Sermaye varlıklarını fiyatlama modeli İMKB”de dengenin araştırılması - Akyüz, Ruşen Mete (My University, 2000)
Although the mechanics of the price formation of investment instruments have been studied since the formation of the capital markets, today, the forces affecting the markets could not still be formulated. One model that caused high repercussion among many others to explain the general structure of the balance is the Capital Assets Pricing Model (CAPM). In this study, in the second section, following the introductory section, primarily the basic concepts regarding the portfolio theory is summarized. In this section, first the general description of risk and return concepts are made and subsequently the way that the portfolio risk and return are perceived in the Markowitz approach is mentioned. In the third section, the relation between risk and return is examined and efforts made to reach a portfolio where risk is minimized. Here, the theoretical infrastructure of the simple diversification and the Markowitz diversification is defined. The fourth section is an introduction to CAPM, known as a market equilibrium model based on the studies of Markowitz' risk and return relationship. In this section the basic hypothesis of CAPM, the security market line and the widely tested CAPM models is dealt with. In the fifth section, the methodologies applied in the studies to test the CAPM and the initial applications of the widely used models and the results obtained by those models is examined. Thus, this section casts light on how the method, that is applied in the study carried out using the shares that are traded in the Istanbul Stock Exchange (ISE) in the following section is determined. In the sixth section the validity of the CAPM model for the Istanbul Stock Exchange has been tested. While this was done, first the selection of the model, then the collection of the data (such as shares which were included in the analysis and the motives thereof, how the portfolios are constructed, the calculation of the riskfree return) and lately the interpretation of the analysis and evidences comprising the first and second step regressions were mentioned. The seventh and eighth sections deal with the application areas of CAPM and the critiques about the model so that the appreciation of it can be comprehended. The theoretical infrastructure of the CAPM, the empirical studies and a

regarding the evidences reached through out this study related with the equilibrium in the ISE are pointed out below. Theoretical Review: The foundation of the CAPM model was laid upon the publication of the famous article of Harry Markowitz: Portfolio Selection. The Modern Portfolio Theory which became popular upon this article of Markowitz, showing the method of constructing portfolios that produce the highest return at a given risk level was later found rather complicated, but it was simplified by his student William Sharpe in 1963 and took its final shape which is today known as the single-indexed model. The theory that found application area in the real world took start in 1970s together with the development of computer technology and the development of techniques to obtain data regarding the model is a normative study telling the investors which instrument to invest in. According to the study, while the individuals consume a part of their incomes that they obtained during a certain period, they keep the remaining part of it in order to meet their needs in the future. While these incomes that are not spent during the period obtained may be kept in form of cash money; they may also be invested in numerous different instruments such as gold, real estate, securities, etc. In order not to loose the buying power of the assets saved the individuals will compare the return ratios of the investment instruments, while they determine the most suitable saving method among all and invest in an instrument that would maximize the value of their assets at the end of the period at most. If the returns of all instruments were known exactly, the assets would be invested in the instrument with the highest return. In the real world however, while the returns of some of the instruments are known at the beginning of the period (such as government securities), a big part may only be estimated since their returns are variable. If the value as at the end of the period is not known but estimated, it is likely that there is a difference between the return that was estimated in the beginning of the period and the actual one in the end of the period. This possibility is the risk of the investment. The variable the return, the greater the risk. In this case, the investor, while comparing the instruments with variable returns, should not be contended with considering the returns that he or she estimates, but also consider the risk, which is the measure of the possible change in the return. As can be seen, in Markowitz' approach, the investors wish to invest in the instrument either with the highest return at a given risk level or with the lowest risk at a given return level. The standard deviation in returns is used as the risk measure in the study. The result is that, it is a better alternative to invest in portfolios that are constructed by gathering instruments that are not perfectly positively correlated than to invest each of these instruments individually. In other words, some in the infinite number portfolios that could be formed will constitute a limit, called the efficient margin, offering the highest return that can be obtained at several levels of risk available and all investors have to invest in one of the portfolios situated in this margin according to their risk preferences. The next step is determining the equilibrium in the market if all the investors are assumed to have taken their decisions as pointed out by Markowitz. Searching for this equilibrium, Sharpe, Lintner and Mossin have developed CAPM in their studies that they carried out separately. According to the model, since the investors take investment decisions by looking into the expected