# Beta And Stock Returns In Economic Crisis Finance Essay

The development of the capital markets and new financial products in the last four decades over the world, undoubtedly constitute the cause of research and developing of models in the finance science. The two most famous financial models are the “Theory of Portfolio” by Markowitz (1952), which determines the relation between return and the risk. By this model the investors estimate the efficient frontier with all possible combinations of risk and return. This frontier is constituted by the efficient portfolios, which are portfolios with highest return in any given level of risk. In this model the relation between risk and return is the basic criterion for the choice of the optimum portfolio for any investor. This model required complicated calculations and that is the disadvantage of its usefulness. The second most famous model in the finance is the mathematical economic analysis by Modigliani and Miller (1958) about the capital structure of the firm. They support that a firm has an optimal capital structure where the firm value is maximized and one way to achieve this aim, the maximization of the firm value is to increase its debt because then low the cost of capital and increase its value.

The main concept in finance, for investors, analysts and portfolio managers is the relationship between return and the risk. The Capital Asset Pricing Model, (CAPM) which developed by Sharpe (1964), Lintner (1965), Mossin (1966) and Black (1972), is the convert of Markowitz theory and constitutes the cornerstone in the science of finance due to is the first model which suggests the relationship between the return an risk among returns of portfolios or shares and market portfolio. The CAPM is a valuation model for stocks which include risk and determines the expected return of the risky shares. The CAPM measures the risk and indicates the relation between expected return and risk. This model estimates the cost of capital for enterprises and using for evaluation of the performance of managed portfolios. Capital Asset Pricing Model suggests that the expected return on an asset above the risk free rate relates linearity with the non diversifiable risk as a measured by asset’s beta, and indicates the linear relation between expected returns of stocks and investments and beta of this stock or investment. This model has been criticized over 30 years. In decades of 1960, 1970 and in the beginning of 1980’s decade the applications of CAPM were successful. The results of empirical studies of the Capital Asset Pricing Model indicate that beta had a relation with return and beta coefficient interpreted the returns.

The main tests in this model are by Douglas (1968), this test showed that while the coefficient of variance of the total risk was statistical significant the coefficient of systematic risk was no statistical significant. Black, Jensen and Scholes (1972), studied the relation between risks and return for portfolios of stocks and dividend the stocks in portfolios proportionally its beta. In this case the test of CAPM was successful. This test suggested the positive relationship between betas of portfolios and monthly returns of investors. Sharpe and Cooper (1972) tested the Capital Asset Pricing Model and suggested again the positive relation between risk and return, but this relation was no ever linear. Miller and Scholes (1972) tested the linearity adding the β squared. Blume and Friend (1973), Fama and MacBeth (1973) attempted to reject the Capital Asset Pricing Model, but the results of this tests confirmed the pricing model, the linearity between beta and return. The test of Roll (1977) showed that the terms of beta weren’t linear in the relation between beta and returns. The linearity of relationship between risk and return and the difference between intercept terms and return of risk free rate had as result the rejection of the CAPM. Next two decades the CAPM has been disputed, but the current days this pricing model continues to constitute again the sovereign model in finance.

Based on the theory of Capital Asset Pricing Model the main factor of the expected return of portfolio or stock is the beta. The coefficient of beta is the measure of systematic or market risk. The beta measures the volatility of the stock price in relation with the changes in prices of whole market and indicates the sensitivity of any firm relative market in where firm operates. Beta is estimated by covariance of stock with return of market portfolio to the variance of return of market portfolio, β=σim/σm^2. Depend on beta we could separate two categories of stocks, defensive stocks which have beta less than one and aggressive stocks which have beta greater than one. The beta coefficient attempts to give to investors only an approach for a future correlation between market and risk and no more about standard expected return of market. There are two types of beta levered for firms with debts and unlevered for firms with zero degree of leverage.

## Literature Review

The main purpose of this academic work, research is to examine the relation between beta and stock returns due to the international financial crisis in the Athens Stock Exchange (ASE). There are a less number of researches and studies in the concrete subject for the Greek equity market, and that constitutes an aim to render this study interesting and important. But there are numerous studies for foreign markets.

