Application of capital asset pricing model (capm) in analysis of listed retail stocks on the vietnam stock market

0 Dissertation submitted in partial fulfillment of the Requirement for the MSc in Finance FINANCE DISSERTATION ON APPLICATION OF CAPITAL ASSET PRICING MODEL CAPM IN ANALYSIS OF LISTE

0

Dissertation submitted in partial fulfillment of the Requirement for the MSc in Finance

FINANCE DISSERTATION ON

APPLICATION OF CAPITAL ASSET PRICING MODEL (CAPM)

IN ANALYSIS OF LISTED RETAIL STOCKS

ON THE VIETNAM STOCK MARKET

NGUYEN THI MAI TRANG

ID No: 19046117 Intake 3

Supervisor: Dr TRAN THI XUAN ANH

September 2020

ACKNOWLEDGEMENTS

Over a year of pursuing Master of Science in Finance of the University of the West of England, the contents designed for the curriculums as well as the dedicated instructing and tutoring of the teachers helped me to improve a lot of financial knowledge and other soft skills I believe that these knowledge and skills will help me develop myself more and more, especially in the better career in the future

First of all, I would like to thank my tutor Dr Tran Thi Xuan Anh who gave me a lot of helpful and wonderful feedbacks, comments and ideas for me to complete my study program Second, I would also like to thank my family, friends and colleagues who have always supported and helped me throughout my study and research Finally, I thank all of the faculty and program staff for supporting

me throughout the course

EXECUTIVE SUMMARY

This dissertation studies knowledges related to CAPM model (Capital Asset Pricing Model), including but not limited to theoretical background of CAPM and its mathematical basis, assumptions, advantages and disadvantages At the same time, this dissertation also delves into the CAPM model's development and expansion over time and through actual studies and researches, as well as summaries of the studies that have been done related to the CAPM model in different countries around the world, especially in Asia and Vietnam

This dissertation researches on Vietnam's Stock market in general and the retail industry in particular, analyzing opportunities and challenges for investing

in retail stocks in the Vietnamese Stock market This dissertation uses CAPM model to value retail stocks that are listed on the Vietnamese Stock market on both official stock exchanges, HOSE and HNX There are 23 stocks of companies

in the retail industry for data and analysis Based on the theories of the CAPM model to calculate, this dissertation shows which stocks are overvalued (8 stock codes) and which stocks are undervalued (15 stock codes) From the evaluation of the value of stocks, the research has selected potential stocks (with 6 selected stock codes) based on the criteria given (having positive return during the period starting from listing to June 30 2020, having positive returns from 2019 to June 30

2020, and is undervalued) to describe how to build an optimal portfolio, based on the lowest level of the risk of portfolio (lowest standard deviation)

From the above research content, this dissertation points out limitations of CAPM application in valuation of retail stocks on the Vietnam Stock Market as well as some recommendations learnt from CAPM application in research