return and the risk values, they will not buy (or sell) the instruments with lower returns in comparison to other investment instruments of same risk level and thus the price of those instruments will decrease. The returns of those non-preferred instruments will increase until they reach a level to be preferred again. Since the contrary of this procedure would occur for investment instruments with higher returns at same risk level, the prices of these instruments shall increase with the demand for them and their returns in turn shall decline. At the equilibrium, since the return levels of the instruments in each risk group will be the same, all instruments shall be in the most suitable portfolio to be invested in. To express it more clearly, all investors, while leaving a part to the riskfree instrument, shall construct a portfolio by investing other part of their assets in a portfolio in which all instruments at various risk levels are included. The risk preferences of the investors shall affect how much of the assets they will invest in the riskfree instrument; but whatever the risk preference is, the composition of the portfolio including risky instruments in which the remainder of the asset is invested shall always be the same. The portfolio of risky instruments, which the composition does not change for any investor, is called market portfolio. The empirical studies testing CAPM actually tested the hypothesis that the returns must be high if the beta coefficients of those shares are high as well, by measuring the relation of the return of each individual share with the return of the market portfolio by means of a coefficient called beta (ß). Since the shares with higher beta values are more risky shares compared to the market, it is expected that the return is a linear increasing function of beta and that the return of an instrument the beta of which is zero, is equal to the return of a riskfree instrument. Practically, the average of the historical returns of the investment instruments has been used as the expected return value. The beta value is found by dividing the covariance of the instrument with the market portfolio to the variance of the market portfolio. Due to the difficulties in constituting such a portfolio in practice, the market indexes have been used as the market portfolio that has to cover all investment instruments according to the theory. In Sharpe's study which is one of the first studies testing the risk-return relation that is stipulated by CAPM, the average annual returns and standard deviations of 24 investment funds during a period between 1954 and 1963 have been analyzed. The result was that, during this period the investment funds with high risk have reached higher returns compared to the funds with lower risks. In the similar study of Michael Jensen, the beta values have been used as the measure of the risk instead of standard deviation; and the risk and return values of 115 funds during the period between 1955 and 1964 have been used. The result is that high returns are related with high risks and that beta values can be used as the measure of risk. In a study covering 37 years period from 1931 to 1967, Sharpe and Cooper constituted 10 different strategies by using the shares traded in the New York Stock Exchange in accordance with their risk levels and compared the annual returns of each of these strategies with their risk levels. They concluded that 95% of the variation of the expected returns could be explained by the variation of the betas. Lintner's study that aimed to test the assumptions of CAPM empirically comprises primarily of a time-series regression model in which beta values are estimated, cross sectional regressions following this and hypothesis tests in which CAPM's assumptions are verified. Lintner calculated the beta values of 301 shares by using the annual returns of a period of ten years between 1954 and 1963. Later he examined the relation between the beta values he found in the previous step and the returns. In the end, the coefficient of the error term was found to be different than zero and positive; the intersection term was high above the riskfree return and the sensitivity to beta, although meaningful from statistical point of view, was far below the estimation. Lintner's results seem to conflict with CAPM. Two important studies that test CAPM empirically and that have taken place in the literature are the studies of Black, Jensen and Scholes (BJS) and Fama and MacBeth (FM). BJS have developed a portfolio test technique that would reduce calculation errors and the variance of the error term by considering the methods that were developed by Miller and Scholes to measure the betas of the shares. BJS, different than Lintner's study, have taken the share returns and the market portfolio returns into the regression equation by purifying these from the riskfree return; thus enabling beta to be a coefficient pointing the direct relation of the risk premium with the return. Besides, BJS have constructed a portfolio instead of using securities individually in order to eliminate the correlation between the error terms. While the portfolio was being constructed, securities with many diverse betas were chosen in order to demonstrate the impact of the systematic risk on return; the portfolios have been constructed by classifying the securities in accordance with their beta values. BJS, in order to avoid upwards deviation of the beta estimation of the portfolio constructed by shares having the highest beta value, have used a technique called instrumental variable in econometrics and have calculated the beta values using the monthly data of the past five years. This technique has set a pattern for other researchers and it has been used as a standard technique in beta calculation in many studies. In BJS's study, the correlation between beta and the return was found to be high (R2 value 0.98) and the relation was linear with positive slope. On the other hand, FM has calculated the beta values of the shares by using the data of the past five years, as BJS did, but