Banz (1981) studied about the size of firm or “size effect” that interpret better than beta the stock returns of firms in American stock market, this study suggested that exist misspecification in CAPM and the relationship between “size effect” and return was not linear. Reinganum (1981) examined the relation between return and size of firm and the fraction of stock price to earnings per share. This study suggested misspecification in CAPM. Gibbons (1982) suggested that the beta was an approach and no the real estimation and then the errors were expected. Stambaugh (1982) used similar methodology to Gibbons (1982) to examine the Capital Asset Pricing Model, using statistic tests of Langrangian Multiplier and no likelihood ratio test. The results of this test supported the zero beta CAPM and was opposite to the basic formula of CAPM. In this test the market portfolio included stocks, real estate, government bonds and treasury bills. Hawawini Michel and Viallet (1983) tested the CAPM in France stock market, the results of this test was the negative risk premium and didn’t exist positive wage for undertaking of risk, despite them CAPM was in effect in France stock market. The relationship between returns and beta was positive in this market. Shanken (1985) used a sample based on the monthly returns and size of firms. Using a regression test the results of this test were that the market index was not efficient but the hypothesis of size effect could not reject as a cause of this deficiency. Another test for January effect rejected the hypothesis of size effect ant that test was pointed out by Keim (1983). Mackinley (1987) suggested that the violations of the CAPM was difficult to point out, despite the model could be rejected. Shanken (1987) suggested that the CAPM was not effect and it was possible to test the theory based on the apriority knowing about correlation between approach of market and the real market. Rubio (1988) tested the CAPM in the Spain stock market and had as result to reject this model. Fama – French (1992) hasn’t important positive slope but the size of firm is important with or without beta. For a large sample of stocks the beta couldn’t interpret the changes in returns, in addition with size of firm which could to interpret these changes. Other factors as book value, market value were showed that were more appropriate to interpret the volatility of average of stock returns. Jagannathan, Wong (1993) studied in the American equity market and supported that the stock index was not adequate, appropriate and complete and included the human resources. The measure of the human resources, was the rate of changes of wage of workforce. In this test examined and the relation between beta and expected return and confirmed that the beta could be estimated by specific variables and interpret the expected return. Stocks with greaten beta should had higher expected return. The “size effect” wasn’t important factor to interpret the expected return of stocks. Cham and Lakonishok (1993) created portfolios based on beta and tested the CAPM based on the methodology and technique of Fama and MacBeth (1993) and the results of this test supported the Capital Asset Pricing Model.

The study of Bhandari (1988) showed that leverage and average of returns related positively between them. Stattman (1980) and Rosenberg, Reid and Lanstein (1985) proved the positive relationship between average returns on US stocks and the ratio of book value to its market value. Chan, Hama and Lakonishok (1991) and Hawawini (1991) proved that the ratio of book to market value of common equity was an important factor to interpret the cross section of average returns on Japanese stock market. Basu (1983) suggested that the earnings price ratio was an attempt of explaining of cross section of average returns on US stock market, in this test also included the size of firm and the beta (market risk). Ball (1978) suggested that the ratio of earnings price interpret the expected returns, this ratio was greater for stocks with higher risks and expected returns.

Calvet and Lefoll (1989) studied the relation between market risk and return on the stock market in Canada, Hawawini Michel and Corhay (1989) studied for the stock market on Belgium, Ostermark (1991) examined this relationship on Finland and Sweden stock market, Hawawini Michel and Corhay (1987) and Chan and Chui (1996) examined about the stocks on United Kingdom stock market, Wong and Tan (1991) on Singapore stock market, Cheung and Wong (1992) tested the relation between market risk and return on the Hong Kong stock market and Cheung, Wong and Ho (1993) in the Taiwan and Korea equity market. All the above researches and studies led that didn’t exist relationship between expected return and market risk as this risk was interpreted by beta. Another study about this relationship was by Karacabey (2001) about Istanbul stock market and proved this study that the relationship between expected returns and market risk was the unique relationship which existed. This study led on conclusion that in emerging equity markets as Istanbul the beta is a useful risk measure.

