Testing the Validity of the Capital Asset Pricing Model in Turkey”

T.C.

İstanbul Üniversitesi

Sosyal Bilimler Enstitüsü

İngilizce İktisat Anabilim Dalı

Yüksek Lisans Tezi

Testing The Validity of The Capital Asset Pricing Model

In Turkey

Veysel Eraslan

2504080001

Tez Danışmanı

Prof. Dr. Nihal Tuncer

İstanbul 2011

“Testing The Validity of The Capital Asset Pricing Model In Turkey”

Veysel ERASLAN

ÖZ

Finansal Varlıkları Fiyatlandırma Modeli yıllardan beri akademisyenlerin üzerinde çalıştığı en popüler konulardan biri olmuştur. Finansal Varlıkları Fiyatlandırma Modeli’nin farklı ekonomilerdeki geçerliliğini test etmek amacıyla birçok çalışma yapılmıştır. Bu çalışmalarda modeli destekleyen veya desteklemeyen farklı sonuçlar elde edilmiştir. Bu çalışmada, Finansal Varlıkları Fiyatlandırma Modeli’nin Sharpe- Lintner-Black versiyonu, Ocak 2006-Aralık 2010 zaman dilimi içerisinde İstanbul Menkul Kıymetler Borsası aylık kapanış verileri kullanılarak test edilmiştir. Çalışmanın amacı modelde risk ölçüsü olarak ifade edilen portföy betası ile portföy getirisi arasındaki ilişkinin belirtilen zaman dilimi içerisinde İstanbul Menkul Kıymetler Borsası’nda test edilmesidir. Çalışmada iki farklı yöntem kullanılmıştır. Bunlardan birincisi koşulsuz (geleneksel) analiz yöntemidir. Bu yöntemin temelini Fama ve French’in (1992) çalışması oluşturmaktadır. İkinci yöntem olarak ise Pettengill v.d. nin (1995) koşullu analiz tekniği kullanılmıştır. Yapılan analizler sonucunda Finansal Varlıkları Fiyatlandırma Modeli’nin İstanbul Menkul Kıymetler Borsası’nda geçerli olduğu bulgusuna ulaşılmış olup betanın bir risk ölçüsü olarak kullanılabilirliği desteklenmiştir.

ABSTRACT

The Capital Asset Pricing Model has been the most popular model among the academicians for many years. Lots of studies have been done in order to test the validity of the Capital Asset Pricing Model in different economies. Various results were obtained at the end of these studies. Some of these results were supportive while some of them were not. In this study, the Sharpe-Lintner-Black version of the Capital Asset Pricing Model is tested in Istanbul Stock Exchange including the years starting from January 2006 through December 2010. The aim of the study is testing the relationship between beta and rate of return in Istanbul Stock Exchange during the given time period. Beta is used as the risk measure in the model. Two different approaches are used in the study. The first one is the unconditional approach which is based on the study by Fama and French (1992). The second approach is based on the work of Pettengill et al (1995). The empirical findings of these models reveal that the Capital Asset Pricing Model is applicable to Istanbul Stock Exchange and beta can be used as a useful measure of risk.

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PREFACE

The Capital Asset Pricing Model (CAPM) has been the most popular model among the academicians for many years. Lots of studies have been done in order to test the validity of the CAPM in different economies. Different results are obtained at the end of these studies. Some of these results validate the CAPM while some of them do not.

In this study, the Sharpe-Lintner-Black version of the CAPM is tested in the Istanbul Stock Exchange including the years starting from January 2006 to December 2010. The aim of the study is testing the relationship between portfolio betas and portfolio returns in ISE during the specified time period. Two different approaches are used in the study. The first one is the unconditional approach which is based on the study of Fama and French (1992). The unconditional approach requires that the periods in which the excess market-portfolio-returns are positive and negative are evaluated together. As a result of this evaluation it is found that the CAPM is not supported by the unconditional test. This bias is attributed to combining the positive excess market-portfolio-return and negative excess market-portfolio-return periods. To avoid this bias, in the second model, based on the work of Pettengill et al. (1995), positive excess market return and negative excess market return periods are separated from each other. Test results of the second model reveal that excess portfolio returns and portfolio betas are positively related when the excess market-portfolio-return is positive and negatively related when the excess market-portfolio-return is negative. That is to say, higher beta portfolios attract higher excess returns when the excess market-portfolioreturn is positive and higher beta portfolios attract lower excess returns when the excess market-portfolio-return is negative. This result proves the existence of a systematic-conditional relationship between portfolio betas and portfolio returns. As a result, we conclude that the CAPM is applicable to ISE and beta can be used as a useful measure of risk.

I would like to express my special thanks to my advisor Prof. Dr. Nihal Tuncer and Assist. Prof. Dr. Salvatore J. Terregrossa for their great help. I also thank to

Assist. Prof. Dr. Yasin Barış Altaylıgil for his help. I also thank to my family for their continued support.

LIST OF TABLES

Page

Table 1 : Test Results and Average Excess Returns (Unconditional) ………………………………………………………………47 Table 2 : Coefficient of Determination Values (Unconditional)……..48 Table 3 : Portfolio Betas and Average Excess Portfolio-Returns (Conditional-Positive)………………………………….…...49 Table 4 : Portfolio Betas and Average Excess Portfolio-Returns (Conditional-Negative)……………………………….…….50 Table 5 : Test Results of the Model 1……..…………………………54 Table 6 : Test Results of the Model 2………..………………………55

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LIST OF FIGURES

Page Figure 1 : TheCapital Allocation Line……………………………………....9 Figure 2 : The Efficient Frontier………………………………...……….…10 Figure 3 : The Capital Market Line and the Market Portfolio…………..….11 Figure 4 : The Sensitivity of Portfolio Return to the Market Return...... 12 Figure 5 : The Security Market Line………………………………….….…14 Figure 6 : The Therotical SML and Empirically Estimated SML……….....16 Figure 7 :Excess Portfolio Return-Portfolio Beta Relationship (Unconditional)……………………………………………...... ….51 Figure 8 : Excess Portfolio Return-Portfolio Beta Relationship (Conditional-Positive)……………….………………...………….52 Figure 9 : Excess Portfolio Return-Portfolio Beta Relationship (Conditional-Negative)……………………………………...…....53

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LIST OF ABBREVIATIONS

APT : Arbitrage Pricing Theory ASE : Athens Stock Exchange CAL : Capital Allocation Line CAPM : Capital Asset Pricing Model CML : Capital Market Line ISE : Istanbul Stock Exchange NYSE : New York Stock Exchange SLB : Sharpe-Lintner-Black Model SML : Security Market Line TSE : Tokyo Stock Exchange

INTRODUCTION

After the specification of the Portfolio Theory by Markowitz, there have been many studies on the asset pricing issue. One of the first and the most important models regarding asset pricing is the Capital Asset Pricing Model (CAPM). The Sharpe- Lintner and Black (SLB) version of the CAPM has been the most popular model due to its testability in the various stock markets around the globe. There are many studies supporting the validity of the CAPM, while there have been some that attempt to invalidate the theory. Still, the CAPM remains an on-going, popular, and current topic in the literature.

The goal of this thesis is testing the validity of the CAPM in Turkey, by using the models of Fama and French (1992) and Pettengill et al. (1995) with Turkish data. In order to test the CAPM, the SLB version of the model is tested with data from firms listed on the Istanbul Stock Exchange (ISE). The SLB version depicts a positive, linear relation between beta and expected portfolio returns, and is illustrated by the Security Market Line.

The SLB version of the CAPM is tested in the present study with both the unconditional approach (of Fama and French (1992), and conditional approach (of Pettengill et al. (1995), respectively.

In the unconditional approach, both positive and negative excess market-portfolioreturn monthly data are combined into a single data set. With this approach, it is found that there is not a direct relationship between portfolio betas and average portfolio excess-returns. However, this finding does not necessarily invalidate the CAPM. As for the conditional approach, periods when the excess market-portfolioreturn is positive, and periods when the excess market-portfolio-return is negative are evaluated separately. It is concluded in the result of the conditional approach that higher beta portfolios attract higher excess-returns when the excess market-portfolioreturn is positive, and higher beta portfolios attract lower excess-returns when the excess market-portfolio-return is negative. This result is consistent with the basic

tenets of the CAPM. Thus, it is reasonably concluded that the CAPM is a valid model regarding firms listed on the ISE from January 2006 through December 2010, the years of the present study.

1. THEORY OF THE CAPITAL ASSET PRICING MODEL

1.1. Sharpe- Lintner-Black (SLB) Model

The CAPM was born at a time when the effect of uncertainty on decision making was new and most of the investors were not aware of the theoretical part of the risk and return relationship in the capital market. The question of how the risk of an investment affects its return has been the basic concern of the investors. The CAPM- SLB has been the first solution to this problem. The model was developed by William Sharpe (1964), Jack Treynor (1961), John Lintner (1965), Jan Mossin(1966) and Fischer Black (1972). This model can be noted as the birth of the asset pricing theory also. The CAPM leads to the development of new asset pricing models such as Arbitrage Pricing Theory (APT). Among these models, the CAPM-SLB has been the most popular one due to its powerful offerings and intuitively pleasing predictions about how to measure the strength of the relation between risk and return. The CAPM is defined as:

“idealized portrayal of how financial markets price securities and thereby determine expected returns on capital investments. The model provides a methodology for quantifying risk and translating that risk into estimates of expected return on equity. The CAPM cannot be used in isolation because it necessarily simplifies the world of financial markets. But financial managers can use it to supplement other techniques and their own judgment in their attempts to develop realistic and useful coast of equity calculations.”1

To be more specific, main suggestion belongs to the CAPM is that high expected return is associated with a high level of risk. There is a linear relationship between expected return on an asset and risk of the asset when the expected return is higher than the risk free rate. In this study, risk refers not to the total risk of the asset but to the systematic risk of the asset.

There are two types of risk which are systematic or non-diversifiable risk and non- systematic or diversifiable risk. The risk related to general economic conditions of

1David W. Mullins, “Does the Capital Asset Pricing Model work?,” Harvard Business Review, January-February 1982, p. 105. 3 both the country and the world is called as systematic risk. In general systematic risk is related to the market. It is not specific to the company. Macroeconomic conditions affecting all the firms in the world or all the firms in that country can be classified as systematic risk factors. In other words, systematic risk is the common risk for all companies and firms. Inflation rate, interest rates, business cycles, economic crisis, exchange rates can be resources of systematic risk.

Another type of risk is non-systematic risk. Firm specific factors are resources to non-systematic risk. These factors are unique to that firm or company and do not affect other companies and firms. Discovering oil in a company’s property, entering a lower-cost competitor to the same market, announcing to make new investments, positive seasonal effects to the company’s returns are all examples of non-systematic risk factors. While non-systematic risk can be reduced by diversification, systematic risk cannot be reduced. The measure of systematic risk is named as beta and this is the only measure of systematic risk. Beta can also be defined as the sensitivity of an asset’s return to the market return. Market return is the return of market portfolio which contains all the assets in the economy. Un-diversifiable risk constitutes the core idea of the CAPM. Since the diversifiable risk can be eliminated, there is no reward for bearing it. That is to say only the un-diversifiable risk is important in determining the expected return of any asset or portfolio.

