ACTIVE VERSUS PASSIVE INVESTMENT - BACHELOR THESIS - DIVA

Bachelor thesis

Active versus Passive
Investment
 - A China and Hong Kong comparison

 Authors: Didrik Brinkestam Persson
 & Johanna Karlsson
 Supervisor: Christopher von Koch
 Examiner: Håkan Locking
 Term: VT20
 Subject: Finance
 Level: Bachelor
 Course code: 2FE32E

Abstract

Investors have been debating whether active or passive management is the better strategy for a
very long time where the majority conclude passive investment the most beneficial strategy in
terms of after cost. Due to limited research in emerging markets, this study examines whether
active or passive management is the most remunerative strategy in mainland China and Hong
Kong, considering the difference in attributes between the regions. Historical data for the Hang
Seng Index (HSI) and the Shanghai Stock Exchange Composite Index (SSE Composite Index)
was used for representing passive funds. To illustrate active management, historical data for
10 active funds for each region were collected. By using two methods including a simple
observation of historical returns and a regression analysis, the results of this study conclude
that no distinct difference can be confirmed between the two regions when regarding whether
the active or passive investment strategy is more beneficial. And in obedience with the majority
of previous literature, passive investments outperform active management in both mainland
China and Hong Kong.

Keywords
Active Investment, CAPM, China, Hong Kong, Index, Passive Investment

 3

Acknowledgments
We would like to express our gratitude to our supervisor Christopher Von Koch and our
examinator Håkan Locking for providing us with valuable guidance and support throughout
this study. Furthermore, we would like to thank our opponents who have given us helpful
comments and constructive criticism.

Thank you,

Didrik Brinkestam Persson & Johanna Karlsson
May 2020

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Table of Content

1. Introduction 7
 1.1 Background 7
 1.2 Problem definition 8
 1.3 Purpose 9
 1.4 Research questions 9
 1.5 Limitations 9
2. Literature review 11
 2.1 Active versus passive investment strategy 11
 2.2 The Hong Kong - China relationship 12
 2.2.1 Geographical disparities 13
 2.2.2 Financial disparities 13
 2.2.3 Social disparities 15
3. Theory 16
 3.1 Metrics for active investment 16
 3.1.1 Active Share 16
 3.1.2 Tracking Error 16
 3.1.3 Combination of Active Share and Tracking Error 17
 3.2 Metrics for passive investment 18
 3.2.1 Index 18
 3.2.2 Sharpe Ratio 18
 3.3 Factor models 19
 3.3.1 CAPM 19
 3.3.2 Fama & French - Three-Factor Model 20
 3.3.3 Carhart - Four Factor Model 21
4. Methodology 22
 4.1 Study Approach 22
 4.2 Data Collection 22
 4.3 Regression analysis 23
5. Empirical Results 25
6. Analysis 29
 6.1 Do active funds outperform the market in terms of historical returns? 29

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6.2 Do active funds outperform the market in terms of regression variables? 30
 6.3 Other aspects of the analysis 32
7. Conclusion 34
8. Further research 35
References 36
Appendix 40

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1. Introduction

 1.1 Background
 In this study, an examination of whether active or passive management is most
 remunerative is being proceeded for two regions; China and Hong Kong. The retrieved
 data is consisting of the output of passive and actively managed funds in China and
 Hong Kong. The hypothesis tested in the paper is whether actively managed funds are
 more beneficial in China than Hong Kong, due to the lower degree of disclosure in the
 mainland of China compared to Hong Kong.

 Investors have been debating whether active or passive management is the most
 beneficial strategy in terms of return, risk, and costs for a very long time. There are
 continuously new takes on the matter presented from various perspectives. During the
 time, several studies of the topic have been developed with different results. A
 pervading theme in these studies is that it has a focus on developed nations.
 Considering previous researches limitation to developed markets, this paper aims to
 further explore the debate in emerging markets with a focus on the role of transparency
 in the matter, and thereby provide the topic with a new perspective.

 Actively managed mutual funds assert that one strives to outperform indexes by using
 research and forecasting. The performance of an actively managed mutual fund depends
 on the management skill of the analysts of the fund and resources for analyzation where
 access to information is of substantial importance. Passively managed mutual funds
 also referred to as index funds, imitates the strategies and investments of a specific
 index so that one may achieve similar results. The active strategy implies higher costs
 than the passive strategy, due to more frequent transactions and research. The usage of
 passive funds has increased during the past years but it is stated that active management
 can benefit the return adjusted for risk (Dan Hunt, 2019).

 When examining the differences in active and passive fund management in China and
 Hong Kong, it is of high importance to be aware of the various trading systems that
 imprint the two areas. The stock market exchange of China was established during the
 beginning of the 19th century and is the largest market in the world, after the United

 7

States. Kimberly Amadeo describes an important aspect of the Chinese stock market is
that the percentage of people in China owning stocks is remarkably low; 7 percent of
China’s population possesses stocks. This has resulted in a situation where several big
investors own a majority of the stocks that are tradeable and have a big impact on the
price movements. In mainland China, there are two stock exchanges; the Shanghai
exchange and the Shenzhen exchange. The Shanghai exchange is the largest one. The
Hong Kong exchange is unified with the Chinese exchanges. It is thereby not a
completely connected part of the Chinese stock market. The Hong Kong exchange was
conveyed from the UK to China during 1997. It has separated jurisdictions from China
and it does also have its own currency. The index for the Hong Kong exchange is Hang
Seng. The corresponding index in China is the Shanghai Stock Exchange Composite
Index. Before 2014, only citizens of China, and a minor amount of fund managers
abroad, were able to trade stocks of mainland China. A program named “Shanghai-
Hong Kong Connect program” was then implemented which made it less restrictive for
foreign investors to trade with shares of companies in China. Today, several companies
are available on the exchanges of both China and Hong Kong (Amadeo, The Balance,
2019).