TABLE OF CONTENTS

ACKNOWLEDGEMENTS 1

EXECUTIVE SUMMARY 2

LIST OF GRAPHS 6

LIST OF TABLES 7

ACRONYMS 8

INTRODUCTION 9

1 Importance of the research topic 9

2 Purposes of the research topic 10

3 Research Subject, Scope and Methods 10

4 Research Structure 11

CHAPTER I: LITERATURE REVIEW 12

1.1 Theoretical background of CAPM and its mathematical basis 12

1.1.1 Overview of the CAPM 12

1.1.2 Assumptions in CAPM 13

1.1.2.1 Assumptions on investors’ attitudes 13

1.1.2.2 Assumptions on capital market 13

1.1.3.1 Market Portfolio (M) 16

1.1.3.2 Risk Premium for Market Portfolio 17

1.1.3.3 Expected Rate of Return of Individual Securities 18

1.1.3.4 Beta Ratio 21

1.1.3.5 Security Market Line 22

1.1.4 Extended CAPM 23

1.1.4.1 CAPM with borrowing restrictions 24

1.1.4.2 CAPM with Zero Beta Ratio 25

1.1.4.3 CAPM with Multiple Investment Terms 27

1.1.4.4 CAPM with Transaction Costs and Taxes 28

1.1.5 Advantages and Disadvantages of CAPM 29

1.1.5.1 Stability of Beta 30

1.1.5.2 Relationship between Expected Rate of Return and Beta 30

1.1.5.3 Effects of Non-normal Distribution 30

1.1.5.4 Unusual Limitations of CAPM application 31

1.1.5.5 Fama and French studies and findings 31

1.1.5.6 Criticism from Researchers of Multi-factor Model 32

1.2 Empirical research 33

SUMMARY OF CHAPTER I 38

CHAPTER II: DATA AND METHODOLOGY 40

2.1 Conditions for the model application 40

2.2 Data and Methodology 41

2.3 Methodology 43

2.3.1 Assessment of retail stocks on the Vietnam stock market 43

2.3.1 Building the Optimal Portfolio 44

SUMMARY OF CHAPTER II 46

CHAPTER III: RESULTS OF APPLICATION OF CAPM IN ANALYSIS OF RETAIL STOCKS ON THE VIETNAM STOCK MARKET 47

3.1 Vietnam Stock Market and Prospect of Retail Stock Investment on the Vietnam Stock Market 47

3.1.1 Overview of the Vietnam Stock Market 47

3.1.2.2 Opportunities and Challenges to Invest in Retail Stocks 55

3.2 Application of CAPM in Analysis of Retail Stocks on the Vietnam Stock Market 59

3.2.1 Database 59

3.2.1.1 Rate of Return 59

3.2.1.2 Standard Deviation 61

3.2.1.3 Coefficient of Variation 62

3.2.2 Estimation of CAPM Parameters 63

3.2.2.1 Risk-free Interest Rate 63

3.2.2.2 Market Portfolio 64

3.2.2.3 Beta Ratio 65

3.2.3 Appliance of CAPM in Retail Stock Valuation 66

3.2.4 Building the Optimal Portfolio 68

3.2.4.1 Stock selection for optimal portfolio 68

3.2.4.2 Building optimal portfolio 71

SUMMARY OF CHAPTER III 74

CHAPTER IV: ASSESSMENT OF CAPM APPLICATION IN ANALYSIS

OF RETAIL STOCKS ON THE VIETNAM STOCK MARKET 75

4.1 Limitations of CAPM application in valuation of retail stocks on the Vietnam Stock Market 75

4.1.1 General Limitations of CAPM Application on the Vietnam Stock Market 75

4.1.2 Limitations of CAPM Application in Valuation of Retail Stocks on the Vietnam Stock Market 76

4.1.2.1 Measure of Risk - Standard Deviation 76

4.1.1.2 Market Portfolio 81

4.1.1.3 Beta Ratio 82

4.1.1.4 Other Limitations 82

4.2 Some recommendations learnt from CAPM application in research 83

SUMMARY OF CHAPTER IV 87

CONCLUSIONS 88

REFERENCES 89

LIST OF GRAPHS

Graph 1.1: Capital Allocation Line (CAL) and Capital Market Line (CML)

Graph 1.4: Efficient Frontier with different borrowing & lending rates

Graph 1.5: Efficient portfolios and zero-beta portfolios

Graph 1.6: SML and zero-beta portfolios

Graph 1.7: CAPM with transaction costs

Graph 3.1: Scale and Growth of Retail Industry in Vietnam

Graph 3.2: Proportion of logistic revenue in total retail sales in Vietnam Graph 3.3: The proportion of households in Vietnam

Graph 3.4: The proportion of ranges of age in Vietnam

Graph 3.5: Median Age of Countries

Graph 3.6: Porter’s Five Forces Model of Retail industry in Vietnam

Graph 3.7: Standard deviations of retail stocks with positve rate of return Graph 3.8: Coefficient of variation of retail stocks with positve rate of return Graph 3.9: Fluctuation of the VN-Index from 2010 to 2020

Graph 3.10: Beta Ratio of Retail stocks

Graph 3.11: The sets of Expected Return and Standard Deviation of Portfolio Graph 4.1: Interest rates of Vietnam 5-year government bonds

from 2018 to 30 June, 2020 Graph 4.2: Distribution of the rate of return of Retail stocks

Table 3.4: Terms and Conditions of Government Bond

Table 3.5: Valuations of Retail stocks

Table 3.6: The stocks are selected for the portfolio

Table 3.7: Average Daily Return and Standard Deviation of selected stocks Table 3.8: Correlation of selected stocks

Table 3.9: Covariance of selected stocks

Table 3.10: The sets of Proportion of stocks in the portfolio

ACRONYMS

INTRODUCTION

1 Importance of the research topic

Along with the current boom of the financial market in general and the stock market in particular, the world has recognized the indispensable role of the financial mathematics in research and decision-making process for investment Financial mathematics has played an important role in modernizing research in the financial and monetary field in general and financial investment in particular The examples are applying financial mathematics through risky business on derivatives market, managing risks in stock market fluctuations, developing and managing portfolios, valuing financial assets, effective market theory, credit rating theory and etc

The stock market has experienced unpredictable fluctuations over the past few years, and the strong ups and downs of the market have made investors realize that sentiment- and rumor-based investment poses lots of risks Risk management requires effective tools to assess investment opportunities and help build effective portfolios Investors also need to strictly follow the new investment strategy

to seek profits on the market in a sustainable way This is an opportunity for financial mathematics to find a firm foothold both in theoretical and practical research

CAPM (Capital Asset Model) was first introduced by Sharpe (1964) and Lintener (1965) nearly 60 years ago It is a typical model for applying financial mathematics to analysis and investment The first success of this model is to show how to assess the risk of capital flows and to estimate the prices and expectations

of future gains that investors will achieve when investing in the project This is a

model that has been developed since 1964 but it is still an effective tool in risk management and investment capital valuation in the world

With the aim of putting financial mathematics into practice as well as improving in-depth knowledge for professional work, the research project

“Application of Capital Asset Pricing Model (CAPM) in analysis of listed retail stocks on the Vietnam stock market” will meet the actual needs of the market, reinforce the theory, and help researchers better understand CAPM both in terms

of economic significance and application of mathematics in economic analysis

2 Purposes of the research topic

To provide theoretical clarification of CAPM and its mathematical basis

To help readers approach the method of researching and analyzing stock prices on the basis of data processing and modern, but not so complicated, calculation techniques

To specify the applicability of CAPM in analyzing listed stocks in the Vietnam retail industry, helping investors to make the right investment decisions when analyzing and investing in these stocks by checking whether the market values such stocks high or low

3 Research Subject, Scope and Methods

The research focuses on CAPM and the application of financial mathematics in the analysis of listed retail stocks in Viet Nam under CAPM

The scope of the research is the group of retail stocks listed on the Hanoi Stock Exchange and Ho Chi Minh City Stock Exchange, by the end of June 2020

