consensus is that unconditionally, mutual funds deliver negative risk-adjusted returns. However, depending on the state of the economy, mutual funds have been found to perform better although still not well enough to justify the fees that investors pay to mutual fund managers. Another recent branch of literature examines whether mutual funds deliver stronger returns when the economy is in recessions, when investors require these funds to perform well and are in fact paying for that skill. There are some drivers that might affect risk-adjusted performance. These drivers can be broadly classified as relating to time-varying underlying stock picking skills and time-varying costs. These costs include transaction costs, implicit liquidity costs, agency costs, and externalities, as well as time variations in risk measures, including the fund portfolio beta and underlying security beta. Corporate managers tend to accumulate and withhold bad news, but reveal good news to investors (Kothari et al., 2005). In expansion periods, when there is mostly good news, corporate managers tend to reveal most relevant news and information is relatively symmetrically distributed in the market. In recession periods, when there is more bad news, corporate managers tend only to partly reveal information, which leads to asymmetric information and higher information uncertainty or variance of 63 information signals. So when the variance of information signals is higher in recession periods, there is higher possibility for fund managers to have different information signals. These information signals are better informed than the average investor, and make them outperform simple passive market benchmarks (Shin, 2003). Or perhaps fund managers have more access to inside information than the public, and thus can manage funds to outperform the market during periods of high volatility. Traditional or unconditional alphas compare returns and risks measured as average over an evaluation period. These averages are taken unconditionally without regard to variations in the state of financial markets or the macro economy. But in the conditional performance evaluation approach, the state of the economy is measured using predetermined, public information variables. A managed portfolio strategy that can be replicated by using readily available public information should not be judged as having superior performance, consistent with a version of semi-strong-form market efficiency as described by Fama (1970). Weak-form efficiency says that past stock prices cannot be used to generate alpha, while semi-strong-form efficiency says that other publicly available variables will not generate alpha. In performance evaluation, if a manager is found to have a positive alpha in a conditional model that controls for public information, the version of the joint hypothesis with semi-strong-form efficiency is rejected. If investors can use the past returns of a fund to earn risk-adjusted abnormal returns, the version with weak-form efficiency is rejected. Traditional unconditional models can attribute abnormal performance to an investment strategy that is based on public information. Using instruments for the time-varying expectations, it is possible to control the common variation caused by public information and reduce this source of bias. Recent studies have documented that the returns and risks of stocks and bonds are predictable over time using dividend yields and interest rates. Fund risk exposures change significantly in response to public information variables such as the levels of interest rates and dividend yields (Ferson and Schadt, 1996). Conditional models are more optimistic in mutual fund performance than unconditional models. The expected return on the market portfolio must be greater than the risk- free rate, according to the traditional wisdom of a positive risk-return trade-off. Prices 64 are established in such a way that riskier assets have higher returns. Otherwise, no investor would hold a positive beta risky. One approach is to differentiate between the up- and down-market risk-premium embedded in the CAPM and develop a conditional CAPM. This is accomplished by separating the full data series into up- and down-market sub-periods and estimating and estimating the coefficients of the model for each sub-period.

One problem that leads to inconsistent estimates of the coefficients is the failure to differentiate between ex-ante expectations and ex-post realizations. The ex- ante relationship between return and risk described by the standard CAPM is usually written as ( ) , ( ) - where ( ) and ( ) are the expected rate of return on asset i and market portfolio at time t, and is the risk-free rate. , ( ) - is the market risk premium, the amount by which the expected return must proportionally rise to compensate investors for bearing higher beta or covariance risk. Most of the empirical tests of the CAPM apply the realized (ex-post) return as a proxy for the unobservable expected (ex-ante) return by

( ) . An obvious problem arises from the fact that the former equation is formulated in terms of return expectations, while in the latter equation is expressed in term of realized return.

One plausible explanation provided by Pettengill et al. (1995) is that the latter equation does not provide a direct indication of the relationship between beta and return, especially when the realized excess market return is negative, and any conclusion from the test of traditional CAPM is based on a biased model aggregating both positive and negative excess market return periods. The direct aggregation ignores the possibility of expectation errors taking place during negative excess market return periods. To deal with the aggregation bias, monthly returns are separated into two groups, the up-market group where and down-market group where , and conditional CAPM is tested leading to significant risk premiums. A study about the risk-return characteristics of the Taiwan stock market finds that the unconditional CAPMs perform poorly regardless of the introduction of coskewness and cokurtosis risks in the model. But when the unconditional four- 65 moment CAPM is extended to a model conditional on up- and down-market conditions, it is found that investors exhibited a preference for a stock whose return distribution has positive skewness and negative kurtosis, particularly over the up- market sub-periods (Chiao et al., 2003).

A structural break appears when an unexpected shift in a time series occurs, which can lead to huge forecasting errors and unreliability of the model in general. Bai and Perron (1998, 2003) introduce multiple structural breaks test which can be automatically detected from data. The NBER indicators are a binary classification and, as a result, fail to capture important phenomena such as economic growth slowdowns (Chauvet and Potter, 2000). Analyses often focus on the ex-post extremes of measured performance, asking if the best managers in a sample are skilled. This question implies a multiple- comparisons analysis and the best managers are expected to deliver a significant alpha at 5% level. Simple approaches to adjust for the number of funds examined based on normality, such as Bonferroni p-value do not account for the correlation across funds, non-normality or heterogeneity. Recent studies have applied bootstrap re-sampling methods to the cross-section of funds in order to address the statistical issues. The bootstrap is a non-parametric approach to statistical inference. The bootstrap allows the researcher to avoid having to make a priori assumptions about the shape of the distribution. By simulating the cross-sectional distribution of performance statistics, it is possible to study whether the estimated alphas of the best funds in a sample are significantly larger than what is expected when the true alphas are zero. Kosowski et al. (2006) concluded that the top 10% of U.S. growth mutual fund alphas reflect skill. But Fama and French (2009) argued that these results are biased by failing to capture uncertainty in the factors. By bootstrapping the factors along with the funds’ residuals, they found little evidence to reject the null hypothesis that the extreme alphas are due to luck. A typical problem in applied statistics involves the estimation of an unknown parameter . The two main questions asked are what estimator should be used, and how accurate is it as an estimator. The bootstrap is a general methodology for answering the latter question. There are reasons to apply a bootstrap procedure to 66 evaluate the performance of equity mutual funds. These include the propensity of individual funds to exhibit non-normally distributed returns, and that the cross-section of funds represent a complex mixture of these individual fund distributions. The non- normality arises for several reasons. Individual stocks within the typical mutual fund portfolio realize returns with non-negligible higher moments. Individual stocks exhibit varying levels of time-series autocorrelations in returns. And funds may implement dynamic strategies that involve changing their levels of risk taking when the risk of the overall market portfolio changes, or in response to their performance ranking relative to similar funds. The bootstrap can improve this approximation (Bickel and Freedman, 1984; Hall, 1986; Kosowski el al., 2006). By recognizing the presence of thick tails in individual fund returns, the bootstrap often rejects abnormal performance for fewer mutual funds.

3.3 Data and Methodology

The database in this chapter consists of monthly total returns of mutual funds, with a focus on equity funds, and total returns of stock market indexes of China, Singapore and Thailand for twelve years between January 2000 and December 2011, obtained from the Bloomberg database. The data of total returns collected includes both active and inactive funds. By collecting both active and inactive fund total returns, the data is free from survivorship bias. Data on the monthly four-factors from the Carhart (1997) model, namely the Market Risk Premium, the SMB (Small Minus Big) factor, the HML (High Minus Low) factor, and the WML (Winner Minus Looser) factor are all created following Fama and French’s (1993) and Carhart’s (1997) methodology as explained in Kenneth

R. French’s website. The predetermined public information variables used are the lagged level of the one-month Treasury bill yield of each country, the lagged dividend yield of the value-weighted stock index of each country, a lagged measure of the slope of the term structure of each country, a lagged quality spread in the corporate bond market of each country. The data are retrieved from the website of the People’s Bank of China, the Monetary Authority of Singapore, the Thai Bond Market Association and the Economic Research and Data of Federal Reserve System. 67

3.3.1 Up- and down-market condition

Following Pettengill et al. (1995) in testing CAPM in cross-sections, the study separates the data set by the market condition into two groups to see the differences between the up and down market. The study uses the four-factor Carhart (1997) plus Coskewness and Cokurtosis risk factor model, which becomes a higher- moment six-factor model, to regress on the excess returns of portfolios of mutual funds. The higher-moment six-factor model equation is:

(3.1)

where is the month t excess return on managed portfolio i,

is the month t excess return on an equal-weighted aggregate market proxy portfolio,

SMBt, HMLt, WMLt, CSKt, and CKTt are the monthly t returns on equal- weighted zero investment factor-mimicking portfolios for size, book-to-market equity, one-year momentum, coskewness and cokurtosis in stock returns respectively. The mutual funds performances are formed in 10 portfolios. Mutual funds are sorted into decile portfolios based on their previous twelve-month’s excess return. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. There are two ways to separate the market condition. First, the positive return market is when the return of the market of that year is positive, and the negative return market is when the return of the market of that year is negative. And second, use breakpoint regression to find the structural changes. The regime breakpoints are estimated by Bai and Perron (1998, 2003) technique. When regime breakpoints are found, data are segregated into groups and analyzed separately to see whether there is any difference between each breaks. If the market condition has influence in the performance of the mutual funds then the result of positive market and negative market should be different. This 68 method will allow all the coefficient of risk factors to vary freely as they may not be the same between different economic conditions. If the alpha in a negative excess market return is higher than the alpha in a positive excess market return period, then the conclusion is that mutual funds perform better in negative excess market return periods than in positive excess market return periods on a risk-adjusted basis. If the alpha in a recessionary period is higher than the alpha in an expansionary period, then the conclusion is that mutual funds perform better in recessionary than in expansionary periods on a risk-adjusted basis.

3.3.2 Conditional performance evaluation

Apply predetermined public information variables into the six-factor model to evaluate the conditional performance evaluation mimicking Ferson and Schadt (1996). The empirical model proposed by Ferson and Schadt (1996) is:

, - (3.2)

where is the return of the fund in excess of a short-term cash instrument, or risk-free rate, ( ) is a vector of the deviations of from the unconditional mean, and is the vector of lagged conditioning variables at time t. The symbol denotes the Kronecker product, an element-by-element multiplication when is a single market index’s total return. When the terms involving are omitted, the equation is Jensen’s alpha. By definition, the Kronecker product, or tensor product, of A and B is defined as the matrix

[ ]

where and From the six-factor model equation:

(3.3)

When apply predetermined public information variables into the six- factor model to evaluate the conditional performance evaluation mimicking Ferson and Schadt (1996), the equation become: 69

, -

(3.4)

The predetermined public information variables used are the lagged level of the one-month Treasury bill yield of each country, the lagged dividend yield of the value-weighted stock index of each country, a lagged measure of the slope of the term structure of each country, and a lagged quality spread in the corporate bond market of each country.

3.3.3 Bootstrap evaluation of fund alphas

To prepare for the bootstrap procedure, this study uses Carhart (1997) plus the coskewness and cokurtosis risk-factors model to compute ordinary least square (OLS) estimated alphas, factor loading, and residuals using the time series of monthly net returns for fund i (rit). For each fund i, the coefficient estimates, ̂ ̂ ̂ ̂ ̂ ̂ { ̂ }, and the time series of estimated residuals,

* ̂ +, and the t-statistic of alpha, ̂ , are saved, where and are the dates of the first and last monthly returns available for fund i respectively. Using a baseline bootstrap, for each fund i, a sample is drawn with replacement from the fund residuals that are saved in the step above, creating a pseudo time series of re-sampled residuals, , where b is an * ̂ + index for the bootstrap number (b = 1 for bootstrap resample number 1), and where each of the time indices are drawn randomly from in way that , - reorders the original sample of residuals for fund i. Next is to construct a time series of pseudo-monthly excess returns for this fund, imposing the null hypothesis of zero true performance ( , or equivalently,

̂ ): ̂ ̂ ̂ ̂

̂ ̂ (3.5) ̂ for and .

This sequence of artificial returns has a true alpha (and t-statistic of alpha) that is zero by construction. Then the above steps are repeated across all funds i=1,…,N to arrive at a draw from the cross-section of bootstrapped alphas. Repeating this for all bootstrap iterations b=1,…,1000 and then building the distribution of these cross-sectional draws of alphas ̂ or their t-statistics ̂ that ̂ result purely from sampling variation while imposing the null of a true alpha that is equal to zero. The distribution of alphas (or t-statistics) for the funds are constructed as the distribution of the maximum alphas (or maximum t-statistics) is generated across all bootstraps. If bootstrap iterations generate far fewer extreme positive values of ̂ (or ̂ ) compared to those observed in the actual data, then the conclusion is that the sampling variation is not the sole source of high alphas.