As previously mentioned, the process of active management of mutual funds requires
information and research. It is important to be aware of the fact that China, as a nation
that is less democratic than the west, has an asymmetric spread of access to information
for domestic and foreign investors. In a study from 2008, Chan and Menkveld conclude
that foreign investors have an informational disadvantage when being compared to
domestic investors on the Chinese stock exchange (Chan and Menkveld, Evidence from
the China Foreign Share Discount, 2008). This transparency aspect needs to be
regarded when comparing the efficiency of active relative to passive fund management.
The reason for this is since active management thereby might be more profitable for
domestic investors than foreign investors when investing in China.

1.2 Problem definition
The majority of previous research on this matter, have proved a passive investment
strategy to be the most beneficial strategy in terms of after cost. Nevertheless, actively
managed funds are widely used in today’s financial markets. Because of the essential

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role information and how easily it is accessed play, along with a domination of studies
on developed markets, China considered being an emerging market known for its lack
of transparency, is chosen. In addition, H. Fromlet (2020) argues, the importance of
examining emerging markets country by country. No country is equal, regardless of
geographical and political similarities, and need to be separated in research. Because of
the unique relationship China have with its SAR Hong Kong, where Hong Kong is both
a part of and independent from the People’s Republic of China, we suggest a
comparison between these two. By carefully studying the two regions' differences and
similarities in attributes, it is possible to evaluate which investment strategy generates
the highest return between the two regions.

1.3 Purpose
This study aims to examine the usage of active and passive management of mutual
funds in Hong Kong and mainland China, considering the difference in attributes
between the regions.

1.4 Research questions
In order to respond to the purpose of this study, two essential research questions will
form the structure of this study. Firstly, the study will compare active and passive
investment management in terms of historical return, risk, and costs.
I. Which strategy of active and passive investment generates the highest return?
Secondly, this study will further examine the results generated in the research question
I. alongside with typical attributes of Mainland China and Hong Kong, with a focus on
the degree of transparency.
II. How is the result of the two investment strategies correlated with the attributes of
Hong Kong and Mainland China?

1.5 Limitations
To give our stated research questions an accurate and reliable answer as possible, this
study contains some limitations. Regarding market selection, a complete limitation is
done to the market in China, including the mainland and Hong Kong region. As for the
time frame, we have chosen to analyze three periods, 3, 5, and 10 years between the
years of 2009-2019. This is done to achieve a detailed investigation of the active and

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passive investment strategies, which according to previous conclusions, is oftentimes
dependent on the underlying time period. In addition, limitations concerning the two
investment strategies have been made. When analyzing passive management, an
assumption that the movements of passive mutual funds are identical to the indices’ is
considered. The chosen indices for Hong Kong and China are the Hang Seng Index
(HSI) respectively the Shanghai Stock Exchange Composite Index (SSE Composite).
The collection of active funds collected have been limited with the requirement that
they must have a primary focus on either of the regions, a combination is not accepted.
Due to limited access to data about the factors included in the extended models of the
CAPM; the Fama & French model and the Carhart model, the test for the hypothesis of
the study will be focused on the CAPM.

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2. Literature review
 Whether actively managed investments are more beneficial than index managed funds is
 an extensive discussion in financial literature. In order to clarify some of these findings we
 have chosen to divide this literature review into two parts; Active versus passive investment
 strategy and The Hong Kong and China relationship, were the latter chapter contains some
 subchapters.

 2.1 Active versus passive investment strategy
 The majority of previous research claims passive management the more beneficial
 strategy. A great part of the literature supporting passive investments is established in
 the theory of the efficient market hypothesis. This theory states that stocks trade at their
 fair market value and it is therefore impossible to outperform the market. A notorious
 supporter of this investment strategy, Malkiel (2003), refers to the efficient market
 hypothesis as the random walk. The random walk indicates that changes in stock prices
 confide in news and that tomorrow’s price changes do not necessarily reflect a departure
 from today’s price changes. Therefore, price changes must be unpredictable and
 random, as well as a reflection of all available information on the market. Further
 Malkiel (2003) argues that even if an inefficient market would occur, passive
 management would still be a winning strategy because of the additional expenses, such
 as transaction costs and management fees, active management entails. A numerous
 researches come to this exact or similar conclusion.

 By the arithmetic of active management, Sharpe (1991) implies that simple principles
 of arithmetic illustrate how two assertions must be true; the average active return will
 equal the average passive return, before costs, and the average actively return will
 underperform the average passive return, net of costs. The latter assertion is due to the
 high fee and transaction costs that come with active management. Likewise, Fama &
 French (2010) support this conclusion were the high costs of active management defeat
 the possibility of actively managed funds outperforming the market. However, by
 bootstrap simulations1, they do conclude that if managers with sufficient skills to

1
 Bootstrap simulations refer to a statistical method were you resample an original dataset in order to create
simulated samples and thereby estimate summary statistics such as standard error and obtaining confidence
interval. This method is an alternative technique to the traditional hypothesis testing.

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outperform the market exists, they are hidden in the aggregate result of insufficient
 skilled managers' performance.

 Sorensen et. al. (1997) continues the debate about active versus passive management
 and conclude that the best strategy depends upon the state of the market. During bear
 market years, active investors will likely come out as winners, and during bull market
 years index investors will be the best performers.

 Despite the above mentioned literature, several researchers are claiming the opposite.
 A supporter of the active management is Kosowski et al. (2006) who introduced a new
 bootstrap statistical technique when measuring equity mutual funds in the U.S. with the
 time series of 1975-2002. Their findings revealed a new perspective were a “sizeable
 minority” of managers turns out to have the ability to select stocks that cover their costs.

 The active management supporters Cremers & Petajisto (2009), introduces Active
 Share as a new way of measuring active portfolio management. Active Share represents
 the deviation of the portfolio holdings from the benchmark index holdings. Hence,
 Active Share can be defined as the “fraction of the portfolio that is different from the
 benchmark index”. This concept will be further interpreted in the following theory
 chapter.