So how do we measure the risk of assets and portfolios? “The standard deviation and the variance are equally acceptable and conceptually equivalent measures of an asset’s total risk.”2 The risk of a portfolio is determined by the proportions of individual assets, variance or standard deviation of the assets and covariances (correlations). The larger the variance or standard deviation of an asset/portfolio the riskier is the asset/portfolio.

As was mentioned above for the presence of a linear relationship between the risk and return of an asset or portfolio, expected return should be higher than risk free rate. A risk free asset is defined as an asset having the lowest level of risk among all

2 Jack Clark Francis, Investments: Analysis and Management, 5th ed., McGraw-Hill, 1991, p. 13.

4 the available asset and risk free rate is known as the rate of return of a risk free asset. Generally Treasury Bills are accepted as risk free asset.

The roots of the CAPM come from the Portfolio Theory developed by Harry Markowitz. In this theory, investors are assumed to be risk averse i.e. they do not like to take risk. As a result of this assumption investors care only about the mean and the variance of a portfolio, which concludes that investors choose “mean-variance efficient” portfolios. These portfolios include assets minimizing the variance of portfolio return given the expected return and maximizing expected return given the variance.3

The earlier version of the CAPM was not detailed as the later ones. It dealt only with the some basic points of capital markets and assumed away the others. Studies on the CAPM contributed much to the improvement of the model. These studies linked the model to the capital markets more realistically by adopting other real world phenomenon. Lintner (1976) takes the returns into consideration in real terms. Brennan (1970) deals with the effects of taxation considering the CAPM. Black (1970) makes a different and beneficiary study by omitting the riskless asset from the model. Merton (1973) incorporates investors’ concern with future investment opportunities. Rubinstein (1974) uses a more generalized utility functions set. Kraus and Litzenberger (1976) deal with the third moment of the return distribution. Levy (1978) incorporates transactions costs. Breeden (1979) takes investors’ preferences for consumption into consideration. Merton (1987) focuses on market segmentation and Markowitz (1990) deals with restrictions on short sales.4

3Eugene F. Fama, Kenneth R. French, “The Capital Asset Pricing Model: Theory and Evidence,” The Journal of Economic Perspectives, Vol. XVIII, No: 3, Summer 2004, p. 26. 4William F. Sharpe, “Capital Asset Prices with and without Negative Holdings,” The Journal of Finance, Vol. XLVI, No: 2, June 1991, p. 490. 5

1.1.1. Assumptions and Implications of the CAPM-SLB

As in other theories or models, the CAPM is also based on some assumptions. These assumptions determine the applicability and the success of the CAPM. Since the model is based on the Markowitz’s Portfolio Theory, it contains all the assumptions belong the Portfolio Theory. These assumptions are summarized as the following:

a) Investors are risk-averse. This assumption implies that investors do not like taking risk. In the presence of two assets having the same expected return, risk- averse investor chose the one which has the lower risk. If investors were not risk- averse, all of them would select the asset having the highest return i.e. they would chose higher return to the lower. Investors evaluate their investment decisions only in terms of expected return and standard deviation of the return including the same single period. In other words they choose the portfolio that they perceive to be mean variance efficient.

b) Capital markets assumed to be perfect in several perspectives. These perspectives can be stated as infinite divisibility of all assets, absence of transaction costs, short selling restrictions, taxes, costless and available information, ability to buy and sell at the risk free rate.

c) All the investors have the same investment opportunities. They have the same opportunity to get the same asset or portfolio. No investor has superior chance than the others. There is no restriction for any investor to reach any asset. Additionally, all investors can select from the alternative portfolios.

d) All the investors have same expected return and expected variance belonging to the any asset or portfolio. This means every investor have homogeneous beliefs about the expected return and risk of any investment.

e) All investors are price takers. They cannot affect the asset prices individually because there are lots of investors in the market. This assumption also asserts that the market is perfectly competitive.

It is impossible that all of these assumptions are accepted by all academicians. There are some objections and criticism to the assumptions of the CAPM. The CAPM assumes that any investor can borrow and lend any amount at riskless rate. This assumption is criticized as a bad approximation for some investors. Lintner states that dropping any of the CAPM assumptions except this one does not change the structure of the model. However, if this assumption is dropped it is assumed that the model changes significantly.5

There are some academicians who find these assumptions unrealistic. Regarding these people Mullins states that the assumptions may be unrealistic but making such simplifications is necessary for the development of new and better models. He also underlines that it is important to test the CAPM not by taking the reasonableness of the assumptions into consideration but checking the validity and usefulness of the model.

The CAPM has a number of important implications. One of the most important ones is that all investors choose the market portfolio in the equilibrium without taking their risk preferences into consideration.

Secondly, the risk measure of the assets or portfolios are based only on the un- diversifiable or systematic risk which means unique risk is diversified away and can not affect the risk level of an asset or portfolio. As was specified earlier, the risk level is measured by beta which stands for the level of systematic risk. Beta is an identification of simultaneous movements of asset or portfolio returns with market returns. In other words beta shows how volatile an asset or portfolio with respect to the market portfolio. Beta is calculated by dividing the covariance of the market return and asset or portfolio return by market variance.

Thirdly, an asset having a high risk (or beta) will have a high expected return to the extent that its risk is measured as sensitivity to the market return.

5Fischer Black, “Capital Market Equilibrium with Restricted Borrowing,” The Journal of Business, Vol. XLV, No: 3, July 1972, p. 445. 7

In this model it is emphasized that expected return for any asset depends on the covariance of asset and market, risk free rate and expected market return.

1.1.2. The Capital Allocation Line and The Capital Market Line

Taking all the assumptions into consideration, it is obvious that all investors hold the identical risky portfolios. If all investors use identical mean-variance analysis in the same market to the same assets in the same time period with same security analysis under identical tax restrictions, it is expected that they all arrive at the same determination of the optimal risk portfolio. In other words, they all chose identical efficient frontier and have the same tangency portfolio for the Capital Allocation Line (CAL).6 It is better to mention about the CAL and the efficient frontier before the Capital Market Line (CML). The CAL is known as the representation of the risk and return relationship of a portfolio. In other words, the expected return-standard deviation combinations that can be obtained by creating portfolios can be generated. The line joining all such combinations is called the Capital Allocation Line. Figure 1 is the graphical representation of the CAL.

6 Zvı Bodie, Alex Kane, Alan J. Marcus, Essentials of Investments, 3rd ed., McGraw-Hill, 1998, p. 200. 8

Figure 1: The Capital Allocation Line

Source: Siaw Peng Wan, (Çevrimiçi) http://www.ifa.com/media/images/pdf%20files/mpttextbook.pdf, 19 January 2011.

In this graph vertical axis represents the expected return of a portfolio while horizontal axis represents standard deviation or risk of that portfolio. Thus a point on the CAL shows the expected return of a portfolio having a specific standard deviation. Vertical intercept represents the risk free rate. The slope of the CAL

ER()− R line which is rrf represents the price for risk. For this equation σ r

ER()rrf− R stands for the risk premium of the risky asset. Risk- premium of an asset is stated as the compensation given to the investors for taking risk more than the risk free asset.

Another important concept that is noteworthy to mention is efficient frontier. Efficient frontier includes only risky assets, meaning that there is no risk free asset on the efficient frontier. If we think all the possible risk (standard deviation) return combinations we get a curve presented as in the Figure 2:

Figure 2: The Efficient Frontier

Source: P.V.Viswanath, “Optimal Portfolio Construction and Selection,” 2000, (Çevrimiçi) http://webpage.pace.edu/pviswanath/notes/investments/assetalloc.html, 15 March 2011.

Global minimum variance portfolio represents the portfolio with the lowest standard deviation that is attainable. The figure should be analyzed partially. Upper half and lower half of the curve are symmetrical to each other with respect to the minimum variance portfolio. Only upper minimum variance frontier is called as efficient frontier this is because any point on the lower variance frontier has lower expected return than the ones on the upper variance frontier, given the standard deviation. Hence the lower variance frontier is inefficient. Portfolios outside the efficient frontier cannot be attained by the investors.

Main concept to be discussed is the CML which is known as the CAL tangent to the efficient frontier. Thus, CML including the optimal risky portfolio is a particular version of CAL. It should be noted that optimal risky portfolio is associated with the market portfolio. Figure 3 shows the relationship between the CML and market portfolio.

Figure 3: The Capital Market Line and the Market Portfolio

E(Rp)

CML

σp

In the figure M represents the market portfolio. Analyzing the figure underlines that given the standard deviation; portfolios on the CML have higher return than the ones on the efficient frontier.

Another important point for the CML is that compared to the efficient frontier one unit increase in the risk level will leads to more return on the CML. This implies that the presence of the risky asset increases the portfolio return without increasing the risk a lot.

Taking all these specifications into consideration, the CML equation is written as the following:

⎡⎤ER( Mrf) − R ER()prf=+ R ⎢⎥σ p (1) ⎣⎦σ M

where, E ()Rp is the expected portfolio return, Rrf is the risk free rate, E ()RM is the expected market return, σ M is the standard deviation of the market and σ p is the standard deviation of the portfolio.

1.1.3. The Characteristic Line

Since the systematic risk is diversified away, the only risk interesting the investor is the market (systematic) risk. Market risk can be viewed as the sensitivity of a portfolio return to the market return. This relationship between market return and portfolio return is denoted by the regression line which is the characteristic line. The slope of the characteristic line is determined by the sensitivity which means by the market risk i.e. by beta. In other words, the slope is the beta of the portfolio. Market beta is assumed to be 1. Portfolios having beta higher than 1 are can be viewed as aggressive portfolios meaning that a 1 per-cent change in the market return will lead to more than 1 per-cent change in the portfolio return. On the other hand, portfolios having beta less than 1 are named as defensive assets meaning that 1 per-cent change in the market return will lead to a lower change in the portfolio return. Neutral portfolios are those whose betas are same with the market portfolio meaning that these portfolios have the same return with the market portfolio. Figure 4 shows the graphical representation of those mentioned above.

Figure 4: The Sensitivity of Portfolio Return to the Market Return

Calculation of the beta (slope) of each portfolio is also related to the correlation between the market and the portfolio. Putting all these together, beta of each portfolio is obtained from the equation (2) :

cov(RRim , ) ρσim i ρσ im i βσim===2 (2) var ()Rmmσσ m

where Ri and Rm stands for the portfolio (asset) return and market return respectively. σ i and σ m represent variance of the portfolio and variance of the market, respectively. ρim is the correlation coefficient between the market and the portfolio.

It is important to underline that the characteristic line is also a regression line. Regression equation of this line is:

RReiiimi= α ++β (3)

where, αi is the vertical intercept of the regression line (characteristic line). The expected value of the error term or residuals denoted by ei is zero. Since the residual term has zero expected value, each intercept is directly related to the security’s beta value.7

1.1.4. The Security Market Line

The relationship between the expected return and the beta is considered as risk- reward equation. It is obvious that the main implication of the CAPM is that appropriate measure of the risk is only beta. This is because beta is proportional to the risk which the asset contributes to the optimal risky portfolio. Thus, the risk ⎡⎤ 8 premium, β ⎣⎦E ()RRmf− , is a function of beta. We can plot the expected risk- return relationship in a graph by putting the expected return on the vertical axis and

7Sharpe, “ Capital Asset Prices with and without Negative Holdings,” p. 497. 8Bodie, Kane, Marcus, Essentials of Investments, p. 204. 13 the risk on the horizontal axis. The regression line representing this relationship is called Security Market Line (SML).

