Testing the Capital Asset Pricing Model in emerging markets

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Testing The Capital Asset Pricing

Model in Emerging Markets

Bram van Bakel: 10782338 Supervised by P. V. Trietsch

Economics and Business: Finance and Organization BSc Thesis (12 ECs)

Academic Year 2016-2017 31-01-16

Abstract

The purpose of this paper is to research the applicability of the Capital Asset Pricing Model (CAPM) in emerging markets for the time period 2010-2015. This model is commonly used in Finance and has been researched by numerous researchers. The hypothesis made in this paper is that the CAPM will be less applicable in emerging stock markets when compared to developed stock markets. The findings show that the CAPM is not less applicable in emerging stock markets and even appears to be more applicable when compared to developed

markets. The answer on the research question, to what extent is the CAPM applicable in an emerging stock market for the time period 2010-2015, remains inconclusive.

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1 Statement of Originality

This document is written by Bram van Bakel who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Table of Content

Chapter 1. Introduction ... 4 1.1 Motivation ... 4 1.2 Existing literature ... 4 1.3 Research question ... 4 1.4 Sub questions ... 4 1.5 Data ... 5 1.6 Research method ... 5 1.7 Structure ... 5

Chapter 2. Literature review ... 6

2.1 The classic model ... 6

2.1.1 The structure of CAPM ... 6

2.1.2 Support ... 7

2.1.3 Criticism ... 7

2.2 Alternative models ... 8

2.2.1 Black CAPM ... 8

2.2.2 The three factor model ... 8

2.2.3 The four factor model ... 9

2.3 CAPM in emerging markets ... 9

Chapter 3. Data ... 11

3.1 Researched markets ... 11

3.2 Time period ... 11

3.3 The stock returns ... 11

3.4 The market portfolio... 12

3.5 The risk-free rate ... 13

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4.1 Step one: Calculate individual betas and group stocks in portfolios ... 14

4.2 Step two: Calculate portfolio betas ... 14

4.3 Step three: Hypothesis testing ... 15

Chapter 5. Results ... 16

5.1 Step 1: Individual regressions ... 16

5.2 Step 2: Portfolio regressions... 16

5.3 Step 3: Hypothesis tests ... 17

5.3.1 The risk-return trade-off hypothesis ... 17

5.3.2 The linearity hypothesis ... 18

5.3.3 The non-systematic risk hypothesis ... 18

5.4 Market comparison ... 19

5.5 Robustness tests ... 20

5.5.1 Assumptions linear regression ... 20

5.5.2 Equal risk-free rates ... 22

5.5.3 Different investor horizon ... 22

Chapter 6. Conclusion ... 24

Chapter 7. Discussion and Future Research ... 25

Reference List ... 26

Appendices ... 28

Appendix 1: Scatter plots with linear and quadratic fitted lines ... 28

Appendix 2: Test results equal risk-free rates ... 32

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Chapter 1. Introduction

1.1 Motivation

The Capital Asset Pricing Model (CAPM) is a commonly used model in Finance and several researchers have tested this model in more developed markets (Black, Jensen and Scholes, 1972; Fama and MacBeth, 1973; Harvey, 1991; Levy and Roll, 2010). Meanwhile, the markets that are still developing and have not been completely integrated, also known as emerging markets, are investigated to a lesser extent (Harvey, 1995). This paper will help to bring a better view on the applicability of the CAPM in markets that are relatively less researched and are only recently developing for 2010-2015.

1.2 Existing literature

The CAPM, which was built upon the work of Markowitz (1952), is developed by Sharpe (1964) and Lintner (1965). Since then, numerous researchers tested, criticized and extended the CAPM theory. Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) used the “double-pass”’ method to test the validity of the CAPM and provided some criticism. Also Roll (1977) and Dempsey (2013) found shortcomings in the CAPM theory. By elaborating the CAPM theory Black (1972), Fama and French (1992) and Carhart (1977) tried to solve some of these shortcomings.

1.3 Research question

To what extent is the Capital Asset Pricing Model (CAPM) applicable in an emerging stock market for the time period 2010-2015?

1.4 Sub questions

What are the assumptions underlying the CAPM and when is this model applicable? What are the shortcomings regarding the CAPM? Which modifications of the CAPM are available as alternatives? What are characteristics of an emerging market and to what extent is the CAPM applicable in such an emerging market?

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1.5 Data

The data used for the research in this paper contains daily stock returns of companies in emerging markets from 2010-2015, which will be compared to daily stock returns of companies in developed markets. Brazil, Russia, India and China are the emerging markets researched and the developed markets are represented by the United States and the Eurozone. The number of companies chosen will be dependent on the size of the stock market index of each specific market. The datasets which are used, each consist of a list of companies from an index in an emerging or developed stock market and will be obtained from Datastream. The market proxy for each market will be obtained by looking at the daily stock returns of the total stock market index in which all existing companies within the index of a specific market are combined. For each market, the daily returns on a risk-free asset will determine the risk-free rate. The risk-free rate in this paper is assumed to be constant over the total time period, because the risk-free rate does not fluctuate substantially.

1.6 Research method

The method that will be used to test whether the CAPM is successful in predicting the return on stocks in an emerging market is an empirical study including a times series test. In this test, a time series regression of excess stock (or portfolio) return on excess market return is executed. The hypothesis in this paper is that the CAPM will be less applicable in emerging markets when compared to developed markets, because emerging markets are less

integrated than developed markets and therefore the complete capital market assumption is violated, which is expected to negatively affect the applicability of the CAPM.

1.7 Structure

In the next chapter the literature regarding the CAPM will be reviewed. This will bring a better view on what the CAPM consists of, how it is criticized and what its alternatives are. The third chapter will describe what kind of data is used for this paper and how the data is obtained. The research method is given in the fourth chapter, which will describe in detail how the research is performed. The fifth chapter presents the research results. After that, conclusions will be drawn regarding the research question in chapter six. The limitations of the paper and remarks for future research will be discussed in chapter seven.