 2.2 The Hong Kong - China relationship
 In 1997, the former British colony, Hong Kong, returned to Chinese control. The
 handover agreement introduced the one-country-two-systems principle, which refers to
 Hong Kong as both a part of and its independence to China (J. Falcioni. 2017). In the
 article “One country Two systems” as Bedrock of Hong Kong’s Continued Success:
 Fiction or Reality?, H. Yeung and F. Huang explain how this principle, later on, was
 converted into the Sino-British Joint Declaration and Basic Law of Hong Kong,
 together with clarifying its main commitments. The following promises for Hong Kong
 apply; The Hong Kong Special Administrative Region (HKSAR 2) government must

2
 Special Administrative Regions, SARs, refer to Hong Kong and Macau as regions within the People’s
Republic of China. The SARs are primarily characterized as regions with an extent sovereignty from the
mainland of China.

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consist of Hong Kong residents; the lawmakers shall be established by election; judicial
 power must be independent and settled by the SAR; all residents shall have the right to
 freedom of speech; Hong Kong's social and economic system and, the residents' way
 of living, will remain unchanged in the forthcoming fifty years (H. Yeung and F. Huang.
 2015). In order to clarify the unique relationship between Hong Kong and China, this
 chapter is subdivided into three subchapters; geographical, financial, and, social
 disparities.

 2.2.1 Geographical disparities
 Hong Kong and China are very different from a geographical point of view, which in
 turn have a huge impact on the regions’ social and financial systems (S. Zhao. Y. Chan.
 C. Ramón-Berjano. 2012). With a population of nearly 1.4 billion in 2018, contributing
 somewhat to 18.5% of the world's total population, China is the most populous country
 in the world. Hong Kong, on the other hand, consisting of a much smaller area, has a
 population of 7.45 million. This makes China almost 200 times larger than Hong Kong.
 As an emerging market3, China is characterized by high economic growth and growth
 potential. In 2018 the GDP growth rate was 6.6%, which is more than two times higher
 than Hong Kong's growth rate of 3% the same year. As anticipated, China had a GDP
 rate of $ 13.61 trillion in 2018, making it the second in the world after the U.S. The
 same year Hong Kong's GDP rate was $ 362.7 billion. (World Bank, 2020)

 2.2.2 Financial disparities
 Despite successful changes in economic policy over the past decades, China's financial
 market is still limited in various ways (H. Fromlet, 2020). A pegged exchange rate,
 limited investments, and a great number of government-owned industries are essential
 aspects when looking at the restrictions in China’s financial market.

3
 The term emerging market, sometimes referred to as an emerging country, was established by the International
Finance Corporation’s (IFC) Antoine van Agtmael in 1981.He changed the often negative attitude towards the
“Third World Countries” by defining emerging markets with “suggested progress, uplift, and dynamism”.
Hence, an emerging market can be defined as a developing country with progress in adapting global economic
and market oriented reforms (H. Fromlet. 2020). Apart from low-to-mid per capita income, high volatility, and
commodity and currency swings, these markets are mostly characterized with high economic growth and growth
potential.

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China's currency comes by two names, Yuan (CNY) and Renminbi (RMB). Renminbi
 means “the people's currency” and is the official name of the Chinese currency,
 announced by the Communist People’s Republic of China in 1949. Yuan, on the other
 hand, refers to the unit of account of the Renminbi currency (BBC, 2010). China has a
 somewhat modified fixed exchange rate since it is pegged to a basket of currencies
 illustrating its trading partners, dominated by the U.S dollar. This is done so as to
 control its export to the U.S. is fairly priced when sold. This is a favorable access
 wanted by most countries but only accomplished by a few. China, with its command
 economy 4, has the ability to manage its currency well (The Balance, 2019).

 Before 2014, investments in mainland China was limited and only Chinese citizens and
 a small number of foreign investor were able to trade at the Chinese stock exchange.
 When the “Shanghai-Hong Kong Connect program” was implemented, investors on
 both markets were able to trade at each stock exchange. This program also made it less
 restrictive for foreign investors to trade stocks in mainland China. Despite the connect
 program, only a small percentage of the people in China own stocks. Instead, the
 primary funding of Chinese companies is bank loans. Although a large number of
 private banks exist, there are restrictions regarding their activities. Consequently, the
 four largest government-owned banks dominate the capital in China. And, with only
 7% of the Chinese citizens owning stocks, the price movements of the tradable stock
 are primarily influenced by a small number of big investors owning a majority of all
 stocks (The balance, 2019).

 The Basic Law of Hong Kong assured Hong Kong with its own monetary and financial
 policies, alongside with its own currency, Hong Kong dollars (HKD) (S. Zhao et.al.
 2012). Hong Kong uses a fixed exchange rate and has been pegged to the U.S. dollar
 since 1983 (Reuters, 2017). As a former British colony, Hong Kong is consequently
 more western-influenced than China. Moreover, the region is seen as a global financial
 leader, and have been ranked as number three by the past two Global Financial Centres
 Indexes (GFCI 25 and GFCI 26), behind London and New York. In the meantime,
 Shanghai was ranked fifth. As for the latest GFCI 27 rank, Hong Kong was surpassed

4
 In a command economy the central government controls a country's economy, and the traditional market
economy laws of supply and demand is ignored.