3.4 Findings and Results

3.4.1 Measure of Mutual Funds performance by different market conditions

Table 3.1 presents summary statistics of mutual funds by positive and negative excess market return during January 2000 to December 2011. For China, the period of positive excess market return is 59 months while the negative period is longer at 81 months. During the positive excess market return period, the mutual funds provide 4.7% total return per month on average while the market provide 5.5%. But in the negative excess market return period, the mutual funds provide -1.6% total return per month on average while the market provides -2.2%, which is better than the market. For Singapore, the period of positive excess market return is 84 months while the negative period is shorter at 60 months. During the positive excess market return period, the mutual funds provide 1.6% total return per month on average while the market provides 2.0%. In the negative excess market return period, the mutual funds provide -2.1% of total return per month on average while the market provides - 71

1.9%. So, in Singapore, the market total return is better than the average of mutual funds in both positive and negative excess market return periods. For Thailand, the period of positive excess market return is 108 months while the negative period is shorter at 36 months. During the positive excess market return period, the mutual funds provide 2.2% total return per month on average while the market provide 2.7%. But in the negative excess market return period, the mutual funds provide -2.2% total return per month on average while the market provides - 2.7%, which is better than the market. So, mutual funds in China and Thailand provide better total return than market in negative excess market return period but provide worse total return than market in positive excess market return period. The differences of the total return between positive and negative excess market return period are significant at 1% level for both of market and mutual funds for all three countries. The average of standard deviation of the total return of mutual funds is less than the market on both during positive and negative excess market return period in China. The average of standard deviation of the total return of mutual funds is less than the market during negative excess market return period in Singapore, and more than the market during positive excess market return period. In Thailand, the average of standard deviation of the total return of mutual funds is less than the market during positive excess market return period and not much different in negative excess market return period. Sharpe Ratio between the total return of mutual funds and market are not much different in China both during the positive and negative excess market return. In Thailand, the Sharpe Ratio is not much different only in positive excess market return period but better in negative excess market return period. But in Singapore, the Sharpe Ratios of market are better than the mutual funds for both periods. The skewness of total return of mutual funds is negatively high in the positive excess market return period while there is a little negative skewness for total return of market in China. But the skewness of total return of mutual funds and market are both close to zero in the negative excess market return period. In Singapore, the skewness is positive for both mutual funds and market during the positive excess market return while the signal of the skewness is stronger for the 72 market. In the negative excess market return, the skewness is both negative and the strength is very close to each other. In Thailand, the skewness is positive, but close to zero, in positive excess market return period and negative in negative excess market return period, and the signal strength are not much different between the mutual funds average and the market. For Singapore and Thailand, the skewness is positive, but not much, when in positive excess market return period and negative when in negative excess market return period. But this is opposite in China where the skewness is more negative in positive excess market return period, especially for the mutual funds. The differences of the skewness of mutual funds between positive and negative excess market return period are significant at 1% level for all three countries. The kurtosis of total return of mutual funds is high in the positive excess market return period while the kurtosis of total return of market is low in China. On the contrary, the kurtosis of mutual funds is lower than the market in negative excess market return period. The kurtosis in positive excess market return period is higher than in negative period for both mutual funds and market. For Singapore, the kurtosis of the market is higher than the mutual funds for both periods and much higher in the positive excess market return period. For Thailand, the kurtosis of the total return of mutual funds and market are not much different both in positive and negative excess market return periods, even the market is a bit higher. The differences of the cokurtosis of mutual funds between positive and negative excess market return period are significant at 1% level for all three countries. [Table 3.1 is here] Table 3.2 shows measures of mutual fund performance using higher moment six-factor model comparing positive and negative return market. The data are split into two market conditions: positive return market, in the year that the average return of the market is positive; and negative return market, in the year that the average return of the market is negative. Mutual funds are sorted into decile portfolios based on their previous twelve-month’s excess return. Funds with the lowest past one- year excess return comprise decile 1 and fund with the highest comprise decile 10. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. By analyzing the data separately in two 73 groups, the coefficients of all risk factors are free from each other and should be more accurate than using dummy variable and share the coefficients. The result shows that the alpha is significantly different from zero in the positive excess market return period for half of the portfolios in China, while there is no any portfolios shows significant alpha in the negative excess market period. SMB and HML risk factors work better in negative excess market period, while WML and CSK risk factors work better in positive excess market period. CKT risk factors show no significant at all portfolio for both positive and negative excess market periods in China. The adjusted r squares in positive excess market period are between .77 - .92 while the adjusted r squares is higher in negative excess market period at .81 – 94. In Singapore, there is no significant alpha in positive excess return market while there are two portfolios show significant alpha. SMB and HML risk factors work better in negative excess market period, while CSK risk factors work better in positive excess market period. CKT risk factor shows significant for five portfolios during negative excess market period and one portfolio in positive excess market period. The adjusted r squares in positive excess market period are between .43 - .80 while the adjusted r squares is much higher in negative excess market period at .80 – 93. In Thailand, there is no significant alpha in both positive and negative excess return market periods. SMB, HML, and WML risk factors are not significant at all in negative excess market period, but work about half of all portfolios in positive excess market period. CSK risk factor is significant at one portfolio in negative excess market return period. The adjusted r squares in positive excess market period are between .89 - .98 while the adjusted r squares are much higher in negative excess return market period at .95 – .99 due to the significance of the market risk factors are very strong. The result in table 2 shows that the higher moment six factor model can fit the data in negative excess return market better than positive excess return market. But unlike Kosowski (2011), it could not be concluded that the mutual fund perform better in negative excess return market than positive excess return market on a risk adjusted basis. In Singapore and Thailand, the alphas of almost all portfolios are not 74 significant different from zero for both market conditions. Only in China, that alphas are positive and significant different from zero. [Table 3.2 is here] The excess returns of China, Singapore and Thailand are tested by Bai and Perron (1998, 2003) technique to see the breaks which create different regimes. The result shows that there are 3 regimes in China, but none for Singapore and Thailand. Table 3.3 shows measures of mutual fund performance using higher moment six-factor model comparing between the three periods. Period 1 is between Year 2000 Month 7 to Year 2005 Month 11, Period 2 is between Year 2005 Month 12 to Year 2007 Month 9, and Period 3 is between Year 2007 Month 10 to Year 2011 Month 12. The excess market return of periods 1 and 3 are negative while the excess market return of period 2 is positive. The result show that the adjusted r squares in positive excess market period (Period 2) are between .52 - .84, while the adjusted r squares are higher in negative excess market period at .65 – 96 in period 1 and .88 - .96 in period 3. All the risk factors, except the market risk factor, are not significant at all in period 2, while all risk factors, including higher moment risk factors, show significance on some portfolios in both period 1 and 3. And only one to two portfolios show significant alpha for all three periods. This confirms that the six-factor model works better in negative excess market period, more significance risk factors and portfolios, and more explanation power. [Table 3.3 is here]

3.4.2 Measure of Mutual Funds performance by conditional model and bootstrap technique

Table 3.4 shows measures of performance using conditional and unconditional six-factor model. The predetermined public information variables used are the lagged level of the one-month Treasury bill yield, the lagged dividend yield of the value-weighted stock index, a lagged measure of the slope of the term structure, and a lagged quality spread in the corporate bond market. 75

The result shows that the alphas of the unconditional and conditional models are not different in China. The adjusted r squares of both models are not different. In Singapore, there is only one portfolio that show significant alpha for unconditional model and no portfolio show significant alpha for conditional model. In Thailand, there is no significant alpha on any portfolio for both models. The adjusted r squares are not different in all three countries. Also most of the predetermined public information variables are not significant for all three countries. It means that the predetermined public information variables do not help explain the equity mutual fund return in these countries. [Table 3.4 is here] Table 3.5 shows measures of performance using unconditional six-factor model and bootstrap technique. The result shows that, in China, when Bootstrap technique is used, all the significant alphas become insignificant. Most of all portfolios in Singapore and Thailand show insignificant alphas, and the adjusted r squares are much lower. There is almost no significant alpha portfolio when using six- factor model with bootstrap techniques. This mean many of the significance alphas that are shown in least square method are from sampling variability. [Table 3.5 is here]

3.5 Conclusion

The study of mutual fund performance in three countries i.e. China, Singapore, and Thailand for 12 years during year 2000-2011 using higher moment six-factor model shows some empirical evidence for the difference in the performance of mutual funds between the positive excess market return period and negative excess market return period. The higher moment six factor model fits better and shows more explanation power in negative excess return market period, both by using Pettengill et al. (1995), and Bai and Perron (1998, 2003) methodology. The predetermined public information variables used in conditional model are not significant at all and the explanation powers are the same for all countries. The predetermined public information variables do not help explain the equity mutual fund return in these countries. 76

The bootstrap technique shows that many of the significance alphas that are shown in least square method are from sampling variability because when bootstrap technique is applied, almost all significant alphas become insignificant. However, if the sample size of the data set is larger and the time frame is longer, the result should be clearer and more reliable.

Table 3.1 Summary Statistics of Mutual Funds by Positive and Negative Excess Market Return

This table reports summary statistics for all mutual funds categorized by country: China, Singapore, and Thailand during January 2000 to December 2011. For each category, mean total excess return (%), standard deviation (%), Sharpe ratio, mean skewness, mean kurtosis, and total number of sample size (fund*month) in each category for all periods, positive excess market return and negative excess market return are reported.

Panel A: China Mutual Fund Market Mean All Periods -0.193 1.071 Excess Positive 4.743 5.521 Return Negative -1.641 -2.171 % t-test between positive and negative 39.3*** 5.12*** Standard All Periods 7.153 9.319 Deviation Positive 8.400 9.419 Negative 6.330 7.831 Sharpe Ratio All Periods 0.056 0.068 Positive 0.659 0.655 Negative -0.289 -0.267 Skewness All Periods -0.050 0.146 Positive -1.176 -0.234 Negative -0.025 0.100 t-test between positive and negative -14.9*** Kurtosis All Periods 0.452 0.405 Positive 3.406 0.987 Negative 0.199 0.712 t-test between positive and negative -14.6*** Sample Size Positive 424 59 (Fund*Month) Negative 894 81

Panel B: Singapore Mutual Fund Market Mean All Periods 0.275 0.386 Excess Positive 1.587 2.034 Return Negative -2.128 -1.921 % t-test between positive and negative 26.1*** 3.68*** Standard All Periods 6.120 6.299 Deviation Positive 5.161 5.049 Negative 6.704 7.143 Sharpe Ratio All Periods 0.099 0.143 Positive 0.397 0.428 Negative -0.318 -0.255 Skewness All Periods -0.312 -0.140 Positive 0.366 1.647 Negative -0.527 -0.547 t-test between positive and negative 8.03*** Kurtosis All Periods 3.418 3.405 Positive 2.495 6.811 Negative 0.598 0.787 t-test between positive and negative 2.60*** Sample Size Positive 790 84 (Fund*Month) Negative 444 60

Panel C: Thailand Mutual Fund Market Mean All Periods 1.178 1.370 Excess Positive 2.171 2.721 Return % Negative -2.202 -2.682 t-test between positive and negative 35.2*** 3.29*** Standard All Periods 6.849 7.695 Deviation Positive 5.956 6.700 Negative 9.133 9.065 Sharpe Ratio All Periods 0.275 0.257 Positive 0.423 0.440 Negative -0.169 -0.292 Skewness All Periods -0.482 -0.520 Positive 0.102 0.137 Negative -0.671 -0.817 t-test between positive and negative 14.2*** Kurtosis All Periods 2.301 1.990 Positive 0.553 0.727 Negative 1.423 1.532 t-test between positive and negative -4.99*** Sample Size Positive 1326 108 (Fund*Month) Negative 386 36

Table 3.2 Measures of Mutual Fund Performance using higher moment (with Coskewness and Cokurtosis Risk Factors) six-factor model comparing positive and negative return

This table shows the estimate of the different asset pricing models for equity mutual funds. Mutual funds are sorted into decile portfolios based on their previous 12- month’s excess return. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. The data are split into two market conditions: positive return market, in the year that the average return of the market is positive; and negative return market, in the year that the average return of the market is negative. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Higher Moment Six Factors Model in positive return market .99* 1.18** 1.61*** 1.14* .93 1.02 1.54** .92 1.01 1.77 (1.73) (2.09) (2.75) (1.75) (1.38) (1.51) (1.86) (1.48) (1.29) (1.64) .54*** .68*** .70*** .75*** .72*** .76*** .70*** .72*** .78*** .71*** (12.4) (15.9) (15.8) (15.3) (14.2) (15.0) (11.2) (15.4) (13.1) (8.7) -.05 -.08 -.13* -.08 -.13* .00 -.07 -.06 -.00 -.04 (-.79) (-1.25) (-1.97) (-1.19) (-1.74) (.05) (-.81) (-.95) (-.04) (-.35) -.04 -.22* -.26** -.21 -.20 -.14 -.18 -.07 -.17 -.16 (-.33) (-1.89) (-2.15) (-1.54) (-1.45) (-1.02) (-1.07) (-.53) (-1.08) (-.72) -.07 .08 .17 .21 .26* .36** .40** .21* .26* .48** (-.59) (.76) (1.45) (1.60) (1.99) (2.70) (2.47) (1.76) (1.70) (2.25) .09 .15* .16* .14 .27** .14 .21 .10 .07 .16 (.98) (1.77) (1.83) (1.43) (2.60) (1.32) (1.61) (1.02) (.60) (.96) .09 .05 -.04 -.01 -.04 .04 .00 -.08 -.07 -.09 (1.22) (.66) (-.58) (-.15) (-.46) (.43) (.00) (-1.11) (-.74) (-.66)

.86 .91 .92 .91 .90 .91 .85 .91 .88 .77

Panel A: China (Continue) Higher Moment Six Factors Model in negative return market -.16 -.27 -.22 -.01 .02 .04 .23 .10 .19 -.07 (-.45) (-.79) (-.68) (-.02) (.05) (.13) (.62) (.29) (.52) (-.16) .79*** .74*** .77*** .77*** .74*** .75*** .69*** .71*** .70*** .60*** (21.2) (20.3) (22.5) (23.8) (19.6) (20.9) (17.1) (19.0) (17.7) (13.3) .10 .13 .17** .18** .19** .21*** .14 .18** .15* .22** (1.27) (1.62) (2.36) (2.65) (2.43) (2.74) (1.58) (2.22) (1.73) (2.29) .02 -.17 -.23* -.12 -.19 -.28** -.32** -.24* -.37** -.05 (.12) (-1.34) (-1.87) (-1.07) (-1.40) (-2.17) (-2.19) (-1.84) (-2.65) (-.30) -.02 -.10 -.01 .15 .11 .23* .02 .15 .21 .40*** (-.15) (-.85) (-.17) (1.40) (.90) (2.01) (.18) (1.24) (1.68) (2.77) -.05 -.22* -.12 -.17 -.17 -.10 -.19 -.16 -.07 -.04 (-.36) (-1.72) (-1.01) (-1.50) (-1.29) (-.77) (-1.35) (-1.22) (-.50) (-.23) -.04 -.08 .04 -.01 -.00 .01 .01 .04 .05 -.04 (-.56) (-1.00) (.63) (-.11) (-.00) (.15) (.09) (.56) (.58) (-.44)

.92 .92 .93 .94 .91 .91 .88 .90 .88 .81

Panel B: Singapore P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Higher Moment Six Factors Model in positive return market -.32 .04 .25 -.40 -.31 -.25 -.09 .02 .05 .22 (-.74) (.09) (.70) (-1.38) (-1.08) (-.92) (-.32) (.05) (.19) (.29) .50*** .48*** .46*** .61*** .61*** .71*** .78*** .85*** .83*** .56*** (4.5) (4.7) (3.7) (8.1) (8.4) (10.3) (10.2) (10.7) (11.3) (2.9) -.07 -.06 -.13 -.05 -.06 -.03 .02 .01 .02 -.22* (-.99) (-.85) (-1.57) (-1.01) (-1.28) (-.72) (.33) (.20) (.45) (-1.75) .17 .19 .25 .21* .28** .18* .10 .07 .12 .42 (1.03) (1.30) (1.35) (1.88) (2.61) (1.82) (.90) (.59) (1.11) (1.52) -.11*** -.04 -.03 -.03 -.01 .01 .02 .04 .07** .03 (-2.71) (-1.09) (-.64) (-1.15) (-.54) (.24) (.62) (1.43) (2.46) (.42) -.26** -.04 -.07 -.07 -.06 -.13** -.08 -.08 -.11 -.43** (-2.50) (-.46) (-.65) (-1.01) (-.94) (-2.09) (-1.10) (-1.17) (-1.62) (-2.44) -.14 -.06 -.09 .00 -.01 .08 .07 .10 .17** -.25 (-1.41) (-.60) (-.82) (.02) (-.15) (1.26) (.93) (1.37) (2.46) (-1.45)