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Chapter 2. Literature review

This chapter first reviews the classical form of the CAPM, then its support and criticism will be discussed. Second, several alternative asset pricing models will be considered. After that, existing literature on the integration of emerging markets will be reviewed and the

hypothesis will be formed.

2.1 The classic model

2.1.1 The structure of CAPM

The theory regarding the CAPM was built upon the work of Markowitz. Markowitz (1952) introduced the Modern Portfolio Theory in his paper: Portfolio Selection. In this paper Markowitz (1952) states that risk-averse investors can select their portfolios in such a way that expected returns are maximized, given a level of market risk. Another implication of Markowitz’ paper is that investors can reduce their level of risk due to diversification, when selecting stocks in their portfolio that are not perfectly correlated.

Sharpe (1964) and Lintner (1965) modified the existing Modern Portfolio Theory of

Markowitz (1952) to a more practical form known as CAPM by adding two key assumptions to the model:

1) Complete agreement: Investors agree on the joint distribution of asset returns from the current period until the next period.

2) Borrowing and lending can be done at a risk-free rate, which is the same for all investors and does not depend on the amount borrowed or lent.

This elaboration of Markowitz’ theory by Sharpe (1964) and Lintner (1965) defined the CAPM as a market model. This model describes a linear relation between market risk and expected return. The formula of the CAPM is stated as follows:

𝐸(𝑅_𝑖) = 𝑅𝑓+ 𝛽𝑖[𝐸(𝑅𝑚) − 𝑅𝑓] (1)

Where 𝐸(𝑅𝑖) is the expected return of an individual stock, 𝑅𝑓 is the risk-free rate of return,

𝛽_𝑖 is the beta coefficient of an individual stock and 𝐸(𝑅𝑚) is the expected return of the

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2.1.2 Support

In the course of time, evidence was found to support the classical form of the CAPM, which shows that the CAPM still seems to be an useful financial asset pricing model. Harvey (1991) tested the model in 17 countries using country-specific stock portfolios. His findings are that most countries support the CAPM theory. Also, Levy (2010) and Levy, Giorgi and Hens (2012) find support that the CAPM is applicable, because in their paper evidence is found for the existence of the Security Market Line.

2.1.3 Criticism

One of the first tests performed to determine the validity of the CAPM theory was done by Black et al. (1972). This test contained the “double-pass” method, where two regressions are being executed. The first regression determines the betas of each individual stock. In the next step, the stocks are grouped in portfolios dependent on their betas. The second

regression regresses the excess portfolio returns on the portfolio betas. The findings of Black et al. (1972) show that the beta coefficient of the Security Market Line is flatter than

suggested by the CAPM. In the test was found that low-beta stocks earn higher returns and high-beta stocks earn lower returns than predicted by the CAPM. Fama and French (2004) provided an updated example of the evidence regarding the flatter relationship. These results are not in line with the classical CAPM theory.

Fama and MacBeth (1973) extended the “double-pass” regression method of Black et al. (1972) by using month-to-month returns. The method of Fama and MacBeth uses three steps to test the validity of the CAPM theory in emerging stock markets:

1. Calculate individual stock betas and group them in portfolios 2. Calculate portfolio betas

3. Hypothesis testing

The results that Fama and Macbeth (1973) found stated that the beta coefficient does not completely explain the variance in the stock returns. This implies that more factors than only the beta coefficient affect the return of an individual stock.

Another main critique regarding the CAPM is Roll’s critique. Roll (1977) argues that the CAPM cannot be tested if the composition of the true market portfolio is unknown.

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Therefore, every individual asset should be included in the sample or the CAPM theory is not testable. Roll states that the only hypothesis that should be tested, is the hypothesis

regarding the efficiency of the market portfolio. But, Roll (1977) also writes that in theory it is impossible to efficiently measure the true market portfolio and therefore the CAPM theory cannot be tested. The second critique of Roll (1977) states that the CAPM is

tautological. This statement is based on the mean-variance efficiency of the market portfolio and the CAPM formula mathematically being the same.

Dempsey (2013) provides a recent critique on the CAPM theory in which he states that the CAPM fails to estimate the return on stocks. His findings are supported by empirical evidence. Also Dempsey (2013) argues that the beta coefficient cannot completely explain the price risk of a stock return, because the beta coefficient stays constant over time while the risk of a stock compared to the market portfolio changes.

2.2 Alternative models

2.2.1 Black CAPM

Black (1972) modifies the classic CAPM and relaxes the assumption of risk-free borrowing and lending. Instead of this assumption he allows unrestricted short sales of risky assets. Black (1972) proves the existence of a portfolio which beta coefficient is zero. The classic model is redefined as a two factor model:

𝐸(𝑅_𝑖) = 𝑅_𝑧+ 𝛽_𝑖[𝐸(𝑅_𝑚) − 𝑅_𝑓] (2) Where 𝑅𝑧 is the return on the minimum-variance zero-beta portfolio.

2.2.2 The three factor model

In the research done by Fama and French (1992), two other factors besides the market risk factor are found to be significant in explaining the expected return. The first factor is related to the size of a firm and is measured by its market capitalization. Fama and French find a negative relation between the size of the firm and the expected return. This relation explains the findings of a flatter beta coefficient from Black et al. (1972). The second factor has to do with the firms book value of equity relative to its market value of equity and is measured by the book-to-market ratio. Fama and French (1992) find a strong positive relationship

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between the book-to-market ratio and the expected return. The two factors are added to the classic CAPM:

𝐸(𝑅𝑖) = 𝑅𝑓+ 𝛽𝑖[𝐸(𝑅𝑚) − 𝑅𝑓] + 𝛽𝑠×𝑆𝑀𝐵 + 𝛽𝑣×𝐻𝑀𝐿 (3)

Where SMB is the Small-Minus-Big factor, HML is the High-Minus-Low factor. The SMB factor can be measured by deducting the excess stock return of firms with a big market

capitalization from the excess stock return of firms with a small market capitalization. The HML factor is measured by subtracting the excess stock return of firms with a high book-to-market ratio from the excess stock return of firms with a low book-to-book-to-market ratio.

