An Overview of Asset Pricing Models 978-3-668-09330-0

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CHAPTER ONE: INTRODUCTION The term financial market is describing any marketplace where lenders those who have excess fund and borrowers those who need fund deficit are meet together for exchange of instruments such as equities, bonds, currencies and derivatives. The lender in the financial market are called as investors who buys financial instruments. The investors are invest their fund to maximize their wealth. In reality investors are unable to achieve their objectives at all due to poor performance of respective stock and the market conditions when they are investing in equities. The reason could be the assets may underpriced or overpriced when making investment decisions. If the investors are priced correctly for the asset by considering all relevant factors which are affecting the value, they can enjoy normal profit by appropriately pricing the asset in an efficient market. It has always been the challenge of explaining the decision process of the investors in the stock market. In this context, the behavior of investor has a close relationship with the investment decisions and the way of enriching. The rate of return and its determinations are the major issues in Finance. The rate of return is one of fundamental criteria for allocation of resources and analysis of risk and return. Their importance can be observed in the field of corporate and personal finance when define the viability of an investment and making investment decisions. Stock returns is always be considered as the principal point when investors going to put

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their money in financial market. More profit have been involved in higher risk, and vice versa. Investors should take into account their decision to invest their money in accordance with their risk-taking abilities. Many theories and models have developed to guide investors in measuring their proper risk for a given level of return, which will help investors to take a decision easier. All such theories and models unable practiced in all times in different markets. Anomalies could occur in all different conditions of the market (Ramdy, 2011). There are number of research on existing models developed in different markets in times and to find out the best model with considering all factors which determines and explain the behavior of assets prices for accurately pricing the assets to perform ideal financial decision making in financial market. However studies has not been able to find a supreme model that incorporate everything that happens in the stock market before last six decades. Currently there are various branches have emerged from research to treat of modeling the behavior of the stocks such as the modern portfolio theory and the theory of behavioral finance. The modern portfolios theory include models that have delivered major adjustment and improvement in predicting behavior of stocks to the reality. Based on the modern portfolio theory subsequent researcher able to deliver the important theoretical framework. There are extensive researches are conducted to develop portfolio strategies to make profit on investment decisions in stock markets in this modern financial era. Investors are adopting complicated technique and advanced approaches for modelling framework towards investment decision making strategy in recent years. Meanwhile introduction of rapid improvement of stock market with automation system and the feasibility of introducing large number of stock listing for

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trading have change the way of investment decisions towards the structure of stock portfolios. This trend of selecting stock portfolios substantially eliminates diversifiable risk and reduces the default risk (Memtsa, 1999). Investment strategy in financial market during the early stage were based on common sense which measures total risk and assumes that the stock with high risk yielding higher return than lover risk investments. This fundamental framework help to introduction of modern portfolio theories. The single factor and multi factor asset pricing models are developed based on the risk return tradeoff relationship. Using the asset pricing model investor can measure the amount of risk the stocks hold. Furthermore it can be measure the magnitudes of the expected return to be rewarded for bearing any specific amount of risk (Memtsa, 1999).

The models for asset pricing have been developing and evolving for more than 50 years since the modern portfolio theory introduced by Markowitz (1959) which explained the risk return relationship. The theory given important contribution for the advancement of a model to determine expected rate of return of an asset. Markowitz states that, the expected return (average) and the variance or the standard deviation (risk) of return of a portfolio are the selection criteria of assets for the portfolio construction. These foundation can be used as a maximum as possible for the manner in which investors need to act. It is interesting to note that, while the model is based on an economic fact of "the Expected Utility ". The concept of utility here is based on the fact that different investors have different investment objectives and can be satisfied in different ways (BOAMAH, 2012). According to his theory investors make

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decision by considering two parameters of probability distribution of various assets of the economy: the mean and the variance. The investors are risk averse, as such they are trying to find a portfolio, consisting risky assets that will maximize the portfolio expected return for a given level of portfolio risk (Jiang, 2013). Generally investors are risk aversions. They prefer more return at less risk. To accept greater risk, they charge more for it in the form of higher expected return.

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CHAPTER TWO: CAPM THE MODERN PORTFOLIO THEORY The mean variance analysis explained in modern portfolio theory was introduced by Harry Markowitz in 1952 published in the Journal of Finance titled as “Portfolio Selection”. This idea of mean - variance analysis become the foundation for many models in current portfolio and investment management. The simple principles introduced in his paper is consistently being incorporated with new findings even after half century has past (Focardi & Fabozzi, 2004). The theory states that the expected return measured by mean and variance of return are the fundamental criteria for selection of stocks for portfolio formation. These two criteria can be used to possible hypothesis the behaviors and guides the investors to be act when making investment decisions (BOAMAH, 2012). His key insight for selection of individual assets for portfolio formations depends on the tradeoff between expected return of individual asset and the contribution of such individual asset for portfolio risk rather than its own risk (Sandberg, 2005).