 14

by Shanghai and put as sixth, whereas Shanghai was put in fourth place. This is most
likely due to the recent political turmoil in Hong Kong. (Long Finance, 2020)

2.2.3 Social disparities
In the article “Social Policy Under One Country Two systems; Institutional Dynamics
in China and Hong Kong since 1997” published in 2003, Ian Holliday and Linda Wrong
highlights four main differences in the social policy between the two regions. With huge
differences in size and complexity, China suffers a larger income disparity than Hong
Kong. China's heterogeneous social policy is displayed in significant differences when
it comes to e.g. social security, insurance, and, income. I. Holliday and L. Wrong
present three groups which represent the Chinese population; an upper deck including
high-income residents, a lower tier with farmers, and lastly a gray zone for residents
somewhere in between. On the other hand, Hong Kong has a homogenous social policy
where all residents have equal rights to public benefits and services. Secondly, the
welfare system in Hong Kong is at a much higher level of maturity than in China. Third,
the direction of the region's reforms differs with China focusing on the social policy
and improving efficiency while Hong Kong concentrates on austerity and cautiousness
with its fiscal policy. Lastly, differences in management structures that are responsible
for overseeing the implementation of social programs exist. (I. Holliday. L. Wrong.
2003)

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3. Theory

 3.1 Metrics for active investment
 Research mainly refers to two methods when discussing active management, the
 traditional method Tracking Error, and the newest developed method Active Share.
 Additionally, a combination of the two is widely used.

 3.1.1 Active Share
 In 2006, Martijn K. J Cremers and Antti Petajisto established a new method to measure
 performance in actively managed portfolios called Active Share. As previously
 mentioned, the method can be defined as the “fraction of the portfolio that is different
 from the benchmark index”. By comparing the weights of each holding in the mutual
 fund with the weights of each holding in the index fund, a proportion of active share
 can be estimated. Cremers and Petajisto (2009) illustrates this with the following
 formula;
 1
 ℎ = 2 ∑ 
 =1| , − , |,

 where , represents the weights of asset i in the fund and , represents the
 weights of assets i in the index. The authors further explain this idea with the terms
 active long position and active short position. Funds where the stock weight exceeds
 the index weight, have an active long position in it. Funds that underweight a stock
 compared to the index weight, or do not buy at all, have an active short position in it.
 According to this, a decomposition can be made by any portfolio into a 100% index
 position, including a zero-net-investment long-short position. The comparison between
 the weight of this long-short portfolio with the total portfolio represents the active share.
 Hence, it is necessary to divide the sum of the portfolio weight differences by two in
 case a deviation of zero would occur, mathematically that fund will receive an active
 share of 100%. I.e. the long and short positions are not separated in calculations.

 3.1.2 Tracking Error
 The traditional way of measuring active management is tracking error. Tracking error
 can be defined as the standard deviation of the difference between the returns of a fund

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and the index over a given time period. A general formula is presented in Cremers and
Petajisto (2009);
 = [ , − , ],

where, , is the return of the fund over a certain time and , refer to the
return of the index over the same given time period. Hence, tracking error illustrates
how actively managed a fund is along with the level of risk. The active fund manager
desire to achieve a greater return of the fund compared to the return of the index.
Simultaneously, the manager has the ambition of a low tracking error as possible.
Consequently, to minimize the risk of underperforming the index, a low standard
deviation percentage should be attained.

3.1.3 Combination of Active Share and Tracking Error
Cremers and Petajisto (2009) recognize two ways active managers can operate, by stock
selection or factor timing. Stock selection involves picking stocks with attributes of
generating a greater return than the return of an index portfolio. Factor timing, on the
other hand, means selecting securities based on factors associated with higher returns.
In order to analyze active management further and capture both of the above mentioned
methods, Cremers and Petajisto (2009) advocate a combination of Active Share and
Tracking Error. Active share with its equal exposure to systematic risk is equivalent to
stock selection, whereas tracking error with more focus on systematic factors is
corresponding to factor timing. The proportions of active management can be
illustrated in figure 1.

Figure 1. The relationship with different investment strategies of the two dimensions of active
management, active share and tracking error (Cremers, M. K. & Petajisto, A. 2009).

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According to Cremers & Petajisto (2009), a portfolio with diversified stock picks can
 achieve a high level of active share regardless of its low tracking error since its selected
 stocks within an industry can still deviate from the index holdings. On the other hand,
 a portfolio consisting of factor bets can achieve a high tracking error without deviating
 much from the index holdings. Further, a portfolio with concentrated stock picks, is a
 combination of diversified stock picks and factor bets, meaning the holdings focus on
 both individual stocks and systematic factors. Lastly, a closet indexing portfolio, have
 a low level of active share as well as tracking error, yet it is still classified as active.
 Consequently, an index fund does not consist of any level of either active share or
 tracking error.

 3.2 Metrics for passive investment
 When measuring the performance of a passively managed portfolio analysts often use
 a benchmark for evaluation. A benchmark often referred to as an index, estimates the
 performance of a portfolio with securities designated to represent a particular area of
 the market.

 3.2.1 Index
 The index chosen to examine the passive investment strategy in this study is the
 Shanghai Stock Exchange Composite Index (SSE Composite Index) and the Hang Seng
 index (HSI). The SSE Composite Index, established in 1990, is the biggest in mainland
 China. The index is capitalization-weighted 5 and tracks the development of all A and
 B shares that are listed on the Shanghai Stock Exchange. The HSI is a free-float
 6
 capitalization index including a selection of companies from the stock exchange of
 Hong Kong. The index is separated into four different categories; Commerce and
 Industry, Finance, Utilities, and Properties (Bloomberg, 2020).

 3.2.2 Sharpe Ratio
 The Sharpe Ratio was created by William Sharpe in 1966. The ratio is a measurement
 of the risk and return relationship and it has been frequently used in the finance sector;
 it is in fact one of the most popular ratios due to its simplicity. Sharpe describes the

5
 A capitalization-weighted index consists of securities that are weighted to their total market capitalization.
6
 A free-float capitalization index consists of all securities that are available for trading in the market.