.61 .56 .46 .76 .77 .79 .80 .80 .80 .43

Panel B: Singapore (Continue) Higher Moment Six Factors Model in negative return market -.56 -.14 -.08 -.08 -.25 -.33 -.33 -.91** -.84 -1.24* (-.93) (-.27) (-.17) (-.18) (-.63) (-.78) (-.76) (-2.25) (-1.61) (-1.85) .53*** .61*** .70*** .67*** .64*** .59*** .60*** .66*** .59*** .41** (3.3) (4.3) (5.9) (5.9) (6.1) (5.1) (5.1) (6.1) (4.2) (2.3) .22 .29** .23** .25** .13 .10 .27** .24** .33*** .31** (1.68) (2.59) (2.42) (2.69) (1.59) (1.04) (2.83) (2.77) (2.96) (2.16) -.26 -.24 -.34 -.39* -.22 -.44** -.44* -.50** -.78*** -1.04*** (-.93) (-.95) (-1.61) (-1.91) (-1.17) (-2.16) (-2.10) (-2.62) (-3.14) (-3.26) -.36** -.29* -.15 -.16 -.11 -.12 -.12 .01 -.08 -.08 (-2.12) (-1.93) (-1.21) (-1.26) (-1.00) (-1.00) (-.96) (.95) (-.57) (-.44) -.15 -.17 .08 .05 -.06 .03 .07 .17 .10 .06 (-.58) (-.78) (.43) (.27) (-.38) (.15) (.37) (.99) (.47) (.22) -.06 -.02 -.07 -.09 -.16** -.20** -.17** -.17* -.15 -.24* (-.55) (-.23) (-.88) (-1.20) (-2.31) (-2.67) (-2.24) (-2.36) (-1.67) (-1.98)

.84 .88 .91 .92 .93 .92 .91 .92 .88 .80

Panel C: Thailand P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Higher Moment Six Factors Model in positive return market -.16 -.19 -.19 -.02 -.11 -.11 -.14 -.03 -.00 .14 (-.81) (-1.62) (-1.53) (-.11) (-.87) (-.82) (-.96) (-.24) (-.01) (.61) .74*** .92*** .93*** .96*** .95*** .96*** .93*** .93*** .89*** .82*** (14.9) (31.3) (29.8) (27.2) (28.8) (28.9) (25.4) (25.2) (21.3) (14.6) .06*** .01 -.00 .00 -.01 -.01 -.01 -.03* -.04** -.05** (2.77) (1.15) (-.53) (.32) (-.68) (-.72) (-.75) (-1.91) (-2.11) (-2.15) -.11* -.10*** -.06* -.13*** -.07* -.04 -.02 .00 -.02 -.02 (-1.88) (-2.86) (-1.76) (-3.10) (-1.72) (-1.12) (-.49) (.02) (-.43) (-.23) -.26*** -.06 .03 .00 .07 .06 .08 .15*** .19*** .25*** (-3.79) (-1.41) (.71) (.06) (1.54) (1.21) (1.65) (2.95) (3.36) (3.22) -.04 -.05 -.01 -.05 -.02 -.04 -.04 -.04 -.05 -.00 (-.54) (-1.13) (-.23) (-.88) (-.33) (-.76) (-.76) (-.65) (-.72) (-.02) .14 .09 .06 -.01 -.01 -.01 -.01 -.01 .01 .03 (1.51) (1.64) (.99) (-.16) (-.15) (-.19) (-.17) (-.16) (.18) (.33)

.89 .98 .97 .97 .97 .97 .96 .97 .95 .91

Panel C: Thailand (Continue) Higher Moment Six Factors Model in negative return market -.04 .53 -.39 -.32 -.66 -.32 -.75 -.91 -1.01 -.75 (-.04) (.86) (-.97) (-.75) (-.92) (-.42) (-.91) (-.79) (-.91) (-.64) .93*** .95*** .88*** .85*** .85*** .91*** .85*** .81*** .79*** .76*** (11.7) (17.5) (24.6) (23.2) (13.4) (13.8) (11.7) (8.1) (8.1) (7.5) .14 .05 -.06 -.09 -.08 .03 -.06 -.12 -.15 -.08 (.85) (.46) (-.87) (-1.17) (-.64) (.26) (-.41) (-.57) (-.77) (-.39) .17 -.25 .11 .27 .35 .10 .25 .42 .47 .30 (.48) (-1.01) (.70) (1.59) (1.20) (.34) (.74) (.91) (1.06) (.65) -.45 -.40 -.09 -.09 -.01 .02 .12 .20 .09 .28 (-1.06) (-1.40) (-.45) (-.48) (-.03) (.07) (.31) (.38) (.18) (.52) .00 -.23 -.24* -.04 .08 .07 .04 .06 .01 .06 (.01) (-1.56) (-2.53) (-.38) (.50) (.39) (.22) (.22) (.03) (.21) .31 .08 .07 .41 .31 .13 .15 .33 .29 .54 (.68) (.27) (.37) (1.93) (.85) (.35) (.36) (.56) (.53) (.92)

.98 .99 .99 .99 .99 .98 .98 .96 .96 .95

Table 3.3 Measures of Mutual Fund Performance using higher moment (with Coskewness and Cokurtosis Risk Factors) six-factor model comparing different excess market return periods of China

This table shows the estimates of the different asset pricing models for equity mutual funds of China for 3 periods during January 2000 to December 2011. Period 1 is between Year 2000 Month 7 to Year 2005 Month 11, Period 2 is between Year 2005 Month 12 to Year 2007 Month 9, and Period 3 is between Year 2007 Month 10 to Year 2011 Month 12. These breaks are from breakpoint regression using Bai and Perron (1998, 2003) technique. Mutual funds are sorted into decile portfolios based on their previous 12-months excess return. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. The data are split into 3 market periods based on the excess market return. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: Period 1: between Year 2000 Month 7 to Year 2005 Month 11 (Average excess market return is -.96, Std.Dev. is 5.8) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Excess -.98 -.90 -.87 -.61 -.04 -.21 -.06 -.72 .25 -.39 Return Std.dev. 4.17 5.17 4.12 4.10 3.76 4.16 3.20 3.49 4.35 4.18 Higher Moment Six Factors Model -.23 -.71 -.52 .15 .37 .69 .67 .11 1.14** -.47 (-.58) (-2.15) (1.02) (.31) (.53) (1.14) (1.09) (.17) (3.22) (-.96) .62*** .64*** .57*** .61*** .56** .75*** .37** .57*** .67*** .51*** (8.2) (10.3) (5.9) (6.9) (4.2) (6.6) (3.2) (4.7) (10.1) (5.6) .26** .13 .18 .15 .19 .22 .12 .13 .15 .30* (2.75) (1.62) (1.49) (1.37) (1.17) (1.52) (.87) (.87) (1.78) (2.67) .52* .55* .84* .75* .69 .49 .37 .36 .37 1.09** (2.15) (2.72) (2.69) (2.63) (1.61) (1.32) (1.00) (.91) (1.72) (3.68) .71** .88*** .87** .85** 1.08* 1.36** .42 .83* 1.28*** 1.17** (3.09) (4.60) (2.97) (3.18) (2.68) (3.93) (1.21) (2.27) (6.36) (4.21) 2.12*** 2.07*** 2.38** 1.50** 1.95* 2.12** 1.04 1.37 1.79** 1.66** (4.60) (5.41) (4.03) (2.79) (2.41) (3.06) (1.48) (1.85) (4.42) (2.97) 1.58** 1.10** 1.55** .81 .99 .90 .74 .68 .59 .80 (4.51) (3.77) (3.46) (1.99) (1.62) (1.71) (1.39) (1.22) (1.93) (1.88)

.95 .96 .90 .91 .77 .88 .65 .79 .95 .90

Panel B: Period 2: between Year 2005 Month 12 to Year 2007 Month 9 (Average excess market return is 9.4, Std.Dev. is 9.7) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Excess 6.37 7.38 8.12 8.25 7.67 7.91 8.16 8.13 8.25 8.19 Return Std.dev. 5.28 6.87 7.05 8.02 7.59 8.53 7.74 7.58 7.92 8.28 Higher Moment Six Factors Model 1.23 1.85 2.07 .96 1.71 1.52 3.26* 1.11 2.90 1.93 (1.39) (1.59) (1.70) (.72) (1.18) (1.07) (1.82) (.87) (1.73) (.80) .49*** .65*** .68*** .79*** .67*** .79*** .63*** .74*** .74*** .66*** (8.2) (8.3) (8.2) (8.8) (6.8) (8.1) (5.2) (8.6) (6.5) (4.0) -.08 -.04 -.10 -.05 -.09 .09 .00 -.06 .12 -.03 (-1.05) (-.37) (-.97) (-.48) (-.77) (.74) (.02) (-.53) (.85) (-.13) .15 -.30 -.25 -.15 -.28 -.33 -.40 -.06 -.57 -.02 (.81) (-1.19) (-.97) (-.53) (-.91) (-1.07) (-1.03) (-.23) (-1.57) (-.03) .08 .07 .13 .22 .32 .38 .36 .05 .02 .60 (.52) (.36) (.61) (.94) (1.21) (1.48) (1.12) (.23) (.06) (1.38) -.00 .14 .08 -.01 .34 .17 .28 .01 .14 .03 (-.05) (.88) (.48) (-.07) (1.75) (.88) (1.18) (.08) (.64) (.08) -.11 .08 -.11 -.22 .06 .12 .21 -.10 .26 -.32 (-.61) (.35) (-.46) (-.86) (.22) (.42) (.61) (-.41) (.79) (-.67)

.84 .84 .83 .84 .79 .84 .70 .84 .74 .52

Panel C: Period 3: between Year 2007 Month 10 to Year 2011 Month 12 (Average excess market return is -1.1, Std.Dev. is 10.6) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Excess -.90 -.90 -.96 -1.10 -1.00 -1.03 -1.04 -.98 -1.08 -.62 Return Std.dev. 7.94 8.07 8.15 8.13 8.02 7.85 7.85 7.62 7.84 7.42 Higher Moment Six Factors Model -.87** -.35 -.13 -.19 -.05 .04 .09 .16 .34 .79* (-2.18) (-1.00) (2.42) (-.63) (-.15) (.13) (.25) (.48) (.99) (1.69) .73*** .76*** .78*** .78*** .77*** .75*** .75*** .73*** .74*** .68*** (21.9) (26.1) (30.4) (30.4) (27.3) (26.8) (24.5) (25.5) (25.8) (17.5) .15 .17** .15** .14** .15** .13* .14 .17** .08 .03 (1.63) (2.12) (2.10) (2.04) (2.02) (1.76) (1.66) (2.17) (1.00) (.29) .12 -.03 -.08 -.10 -.12 -.19 -.18 -.10 -.26* -.22 (.76) (-.18) (-.67) (-.78) (-.85) (-1.41) (-1.20) (-.72) (-1.84) (-1.16) -.20* -.07 .04 .12 .10 .18* .21** .23** .27*** .42*** (-1.77) (-.74) (.49) (1.34) (1.04) (1.90) (2.05) (2.39) (2.80) (3.19) -.04 -.17 -.16 -.11 -.17 -.11 -.13 -.21* -.12 .09 (-.36) (-1.54) (-1.64) (-1.18) (-1.60) (-1.01) (-1.13) (-1.99) (-1.13) (.60) -.03 -.00 .06 .06 .03 .05 .09 .07 .11* .02 (-.33) (-.03) (1.06) (1.00) (.39) (.82) (1.22) (1.11) (1.75) (.23)

.92 .94 .96 .96 .95 .94 .93 .94 .94 .88

Table 3.4 Measures of Performance using Conditional and Unconditional Six-Factor Model

This table shows the estimates of the different asset pricing models for equity mutual funds. The unconditional and conditional equations are:

(3.4)

, -

(3.5)

Where ( ) is a vector of the deviations of from the unconditional mean, and is the vector of lagged conditioning variables. The symbol denotes the Kronecker product, element-by-element multiplication when is a single market index’s total return. The predetermined public information variables used are the lagged level of the one-month Treasury bill yield, the lagged dividend yield of the value-weighted stock index, a lagged measure of the slope of the term structure, and a lagged quality spread in the corporate bond market. Mutual funds are sorted into decile portfolios based on their previous 12-months excess return. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China Unconditional model (3.4) Conditional model (3.5)

 t() t(  Rsq  t() t( ) Rsq P1 -.27 -.94 .67*** 25.4 .91 -.27 -.95 .68*** 24.5 .92 P2 .20 .76 .75*** 30.4 .93 .13 .48 .77*** 29.2 .93 P3 .56** 2.07 .77*** 30.4 .93 .49* 1.76 .78*** 28.1 .93 P4 .63** 2.32 .79*** 31.3 .94 .57** 2.12 .81*** 30.4 .94 P5 .59** 1.99 .75*** 27.1 .92 .56* 1.79 .76*** 24.6 .91 P6 .60** 2.10 .79*** 29.6 .93 .52* 1.80 .81*** 28.2 .93 P7 .85** 2.48 .74*** 23.1 .89 .79** 2.23 .76*** 21.4 .89 P8 .69** 2.42 .74*** 27.8 .92 .64** 2.21 .76*** 26.3 .92 P9 .87*** 2.67 .76*** 25.2 .90 .76** 2.25 .79*** 23.5 .90 P10 1.16*** 2.75 .70*** 17.8 .83 1.13*** 2.68 .74*** 17.6 .84