2.2.3 The four factor model

The four factor model by Carhart (1997) is an extension of the three factor model by Fama and French (1992) described above. This model takes into account the momentum effect. The momentum effect states that stocks with high past returns continue to achieve high returns and stocks with low past returns continue to achieve low returns. The formula with the momentum factor included is written as follows:

𝐸(𝑅_𝑖) = 𝑅𝑓+ 𝛽𝑖[𝐸(𝑅𝑚) − 𝑅𝑓] + 𝛽𝑠𝑚𝑏×𝑆𝑀𝐵 + 𝛽ℎ𝑚𝑙×𝐻𝑀𝐿 + 𝛽𝑢𝑚𝑑×𝑈𝑀𝐷 (4)

Where UMD is the Up-Minus-Down factor. The UMD factor is measured by subtracting the excess return of “loser” stocks from the excess return of the “winner” stocks.

2.3 CAPM in emerging markets

One of the assumptions made in the CAPM theory by Sharpe (1964) and Lintner (1965), underlying all of the models listed earlier, is the assumption of perfect capital markets. On an international level this assumption implies that markets are completely integrated. However, Bekaert (1995) describes three barriers of complete integration for emerging markets:

1. Legal barriers. Legal barriers arise from the different legal status of foreign and domestic investors. For example, ownership restrictions and taxes.

2. Indirect barriers. Indirect barriers arise from differences in available information, accounting standards, and investor protection.

3. Risk barriers. Risk barriers arise from emerging-market-specific risks (EMSRS) that discourage foreign investment and lead to de facto segmentation. EMSRS include

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liquidity risk, political risk, economic policy risk, macro-economic instability and currency risk.

Therefore, emerging markets are less likely to be completely integrated than developed markets and the classic CAPM as well as its alternatives might be less applicable in emerging markets than in developed markets. Bekaert (1995) uses the expected return correlation with the U.S. market as a measure for the degree of market integration. Since emerging markets are less likely to be completely integrated, the expected return correlation with the U.S. market can be seen as a measure for the degree of emerging .

Accordingly, the hypothesis of this paper is that the CAPM is less applicable in emerging markets than in developed markets. This is in line with the findings of Harvey (1991), who proves that the CAPM is able to predict returns in developed markets. On the other hand, Harvey (1995) also finds that the same CAPM is not able to predict returns in emerging markets. Since the research by Harvey considers data from 1976-1992, this paper will research if the CAPM is less applicable in emerging stock markets than in developed stock markets for a more recent time period: 2010-2015.

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Chapter 3. Data

This chapter will explain which data is used and how the data is obtained. First, the chosen markets will be presented. Second, the time period of the research will be discussed. The third part explains how the stocks are chosen and from which stock market index. After that, the composition of the market portfolio will be reviewed. The last part discusses the risk-free rates used.

3.1 Researched markets

The six markets chosen for this paper are two developed markets (United States and Eurozone) and four developing markets (Brazil, Russia, India and China). The choices

regarding the markets are based on MSCI indices. Morgan Stanley Capital International, also known as MSCI, is a US company that provides investment tools to institutional investors and hedge funds. MSCI classifies countries into three markets for which it also conduct indices: Developed markets, emerging markets and frontier markets. The four biggest emerging markets in the MSCI Emerging Market Index are Brazil (6.58%), Russia (3.75%), India (8.10%) and China (23.98%). The two biggest developed markets in the MSCI World Index are the United States (54%) and the Eurozone (15%). Therefore these six markets are selected to represent the emerging markets and the developed markets.

3.2 Time period

The time period used in this paper is running from the 1st_{of January 2010 until the 31}st_of

December 2015, resulting in 1564 data points per observed stock. This time period is chosen, because there is relatively less existing literature available for this time period compared to earlier time periods and it contains a substantial amount of data points.

3.3 The stock returns

For each of the six markets one stock market index is obtained from Datastream. It is preferable to have a big sample size and therefore the biggest indices available are chosen. All indices are weighted using a free-float capitalization method. This method weighs the components of the indices based on the total market value of their number of shares held and traded by the general public, also known as floating traded stocks. The indices are

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conducted in such a way that each index represents a large part of the total market

capitalization of that stock market. The estimated market capitalization of the index relative to the total market capitalization of the related stock market is calculated by adding up the market capitalizations of each stock within the index and comparing it to the total stock market capitalization. For Brazil and Russia all stocks with data available for 2010-2015 are used. For the United States, Eurozone, India and China 400 stocks are randomly selected from all stock with available data for 2010-2015. The number of observations for each stock equals 1564. The indices chosen and its size are presented in Table 1 below.

Table 1: Index information

Classification Market Index

Estimated market cap. relative to total market cap. Index size Sample size 2010-2015 Related Stock Exchange Developed Markets United

States S&P 500 70% - 80% 505 400 NYSE & Nasdaq

Eurozone

Stoxx

Europe 600 90% 600 400 -

Emerging Markets

Brazil Bovespa 70% 59 54 B&F Bovespa

Russia RTS 85% 50 40 MICEX

India Nifty 500 94% 493 400 NSE

China

SSE

Composite 100% 1218 400 SSE

Total 2925 1694

Each dataset consists of daily price indices of stocks. The price indices express the stock price as a percentage of its value on the base date, adjusted for capital changes. The daily price indices can be converted to daily stock returns by using the following formula:

𝑅_𝑖 =𝑃𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥𝑡 − 𝑃𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥𝑡−1

𝑃𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥𝑡−1 (5)

3.4 The market portfolio

In this paper the market portfolio is conducted by combining all stocks within an index. After that, the daily return of the total index is calculated. These daily returns represent the daily returns of the market portfolio and will be used as the market proxy. The calculations regarding the daily market returns are made using formula (5), but instead of using the individual price indices the total list price indices are used.