The research uses the statistical method, collects data on price fluctuations

of listed stocks of companies in the retail industry in the form of exel data sheets for a period of five years, uses Eviews software for analysis of average, standard deviations, for graphs and for calculating the correlation coefficient between the random variables Eviews is a common statistical software, easy to use in practice, particularly in economics

4 Research Structure

Chapter I: Literature review

Chapter II: Data and Methodology

Chapter III: Results of application of CAPM in analysis of retail stocks on

the Vietnam Stock market

Chapter IV: Conclusion and recomention of the application of CAPM in

analysis of retail stocks on the Vietnam Stock market

CHAPTER I: LITERATURE REVIEW 1.1 Theoretical background of CAPM and its mathematical basis

1.1.1 Overview of the CAPM

CAPM is considered the essence of the modern economics and finance theory Hary Markowitz was the first to lay the foundation for the current investment theory in 1952 12 years later, CAPM was developed by William Sharpe, John Linner and Jan Mossin

In this model the expected rate of return equals the risk-free rate plus the risk premium calculated on the basis of systematic risks of each security Non-systemic risks are not taken into account because they have been eliminated by the perfectly diversified portfolio Based on this, CAPM is known as a model that reflects the relationship between risk and expected return for each asset as well as the portfolio

The research on CAPM brings about three key benefits:

- Provide a standard rate of return for assessing and selecting various investment options

- Provide a useful tool to predict the expected rate of return on unresolved assets on the market

- Determine the cost of equity for joint stock companies

Although in fact, CAPM is not accurate in all cases, it is still considered to

be the most common method due to its ability to produce relatively exact results

in many analytical applications In 1990, William Sharpe, Harry Markowitz and Merton Miller received the Nobel Prize in Economics of the co-Nobel Prize for Science for their active contributions to the development of CAPM theory

1.1.2 Assumptions in CAPM

1.1.2.1 Assumptions on investors’ attitudes

Assumption 1: Investors, when making their decisions, always bases on an

analysis of two factors: the expected rate of return and the expected risk of the security The higher the level of security risk is, the bigger the expected return are

to compensate for the risks

Assumption 2: Investors will minimize risk by diversifying their portfolio -

combining various stocks in their portfolio

Assumption 3: Investment decisions are made and the process completed

within a certain period of time which can be calculated by 6 months, 1 year and etc In fact, investment decisions are much more complicated and it is usually not just a one-stage process The assumption that investment decisions last for and end within a certain period is to simplify in calculation and analysis

Assumption 4: Investors have the same expectations about the input

parameters to create a modern Markowitz portfolio such as: expected return rate, risk level or correlation coefficients

Assumption 5: All investors want to hold the portfolio on the efficient

frontier according to Markowitz theory

1.1.2.2 Assumptions on capital market

Assumption 1: Capital market is a perfectly competitive market, with

multiple sellers and buyers The capacity of an individual investor is very small compared to the whole market Therefore, the activities of investors do not affect

the market Market prices are solely determined by the supply-demand relationship

Assumption 2: There are no transaction fees, taxes or any obstacle in the

supply and demand of a security No inflation, or no change in interest rates or inflation, are fully reflected

Assumption 3: On the market exist risk-free assets in which investors can

invest Moreover, investors can borrow money at an interest rate which equals the risk-free rate It means that the lending and borrowing interest rates are the same and equal to the risk-free rate

These assumptions overlook many of the real-world complexities However, with these assumptions, we can derive important conclusions on the equilibrium in capital markets

First, all investors will choose to hold a portfolio of risky assets (stocks) in proportion to the proportion of each asset in the market portfolio (M), including all assets traded on the market

Second, not only will the market portfolio be on the efficient frontier, but this portfolio is also tangential to the optimal capital allocation line (CAL) for each investor and all investors Therefore, the capital market line (CML), starting from the risk-free rate to the market portfolio, M, is also the best capital allocation line possible All investors hold the portfolio M as an optimal risk portfolio, only differing in their investment rates and risk-free assets

Graph 1.1: Capital Allocation Line (CAL) and Capital Market Line (CML)

Third, the level of risk premium on the market portfolio will be

proportional to the risk level of that portfolio and the level of risk aversion of each

investor Mathematically, we have the followings:

𝐸(𝑟𝑀) − 𝑟𝑓= 𝐴̅𝜎𝑀2𝑥0,01 (1.1) 𝐸(𝑟𝑀): the expected rate of return of the market portfolio

𝜎𝑀2 : the variance of market portfolio 𝐴̅: the level of risk aversion of investors

𝑟𝑓: the rate of return of risk-free assets Since M is an optimal portfolio, it is a perfectly diversified portfolio of all

securities Therefore, 𝜎𝑀2 is the systematic risk of market portfolio

Fourth, the risk premium for each individual asset will be proportional to

the risk premium of the market portfolio (M), and be the beta of a security against

the market portfolio Beta measures the level of volatility of a stock's rate of

return in relation to the volatility of the market’s rate of return Beta is defined as

a formula as follows:

𝛽𝑖 =𝐶𝑜𝑣(𝑟𝑖 ,𝑟𝑀)

𝜎𝑀2 (1.2)

𝐶𝑜𝑣(𝑟𝑖, 𝑟𝑀): the correlation coefficient between individual stock i and the market portfolio

The level of risk premium for each asset is calculated as below:

If Nj is the number of Asset j on the market,

Pj is market value of Asset j,

X is the total risk assets on the market,

Then the proportion of Asset j corresponding on the market is 𝜔𝑗 = 𝑃𝑗𝑁𝑗

to the wealth of the entire economy This is how to measure the market portfolio

M CAPM implies that when an individual tries to optimize their own portfolio, they will reach the same portfolio, with the proportion of each asset equal to the proportion of that asset in the market portfolio

The value of the market portfolio is not published on a daily basis Only indices for the major securities can be published In the US, one of the very

popular indices is the S&P500, which gathers the value of 500 large stocks trading mainly on the market This index can be considered as representing the entire stock market trading

Now suppose that the optimal portfolio of all investors does not include stocks of some companies, such as company Y When all investors avoid Stock Y, demand for this stock is zero, and Y's stock price will fall freely When Stock Y becomes a lot cheaper, it turns into a more attractive stock and other stocks will become less attractive Eventually, Y will reach a price at which it becomes attractive enough to be included in the risky portfolio of stocks

The above price adjustment process ensures that all stocks will be included

in the optimal portfolio This means that the market portfolio must include all assets It is an asset with a price at which the investor is willing to put in their risky portfolio

Thus it can be concluded that if all investors hold the same risky portfolio, then this portfolio is M portfolio, the market portfolio

1.1.3.2 Risk Premium for Market Portfolio

The risk premium of the market portfolio under balanced capital market conditions, E(rM) - rf, is proportional to the average risk aversion level of investors and the risk level of the market portfolio, 𝜎𝑀2 Assume that each individual investor chooses the ratio y and invests in the optimal portfolio M, as follows:

𝑦 =𝐸(𝑟𝑀)−𝑟𝑓

0,01𝐴̅𝜎𝑀2 (1.4)

As long as CAPM assumptions are maintained, risk-free investment involves borrowing and lending between investors Any borrowing position is

offset by the lender's loan position This means that the net of borrowing and lending between investors must be zero, and therefore, the average position on the risky portfolio is 100%, or y = 1 Put y = 1 in the equation above, and rearrange the equation, we will find that the risk premium for the market portfolio is proportional to the variance of the portfolio itself multiplied by the average risk aversion level of the investors

𝐸(𝑟𝑀) − 𝑟𝑓 = 0,01𝐴̅𝜎𝑀2 (1.5)

1.1.3.3 Expected Rate of Return of Individual Securities

CAPM is based on the idea that the appropriate risk premium for an individual asset will be determined by its contribution to the risk aversion of investors in the overall portfolio Portfolio risk is an issue for investors and relates

to the level of risk premium required by the investors

According to the portfolio theory, portfolio risk is measured by portfolio variance The specific formula is as follows:

𝜎𝑝2 = ∑𝑛𝑖=1𝑤𝑖2𝛿𝑖2∑𝑛𝑖=1∑𝑛𝑗=1𝑤𝑖𝑤𝑗𝑐𝑜𝑣(𝑟𝑖, 𝑟𝑗) 𝑣ớ𝑖 𝑖 ≠ 𝑗 (1.6) This variance can be rewritten according to the covariance matrix, showing the correlation of each pair of stocks in the portfolio The metric in the diagonal row of the matrix is the covariance of the rate of return of an asset to itself, which is simply a variance of a security

Below is the covariance matrix to calculate portfolio risk:

The variance of the portfolio is calculated by summing all the variables in the followed covariance matrix, first multiplying each variable by the portfolio weight from the row and column For example, the contribution of Stock Y to the market portfolio variance is:

𝑤𝑌[𝑤1𝐶𝑜𝑣(𝑟1,𝑟𝑌) + 𝑤2𝐶𝑜𝑣(𝑟2,𝑟𝑌) + ⋯ 𝑤𝑌𝐶𝑜𝑣(𝑟𝑋,𝑟𝑌) + 𝑤𝑛𝐶𝑜𝑣(𝑟𝑛,𝑟𝑌)] (1.7)

If the covariance between Stock Y and the market portfolio is negative, then Y has a "negative" contribution to the risk of the portfolio by giving a rate of return that fluctuates in the opposite direction to that of the market portfolio Y stabilizes the rate of return of the overall portfolio, and vice versa

To see this relationship more clearly, plese note that the market portfolio's rate of return can be rewritten as follows:

𝑟𝑀 = ∑𝑛𝑘=1𝑤𝐾𝑟𝐾 (1.8) Therefore, the covariance of the rate of return of Stock Y with the market portfolio is:

𝐶𝑜𝑣(𝑟𝑌, 𝑟𝑀) = 𝐶𝑜𝑣(𝑟𝑌, ∑𝑛𝑘=1𝑤𝐾𝑟𝐾) = ∑𝑛𝑘=1𝑤𝐾𝐶𝑜𝑣(𝑟𝑌, 𝑟𝐾) (1.9)

The level of contribution of holding Stock Y to the premium of the market portfolio is 𝑤𝑌[𝐸(𝑟𝑀) − 𝑟𝑓] Therefore, the reward - risk alpha ratio for investing

in Y can be expressed as follows:

Y′s contribution to the risk premium Y′s contribution to the variance (1.10) The reward - risk alpha ratio for an investment in the market portfolio is:

Market risk premium Market portfolio variance= 𝐸(𝑟𝑀)−𝑟𝑓

𝜎𝑀2 (1.11) The basic principle of a balanced market is that all investments should yield the same reward-risk ratio If this ratio is better for this investment asset than another investment asset, then the investor will restructure the portfolio by switching to investment in assets that have a better tradeoff between rate of return and risk, and lessening investment in other assets Therefore, we conclude that the reward-risk ratio of Y and the market portfolio should be equal to:

𝐸(𝑟 𝑌 )−𝑟𝑓𝐶𝑜𝑣(𝑟 𝑌 ,𝑟 𝑀 )= 𝐸(𝑟𝑌)−𝑟𝑓

as follows:

𝐸(𝑟𝑌) = 𝑟𝑓+ 𝛽𝑌⌊𝐸(𝑟𝑀) − 𝑟𝑓⌋ (1.14)

This relationship between expected rate of return and beta is the best representation of CAPM for investors

1.1.3.4 Beta Ratio

In CAPM the risk level of each security is not measured by standard deviation because part of the standard deviation has been eliminated by portfolio diversification When the securities participate in the market portfolio, they interact to lessen each other’s non-systematic risks In this case, the portfolio is the perfectly diversified market portfolio (M) Therefore, the non-systematic risk

of each individual security is eliminated, leaving only the systematic risk which is measured by the β ratio

𝛽𝑖 =𝐶𝑜𝑣(𝑟𝑖 ,𝑟𝑀)

𝜎𝑀2 =𝐶𝑜𝑣(𝑟𝑖 ,𝑟𝑀)

𝑣𝑎𝑟(𝑟 𝑀 ) (1.15) The βi ratio indicates the sensitivity of Asset i's expected rate of return in

relation to the change in expected rate of return of the market portfolio M It is

considered as a measure of market risk of Asset i

When the βi ratio > 1, then the risk level of Asset i is higher than that of

the market portfolio M, and the expected rate of return E(𝑟𝑖) of the asset is clearly higher than that of the market portfolio, and vice versa

In case of βi = 1, the expected rate of return of Asset i is equal to that of

the market portfolio M

Besides, β is also considered as the leverage factor for the average rate of return of that asset, that is, when the average risk premium of the market portfolio [𝐸(𝑟𝑀) − 𝑟𝑓] changes by 1%, the average risk premium of Asset i increases by

β%

1.1.3.5 Security Market Line

The relationship between the expected rate of return and beta can be described graphically as the stock market line (SML) as follows:

Graph 1.2: Stock Market Line (SML)

The SML provides a benchmark for the evaluation of investment performance Given the level of investment risk, measured by the beta, the SML provides the rate of return needed to compensate for investors both in terms of risks and time value of money The SML applies to both effective portfolios and individual assets

The difference between the expected return and the required return for a security is called Alpha, denoted as α

The reasonably priced asset will lie exactly on the SML (α = 0), that is, the expected rate of return of this asset corresponds to its own risk If the stock is underpriced (α > 0), it will lie above the SML and vice versa

Graph 1.3: Stock Market Line (SML) and Alpha

1.1.4 Extended CAPM

The above is the original CAPM, but in fact, the expected rate of return of

an asset depends on many factors such as changes in inflation expectations, production situation, changes in differences between the profitability of short-term and long-term bonds, and even the crowd psychology over time Therefore, CAPM has been adjusted and become different versions to meet with actual requirements As a result, many mathematical models are created to evaluate the estimated beta ratio of assets In fact, each company in each industry has its own beta In countries with developed financial markets, there are often financial organizations and financial services companies with strong potential, great reputation and a team of professional experts who will periodically calculate and publish the beta ratio of listed companies on the market

The assumptions that allow Sharpe to make a simplified version of CAPM are admitted to be impractical Financial economists have worked for a long time

to adjust CAPM and extend it into more realistic cases

There are two forms of extension for the simplified CAPM version

- Loosen the assumptions introduced early in the chapter

- Accept the truth that investors care more about the source of risks rather than the uncertainty about the value of their stocks in the future, such as unexpected fluctuations in consumer goods prices This idea involves introducing additional risk factors beyond stock returns

1.1.4.1 CAPM with borrowing restrictions

CAPM is predicted based on the assumption that all investors have the same list of inputs of the Markowitz model Therefore, all investors agree on the position on the efficiency curve, where each portfolio has the smallest variance among feasible portfolios at the expected rate of return initially targeted When all

investors can borrow and lend at a safe rate rf, they all accept the optimal

tangential portfolio and choose to hold stocks of the market portfolio

However, when borrowing is restricted, especially for many financial institutions, or when the borrowing interest rate is higher than the lending one because the borrower has to pay the default risk, the market portfolio is no longer

a common risk portfolio for all investors

ơ Graph 1.4: Efficient Frontier with different borrowing & lending rates

- The rf - F segment represents the investment opportunities available

when the investor combines lending with risk-free interest rate and portfolio F on the Markowitz efficient frontier

- However, the investor cannot extend the rf - F line to the right if the

investor is unable to borrow at risk-free rates

- If the interest rate is Rb (riskier than rf), then the point of contact of the

line starting from Rb and the efficient frontier is K

- The CML is made up of rf - F - K - G This implies that we can borrow

or lend, but the portfolio when we borrow is not as profitable as it is with the assumption that we can borrow at risk-free rates

When investors can no longer borrow at risk-free rates, they can choose a risky portfolio from a set of portfolios on the efficient frontier corresponding to the level of risk they accept The market portfolio is no longer a common risk portfolio If the market portfolio is no longer an efficient portfolio with the smallest variance, then the expected return-beta relationship of CAPM is no longer a feature of the balanced capital market

1.1.4.2 CAPM with Zero Beta Ratio

An important extension of CAPM is the model related to the environment with no risk-free asset, developed by Black in 1972 Zero Beta CAPM was generated for loosening the assumption of a risk-free capital asset and based on the three following characteristics:

First, every portfolio is built with a combination of efficient portfolios that lie on the efficient frontier

Second, all portfolios that lie on the efficient frontier have a companion portfolio on the lower half of the efficient frontier (the non-efficient part) The underlying portfolio has no correlation with the portfolios on the upper half of the efficient frontier, so this “companion” portfolio is considered a zero-beta portfolio

of an efficient portfolio

Third, the expected rate of return of a zero-beta portfolio of an efficient portfolio is determined in the procedure below From any efficient portfolio, for example, Portfolio P in the chart, draw a tangent to the vertical axis The point of intersection will be the expected rate of return of Portfolio P’ with zero beta, denoted Z(P) The horizontal line connecting the intersection point and the minimum-variance frontier determines the standard deviation of a portfolio with zero beta In the following graph, there are different efficient porfolios, eg P and

Q, with zero-beta “companion” portfolios

Graph 1.5: Efficient portfolios and zero-beta portfolios

These tangents are only useful when we develop portfolios determined by

a combination of risk-free assets and tangent portfolios However, in this case, we

assume that the risk-free assets are not available to investors The SML is, therefore, linear as shown in the following figure:

Graph 1.6: SML and zero-beta portfolios

Suppose that the rate of return of a zero-beta portfolio is greater than that

of risk-free assets, then the straight line going through the market portfolio will be less steep It means that the market risk premium will be smaller The market risk premium is a product of β and the market risk premium [E(Rm)-E(Rz)] Therefore, the equation of CAPM with β = 0 will be:

𝐸(𝑅𝑖) = 𝐸(𝑅𝑧) + 𝛽𝑖[𝐸(𝑅𝑚) − 𝐸(𝑅𝑧)] (1.16) With these characteristics, the Black model can be applied to any exception: risk-free assets, lending at risk-free rates but borrowing at risky rates,

and borrowing at an interest rate higher than r f

1.1.4.3 CAPM with Multiple Investment Terms

One of the restrictive assumptions of CAPM is simply that investors are rationalists - they plan to hold stocks for an investment term Investors really care

about the time the investment has passed and they desire to leave legacy to their descendants Current consumption depends on current wealth and future rate of return from the portfolio These investors will want to rebalance their portfolio as often as required by the change in their wealth

However, Eugene Fama points out that even if the analysis extends to multiple investment stages, the one-phase CAPM model will still make sense The key assumption that Fama uses to replace the one-period assumption is that investors' preferences do not change over time, and risk-free interest rates and the probability of allocating securities’ rates of return remain unchanged and unpredictable over time

1.1.4.4 CAPM with Transaction Costs and Taxes

In the presence of transaction costs, investors will not adjust all price deviations, because in some cases the cost of buying and selling securities that are mispriced will offset all potential outstanding rates of return Thus, the securities will lie very close to the SML but not on it The SML will be a range that gathers securities rather than a single straight line

The width of this distribution range is a function of the sum of the transaction costs In a world where a large percentage of transactions are made by institutions with a small cost per share and brokers enjoy discounts available to investors, this range can be quite narrow

Graph 1.7: CAPM with transaction costs

In the CAPM, the rate of return we achieve is one before tax In fact, investors’ rate of return is demonstrated as follows:

𝐸(𝑅𝑖)(𝐴𝑇) = (𝑃𝑒−𝑃𝑏)(1−𝑇𝑃𝑐𝑔)+𝐷𝑖𝑣(1−𝑇𝑖)

Herein:

Tcg : tax on capital gains

Ti : tax on dividend income

If the investor bears the tax burden, this will make a major difference in CML and SML among investors

1.1.5 Advantages and Disadvantages of CAPM

CAPM has the advantage of being simple and practically applicable However, like many other models, CAPM is not immune to limitations and criticism by other researchers

1.1.5.1 Stability of Beta

Many empirical studies indicate that the beta of a market portfolio is more stable than that of an individual security In addition, the more stocks the portfolio include (over 50 stocks) and the longer its period lasts (over 26 weeks), the more stable the beta of the portfolio is

In fact, stock traders often use a regression model based on historical data

to estimate beta, so it is possible to explain why the beta of individual securities is more volatile than that of the portfolio

While beta is not a good predictor of future stock returns, it is still an appropriate variable to measure risk For investors who are risk averse, beta provides a basis for expecting a minimum rate of return required to make a rational decision on capital allocation for investment

1.1.5.2 Relationship between Expected Rate of Return and Beta

Several test results of researchers have shown that although the relationship between expected rate of return and system risk (measured by beta) is

a positive relationship, it is not completely linear Most SMLs measured have a positive slope, but the slope changes over time

1.1.5.3 Effects of Non-normal Distribution

Based on the beta-based analysis of expected rate of return, several researchers have also reviewed the effects of the non-normal distribution (asymmetric) on the expected rate of return Normal distribution (symmetric) means that there is a balance between positive and negative observations about the

rate of return In contrast, the non-normal distribution (asymmetric) represents an unusual number of large positive changes in stock prices

Kraus and Litzenberger tested CAPM for asymmetry and confirmed that investors were willing to pay for positive asymmetry because it offered a great chance of very high expected rates of return

1.1.5.4 Unusual Limitations of CAPM application

Some researchers who apply CAPM discover some anomalies that make this model no longer the same as in normal cases These anomalies include:

- Influence of firm size: Stocks of companies with a small market value often yield a higher return than stocks of those with large market capitalization, when other factors remain constant