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DIVERSIFICATION The return and risk are the important concepts in portfolio management theory and practices. The higher risk of an investment expects to have higher return. The risk of an investments is not measures what actually happening, but it measures of what is likely to be happen for investment. Markowitz, Harry (1952) Proposed that a well-diversified portfolios will gives highest level of return at given level of risk or provide minimum risk for given level of return. The individual assets combined into a set of portfolio, the expected returns of the portfolio return becomes the weighted average of the individual asset’s expected return. The weights are assigned based on the proportions of these assets held in the portfolio. However the risk of portfolio is not only depends on the weight of the respective individual asset’s risk. But also depends on the correlation between the assets includes in the portfolio (Sandberg, 2005). Markowitz (1952) provided theoretical justification for his theory of diversification which is derived from the statistical principle ‘Variance of the sample mean tends to zero when sample size tends to infinity. Though investors aware and understood this statistical norm of divarication by saying like “do not put all your eggs in one basket” (Francy, 2014). Based on his principal Markowitz, Henry (1959) advocated that the investors should diversify their portfolios to being as risk adverse investor. Markowitz understood that through well Diversification and cast diversification in the framework of optimization, the risk-return trade-off of investments could be improved (Focardi & Fabozzi, 2013).

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Markowitz delivered an approach for portfolio diversification based on measure of weighs of individual assets to be invested and measure of risk and return relationship between such individual assets. The degree of the diversification benefit is depends on the degree of correlation of return of individual securities includes in the portfolio. Markowitz explained this concept of diversification benefit through the statistical notion of covariance, or correlation. The investors should select securities to construct well diversified portfolios. They should consider the correlation of return among the individual securities. In the sense that the investors may face poor performance on portfolio when they invested on portfolio of assets which returns are highly correlated each other. In this case if an individual asset perform badly, other stocks of the portfolio also trend perform in such manner due to higher return correlation. This kind of investment are not a very prudent strategy. However in practice no assets which are perfectly correlated each other due to fact that different factors are affect their returns. As such when including more and more assets in the portfolio, the total risk trend to become less than the weighted average their risk. The reduction of risk is depends on the correlation between the assets selected in the portfolio. Investors can enjoy the greater benefit of diversification by selecting assets with lower correlation of returns between assets. As such investors can be hold well diversified portfolios by selecting assets which are not perfectly correlated, could eliminate the risk associated with the individual assets (Sandberg 2005).

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SELECTION OF THE OPTIMAL PORTFOLIO Under the assumption of risk averse and rational investors, Markowitz approach is based on the fact that the investors expects higher return from their investment portfolio and wanted to minimize risk of that return (Sandberg 2005). Therefore the investors make decisions based on the tradeoff between risk and return. The investors expects to be maximize their return for a certain level of risk, or minimize the risk for a certain level of return. The expected return measured in mean value and the risk is measured in variance. The optimization of portfolio return and risk is called mean variance optimization. Markowitz considered mean-variance on his work and use as the whole criteria for portfolio selection (BOAMAH, 2012). Markowitz developed a mathematical model for portfolio selection using an efficient portfolio that maximize expected return for a certain level of variance or minimize variance for certain level of return (Salomons, 2007). Markowitz argued that investor should choose the portfolio for any level of expected return with minimum variances from set of possible portfolios that can be made. The set of possible portfolios called as feasible set. In the feasible set, the portfolios with minimum variance are called mean-variance-efficient portfolios. As such the efficient frontier is formed from the combination of mean-variance-efficient portfolios. Each portfolios constructed in the efficient frontier has highest expected return at certain level of risk or lowest risk for a given level of expected return than any portfolios below the efficient frontier. This benefit arises due to the diversification effect where correlation among return of assets are imperfect. Because the efficient frontier is constructed with portfolios of assets rather than individual assets. The end one point of efficient

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frontier represent the portfolio with highest expected return and another and point represents portfolios with lowest risk (Reilly & Brown, 2011).

SELECTION OF THE OPTIMAL PORTFOLIO Investors are normally risk averse and they are expect to have higher return at minimum risk. The risk averse investors tradeoff more risk to get more expected return. In other words they expects higher return for assuming high risk of investments (Sharifzadeh, 2010). However in practice the risk attitude is varies among investors. Therefore selection of portfolio also varies among investors. They choice the portfolios in the efficient frontier based on the risk tolerance of the investors. Because Different portfolios have different risk return combinations in the efficient frontier. The selection process of optimal portfolio and behavior of investor can be explained by theory of choice, utility function, indifference curve and efficient frontier. Individual solves the choice problems by selecting the one which gives maximum utility value in given set of constrains. The theory assumed that the decision making process of individuals based on optimization of utility function. The utility function can be express by indifference curves. For a given investor all points in an indifference curve gives same level of utility with different risk return combination. The indifference curves are parallel for an individual and different for each individual according to the risk return combination. The indifference curve has higher utility than the indifference curve below it and lower utility than above curve in it.