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3.5 The risk-free rate

The risk-free rate is determined by calculating the return on a risk-free asset. The risk-free assets are represented by the Government bonds. For each market the average yearly yield on 5-year Government bonds for 2010-2015 is taken. For the Eurozone, the Euro Area yield is taken. After that the yearly yields are converted to daily returns. The risk-free rate is assumed to be constant, because the risk-free rate for the period 2010-2015 does not fluctuate substantially. The risk-free rate per market is presented below.

Table 2: Risk-free rates

Classification Market Yearly risk-free rate Daily risk-free rate

Developed markets United States 1.398% 0.00380%

Eurozone 1.387% 0.00377% Emerging markets Brazil 11.548% 0.02995% Russia 8.334% 0.02193% India 8.250% 0.02172% China 3.391% 0.00914%

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Chapter 4. Methodology

In this chapter the method used to test whether the CAPM is applicable or not will be discussed. This paper applies the double-pass regression method of Fama and MacBeth (1973) for its research regarding the CAPM. This method consists of three steps, which will be discussed below.

4.1 Step one: Calculate individual betas and group stocks in portfolios

First, the betas of each individual stock are calculated by regressing the daily excess stock return of an individual stock on the daily excess market return using the following formula:

𝑅𝑖 − 𝑅𝑓 = ∝𝑖 + 𝛽𝑖(𝑅𝑚− 𝑅𝑓) + 𝜀𝑖 (6)

Where 𝑅_𝑖 is the return on an individual stock, 𝑅_𝑓 is the risk-free rate, 𝑅_𝑚 is the return on the market portfolio, ∝𝑖 is the intercept of the regression, 𝛽𝑖 is the beta coefficient of an

individual stock and 𝜀𝑖 is the random disturbance term of the regression.

After that, following Fama and MacBeth (1973) & Fama and French (2004), the stocks are grouped into N/20 portfolios, where N is the total number of observed stocks and the minimum number of portfolios is 10. The portfolios are grouped in such a way that the first portfolio contains the stocks with the lowest betas and the last portfolio contains the stocks with the highest betas. Black et al. (1972) argue that grouping and ranking the stocks into portfolios according to their beta can reduce the measurement error in the portfolio beta, if the estimation errors of the grouped and ranked stocks are uncorrelated.

4.2 Step two: Calculate portfolio betas

The second step is to estimate the portfolios betas using the same formula (6) but instead of using the return of each individual stock, the average daily return of each portfolio is

regressed on the daily excess return of the market. The formula will therefore be:

𝑅_𝑝− 𝑅_𝑓= ∝_𝑝 + 𝛽_𝑝(𝑅_𝑚− 𝑅_𝑓) + 𝜀_𝑝 (7) Where 𝑅𝑝 is the return on the portfolio, ∝𝑝 is the intercept of the regression, 𝛽𝑝 is the beta

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4.3 Step three: Hypothesis testing

In the third step three hypotheses of the CAPM are tested using three variables in three regressions. In every regression the gammas are estimated. These gammas are the coefficients of the independent variables and can explain something about the relation between the independent variable and the dependent variable. The gammas are used to test the sub-hypotheses.

The first regression tests the risk-return trade-off by regressing the excess portfolio returns on the portfolio betas with the following formula:

𝑅_𝑝− 𝑅_𝑓= 𝛾₀+ 𝛾₁𝛽_𝑝+ 𝜀_𝑝 (8)

The second regression tests the non-linearity of the model by regressing the excess portfolio returns on the portfolio betas and the squared portfolio betas using the following formula:

𝑅_𝑝− 𝑅_𝑓 = 𝛾₀+ 𝛾₁𝛽_𝑝+ 𝛾₂𝛽_𝑝2_{+ 𝜀}

𝑝 (9)

The third regression tests if the beta coefficient explains the full risk of an individual stock or portfolio. The test is performed by regressing the excess portfolio returns on the portfolio betas, the squared portfolio betas and the portfolios residual standard deviations using the following formula:

𝑅_𝑝− 𝑅_𝑓 = 𝛾₀+ 𝛾₁𝛽_𝑝+ 𝛾₂𝛽_𝑝2_{+ 𝛾}

3𝑠𝑝+ 𝜀𝑝 (10)

Where 𝑠𝑝 is the residual standard deviation of the portfolio.

The sub-hypotheses if the CAPM theory is valid are:

1. 𝛾0 should equal zero and 𝛾1 should be positive if the average excess market return is

positive and negative if the average excess market return is negative, which implies a positive relation between risk and return

2. 𝛾₂ should equal zero, which implies a non-quadratic relation between risk and return 3. 𝛾₃ should equal zero, which implies that the beta coefficient explains all the risk of

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Chapter 5. Results

In this chapter the results will be presented. Firstly, the results of the individual regressions and the portfolio composition will be discussed. Secondly, the results of the portfolio regressions are explained. Thirdly, the hypothesis tests will be tabularized and their results will be interpreted and analysed. Fourthly, the results will be compared between the markets. Fifthly, the robustness tests are presented.

5.1 Step 1: Individual regressions

The first step consists of calculating the individual stock betas. The information regarding the individual stock betas is presented per market in Table 3. The results of India are remarkable, because the minimum beta of the Indian market is negative. The reason for this negative beta could be because the stock related to this beta has no return on 452 days.

Table 3: Individual stock betas

Classification Market Number

of Stocks Minimum Beta Maximum Beta Developed markets United States 400 0.41 2.00 Eurozone 400 0.06 1.91 Emerging markets Brazil 59 0.35 1.42 Russia 40 0.26 0.95 India 400 -0.38 2.43 China 400 0.16 1.57

5.2 Step 2: Portfolio regressions

The second step was to calculate the portfolio betas. The results of the portfolio regressions are presented for each market in Table 4. The average excess market returns of Brazil and Russia are negative, which is remarkable. The negative excess market returns can be explained by the high return on risk-free assets in these markets or the negative average market return.