Panel B: Singapore Unconditional model (3.4) Conditional model (3.5)

 t() t( ) Rsq  t() t( ) Rsq P1 -.45 -1.38 .56*** 7.1 .74 -.35 -1.05 .29* 1.89 .76 P2 -.22 -.70 .60*** 7.9 .72 -.09 -.26 .44*** 2.82 .72 P3 -.01 .04 .59*** 6.7 .67 .12 .30 .53*** 2.89 .66 P4 -.39 -1.57 .65*** 10.8 .83 -.32 -1.20 .60*** 4.80 .82 P5 -.42* -1.76 .64*** 11.2 .85 -.28 -1.10 .65*** 5.45 .84 P6 -.36 -1.50 .66*** 11.4 .84 -.21 -.81 .66*** 5.53 .84 P7 -.16 -.64 .72*** 11.8 .85 -.04 -.15 .80*** 6.36 .84 P8 -.17 -.66 .77*** 12.1 .84 -.13 -.46 .86*** 6.62 .84 P9 -.19 -.67 .75*** 11.0 .81 -.03 -.11 1.02*** 7.45 .81 P10 .07 .12 .55*** 4.1 .56 -.01 -.02 .94*** 3.45 .56

Panel C: Thailand Unconditional model (3.4) Conditional model (3.5)

 t() t( ) Rsq  t() t( ) Rsq P1 -.27 -1.44 .82*** 24.4 .93 -.10 -.53 .73*** 15.7 .94 P2 -.11 -.99 .92*** 44.7 .98 -.12 -1.09 .84*** 30.5 .98 P3 -.09 -.82 .89*** 42.8 .98 -.12 -.98 .91*** 29.4 .98 P4 .13 1.02 .91*** 38.7 .98 .08 .59 .97*** 29.4 .98 P5 -.01 -.08 .90*** 40.0 .98 -.07 -.63 .98*** 33.2 .98 P6 -.01 -.12 .92*** 41.3 .98 -.05 -.47 1.02*** 33.6 .98 P7 -.09 -.69 .89*** 37.2 .98 -.14 -1.19 1.01*** 35.5 .98 P8 .04 .24 .87*** 32.9 .97 -.01 -.10 1.02*** 33.9 .98 P9 .05 .30 .85*** 29.8 .96 -.05 -.38 1.01*** 31.7 .98 P10 .13 .66 .80*** 21.8 .94 -.01 -.05 .99*** 21.9 .95

Table 3.5 Measures of Performance using Unconditional Six-Factor Model and Bootstrap

This table shows the estimates of the different asset pricing models for equity mutual funds using Unconditional Six-Factor Model and Bootstrap (1,000 iterations). Mutual funds are sorted into decile portfolios based on their previous 12-months excess return. Funds with the lowest past one-year excess return comprise decile 1 and fund with the highest comprise decile 10. The portfolios are reformed and equally weighted monthly so the weights are readjusted whenever a fund disappears. The t-statistics are in parentheses. * indicates statistical significance at 10% level. ** indicates statistical significance at 5% level. *** indicates statistical significance at 1% level.

Panel A: China Least Square Bootstrap

 t() p-value Rsq  t() p-value Rsq P1 -.27 -.94 .35 .91 -.30 -.89 .37 .70 P2 .20 .76 .45 .93 .26 .62 .54 .73 P3 .56** 2.07 .04 .93 .28 .58 .56 .72 P4 .63** 2.32 .02 .94 .53 1.29 .20 .73 P5 .59** 1.99 .05 .92 .72 1.62 .11 .70 P6 .60** 2.10 .04 .93 .34 1.01 .31 .74 P7 .85** 2.48 .02 .89 .37 .87 .39 .68 P8 .69** 2.42 .02 .92 .11 .24 .81 .70 P9 .87*** 2.67 <.01 .90 .56 1.24 .22 .68 P10 1.16*** 2.75 <.01 .83 .68 1.52 .13 .63

Panel B: Singapore Least Square Bootstrap

 t() p-value Rsq  t() p-value Rsq P1 -.45 -1.38 .17 .74 -.38 -.82 .41 .42 P2 -.22 -.70 .49 .72 -.46 -1.41 .16 .44 P3 -.01 -.04 .97 .67 -.30 -1.01 .32 .43 P4 -.39 -1.57 .12 .83 -.59* -1.87 .06 .49 P5 -.42* -1.76 .08 .85 -.45 -1.57 .12 .55 P6 -.36 -1.50 .14 .84 -.42 -1.19 .24 .52 P7 -.16 -.64 .52 .84 -.06 -.21 .84 .56 P8 -.17 -.66 .51 .84 -.14 -.46 .64 .57 P9 -.19 -.67 .50 .81 .02 .08 .94 .56 P10 .07 .12 .90 .56 -.27 -.59 .56 .39

Panel C: Thailand Least Square Bootstrap

 t() p-value Rsq  t() p-value Rsq P1 -.27 -1.44 .15 .93 -.17 -.78 .44 .71 P2 -.11 -.99 .32 .98 -.17 -1.48 .14 .85 P3 -.09 -.82 .42 .98 -.13 -.92 .36 .86 P4 .13 1.02 .31 .98 -.02 -.13 .89 .86 P5 -.01 -.08 .94 .98 -.20 -1.26 .21 .86 P6 -.01 -.12 .90 .98 .01 .05 .96 .86 P7 -.09 -.69 .49 .97 -.29* -1.75 .08 .83 P8 .04 .24 .81 .97 -.07 -.40 .69 .83 P9 .05 .30 .76 .96 -.02 -.08 .94 .81 P10 .13 .66 .51 .94 .35 1.03 .31 .74

CHAPTER 4 INDIVIDUAL MUTUAL FUND PERFORMANCE MEASUREMENT USING HIGHER MOMENT APPROACH

4.1 Introduction

A fund is considered to have investment ability if it generates returns that exceed the benchmark before costs and fees. A fund that outperforms the benchmark on an after-cost basis is considered to add value for investors. Fund managers believe they have the ability to better estimate the true securities’ risks and returns, to spot any mispriced securities, and to time the market, thus generating excess returns for the fund. Therefore they frequently adjust their fund portfolios seeking opportunities to beat the market. Mutual fund managers that actively trade generally possess significant stock-picking talents and have the ability to choose stocks that outperform their benchmarks before any expenses are deducted. However, on a net-return level (after expenses), the funds underperform the broad market index by 1% per year (Wermers, 1997, 2000). Many studies suggest that more than half of the mutual funds have negative alphas, good performance does not persist, funds just have enough investment ability to cover their fees and trading costs, and they do not add value for investors after costs. Thus, investors are better off, on average, buying a low-expense index fund. So why do some investors continue to buy mutual funds rather than index funds? This chapter studies mutual fund performance in three selected Asian countries—China, Singapore and Thailand—for twelve years during 2000 to 2011 to determine whether any equity mutual funds significantly outperformed, or beat the market. Rather than forming portfolios, this study tests the equity mutual fund individually fund by fund with different types of measure. The study begins with direct and simple single-dimensional comparisons of total returns, and then moves to multi-dimensional comparisons of return-to-risk ratios in second-moment frameworks, lower-partial-moment frameworks and higher-moment frameworks to see whether there are any differences in the results of the different measures in the various moment frameworks. 98

The remainder of this chapter is organized in four sections: the review of literature in Section 2, the data and methodology in Section 3, the findings and results in Section 4, and conclusion in Section 5.

4.2 Review of Literature

Since Jensen’s study (1968), there have been two major approaches to test the performance of fund, or fund manager: (1) returns-based performance evaluation and (2) portfolio-holding-based performance evaluation (Wermers, 2011). Most returns-based models use the four-factor model of Carhart (1997) to determine if the alpha is statistically significantly greater than zero and large enough to compensate for the costs of the fund and add value to the investor. If a person wants to invest in a mutual fund with professional investment management which includes a fee, he/she should expect a higher performance compared to the market; otherwise a passively-managed low-expense index fund should be purchased. An investor should be able to make this decision by simply comparing the total return (which also includes any dividends) of the mutual fund with the total return of the market, or index. In the end, the investor wants to earn a profit on the investment, which is the total return—the real performance of the investment. However, this simple and direct comparison between total returns does not take the risk of the portfolio—the standard deviation—into account. It may be more fair and appropriate to compare a return-to-risk ratio, e.g. the Sharpe ratio, between a mutual fund and the market, rather than just the total return alone, as an investor wants to construct a portfolio which maximizes the expected return while reducing risk, or the variance of the portfolio (Markowitz, 1952). But the mean-variance model is appropriate only if the investor’s utility is quadratic or the joint distribution of returns is normal. The higher moments cannot be neglected unless there is a reason to believe that the asset returns are normally distributed or the utility function is quadratic (Arditti, 1967, 1971; Rubinstein, 1973). Arrow (1971) argued that desirable properties for an investor’s utility function are: (1) positive marginal utility for wealth—non-satiety with respect to wealth, (2) 99 decreasing marginal utility for wealth—risk aversion and (3) non-increasing absolute risk aversion—risky assets are not inferior goods. The first two conditions are consistent with mean-variance preference, and Arditti (1967) has shown that the decreasing absolute risk aversion (ARA) condition implies preference for positive skewness. Chunhachinda et al. (1994, 1997) and Prakash et al. (2003) found that the return distributions of portfolios are not symmetrical and an investor trades the expected return of the portfolio for skewness; thus the higher moment should also be incorporated into the portfolio performance measurement. This might be done by factoring skewness and/or kurtosis into the Sharpe ratio to make it a better measure as the traditional measures of risk (i.e. variance or standard deviation) do not fully capture the ―true risk‖ as the probability of loss of the distribution of portfolio returns. Conventional measures of skewness and kurtosis are essentially based on sample averages, which as is well known, are very sensitive to outliers. The impact of outliers is greatly amplified in conventional measures of skewness and kurtosis because they are raised to the third and fourth powers. This might be the reason why some research found that the return distributions are negatively skewed, while some demonstrated that they are positively skewed, yet others insisted that they are symmetrically distributed. Some researchers found that the skewness changes with time and investment intervals (Peiro, 2002). The lower-partial-moment (LPM) approach identifies risk as the left-hand tail of the distribution (Bawa, 1975) rather than viewing return dispersion in a symmetric way, e.g. the reward-to-target absolute semi-deviation ratio (RTASD) and the downside deviation-based Sharpe ratio (DDSR) (Pätäri, 2008). LPM for an empirical distribution of portfolio returns can be calculated (Harlow, 1991) as:

∑ ( ) ( ) where Pr(i) = probability of outcome Ri, t= target level of return,  = ordinal of moment

For  = 0, LPM0 is the probability of falling below the target level, or probability of target short fall (van de Meer, 2011). For  = 1, LPM1 is the linearly weighted sum of probability of falling below the target level, or first-order lower- partial-moment target absolute semi-deviation (TASD), which can be calculated as: 100

∑ for all Ri < t where n = number of outcomes in the whole distribution. The reward-to-target absolute semi-deviation ratio (RTASD) can be calculated as: .

Another approach of LPM is the target semi-standard deviation (TSSD)

∑ ( ) which can be calculated as: √ for all Ri < t. And the downside

deviation-base Sharpe ratio (DDSR) can be calculated as: .

Zakamouline and Koekebakker (2009) suggested that the investor’s individual performance measure in the mean-variance-skewness framework as Adjusted for Skewness Sharpe Ratio (ASSR), and in the mean-variance-skewness- kurtosis framework as Adjusted for Skewness and Kurtosis Sharpe Ratio (ASKSR). Shadwick and Keating (2002b) presented a new measure of performance called Omega, to overcome the inadequacy of many traditional performance measures when applied to investments that do not have normally distributed return distributions. Unlike other measurements of performance, Omega is developed with the intention to take the entire return distribution into account. Omega is the ratio of integration from L to b of (1-F(x))dx divided by the integration from a to L of F(x)dx; ( )

( ) ∫ ( ) where x is the random one-period rate of return on an investment, L is ∫ ( ) the threshold selected by the investor, and (a, b) represent the upper and lower bounds of the return distribution respectively. When higher moments are of little significance, Omega agrees with traditional measurements while avoiding the need to estimate means or variances. In the case where higher moments do matter and their effects have significant financial impact, Omega provides the corrections to these simpler estimations. Omega can be thought of as a pay-off function, because it provides a probability-adjusted ratio of gains to losses relative to the selected threshold return. An asset with a higher value of Omega is preferable to one with a lower value. Barras et al. (2010) found that almost no mutual funds have positive alphas (excess returns) after 2006. If mutual funds do not add value for investors after cost, why does the mutual fund business still survive today and even grow bigger? 101

Why are people still investing in mutual funds—not just retail investors, but also institutions? This research tries to test the equity mutual fund portfolio performance by various measures whether they can beat the market. And whether those mutual fund performance measures can be substituted one for another as choices of calculation. In this chapter, twelve years of equity mutual fund data for three Asian countries—China, Singapore, and Thailand—during 2000 to 2011 are collected and are analyzed to determine whether any equity mutual funds significantly outperformed, or beat the market. This study begins with direct and simple single- dimensional comparisons of total return, and then moves to multi-dimensional comparisons of return-to-risk ratios in a second-moment framework (i.e. the Sharpe ratio), lower-partial moment frameworks (i.e. RTASD, DDSR), and higher-moment frameworks (i.e. ASSR, Omega ratio). Then the rank of each measure is compared to see whether they are similar and can be substituted for each other, or if they are significantly different from each another.

4.3 Data and Methodology

This research collected monthly total return data of equity mutual funds, and the total return of stock market indexes of China, Singapore, and Thailand, for twelve years during January 2000 to December 2011 from the Bloomberg database. The data of total returns collected includes both active and inactive funds. By collecting both active and inactive fund total returns, the data is free from survivorship bias.

4.3.1 First-Moment Measure

Net Asset Value (NAV) reflects the value of a fund share to investors after deducting management fees and trading costs, but before deducting any load fees or payment of personal taxes. Total returns reflect the change in NAV plus any dividend or capital gain distributions over the performance period. 102

( ) (4.1)

The difference between the total return of each fund and the total return of a stock index is calculated on a monthly basis, and are hypotheses tested to determine whether the difference is equal to zero, to see if the mutual fund beat the market. As this study focuses on the difference between the actual return of a fund and a stock market index, the risk-free rate can be omitted from the calculation.

( ) ( ) (4.2) The hypotheses are:

; where i is each individual mutual fund and t is the month. As the distribution of total returns is not guaranteed to be a normal distribution, the Wilcoxon-signed rank test is used to test the difference, and the t-test also is used as a robustness check. The hypotheses are tested fund by fund, and the funds which beat the market statistically significantly or insignificantly, or are beaten by the market statistically significantly or insignificantly, are counted and recorded.

4.3.2 Second-Moment Measure

The return-to-risk ratio (Sharpe ratio) of each fund each year is calculated, and then the difference between the Sharpe ratio of each fund and the Sharpe ratio of the stock index is calculated on a yearly basis, and the hypotheses are tested whether the differences are equal to zero to see if the fund beat the market. As this study focuses on the return-to-risk ratio of funds compared with the stock market, the risk- free rate can be omitted from the calculation.