Figure 5: The Security Market Line

In the Figure 5, M represents the market portfolio whose beta is 1. The slope of the SML is the excess return on the market portfolio. If the market is in equilibrium, the CAPM implies that all the securities lie on the SML. If the securities are not on the SML then the market is accepted as inefficient. This implies that the SML provides a necessary and sufficient condition for mean variance efficiency of the market portfolio.9 This relationship again proves that expected return of a security is dependent on the market risk, not total risk. SML line is represented by the equation (4):

⎡⎤ ER()ifimf=+ Rβ ⎣⎦ ER( ) − R (4)

9Gulnara Rejepova, “Test of the Capital Asset Pricing Model in Turkey,” Unpublished Master of Science Thesis, Doğuş University Institute of Social Sciences, 2005, p. 12. 14

Rearranging the equation gives the equation (5):

⎡⎤ ER()ifi−= Rβ ⎣⎦ ER( mf) − R (5)

Right hand side of the equation (5) stands for the risk premium described before. It is assumed that market return is higher than the risk free rate because investors require a positive risk premium. This assumption implies that securities having higher beta or higher risk associate with higher risk premiums. In other words, an investor who is not risk-averse can receive a higher return from a more risky asset. This means that there is a positive risk return trade-off. However it should be noted that this inference cannot be hold all the time for the individual assets because undiversified portfolios and individual assets have unsystematic risk factor affecting the expected return. Analyzing different values of beta reveals that when the beta is 1, portfolio return equals market return. A more risky portfolio which has a beta higher than 1 attracts more excess return than the excess market portfolio return. And the vice versa for the less risky assets.

The empirical results bring some different approaches to the SML debates. There are some differences between empirical SML and theoretical SML. As a result of empirical studies it is concluded that theoretical SML is steeper than the empirical SML. It is obvious in the Figure 6 that high beta portfolios earn less than the CAPM assumes and low beta portfolios earn more than expected.10

10Mullins, “Does the Capital Asset Pricing Model work?,” p. 112. 15

Figure 6: The Theorotical SML and Empirically Estimated SML

Taking all the results about the SML into consideration, William Sharpe concluded that investors and decision makers can use the SML relationship to determine the desirability of an investment by comparing its expected return with that available in the capital market for investments with similar beta values.

Evaluating CML and SML together is useful in understanding the relation of these two lines. The CML indicates the relationship between portfolio returns and their standard deviations. Risk free asset is included in this relationship. On the other hand, the SML shows the relationship between an individual asset and its risk including the risk free asset. The SML is also used for portfolios. “The security market line provides a benchmark for evaluation of investment performance. Given the risk of an investment as measured by its beta, the SML provides the required rate of return that will compensate investors for the risk of that investment, as well as for the time value of money.”11 Stocks which are overpriced appear above the SML while stocks which are underpriced appear under the SML.

The SLB version of the CAPM is found to have some weaknesses by some researchers and some of the earlier tests reject the model in various respects. They assert that a positive relationship between return and beta is true but it is too flat. They also underline that although the SLB model argues that the intercept value is the risk free rate and coefficient of beta is excess market return, some tests find that

11Bodie, Kane, Marcus, Essentials of Investments, p. 205. 16 the intercept value is greater than the average risk free rate and the coefficient of beta is less than the excess market return.12

Another objection comes from Fischer Black (1972). He stated that risk free borrowing and lending is an unrealistic assumption and he developed a different version of the CAPM including without risk free borrowing or lending. He finds that core results of the CAPM can also be obtained by allowing unrestricted short sales of risky assets.

Fama and French (2004) underline that the unrestricted short-selling is as unrealistic as unrestricted risk free borrowing and lending. They claim that when there is no risk free asset and short sales of risky assets are not allowed; mean variance investors still choose efficient portfolios. On the other hand, they mention that if there is no short selling of risky assets and no risk free asset, efficient portfolios are not efficient actually. This also leads to a fact that market portfolio is not efficient meaning that the CAPM relation between expected return and market beta is lost.

In another article Fama and French (1996) make two additional negative conclusions about Sharpe and Lintner’s study in 1965. They assert that allowing variations in the CAPM market betas that is unrelated to the size, the univariate relation between beta and average return is weak. Another implication in their study is that beta is not the only variable explaining the returns. The ratio of book to market equity and other variables help to explain average return.13

1.1.5. Testing the CAPM

Taking all the information above into the consideration it is easy to summarize that the SLB version of the CAPM implies a positive risk –return trade off. According to the model, expected return of an asset only depends on risk free rate, beta and the

12Fama, French, “The Capital Asset Pricing Model: Theory and Evidence,” p. 35. 13Eugene F. Fama, Kenneth R. French, “The CAPM is wanted, Dead or Alive,” The Journal of Finance, Vol. LI, No: 5, December 1996, p. 1947.

17 market return. Additionally, the model implies that beta is the only reason that expected returns differ.14

Most of the tests of the CAPM are based on the idea above. Studies aiming to test the CAPM followed the test techniques developed by Black, Jensen and Scholes (1972) and Fama and MacBeth in 1973. In their study, Black et al. state that cross-sectional tests can be misleading15, thus they use the time series test for the regression equation below:

RRe%%jt=+αβ j j Mt +% jt (6)

Left hand side of the equation represents the excess return on asset or portfolio j and

R%Mt stands for the excess return for the market portfolio. Another common regression equation used for testing the CAPM is:

ˆ Rujjj=+γγβ01 +% (7) where left hand side stands for the mean excess return for the asset or portfolio and ˆ β j represents estimate of the systematic risk. The equation (6) tests the relationship between the excess portfolio return and excess market return. In other words, it is the regression equation used for calculating the betas of the portfolios or individual assets. The equation (7) tests the linear relationship between the mean excess portfolioreturn and the systematic risk of the portfolio. It tests the positive risk return trade-off. If the value of γ1 is greater than zero, it is concluded that there is a positive relationship. However, Pettengill et al. state that this test can be a check for usefulness of beta as a risk measure, but it is not a direct test for the validity of the SLB model.16 They also argue that the relationship between high or low beta portfolios and the portfolio return is conditional according to the values of market

14Richard A. Brealey, Stewart C. Myers, Principals of Corporate Finance, 4th ed., McGraw-Hill, 1991, p. 166. 15Fischer Black, Michael C. Jensen, Myron Scholes, “ The Capital Asset Pricing Model: Some Empirical Tests,” (Online) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=908569, 23 January 2011. 16Glenn Pettengill, Sridhar Sundaram, Ike Mathur, “ The Conditional Relation between Beta and Returns,” The Journal of Financial and Quantitative Analysis, Vol.XXX, No: 1, March 1995, p. 105. 18 return and risk free rate. If the market portfolio return is less than the risk free rate, there is a negative relationship between portfolio betas and the portfolio expected return.

There is a most common step for running these equations by using data related to the testing period. Testing the CAPM can be in various steps in this procedure. First step is the beta estimation period for each stock in the analysis. By using the equation (6), excess stock returns are regressed against the excess market portfolio return to obtain the beta value for each stock. For this regression, weekly, monthly or yearly data can be used. After obtaining the beta values for each stock, the ranking procedure begins. All individual stocks are ranked according to their betas from lowest to the highest.

After completing beta ranking procedure, stocks are placed to the portfolios. This step is named as portfolio formation period. Placement of the stocks is not random. Firstly, number of portfolios to be constructed is specified and the stocks are assigned to each portfolio in equal numbers. For example; if we have 100 stocks and want to construct 10 portfolios, we assign 10 stocks to each portfolio. According to the individual betas, the lowest 10 stocks are assigned to portfolio 1, the next 10 lowest beta stocks are assigned to portfolio 2 and so on up to portfolio 10 which includes 10 stocks having the highest beta.

The last period is portfolio-beta estimation period. After assigning the stocks into the portfolios, excess return of each portfolio is regressed upon the excess market return to obtain portfolio betas (by using the equation (6)). Then, equation (7) is used to test the linearity of the excess portfolio returns and portfolio betas.

2. MAJOR STUDIES ABOUT THE CAPM

Many studies have been done about the CAPM since 1950s. Main goals of these studies are testing the validity of the CAPM. Some of the earlier main studies on Sharpe-Lintner-Black (SLB) model are Black, Jensen and Scholes; Blume and Friend; Fama and MacBeth; Reinganum; Gibbons; Pettengill. These are the main studies made in order to test the CAPM. There are also other studies testing the model. Recent studies based on the methodology used in the earlier studies. Some of the researchers such as Pettengill, Sundram and Mathur (1995) brought a different approach on testing the CAPM method. Results of the tests, in general, have offered very little support of the CAPM.

“These studies have suggested that a significant positive relation existed between realized return and systematic risk as measured by β and relation between risk and return appeared to be linear. But the special prediction of Sharpe-Lintner version of the model, the portfolio uncorrelated with the market have expected return equal to risk free rate of interest, have not done well, and the evidence have suggested that the average return on zero-beta portfolios are higher than risk free rate. Most of early tests of CAPM have employed the methodology of first estimating betas using time series regression and than running a cross section of regression using the estimated betas as explanatory variables to test the hypothesis implied by the CAPM.”1

One of the most famous studies on the CAPM was done by Black, Jensen and Scholes (1972). In this study it is mentioned that the cross-sectional test of significance can be misleading and it cannot test the validity of the equation which is: ER()%%j = ER (Mj )β where E (R% j ) is expected excess return on the jth asset,

ER()M is expected excess return on a market portfolio and β j is the systematic risk of the jth asset. Because of this reason they used both a time series test and a cross- sectional test in order to test the validity of the model. In the time series test of the model they used the equation RRe%%jtjjMtjt= αβ++% as the regression equation. In the

1Attiya Y. Javed, “Alternative Capital Asset Pricing Models: A Review of Theory and Evidence,” (Online) http://catalogue.nla.gov.au/Record/3006816, 12 January 2011.

20 test, excess individual stock returns are regressed upon excess market portfolio returns. If the assumptions of the CAPM hold, α j is expected to be zero. Since it is also important to test not only for individual assets but also for a large number of assets, they aggregate the data on a large number of securities. They wish to group their securities such that they obtain the maximum possible dispersion of the risk coefficients. They mention that if they were to construct the portfolios by using the ranked values of the betas, they would introduce a selection bias into the procedure. They also mention that those securities entering the first portfolio or highest-beta portfolio would tend to have positive measurement errors in their betas. This can lead to positive bias in the estimated portfolio risk coefficient. The positive bias in the estimated risk coefficient leads to a negative bias in their estimate of the intercept. On the other hand, they emphasize that the case is the opposite for the lowest beta portfolio. Another important point that is underlined in this study is that if the traditional model was true, this selection bias would lead to lower-beta portfolios to have positive intercepts and higher-beta portfolios to have negative intercepts. In order to get rid of the bias, they use an instrumental variable that is highly correlated with estimated betas of securities. This instrumental variable is an independent estimate of the beta of the security obtained from historical data.2

Data used in their study include monthly prices and dividends of the securities listed on the New York Stock Exchange. Data include the period from January 1926 through March 1966. Two different risk-free rates are used in the study. The first one is the 30-day rate on U.S. Treasury Bills for the period 1948-1966. The second one is the dealer commercial paper rate for the period 1926-1947 due to the absence of T-Bill rate in this period.