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Investors wants to be in higher indifference curve, because they prefers highest possible utility from their investment opportunity. According to the Markowitz model the investors can maximize their return for given level of risk at efficient frontier (Sharifzadeh, 2010). The portfolios are independent from other portfolios in the efficient frontier. All of the portfolios have different expected return and risk characteristics. The expected return increases toward higher risk. The indifference cure of an individual investor specify the tradeoff between risk and return (Reilly & Brown, 2011). The optimal portfolio set to be select for investment for an investor can be found at the tangent point of the utility indifference curve on efficient frontier. Each individual has different attitude toward risk and they has different degree of risk aversion which leads to different utility indifference curves. As such the optimal portfolios varies for different investors. (Sharifzadeh, 2010).

OPTIMAL PORTFOLIO SELECTION AND THE RISK FREE ASSET Markowitz portfolio selection theory has further developed with the contribution of James Tobin by introducing risk free asset in optimal portfolio selection process which determine the equilibrium prices for assets in capital markets. (Sharifzadeh, 2010). Before introducing risk free assets, portfolios consist risky assets only. After the introduction of the risk free assets investors includes assets that has zero variance of expected return in their portfolio. The inclusion of risk free assets in the portfolio has changed the portfolio selection problem. The problem has investigated by Tobin (1958) and developed the separation theorem. With the combination of risk free asset and

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tangency portfolio formed a new efficient frontier call as CML which makes a better risk return tradeoff. (Salomons, 2007). The CML represents the existence of risk free asset and distribution of fund allocation for investment among risk free assets and risky assets in portfolio. Further the CML facilitate to find out the weighted average of expected return and risk of the portfolio (Leontis, 2013). Tobin (1958) Separation theory is different from Markowitz approach in selecting portfolios to be invest. The separation theorem has contributed for the next development of modern portfolio theory (Salomons, 2007). Tobin (1958) separation theory considered that how investors allocate their investment in between risk free asset and the portfolios on the efficient frontier (Sharifzadeh, 2010). This consideration make two problems in portfolio selection. First determination of tangency portfolio in the efficient frontier that is market portfolio and then adjust the tangency portfolio based on the preferred level of risk along CML by going short or long from the risk-free asset that is borrow or lend at risk free rate. Based on the Tobin’s idea Sharpe (1964) assuming that all investors can be able to borrow and lend money at risk free rate. Investors select their portfolio combination of risk free asset and a specific portfolio on the efficient frontier. As such the selected portfolio lie in the CML which connects the rate of risk free asset and through the market portfolio on the efficient frontier. The decision for the selection of position on CML is depends on the individual investors risk preference. That is the decision for borrowing or lending at risk free rate is depends on their risk preferences. The risk averse investors lend part of their money at risk free rate by investing risk free assets and invest another part of their investment on market portfolio of risky assets. On

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other hand the risk lovers who prefer more risk, borrow money at risk free rate and invest on all of their money on market portfolio of risky assets. The risk lovers face more risk as such they expect to have more return that is above market return. The investors should decide the position on the CML based on their risk preferences. The risk free lending and borrowing assumption lead to a significant contribution of the Markowitz portfolio theory and initiated a foundation for the development of CAPM (Sharifzadeh, 2010). Based on the separation theory Sharpe, Lintner, Mossin and Treynor developed the CAPM (Salomons, 2007).

A RISK MEASURE FOR THE CML The risk free assets made a significant impact of their portfolio selection decision. Markowitz efficient frontier has changed into a new efficient frontier called CML by the existence of the risk free asset. All investors wanted to be select their portfolio on the CML. The CML leads all investors to invest on the market portfolio. Individual investors differ in the selection of the position on the CML is based on their risk preference. When they make choice on their individual asset for a portfolio, the relevant risk measure of an assets is the covariance between the asset and market portfolio (Reilly & Brown, 2011). The market portfolio consist of every risky asset in the market, including stocks, bonds, options, real estate, coins, stamps, art and antiques. As such the market portfolio become as the completely diversified portfolio because the specific risk relevant to individual assets diversify away when combing all of assets in one portfolio.

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The specific risk relevant to a particular asset is called as unsystematic risk. The unsystematic risk of an asset can be eliminated when an individual asset is become part of the market portfolio. Therefore unsystematic risk is not relevant for investors and they not expect additional return to facing unsystematic risk. Another portion of risk which cannot be able diversify away trough diversification. This undiversifiable risk through diversification is called as systematic risk. The systematic risk determined by the macro economic factors which are common for all assets in the market and is not affected by firm specific factors. Therefore investors can expect additional return for assuming systematic risk. This is the core principal behind the CAPM that is beta return relationship (Sharifzadeh, 2010).