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Sharpe Ratio as a ratio that is used to estimate the expected increase in return that one
 will retrieve by enhancing the volatility. The formula for the Sharpe Ratio is illustrated
 below.
 ( − )
 ( ) =
 ( )

 The computation of the ratio is consisting of the following variables; the investment
 ( ), the average rate of return ( ), the return of a risk-free security ( ), and the
 standard deviation of ( ( ) ). To understand the function of each variable in
 the formula, a further explanation is necessary. The average rate of return, , can be
 structured in various perspectives of time, e.g. daily, weekly, monthly. On the other
 hand, the criteria that are needed for one to be able to use different time perspectives is
 that the returns have to be normally distributed. The previous fact is also the deficiency
 of the ratio. In other words, a skewed distribution of the returns can be problematic
 when computing the Sharpe Ratio due to the lower impact of the standard deviation as
 a result. Using the formula of the Sharpe Ratio with a data set that is not normally
 distributed can result in a misleading result. The risk-free rate of return, , is included
 in the formula to examine whether one is accurately compensated for the risk that is
 taken with the investment. Short-dated T-bills are common securities used to
 correspond to the risk-free rate of return. With the variables explained above, one will
 be able to compute the excess return. The last step is to divide the excess return with
 the standard deviation of the risky asset (Morningstar, 2015).

3.3 Factor models
 3.3.1 CAPM
 The Capital Asset Pricing Model, CAPM, is widely used. The Corporate Finance
 Institute describes CAPM as a model that displays the relationship between non-
 diversifiable risk and expected return (Corporate Finance Institute, What is CAPM,
 2017). Damodaran (2012) further explains that when computing the expected return
 with the capital asset pricing model, one will use the variance as an indicator of risk.
 As mentioned above, the non-diversifiable risk, systematic risk, is an important factor
 in the model. The systematic risk is symbolized by beta, , which then is translated into
 the expected return. The CAPM-formula is displayed below,

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 = + ( − ),

Where, corresponds to the risk-free rate, is the expected return on the market
index, and is the cost of equity. The process of subtracting with results in the
market risk premium. It is vital to be attentive to the limitations of the Capital Asset
Pricing Model. Damodaran elucidates the fact that the variables of the model might lack
precision as well as that the model needs unrealistic assumptions (Damodaran, “Models
of Risk and Return”, 2012). The CAPM is thereby not completely reliable but as long
as the risk aspect is taken into account as well as combining CAPM with other models,
of similar purposes, it can be useful.

3.3.2 Fama & French - Three-Factor Model
The Fama & French Three-Factor Model was developed by two professors at the
University of Chicago. It is described as an extension of the Capital Asset Pricing
Model. With the Fama-French model, one is able to explain returns on stocks with three
different factors. These factors are market risk, the outperformance of small-cap
companies compared to large-cap companies, and the outperformance of high book-to-
market value companies, value stocks, relative to low book-to-market value companies,
growth stocks. An underlying theory in the Fama-French model is that small-cap, as
well as high-value companies, tend to continuously perform better than the general
market. The Corporate Finance Institute displays the Fama-French model as follows:
Expected Rate of Return = Risk-free Rate + Market Risk Premium + SMB + HML
SMB denotes small minus big and HML corresponds to high minus low. The
mathematical way to illustrate the relationship that Fama-French examines is by using
the following formula;

 = + 1 ( − ) + 2 ( ) + 3 ( ) + 

 represents the historic excess return of small-cap companies over large-cap
companies. is the historic excess return of value stocks over growth stocks
(Corporate Finance Institute, Fama-French Three-Factor Model, 2020).

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3.3.3 Carhart - Four Factor Model
As mentioned above, the Fama-French Three-Factor model is an extension of the
Capital Asset Pricing Model. The Carhart Four Factor model is another model with a
further extension of the Fama-French Three-Factor Model. The model was introduced
by Mark Carhart in 1997, four years after the Fama-French model. The Breaking Down
Finance describes that it has the same structure as the Fama-French model but it does
also include a variable for cross-sectional momentum. The purpose of including this
variable in the model is to strengthen the result in an explanatory aspect. Carhart
discovered how the usage of a momentum factor in the model made it possible to
explain the performance of mutual funds in a better way. The formula below illustrates
the complete Carhart model.

 = + 1 ( − ) + 2 ( ) + 3 ( ) + 4 ( ) + 

The different variables are explained in the chapter of the Fama-French model. The new
factor included making it an extended model from the Fama-French, is , which
corresponds to the cross-sectional momentum factor (Breaking Down Finance, Carhart
4 Factor Model, 2019).

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4. Methodology

 4.1 Study Approach
 To be able to test the hypothesis whether actively managed funds are more yielding in
 Hong Kong or China, a time series approach will proceed with comparisons of the
 returns of the different strategies in the two areas. As presented in the literature review,
 previous studies, of different aspects of the matter, use time series when examining the
 topic. This study will thereby follow the same approach during the investigation. To
 calculate the return in the different time periods for the two investment types, the
 holding period return formula, HPR, will be used;

 ( 1 − 0 )
 =
 0

 After calculating the daily return for the three time periods, an average will be computed
 for each term. To further examine the hypothesis, a regression analysis will be
 performed. The regression analysis will display whether the hypothesis will be rejected
 or not, on different levels of significance. The regression will be performed with the
 regression of the Capital Asset Pricing Model. With regard to the two methods
 performed in the study, the results will be analyzed and a conclusion will be made.

 4.2 Data Collection
 The data used to examine the relationship between actively and passively managed
 funds in China and Hong Kong was retrieved from Datastream. All data was gathered
 on a daily basis between the years of 2009 - 2019. This will benefit the study when
 performing the regression analysis since a greater number of observations will result in
 a more precise estimation as well as a higher level of reliability in the variance and
 standard deviation. Also, the data is collected in each region’s currency, Hong Kong
 Dollar for Hong Kong and Renminbi (Yuan) for China. This is done to be able to regard
 the exchange rate changes when analyzing. The data was collected on the 20th of April,
 2020.