( ) (4.3) ( )

( ) ( ) (4.4) The hypotheses are:

; where i is each individual mutual fund and t is the year. The hypotheses are tested fund by fund and the funds which beat the market statistically significantly or insignificantly, or are beaten by the market 103 statistically significantly or insignificantly, in terms of the return-to-risk ratio, are counted and recorded.

4.3.3 Lower-Partial--Moment Measures

Markowitz (1959) used semi-variance as a measure of risk, as semi- variance measures downside losses rather than upside gains. The idea behind downside risk is that the left-hand side of a return distribution involves risk while the right-hand side contains better investment opportunities (Grootveld and Hallerbach, 1999). There are two common measures for Lower-Partial-Moment: Reward-to- Target Absolute Semi-Deviation Ratio (RTASD), and Downside Deviation-Based Sharpe Ratio (DDSR).

4.3.3.1 Reward-to-Target Absolute Semi-Deviation Ratio

The reward-to-target absolute semi-deviation ratio (RTASD) of each fund each year is calculated where the target is set as the mean of the fund’s total return. The difference between the RTASD of each fund and the RTASD of the stock index is calculated on a yearly basis, and the hypotheses are tested whether the differences are equal to zero to see if the fund beat the market.

̅ (4.5) ∑

for all ̅

( ) ( ) (4.6) The hypotheses are:

; where i is each individual mutual fund and t is the year. The hypotheses are tested fund by fund and the funds which beat the market statistically significantly or insignificantly, or are beaten by the market statistically significantly or insignificantly, in terms of the reward-to-target absolute semi-deviation ratio, are counted and recorded.

104

4.3.3.2 Downside Deviation-based Sharpe Ratio

The downside deviation-based Sharpe ratio (DDSR) of each fund each year is calculated where the target is set as the mean of the fund’s total return. The difference between the DDSR of each fund and the DDSR of the stock index is calculated on a yearly basis, and the hypotheses are tested whether the differences are equal to zero to see if the fund beat the market.

(4.7) ̅ √∑ ( )

for all ̅

( ) ( ) (4.8) The hypotheses are:

; where i is each individual mutual fund and t is the year. The hypotheses are tested fund by fund and the funds which beat the market statistically significantly or insignificantly, or are beaten by the market statistically significantly or insignificantly, in terms of the downside deviation-based Sharpe ratio, are counted and recorded.

4.3.4 Higher--Moment Measures

The normality test is performed using Stata’s Skewness-Kurtosis test (sk test) and the Shapiro-Wilk W test. Stata’s Skewness-Kurtosis test uses χ2 as test statistics, same as the Jarque-Bera test. The Shapiro-Wilk W is the ratio of the best estimator of the variance to the usual corrected sum-of-squares estimator of the variance. Then skewness factors is added into the Return-to-Risk ratios as the previous measures take into account only downside risk, while the upside return potential is not appreciated.

4.3.4.1 Adjusted for Skewness Return-to-Risk Ratio

Zakamouline and Koekebakker (2009) suggested that the investor’s individual performance measure in the mean-variance-skewness framework is: 105

√ (4.9)

where SR is the Sharpe ratio and ASSR stands for Adjusted for Skewness Sharpe ratio, under the condition that the ASSR is a positive real number. When either the skewness of a distribution is zero or the investor is indifferent to skewness, b3 = 0 for quadratic utility, and the ASSR is reduced to the standard Sharpe ratio. For CARA utility, b3 = 1, and for CRRA utility,

where is the coefficient of the relative risk aversion. The lower  the more the investor appreciates positive skewness and the more the investor dislikes negative skewness. From the b3 equation, when  approaches zero, b3 approaches infinity. And when  approaches infinity, b3 approaches 1. So b3 is a positive integer, varying from 1 to infinity. Because SR = return / sigma, the ASSR formula can be rewritten as:

√ (4.10)

√ (4.11) ⁄

where r is the return,  is the standard deviation, = a positive integer, varying from 1 to infinity. In order to compare from fund to fund by a particular investor which has CARA or CRRA utility, could be a constant. From this equation, skewness can be thought of as a factor applied into the risk measure. Because a higher positive skewness implies a potentially higher return on an investment, and a lower negative skewness implies a possible loss on an investment. The ―risk of loss‖ can be adjusted from sigma alone to be factored with the skewness measure so that the ―risk of loss‖ is smaller when skewness is a higher positive, and is larger when the skewness is a lower negative. So, the measure of probability of loss can be suggested as rather than just sigma alone.

For CARA and CRRA utility investor, b3 is assumed to be 1. The ASSR ratio of each fund each year is calculated, and then the difference between the ASSR ratio of each fund and the stock index is calculated on a yearly basis. The hypotheses are tested whether the differences are equal to zero to see if the fund beat the market.

( ) ( ) (4.12) 106

The hypotheses are:

; where i is each individual mutual fund and t is the year. The hypotheses are tested fund by fund and the funds which beat the market statistically significantly or insignificantly, or are beaten by the market statistically significantly or insignificantly, in terms of the ASSR ratio, are counted and recorded.

4.3.4.2 Omega

Omega is the ratio of integration from L to b of (1-F(x))dx by the

( ) ∫ ( ) integration from a to L of F(x)dx; ( ) , where x is the random one- ∫ ( ) period rate of return on an investment, L is the threshold selected by an investor, and (a, b) represent the upper and lower bounds of the return distribution respectively (Shadwick, W. F., and Keating, C., 2002). When investors select the total return of the market as the threshold to measure mutual fund performance, Omega is the ratio of the sum of the amounts considered as a win multiplied by their corresponding probabilities that equity mutual funds beat the market, divided by the sum of the amounts considered as a loss, multiplied by their corresponding probabilities that equity mutual funds are beaten by the market. The Omega function is mathematically equivalent to the cumulative distribution function (CDF) and also is equivalent to the call-put ratio and the partial- moment function ratio, which is the upper-partial-moment divided by the lower- partial-moment:

∑ √( )

( ) (4.13)

∑ √( )

The only calculation problem with this formula is when the frequency of loss is zero, then the omega calculation result infinity or un-identifiable. Similar to the calculation of x/y, when the denominator y is zero, the term x/y is un-identifiable. 107

One solution to avoid this problem is by modifying the calculation formula of x/y to be x/(x+y). The result of this modified calculation formula will be ranging from 0 to 1. Even the values of the two calculation formulas are different but they will be perfectly correlated as long as the value of y is not zero. By this concept, the Omega

( ) ( ) ∫ ( ) ∫ ( ) formula in 4.13 could be modified from to be . ( ) ∫ ( ) ∫ ( ) ∫ ( ) This modified Omega measure solves the unidentifiable problem and has a minimum value of 0 and maximum value of 1, so it is easier to standardize as a measure for comparison. It indicates the probability of a mutual fund beating the threshold and the value of this win, based on history, assuming that history repeats itself. Because when x = y, then the value of x/(x+y) will be 0.5. Thus, if the modified Omega is more than 0.5, then it’s a winning bet. But if the modified Omega is less than 0.5, then it’s a losing bet. As this study wants to determine whether a mutual fund can beat the market, the average of the total return of the market is selected as threshold L. The modified Omega of each fund each year is calculated using the average of the total return of the stock index of the same year as threshold L, and the hypotheses are tested whether the modified Omega value is equal to 0.5 to see if the fund beat the market.

( ) ∫ ( ) ( ) (4.14) ( ) ∫ ( ) ∫ ( )

where ( ) is modified Omega. The hypotheses are:

( ) 0.5; ( ) 0.5 where i is each individual mutual fund and t is the year. If the modified Omega (index) of a fund is statically significantly above 0.5, it means that the fund has more than 50% probability of beating the market. The hypotheses are tested fund by fund and the funds which beat the market statistically significantly or insignificantly, or are beaten by the market statistically significantly or insignificantly, in terms of modified Omega (index), are counted and recorded.

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4.4 Findings and Results

4.4.1 First-Moment Measure

Table 4.1 provides summary statistics for the mutual funds and stock index in each year and overall average of 12 years during 2000-2011. By looking at overall mean of total return of stock index compare to total return of equity mutual funds, it shows that mutual funds provide less total return compare to their stock index. On average of total 12 years, the mean of the total return of equity mutual funds is 0.82% per month while the mean of the total return of the index is 1.01% for China, the mean of the total return of equity mutual funds is 0.11% per month while the mean of the total return of the index is 0.39% for Singapore, and the mean of the total return of equity mutual funds is 1.33 % per month while the mean of the total return of the index is 1.37% for Thailand. There is no country that has the 12 years average of monthly total return of equity mutual funds higher than the average monthly total return of their stock market index. On yearly basis, some years the mutual funds have higher average monthly total return than the stock market, or beat the market, and some years they have lower average monthly total return than the stock market, or got beaten by the market. But in the long term, from 12 years example in this data set, the mutual funds, on average, cannot beat the market. (Table 4.1 is here) So, on 12 years average, the total return of equity mutual fund is less than of stock market index of the country. But is there any equity mutual fund that can beat the market? In order to understand whether there is any equity mutual fund that can beat the market, and whether the differences between the monthly total return of equity mutual funds and their stock indexes are statistically significant or not, the individual data of total return by fund and by month are subtract with the individual data of total return by month of the stock index and test hypothesis whether the difference is equal to zero by using Wilcoxon signed-rank test and t-test. As shown in Table 4.2, the result of the Wilcoxon signed-rank test show that there are 8 out of 363 funds (2.21%) in China, 22 out of 157 funds (14.02%) in Singapore, and 38 out of 216 funds (17.6%) in Thailand, that their total return are significantly different from total 109 return of stock index of their countries. From t-test also show similar result—8 out of 363 funds (2.20%) in China, 21 out of 157 funds (13.38%) in Singapore, and 19 out of 216 funds (8.79%) in Thailand, that their total returns are significantly different from total return of stock index of their countries. In those equity mutual funds that their total return are statistically significantly from the index of their countries, almost all of them are less than. There are only 1-2 equity mutual funds in China, 1 in Singapore and none in Thailand that their total returns are statistically significantly more than the total return of stock market. In the contrary, almost all of them are beaten by the market statistically significantly. Both Wilcoxon signed-rank test and t-test yield very similar result for all three countries. The majority of equity mutual funds for all three countries are not statistically significantly different from their index’s total return, but there are more number of funds that the total return of funds are less than their index’s total return than the number of funds that total return are more than their index’s. In Singapore, there are 18-20% of funds that their total returns are more than their index’s total return, while there are 66-67% of funds that their total returns are less than their index’s total return. In Thailand, there are 21-22% mutual funds that their total returns are more than their index’s total return, while there are 61-69% mutual funds that their total returns are less than their index’s total return. In China, there are 45-79% of funds that their total returns are more than their index’s total return, while there are 19-52% of funds that their total returns are less than their index’s total return. These numbers tell us that, on monthly basis, most of the equity mutual funds’ performances are not statistically significantly different from the total return of stock market. If the differences are statistically significant, they tend to be in the way that equity mutual fund performance is underperformed than the market. (Table 4.2 is here)

4.4.2 Second-Moment Measure

After looking at the number of the total return alone, continue to the second moment using risk as factor into the measure and produce Sharpe ratio on both equity mutual funds and index, and compare them. Table 4.3 shows the average of 110

Sharpe ratio of mutual funds and their indexes in yearly basis and their overall 12- year’s average. Descriptive statistics show average of Sharpe ratio of equity mutual funds in China is 0.06 while Sharpe ratio of the index is 0.09. Sharpe ratio of equity mutual funds in Singapore is 0.10 while Sharpe ratio of the index is 0.14. Sharpe ratio of equity mutual funds in Thailand is 0.28 while Sharpe ratio of the index is 0.26. These numbers tell us that, by looking at the 12-years average, the result of first moment measures and second moment measures are different. When risk is factored into the measures, the result changed to be closer in performance and look like there is no difference between the Sharpe ratio of equity mutual funds and their indexes. (Table 4.3 is here) In order to understand whether there is any mutual fund that can beat the market, and whether the differences between the Sharpe ratio of mutual funds and their stock indexes are statistically significant or not, the individual data by fund and by year are subtract with the data by year of the stock index and test hypothesis whether the delta is equal to zero by using Wilcoxon signed-rank test and t-test. As shown in Table 4.4, the result of the Wilcoxon signed-rank test and t-test are similar. There are only 1 fund in China, 2-3 funds in Singapore and no fund in Thailand that can beat the market by using Sharpe ratio as measurement. In the contrary, there are 4-6 (1-2%) in China, 11-14 (7-9%) in Singapore, and 6-11 (3-5%) of funds in Thailand that is beaten by the market in term of Sharpe ratio. The majority of mutual funds for all three countries are not statistically significantly different from their index’s Sharpe ratio. In Singapore, there are 27-29% of funds that their Sharpe ratios are more than their index’s Sharpe ratio, while there are 60-64% of funds that their Sharpe ratios are less than their index’s. In Thailand, there are 31-34% of funds that their Sharpe ratio are more than their index’s Sharpe ratio, while there are 61-67% of funds that their Sharpe ratios are less than their index’s Sharpe ratio. But in China, there are 61-62% of funds that their Sharpe ratios are more than their index’s Sharpe ratio, while there are 36-37% of funds that their Sharpe ratio are less than their index’s. This pattern is similar to Table 4.1 where total return is used as the measure. The number of funds that can beat the market are very close but the number of funds that is beaten by the market is less when use Sharpe ratio as measure. 111

(Table 4.4 is here)