In order to assign securities into different portfolios, they used a ranking procedure that is independent of the measurement errors in estimated betas. In order to apply this procedure, they used previous five-year-monthly data to calculate the beta estimates for each stock. Beta values are ranked in order to assign stocks into the portfolios. Since beta coefficients are not stationary, they have used a procedure for

2 Black, Jensen, Scholes, “ The Capital Asset Pricing Model: Some Empirical Tests,” p. 9

21 grouping the firms which allows for any non-stationary in the coefficient through time. The data for estimating the betas is taken from the period January 1926 and December 1930 for all stocks on NYSE at the beginning of January 1931. Those stocks having available number of observations less than 24 months are omitted from the list. The individual stock betas are ranked from highest to the lowest one. 10% of the securities with highest betas assigned to the first portfolio, the second 10% assigned to the second portfolio and so on. Then they calculated the returns of each portfolio for the each of the next 12 months. They repeated this procedure for January 1932, January 1933, January 1934 and so on up to January 1965. They used total number of stocks varying from 582 to 1094 as a result the number of the securities in each portfolio changed from year to year.

They analyzed their results both for the entire period and sub periods. One of the findings including entire period is that the intercept term is negative for high-beta portfolios (beta higher than 1) and positive for low-beta portfolios (beta lower than 1). This finding is contrary to the traditional form of the CAPM. As for the sub- periods, for the first period which is January 1931-September 1939; intercept terms are positive for high –beta portfolios and negative for low- beta portfolios. However; they mention that “In the three succeeding periods (October, 1939-June, 1948; July, 1948-March, 1957, and April, 1957-December, 1965) this pattern was reversed and the departures from the model seemed to become progressively larger; so much larger that six of the ten coefficients in the last sub-period seem significant.”3

Since time series regression cannot test the two-factor model directly, they also used cross-sectional test in the study. Mean excess returns of the portfolios are regressed upon the estimated betas and a linear relation was found between mean excess returns and betas. On the other hand, results for the sub periods do not support the traditional model and both the slope and the intercept term is different for each sub periods. In the two pre-war 105-month sub-periods the slope is steeper in the first period than predicted in the traditional model and flatter in the second period. And for both periods after the war, the slope is flatter than the traditional model.

3 Black, Jensen, Scholes, “ The Capital Asset Pricing Model: Some Empirical Tests,” p. 15

Taking all the test results into consideration, they conclude that the traditional form of the asset pricing model is not consistent with the data.

After Black, Jensen and Scholes, Fama and MacBeth (1973) made an important empirical study on the CAPM. In this study, the relationship between average return and risk is tested in New York Stock Exchange common stocks. They based their test on the two-parameter portfolio model and models of market equilibrium derived from the two-parameter portfolio model. In this model it is assumed that “the pricing of common stocks reflects the attempts of risk-averse investors to hold portfolios that are efficient in terms of expected value and dispersion of return.”4 One of the equations analyzed in the study is:

ER%%=+ ER⎡⎤ ER %% − ER β (8) ()tmi( 00) ⎣⎦( ( ) ( ))

According to Fama and Macbeth, equation (8) has three important implications to be tested. First one is that in any efficient portfolio m, the relation between the risk of a stock and its expected return is linear. Secondly, β is the only risk measure for any stock and no other measure exists for the risk in the equation (8). As for the last implication, assuming risk-averse investors, higher risk is associated with higher returns. For testing these implications a model of period-by-period returns that allow using observed average returns is determined. A stochastic generalization of the equation (8) is made as the Equation (9):

2 ()RS%it=+++γγβγβγ%%01 t+ t i % 2 t i % 3 t i η % it (9)

2 The variables γ%0t and γ%1t vary stochastically from period to period. The variable βi is inserted to test the linearity. The variable Si is the measure of the risk of ith security that is not related to βi . Mean of the disturbance term is assumed to have zero mean and is unrelated to the other variables.

4Eugene F. Fama, James D. MacBeth, “ Risk, Return and Equilibrium: Empirical Tests,” The Journal of Political Economy, Vol. LXXXI, No: 3, May-June 1973, p. 607

The data for running the equation (9) is monthly percentage returns including dividends and capital gains for all common stocks listed in the NYSE. Testing period includes from January 1926 through June 1968. In the study, it is mentioned that a wide range of portfolio betas are obtained according to the ranked betas of the portfolios in order to reduce the loss of information as a result of using portfolios rather than individual stocks. Additionally, it is also stated in the study that forming portfolios on the basis of ranked individual betas can lead to both positive and negative biases in the portfolios. For the portfolio formation period, first four years of the sample period, 1926-1929, is used to assign each individual stock to 20 different portfolios according to their ranked betas. Next five years, 1930-1934, are used to re-compute the individual stock betas. These betas are averaged across securities within portfolios to obtain 20 initial portfolio betas for the test. For the period from 1935 to 1938, under the assumption of equally weighted stocks, return for each month is calculated and, for each month t in this period, an analogous of the Equation (9) is run. The results of this regression are used as inputs for testing the two parameter model in this period. Same procedure is applied for other periods. In the study, some sub periods are chosen in order to separate the periods before and after the World War II from the others. Fama and MacBeth analyzed the results on the basis of the Sharpe-Lintner model. For the one variable model, Fama and MacBeth’s negative assumption about the SLB model is supported. On the other hand, in the two-variable model there are more supportive results about the SLB model with respect to the one variable model. They conclude that NYSE common stocks reflect the assumption that risk-averse investors hold efficient portfolios. They emphasize the existence of a positive risk return trade off. Their findings cannot reject the linear relation between portfolio risk and return. Their results cannot reject the assumption asserting that there is no variable but beta explaining the stock or portfolio returns.

Marshall Blume and Irwin Friend (1973) investigated the risk-return trade off for the common stocks. In order to estimate the trade off, they regressed the returns on the corresponding betas. However, they argued that this procedure can be deficient in several ways. First of all, estimated betas can differ from the true coefficients,

24 resulting possible large measurement errors. Secondly, the realized returns for individual stocks will be a poor estimate for the ex ante expected returns. Lastly, in order to make comparison among the stocks the realized returns should be estimated in the same period. This may introduce again a bias.5 To get rid of these problems, they used grouping procedure. They estimated the beta coefficient of each common stock listed in the NYSE by regressing monthly investment relatives upon the corresponding values of the Fischer Combination Link Relatives. Fischer Combination Link Relatives refers to the dividend-adjusted return on the market portfolio.

In the study, beta estimation period includes the five year period from January 1950 through December 1954. Twelve portfolios, each including eight common stocks, were constructed by the procedure described before. The first portfolio consists of the lowest beta stocks. The second portfolio contains the next lowest beta stocks and so on. Monthly returns of each portfolio for January 1955 and December 1959 were calculated. These monthly returns are averaged in order to obtain the portfolio monthly returns and then regressed on the Fischer Combination Link Relatives to yield an estimate of the portfolio beta. Lastly, these average returns are regressed on the beta coefficient in both linear and quadratic forms. All of these steps were repeated to yield similar regressions from January 1960 through December 1964 and from January 1965 through June 1968. The results of the study seem to require a rejection of the capital asset pricing theory.

The main goal of the study done in Tokyo by Sheila Lau, Stuart Quay and Carl Ramsey (1974) was to determine the validity of the CAPM in the Tokyo Stock Exchange (TSE). Another goal of the study was to estimate the degree of dependence between the TSE and the NYSE. The study covers all the securities listed on the first section of the TSE. For each security, prices of the period from January 1961 through September 1964 were used to obtain an independent estimate of the systematic risk. Prices of the period from October 1964 through September 1969 were used for the test period of the study.

5 Marshall E. Blume, Irwin Friend, “A New Look at the Capital Asset Pricing Model,” The Journal of Finance, Vol. XXVIII, No: 1, March 1973, p. 23

The first step of the study is to determine an independent estimate of the systematic risk for each stock from the regression of the excess returns of the issues on those of the market index. This procedure is applied with the following regression model:

RRMeit,,=+αβ i i( t) + it (10) where,

Rit,,=−rr it ft = excess return of stock i for month t.

RMrmrfttt=− = excess return of the market index for month t.

αi = risk adjusted return for issue I (intercept from the regression).

βi = systematic risk for stock i (slope coefficient of the regression).

eit, = residual error of the regression for stock i.

After obtaining the beta values for each stock, these stocks are placed into ten portfolios in equal numbers. First highest beta stocks are placed into first portfolio, next highest group is placed to the second portfolio and so on. Portfolio 10 includes the lowest beta stocks. In the study, time series analysis is used to test whether the intercept, , is equal to zero. Time series regression results imply that the expected excess return on a stock is directly proportional to its systematic risk. This is a supportive result of the CAPM in the TSE. Additionally, cross-sectional analysis results show that there is linear relationship between excess return and risk as measured by the beta. The study finds that the slope is significantly positive, which is a supportive result for the validity of the CAPM in TSE from October 1964 to September 1969.

Marc R. Reinganum (1981) made a study on the validity of the CAPM. The purpose of the study was defined as to investigate empirically whether securities with different estimated betas experience different rates of returns.6 Data used in the study

6 Marc R. Reinganum, “ A New Empirical Perspective on the CAPM,” The Journal of Financial and Quantitative Analysis, Vol. XVI, No: 4, June 1981, p. 439

26 is obtained as monthly and daily data. The daily data contains daily stock returns listed on the NYSE from July 1962 through December 1979. The study with monthly data starts from January 1926. Security betas are estimated and the composition of the ten beta portfolios is revised. In the study with the daily data, the sample changes yearly. With the monthly data, portfolios are updated every five years.

Methodology of the study with daily returns is very familiar. The first step is beta estimation and portfolio formation period. Additionally, three different beta estimates are used to compose three sets of ten beta portfolios. The daily returns of the ten beta portfolios are calculated by combining the equal-weights with the daily returns of each security in each portfolio. The null hypothesis of the study with daily data is that the mean returns of the ten portfolios are identical. However, test results imply that the null hypothesis is rejected but this rejection is not interpreted as a support to the validity of the CAPM because the return of the lowest-beta portfolio is greater than the return of the highest-beta portfolio. Similar results are obtained with the monthly data. The findings of the study show that the high-beta portfolio returns are not significantly different from the low-beta portfolio returns. It can be inferred that the study does not validate the CAPM.

A different study was made by Stahambaugh (1982). He used the Lagrange multiplier method. This method finds a support to the Black’s version of the CAPM but not confirm the validity of the Sharpe –Lintner version of the CAPM.7

Another different study was done by Glenn Pettengill, Sridhar Sundaram and Ike Mathur (1995). They provided a test for a systematic conditional relationship between betas and realized returns. Another purpose of the study is testing a positive long-run tradeoff between beta and the return. In this study, Fama and MacBeth (1973) version is used for testing the systematic relationship. The sample period of the study includes January 1926 through December 1990. Monthly returns of the securities listed on CRSP index is analyzed in the study. The three-month Treasury bill rate is used as the risk free rate.