- Influence of P/E and BV: stocks of companies with lower P/E (Price/Earning) and BV (Book Value) often yield a higher return, when other factors remain constant

- January effect: Investors who hold stocks between December and January often have a higher return than other months However, although the January effect has been detected for many years, it does not occur every year

1.1.5.5 Fama and French studies and findings

Eugene Fama and Kenneth French conduct empirical studies on the relationship between stock’s returns, firm size, BV and β ratio (Fama & French, 1995) Test results based on historical data from the period of 1963-1990 show that the variables of firm size and BV strongly affect the stock returns When

these variables are first included in the regression analysis and then β ratio is added, the results show that the variable β is not as strong as the other variables in explaining stock returns This led Professor Fama, a prestigious professor, to come to the conclusion that β is not the only variable that explains returns He launched an attack on the possibility of using CAPM to explain stock returns and suggested that the variables of firm size and BV were more appropriate to explain returns than risk What do other researchers say?

Fama and French explained returns with two variables based on market value, hence no surprise that there exists a very high correlation between these variables Fama and French were too focused on the variable of returns instead of risk, so there was no theoretical basis for their debatable findings

Although β may not be a good variable to predict stock returns, it is still the right variable to measure risk For investors who are risk averse, β provides a basis for expecting a minimum return Although not all investors can accept this return, for financial purposes, it is still useful to help guide the company in allocating capital to investment projects

1.1.5.6 Criticism from Researchers of Multi-factor Model

Proponents of the multi-factor model argue that while CAPM is still useful for financial purposes, it does not provide an accurate measure of the expected return of a particular stock The multi-factor model indicates that stock returns fluctuate depending on many other factors than just the changes of the market in general Therefore, if other factors are added along with the factor of risk to

explain returns, it will be more convincing than relying on merely a single factor like CAPM

In summary, the tests of CAPM show that β of individual securities is not stable but β of the portfolio is stable with the assumption that the period in the sample is long enough and there are a suitable number of stock transactions There are many opinions supporting the linear (positive) relationship between the rate of return and the systemic risk of the portfolio, however, there are also new evidences suggesting that it is essential to add risk variables or other risk representatives on the measurement

1.2 Empirical research

The purpose of the review on the previous empirical studies is to put together a comprehensive picture on the examination of CAPM validity, especially on the Vietnam stock market

Black, Jensen and Scholes (1972) were among the first to conduct the tests

of CAPM traditional formula applying the basic time-series model, aimed at assessing the validity of this asset pricing model in the United States (Black, et al., 1972) They estimated beta using monthly rate of returns and ‘equally weighted portfolio’ of all stocks on the New York Stock Exchange (NYSE) between 1926 and 1930, computed the next 12-month return of each stock, and then repeated the whole projection for the following years, through January, 1965 They presented the finding that the expected return and risks (the beta) of an asset had a linear relationship, which proved the CAPM validity

(Fama & MacBeth, 1973) Another empirical study in favor of CAPM was conducted by Fama and MacBeth in 1973 In their study, the ‘two-parameter’ model was tested with univariate tests and squared returns, instead of time series model The data collected was also average monthly returns of all common stocks for the period between January 1926 and June 1968 They failed to demonstrate a non-linear relationship between risks and expected return However, in their next studies, Fama and MacBeth (1992, 1993 and 1995) showed rejection that systematic risk was the only factor affecting the expected returns on assets In addition to demonstration of a vanishing relation between the beta and returns on NYSE stocks during 1941-1990 period, (Fama & French, 1992) also reported their finding that size, P/E, book-to-market’ values allowed explaining average stock returns The efficiency of CAPM was negated as a consequence

The CAPM efficiency was also examined in several emerging stock markets in Central and South-East Europe (Džaja & Aljinović, 2013) tested the validity of CAPM on the context of the region by applying cross-sectional method, conducted on a sample of ‘10 most liquid stocks’ traded on each of nine European countries’ stock markets between January 2006 and December 2010 In this study, no relationship between risks and estimated rate of returns of stocks was found, which resulted in the rejection of CAPM assumption

CAPM’s efficiency is also well regarded on smaller-sized stock markets such as Singapore, India, Hong Kong, China and Viet Nam

Also applying the time-series method as (Black, et al., 1972) to test CAPM validity on the Singapore security market, (Hoe, 2002) chose a sample of stocks traded on the Singapore Stock Exchange Main Board (SESMB) between

December 1985 and December 1993 With the results of successful forecast on stock returns, the study proved that the model worked in Singapore

(Choudhary & Choudary, 2010) proved the failure of CAPM in India after testing the model on a sample of 278 stocks traded on the Indian market with monthly returns between January 1996 and December 2009 The study showed that the risk-return relationship was non-linear whereas the CAPM’s hypothesis said otherwise Another finding was that the systematic risk did not impact the estimated rate of returns (Bajpai & Sharma, 2015) also reached the same conclusion as (Choudhary & Choudary, 2010) It applied the rolling regression methodology to test CAPM with daily data for a 10-year period of January 2004 – December 2013, and the results showed CAPM was not valid in India

(Lam, 2001) conducted an empirical study on a sample of 132 stocks listed

on Pacific Basin Capital Markets (PACAP) for the period between January 1980

to December 1995 His study supported the practicality and validity of CAPM on the Hong Kong stock market

CAPM validity was also tested for the case of Shanghai Stock Exchange market (SSE), which was among the fastest developing financial market in the world (Guo, 2011) carried out the study with daily data of stocks collected between January 2005 and December 2009 The author grouped them into ten portfolios and sorted into the beta value order to test the risk-return relationship The results showed no CAPM validity on the SSE