4.4.3 Lower-Partial--Moment Measures

From second moment measure, continue to the lower partial moment measures which are Reward-to-Target Absolute Semi-Deviation (RTASD) ratio and Downside Deviation-based Sharpe Ratio (DDSR) which using only lower part of distribution as risk factor into the measure. RTASD and DDSR ratio are calculated on both equity mutual funds and indexes, and then compare. Table 4.5 show the average of RTASD ratio of equity mutual funds and their indexes in yearly basis and their overall average. Descriptive statistics show average of RTASD ratio of equity mutual funds in China is at 0.1, equal to the RTASD ratio of index. The average of RTASD ratio of equity mutual fund in Thailand is at 0.40 while RTASD ratio of index is slightly less at 0.36. But the average of RTASD ratio of mutual fund in Singapore is 0.13, less than their index’s at 0.18. (Table 4.5 is here) Table 4.6 shows the average of DDSR ratio of equity mutual funds and their indexes in yearly basis and their overall average. Descriptive statistics show that the averages of DDSR and RTASD for all three countries are in similar pattern. The average of DDSR of equity mutual fund in Thailand is 0.33, slightly higher than the index’s at 0.30. The average of DDSR of equity mutual fund in Singapore is 0.11, less than their index’s at 0.15. The averages of DDSR of equity mutual fund and index in China are close to each other at 0.07 and 0.06. These numbers tell us that the result of lower partial moment measures are in sync to each other, but slightly different from the first moment measures and second moment measures. (Table 4.6 is here) Similar to the first and second moment measures, the individual data of RTASD and DDSR by fund and by year are subtract with the data by year of the stock index and test hypothesis whether the delta is equal to zero by using Wilcoxon signed- rank test and t-test. As shown in Table 4.7, there are less than 6% of equity mutual funds in Thailand that their RTASD are significantly different from RTASD of stock index, and almost all of them are less than. There is only 1 fund in Thailand that can 112 beat the market using RTASD as measurement, by t-test. There are only 1-2% of funds in Singapore that can beat the market while there are 10-13% of funds that is beaten by the market index. In China, there are 1-4% of funds that can beat the market while there is only 1 fund that is beaten by the market significantly by using RTASD and Wilcoxon sign rank test. For the majority of funds that are not significantly different from their index, the pattern are the same as for the first and second moment measure. There are more percentage of funds that RTASD are worse than their index’s RTASD for Thailand and Singapore while there are more percentage of funds that RTASD is better than their index’s in China. The differences between lower and upper partial of moment has more impact to the China distribution compare to the other countries. (Table 4.7 is here) Table 4.8 shows the test of difference between equity mutual funds’ DDSR and their index’s DDSR, and the pattern is very similar to the RTASD ratio in table 7. For all three countries, the percentage of funds that can beat the market is 0- 2% for Sharpe Ratio, 0-4% for RTASD and 0-5% for DDSR. The percentage of funds that is beaten by the market is 1-9% for Sharpe ratio, 0-13% for RTASD and 0-12% for DDSR. (Table 4.8 is here)

4.4.4 Higher--Moment Measures

From second moment and lower partial moment measure, then continue to the higher moment measures which use skewness and kurtosis to factor into the measure. The descriptive data in table 4.9 show that, by Stata’s sk test, there are only 28% of funds in Thailand that has normal distribution of total return. In Singapore, there are 36% of distributions that are normally distributed. But China are different from others, 90% of the distributions are normally distributed. For the 72% of non-normal distribution of Thailand, 43% are skewed; 32% are negatively skewed and 11% are positively skewed. In Singapore, 49% of distributions are skewed from 64% of non-normal distribution; almost of them are 113 negative skew. In China, the percentage of negative and positive skewed are close to each other at 5.5 and 8.5%. In Thailand, 77% of distributions are excess kurtosis, and 69% of them are positive excess kurtosis. In Singapore, 61% of distributions are excess kurtosis, and 59% of them are positive excess kurtosis. In China, the excess kurtosis is only 7%, and almost all of them are positive excess kurtosis. Both Stata’s sk test and Shapiro Wilk W test for skewness and kurtosis test are used and both test agree to each other very well. When sk test say the distribution is normal, Shapiro wilk test also say the same, and when sk test say the distribution is not a normally distributed, Shapiro wilk test also say the same. (Table 4.9 is here) So the distributions are mostly not normally distributed, then the first and second moment measurements could not be relied on to measure the fund performance. So skewness and kurtosis are needed to be added into the measures to become higher moment measure. Adjusted-for-Skewness Sharpe Ratio (ASSR) is the measure which will use skewness to factor into the measure. ASSR is calculated on both equity mutual funds and index for the comparison purpose. Table 4.10 shows the average of ASSR of equity mutual funds and their market indexes in yearly basis. Descriptive statistics show average of ASSR of equity mutual funds in China is 0.02, less than their index’s at 0.06. The average of ASSR of equity mutual funds in Singapore is 0.08, less than their index’s at 0.13. The average of ASSR of equity mutual fund in Thailand is at 0.25, slightly less than their index’s at 0.27. The result shows that there is no country that the average of ASSR of equity mutual fund is higher than their country’s indexes. (Table 4.10 is here) Similar to the first, second, and lower partial moment measures, the individual data of ASSR by fund and by year are subtract with the data by year of the stock index and test hypothesis whether the delta is equal to zero by using Wilcoxon signed-rank test, and t-test as robustness test. As shown in Table 4.11, there are only 0.55% of equity mutual funds in China that their ASSR are significantly more than ASSR of stock index, while there are only 1.38% of equity mutual funds in China that their ASSR are significantly less than ASSR of stock index. More than 98% of the 114 equity mutual funds are not significantly different from the index’s ASSR. In Singapore, there are only 1.27% of equity mutual funds that their ASSR are significantly more than ASSR of stock index, while there are 8.92% of equity mutual funds that their ASSR are significantly less than ASSR of stock index. 90% of the equity mutual funds are not significantly different from the index’s ASSR but 62.42% of them are less than their index’s ASSR. In Thailand, there is none of equity mutual funds that their ASSR are significantly more than ASSR of stock index, while there are 2.31% of equity mutual funds that their ASSR are significantly less than ASSR of stock index. 97.7% of the equity mutual funds are not significantly different from the index’s ASSR but, similar to Singapore, 73.15% of them are less than their index’s ASSR. For the robustness t-test, the result is similar to Wilcoxon Sign Rank test. (Table 4.11 is here) The modified Omega (index) ratio is used as the last measure. Table 4.12 show the descriptive statistics of the modified Omega (index) ratio for all three countries. The mean of the modified Omega (index) ratio are all slightly less than 0.5 for all countries: 0.48 for China, 0.46 for Singapore, and 0.49 for Thailand. This means that, on 12 years average, no country has mutual fund performance that can beat their market index’s performances. (Table 4.12 is here) Table 4.13 shows the test result of the modified Omega (index) ratio of the equity mutual funds whether they are significantly different from 0.5. If the modified Omega (index) ratio of any equity mutual fund is significantly more than 0.5, that means the equity mutual fund can beat the market. If the modified Omega (index) ratio of any equity mutual fund is significantly less than 0.5, that means the equity mutual fund is beaten by the market. And the result shows that, there is no equity mutual fund in China that can beat the market while there is only 1 fund is beaten by the market. There is only 1 fund in Singapore that can beat the market while 6.37% of them are beaten by the market. And there is no equity mutual fund in Thailand that can beat the market while there are less than 1% of funds that is significantly beaten by the markets by using the modified Omega (index) ratios as measurement. For the funds that are not significantly different from their index, the patterns are the same as the previous measure. There are more percentage of funds 115 that the modified Omega (index) ratio is worse than their index for Thailand and Singapore. But there are slightly more of funds that the modified Omega (index) ratio is better than their index in China. The robustness t-test also shows the similar result but higher probability of fund that can beat the market in Singapore and Thailand. (Table 4.13 is here) Table 4.14 shows the summary of all 6 performance measures by using Wilcoxon Sign Rank test, and by t-test as robustness test. In China, the equity mutual fund that can beat the market index is only less than 1% while the fund that is beaten by the market is less than 2% by all measures. In Singapore, the equity mutual fund that can beat the market index is only less than 2% while the fund that is beaten by the market is between 6-13%. In Thailand, the equity mutual fund that can beat the market index is only less than 0.5% while the fund that is beaten by the market is between 1-18%. Looking by the measure perspective, the percentage of funds that can beat the market is less than 1% for Total Return, 0-2% for Sharpe Ratio, 0-1% for RTASD, 0-2% for DDSR, 0-1% for ASSR, and 0-1% for modified Omega (index) ratio. The percentage of funds that is beaten by the market is 2-18% for Total Return, 1-7% for Sharpe ratio, 0-10% for RTASD, 0-10% for DDSR, 1-9% for ASSR, and 0-6% for modified Omega (index) ratio. The robustness t-test also shows the similar result. (Table 4.14 is here)

4.5 Conclusion

The study of mutual fund performance in three countries i.e. China, Singapore, and Thailand for 12 years during year 2000-2011 shows that the chance for equity mutual fund to beat the market is very slim but the chance that equity mutual funds perform poorer than their index performance is much higher. Even the difference of performance of the majority of equity mutual funds and their indexes’ are not significant the chance to be beaten by the market higher than the chance to beat the market, particularly in Singapore and Thailand. No matter what performance measures we use, from the first moment, second moment, lower partial moment, till higher moment, the result is pretty much in the same pattern. This result confirms the 116 studies of the literatures in this area that, in the long run, most of equity mutual funds herd with the index i.e. they behave themselves not significantly different from the performance of the index. If there are any equity mutual funds that perform statistically significantly different from their index performances, the chance is likely that their performances are poorer than the index. Thus, investors are better off, buying a low-expense index fund.

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Table 4.1 Descriptive Statistics of Total Return of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Descriptive Statistics of average of monthly Total Return of Stock Market Indexes of China (Shenzhen Stock Exchange Constituent Stock Index SICOM), Singapore (Straits Times Index FSSTI), and Thailand (SET) along with the Equity Mutual Funds in their countries during years 2000 to 2011.

China Singapore Thailand Mean Mean No of Mean Mean No of Mean Mean No of Year Index Fund Funds Index Fund Funds Index Fund Funds 2000 1.79 N/A 0 -1.93 -2.95 39 -4.09 -3.60 71 2001 -2.45 -3.04 1 -1.27 -0.86 69 2.55 1.28 78 2002 -1.40 -1.87 2 -1.70 -1.68 83 1.99 2.31 84 2003 1.88 1.05 10 1.75 2.16 91 7.52 7.85 96 2004 -0.55 -0.20 20 1.23 0.67 96 -0.80 0.02 129 2005 -0.38 0.49 41 1.17 1.49 108 0.99 0.86 146 2006 8.44 9.30 77 2.03 1.69 117 0.37 0.54 156 2007 8.50 5.93 121 1.49 1.34 118 2.57 2.73 176 2008 -7.64 -5.14 161 -3.93 -3.79 126 -3.16 -2.68 187 2009 6.68 4.19 215 5.84 3.56 127 4.86 4.00 197 2010 -0.52 0.26 314 0.73 0.58 133 3.05 2.52 196 2011 -2.23 -1.99 358 -0.77 -0.95 127 0.59 0.12 197 Avg 1.01 0.82 363 0.39 0.11 157 1.37 1.33 216 118

Table 4.2 Test of Difference between Total Return of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Test of difference between Equity Mutual Funds monthly Total Return and Stock Market Indexes monthly Total Return of China, Singapore, and Thailand during years 2000 to 2011 whether Mutual Funds can beat the market.

China Singapore Thailand Wilcoxon t-test Wilcoxon t-test Wilcoxon t-test Sign Rank Sign Rank Sign Rank Total Funds 363 363 157 157 216 216 Number of funds 1 2 1 0 0 0 that Total Return (0.28%) (0.55%) (0.64%) (0.00%) (0.00%) (0.00%) is more than Stock Market Index Number of funds 165 286 29 32 46 47 that Total Return (45.45%) (78.79%) (18.47%) (20.38%) (21.30%) (21.76%) is more than but not significant Number of funds 190 69 106 104 132 150 that Total Return (52.34%) (19.01%) (67.52%) (66.24%) (61.11%) (69.44%) is less than but not significant Number of funds 7 6 21 21 38 19 that Total Return (1.93%) (1.65%) (13.38%) (13.38%) (17.59%) (8.79%) is less than Stock Market Index 119

Table 4.3 Sharpe Ratio of Average of Monthly Total Return of Stock Market Indexes and Equity Mutual Funds of China, Singapore, and Thailand

Sharpe Ratio of average of monthly Total Return of Stock Market Indexes of China (Shenzhen Stock Exchange Constituent Stock Index SICOM), Singapore (Straits Times Index FSSTI), and Thailand (SET), along with the Equity Mutual Funds in their countries during years 2000 to 2011.

China Singapore Thailand Mutual Mutual Mutual Year Index Fund Index Fund Index Fund 2000 0.28 N/A -0.27 -0.59 -0.42 -0.34 2001 -0.35 -0.46 -0.16 -0.11 0.23 0.17 2002 -0.20 -0.78 -0.26 -0.23 0.30 0.41 2003 0.36 0.27 0.40 0.53 1.20 1.03 2004 -0.09 -0.07 0.51 0.27 -0.19 0.10 2005 -0.06 0.18 0.40 0.43 0.22 0.20 2006 0.96 1.10 0.55 0.62 0.07 0.29 2007 0.65 0.60 0.32 0.30 0.50 0.47 2008 -0.70 -0.54 -0.44 -0.46 -0.26 -0.27 2009 0.66 0.69 0.62 0.60 0.71 0.69 2010 -0.05 0.05 0.20 0.03 0.64 0.53 2011 -0.40 -0.37 -0.16 -0.19 0.09 0.02 Avg 0.09 0.06 0.14 0.10 0.26 0.28

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Table 4.4 Test of Difference between Sharpe Ratio of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Test of difference between Equity Mutual Funds yearly Sharpe Ratio of Total Return and Stock Market Indexes yearly Sharpe Ratio of Total Return of China, Singapore, and Thailand during years 2000 to 2011 whether Mutual Funds can beat the market.

China Singapore Thailand Wilcoxon t-test Wilcoxon t-test Wilcoxon t-test Sign Rank Sign Rank Sign Rank Total Funds 363 309 157 156 216 212 Number of funds 1 1 3 2 0 0 that Sharpe Ratio is (0.28%) (0.32%) (1.91%) (1.28%) (0.00%) (0.00%) more than Stock Market Index Number of funds 224 191 42 46 66 72 that Sharpe Ratio is (61.71%) (61.81%) (26.75%) (29.49%) (30.56%) (33.96%) more than but not significant Number of funds 134 111 101 94 144 129 that Sharpe Ratio is (36.91%) (35.92%) (64.33%) (60.26%) (66.67%) (60.85%) less than but not significant Number of funds 4 6 11 14 6 11 that Sharpe Ratio is (1.10%) (1.94%) (7.01%) (8.97%) (2.78%) (5.19%) less than Stock Market Index

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Table 4.5 The Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

The Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio of average of monthly Total Return of Stock Market Indexes of China (Shenzhen Stock Exchange Constituent Stock Index SICOM), Singapore (Straits Times Index FSSTI), and Thailand (SET), along with the Equity Mutual Funds in their countries during years 2000 to 2011.