THE CAPITAL ASSET PRICING MODEL: EXPECTED RETURN AND RISK The introduction of risk free asset derived CML that become relevant efficient frontier. Investors selects their portfolio in the CML based on their risk preference that is become borrowing portfolio and lending portfolios. The decision of selection of assets in a portfolio performed based on the covariance of return between the risky asset and the market portfolio. As such the covariance become the relevant risk measure of asset and determine the appropriate asset expected return of risky asset. Based on this concept Sharpe, Lintner, Mossin and Treynor developed model indicating the expected return of an asset on risky assets. The model called as CAPM. The model helps investors and analyst to value of assets by providing appropriate discount rate to use in any valuation model and help to

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determine whether an asset overvalued, undervalued or correctly valued in the market (Reilly & Brown, 2011). The CAPM all about explain how determine the required rate of return for an asset for discounting future cash flows to make investment decision. Investors discount their future payoffs from the investment by the expected rate of return / cost of capital estimated for the investment on the basis of risk return relationship. Then investors will sell the asset if the market price of the asset is excess of the discounted pay offs And buy the assets if the market price less than the discounted pay offs until the market price become equals to the discounted value. When all assets are priced equal to discounted value of their future pay offs the capital market become at equilibrium (Sharifzadeh, 2010). The CML shows the relationship between the expected return of an efficient portfolio and its standard deviation but fails to show the relationship between the expected return of the individual asset and its risk. However the CAPM is shows such relationship (Shahid, 2007). There were no model which explains clear risk return relationship before origin of the CAPM. the previous theories explains the behavior of investors in selection of optimal portfolio but no any theory extend their model to deliver market equilibrium of asset prices under risk and also not specify the explanation of individual asset prices related different component of risk. Sharpe (1964-pp. 425-427). The CAPM simply and logically explains asset risk return relationship. After introduction of the model which is widely used to evaluate performance of managed portfolios and calculate cost of equity. Perhaps due to its simplicity empirical result almost shows a poor performance of the model. However the poor performance arise due to the consequence of weakness

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of the empirical test, such as used inappropriate proxies which are critical for model predictions (Vicente 2004).

THE SECURITY MARKET LINE (SML) Sharpe (1964) develops the CAPM by interpreting the expected return- beta relationship using the liner equation. The visual representation of such relationship is called as SML. The CAPM equation of the SML can be drawn with the return of risk free asset and the return of market portfolio. The Bata value assigned for market portfolio return equal to one. According to the CAPM, the SML expresses the risk reward structure of assets (Shahid, 2007). SML help to estimate expected return for a given asset based on systematic risk of assets. The systematic risk is measured by Beta. The expected rate of return increases linearly when the beta increases. Investors can be determine whether the assets is undervalued or overvalued by comparing rate of return of the asset and rate of return estimated by the CAPM for the asset. That is above, below or on the SML. The models states that if the assets are fairly priced then the rate of return of the asset equal to the expected rate of return estimated by the CAPM in a market equilibrium. According to the CAPM for valuing a particular asset, every investor use same required rate of return for discounting expected future pay offs of a particular asset. As such every asset traded in a capital market will get a same value by all investors which leads every assets valued at equilibrium price in capital market. If a particular asset trades in a fair price then the expected return will plotted on SML (Sharifzadeh, 2010). The actual rate of return estimated independent of CAPM of a particular asset which plotted above or below on the SML which indicates that

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the assets is mispriced. That is the asset is not traded at equilibrium price. The differences between actual rate of return and rate of return estimated by CAPM is typically called as Jenson Alfa (Leontis, 2013). The Jenson Alfa is the deviation from SML and actual rate of return which is considered as abnormal return.

THE MARKET BETA The beta is a standard measure to estimate the systematic risk of an asset. The CAPM states that when combine more and more asset in a portfolio, specific risk for a particular assets become negligible. Therefore in the market portfolio the unsystematic portion of total risk is become insignificant. However the macro economic factors that are affecting the market return as whole. Therefore all individual assets in the market affected by such macro-economic factors. These factors cannot be avoidable trough diversification and become significant risk factor. This risk factor is called as systematic risk. All individual asset contributes forming optimal market portfolio and return. Therefore the systematic risk of each individual assets contributes risk of optimal market portfolio propositionally and also determined by the covariance of an asset with market portfolio. As a result the beta of an asset is the covariance between market return and the respective individual asset return. Therefore there is a liner relationship exist between expected asset return and beta of respective asset. The beta for the market portfolio becomes equal to 1. Any assets having the beta value greater than 1, the assets considered as riskier than market portfolio and expects higher return than market return and vice versa. (Reilly & Brown, 2011)

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According to the model the investors have to be rewarded in two means such as time value of money and systematic risk. The free rate is the measure of time value of money and the beta is the measure of systematic risk. The model simply explain the relationship between risk and return of an asset. The risk and return relationship is explained by the CAPM equation as follows. �� = �� + �� (�� − �� )

Where: �� = The asset i expected return or cost of capital �� = The risk free rate �� = The beta of asset i �� = The expected return on the market

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CHAPTER FOUR: THREE FACTOR MODEL The CAPM is a single factor model which is used by financial analysis and practitioners for valuing assets and determining cost of capital. The model states that assets’ expected return related only with the market portfolio. That is all security returns are correlated with the market portfolio only (Al-Rayes, 2009). After development of the CAPM researchers were come up with doubt on the beta and return relationship and criticized about the model. The study of (Reinganum, 1981) and (Lakonishok & Shapiro, 1986) found insignificant relationship between beta and stock return in the US market. Researchers found that other factors also such as size, P/E ratio, leverage and book to market equity ratio impacts on asset return. The study of Basu (1977) found that the stocks with lower P/E ratio earned higher return and high P/E stocks earned lower return than estimated by the CAPM. The size effect found by Banz (1981). He states that small firms earns higher return and big firms earned lower return than estimated by CAPM. The study of Bhandari (1988) found a positive relationship between leverage and return. Rosenberg, Reid and Lanstein (1985) Found the stocks with high book to market ratio earned higher return than lower book to market ratio (Cakici, Fabozzi & Tan, 2013).