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Table 4: Portfolio Betas

Classification Market Portfolios Minimum

Beta Maximum Beta Average Excess Portfolio Return Average Excess Market Return Developed markets United States 20 0.53 1.68 0.000562 0.000398 Eurozone 20 0.43 1.64 0.000499 0.000253 Emerging markets Brazil 10 0.42 1.27 -0.000082 -0.000496 Russia 10 0.31 0.90 0.000178 -0.000459 India 20 0.35 1.94 0.000599 0.000114 China 20 0.54 1.41 0.000586 0.000060

5.3 Step 3: Hypothesis tests

The third step tests the three sub-hypotheses made in chapter 4.3.

5.3.1 The risk-return trade-off hypothesis

If the CAPM theory is valid, the beta coefficient should be positive if the average excess market return is positive or negative if the average excess market return is negative and the constant should not be significantly different from zero. The results are given in Table 5. The beta coefficients are significantly negative at a 1% significance level for all markets except for the United States for which it is insignificantly positive. For Brazil and Russia this can be explained by the negative average market returns causing the relation between beta and the stock returns to be positive, which is in line with the CAPM. For the Eurozone, India and China the coefficient is significantly negative, which implies a negative risk-return trade-off. All constants are significantly different from zero. Therefore, for all markets no evidence is found to support the first sub-hypothesis, but a positive relation between risk and return is found for Brazil and Russia. The squared of the emerging markets is higher than the R-squared of the developed markets, which implies that the beta coefficient is a better predicter for the stock returns in emerging markets than in developed markets.

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Table 5: Sub-hypothesis 1

Variables United States Eurozone Brazil Russia India China

Beta 0.000097 -0.0002134*** -0.001597*** -0.001984*** -0.000959*** -0.000527*** (0.000088) (0.000047) (0.000111) (0.000380) (0.000120) (0.000113) Constant 0.000458*** 0.000704*** 0.001207*** 0.001318*** 0.001543*** 0.001141*** (0.000096) (0.000044) (0.000103) (0.000254) (0.000142) (0.000111) Observations 20 20 10 10 20 20 R-squared 0.0803 0.3896 0.9451 0.8025 0.7838 0.6467

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.10 5.3.2 The linearity hypothesis

The second sub-hypothesis states that the coefficient of beta squared should not be significantly different from zero. The results regarding the linearity test are presented in Table 6. For all markets the coefficient of beta squared is not significantly different from zero. Therefore, evidence is found to support sub-hypothesis 2 for all markets, which implies an non-quadratic estimated model. Again, the R-squared for the emerging markets are higher than for the developed markets.

Table 6: Sub-hypothesis 2

Beta 0.00092 -0.000145 -0.002315*** -0.002129 -0.000593 0.000426 (0.000576) (0.000267) (0.000598) (0.002709) (0.000743) (0.000822) Beta squared -0.000380 -0.000034 0.000432 0.000119 -0.000165 -0.000481 (0.000284) (0.000123) (0.000361) (0.001996) (0.000300) (0.000431) Constant 0.000042 0.000672*** 0.001476*** 0.001359 0.001370*** 0.000692* (0.000279) (0.000122) (0.000204) (0.000880) (0.000418) (0.000384) Observations 20 20 10 10 20 20 R-squared 0.2327 0.3908 0.9495 0.8026 0.7889 0.6887

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.10 5.3.3 The non-systematic risk hypothesis

The sub-hypothesis regarding the non-systematic risk implies that the coefficient of residual standard deviation should not be significantly different from zero. For the markets United States, India and China the coefficients of the residual standard deviation are significantly

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different from zero at a 5%, 1% and 1% significance level respectively. This implies that the variance in the return of the stocks in these markets is not completely explained by the beta coefficient, which is contradictory to the CAPM theory. Therefore, no evidence is found to support the third sub-hypothesis for the United States, India and China. For the Eurozone, Brazil and Russia the residual standard deviation coefficient is not significantly different from zero, which supports the third sub-hypothesis. Also, the R-squared is lower for the

developed markets than for the emerging markets.

Table 7: Sub-hypothesis 3

Variables United

States Eurozone Brazil Russia India China

Beta -0.000124 0.000602 -0.002348** 0.000486 0.000254 0.000362

(0.000609) (0.000529) (0.000722) (0.003030) (0.000607) (0.000539)

Beta squared 0.000210 -0.000569 0.000451 -0.002314 -0.000541* -0.000489*

(0.000322) (0.000376) (0.000425) (0.002473) (0.000277) (0.000274)

Residual standard deviation -0.110437** 0.086376 0.007781 0.082390 0.029630*** 0.045350***

(0.041485) (0.053179) (0.029958) (0.048692) (0.006843) (0.011907)

Constant 0.000878** 0.000082 0.001427*** -0.000238 0.000724* 0.000346

(0.000391) (0.000368) (0.000215) (0.001220) (0.000348) (0.000299)

Observations 20 20 10 10 20 20

R-squared 0.4145 0.4896 0.9499 0.8571 0.8526 0.7877

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.10

5.4 Market comparison

The United States only showed evidence to support the sub-hypothesis regarding the linearity test and in all regressions presented the lowest R-squared. For the Eurozone the results supported the second and third sub-hypotheses, but showed a negative relation between risk and return which cannot be explained. Also the Eurozone showed a relatively low R-squared in every regression. The results of India and China only presented evidence to support the second sub-hypothesis and showed a medium R-squared in every regression. These findings imply that for the United States, Eurozone, India and China no evidence is found to proof the applicability of the CAPM. On the other hand, the results of Brazil and Russia showed support for the second and third sub-hypotheses and showed support for a positive relation between risk and return. Also, Brazil and Russia presented the highest two R-squared in every regression. Therefore the CAPM is found to be more applicable in Brazil

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and Russia than in the other markets, which is contradictory to the main hypothesis made in chapter 2.3. The results are combined and presented in Table 8.

Table 8: Comparison table

Classification Market Sub-hypothesis 1

supported? Sub-hypothesis 2 supported? Sub-hypothesis 3 supported? CAPM applicable?

