A major sector in finance is the optimization of portfolio. The target is to maximize the excepted return and minimize the risk. In 1952 Harry Markowitz with his theory about portfolio selection made two observations. The first one was that the combinations of two risky assets provide non-cumulative standard deviations since the two assets are positive correlated. Secondly, when a portfolio of risky assets is built, the standard deviation risk of the portfolio is less than the sum of the standard deviations of its contents. Tobin (1958) suggested a methodology to recognize the appropriate portfolios among the efficient ones. Economists William Sharpe (1964) and John Lintner (1965) simplified this first model by measuring the systematic risk which is related with the general market and it is often called market risk. The result was the development of the Capital Asset Pricing Model (CAPM) which became the groundwork of portfolio measurement. CAPM is applied to help investors, managers and owners to solve decision problems of modern financial management. CAPM is used as a measurement of risk and return and shows the relationship between these two factors. The CAPM relates expected returns of an asset with the risk factor. Moreover it estimates the asset returns and try to modify the risk. In efficient markets the expected returns are correlated by a linear function of their characteristic degrees with market risk. The CAPM says that the expected risk on each asset is relative to its beta. Beta measures the role of a stock to the risk of the market portfolio. The Capital Asset Pricing Model can be defined as:

R = rf + B ( rm - rf )

where: R = the expected return on asset rf = a risk free rate B = a risk measure of asset rm = the expected market return The CAPM is developed under quite strong assumptions and that means it is hold only in specific situations. The major assumptions of the CAPM are: Investors have homogeneous beliefs There is no limitation on borrowing and lending There are no transactions costs and taxes Mean-Variance is optimal Any investment is equilibrium Investors behave competitively Capital market Line (CML) and Security Market Line (SML) are two deep-rooted models that are useful for derivation of CAPM. Capital Market Line (CML) and efficient frontier The CML shows the expected return for a given level of risk in a combined portfolio. CML measures the risk by Ïƒ. CML is hold for efficient portfolios and is applicable by investors with combined and final portfolio which is efficiently diversified. The efficient frontier says that a set of portfolio has the maximum return with a given risk or the minimum risk with a given return. The objective is to move up and left so that investors have low risk and high return. Return Risk Security Market Line (SML) The SML is a linear function between market risk and expected return. SML is applicable to portfolio analysis to experiment whether the securities are comparatively priced or not. The SML expresses the return an investor can expect in terms of a free-risk rate and the relative risk of a portfolio. In the SML risk is measured by Î² and every asset, security or portfolio is positioned on it. Assets over the SML are underpriced relative to CAPM and assets under the SML are overpriced. Empirical tests Tests of the CAPM are quite difficult to perform. The CAPM and its alterations have been generally tested in the literature but many problems have risen, mainly in the variables bias. Recent papers with the use of highly complicated techniques managed to increase the efficiency of the tests by working with more classified data. Studies on individual security returns by Lintner (1965) and Douglas (1969) werenâ€™t so hopeful. Fama and McBeth (1973) investigated the relationship between the average returns and beta using data in a durable period. Roll (1977) made two observations by testing the CAPM. The first one is that the market portfolio is mean-variance efficient when beta and expected return is linear correlated. The second is that if you do not know exactly the market portfolio is ineffective to judge the validity of CAPM. A lot of studies (Banz, 1981; Basu, 1983; Chan et al., 1991; Rosenberg et al., 1985) showed that not only the market beta affects the expected return but also other variables like the size, macroeconomics variables, p/e ratio and book to market value ratio have an important impact on security returns. Fama and French (1992) testing the validity of CAPM found that to reduce errors in beta measurement is powerful to take into account also non-market risk factors such as differences between return and low/high book to market stocks or portfolio of small/large stocks. Kothari et al,( 1995); instead of monthly returns data used twelve-monthly to approximate beta and found a considerable relationship between cross-sectional returns and beta. A study on US-stocks during 1926-1990 made by Pettengill et al, (1995) described a systematic correlation on beta and return for the whole period when market varies up and down. Downs and Ingram (2000) found that the average of returns are positive correlated with beta, negative with total risk and far from firm-size. Galagedera and Silvapulle (2003) reported strong empirical evidence to show the bond between returns and systematic co-moments in markets. Another approach in 2005 by Galagedera and Faff who developed a three-beta (low-neutral-high) asset pricing model to observe if the relation beta-return varies on up and down market environment was encouraging. Validity of the CAPM and the alternative theory of APT After many empirical tests through the years on the CAPM by literature it is commonly accepted by financial world and it is used to approximate the cost of capital. It is a safe method to measure the expected return with risk and show strong correlation between them. That does not guarantee that the CAPM is infallible but certainly is a practical model until now. However alternative theories came out and a well known is Stephen Rossâ€™s (1976) Arbitrage Pricing Theory (APT). Like the CAPM, Arbitrage Pricing Theory deals with expected return and risk but also assumes macroeconomic factors and applies to well-diversified portfolios where unique risk does not exist. The main idea is the measurement of systematic risk with more than one ways. Market and efficient portfolios are not the objective of APT in contrast with the Capital Asset Pricing Model. Both models have advantages and disadvantages but there are undeniable useful tools for financial aims. Implications of CAPM to investors and financial managers The CAPM shed light on many fields of security analysis and portfolio management. Progress on the analysis of stock exchange-market exists from early practical applications of CAPM. Many studies involved with the course of risk redaction by diversification and the measurement of systematic risk by beta factor. Beta is in a great interest for investors and financial managers as help them to choose the best portfolio by representing the expected returns and shows the level of risk. Beta associates security return with market return so when the market goes up investments behave with the same way and that forces investors for better decisions. The CAPM gave a framework to estimate the performance of investments. Moreover beta-equity can be useful for a company without debt to point the systematic risk of assets. The debt of a company increases the risk of shareholders and therefore the rate of return that is required. An additional risk exists from financial influence and that drives to a higher beta. The CAPM consequently specifies the foundation that a firms-adjusted risk cost of capital must be measured to find out its going concern.

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Conclusion This study uses theoretically earlier information about the CAPM and presents empirical facts to support the validity of this model. A summary of the principals of the CAPM are analyzed such as the assumptions under the CAPM, the Security Market Line (SML) and the Capital Market Line (CML). The CAPM provides a practical method to handle both return and risk. Market risk is measured by beta factor and is actually related to the investment decision. It is a substantial variable for portfolio management. Using CAPM is important not only for investors but also for financial managers for choosing the efficient projects. Benefits exist also for individuals and the economy as the CAPM built the foundations of finance theory. In addition the alternative theory of Arbitrage Pricing Theory (APT) is also useful and significant but more theories have to be developed. However more empirical tests and examinations should be done in the future regarding the assumptions of the CAPM and the suitable measure of risk to object the best performance.

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