 As presented, we assumed that the passive funds would correspond to the index
 development for the Hang Seng Index (HSI) and the Shanghai Stock Exchange

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Composite Index (SSE Composite Index). The SSE Composite Index is the largest
index in China and was thereby used to represent the Chinese index. Due to restrictions
in time, both the Shanghai Stock Exchange and the Shenzhen index could not be
included. The data gathered for the passive funds was thereby collected from the index
performance during the last decade for the HSI and SSE Composite Index. The average
return on the index, during the decade, was separated into three, five, and ten year
periods to enable an investigation of the changes for different time periods. When
computing the return for the three and five year periods, data for all possible three and
five year periods in the 10-year interval was used. This strategy was used in order to
get a more reliable computation of the average returns for the different periods.

As can be seen in Appendix 1 List of mutual funds in the sample, historical data was
collected for a total of 20 different active funds. 10 funds representing mainland China
and vice versa. During the process of finding appropriate funds to use for the study, an
underlying requirement was formulated; the selected funds representing active funds in
China had to have a primary focus on mainland China and the funds representing Hong
Kong needed to have a main focus on Hong Kong. More concrete, the objective of
funds representing active investments in China can be identified with words such as
mainland China, the People’s Republic of China, and, exclusion of SARs. Equivalently,
the active Hong Kong funds have objectives that emphasize a mainly, primarily,
principally focus on Hong Kong. The requirement presented when selecting the active
funds was of high importance since mixed funds would give unreliable results when
examining the hypothesis. As a result, the number of active funds selected for the
regions was limited to 10 each. When computing the average return for the different
active funds, it was divided into the same time periods as for the passive funds to
retrieve comparable data.

After dividing the two data sets into different time periods, one will be able to relate it
to the efficient market hypothesis which was presented in earlier chapters of the study.

4.3 Regression analysis
Harvard Business Review explains regression analysis as a tool to explore what
variables that have an impact on a certain dependent variable. It does also explain the

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interaction between these impacting variables. By using the Capital Asset Pricing
Model as a regression, an examination of the hypothesis of the study is performed.
Since the CAPM is the tool for the regression, the following variables will be included;
 = + ( − ). Before including a beta in a model, one needs to get further
insight into what beta measures and how it is used. Aswath Damodaran depicts that
beta corresponds to the risk that a fully diversified portfolio implies, in other words, the
systematic risk. Another aspect one needs to be aware of with the beta is that it is a
measurement of an assets’ relative risk and is thereby positioned around one
(Damodaran, 2012). To obtain the beta for the study, Stata was used which provides
one with the beta after performing a regression.

Another variable required for the regression is the risk-free rate. Damodaran describes
two conditions that need to be fulfilled when retrieving a risk-free rate. The first
condition is that there cannot be a default risk. The second condition displays that there
cannot be any reinvestment risk either (Damodaran, 2012). For this study, an
assumption that each regions’ fixed coupon government bond bid yield fulfills the
requirements of being a risk-free rate is being made. The risk-free rate chosen for China
is a treasury bond issued by the government of the People’s Republic with a 10-year
maturity. It has received an A+ rating by S&P. The risk-free rate representing Hong
Kong is issued by the government of Hong Kong with a 10-year maturity and is rated
by the S&P with an AA+ (Datastream, 2020). The risk-free rates for both China and
Hong Kong were retrieved from datastream and before put in use, recalculated to a ten-
year daily basis.

Once the variables were all gathered, it was possible to perform the CAPM regression
in Stata. With the computation, one could conclude whether the active funds have been
overperforming the index or not, depending on a positive or negative result, in China
and Hong Kong.

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5. Empirical Results

 5.1 Observation of returns
 The first method computed is primitive and is based on an observation of the returns
 for Hong Kong and China’s active and passive funds.

 Figure 2. Hong Kong returns of active funds and index.
 Series1 = average return of active funds
 Series2 = average return of index

 First, a comparison of the returns of the active funds in Hong Kong with the returns of
 the index funds was proceeded. The three-year return for the passive funds in Hong
 Kong amounted to 0.0231%. The return for the selected active funds in Hong Kong was
 slightly higher, 0.0318%. In other words, the active funds had a higher return with
 0.0087 percentage points. When regarding the five year period, the result was similar
 to the first period measured. The passive funds for the five year period had a return of
 0.0210% and the active funds a return of 0.0293%, thus a difference of 0.0083
 percentage points. Last, the returns of the ten year period were measured. When
 observing the returns for the ten year period, one can conclude that the passive funds
 had a return of 0.0314%. The return of the active funds was 0.0421%. The return for
 the active funds did thereby outperform the index funds with 0.0107 percentage points.

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Figure 3. Chinese returns of active funds and index
 Series1 = average return of active funds
 Series 2 = average return of index

When observing the performance in the three year period for the Chinese funds, one
can easily comprehend that the return for the active funds is larger than the one for the
passive funds. In a three year perspective, the passive fund had a return of 0.0149%,
whilst the usage of active funding resulted in a return of 0.0245%. For the first time
period, the actively handled funds did thereby outperform the passively managed funds
with 0.0096 percentage points. However, when examining the five year period, it is
comprehensible that the gap between the two types is smaller than for the first time
period. In the period, the passive funds achieved a yield of 0.0229%. The return for the
active funds in the same period was 0.0270%. Hence, a difference of 0.0041 percentage
points between the index-tracking funds compared with the active funds. Moreover, for
the last time period, the gap is once again large between the two types of funding. The
rate of return for the active funds in the 10 year period reached a level of 0.0378%. The
passive funds had a yield of 0.0274%, thence a difference of 0.0104 percentage points.

To conclude, the actively managed funds did thereby outperform the index funds for
each of the different time periods, both for Hong Kong and China.

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5.2 Regression analysis
To examine whether the actively managed funds over- or underperformed the index,
the CAPM regression (see 4.3 Regression Analysis) was performed in Stata. The data
used for the regression amounted up to a total of 2868 observations.