China Singapore Thailand Mutual Mutual Mutual Year Index Fund Index Fund Index Fund 2000 0.62 N/A -0.39 -0.82 -0.53 -0.34 2001 -0.50 -0.58 -0.18 -0.14 0.30 0.23 2002 -0.35 -0.98 -0.51 -0.32 0.42 0.57 2003 0.40 0.39 0.60 0.65 1.83 1.76 2004 -0.11 -0.08 0.62 0.35 -0.31 0.14 2005 -0.08 0.22 0.58 0.50 0.22 0.25 2006 1.47 1.61 0.57 0.77 0.08 0.30 2007 0.81 0.73 0.42 0.41 0.49 0.52 2008 -0.85 -0.58 -0.46 -0.49 -0.29 -0.32 2009 0.57 0.81 0.90 0.83 1.10 0.99 2010 -0.07 0.08 0.21 0.04 0.94 0.67 2011 -0.68 -0.51 -0.17 -0.24 0.09 0.03 Avg 0.10 0.10 0.18 0.13 0.36 0.40

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Table 4.6 The Downside Deviation-Based Sharpe Ratio (DDSR) of Equity Mutual Funds and Stock Market Index of China, Singapore, and Thailand

The Downside Deviation-Based Sharpe Ratio (DDSR) of average of monthly Total Return of Stock Market Indexes of China (Shenzhen Stock Exchange Constituent Stock Index SICOM), Singapore (Straits Times Index FSSTI), and Thailand (SET) along with the Equity Mutual Funds in their countries during years 2000 to 2011

China Singapore Thailand Mutual Mutual Mutual Year Index Fund Index Fund Index Fund 2000 0.41 N/A -0.28 -0.69 -0.41 -0.27 2001 -0.39 -0.47 -0.13 -0.11 0.24 0.18 2002 -0.30 -0.93 -0.40 -0.28 0.36 0.50 2003 0.32 0.32 0.46 0.55 1.50 1.40 2004 -0.09 -0.08 0.51 0.31 -0.21 0.17 2005 -0.06 0.20 0.41 0.43 0.20 0.19 2006 1.16 1.40 0.38 0.60 0.07 0.27 2007 0.63 0.56 0.33 0.33 0.42 0.44 2008 -0.75 -0.50 -0.36 -0.42 -0.23 -0.26 2009 0.39 0.60 0.83 0.70 0.87 0.81 2010 -0.06 0.06 0.17 0.03 0.70 0.54 2011 -0.56 -0.42 -0.15 -0.19 0.08 0.02 Avg 0.06 0.07 0.15 0.11 0.30 0.33

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Table 4.7 Test of Difference between Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio of Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Test of difference between Equity Mutual Funds yearly Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio of Total Return and Stock Market Indexes yearly Reward-to-Target Absolute Semi-Deviation (RTASD) Ratio of Total Return of China, Singapore, and Thailand during years 2000 to 2011 whether Mutual Funds can beat the market.

China Singapore Thailand Wilcoxon t-test Wilcoxon t-test Wilcoxon t-test Sign Rank Sign Rank Sign Rank Total Funds 363 309 157 156 216 212 Number of funds 4 12 2 1 0 1 that RTASD Ratio is (1.10%) (3.88%) (1.27%) (0.64%) (0.00%) (0.47%) more than Stock Market Index Number of funds 279 223 40 52 74 75 that RTASD Ratio is (76.86%) (72.17%) (25.48%) (33.33%) (34.26%) (35.38%) more than but not significant Number of funds 79 74 99 83 140 126 that RTASD Ratio is (21.76%) (23.95%) (63.06%) (53.21%) (64.81%) (59.43%) less than but not significant Number of funds 1 0 16 20 2 10 that RTASD Ratio is (0.28%) (0.00%) (10.19%) (12.82%) (0.93%) (4.72%) less than Stock Market Index 124

Table 4.8 Test of Difference between Downside Deviation-Based Sharpe Ratio (DDSR) of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Test of difference between Mutual Funds yearly Downside Deviation-based Sharpe Ratio (DDSR) of Total Return and Stock Market Indexes yearly Downside Deviation- based Sharpe Ratio (DDSR) of Total Return of China, Singapore, and Thailand during years 2000 to 2011 whether Equity Mutual Funds can beat the market.

China Singapore Thailand Wilcoxon t-test Wilcoxon t-test Wilcoxon t-test Sign Rank Sign Rank Sign Rank Total Funds 363 309 157 156 216 212 Number of funds 4 16 3 2 1 1 that DDSR Ratio is (1.10%) (5.18%) (1.91%) (1.28%) (0.46%) (0.47%) more than Stock Market Index Number of funds 279 222 42 48 63 76 that DDSR Ratio is (76.86%) (71.84%) (26.75%) (30.77%) (29.17%) (35.85%) more than but not significant Number of funds 80 71 96 88 147 122 that DDSR Ratio is (22.04%) (22.98%) (61.15%) (56.41%) (68.06%) (57.55%) less than but not significant Number of funds 0 0 16 18 5 13 that DDSR Ratio is (0.00%) (0.00%) (10.19%) (11.54%) (2.31%) (6.13%) less than Stock Market Index

125

Table 4.9 Skewness and Kurtosis Test of Mutual Funds of China, Singapore, and Thailand

Skewness and Kurtosis Test of distribution of Total Return of Equity Mutual Funds of China, Singapore, and Thailand during years 2000 to 2011 (in percentage of funds)

China Singapore Thailand Shapiro Shapiro Shapiro Stata’s Stata’s Stata’s Wilk Wilk Wilk sk test sk test sk test W Test W Test W Test Normal Distribution 89.78 90.33 35.67 36.94 27.78 49.54 Not Normal Distribution 10.22 9.67 64.33 63.09 72.22 50.46 Skewed Distribution 14.09 49.04 42.59 Negative Skewness 5.52 45.86 31.48 Positive Skewness 8.56 3.18 11.11 Excess Kurtosis 6.63 60.51 77.31 Negative Excess 0.55 1.27 8.33 Kurtosis Positive Excess Kurtosis 6.08 59.24 68.98 Sk agrees with Shapiro 91.16 91.08 78.24 Wilk W Test

* Sk test agrees with Shapiro Wilk W test, means that when sk test says the distribution is normal, Shapiro Wilk test also says the same, and when sk test says the distribution is not normally distributed, Shapiro Wilk test also says the same.

126

Table 4.10 The Adjusted-for-Skewness Sharpe Ratio (ASSR) of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

The Adjusted-for-Skewness Sharpe Ratio (ASSR) of average of monthly Total Return of Stock Market Indexes of China (Shenzhen Stock Exchange Constituent Stock Index SICOM), Singapore (Straits Times Index FSSTI), and Thailand (SET) along with the Equity Mutual Funds in their countries during years 2000 to 2011.

China Singapore Thailand Mutual Mutual Mutual Year Index Fund Index Fund Index Fund 2000 N/A N/A -0.26 -0.56 -0.43 -0.31 2001 -0.34 -0.49 -0.16 -0.09 0.23 0.12 2002 -0.19 -0.68 -0.25 -0.23 0.30 0.45 2003 0.35 0.28 0.40 0.53 1.33 1.15 2004 -0.09 -0.04 0.49 0.22 -0.20 -0.05 2005 -0.06 0.10 0.40 0.37 0.22 0.19 2006 1.01 0.94 0.43 0.45 0.07 0.13 2007 0.60 0.62 0.32 0.25 0.47 0.37 2008 -0.68 -0.62 -0.47 -0.50 -0.27 -0.27 2009 0.46 0.43 0.68 0.67 0.75 0.71 2010 -0.05 0.06 0.19 0.05 0.62 0.51 2011 -0.38 -0.36 -0.16 -0.19 0.09 0.02 Avg 0.06 0.02 0.13 0.08 0.27 0.25

127

Table 4.11 Test of Difference between Adjusted-for-Skewness Sharpe Ratio (ASSR) of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Test of difference between yearly Adjusted-for-Skewness Sharpe Ratio (ASSR) of Total Return of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand during years 2000 to 2011 whether Mutual Funds can beat the market.

China Singapore Thailand Wilcoxon t-test Wilcoxon t-test Wilcoxon t-test Sign Rank Sign Rank Sign Rank Total Funds 363 306 157 156 216 209 Number of funds 2 6 2 1 0 1 that ASSR is more (0.55%) (1.96%) (1.27%) (0.64%) (0.00%) (0.48%) than Stock Market Index Number of funds 210 180 43 44 53 55 that ASSR is more (57.85%) (58.82%) (27.39%) (28.21%) (24.54%) (26.32%) than but not significant Number of funds 146 113 98 96 158 139 that ASSR is less (40.22%) (36.93%) (62.42%) (61.54%) (73.15%) (66.51%) than but not significant Number of funds 5 7 14 15 5 14 that ASSR is less (1.38%) (2.29%) (8.92%) (9.62%) (2.31%) (6.70%) than Stock Market Index

128

Table 4.12 Modified Omega (Index) Ratio of Equity Mutual Funds and Stock Market Indexes of China, Singapore, and Thailand

Modified Omega (index) Ratio of average of monthly Total Return of Stock Market Indexes of China (Shenzhen Stock Exchange Constituent Stock Index SICOM), Singapore (Straits Times Index FSSTI), and Thailand (SET) along with the equity mutual funds in their countries during years 2000 to 2011.

China Singapore Thailand Year Min Mean Max Min Mean Max Min Mean Max 2000 N/A N/A N/A 0.05 0.42 0.76 0.44 0.52 0.80 2001 N/A N/A N/A 0.17 0.55 0.90 0.20 0.41 0.90 2002 0.20 0.35 0.50 0.28 0.50 0.10 0.26 0.53 0.94 2003 0.06 0.35 0.63 0.00 0.57 0.93 0.09 0.47 0.99 2004 0.09 0.58 0.92 0.00 0.38 0.93 0.25 0.61 0.97 2005 0.46 0.64 0.98 0.03 0.52 0.95 0.19 0.48 0.85 2006 0.01 0.46 0.85 0.03 0.38 0.97 0.37 0.54 0.78 2007 0.04 0.37 0.66 0.01 0.44 0.78 0.06 0.52 0.80 2008 0.45 0.63 0.92 0.11 0.50 0.92 0.32 0.52 0.81 2009 0.01 0.28 0.52 0.00 0.29 0.68 0.01 0.40 0.71 2010 0.05 0.58 0.96 0.16 0.43 0.99 0.02 0.44 0.68 2011 0.12 0.54 0.87 0.21 0.50 0.88 0.05 0.45 0.61 Avg 0.15 0.48 0.78 0.09 0.46 0.82 0.19 0.49 0.82

129

Table 4.13 Test of Difference between Modified Omega (Index) of Equity Mutual Funds of China, Singapore, and Thailand

Test of difference of Mutual Funds yearly modified Omega (index) of Total Return (Stock Market Index Total Return as benchmark) of China, Singapore, and Thailand during years 2000 to 2011 whether Mutual Funds can beat the market.

China Singapore Thailand Wilcoxon t-test Wilcoxon t-test Wilcoxon t-test Sign Rank Sign Rank Sign Rank Total Funds 361 307 157 151 215 208 Number of funds that 0 4 1 1 0 0 modified Omega (0.00%) (1.30%) (0.64%) (0.66%) (0.00%) (0.00%) (Index) is more than 0.5 (beat the market) Number of funds that 204 157 42 34 81 83 Omega (Index) is more (56.51%) (51.14%) (26.75%) (22.52%) (37.67%) (39.90%) than but not significant Number of funds that 156 146 104 102 132 114 Omega (Index) is less (43.21%) (47.56%) (66.24%) (67.55%) (61.40%) (54.81%) than but not significant Number of funds that 1 0 10 14 2 11 Omega (Index) is (0.28%) (0.00%) (6.37%) (9.27%) (0.93%) (5.29%) significantly less than 0.5 (beaten by the market)

130

Table 4.14 Comparison of All Measures of the Mutual Funds of China, Singapore, and Thailand

Comparison of all measures (in %) of the equity mutual funds of China, Singapore, and Thailand during years 2000 to 2011 whether they beat the market or are beaten by the market (in percentage). China Singapore Thailand beat are beat are beat are Measures market beaten market beaten market beaten By Wilcoxon Sign Rank Test 1.Total Return Difference 0.28 1.93 0.64 13.38 0.00 17.59 2.Sharpe Ratio Difference 0.28 1.10 1.91 7.01 0.00 2.78 3.Return-to-Target 1.10 0.28 1.27 10.19 0.00 0.93 Absolute Semi-Deviation Ratio (RTASD) 4.Sortino Ratio (DDSR) 1.10 0.00 1.91 10.19 0.46 2.31 5. Adjusted-for-Skewness 0.55 1.38 1.27 8.92 0.00 2.31 Sharpe Ratio (ASSR) 6.Modified Omega (index) 0.00 0.28 0.64 6.37 0.00 0.93 by t-test 1.Total Return Difference 0.55 1.65 0.00 13.38 0.00 8.79 2.Sharpe Ratio Difference 0.32 1.94 1.28 8.97 0.00 5.19 3.Return-to-Target 3.88 0.00 0.64 12.82 0.47 4.72 Absolute Semi-Deviation Ratio (RTASD) 4.Sortino Ratio (DDSR) 5.18 0.00 1.28 11.54 0.47 6.13 5. Adjusted-for-Skewness 1.96 2.29 0.64 9.62 0.48 6.70 Sharpe Ratio (ASSR) 6.Modified Omega (index) 1.30 0.00 0.66 9.27 0.00 5.29 131

REFERENCES

1. Arditti, F. (1967). Risk and the required return on equity. Journal of Finance, 22, 19-36. 2. Arditti, F. (1971). Another look at mutual fund performance. Journal of Financial and Quantitative Analysis, 6 (2), 909-912. 3. Arrow, K. (1971). Essays in the theory of risk-bearing. Chicago: Markham Publishing Co. 4. Bai, J. and Perron, P. (1998). Estimating and testing for multiple structural changes in linear models. Econometrica 66, 47-78. 5. Bai J and Perron P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18: 1–22. 6. Banz, R. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3-18. 7. Barras, L., Scaillet, O., and Wermers, R. (2010). False discoveries in mutual fund performance: measuring luck in estimated alphas. Journal of Finance, 65, 179- 216. 8. Basu, S. (1977). Investment performance of common stocks in relation to their Price-Earnings ratios: A test of the efficient market hypothesis. Journal of Finance, XXXII (3), 663-82. 9. Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2, 95-121. 10. Bhandari, L. (1988). Debt/Equity ratio and expected common stock returns: Empirical evidence. Journal of Finance, XLIII (2), 507-28. 11. Bickel, P. J., and Freedman, A. D. (1984). Some asymtotics on the bootstrap. Annals of Statistics, 9, 1196-1271. 12. Black, F. (1972). Capital market equilibrium with restricted borrowing. Journal of Business, 45, 444-55. 13. Black, F., Jensen, M., and Scholes, M. (1972). The capital asset pricing model: Some empirical tests, in: M. Jensen, ed. Studies in the theory of capital markets (Praeger, New York, NY). 132