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Fama and French (1992) performed a comprehensive study including multiple factors such as market beta, size of firm, book to market equity ratio (BE/ME), leverage and earing to price ratio (P/E). The study provided evidences confirming result of previous studies mentioned above. The size and Book to Market (BE/ME) factors were founded as significant factors in explaining cross sectional variations in average stock return. While leverage and P/E ratio not significant as size and Book to Market (BE/ME) factors. Because size and Book to Market (BE/ME) factors seems to be absorbs the role of the leverage and P/E ratio. Therefore The study confirmed that market beta of CAPM is not only the factor to determining expected stock return and provided evidence the incapability of the CAPM in explaining cross-sections of average stock returns. Other factors identified also should be included in the model in addition to the market beta to get more concise stock return. This idea provided the foundation for developing multi factor model by replacing traditional CAPM. Fama and French (1993) Developed a three factor model based on the finding of previous studies. The model included two factors such as size and Book to Market equity (BE/ME) in addition to the market beta of CAPM. These two factors were identified based on the study of Fama and French (1992). By including the two additional factors the CAPM became as three Factor model. Therefore the TFM is the improved and extended version of the traditional CAPM. The model propose that the expected security return depends on the sensitivity of the security return to the market, the return difference between the portfolio consisting small size stock and portfolio consist of Big stocks in terms of Market capitalization (SMB) and the return difference between the portfolio consisting stocks with higher

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BE/ME and the portfolio consisting stocks with lower BE/ME (HML). The FF3FM is given in equation 01 as follows

Equation 01 ��� = ��� + �� ���� − ��� � + �� ���� + ℎ� ���� Where ��� is the rate of return on asset (or portfolio) i at time t, ��� is the risk-free rate of interest at time t, �� is the market beta of asset taken from time series regression �� is slope of size factor of asset taken from time series regression ℎ� is slope of Value factor of asset taken from time series regression ��� is the rate of return on the market portfolio at time t. ���� is the size premium (Small minus Big) ���� is the Value premium (High minus Low)

The motivation behind the selection of SMB and HML are to capture the size premium and value premium respectively. Fama and French (1993) Provided theoretical justification for the selection of size and BE/ME factors. Such as the small size firm tend to earn higher return than big size firms and high BE/ME firms tend to earn higher return than Lower BE/ME firms. The theoretical argument for size premium are transaction costs and liquidity risk. Stock dealers expects and require higher spread on bid and ask for trading small firms stock. Because small size firms stocks are traded infrequently and it has higher risk (Stoll & Whaley, 1983). The small firms are more illiquid than big firms stocks. The expected market illiquidity affects stock returns positively. Because illiquidity

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affects more on small firm rather than big firms (Amihud, 2002). Lakonishok, Shleifer and Vishny (1994) Provided explanation for the value premium. They states that investors overreact and buys much more stocks when they knows that the stock performed well in the past and they get good news about the stock. The past performance and good news make the stock attractive which leads to overpriced the stock and therefore the stock become low BE/ME. Likewise the investors overreact and try to sell more stocks when they understood that the stock performed badly in the past and get bad news about the stock which leads to make the share price down and underpriced which leads the BE/ME become high. As a result the higher BE/ME performed over lower BE/ME firms when the market corrects its overreactions.

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CHAPTER FIVE: FOUR FACTOR MODEL The FF3FM used and considered as a better model by financial analyst and practitioners for explaining expected return of stocks. Jegadeesh and Titman (1993) found the momentum anomaly that is short term return of stock in the past will tend to continue in future. The stocks with higher (poor) return in the past 12 months tend to have a higher (poor) in future. Fama and French (1996) test whether 3FM can explain the relationship between average stock return and the momentum anomaly (long term past returns and short term past returns) in addition to firm characteristics such as size, E/P ratio, cash flow/price, book-tomarket equity and past sales growth. They found that the 3FM performed well in all cases but not performed well when considered the short term momentum effect. That is the short term past returns. Therefore Fama and French (1996) concluded that the 3FM cannot explain the continuation of short-term returns documented by Jegadeesh and Titman (1993) and (Asness, 1994). Based on the finding of FF96 the 3FM is not able to explain the variations due to the momentum anomaly which is exist in the different stock markets and different time periods. Therefore incorporating the momentum factor with 3FM will increase the robustness of the model. As such Carhart (1997) modified the FF3FM by including momentum factor that comprised stocks’