Developed markets United States No (0.0803) Yes (0.2327) No (0.4145) No

Eurozone No (0.3896) Yes (0.3908) Yes (0.4896) No

Emerging markets

Brazil No (0.9451)* Yes (0.9495) Yes (0.9499) No

Russia No (0.8025)* Yes (0.8026) Yes (0.8571) No

India No (0.7838) Yes (0.7889) No (0.8526) No

China No (0.6467) Yes (0.6887) No (0.7877) No

R-squared values in parentheses

* Positive relation found between risk and return

5.5 Robustness tests

5.5.1 Assumptions linear regression

When a linear regression is performed, the four assumptions of the linear regression should be met:

1. Linearity

2. Constant variance of the residuals (Homoscedasticity) 3. Normality of the residuals

4. Independency of the residuals (No serial correlation)

Since this paper has to perform a linear regression to calculate the beta for every individual stock, checking the assumptions for every linear regression performed would be very time consuming. Accordingly, the assumptions are only tested for the regressions performed to test the first sub-hypothesis in chapter 5.3.1 using formula (8).

Linearity: The linearity of the model was already tested in 5.3.2 to see if the model was

quadratic instead of linear. Appendix 1 now also presents a graphical view of the estimated models, displayed in scatter plots with a linear and quadratic best fitted line. The Eurozone, Brazil, Russia and India seem to have a linear best fitted line, meaning that the linearity assumptions for these markets is met. While, the United States and China appear to have a non-linear best fitted line, which violates the linearity assumption.

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Constant variance of the residuals: To test if the variance of the residuals is constant, also

known as homoscedasticity, the Breusch-Pagan/Cook-Weisberg test for heteroskedasticity is performed. This test has the null hypothesis that assumes homoscedasticity. The Chi-square values and p-values are presented in Table 9. All p-values are above 0.01, which means that for all market evidence was found to support the null hypothesis of homoscedasticity.

Table 9: Homoscedasticity results

Classification Market Chi-square

value P-value Homoscedasticity?*

Developed markets

United States 0.01 0.9199 Yes

Eurozone 0.37 0.5416 Yes Emerging markets Brazil 0.16 0.6935 Yes Russia 1.75 0.1853 Yes India 1.20 0.2732 Yes China 3.74 0.0532 Yes * At 1% significance level

Normality of the residuals: To test the normality of the residuals, the Shapiro-Wilk test for

normal data is performed. The null hypothesis of this test is that the residuals are normally distributed. The z-values and p-values are presented in Table 10. As can be seen in the table, all markets show evidence to support the null hypothesis of normality.

Table 10: Normality results

Classification Market Z-value P-value Normality?*

Developed markets

Eurozone -2.087 0.01843 Yes Emerging markets Brazil 1.200 0.11502 Yes Russia -0.522 0.30083 Yes India 0.210 0.41702 Yes China 0.076 0.46969 Yes * At 1% significance level

Independency of the residuals: If the residuals are independent, it means that the residuals

are uncorrelated. To test the independency of the residuals the Breusch-Godfrey test for serial correlation is executed. This test has the null hypothesis which assumes no serial correlation and thus independency of the residuals. The Chi-squared values and p-values are presented in Table 11. The table shows that all markets have independent residuals.

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Table 11: Independency results

Classification Market Chi-square

value P-value Independency?*

Developed markets

Eurozone 0.409 0.5223 Yes Emerging markets Brazil 0.279 0.5970 Yes Russia 2.128 0.1446 Yes India 0.003 0.9554 Yes China 2.597 0.1071 Yes * At 1% significance level

So, for all market all assumptions to perform a linear regression are met, except for the United States and China. The models estimated for these two markets appear to be non-linear.

5.5.2 Equal risk-free rates

To test whether the high risk-free rates in the emerging markets affect the regression results, an alternative test is executed in which the risk-free rate is assumed to be low and equal for every market. The lowest daily yield on 5-year US treasury bills between 2010-2015 is chosen as the risk-free rate for every market. This daily risk-free rate equals: 0.001486%. The results are presented in the tables in Appendix 2. The results show negligible differences in the coefficients, standard errors and R-squared. This means that the conclusions remain the same as stated above.

5.5.3 Different investor horizon

The fist sub-hypothesis tests if there exists a positive risk-return trade-off and since the research in this paper was based on daily data, the relation between risk and return was tested on a short investor horizon. This means that investors make their investment decisions on a day-to-day basis. In reality the relation between risk and return might be based on a longer investor horizon, especially in developing and volatile markets. So, risk might be changing in a short time period while return only adjusts within a longer time period. If this is the case, the relation between risk and return, described by beta, may only exist based on a longer time period. Therefore, the next step is to examine if the results change when a broader investor horizon is chosen using monthly returns instead of daily

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returns. Since the time period is 2010-2015, the number of observations per stock is now 72. The results are presented in Appendix 3 and summarized in Table 10.

Sub-hypothesis 1: The results are almost the same as the results based on daily data, but do

change a little. For every market the R-squared drops about 5%-20%, except for China. The R-squared of China drops almost with 65%. Also the beta coefficient for China is now insignificant.

Sub-hypothesis 2: The results regarding the linearity of the model do change more. Instead

of all markets having an insignificant beta squared coefficient, the Russian and Chinese market now show a significant beta squared coefficient at a 10% and 5% significance level respectively. This means that for the Russian and Chinese market the estimated model is not linear, which violates the second sub-hypothesis.

Sub-hypothesis 3: For the test of the third sub-hypothesis, China and India still show a

significant residual standard deviation coefficient. In this case also the Eurozone has a significant residual standard deviation coefficient at a 5% significance level. For the other markets the coefficient is not significantly different from zero.

Table 10: Comparison table different time horizon

Classification Market Sub-hypothesis 1

supported? Sub-hypothesis 2 supported? Sub-hypothesis 3 supported? CAPM applicable?