Hong Kong was the first subject for the regression. After performing the regression,
one could easily observe the key variables for the result. The first variable significant
when analyzing was the beta, which indicates the correlation between the fund and the
index. The second variable of significance was the alpha, which describes the
performance of the fund in relation to the index. Lastly, the results of R-squared and
the level of significance will be presented.

 Table 1. Regression variables for 10 Hong Kong Funds; alpha, beta, R-squared, and, level of
 significance

The beta for the first Hong Kong fund was 0.976. The computation of the alpha for the
first Hong Kong fund resulted in a value of -0.0000292. The distribution of the result
was very similar for all of the Hong Kong funds. They all followed a homogenous
pattern, chiefly for the alpha, as illustrated above. The average beta and alpha for the
10 Hong Kong funds approximated to 0.9916 respectively -0.0001. The stars to the
right of the different funds indicate on what level of confidence that the result is
significant. All funds are significant on a 99% level of confidence, explained by the
three stars. The R-squared illustrates to what extent changes in the return of the index
can be explained by variations in the return of the active funds. The average R-squared
for Hong Kong was 0.8336.

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Table 2. Regression variables for 10 China Funds; alpha, beta, R-squared, and, level of significance

After proceeding the regression for Hong Kong, an identical regression was performed
for China. When regarding the result of the regression for the Chinese funds, it is close
to the result of the Hong Kong funds. The first Chinese fund had a correlation with the
index, beta, of 0.562. The alpha of the fund corresponds to a digit of -0.000145. As for
the Hong Kong Funds, the variables of the different Chinese funds were very much
alike as one can conclude from observing the table above. The average alpha for the 10
Chinese funds, equivalent to the result for Hong Kong, was around -0.0001. The
average beta amounted up to 0.5202 which is a noteworthy difference compared to the
Hong Kong result. The active funds in China received three stars, as well as the Hong
Kong funds. The R-squared reached a level of 0.2762.

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6. Analysis
In this chapter, we analyze whether our active funds outperform the market or not. This is
done in three subchapters; first, we simply examine the returns of the funds compared to
the returns of the indexes for both regions. Secondly, we analyze the outcome of the
regression variables, such as alpha, beta, R-squared, and significance level. Lastly, we will
do a final analysis where we combine the analysis with other important aspects of the
matter.

Before proceeding the analysis for this study, it can be beneficial to once again present the
hypothesis of the matter. The hypothesis of the study was whether actively managed funds
would be more remunerative in China compared to Hong Kong since the degree of
disclosure is of a lower level in the mainland of China in relation to the region of Hong
Kong. It is also significant to once again remind one of the efficient market hypothesis. As
presented in the literature review, the theory of the efficient market hypothesis claims that
all stocks do trade at the fair market value, hence it is not possible to outperform the market.
Further, the theory states that even if a market would be inefficient, the passively managed
funds would still be more profitable, since active management entails expenses such as
transaction costs and fees. The majority of previous research presented in this study come
to this exact or similar conclusion.

 6.1 Do active funds outperform the market in terms of historical returns?
 When observing the returns of the funds and the indexes, it was clear that the actively
 managed funds amounted up to a higher return than the return of the passive funds, for
 all of the different time periods in both China and Hong Kong. However, the
 outperformance of the actively managed funds towards the index funds was not large.
 One can easily realize that including eventual expenses carried by the active funds,
 would minimize the difference between the two strategies. So, if expenses are not
 included, the efficient market hypothesis would be applicable to this situation since it
 is clear that the passive funds are not far away from the same performance as the
 actively managed funds. Expenses entailed with the strategy is though in most cases
 included. On the other hand, there is still a difference in the return of the two strategies,
 large or not, that indicates that the theory of the efficient market hypothesis is, in this
 case, false. The largest difference between the two strategies was when measuring the

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10 year period, for both of the regions. This fact is not in line with the theory of the
efficient market hypothesis since it states that there might be deviations from the fair
market value of stocks in the short run, but not in a long perspective. However, the
efficient market hypothesis is not in line with the excess returns that are presented for
the active funds in both China and Hong Kong. When further evaluating Sharpes (1991)
simple principles of arithmetic, the outcome of the results does not completely
correspond to his assertions. The first assertion that the average active return will equal
the average passive return before costs cannot be confirmed. By assuming that the
expenses active funds entail are included, neither can the second assertion, that the
average active return will underperform the average passive return, net of costs be
applicable in this study.

6.2 Do active funds outperform the market in terms of regression variables?
The computation of the CAPM regression was of a more advanced level than the
observation of the pure returns. It was used to test the hypothesis of the study in a more
reliable way, rather than just observing rates of returns for different periods of time. As
one clearly can conclude, the result was similar for all of the funds in the respective
region; the average alpha, over/underperformance of the index, was -0.0001 in China
and Hong Kong. The funds do thereby perform slightly worse than the index. Since the
data is daily, this difference can on a yearly basis give rise to a great monetary
difference. On the other hand, an interesting aspect is the betas for Hong Kong and
China. The distribution of the Hong Kong betas is close to 1; an average beta of 0.9916.
Moreover, when regarding the betas for the Chinese funds, an average was computed
to 0.5. From this, one can terminate that the Chinese funds have a lower correlation
with its index compared to the Hong Kong funds with the Hang Seng Index. This can
be due to the chosen Chinese index for this study, the Shanghai Stock Exchange
Composite Index. Since China is consisting of two indices, the Shanghai Stock
Exchange Composite Index and Shenzhen Index, excluding the Shenzhen index from
the regression analysis can be an explaining factor in the low betas for China. The cause
of this is that investments and returns on the Shenzhen index by the chosen funds are
not included in the data. If a number of the active funds in China, chosen for the study,
competes with the Shenzhen index, it is not unclear that the funds do not have a high
correlation with the Shanghai Stock Exchange.

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Another explaining factor for the outcome of the betas can be exchange rate changes.
Even though the collected data is in each region's currency, the funds' primary trading
exchange rate can differ depending on the type of shares. Generally, A-shares are traded
in Renminbi in contrast to B-shares which are oftentimes traded in U.S. dollar. When
converting the share price, values may deviate because of the different exchange rate
changes.