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one year momentum effect and developed four factor model which called as Carhart Four Factor model (Vosilov & Bergström, 2010). The momentum factors introduced in the model based on finding of Jegadeesh and Titman (1993). They found that the stocks that performed well in the last 3-12 month will tend to perform well in the following year. The stock performed badly in the last 3-12 month will tend to perform badly in the following year. Therefore the strategy involving buying well performed stocks and selling badly performed stocks over the past 3-12 months will tend to produce a significant positive abnormal return in the following year (Michael, 2011). The C4FM works well in explaining crosssectional variation of average stock returns. Further the C4FM considerably improves the asset pricing error of the previous models namely FF3FM and CAPM (Vosilov & Bergström, 2010). The C4FM is given in equation 02 as follows Equation 2 ��� − ��� = �� + �� ���� − ��� � + �� ���� + ℎ� ���� + �� ���� + ��� Where ��� is the rate of return on asset (or portfolio) i at time t, ��� is the risk-free rate of interest at time t, �� is the intercept. �� is the market beta of asset taken from time series regression �� is slope of size factor of asset taken from time series regression ℎ� is slope of Value factor of asset taken from time series regression �� is slope of momentum factor of asset taken from time series regression

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��� is the rate of return on the market portfolio at time t. �� is the intercept. ���� is the size factor (Small minus Big) ���� is the Value factor (High minus Low) ���� is the momentum factor (Up minus Down) ��� is the residuals which explains unsystematic risk of the asset i at time t The C4FM assumes four risk factors to estimate the crosssectional distribution of expected stock returns. The four factors are market, size, BE/ME and momentum. The market risk factor usually estimated from the share price index, the size factor is the rate of return differences between the small capitalized firm and large capitalized firm in terms of market value. The BE/ME factor is the rate of return differences between higher BE/ME firms stock and lower BE/ME firms stocks. Finally the momentum factor is the rate of return differences between winner stock and loser stocks (Garyn-Tal & Lauterbach, 2015). The fourth factor represent a tendency that the firms with positive normal return in the past will give positive return in near future and firms with negative past return will give negative return in future. In other words the past performance continue in future (Michael, 2011). The momentum factor is derived by deducting the average rate of return of the badly performed stocks from the average rate of return of the well performed stocks. In other words the momentum factor is the differences between the rates of return of portfolio of stocks with g performance in the past and the rates of return of portfolio of stocks with bad performance in the past. The momentum factor is usually donated as WML or UMD. WML indicates that winner minus loser. The stocks with highest past average return is called as winner and the stock with lowest past average return called as loser. The winner stocks also termed as

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up and the loser stocks also termed as down. The momentum premium is the difference between return of the winner portfolio and return of loser portfolio. The four factor model was tested in various market around the world. The test result gives mixed result. Some studies provide evidence that the models works successfully such as Unlu (2013), Lam, Li and So (2010), Ben Naceur and Chaibi (2007) and L’Her, Masmoudi and Suret (2004) while some are not successful (eg Nartea, Ward and Djajadikerta (2009)). Also studies found that the value and momentum factors affecting the expected stock return estimation (Fama & French, 1998), (Chui, Titman & Wei, 2010), and (Asness, Moskowitz & Pedersen, 2013). However some empirical test states that the four factor model not adequately in explaining expected return of stocks when the portfolios were shorted based on size and momentum ((Fama & French, 2012), (Gregory, Tharyan & Christidis, 2013) and (Garyn-Tal & Lauterbach, 2015). The four factor model further extended into local, regional and global versions. The empirical comparative test on local and global versions shows a favorable finding for local versions. Griffin (2002) found that local version of the model works well in U.S., U.K., Canada and Japanese market. Cakici et al. (2013) found that the regional version of the model performed better than the global version in emerging stock markets, such as Asia, Latin America and Eastern Europe. Further Fama and French (2012) found that the regional version of the model are sometimes "passable" in North America or Europe regions (Garyn-Tal & Lauterbach, 2015).

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CHAPTER SIX: REWARD BETA MODEL Sharpe-Lintner version of CAPM used for estimate expected return and cost of capital. Subsequent empirical studies were raised doubt and then invalidate the model. Fama and French (1993) Introduced a three factor model by incorporating additional factors to overcome the weakness in the CAPM. Then the FF3FM got received more attention from researchers and practitioners. Among them Graham Bornholt in 2007 introduced reward beta approach for estimating expected return and cost of capital as an alternative model by criticizing the existing CAPM and FF3FM. He argues that the FF3FM also not perfect model due to two main problem in the model. The first problem is that the model lacks in a strong theoretical basis derived from asset pricing theory. Because FF used the method to construct their size and book-to- market factors is empirically driven and seems ad-hoc. The second reason he states that “its appeal in practice is limited by the need to find reliable forwardlooking estimates of the three factor-sensitivities and the three factor-premiums.”(Bornholt, 2007)).