Pettengill (1995) examined the US stock market and led in a significant conditional relationship between beta and returns. Similar studies with same results were by Fletcher (1997), Hung (2004) and Morelli (2007) on United Kingdom equity market. Isakov (1999) studied the Swiss stock market, Faff (2001) studied the Australian capital market, Lam (2001) examined the Hong Kong stock market, Elsas (2003) studied about the German equity market, Sandoval and Saens (2004) examined the Latin Americans market supported the positive relationship between market risk end returns and the beta was a significant risk measurement.

Another important study in this relevant literature was by Fletcher (2000), who examined the conditional relation between beta and stock returns in international stock markets. The data of this test was monthly stocks returns from January 1970 to July 1998 of the MSCI equity indices of eighteen countries and MSCI world index. The results of this test were the existence of consistent relationship between betas and returns. It existed a significant positive relationship between betas and expected returns in time periods when the world market had positive returns and existed significant negative relationship when the returns of world market was negative.

Pettengill (2002) examined the effects of beta, size of the firm and book-to-market equity in the US market. This test proved that exist beta – return relationship even in the presence of both size and book to market equity. Brown, Kleidom and Marsh (1983) proved that the relationship between size of firm and returns was logarithm and no linear. Hadoshima (2000) studied the equity market in Japan. This test led to a conditional beta return relationship, the book market to market value of equity had not important role and size of firm was priced negatively. Ho (2006) tested the Hong Kong stock market and suggested that exist conditional and unconditional relationship between returns and size and book to market value of common equity. Ning and Lui (2004) examined the stock market in Shanghai and found no unconditional relationship. Wang and Iorio (2007) examined the Chinese stock market and suggested the effect of size and book to market value to returns and beta was an insignificant risk measure.

The Athens stock exchange is “small” in contrast with others stock markets over the world and is expected the less studies about this market. Niarchos (1972) examined about the efficiency of Greek equity and money market. Papaioannou (1979) examined the efficiency of Athens stock market using a larger sample than Niarchos (1972) and found inefficiency of ASE. Papaioannou (1982, 1984) examined the dependency of prices in stock returns for at least six days. Gklezakos (1987) suggested that the CAPM is not an appropriate model to describe the mechanism of shaping of stock prices in Athens market. Factors which influent the shaping of prices could be the size of firms, the efficiency of market and the degree of stock dissemination. In agreement with Niarchos (1972) the prices of stocks shaping under unsystematic conditions as speculators, the CAPM wasn’t in effect in Athens stock exchange. Panas (1990) suggested the lack of efficiency for the ten large companies in ASE. Koutmos, Negakis and Theodosiou (1993) proved that ARCH model was appropriate of volatility in weekly returns of stocks in ASE.

Diakogiannis and Segredakis (1996) examined the effect of systematic or market risk (beta) and size of firms to the returns of stocks in ASE. Empirical studies showed the no existence relationship between expected return and market risk to firms in Athens stock exchange. The “size effect”, in addition with others stock markets as NYSE, UK, Canada, isn’t significant in prices in ASE.

Spyrou (1999) empirically studied the stocks of small capitalization. The data which have been used, were the stock prices from December on 1988 to January on 1997. As market portfolio was the general price index. This test showed that for the time period from 1992 to 1997 stocks of small capitalization had greater returns than stocks of large capitalization, but in whole time period of test the stocks of large capitalization had greater returns than stocks of small capitalization. Spyrou examined and the hypothesis that “cheap” stocks had greater returns than high priced stocks but the results of this test was negative. Maliaropoulos, Hardoubelis (1999) evaluated the stock prices of ASE relate on expected returns. Xanthakis, Alexakis (1995) examined the day of the week effect on the Greek stock market and found that on Monday stocks on ASE had high positive returns and on Tuesday had negative returns or loses. After 1988 the stocks in ASE on Friday have had positive returns, on Monday neutral attitude or negative and on Tuesday tend to reduce the losses on returns of stocks, which had before 1988.