this time constructed 20 different portfolios from different risk groups by using these values. They calculated 402 monthly return values in respect with these 20 portfolios during the period between January 1935 and June 1968 and formed a cross-sectional regression equation in which these 20 values were used for each month. FM's model is a multiple regression model aiming the examination of the impact of the beta square and the standard deviation on the return of the portfolio. The conclusion is that the coefficient of beta is different than zero and positive at 95% confidence level. This situation points out the positive relation between risk and return. Besides, standard deviation and the coefficients of beta square are not different than zero. This shows that non-systematic factors have no power to define price formation and that the relation between risk and return during the examined period is linear. Since the result is that non-systematic factors have no impact in defining price formation, FM this time excluded these variables from the regression equation and designed a new test by using beta as explanatory variable. By this way, the impact of the multicolinearity between beta and beta square and beta and error term has been excluded from the equation. This time the coefficient of beta is positive and it is verified that the relation between risk and return is positive. The intersection value, too, is positive and different than zero as per t-statistics. Conclusively, FM has determined that there is no correlation between the error terms. The tests of BJS and FM contain evidences that support CAPM. Both studies have caused repercussion and the methods used have constituted basis for many studies in which data regarding shares that are traded in the market were used. Empirical Study: The methodology of the widely accepted study of BJS is also carried out in this study, searching for a pattern of the returns of the shares that are traded in the Istanbul Stock Exchange. In the analysis in which the monthly rate of returns regarding 121 shares traded during a five year period between 1992 and 1996 in the Istanbul Stock Exchange were used, we tried to construct a portfolio that would represent the market portfolio because in our market there is no 'market portfolio' information published in the sense that is described by CAPM. For this purpose, the market capitalization of these 121 shares at the beginning of each month is calculated and then these values were added as of months and thus 60 total market capitalization were found. Later, the returns of these 121 shares which were modified by considering the dividends and capital increases have been weighted in accordance with their shares in the market capitalization and a single rate of return for each month was reached. This is used to represent market portfolio as an index that was weighted in accordance with capitalization. To find the data regarding riskfree interest rates, the annual compound rate of return of each security traded in the bond market of the ISE were found by using their daily closing prices and the calculated average of these values on the monthly basis was reduced to 60 annual return values. Lastly the 12th degree square root of these 60 annual return rates has been taken to reach the monthly riskfree rate of returns. Due to the economic crisis experienced first in between February 1994 and June 1994 and than in between December 1995 and February 1996, extraordinary increases were observed in the rates calculated. The model that is formed tends towards defining the equilibrium, which is accepted as the normal course of the market. Thus, since the inclusion of crisis periods in which extraordinary movements were experienced that lead to removal from the equilibrium would cause deviation, the riskfree return rates regarding these periods have been normalized by assuming as if they were at the average rate of return level when such periods were excluded. The data were entirely purified from the impacts of crisis by normalizing the rate of returns of the market portfolio regarding crisis periods and the return ratios of each individual share. In the first step regressions where modified data were used, the calculated beta values were ranked from minor to major and 10 portfolios comprising 10 shares each were obtained. The 10 shares having the lowest beta value formed the first portfolio; the remaining 10 shares containing the lowest beta value formed the second portfolio, so on so forth. 21 shares, which were not traded for rather long periods, were not included in the portfolios. Finally, it was observed that the average returns have generally increased as the beta values increased from the first portfolio to the last. While the ?0 with calculated t-statistics as -1,1501 is equal to zero; the ?1, the t-statistics of which was calculated as 4,2545 is different than zero and positive. Besides ?1 is equal to 0.0082 which is equal to the risk premium at 95 % confidence level (rm-rf) (t-statistics value 0.0077) Since the t-statistics value found from the table with a degree of freedom of 9 and confidence level of 95% is 2,262, as these 10 portfolios subjected to second step regression, the intersection value ?0 that is calculated to be -1,1501 is equal to zero and the beta coefficient (?1), which the t-statistics is calculated as 4.2545 observed to be different than zero and positive. Besides, the beta coefficient ?1 (0.0082) is equal to the risk premium (rm-rf) at 95% confidence level (t-statistics value 0.0077). This shows that the slope of the regression line is positive, that the intersection value is the riskfree rate of return and that the slope of the regression line is equal to the risk premium (as prescribed by CAPM). On the other hand, the R2 value, expressing the power of the rate of return defining beta has been calculated as 0,6935 and the modified R2 value of it has been calculated as 0.6552. So, it can be said that the portfolio risk can be effective in the constitution of the rate of return and that there could still be