According to Bornholt (2007) the reward beta model incorporates both CAPM and FF3FM. The CAPM developed

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based on mean – variance efficient portfolio approach. However the reward beta is developed based on the mean – risk approach. He states that The mean-risk assumption was previously replaced for mean variance assumption by several authors such as (Kaplanski, 2004) and (Bawa & Lindenberg, 1977). Therefore the reward beta is different from the CAPM beta. The estimated reward beta used to replace the CAPM beta estimates in the security market line. Bornhold considered size and Book to market effect into the reward beta directly through use of portfolios. The risk measures used in the derivation of the model consistent with the risk aversion and expected utility theory. Bornhold introduces an alternative method to estimate beta which different from CAPM Bata. He argued that the correct mean –risk beta is calculated by the ratio of the risk premium of the asset to market risk premium. He justified this derivation of the reward beta using theoretical framework of APT. the reward beta calculation is estimated in the equation 03 and the expected return is estimated using right hand side of the equation 04. However to test the model he introduced a market version compatible with reward beta approach is given in equation 05. This model is called as Bornhold Reward Beta Model. Equation 03 ��� =

���� − �� �

���� − �� �

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Equation 04 �[�� ] = �� + ��� ��[�� ] − �� � Equation 05

�� − �� = ��� �� [�� ] − �� � + �� (�� − �[�� ]) + ��� Bornholt (2007) argues that to estimate expected returns, the reward beta uses forward looking portfolio reward beta. In this approach all equities in the market divided into portfolio of stocks periodically in such a way that the stocks in a same portfolio should consist similar risk at the time of portfolio construction which is decided by researcher. Then the reward beta of a portfolio can be estimated using the stocks currently belongs to the portfolio as estimation for individual stocks’ reward beta. Therefore the portfolio reward beta estimated in equation 06 as follows. Equation 06 ̅ = ���

(�̅� − �̅� ) (�̅� − �̅� )

Where ̅ ��� = ������ ���� �� ��������� � ��� � ����� ���������� ������ �̅� = ������ ������� ������ �� ��������� � �̅� = ���� ���� ���� �̅� = ������ �����

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Bornhold (2007) argues that if a portfolio consist stocks with similar, the reward beta of the portfolio can be assigned to the individual stock which was included in the respective portfolio. Therefore if the portfolio j consist the stock i, then the estimated reward beta of the portfolio j can be used reward beta of the stock i. “This process means that an individual security’s beta estimate is based on the post portfolio-inclusion returns of securities that were in its current portfolio in the past. It is this feature that makes these beta estimates forward-looking”. Pp74 Bornhold (2007).

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References Al-Rayes, F (2009), "Implementing the three factor model of Fama and French on Kuwait's equity market". Amihud, Y (2002), "Illiquidity and stock returns: cross-section and time-series effects", Journal of Financial Markets, vol. 5, no. 1, pp. 31-56. Asness, CS (1994), 'Variables that explain stock returns: Simulated and empirical evidence', Master thesis, Graduate School of Business, University of Chicago. Asness, CS, Moskowitz, TJ & Pedersen, LH (2013), "Value and momentum everywhere", The Journal of Finance, vol. 68, no. 3, pp. 929-85. Banz, RW (1981), "The relationship between return and market value of common stocks", Journal of Financial Economics, vol. 9, no. 1, pp. 3-18. Basu, S (1977), "Investment performance of common stocks in relation to their price‐earnings ratios: A test of the efficient market hypothesis", The Journal of Finance, vol. 32, no. 3, pp. 663-82. Bawa, VS & Lindenberg, EB (1977), "Capital market equilibrium in a mean-lower partial moment framework", Journal of Financial Economics, vol. 5, no. 2, pp. 189-200. Ben Naceur, S & Chaibi, H (2007), "The best asset pricing model for estimating cost of equity: evidence from the stock exchange of Tunisia", Available at SSRN 979123. Bhandari, LC (1988), "Debt/equity ratio and expected common stock returns: Empirical evidence", Journal of Finance, pp. 50728. BOAMAH, AE (2012), 'Risk–Return Analysis of Optimal Portfolio using the Sharpe Ratio', KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY. Bornholt, G (2007), "Extending the capital asset pricing model: the reward beta approach", Accounting & Finance, vol. 47, no. 1, pp. 69-83. Cakici, N, Fabozzi, FJ & Tan, S (2013), "Size, value, and momentum in emerging market stock returns", Emerging Markets Review, vol. 16, pp. 46-65. Carhart, MM (1997), "On persistence in mutual fund performance", The Journal of Finance, vol. 52, no. 1, pp. 57-82.