7 Attiya Y. Javed, “Alternative Capital Asset Pricing Models: A Review of Theory and Evidence,” (Online) http://catalogue.nla.gov.au/Record/3006816, 12 January 2011.

First of all, the sample period is divided into 15-year sub periods. Each of these sub- periods are divided into three parts, each including five years. These parts are named as portfolio formation period, beta estimation period and test period, respectively. In the formation period, betas of the stocks are estimated by regressing the stock return on the market return. After obtaining the beta value of each stock, they are placed in the 20 different portfolios according to their ranked beta values. Securities with lowest beta are placed in the first portfolio, the next lowest in the second portfolio and so on. For the second five year period, portfolio betas are estimated for each portfolio by regressing portfolio returns on the market return. For the last step, the systematic relation between the portfolio beta and the portfolio returns are tested with the following equation:

Rit=+γγδβγˆˆ01 t t* * i + ˆ 2 t *( 1 − δβε) * i + t (11)

In this model when market risk premium is positive i.e. RRmt− ft >=0, δ 1 and when market risk premium is negative i.e. RRmt− ft < 0 ,δ =0. By regressing the model denoted by the equation (11), two hypotheses are tested. The first one is H01:0γ = and its alternative hypothesis is H a :0γ > . The other null hypothesis is H02:0γ = and its alternative hypothesis is H a :0γ 2 > .

This three step procedure is applied for each sub-period. As was previously mentioned, the second goal of the study is testing the positive risk return tradeoff for each portfolio. A direct test of the risk return tradeoff is applied by using the regression model of portfolio betas against portfolio returns.

This study performs a supportive result for the relationship between beta and portfolio returns. They underlined that the difference between their study and the others is that the positive relationship between returns and beta estimated by the SLB model is based on expected rather than realized returns. They conclude that when the excess market portfolio return is negative there is an inverse relationship between betas and the portfolio returns. When the excess market portfolio return is positive the relation is positive. Finally, it is concluded that for total period and the sub-

28 periods there is a systematic relationship between portfolio beta and the portfolio returns. Additionally a positive tradeoff between beta and portfolio returns is obtained.8

Valeed A. Ansari (2000) tested the validity of the CAPM for India. 96 stocks listed on the BSE during the period from January 1990 through December 1996. Deposit rates with commercial banks are used as the risk free rate. There are five equally weighted portfolios in the study. These portfolios are analyzed using time series and cross-sectional regression techniques. Beta of each stock is calculated by using 24 months of past return data. After obtaining the individual betas, each stock is placed to the portfolios according to their ranked betas. Portfolio 1 consists of the highest stocks and portfolio 2 includes the next highest stocks and so on. Return of each portfolio is computed for the next 12 calendar months for each year. Portfolio returns are regressed upon the market return for each portfolio. Additionally, by using cross- sectional analysis portfolio returns are regressed against portfolio betas for the entire period and sub periods.

Results of the study show that the intercept term is positive, however it is very close to zero both for the entire period and sub-periods. Also the negativity of the slope is insignificant for the entire period and the sub-periods. It is concluded that beta leaves returns unexplained during the testing period in India and it is not true to make inference about the insignificant positive intercept because this does not give a valid idea about the validity of the CAPM in India.9

Grigoris Michailidis, Stavros Tsopoglou, Demetrios Papanastasiou and Eleni Mariola (2006) tested the validity of the CAPM in Greek stock market during the period from January 1998 through December 2002. 100 stocks, listed on the Athens Stock Exchange (ASE), are used in the study. There are 260 weekly observations available for each stock. They emphasize that weekly data is used in order to attain better estimates for the beta values. The ASE Composite Share index is used as the

8Pettengill, Sundaram, Mathur, “ The Conditional Relation between Beta and Returns,” p. 115

9Valeed A. Ansari, “Capital Asset Pricing Model: Should We Stop Using It?,” Vikalpa, Vol. XXV, No: 1, January-March 2000, p. 61

29 market proxy because this index reflects general movements of the Greek stock market. The three-month Greek Treasury bill rate is used as the risk free rate.

In the study, first step is estimating a beta coefficient for each of the stocks by using data for the years from January 1998 through December 2002. The beta is calculated by the regression model given by the equation (11) below:

RRit−=+ ftαβ i i( R mt − R ft) + e it (12)

After obtaining individual stock betas, these stocks are assigned to ten portfolios each including ten stocks according to their ranked betas. In order to estimate the SML, following model is used:

reppp= γ 01++γβ (13)

Here rp is the average excess return on a portfolio p,γ 0 is the expected return on a stock which has a beta of zero and γ1 is the risk premium for bearing a one unit of risk. This equation is used for testing the relation between the portfolio return and the portfolio beta.

In the study, the nonlinearity between total portfolio returns and portfolio betas are tested with the following regression equation:

2 repppp=+γγβγβ01 + 2 + (14)

Another regression equation is used to learn whether residual variance of stocks affects portfolio returns. The equation is:

2 rRVeppppp=+γγβγβγ01 + 2 + 3 + (15) where, RV represents the residual variance of portfolio returns.

As for the results of the study, it is not supported that high-beta portfolios have high portfolio returns. The highest-beta portfolio has a negative return while the lowest- beta portfolio has a positive return. The value of the intercept is calculated different from zero which contradicts with the assumption of the CAPM. While the theory of

30 the CAPM stresses that the slope should be the same with the excess return on the market portfolio, it is not the case in this study. This is also additional evidence against the validity of the CAPM in the Greek market during the specified test period.

Empirical studies about the validity of the CAPM have been made for Turkey as well. Summaries of some of these studies are given below.

Temizkaya (2006) made an empirical study testing whether the CAPM is valid on ISE or not. In the study, Lintner’s two stage regression model is used as testing tool. First stage equation of the model is the most common one used in the studies testing the CAPM. The model is:

RReit= α i++β i mt it (16)

In this equation Rit is defined as the return of the stock i in time t, Rmt is the return of the market portfolio in time t and βi is the beta coefficient of stock i. By using the equation (16), beta of each stock is determined and this beta is used as an independent variable in the second stage equation which is:

2 Raaiieii=+12β + aSu 3 + (17)

2 where Ri denotes average return of stock i and Sei denotes the variance of the error term. Equation (17) is a cross-sectional regression equation. Main goal of running this equation is to determine whether the CAPM can truly explain the prices of the stocks. It is argued that if a1 is not equal to risk free rate, a2 is not equal to risk premium and a3 is not equal to zero. It is concluded that the CAPM cannot explain stock prices correctly. However; if the estimated values of the parameters are equal to the theoretical values than the CAPM is not valid.

Running equation (16) includes time series monthly data taken from ISE. The study focuses on the period from January 1995 through December 2004. 33 stocks operating on ISE-100 are analyzed in the study.

Results of running the equation (16) showed that constant term is insignificant and it is omitted from the model in the next parts of the study. As for the second stage, regression constant term and the coefficient of the independent variable is insignificant. Because of this, they used a logarithmic version of the same model in later parts. In the results of the analysis, it is obtained that estimated values of coefficients are bigger than the theoretical value and the coefficient of the variance of the error term is bigger than zero. At the end, it is concluded that the CAPM is not valid.

Another study about the CAPM was done by Tanık (2006). The objective of the study is testing the validity of the CAPM on ISE-100 stocks. Data from ISE-100 stocks used to test the success of the model in determining the relationship between risk and return. The essential goal of the study is defined as testing the relation between stock returns and the market return, which is specified as ISE-100 index return. The regression equation is defined as the following:

⎡⎤ ER()if=+ R⎣⎦ ER( mfi) − R β (18)

The null hypothesis of the study is that a small part of the variance of the expected stock returns operating on ISE-100 is related to the beta coefficient. Thus, the beta coefficient is statistically insignificant and does not give successful results in estimating expected returns. Alternative hypothesis is specified as the contrary which is; beta composes an important part of the variance of expected stock returns. Thus beta coefficient is statistically significant and reveals successful results in estimating expected returns.

Data used in the study belongs to stocks operating on ISE between the years 1996 and 2005. Annually average stock returns in these ten years are composing the data. Beta of each stock is obtained by using equation (18). Significance test results revealed that systematic risk has significant effect on explaining stock returns. It is concluded that the CAPM is valid on ISE-100 between 1996 and 2005.

Gürsoy and Rejepova (2007) made an extensive study about the CAPM and Arbitrage Pricing Model. The study covers the period from January 1995 through

December 2004. All the qualifying stocks operating on ISE is chosen as the market proxy. This period is divided into six-year sub-periods with one overlapping year in each. Overlapping year in each of two consecutive sub-periods is expected to smoothen possible volatility of beta coefficients estimated in each sub-period. Additionally, each period has divided into three two-year sub-periods also. Firs two- year period is portfolio formation period, next two-year period is beta estimation period and last two-year period is testing period.

In the analysis, 200 stocks are used. These stocks are divided into 20 portfolios each including 10 stocks. In the portfolio formation period, beta coefficient of each stock is determined by regressing weekly risk premium of stock returns on weekly risk premium of ISE-100 returns over 104 weeks. Since the real interest rate was very high in Turkey, they used weekly returns of US three-month Treasury bill rate as the risk free rate. The adjustment for the inflation rate differences between two countries also done by using Fisher equation. Stocks are placed to the portfolios according to the ranked betas. First ten stocks having the highest betas placed to the first portfolio, second ten to the second portfolio and so on. Last ten stocks having the lowest betas placed to portfolio 20. In the beta formation period i.e. second sub period; beta of each stock is recalculated. But their places in the portfolios do not change after recalculation period. In the testing period, average weekly return of each portfolio is calculated. Additionally, beta of each portfolio is calculated.

The relationship between portfolio risk and the portfolio return through the specified period is tested by using cross-sectional test. This cross-sectional test is done by using the Fama and MacBeth’s traditional model and Pettengill et al.’s conditional model. For the first model the equation is the following:

RRip,,01,1 t− f t=+ yy t tβ ip t− +ε t (19)

where βip,1 t− is defined as the beta of ith portfolio calculated in the previous 2-year time slice. Analyzing the summary of the regression results related to this equation reveals that the intercept term which is y0 seems not to be different from zero. As for the slope term, which is y1, test results show that it is significantly different from

33 zero. Taking these values into consideration, it is concluded that Fama and MacBeth’s traditional approach is not valid in ISE. In other words, there is no ex- post relationship between beta and portfolio risk premiums.

As for the Pettengill and his friends’ approach; the model used is the following:

RRip,,01 t−=+ f t yy t t*δβ * ip ,12 t−− + y t *( 1 − δ) * β ip ,1 t + ε t (20)

In this model when market risk premium is positive i.e. RRmt− ft > 0 ,δ =1 and when market risk premium is negative i.e. RRmt− ft < 0 ,δ =0. After regressing this equation, it is obtained that in 155 out of 312 weeks risk free rate is higher than the market return. In order to get a better result, positive market risk premium-weeks are separated from the negative market risk-premium weeks. This part is called as conditional part. Positive market risk premium periods are called as up-market and negative ones called as down-market. Evaluating all sub-period results reveal that there is a strong correlation between beta and risk premiums. This is valid for both up-market and down-market weeks. An important conclusion of this study is that if the market risk premiums are analyzed separately as positive and negative, it is clear that there is a strong relationship between portfolio beta and portfolio return. This relation can be summarized as saying that there is a positive beta-return relationship when the market risk premium is positive and there is a negative beta-return relationship when the market risk premium is negative.

