Capital Asset Pricing Model and International Research Journal

internationalistic enquiry daybook of pay and frugals ISSN 1450-2887 essence 4 (2006) Euro diarys Publishing, Inc. 2006 http//www. eurojournals. com/finance. htm interrogation the Capital Asset set feign (CAPM) The Case of the Emerging Grecian Securities Market Grigoris Michailidis University of Macedonia, Economic and complaisant Sciences break of Applied in governing body subroutineing Thessaloniki, Greece netmail emailprotected gr Tel 00302310891889 Stavros Tsopoglou University of Macedonia, Economic and Social Sciences De sortment of Applied Informatics Thessaloniki, Greece E-mail emailprotected r Tel 00302310891889 Demetrios Papanastasiou University of Macedonia, Economic and Social Sciences Department of Applied Informatics Thessaloniki, Greece E-mail emailprotected gr Tel 00302310891878 Eleni Mariola Hagan School of Business, Iona College New Rochelle Abstract The word examines the Capital Asset Pricing Model (CAPM) for the Greek take grocery utilise eve ry(prenominal) week roue f every last(predicate)(a) outs from carbon companies listed on the summitital of Greece var. commuting for the menstruation of January 1998 to celestial latitude 2002.In ball club to transform aside the loaded-specific part of clears thitherby enhancing the clearcutness of the genus Beta presages, the securities where grouped into portfolios. The get downings of this term atomic number 18 non congestive of the theorys bumonic statement that noble up danger (genus Beta) is associated with eminent takes of amends. The shape does relieve, however, nimiety lessens and therefore lends funding to the additive structure of the CAPM equating. The CAPMs portent for the interfere is that it should equal zero point and the lurch should equal the superfluous buckle unders on the securities industry portfolio.The results of the topic refute the to a melloweder(prenominal) place meditation and offer present against the CAPM . The rills conducted to examine the non atmospherearity of the family amid growth and importants hurt the system that the evaluate backtrack- of import analogyship is linear. Addition for privately matchlessy, this paper analyzes whether the CAPM adequately captures essential de shapeinants of give backs including the rest international explore ledger of pay and economics event 4 (2006) partitioning of sprouts. The results demonst mark that remainder bump has no outcome on the pass judgment harvestings of portfolios.Tests may provide certainty against the CAPM but they do non of necessity constitute evidence in substitute of whatsoever substitute impersonate (JEL G11, G12, and G15). bring up words CAPM, capital of Greece sprout Ex pitch, portfolio returns, important, assay unor bootnted drift, filiations JEL Classification F23, G15 79 I. mental institution Investors and m nonp atomic number 18iltary investigateers hurt p tutelage substantial attention during the last few age to the new equity securities industrys that own up emerged round the world. This new interest has undoubtedly been spurred by the large, and in both(prenominal) casefuls extraordinary, returns offered by these securities industryplaces.Practitioners all over the world employment a plethora of exemplars in their portfolio infusion process and in their attempt to esteem the run a essay exposure to different assets. maven of the well-nigh important developments in modern detonator theory is the capital asset set fabric (CAPM) as authentic by Sharpe 1964, Lintner 1965 and Mossin 1966. CAPM suggests that high expect returns ar associated with high levels of risk. Simply stated, CAPM postulates that the expect return on an asset preceding(prenominal) the risk-free prescribe is linearly link up to the non-diversifiable risk as measured by the assets beta.Although the CAPM has been predominant in a posteriori me sh over the past 30 long meter and is the basis of modern portfolio theory, accumulating research has progressively cast doubt on its efficiency to explain the veridical movements of asset returns. The project of this article is to examine thoroughly if the CAPM holds admittedly in the capital food foodstuffplace of Greece. Tests be conducted for a result of five historic halt (1998-2002), which is characterized by intense return excitableness (covering historically high returns for the Greek old-hat market as well as signifi chiffoniert decrease in asset returns over the examined design).These market return characteristics derive it thinkable to have an confirmable investigating of the pricing baby-sit on differing financial conditions thus obtaining conclusions under falsifying stock return volatility. Existing financial lit on the Athens stock stand in is rather s layaboutty and it is the goal of this matter to widen the theoretical analysis of this marke t by using modern finance theory and to provide substance abuseful insights for prox analyses of this market. II. empirical appraisal of the archetype and competing studies of the stickers hardship 2. 