30

Chui, AC, Titman, S & Wei, KJ (2010), "Individualism and momentum around the world", The Journal of Finance, vol. 65, no. 1, pp. 361-92. Fama, EF & French, KR (1992), "The cross‐section of expected stock returns", The Journal of Finance, vol. 47, no. 2, pp. 427-65. Fama, EF & French, KR (1993), "Common risk factors in the returns on stocks and bonds", Journal of Financial Economics, vol. 33, no. 1, pp. 3-56. Fama, EF & French, KR (1996), "Multifactor explanations of asset pricing anomalies", The Journal of Finance, vol. 51, no. 1, pp. 55-84. Fama, EF & French, KR (1998), "Value versus growth: The international evidence", Journal of Finance, pp. 1975-99. Fama, EF & French, KR (2012), "Size, value, and momentum in international stock returns", Journal of Financial Economics, vol. 105, no. 3, pp. 457-72. Focardi, SM & Fabozzi, FJ (2004), "The mathematics of financial modeling and investment management, illustrated edn, vol. 138, John Wiley & Sons. Focardi, SM & Fabozzi, FJ (2013), "Principal Components Analysis and Factor Analysis", Encyclopedia of Financial Models. Francy, T (2014), "Mean variance approach of portfolio management an empirical analysis of Indian experience". Garyn-Tal, S & Lauterbach, B (2015), "The Formulation of the Four Factor Model when a Considerable Proportion of Firms is Dual-Listed", Emerging Markets Review. Gregory, A, Tharyan, R & Christidis, A (2013), "Constructing and testing alternative versions of the Fama–French and Carhart models in the UK", Journal of Business Finance & Accounting, vol. 40, no. 1-2, pp. 172-214. Griffin, JM (2002), "Are the Fama and French factors global or country specific?", Review of Financial Studies, vol. 15, no. 3, pp. 783-803. Jegadeesh, N & Titman, S (1993), "Returns to buying winners and selling losers: Implications for stock market efficiency", The Journal of Finance, vol. 48, no. 1, pp. 65-91. Jiang, Y (2013), 'Testing asset pricing models under non-linear assumptions: evidence from UK firm level panel data', Master thesis, University of Birmingham.

31

Kaplanski, G (2004), "Traditional beta, downside risk beta and market risk premiums", The Quarterly Review of Economics and Finance, vol. 44, no. 5, pp. 636-53. L’Her, J-F, Masmoudi, T & Suret, J-M (2004), "Evidence to support the four-factor pricing model from the Canadian stock market", Journal of International Financial Markets, Institutions and Money, vol. 14, no. 4, pp. 313-28. Lakonishok, J & Shapiro, AC (1986), "Systematic risk, total risk and size as determinants of stock market returns", Journal of Banking & Finance, vol. 10, no. 1, pp. 115-32. Lakonishok, J, Shleifer, A & Vishny, RW (1994), "Contrarian investment, extrapolation, and risk", The Journal of Finance, vol. 49, no. 5, pp. 1541-78. Lam, KS, Li, FK & So, SM (2010), "On the validity of the augmented Fama and French’s (1993) model: evidence from the Hong Kong stock market", Review of Quantitative Finance and Accounting, vol. 35, no. 1, pp. 89-111. Leontis, K (2013), "Determinants of Cross-Sectional Stock Returns During a Turbulent Period: An Application to the Athens Stock Exchange". Markowitz, H (1952), "Portfolio selection", The Journal of Finance, vol. 7, no. 1, pp. 77-91. Markowitz, H (1959), "Portfolio selection: efficient diversification of investments", Cowies Foundation Monograph, no. 16. Memtsa, CD (1999), 'Factor models, risk management and investment decisions', Ph.D in Finance thesis, Durham University. Michael, dJ (2011), 'Review of asset pricing models ', University of Tilburg Nartea, GV, Ward, BD & Djajadikerta, HG (2009), "Size, BM, and momentum effects and the robustness of the Fama-French three-factor model: Evidence from New Zealand", International Journal of Managerial Finance, vol. 5, no. 2, pp. 179-200. Ramdy, Z (2011), 'Testing Fama and French Three-Factor Model and Earnings-to-Price on Stock Excess Return', Universiti Utara Malaysia. Reilly, F & Brown, K (2011), "Investment analysis and portfolio management, Cengage Learning. Reinganum, MR (1981), "Misspecification of capital asset pricing: Empirical anomalies based on earnings' yields and market

32

values", Journal of Financial Economics, vol. 9, no. 1, pp. 19-46. Rosenberg, B, Reid, K & Lanstein, R (1985), "Persuasive evidence of market inefficiency", The Journal of Portfolio Management, vol. 11, no. 3, pp. 9-16. Salomons, A (2007), 'The Black-Litterman model hype or improvement', Ms thesis, University of Groningen. Sandberg, P (2005), "How Modern is Modern Portfolio Theory", Journal of Financial Economics, vol. 9, pp. 3-18. Shahid, M (2007), 'Measuring portfolio performance', Master in Financial Mathematics thesis, Uppsala University. Sharifzadeh, M (2010), "An Empirical and Theoretical Analysis of Capital Asset Pricing Model, Universal-Publishers. Sharpe, WF (1964), "Capital asset prices: A theory of market equilibrium under conditions of risk", The Journal of Finance, vol. 19, no. 3, pp. 425-42. Stoll, HR & Whaley, RE (1983), "Transaction costs and the small firm effect", Journal of Financial Economics, vol. 12, no. 1, pp. 57-79. Tobin, J (1958), "Liquidity preference as behavior towards risk", The review of economic studies, pp. 65-86. Unlu, U (2013), "Evidence to support multifactor asset pricing models: The case of the Istanbul stock exchange", Asian Journal of Finance & Accounting, vol. 5, no. 1, pp. 197-208. Vosilov, R & Bergström, N (2010), 'Cross-Section of Stock Returns:: Conditional vs. Unconditional and Single Factor vs. Multifactor Models', Master thesis, Umeå School of Business.

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