Another study about the validity of the CAPM was done by Bozkurt (2008). The objective of the study is summarized as testing whether there is a linear relation between risk and return. Also it is aimed to test whether there is any other risk measure other than beta. A final objective is defined as determining the efficiency of the market.

As was the case in other studies, this study also tested the objectives on ISE. Two different equations are used as the regression models. The first one is the same with equation (16). Using this equation, beta of each stock is calculated. Data set is obtained from 84 different stocks operating on ISE-100 index from January 2002

34 through September 2007. By using different sub-period such as January 2002- December 2004, January 2002-March 2005 and so on up to January 2002- June 2007, eleven betas are calculated for each stock. After calculating betas, mean return of each stock is also calculated. Data between January 2005 and March 2005 are used for calculating the mean returns. This calculation is repeated for every 3 month periods such as April 2005-June 2005, July 2005-September 2005 and so on. Mean return for each three-month period is related with the beta of previous period. Panel data analysis is used with the equation given below:

RSe=+γγβγβγ +2 + + (21) it01it()−−11 2 it () 3()eti ()−1 it

In the equation (21) β 2 is used to determine the linearity of the model.

Throughout the study, monthly Treasury bill rates are used as the risk free rate. Realized returns of each stock are used instead of expected returns of the stocks.

As for the results, regression results show that there is not a positive relation between beta and return in the testing period. For the linearity of the relationship, it is concluded that there is a linear relationship between portfolio beta and portfolio returns. This also means that β 2 is statistically insignificant. Another result is about the uniqueness of beta as the risk measure. In the test results is obvious that unsystematic risk which is denoted as Se in equation (21) has an insignificant effect on returns. This implies that only risk measure for the stocks is beta. For the efficiency of the market, it is inferred that expected values and realized values are different which means ISE is not an efficient market and the CAPM is not valid on ISE.

The main objective of the study, done by Çomak (2009), is testing the success of beta in explaining stock returns in ISE. This also means testing the significance of beta as a risk measure. The study was done by using the highest volumed 17 stocks on ISE in 2006. These stocks are chosen because of the high activity of them. Testing period divided into two parts. First one is 12.05.2006-29.12.2006 which includes 33 weeks. The second part is 16.03.2007-20.02.2009 which includes 100 months. Reason for

35 this partition is explained as figuring out the effect of beta by comparing portfolios, created by using beta values, with their future values. ISE-100 index is used as market proxy and its return is calculated as individual stock returns by using weekly closing prices. Weekly Treasury bill rate is used as the risk free rate.

As for the regression models, in the first step a classical model denoted in equation (16) is used to calculate the stock betas. In order to investigate the relationship between each stock’s beta and return following model is used:

Ruiii= γ 01++γβ (22)

After running this equation it is seen that there is an inverse relation between portfolio betas and expected portfolio returns. For the time between 2007 and 2009,

222 unique risk for each stock is calculated by using the equation UR =−σ iimβσ where UR is used to denote unique risk. Since beta can explain only 24.5% of the mean returns, additional variables, which are out of the model, added to the model in order to make the model more explanatory. Here is the new form of the equation (22):

2 RURSeiii=+ααβαβα01 + 2 + 3 + α 4 + i (23) where, S is defined as the skewness of each stock. After adding additional variables the model is more explanatory which 87.75% is. The result of this multiple- regression model implies that beta has a negative coefficient which contradicts with the theory. Plotting the expected return and beta values in a graph shows that the relation between them is non- linear. Skewness of each stock cannot pass the test which means S is insignificant. After omitting S from the model, there occurs a U shaped relation between expected portfolio return and the portfolio beta. This relationship is negative until beta equals 1.22 and positive when beta is higher than 1.22.

As the last part in the study, these 17 stocks are placed into 5 different portfolios according to their ranking betas. Then calculating the portfolio returns revealed that the lowest-beta portfolio has higher return than the highest-beta portfolio.

Kavurmacı (2009) did a study comparing the two popular asset pricing models which are the CAPM and Arbitrage Pricing Theory (APT). Objective of this study is different than the others mentioned above. In the study, the CAPM is tested by using average variance model. Testing the CAPM includes the regression equations similar to the equations (16) and (22). Data set includes the data related to the 41 stocks operating on ISE-50. Stock betas are calculated from the equation (16) as usual. By regressing equation (22), relationship between portfolio return and portfolio beta is tested. The comparison is based on the values of R2 and adjusted-. Comparison results imply that APT is more explanatory than the CAPM in explaining this relationship.

Kısmet (2009) made a dynamic analysis of the CAPM. In this study, the model is based on the fact that betas are not stationary, it changes throughout the time i.e. betas are not static, they are dynamic. The standard form of the CAPM takes a different form by relating expected excess returns of the stocks and expected excess return of the market with the information set belongs to time t-1. Re-arranged version of the standard equation of the CAPM is the following:

| | (24)

After making some new adjustments, the conditional version of the equation (24) takes the form of and where R is the excess return of stock i in time t, is the excess return for the market in time t, is the conditional covariance between stock i and the market. is the conditional covariance of the market.

ISE-100 index is used as the market proxy in the test. The model is tested on ISE-100 index from January 2002 through December 2007 by using 16 different stocks. Stocks are grouped according to their sectors which are service sector, financial sector, industrial sector and technology sector. These sectors are divided into subsectors each including one stock. Risk free rate is calculated by dividing the annually simple interest rate of the Treasury bill, which has the shortest maturity date, by 365.

In the study, only daily data is used. GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model is used for the analysis of data.

After interpreting the results, it is obvious that GARCH model is significant in the industrial sector and its subsectors. It is also found that a change in the variance in the previous period effects the next period in the same way, that is an increase in the variance leads to an increase in the next period and a decrease in the variance leads to a decrease in the next period. Another finding is that in the industrial sector, previous period error term is more significant than previous period variance in determining next period variance. GARCH model is also significant in the service sector. As happened in the industrial sector, previous period error term is significant in determining next period variance. Financial sector has also supportive results for GARCH model. However, in this sector previous period variance is more significant in determining the next period variance. The model is significant for the technology sector as well. Significance of these results showed that ISE-100 can be used as market portfolio. It is also concluded that the economical crisis in Turkey in 2001 affected all stocks negatively.

A study about the applicability of the CAPM in ISE-100 index is done by Korkmaz (2010). In this study, panel data analysis is used as the testing method. 87 stocks operating in ISE-100 index between the years in 1993 and 2007 are used in the study. A similar version of the equation (16) with different notations is used for the regression. The study is based on the fact that the CAPM is valid on the ISE. In line with this assumption the null hypothesis is tested. Null hypothesis is declared as it is possible to calculate the expected value of stocks by using the CAPM in ISE.

As happened in time series analysis and cross-sectional analysis methods, variables are set to be static in the panel data analysis. By using the Breusch-Pagan test, it is seen that the model cannot be pooled. Then, after applying Hausman test it is decided that Random Effect model is not appropriate for using in the analysis. Thus Fixed Effect model is used in the analysis. Test results are statistically significant which means beta coefficient is statistically significant. By this result, it is concluded that

38 the CAPM is valid in ISE and panel data analysis can also be used as an alternative model for estimating stock returns.

The objective of the study done by Üçüncü (2010) is investigating the risk of the firms operating in ISE-30 by using traditional CAPM, CAPM-GARCH and the conditional CAPM. Daily closing prices of 23 stocks operating on ISE-30 between 03.01.2002 and 08.052009 are used in the study. Risk free rate is determined as nightly interest rate. ISE-100 index is used as the market proxy. The systematic risks of the stocks are explored by the CAPM model. Regression results belong to the traditional CAPM show that risk measure beta is significant for all stocks, except one, which means stock returns are related to the market return. GARCH model gives a very close result with the traditional method by supporting the relation between stock returns and market return. Although these two models give very close results, GARCH model has more reliable results than the traditional model.

As for the conditional CAPM, all parameters found to be statistically significant. In this model risk of the stocks are calculated higher than the ones in the traditional model. Taking all the beta values obtained from three models into consideration, it is mentioned that there is a very strong relationship between these values. Betas are very close to each other in all three models. Considering all the results belong to three models, it is concluded that there is a significant relationship between stock returns and the market return during the test years in ISE index.

3. TESTING THE CAPM WITH TURKISH EQUITY MARKET DATA

3.1.Methodology

The aim of this study is testing the existence of a relationship between beta and portfolio returns. Two different models are used for testing the relation. An unconditional method fortesting the existence of a relationship between beta and return is based on the study of Fama and French (1992). The regression equation for this model is the following:

rit=+α γβ i + ε it (Model 1) where;

rRRit=− it ft : (The excess return on portfolio i at time t)

Rit : The return on portfolio i at time t

R ft : The risk-free rate of return

βi : Estimated historical beta of portfolio i in month t

α : Constant

Expected value of ε it is zero.(Portfolio construction process is explained below)

Portfolio return in month t is calculated by averaging the total individual stock returns, in month t, in that portfolio assuming that stocks are equally-weighted.The same procedure is applied for each portfolio. The beta of each portfolio is obtained by beta estimation process. (Beta estimation process is explained below) .The beta value of a portfolio is assumed to be stationary i.e. it does not change in the testing period from January 2006 through December 2010.It takes the same value for each month. “It has been well established that most firms' probability distributions of returns and betas are relatively stable through time.[i] In fact, in their published

40 research on beta-stationarity, Kolb and Rodriguez (1990) find that betas may be regarded as stationary for practical purposes, especially for five-year estimation periods. Further, they find that betas exhibit stationarity from one five-year period to another. Based on these findings, the assumption of a stable beta distribution over a multi-year horizon seems reasonable.”1 ([i]See Sharpe and Cooper (1972), Blume (1974), Jacob (1971), Klemkosky and Martin (1975) and Francis (1979))

In order to run the regression of the Model 1, observations for each variable in each portfolio are combined in a new data set. There are 60 monthly observations for the excess return of each portfolio which means there are 600 observations for the excess return, r, in the new data set. Each portfolio has only one beta value for the entire period thus;beta values of a portfolio for every month are the same. This is valid for all of the ten portfolios (Portfolio construction process is explained below).In the new dataset there are 600 observations for the variable β.

Existence of a relationship between portfolio beta and portfolio returns requires that the coefficient of the beta in Model 1 is nonzero. Hence the null-hypothesis and the alternative hypothesis for the model 1 are:

H0 :0α = andHa :α ≠ 0

Rejecting the null hypothesis, at 1% and 5% levels of significance, in favor of the alternate, proves that the intercept term is zero as stated in the CAPM.

H0 :0γ = andH a :γ ≠ 0

Rejecting the null hypothesis, at 1% and 5% levels of significance, in favor of the alternate proves the existence of unconditional relationship between portfolio beta and portfolio returns.