(Taoyuan & Huarong, 2018) tested the time series and cross-sectional data

of the capital asset pricing model on the Chinese stock market with input of monthly data of 100 stocks from January 01, 2007 to February 01, 2018 It aims at

exploring the risk-return relationship to withdraw the conclusion that CAPM, regardless of its roots in developed Western markets, is also applicable in the market of China The study also looks into the analysis results to assess the characteristics and existing issues facing the capital market of China However, the paper does not refer to the application of CAPM in assessing whether stocks

of a specific industry are overvalued or undervalued There is also no research on building optimal investment strategies

(Coffie, 2012) analyzed two models for asset pricing, the capital asset pricing model (CAPM) and the Fama-French three factor model, by exploring their applicability in Emerging African Stock Markets (EASM) CAPM has been widely researched and put into practice since (Sharp, 1964) and (Lintner, 1965) developed it Its bottom line is that the market factor (beta) is the only risk variable affecting asset returns Nonetheless, it is proved with empirical evidence that the market factor alone cannot provide a full explanation for variation in asset returns (Jensen, 1968) (Jensen, et al., 1972), hence the need for a more comprehensive model Multifactor models were developed, as a result (Ross, 1976) (Fama & French, 1992) (Carhart, 1997) However, with its focus on macro analysis of emerging markets in Africa at the time of research, the paper makes no further research into stocks of a specific industry in a specific market to assess whether they are overvalued or undervalued

(Vo & Pham, 2012) was among the few empirical studies on CAPM in Viet Nam They selected 39 individual stocks on HOSE, conducted the estimation of their monthly beta values between December 2006 to December

2012 with Jarque bera test, and examined CAPM validity with General Method

of Moments (GMM) The results provided justification for the CAPM efficiency on the Vietnam stock market, which means beta could be applied to measure systematic risk

(Hoang, 2013) was another CAPM empirical study in Viet Nam Her sample was 20 stocks traded on HOSE and their daily prices between January

2005 and August 2011 were collected Due to the limited quantity, the author put them into four groups, and then sorted them into book-to-market ratio order After applying correlation and linear analysis for data test, her study produced similar results to (Vo & Pham, 2012)

(Bach, 2018) analyzed a data sample of 200 public stocks from HOSE during 48 months from January 2012 to December 2015 The regressions carried out to evaluate the applicability of CAPM and the Fama French Three-factor Model on the Vietnam stock market indicate that the latter provides a significant performance and is also better than the former in explaining both stock returns and value premium effects In the three-factor model, the market risk premium is the factor that most affects stock returns followed by the other two factors, value and size, respectively The applicability of CAPM on the Vietnam stock market is also supported in the paper However, it does not refer to the application of CAPM in evaluation of stocks of specific industry groups

A project for the Student Scientific Research Award "Young Economist - 2011": Applying the CAPM and Fama French Model to Forecast the Rate of Return for Business in the Market of Vietnam reviewed the theory of the CAPM model, Fama French and some popular pricing models such as Discounted Cash Flows (DCF), and Relative Comparison to evaluate stocks on the market

However, the study only focuses on analyzing the pricing models while the CAPM and Fama French models are discussed more briefly, as an input factor for pricing At the same time, the research period from January 2007 to December

2009 is also quite far from the present time (2020), when more statistics are available, and the market is also more active with more diverse stocks traded

In (Pham, 2017), the null hypothesis was rejected and the relationship between beta and actual returns was non-linear All the three testing hypotheses were rejected at the level of significance of 5% The author, therefore, withdrew the conclusion of no CAPM validity on the Vietnamese stock market between 01 January 2006 and 31 December 2016 The study selected only 100 out of 800 stocks traded in 2016 With its aim to focus on those stocks with uninterrupted trading in the selected period, the sample only managed to provide a small number which meets the criteria Also, the period chosen was regarded relatively short for the Vietnam stock market Therefore, in the long term, the sample failed to represent the whole market To produce results with better representation requires

an extension of samples in the future studies Its mere focus on the return-risk relationship also restricted the test scope in examination of CAPM validity The study also neither dug deep into a certain industry nor referred to the building of

an optimal portfolio

SUMMARY OF CHAPTER I

Chapter I presents a thorough overview of CAPM and related reseachs It provides the model's assumptions, which help the researcher eliminate factors that

are too complicated for calculations, to include assumptions on investors’ attitude and capital market

Chapter I gives details of CAPM, including market portfolio - a reference

list to help investors make investment decisions, risk premium of market portfolio

- to help investors identify how much difference the market portfolio is required to

gain from the interest earned on risk-free assets; and expected rate of return on

individual securities - the minimum return required by investors corresponding to the risk level of each security Based on the level of risk reflected by the beta, the investors will accordingly calculate the minimum rate of return required and this

is demonstrated by SML

CAPM is also analyzed in terms of extensions to better suit the real life conditions, such as CAPM with borrowing restrictions; CAPM with z ero beta; CAPM with multiple investment terms and CAPM with transaction costs and taxes

-Chapter I also present criticisms and arguments against CAPM from some researchers in the world These criticisms and arguments gives different perspectives to view CAPM and therefore, contributingly build a proper assessment of the effectiveness of CAPM in stock market analysis

In chapter I, related researchs have also been summarized, as well as pointing out the contents that have not been done in these studies, since then the author has inherited a part of the researchs and built new research goals