Developed markets United States No (0.0323) Yes (0.2378) Yes (0.2877) No

Eurozone No (0.2073) Yes (0.2827) No (0.5381) No

Emerging markets

Brazil No (0.7556)* Yes (0.7637) Yes (0.8193) No

Russia No (0.7098)* No (0.7655) Yes (0.7805) No

India No (0.6829) Yes (0.6879) No (0.8688) No

China No (0.0025) No (0.1416) No (0.5694) No

R-squared values in parentheses

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Chapter 6. Conclusion

The classical CAPM theory, as developed by Sharpe (1964) and Lintner (1965), is tested by numerous researchers in different markets and across different time periods. Some found supporting evidence (Harvey, 1991; Levy, 2010; Levy and Roll, 2010; Levy, Giorgi and Hens, 2012) and some found aspects of the CAPM which are not valid (Black et al., 1972; Dempsey, 2013; Fama and French, 2004; Fama and MacBeth, 1973; Roll, 1977). Most researches were performed in developed markets, but Harvey (1995) researched the CAPM in emerging markets and found no evidence of its applicability. Bekaert (1995) stated that three kinds of barriers keep emerging markets from complete integration, which violates one of the main assumptions of the CAPM.

This paper elaborated the study of the CAPM in emerging market by researching its applicability in four emerging markets and comparing them to two developed markets for the time period 2010-2015. The results showed almost no evidence that the CAPM is applicable in the developed markets United States and Eurozone, which is contradictory to the main hypothesis made in this paper but match the findings of Fama and MacBeth (1973) and Fama and French (2004). Also, no evidence was found for the emerging markets India and China, which is in line with the findings of Harvey (1995). On the other hand, evidence was found to partially support the applicability of the CAPM in the emerging markets Brazil and Russia, which is inconsistent with the results presented by Harvey (1995).

The R-squared values of the emerging markets exceed the R-squared values of the developed markets by far. Also, two out of the four emerging markets show evidence to support positive relation between risk and return against zero out of the two developed markets. Therefore, the hypothesis which states that the CAPM is less applicable in emerging markets when compared to developed markets, is rejected. The answer on the research question regarding the applicability of the CAPM in emerging markets for the time period 2010-2015 remains inconclusive, because two out of the four researched emerging markets show no evidence regarding the applicability of the CAPM and two markets partially do show evidence.

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Chapter 7. Discussion and Future Research

First, one of the main limitations of this paper is that the risk-free rate is assumed to be constant over the total time period researched while it fluctuates (moderately). If fluctuating risk-free rates are assumed, precision of the results may be enhanced.

Second, the choice of the market portfolio is also a limitation. It is possible that the chosen indices are not representative for the total market. If that is the case, the results cannot be generalized to the population.

Third, the stocks in the sample were randomly chosen from the stocks within an index that had available data for 2010-2015. So, stocks that only had data for a part of the researched time period were excluded. If the stocks in the sample size are chosen from the total index, including the stocks with only partially available data, the research can be improved. Also, the time period could be divided in multiple time periods, for example in 6 years, and the applicability of the CAPM could be tested for every year.

Fourth, another enhancement can be made by increasing the number of markets

researched. This paper only used two developed markets and four emerging markets. Also the number of stocks researched per market can be increased or the time period researched could be extended. If these numbers increase the external validity can be improved.

Furthermore, other variables can be used as control variables in the double-pass regression method. If the right variables are chosen, this can enhance the results.

Last, the assumptions to do a linear regression are not tested for every regression performed in this paper. It is thus unknown if these assumptions are met. It might be possible that some of these assumptions are violated, meaning that the results are biased. To strengthen the power of the results, these assumptions should be tested. When these assumptions are not met, solutions should be found.

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Reference List

Bekaert, G., 1995. Market Integration and Investment Barriers in Emerging Equity Markets. The World Bank Economic Review. Vol. 9: 75-107.

Black, F., 1972. Capital Market Equilibrium with Restricted Borrowing. The Journal of

Business. Vol. 45: 444-455

Black , F., Jensen, M. C. and Scholes, M. S., 1972. Studies in The Theory of Capital Markets. New York: Praeger Publishers Inc.

Dempsey, M., 2013. The Capital Asset Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance?. ACABUS A Journal of Accounting, Finance and

Business Studies. Vol. 49: 7-23

Fama, E. F. and French, K. R., 1992. The Cross-Section of Expected Stock Returns. The Journal

of Finance. Vol. 47: 427-465

Fama, E. F. and French, K. R., 2004. The Capital Asset Pricing Model: Theory and Evidence.

The Journal of Economic Perspectives. Vol. 18: 25-46

Fama, E. F. and MacBeth, J. D., 1973. Risk, Return, and Equilibrium: Empirical Tests. The

Journal of Political Economy. Vol. 81: 607-636

Harvey, C. R., 1991. The World Price of Covariance Risk. The Journal of Finance. Vol. 46: 111-157

Harvey, C. R., 1995. Predictable Risk and Returns in Emerging Markets. The Review of

Financial Studies. Vol. 8: 773-816

Levy, H., 2010. The CAPM is Alive and Well: A Review and Synthesis. The European Financial

Management. Vol 16: 43-71

Levy, H., De Giorgi, E. G., Hens, T., 2012. Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?. The European Financial Management. Vol 18: 163-182 Levy, H., Roll, R., 2010. The Market Portfolio May Be Mean/Variance Efficient After All. The

Review of Financial Studies. Vol. 23: 2464-2491

Lintner, J., 1965. The Valuation of Risk Assets and The Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics. Vol. 47: 13-37

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Roll, R., 1977. A Critique of The Asset Pricing Theory’s Tests Part I: On Past and Potential Testability of the Theory. The Journal of Financial Economics. Vol. 4: 129-176 Sharpe, W. F., 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions

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Appendices

Appendix 1: Scatter plots with linear and quadratic fitted lines

United states linear:

United states quadratic:

Eurozone linear: .0 0 0 3 .0 0 0 4 .0 0 0 5 .0 0 0 6 .0 0 0 7 0.60 0.80 1.00 1.20 1.40 1.60 Beta