⎡⎤ The equation of the SLB model is stated as: E (RRifimf)()=+β ⎣⎦ ERR − . Assuming that investors are risk averse, it is obvious that higher beta (higher risk)

1Salvatore J. Terregrossa, “Combining Analysts’ Forecasts with Causal Model Forecasts of Earnings Growth,” Applied Financial Economics,Vol.IX, No: 2, 1999.

41 portfolios have higher returns while lower beta (lower risk) portfolios have lower returns. This is the unconditional assumption of the SLB model. The model also says that any stock or portfolio which has zero risk has the return equals to the risk free rate. However; it is not the case that the SLB modelrequires only the direct and unconditional relationship between beta and portfolio returns. The SLB model also requires that the relationship between beta and portfolio returns may vary. The

CAPM equation ()Rit−=+RRR ftαβ( Mt − ft ) implies that there is a positive relationship between excess portfolio return and portfolio beta when market portfolio return is higher than the risk free rate. On the other hand, it implies that there is a negative relationship between excess portfolio return and portfolio beta when market portfolioreturn is lower than the risk free rate. This is an implication for the existence of a conditional relationship.Thus, the second model based on the work of Pettengill et al. (1995) is used for testing the conditional relationship between portfolio beta and portfolio return.Thefollowing time series regression model is specified for testing this hypothesis.

rabDbit= i++−+12 tβ it(1 D t )βε it it (Model 2) where;

rRRit=− it ft : (The excess return on portfolio i at time t)

Rit : The return on portfolio i at time t

R ft : The risk-free rate

βi : Estimated historical beta of portfolio i in month t

Denoting the excess return on the market portfolio as rRRMtMtft= − where RMt is the return on the market portfolio at time t, the dummy variable Dtis defined as Dt = 1 if rMt>0 and Dt = 0 otherwise. Parameters ai , b1 and b2 are constants. E[εit ] = 0 where E is the expectation operator.

It is obvious from the model 2 regression equation that the expected sign for b1 is positive because it is expected in periods when the excess return on the market portfolio is positive. Therefore, the null hypothesis and the alternative hypothesis are:

Hb01:0= and Hba :01 >

Since it is expected in periods when the excess return on the market portfolio is negative, the expected sign forb2 is negative. Therefore, the null hypothesis and the alternative hypothesis are:

Hb02:0= and Hba :02 <

Existenceof a systematic conditional relationship is proved if the null hypothesis is rejected in favor of the alternate, at 1% and 5% levels of significance, in both cases.

These two models are tested by using OLS (Ordinary Least Squares) method.

3.2. Data

This study covers the period from January 2006 to December 2010. The reason for choosing this time period is that ISE achieved its maximum values in this period both in terms of individual stock prices and the volume of the whole market.ISE-100 equally weighted index consists of 100 stocks whose volumes are the highest ones in a trading day in the market. These firms constitute the biggest part of the Turkish economy. Thus, ISE-100 index is chosen as the market proxy in the study. Stocks listed on the ISE-100 index are being updated in each quarter. Stocks used in this study are selected from the ISE-100 list published in December 2010.

Monthly return data for each individual stock is used for the test. During the data selection process a rule is followed such that an individual stock is deleted from the list if less than 36 monthly return observations are available for that stock. In other words; since the study is based on the monthly data during the testing period which includes 60 months, it is expected for an individual stock to have at least 36 available

43 monthly observations. In the ISE -100 index list, 10 individual stocks have available monthly observation less than 36. Thus they are not included in the study which means the study includes 90 individual stocks listed on the ISE-100 index.

Data of monthly individual stock returns are obtained from the website of the ISE. In the site, individual monthly returns are calculated by using the equation below:

FBDLBDZRBDLFii*1*( ++−−) −1 Gi = (25) Fi−1 where;

Gi : Return for the month i.

Fi : The closing price of the stock on the last trading day of the month i.

BDL: The number of rights issues received during the month.

BDZ: The number of bonus issues received during the month.

R: The Subscription price.

T: The amount of net dividends received during the month for a stock.

Fi−1 : The closing price of a stock on the last trading day of the month i-1.

Monthly market return values are calculated by using the daily closing prices of the ISE -100 index. Market portfolio return is calculated by the following equation:

PPtt− −1 Rmt = (26) Pt−1 where;

Rmt : Market portfolio return in month t (ISE-100 monthly return).

Pt : Closing Price of ISE-100 index in month t.

Pt−1 : Closing Price of ISE-100 index in month t-1.

Three-month Treasury bill is assumed to be the least risky asset in the economy. Thus monthly return of the three-month Treasury bill is used as the risk free rate. However, in the test period three-month Treasury bill is not issued in some months. In these months monthly return of the six-month Treasury bill is used as the risk free rate. The Treasury bill pricesare obtained from the database of Central Bank of the Republic of Turkey. Treasury bill monthly returns are also calculated by using the equation (26).

Portfolio construction process is an important part of the study. Since unsystematic risk can be reduced by diversification, individual securities placed to the portfolios according to their ranked beta values. In order to place the individual securities to the portfolios, beta values for each stock is estimated. The following regression model is used to calculate the individual betas:

rrit=+α βε i Mt + it (27)

where rit represents the excess return for each individual stock, β represents the beta of individual stocks and rMt represents the excess market portfolio return.

Individual stock betas can also be calculated as βit = cov (Rit, RMt)/var (RMt) 2 =(ρi,M)(σit)(σMt)/ (σMt) where (σit) is the standard deviation of return for firm i in month t; (σMt) is the standard deviation of return for the market portfolio in month t; 2 (σMt) is the variance of return for the market portfolio in month t; (ρi,M) is the correlation coefficient between the return for firm i in month t and the corresponding return for the market portfolio in month t.

Next, we consider theportfolio construction process:

Ten portfolios are to be constructed, each including 9 stocks, based upon pre- formation beta criteria, as follows:

In each month, firms are sorted based upon their pre-formation beta measure calculated by the equation (27) and assigned to one of ten portfolios comprising an

45 equal number of firms: The lowest 10% of pre-formation beta firms are assigned to portfolio 1, the next highest 10% of pre-formation beta firms are assigned to portfolio 2, and so on until the highest 10% of pre-formation beta firms are assigned to portfolio 10.

Following the Portfolio formation period, beta values for each portfolio are estimated by the regression of excess portfolio returns on the excess market portfolio return, which is a similar procedure with the individual stock beta estimation period. For this regression the SLB equation can also be restated as:

rrpt=+α βε i Mt + it (28)

where rpt represents excess portfolio return for portfolio i. Excess portfolio return for a portfolio is calculated by averaging the total stock returns for that portfolio, assuming that the stocks are equally-weighted, and subtracting the risk free rate from this average.

Next, we can further analyze the data as follows:

By examining average realized excess-returns on the ten portfolios over the entire sample period, during periods when excess market-returns are positive, and during periods when excess market-returns are negative. We can use three diagrams to display average monthly equally-weighted returns for each of the ten portfolios over the sample period: unconditioned upon excess market-returns, conditioned upon positive excess market-returns and conditioned upon negative excess market-returns, respectively.

3.3. Empirical Analysis

Table 1 shows the beta values of 10 portfolios constructed in the portfolio formation period according to the ranked stock betas. The table also includes t-statistics values of regression parameters, mean value of excess portfolio returns, standard error of the excess returns and the standard error of the regression. In order to see theportfolio

components and its betas, see the Appendix I. For the excess market portfolio returns and the risk free rates see the Appendix II and Appendix III.

Table 1:Test Results and Average Excess Returns (Unconditional)

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

α 2.251 0.764 0.667 0.878 2.220 0.398 0.498 0.918 0.191 0.667 t(α) 2.766 0.871 1.001 1.264 1.111 0.522 0.590 2.143 0.276 1.192

β 0.347 0.581 0.712 0.815 0.910 0.995 1.104 1.212 1.316 1.467 t(β) 3.965 6.166 9.921 10.913 4.235 12.136 12.155 26.273 17.722 24.351

Mean 2.305 0.854 0.778 1.004 2.361 0.552 0.669 1.106 0.395 0.895 r

σ(r) 7.046 8.663 8.412 9.318 17.553 11.013 12.209 11.825 13.421 14.407

σ(ε) 6.303 6.791 5.166 5.378 15.471 5.904 6.537 3.320 5.344 4.337

The alpha values are insignificant, both at %1 and %5 significance level, for all portfolios except portfolio 1 and portfolio 8. When the value is insignificant it can be omitted from the regression which means it has a value of zero. Hence, the CAPM assumption which states that the intercept is zero cannot be rejected.

All of the portfolios have significant beta values both at the significance level of %1 and%5. Comparing the beta values of portfolios with their average excess returns implies that higher beta values are not related with higher returns. It is stated that the CAPM indicates that higher beta is associated with higher level of portfolio return. Results included in the table do not support this hypothesis. (However, this is not a reason to reject the CAPM theory because the CAPM and the SLB equation also assert that there is a conditional relationship which should be tested when excess market portfolio is positive or negative.)

Table 2 shows the coefficient of determination values of the portfolios.

Table 2:Coefficient of Determination Values(Unconditional)

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

R2 0.213 0.395 0.629 0.672 0.236 0.717 0.718 0.922 0.844 0.910

In the next stage of the analysis, portfolio betas and returns, with thesame stocks, are calculated again for the conditional positive and conditional negative periods. Conditional positive period refers to the period when the excess market portfolio is positive and conditional negative period refers to the period when the excess market portfolio is negative. In each period equation (28) is used as the regression equation. Table 3 below shows the portfolio betas and average excess portfolio returns calculated in the conditional positive period.

Table 3:Portfolio Betas and Average Excess Portfolio-Returns (Conditional- Positive)

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

Beta 0.031 0.154 0.366 0.432 0.207 0.739 0.841 1.278 1.242 1.554

(-)

Average excess 5.378 4.764 5.364 6.453 9.195 6.578 7.468 8.609 8.536 10.033 return

Table 4 below shows the portfolio betas and average excess portfolio returns calculated in the conditional negative period.

Table 4:Portfolio Betas and Average Excess Portfolio-Returns (Conditional- Negative)

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

Beta 0.241 0.898 1.019 1.038 1.025 1.399 1.460 1.185 1.451 1.395

Average 1.997 4.618 5.642 6.622 7.206 7.883 8.849 9.396 11.002 11.896 excess (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) return

Now, we can use three diagrams to show the average monthly equally-weighted returns for each of the ten portfolios over the sample period.

Figure 7 shows the relationship between portfolio beta and excess portfolio returns in the unconditional case. As can be seen from the figure that the best fitting line is downward sloping which means there is a negative relationship between portfolio betas and average excess portfolio returns. In other words, higher beta portfolios bring lower returns. (This contradicts with the CAPM but does not refute the validity of the model in ISE. This is because the model also implies the conditional relationship.)

Figure 7: Excess Portfolio Return- Portfolio Beta Relationship (Unconditional)

Figure 8 shows the relationship between portfolio beta and excess portfolio returns in the conditional positive case. It’s obvious that there is a positive relationship between portfolio betas and average excess portfolio returns. This means higher beta portfolios bring higher excess returns when the excess market portfolio return is positive.