Diakogiannis, Glezakos and Segretakis (1998) tested the effects of price to earnings ratio (P/E) and dividend yield (DY) on expected returns of stocks in Greek stock market, from 1990 to 1995. This study suggested the interpretation of the price to earnings ratio to expected returns, and the weak of dividend yield to interpret the expected returns on common stocks in ASE. Similar study was by Karanikas (2000), who examined the effects of the size of firm, book to market ratio and dividend yield on average stock returns in the Greek equity market. This test suggested the significant positive relationship between book to market ratio, dividend yield and average stock returns, while the size of firm was not an important variable to interpret the average stock returns in ASE. Niarchos, Alexakis (2000) rejected the hypothesis of efficient market for the Athens stock exchange, by using macroeconomic variables on monthly base for the time period 1984 – 1995.

## Data selection

Assumptions for the wrong or inadequate results and conclusions of previous studies of the relationship between beta and stock returns in ASE present as cause of this inadequacy the inappropriate data which was used. In this dissertation, I have chosen 70 firms of Athens stock exchange for the time period 1/1/1998 to the 31/12/2009, I exclude the year of 2010 of my study because the Greece has been under the monitoring by International Monetary Fund from March of 2010, as consequently effected on stock returns in ASE. These firms constitute the portfolio of my analysis and the Index 140 constitutes the market portfolio of my study.

These companies aren’t from the bank sector due to the bank weighted general index of Athens stock exchange, are from competitive sector and no from oligopoly, are profitable for all the years of examining period. The data which I will need in my analysis are elements of financial statements, stock prices, stock returns, earnings per share, book to market ratios, dividend yields, book value to debt for whole examining time period. The stocks of selected firms have normal trading in ASE and don’t are characterized of time periods without trade in ASE, thin trading. My data are weekly closing prices of choosing companies and of Index 140 data should be cross sectional. The risk free rate for my analysis, I assume is the three month Government Treasury Bill rate.

## Methodology

The methodology which I will use on my current study is similar with the methodology of Fama and MacBeth (1992) and with them, which used by Diakogiannis, Segredakis (1996). I will divide the period in five successive sub periods (1998-2001, 2000-2003, 2002-2005, 2004-2007, 2006-2009). Each sub period should be divided in three periods. In the first period, the first year of each sub period I will construct portfolio of my analysis, in the second period, the second year of each sub period, I will estimate betas of portfolio and in the third period, the third year of each sub period is the testing period. This methodology follows the three step approach of Fama and MacBeth (1973) and of Fama and French (1992).

In the first year of sub period, is estimated the size of firm by multiply the number of stocks with closing price on 31 December, the size of firm is the LN of this product. The LN is used due to the Brown, Kleidon and Marsch (1983) who suggested that the relation between size of firm and return isn’t linear and the logarithm formula interprets better this relation. Then all stocks are grouped into seven portfolios with ten stocks per each based on the size of firm, the fist portfolio includes the highest of size firms and the seventh the lowest of size firms.

In the second year of sub period, I will estimate the coefficient of beta foe any stock in each portfolio. Each weighted expected returns for any of ten portfolios are calculated and I will estimate the coefficient of beta (β) for each portfolio by a time series regression: Rpt- Rft = β (Rmt- Rft) + εpt. The (Rpt- Rft) is the expected return of portfolio and the (Rmt- Rft) is the expected return of market portfolio.

The last year of each sub period constitutes the testing period by cross sectional regressions. I will take hypothesis for the examining of the relation between beta and stock returns, beta and earnings per share, beta and dividend yields and size and book to market value and I will examine about that and I will present the results of these tests.

## Resources

The main source for the literature in this dissertation will be the e- journals, the access in the on line articles is provided through the VPN connection of TEI of Crete and through the on line library of University of Portsmouth. The necessary data is provided by database of Athens stock exchange and by individual web sites of each company. The main tool which I will use in this study is the E- views econometric software, to estimate and evaluate the coefficients of variables in my model.

## Discussion and Conclusions

The main purpose of this academic work is to examine the relationship between beta – stock returns and size of firm – book to market value based on the methodology of Fama and MacBeth (1973). The empirical studies in large capital markets (USA, UK, etc) almost proved the existence of these relations. But the previous empirical studies in Athens stock exchange did not present the same results as developed markets. In this study could be interpreted the stock returns by beta and present the significance of the size of firm due to the appropriate data which will be used.

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