Average Excess Rp Fitted values

.0 0 0 3 .0 0 0 4 .0 0 0 5 .0 0 0 6 .0 0 0 7 0.60 0.80 1.00 1.20 1.40 1.60 Beta

.0 0 0 3 .0 0 0 4 .0 0 0 5 .0 0 0 6 .0 0 0 7 0.50 1.00 1.50 2.00 Beta

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29 Eurozone quadratic: Brazil linear: Brazil quadratic: .0 0 0 3 .0 0 0 4 .0 0 0 5 .0 0 0 6 .0 0 0 7 0.50 1.00 1.50 2.00 Beta

-. 0 0 1 -. 0 0 0 5 0 .0 0 0 5 0.40 0.60 0.80 1.00 1.20 Beta

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30 Russia linear: Russia quadratic: India linear: -. 0 0 0 5 0 .0 0 0 5 .0 0 1 0.20 0.40 0.60 0.80 1.00 Beta

-. 0 0 0 5 0 .0 0 0 5 .0 0 1 0.20 0.40 0.60 0.80 1.00 Beta

-. 0 0 0 5 0 .0 0 0 5 .0 0 1 .0 0 1 5 0.00 0.50 1.00 1.50 2.00 Beta

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31 India quadratic: China linear: China quadratic: -. 0 0 0 5 0 .0 0 0 5 .0 0 1 .0 0 1 5 0.00 0.50 1.00 1.50 2.00 Beta

.0 0 0 2 .0 0 0 4 .0 0 0 6 .0 0 0 8 .0 0 1 0.60 0.80 1.00 1.20 1.40 Beta

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Appendix 2: Test results equal risk-free rates

Sub-hypothesis 1:

Beta 0.000097 -0.000214*** -0.001597*** -0.001984*** -0.000959*** -0.000527*** (0.000088) (0.000468) (0.000111) (0.000380) (0.000120) (0.000113) Constant 0.000482*** 0.0007264*** 0.001492*** 0.001523*** 0.001745*** 0.001217*** (0.000096 (0.0000438) (0.000103) (0.000254) (0.000142) (0.000111) Observations 20 20 10 10 20 20 R-squared 0.0803 0.3896 0.9451 0.8026 0.7838 0.6474

Variables United

Beta 0.000921 -0.000145 -0.002315*** -0.002128 -0.000594 0.000425 (0.000580) (0.000267) (0.000598) (0.002709) (0.000743) (0.000822) Beta squared -0.000380 -0.000034 0.000432 0.000119 -0.000165 -0.000481 (0.000284) (0.000123) (0.000362) (0.001996) (0.000300) (0.000431) Constant 0.000066 0.000695*** 0.001761*** 0.001563 0.001572*** 0.000768* (0.000279) (0.000122) (0.000204) (0.000880) (0.000418) (0.000384) Observations 20 20 10 10 20 20 R-squared 0.2327 0.3909 0.9495 0.8027 0.7888 0.6887

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Variables United

Beta -0.000123 0.000602 -0.002348** 0.000486 0.000254 0.000362

(0.000609) (0.000529) (0.000722) (0.003029) (0.000607) (0.000539)

Beta squared 0.000210 -0.000569 0.000451 -0.002314 -0.000541* -0.000489*

(0.000322) (0.000376) (0.000425) (0.002473) (0.000277) (0.000274)

Residual standard deviation -0.110414** 0.086365 0.007764 0.082377 0.029629*** 0.045356***

(0.041481) (0.056179) (0.029957) (0.048692) (0.006843) (0.011907)

Constant 0.0009014** 0.000104 0.001711 -0.000033 0.000927** 0.000423

(0.000391) (0.000368) (0.0002152) (0.001220) (0.000348) (0.000299)

R-squared 0.4144 0.4897 0.9499 0.8571 0.8526 0.7878

Appendix 3: Test results different investor horizon

Beta 0.000880 -0.002611** -0.211608*** -0.18344*** -0.012813*** -0.000424 (0.001303) (0.000994) (0.003359) (0.003455) (0.002333) (0.002383) Constant 0.012615*** 0.014118*** 0.020902*** 0.020653*** 0.034210*** 0.015041*** (0.001532) (0.001201) (0.002374) (0.002313) (0.003650) (0.002562) Observations 20 20 10 10 20 20 R-squared 0.0323 0.2073 0.7556 0.7098 0.6829 0.0025

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Beta 0.010561* 0.004192 -0.030141 -0.001751 -0.008726 -0.017632** (0.005620) (0.005105) (0.016305) (0.010306) (0.012299) (0.006446) Beta squared -0.004448 -0.003355 0.005139 -0.011650* -0.001513 0.008558** (0.002840) (0.002668) (0.008317) (0.006132) (0.003765) (0.002964) Constant 0.008090*** 0.011223*** 0.023758*** 0.015881*** 0.031994*** 0.023083*** (0.002536) (0.002055) (0.006165) (0.002595) (0.008919) (0.003678) Observations 20 20 10 10 20 20 R-squared 0.2378 0.2827 0.7637 0.7655 0.6879 0.1416

Variables United

Beta 0.003500 0.018684** -0.027934** 0.008013 0.013787* -0.02136***

(0.009041) (0.007492) (0.013267) (0.020570) (0.007908) (0.00563)

Beta squared -0.000376 -0.014695** 0.002861 -0.020069 -0.010135*** 0.011448***

(0.004908) (0.005050) (0.006521) (0.017685) (0.002759) (0.002871)

Residual standard deviation -0.263271 0.585146** 0.372087 0.134974 0.233309*** 0.233401***

(0.222106) (0.232849) (0.214688) (0.277107) (0.042655) (0.051279)

Constant 0.015524** -0.003341 0.009944 0.005753 0.010572 0.012388***

(0.007295) (0.006063) (0.008322) (0.020279) (0.006627) (0.003111)

R-squared 0.2877 0.5381 0.8193 0.7805 0.8688 0.5694