other factors effective, as well. When the same study is repeated with the nominal portfolio return values, both of the coefficients ?0 (t-statistics 4,7224) and ?1 (t-statistics 4,3088) were found to be different than zero and positive at 95% confidence level; in addition, ?0 which is the intersection value of the y-axis became to be equal to the riskfree rate of return at 95% confidence level (t-statistics value 1.1006). All these results are consistent with the structure prescribed by CAPM. In this analysis R2 value representing the definition power of beta of the return ratio has been calculated as 0,6989 and the modified R2 value as 0.6612. In the light of these results it can be stated that there is enough evidence for the relation between risk and return to be generally of a linear structure and that furthermore, the portfolio risk is effective in the constitution of rate of return but there are some other factors effective, as well. Although it is not the subject of this study, two indexes in addition to the capitalization weighed index have been calculated while the market portfolio that will be used in the analysis was being calculated. The monthly rate of returns of the 121 shares that were included in the analysis have been weighed according to the proportion of the monthly transaction volumes of each share in the total monthly transaction volume; so a volume weighted index has been formed. Than a simple weighed index by taking the simple average of the monthly modification ratios calculated with modified prices was formed too. While the monthly average productivity of the National-100 Index during the period 1992-1996 was 0,0645, this value has been calculated as 0,0659 in the capitalization weighed index, as 0,1135 in the volume weighed index, and as 0, 0908 in the simple weighed index. The correlation coefficients of the four indexes vary between 0.89 and 0.96. The rate of return of the capitalization weighed index is 0.43% higher than the rate of return of the National-100 Index. Both indices are calculated by the same weighing method. The difference arises from the dividend yield that is taken into account while calculating the capitalization weighed index, which is not considered while calculating the National-100 Index. Thus, it can be said that the average annual dividend yield during the period 1992-1996 was approximately 5,34%. Besides, the return of the index that is calculated by taking the simple average of the share returns (Simple Weighed Index) is higher than the capitalization weighed index. Out of this, a claim can be made that the rate of returns of the shares with low market capitalization are higher than those with higher market capitalization. Furthermore, it is observed that the volume weighed index offered the highest yield among the calculated indices. This can be interpreted as the transaction volume (number of transactions x price) escalates higher, rate of returns of shares becomes higher, too. Since this is not the subject of the study, no further tests have been implemented for these last two issues. Critiques on CAPM: As can be seen, in our study, which is based on BJS' study, the results contain evidences that support CAPM. But besides this, our study is equally subject to critiques as brought forward by Richard W. Roll for the studies of BJS and FM. Roll in his article published in 1976 has been criticizing the model basically in terms of the methodology used in the empirical studies, the concept of the market portfolio and the calculatability of the real values of beta that are calculated in connection with this market portfolio and finally, the use of the security market line in measuring the portfolio performance. According to Roll, since the statistical methods used were totological, even the portfolio that was considered as market portfolio was any portfolio which was situated in the efficient margin -although it was not a real market portfolio- it has shown that the relation between the return and the beta value shall be linear. Thus, whatever the way that the securities are priced is, it is likely that the results obtained in the studies of BJS or FM may be obtained. The logical result of Roll's studies is that the testing of the balance model would be impossible if real market portfolio were not used. On the other hand the market portfolio, by definition, has to include all sorts of assets that are supplied by the global economical system. While it is impossible to construct such a portfolio which contains all instruments from Japanese electronics companies to the real estates in Nigeria at a certain rate, the use of a market index such as S&P 500 will lose its representation capability since it would mean to be an enormous simplification. Another problem regarding the estimated beta values is the possibility that the beta values may not remain the same by time. The most famous one among the studies carried out in this respect is the study made by Blume. Blume has estimated the beta values by using the monthly data for two subsequent periods of seven years. Conclusively, he determined that the beta values in the second period got closer to 1 compared to the 1st period (the betas of which were higher than 1 in the first period were decreasing and the betas of which were lower than 1 in the first period were increasing). While the reason for that could be that the beta values could change in accordance with factors such as the sizes of companies, it can also be a calculation error due to the difficulty of beta calculation. CAPM has been empirically tested in many countries by numerous researchers; yet, no definite judgement could be made regarding the validity of the model for the moment. Today there are studies that contain results that support the model but there are also many that contain findings that refuse it. Still, owing to its information supply regarding the price formation in the stock market and its existence as a basic step in developing equilibrium models, CAPM has taken its place in a central place in the finance world.
Keywords: Borsa-Türkiye