14. Breeden, T. (1979). An intertemporal asset pricing model with stochastic consumption and investing opportunities. Journal of Financial Economics, 7, 265- 296. 15. Breeden, T. (1986). Consumption, Production, Inflation and Interest Rates: A Synthesis. Journal of Financial Economics, 16, 3-398. 16. Brown, J., W. Goetzmann, Ingersoll Jr., J. and Ross S. A. (1992). Survivorship bias in performance studies. Review of Financial Studies, 5(4), 553-580. 17. Campbell, J. Y., and Viceira, L. M. (2002). Strategic Asset Allocation. Oxford University Press, Oxford. 18. Carhart, M. (1997). On persistence in mutual fund performance. Journal of Finance, 52, 57-82. 19. Chan, K., and Chen, N. (1991). Structural and return characteristics of small and large firms. The Journal of Finance, XLVI (4), 1467-1484 20. Chan, L., Hamao, Y., and Lakonishok, J. (1991). Fundamentals and stock returns in Japan. The Journal of Finance, XLVI (5), 1739-1764 21. Chang, C., and Lewellen, W. (1984). Market timing and mutual fund investment performance. Journal of Business, 57, 57-72 22. Chauvet, M., and Potter S. (2000). Coincident and leading indicators of the stock market. Journal of Empirical Finance, 7(1), 87-111 23. Chiao, C., Hung, K., and Srivastava, S. (2003). Taiwan stock market and four- moment asset pricing model. Journal of International Financial Markets, Institutions and Money 13(2003), 355-381 24. Christie-David, R., and Chaudry, M. (2001). Coskewness and cokurtosis in future markets. Journal of Empirical Finance, 8, 55-81 25. Chunhachinda, P., Dandapani, K., Hamid, S., and Prakash, A. J. (1994). Efficacy of portfolio performance measure: An evaluation. Quarterly Journal of Business and Economics, 33, 74-87 26. Chunhachinda, P., Dandapani, K., Hamid, S., and Prakash, A.J. (1997). Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking and Finance, 21 (2), 143-167 27. Dittmar, R. (2002). Nonlinear pricing kernels, kurtosis preference, and evidence from the cross section of equity returns. Journal of Finance, 57, 369-403 133

28. Edelen, M. (1999). Investor flows and the assessed performance of open-end mutual funds. Journal of Financial Economics, 53, 439-466 29. Elton, E., Gruber, M., Das, S., and Hlavka, M. (1992). Efficiency with costly information: A reinterpretation of evidence for managed portfolio. Review of Financial Studies, 6, 1-22 30. Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25, 383-417 31. Fama, E. F., and French, K. R. (1992a). The cross section of expected stock returns. The Journal of Finance, 47, 427-465 32. Fama, E. F., and French, K. R. (1992b). The economic fundamentals of size and book-to-market equity. Working paper (Graduate School of Business, University of Chicago, Chicago, IL.) 33. Fama, E. F., and French, K. R. (1993). Common risk factors in the return on stocks and bonds. Journal of Financial Economics, 33, 3-56 34. Fama, E. F., and French, K. R. (1996). Multifactor explanations of asset pricing anomalies. Journal of Finance, 51, 55-84 35. Fama, E. F., and French, K. R. (1998). Value versus growth: The international evidence. Journal of Finance, 53, 1975-1999 36. Fama, E. F., and French, K. R. (2008). Dissecting anomalies. Journal of Finance, 63, 1653-1678 37. Fama, E. F., and French, K. R. (2009). Luck versus skill in the cross section of mutual fund alpha estimates. Journal of Finance, Vol. LXV, No. 5, 1915-47 38. Fama, E. F., and Macbeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 607-36 39. Fang, H., and Lai, T. (1997). Cokurtosis and capital asset pricing. The Financial Review, 32, 293-307 40. Ferson, E. W. (2010). Investment Performance Evaluation. CenFIS Working Paper 10-01 41. Ferson, E. W., and Schadt, W. R. (1996). Measuring Fund Strategy and Performance in Changing Economic Conditions. Journal of Finance, 51, No 2, 425- 461 134

42. Friend, I., and Westerfield, R.. (1980). Coskewness and capital asset pricing. Journal of Finance 35, 897-913. 43. Gollier, C., and Pratt, J., W. (1996). Risk vulnerability and the tempering effect of background risk. Econometrica, 64, 1109-1123 44. Grinblatt, M. and Titman, S. (1989). Mutual fund performance: An analysis of quarterly portfolio holdings. Journal of Business, 62, 393-416 45. Grinblatt, M., and Titman, S. (1993). Performance measurement without benchmarks: An examination of mutual fund returns. Journal of Business, 66, 47-68 46. Groeneveld, A. R., and Meeden, G. (1984). Measuring skewness and kurtosis. Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 33, No. 4, 391-399 47. Grootveld, H., and Hallerbach W. (1999). Variance vs downside risk: Is there really that much difference? European Journal of Operational Research, 114, 304- 319 48. Grossman, S., and Shiller, R. (1981). The determinants of the variability of stock market prices. American Economic Review, 71, 222-227 49. Gruber, J. (1996). Another puzzle: The growth in actively managed mutual funds. Journal of Finance 51, 783-810 50. Hall, P. (1986). On the bootstrap and confidence intervals. Annals of Statistics, 14, 1431-1452 51. Harlow, W. V. (1991). Asset allocation in a downside-risk framework. Financial Analysts Journal, 47, 28-40 52. Harrison, J., and Kreps, D. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381-408 53. Harvey, C., and Siddique, A. (2000). Conditional skewness in asset pricing tests. Journal of Finance, 55, 1263-1295 54. Heaney, R. A., Yihui, L., and Treepongkaruna, S. (2011). Are Co-Skewness and Co-Kurtosis Factors Priced? 24th Australasian Finance and Banking Conference 2011 Paper. Available at SSRN: http://ssrn.com/abstract=1917084 or http://dx.doi.org/10.2139/ssrn.1917084. 55. Henriksson, D. (1984). Market timing and mutual fund performance: An empirical investigation. Journal of Business, 57, 73-96 135

56. Henriksson, R., and Merton, R. (1981). On market timing and investment performance II: statistical procedures for evaluating forecasting skills. Journal of Business, 54, 513-533 57. Huberman, G., and Kandel, S. (1987). Mean-variance spanning. Journal of Finance, XLII (4), 873-888 58. Hung, Chi-Hsiou (2007). The four-moment CAPM and non-linear market models in momentum and size strategies. Working paper 59. Hwang, S., and Satchell, S. (1999). Modeling emerging market risk premia using higher moments. Financial Econometrics Research Centre, Working Papers Series WP99-17 60. Investment Company Fact Book. (2004, 2011). Investment Company Institute. 61. Jarjir, Souad Lajili, (2004). Size and Book to Market Effects vs. Co-skewness and Co-kurtosis in Explaining Stock Returns. Working paper. Available at SSRN: http://ssrn.com/abstract=634684, http://dx.doi.org/10.2139/ssrn.634684 62. Jegadeesh, N., and Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance, 48, 65-91 63. Jensen, M. C. (1968). The performance of mutual funds in the period 1945- 1964. Journal of Finance, 23, 389-416 64. Kaplansky, I. (1945). A common error concerning kurtosis. Journal of the American Statistical Association, 40, 259. 65. Kendall, M. G. and Stuart, A. (1977). The Advanced Theory of Statistics, Vol. 1. Distribution Theory, 4th edn. Charles Griffin and Co, London 66. Kimball, M., S. (1990). Precautionary saving in the small and the large. Econometrica, 58, 53-73

67. Kimball, M., S. (1992). Precautionary motives for holding assets, In: Newman, P., Miligate, M., and Falwell, J. (Eds.). New Palgrave Dictionary of Money and Finance, MacMillan, London.

68. Kosowski, R., Timmermann, A., Wermers, R., and White, H. (2006). Can mutual fund ―stars‖ really pick stocks? New evidence from a bootstrap analysis. The Journal of Finance, Vol. LXI, No.6, 2551-2595 136

69. Kosowski R. (2011). Do mutual funds perform when it matters most to investors? U.S. mutual fund performance and risk in recessions and expansions. Quarterly Journal of Finance, Vol. 1 No. 3, 607-664 70. Kostakis, A., Muhammad, K., and Siganos, A. (2012). Higher co-moments and asset pricing on London Stock Exchange. Journal of Banking and Finance, Vol 36, Issue 3, 913-922 71. Kothari, P., Shu, S., Wysocki, P. (2005). Do managers withhold bad news? MIT Sloan School of Management Working Paper 4556-05 72. Kraus, A., and Litzenberger, R. (1976). Skewness preference and the valuation of risk assets. Journal of Finance, 31, 1085-1100 73. Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolio and capital budgets. Review of Economics and Statistics, 47, 13-37 74. Lynch, A., Wachter, J., and Boudry, W. (2002). Does mutual fund performance vary over the business cycle. NYU Working Paper No. S-MF-03-01 75. Malkiel, B. (1995). Return from investing in equity mutual funds. Journal of Finance, 50, 549-72 76. Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7 (1), 77– 91. 77. Markowitz, H. M. (1959). Portfolio selection; Efficient diversification of investments. John Wiley and Sons, New York. 78. Markowitz, H. M. (1991). Foundations of portfolio theory. Journal of Finance, 46 (2), 469–478. 79. Moreno, D., and Rodriguez, R. (2009). The value of coskewness in mutual fund performance evaluation. Journal of Banking and Finance, 33 (2009), 1664-1676 80. Moskowitz, J. (2000). Discussion: Mutual fund performance: An empirical decomposition into stock-picking talent, style, transaction costs, and expenses. Journal of Finance, 55, 1655-1703 81. Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34 (4), 768-783 82. Pätäri, E. (2008). Comparative analysis of total risk-based performance measures. The journal of risk, Vol.10, No.4, 69-112 137

83. Peiró, A. (2002). Skewness in Individual Stocks at Different Investment Horizons. Quantitative Finance, 2, 139-146. 84. Pettengill, G., Sundaram, S., and Mathur, I. (1995). The conditional relation between beta and returns. The Journal of Financial and Quantitative Analysis, Vol.30, No.1, 101-116 85. Prakash, A. J., and Bear, R. M. (1986). A simplifying performance measure recognizing skewness. Financial Review, 21 (1), 135–144. 86. Prakash, A. J., Chang, C., and Pactwa, T. E. (2003). Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets. Journal of Banking and Finance, 27, 1375-1390 87. Pratt, J. W. (1964). Risk aversion in the small and in the large. Econometrica 32 (1-2), 122-36 88. Poti, V., and Wang, D. (2010). The coskewness puzzle. Journal of Banking and Finance 34 (8), 1827–1838 89. Rouwenhorst, K. G. (2004). The Origins of Mutual Funds. Yale ICF Working Paper No. 04-48 (December 12, 2004) 90. Roy, S., and Wagenvoort, R. (1996). Risk preference and indirect utility in portfolio-choice problems. Journal of Economics, 63 (2), 139-150 91. Rubinstein, M. (1973). A comparative statics analysis of risk premiums. Journal of Business, 46, 605-615 92. Rubinstein, M. E. (1973). The fundamental theorem of parameter-preference security valuation. Journal of Financial and Quantitative Analysis, 8 (1), 61–69. 93. Rubinstein, M. (1976). The valuation of uncertain income streams and the pricing of options. Bell Journal of Economics, 7, 407-425 94. Shadwick, W. F., and Keating, C. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59-84 95. Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under condition of risk. Journal of Finance, 19, 425-442 96. Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39, 119- 138 97. Shin, H. (2003). Disclosures and Asset Prices. Econometrica, 71(1), 105-133. 138

98. Smith, D. (2007). Conditional coskewness and asset pricing. Journal of Empirical Finance 14, 91-119. 99. Stephens, A., and Proﬃtt, D., (1991). Performance measurement when return distributions are nonsymmetric. Quarterly Journal of Business and Economics, 30 (4), 23–41. 100. Trenor, J., and Mazuy, K. (1996). Can mutual funds outguess the market? Harvard Business Review, 44, 131-136 101. U.S. Securities and Exchange Commission (SEC). (2011). U.S. Securities and Exchange Commission Information on Mutual Funds. Retrieved 2011-04-06. 102. van de Meer, R. (2011). The Dutch view: developing a strategic benchmark in an ALM framework. Managing downside risk in financial markets, Sortino, F. A., Satchell S. A. (eds), Butterworth-Heinemann, Oxford, 26-40 103. Wermers, R. (1997). Momentum investment strategies of mutual funds, performance persistence, and survivorship bias. Working paper, University of Colorado 104. Wermers, R. (2000). Mutual Fund Performance: An Empirical Decomposition into Stock-Picking Talent, Style, Transaction Costs and Expenses. Journal of Finance, Vol. LV, No.4, August 2000 105. Wermers, R. (2011). Performance Measurement of Mutual Funds, Hedge Funds, and Institutional Accounts. Annual Review of Financial Economics, 2011 (3), 537-574 106. Zakamouline, V., and Koekebakker, S. (2009). Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance. Journal of Banking and Finance, 33, 1242-1254

107. Zwet, W. R. van. (1964). Convex Transformations of Random Variables. Math. Centrum, Amsterdam

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BIOGRAPHY

Name Mr. Nathee Naktnasukanjn Date of Birth May 7, 1965 Educational Attainment 2009-2014: Doctoral of Business Administration 1995-1996: Master of Business Administration 1983-1987: Bachelor of Engineering Work Position Managing Director Supply Chain System Co., Ltd. Work Experiences 2007-2008: Senior Operation Development Manager Ek-Chai Distribution System Co., Ltd. 2005-2007: Senior Costing Manger Nike Incorporation Thailand Liaison Office 2004-2005: Senior Business Unit Manager KR Precision Public Co., Ltd. 1990-2004: Senior Manager Seagate Technology Thailand Co., Ltd. 1990: Quality Engineer Chicony Electronic Thailand Co., Ltd. 1989: Engineer Bangkok Datacom Co., Ltd. 1988: Instructor Sritana Commercial and Technology College