When considering Sorensen et. al. (1997) argument that the best investment strategy
depends upon the state of the market, the results of the regression may be suitable. The
chosen time period of this study, 2009-2019, has been recognized as the longest bull
market in history (Forbes, 2019). According to Sorensen et. al., during bull market years
passive investors will most likely come out as winners. When analyzing the outcome
of the alphas in the computed regressions, one can conclude that the funds underperform
the index for both regions and thereby have index investment been the most profitable
strategy in the past 10 years.

As mentioned when presenting the results for the regression analysis, the variable titled
r-squared describes to what extent the variations in the index can be explained by
variations in the active funds. One could observe that the level of the r-squared for
China, 0.2762, was substantially lower than the r-squared for Hong Kong, 0.8336. In
other words, the variations of the Hang Seng index can be explained by the variations
of the active fund for Hong Kong in a higher degree than the Shanghai index related to
the active Chinese funds. This fact is most likely connected to the aspects of the low
betas for the Chinese funds; that the Shenzhen index is excluded and the correlation is
thereby misleading since the funds might have a main focus on the Shenzhen index and
not the Shanghai index. For the Hang Seng index, the variations of the index can be
explained in a high degree by the variations of the active funds. Another important
aspect of the result is the level of significance of the result. All funds received three
stars which indicate that the result is significant on a 99% level of confidence.

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6.3 Other aspects of the analysis
When looking back at the methods of active management one can easily separate them.
The traditional method tracking error is based on historical returns where you compare
the differences in returns and standard deviation of a fund and its index. Active share,
however, displays the present position when comparing the holdings of a fund with the
holdings of the index. In order to analyze the outcome of the active funds in this study,
we regard Cremers and Petajisto (2009) suggested model illustrating a combination of
Active Share and Tracking Error.

Figure 2. The relationship with different investment strategies of the two dimensions of active
management, active share and tracking error (Cremers, M. K. & Petajisto, A. 2009).

The active funds chosen in this study are concentrated on an assumption of a primary
focus on either mainland China or Hong Kong. Based on the outcome of the regression
analysis, one can examine the active management of the funds in figure 1. If the fund
manager diversifies its stock picks within an industry, it will receive a high level of
active share. If the manager simultaneously diversifies its stock picks across industries,
given no systematic risk relative to its index, a low tracking error can be accomplished.
In contrast, fund managers betting on factors will achieve a high tracking error without
deviating much from the index. When looking at the funds for both China and Hong
Kong, one cannot say if the fund managers focus on factor bets or diversified stock
picks. Hence, most likely a combination of the two is used and the managers may use
concentrated stock picks. This assumption concludes that the funds possess a high level
of both active share and tracking error. However, when regarding the results of both
historical returns and beta for Hong Kong, one may conclude that the fund managers

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use closet indexing. This because of the similar result of the returns between the active
funds and the Hang Seng Index and the average beta of 0.9916 which indicates that the
active Hong Kong funds have a very close correlation with the index. Although a low
level of active share and tracking error, the funds are classified as active. In addition,
as Cremers & Petajisto (2009) says, a fund can only outperform the index by deviating
from it. The close correlation of the funds with the index results in an underperformance
compared to the index as can be seen in the negative alphas for the Hong Kong funds.
When looking at the active Chinese funds, similar conclusions can be drawn, apart from
the funds significantly lower average beta of 0.5202. This is due to the exclusion of the
Shenzhen Index and it is therefore not possible to estimate the level of active
management in these funds. If one would include the Shenzhen index as well, one
would be able to do a further analysis of the Chinese funds in this matter. In summary,
for a more precise and reliable estimate of the degree of active management these funds
contain, extended and more encompassed data must be controlled for.

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7. Conclusion
After presenting and analyzing the two different methods when examining the hypothesis,
one can conclude that the result was split. The first method indicated that the active funds
generated a higher return rather than investing in the index funds for both Hong Kong and
mainland China. On the other hand, when observing the result and analysis of the regression
analysis, the result is different. When regarding the variables from the regression for Hong
Kong, it was clear that the passive funds outperformed the active funds. The alpha of -
0.0001 might from a quick observation look insignificant, but as mentioned in the earlier
chapter, the data is daily so on a yearly basis it can result in a crucial monetary difference.
The same reasoning applies to China since the average alpha was identical. Further, the
regression analysis, which entails a higher degree of reliability than the first method,
illustrates that the passively managed funds were more gainful than the actively managed
funds.

To reconnect to the hypothesis, one is thereby not able to observe differences in China and
Hong Kong regarding the efficiency of the different managing methods of funds, despite
the difference in the systems between China and Hong Kong. Even though the results are
split, regarding the two examining methods, the regression analysis is more detailed and is
more reliable when proceeding with a concluding argument. Also, it is still of high
importance to be aware of the fact that the movements of the Chinese index, is primarily
affected by a minority of the population with holdings in these funds. With China being the
most populous country in the world, their high income diversification must be regarded
when analyzing the outcome of this study.

In conclusion, no distinct difference can be confirmed between the two regions when
regarding whether the active or passive investment strategy is more beneficial. And in
obedience with the majority of previous literature, passive investments outperform active
management in both mainland China and Hong Kong.

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8. Further research
For future studies within this subject, both deepened and different perspectives can be
considered in order to improve the accuracy and reliability of the research. Firstly, a greater
number of observations is advocated when it comes to the precision of the estimations and
reliability in variance and standard error. As a suggestion, a greater number of active funds
should be collected along with comparing the studies with several indices. Also, extended
data to estimate the level of active management can be collected. To further be able to
understand the relationship between China and its SARs, in addition to Hong Kong one
may also include Macau in the research. Lastly, to get a more precise result when examining
the two investment strategies, one may correct for before and after transaction costs.

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