Figure 8: Excess Portfolio Return- Portfolio Beta Relationship (Conditional- Positive)

Figure 9 shows the relationship between portfolio beta and excess portfolio return in the conditional negative case. It’s obvious that there is a negative relationship between portfolio betas and average excess portfolio returns. This means higher beta portfolios bring lower excess returns when the excess market portfolio return is negative.

Figure 9: Excess portfolio Return- Portfolio Beta Relationship (Conditional- Negative)

Empirical Results of Model 1 and Model 2:

Table 5 summarizes the regression results of the Model 1.

Table 5:Test Results of the Model 1

Parameters R2 σ(ε)

α γ

Parameter Parameter Model 1 estimate estimate 0.000752 11.717 2.019 -0.979

Parameter Parameter t-ratio t-ratio 1.380 -0.670

The parameter α is estimated as positive but the t-ratio of this estimate implies that the value of parameter α is insignificant. Thus null hypothesis is not rejected which means 0 . This is a consistent result with the theory of the CAPM.

The parameter γ estimated as positive but its t-ratio implies that γ is insignificant. Thus, we conclude that the null-hypothesis is not rejected. It is concluded that this result is inconsistent with the theory of the CAPM. The model has a very low 2 R which is very close to zero.

However, as mentioned earlier, this does not mean that the CAPM is not valid. Since the model is estimated in the unconditional case in which both positive and negative excess market portfolio returns are combined, the results might be biased.

So, for a more precise test of the relationship, Model 2 results are presented in Table 6 below.

Table 6: Test Results of the Model 2

Parameters R2 σ(ε)

a b1 b2

Parameter Parameter Parameter 0.418 8.947 Model Estimate estimate estimate 2 2.019 5.402 -9.915

Parameter Parameter Parameter t-ratio t-ratio t-ratio 1.807 4.667 -8.288

The parameter b1 is estimated in periods when the excess return on the market portfolio is positive. It is expected to be positive in this period. T- statistics of b1 implies that its estimated value is significant which means there is a positive relationship between portfolio betas and average excess portfolio returns. Thus, the null hypothesis is rejected both at %1 and %5 level of significance. In other words, higher beta portfolios have higher average excess portfolio returns when the excess market portfolio return is positive. This supports the theory of the CAPM.

The parameter b2 is estimated in periods when the excess return on the market portfolio is negative. It is expected to be negative in this period. T- statistics of b2 implies that its estimated value is significant which means there is a negativerelationship between portfolio betas and average excess portfolio returns.

Thus, the null hypothesis is rejected both at %1 and %5 level of significance. In other words, higher-beta portfolios have lower average excess portfolio returns when the excess market portfolio return is negative. This supports the theory of the CAPM. Rejecting the two null-hypotheses in favor of the alternate implies that there is a systematic-conditional relationship between portfolio betas and average excess portfolio returns. In other words, the theory of the CAPM is validated in ISE from January 2006 to December 2010.

CONCLUSION

There are many studies testing the validity of the CAPM. These studies have different results regarding the validity of the SLB version of the CAPM. This is the case as well regarding studies done in Turkey with Turkish data. Some of the results are validating the theory while others are not.

The first part of the present study employs the unconditional approach based on the Fama and French (1992) model, and as expected does not support the validity of the CAPM regarding firms listed on the ISE. The unconditional approach is testing the direct relationship between portfolio betas and average excess portfolio-returns. The statistical results of the present study show that this relationship is not valid when the unconditional approach is used. However, one cannot claim that the CAPM is not valid with this particular approach, because in the unconditional approach positive excess market-portfolio-return periods and negative excess market-portfolio-return periods are grouped together into a single data set. This can lead to a bias in the statistical results. More appropriately in the conditional approach, positive excess market-portfolio-return periods and negative excess market-portfolio-return periods are evaluated separately in order to correctly test the relationship between portfolio betas and average excess portfolio-returns. The model of Pettengill et al. (1995) is employed for this more relevant test of the CAPM with Turkish data. Accordingly, it is found that there is a positive relationship between portfolio betas and average excess portfolio-returns when the excess market-portfolio-return is positive. In other words, if the market-portfolio-return is higher than the risk-free rate, higher beta portfolios attract higher excess-returns. And as expected, it is also found that there is a negative relationship between portfolio betas and average excess portfolio-returns when the excess market-portfolio-return is negative. In other words, if the market- portfolio-return is lower than the risk-free rate, higher beta portfolios attract lower excess-returns. Therefore, we can reasonably conclude that there exists a systematic, conditional relationship between portfolio-betas and -returns. This empirical result appears to be a validation of the CAPM regarding firms listed on the ISE from

January 2006 to December 2010, the dates of the data set employed by the present study.

In conclusion, our results seem to indicate that the systematic risk of a security as measured by beta is a relevant and appropriate measure of portfolio- or security-risk; and in turn helps to significantly explain the variation in portfolio- or security- returns, regarding firms listed on the ISE.

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APPENDIX I: PORTFOLIO COMPONENTS AND INDIVIDUAL STOCK-BETAS

PORTFOLIO 1 PORTFOLIO 2 PORTFOLIO 3 PORTFOLIO 4

Stock Beta Stock Beta Stock Beta Stock Beta GSRAY 0.151 METRO 0.520 ECZYT 0.685 ENKAI 0.778 TIRE 0.237 DEVA 0.546 BRISA 0.690 TUPRS 0.782 GUBRF 0.269 AEFES 0.549 EGGUB 0.690 KOZAA 0.787 TSPOR 0.290 KONYA 0.563 GOLTS 0.693 PTOFS 0.805 FENER 0.337 NTHOL 0.566 IZDMC 0.706 ALARK 0.822 BAGFS 0.427 TCELL 0.576 KIPA 0.727 AKSA 0.824 KARTN 0.452 BSHEV 0.659 ADNAC 0.730 AKENER 0.829 NTTUR 0.480 TEKTU 0.666 ECILIC 0.739 EREGL 0.838 BIMAS 0.481 TKFEN 0.666 ALBRK 0.775 AYGAZ 0.872

PORTFOLIO 5 PORTFOLIO 6 PORTFOLIO 7 PORTFOLIO 8

Stock Beta Stock Beta Stock Beta Stock Beta FROTO 0.885 DOHOL 0.931 PEGYO 1.065 ISCTR 1.154 NETAS 0.886 IPMAT 0.942 SISE 1.090 YKBNK 1.157 THYAO 0.901 MARTI 0.960 BJKAS 1.091 YKSGR 1.177 SASA 0.907 ISGYO 0.989 IHLAS 1.109 ASYAB 1.184 BANVT 0.909 TTRAK 0.995 KRDMD 1.112 TSKB 1.216 ULKER 0.921 TRKCM 1.013 ANSGR 1.119 AKBNK 1.221 CLEBI 0.926 EGSER 1.038 ZOREN 1.121 GSDHO 1.221 TAVHL 0.927 ASELS 1.042 GOLDS 1.128 HALKB 1.262 AFYON 0.928 TEKST 1.049 RYSAS 1.133 KCHOL 1.267

PORTFOLIO 9 PORTFOLIO 10

Stock Beta Stock Beta ARCLK 1.269 SNGYO 1.364 TOASO 1.280 AKGRT 1.428 GLYHO 1.283 SKBNK 1.446

VESTL 1.304 GARAN 1.451 ISFIN 1.314 TEBNK 1.454 SAHOL 1.341 DOAS 1.490 HURGZ 1.343 DYHOL 1.490 IHEVA 1.345 BOYNR 1.503 KARSN 1.362 VAKBN 1.562

APPENDIX II: MONTHLY EXCESS MARKET RETURN (%)

DATE EXCESS MARKET RETURN DATE EXCESS MARKET RETURN 06/01 10.988 08/11 -9.079 06/02 4.329 08/12 2.998 06/03 -9.780 09/01 -4.720 06/04 1.208 09/02 -8.616 06/05 -14.149 09/03 5.974 06/06 -8.265 09/04 21.588 06/07 0.493 09/05 9.327 06/08 2.137 09/06 4.300 06/09 -2.508 09/07 14.635 06/10 8.535 09/08 8.399 06/11 -7.317 09/09 2.149 06/12 1.116 09/10 -2.284 07/01 3.819 09/11 -4.658 07/02 -0.856 09/12 15.712 07/03 3.922 10/01 2.845 07/04 1.620 10/02 -9.658 07/05 3.251 10/03 13.136 07/06 -1.384 10/04 3.671 07/07 10.889 10/05 -8.368 07/08 -6.251 10/06 0.225 07/09 6.380 10/07 8.527 07/10 5.258 10/08 -0.463 07/11 -7.254 10/09 9.034 07/12 1.092 10/10 3.899 08/01 -24.380 10/11 -5.598 08/02 3.609 10/12 0.360 08/03 -14.127 08/04 10.062 08/05 -9.398 08/06 -13.559

08/07 18.795 08/08 -7.053 08/09 -10.990 08/10 -24.266

APPENDIX III: MONTHLY RISK-FREE RATE (%)

DATE RISK-FREE RATE DATE RISK-FREE RATE 06/01 1.110 08/11 1.470 06/02 1.110 08/12 1.470 06/03 1.050 09/01 1.260 06/04 1.050 09/02 1.260 06/05 1.050 09/03 1.260 06/06 1.240 09/04 1.260 06/07 1.240 09/05 1.260 06/08 1.240 09/06 1.260 06/09 1.540 09/07 1.260 06/10 1.370 09/08 0.770 06/11 1.370 09/09 0.770 06/12 1.370 09/10 0.770 07/01 1.460 09/11 0.770 07/02 1.460 09/12 0.770 07/03 1.460 10/01 0.610 07/04 1.410 10/02 0.610 07/05 1.410 10/03 0.610 07/06 1.410 10/04 0.610 07/07 1.280 10/05 0.610 07/08 1.280 10/06 0.610 07/09 1.280 10/07 0.640 07/10 1.350 10/08 0.640 07/11 1.350 10/09 0.640 07/12 1.350 10/10 0.640 08/01 1.260 10/11 0.640 08/02 1.260 10/12 0.640 08/03 1.260 08/04 1.350 08/05 1.350 08/06 1.350 08/07 1.470 08/08 1.470 08/09 1.470 08/10 1.470

APPENDIX IV: CONDITIONED POSITIVE/NEGATIVE PORTFOLIO BETA –EXCESS PORTFOLIO RETURN (%)

Conditional-Positive Period

PORTFOLIO BETA EXCESS RETURN 1 -0.0319 5.3788 2 0.1549 4.7641 3 0.3669 5.3648 4 0.4323 6.4532 5 0.2076 9.1954 6 0.7390 6.5780 7 0.8413 7.4685 8 1.2782 8.6093 9 1.2425 8.5366 10 1.5540 10.0331

Conditional-Negative Period

PORTFOLIO BETA EXCESS RETURN 1 0.241 -1.9973 2 0.898 -4.6189 3 1.019 -5.6424 4 1.038 -6.6229 5 1.025 -7.2062 6 1.399 -7.8831 7 1.460 -8.8490 8 1.185 -9.3963 9 1.451 -11.0025 10 1.395 -11.8966