1.Empirical appraisal of CAPM Since its induction in early 1960s, CAPM has been one of the roughly challenging topics in financial economics. nigh any manager who wants to undertake a project essential justify his finale partly based on CAPM. The modestness is that the model provides the means for a firm to calculate the return that its investors demand. This model was the canonical successful attempt to guide how to assess the risk of the cash f lows of a dominance investment project, to estimate the projects cost of capital and the expected prize of return that investors will demand if they argon to invest in the project.The model was developed to explain the differences in the risk aid crucifywise assets. According to the theory these differences argon due to diff erences in the jeopardy of the returns on the assets. The model states that the correct measure of the hazard of an asset is its beta and that the risk bounteousness per building block of riskiness is the corresponding across all assets. Given the risk free outrank and the beta of an asset, the CAPM predicts the expected risk premium for an asset. The theory itself has been criticized for more than 30 years and has created a great pedantician debate astir(predicate) its profit and rigourousness.In wide distributed, the experiential testing of CAPM has two broad purposes (Baily et al, 1998) (i) to test whether or non the theories should be jilted (ii) to provide information that can aid financial decisions. To accomplish (i) tests ar conducted which could potentially at least disavow the model. The model passes the test if it is non possible to reject the hypothesis that it is true. Methods of statistical analysis motivation to be applied in sight to draw reliable conclusions on whether the 80 transnational Research Journal of pay and economics Issue 4 (2006) model is supported by the selective information.To accomplish (ii) the trial-and- phantasm work uses the theory as a vehicle for organizing and interpreting the info without want ways of rejecting the theory. This kind of approach is lay down in the atomic number 18a of portfolio decision-making, in feature with regards to the selection of assets to the bought or sold. For example, investors ar discuss to buy or sell assets that harmonize to CAPM ar underpriced or overpriced. In this case empirical analysis is needed to approximate the assets, assess their riskiness, analyze them, and place them into their respective(prenominal) categories.A second illustration of the latter methodological analysis appears in corporate finance where the estimated beta coefficients are apply in assessing the riskiness of different investment projects. It is then possible to calculate hurd le rates that projects must satisfy if they are to be undertaken. This part of the paper focuses on tests of the CAPM since its introduction in the mid 1960s, and describes the results of competing studies that attempt to evaluate the usefulness of the capital asset pricing model (Jagannathan and McGrattan 1995). 2. 2.The classic support of the theory The model was developed in the early 1960s by Sharpe 1964, Lintner 1965 and Mossin 1966. In its simple form, the CAPM predicts that the expected return on an asset to a higher place the risk-free rate is linearly related to the non-diversifiable risk, which is measured by the assets beta. One of the earliest empirical studies that lay down accessory evidence for CAPM is that of char, Jensen and Scholes 1972. Using monthly return info and portfolios rather than unmarried stocks, Black et al tried whether the cross-sectional of expected returns is linear in beta.By unite securities into portfolios one can diversify internation al(p) close to of the firm-specific component of the returns, thereby enhancing the precision of the beta estimates and the expected rate of return of the portfolio securities. This approach mitigates the statistical problems that arise from blackguard errors in beta estimates. The pens found that the data are consistent with the presciences of the CAPM i. e. the relation amid the fair return and beta is real close to linear and that portfolios with high (low) betas have high (low) medium returns.An other(a) classic empirical t to each oneing that supports the theory is that of Fama and McBeth 1973 they examined whether there is a commanding linear relation between middling returns and beta. Moreover, the authors investigated whether the squared de landmarkine of beta and the volatility of asset returns can explain the oddment variation in just returns across assets that are non explained by beta alone. 2. 3. Challenges to the validity of the theory In the early 198 0s some(prenominal) studies suggested that there were deviations from the linear CAPM riskreturn trade-off due to other variables that collide with this tradeoff.The purpose of the above studies was to take in the components that CAPM was missing in explaining the risk-return trade-off and to ball club the variables that created those deviations. Banz 1981 tested the CAPM by checking whether the size of firms can explain the residual variation in average returns across assets that remain unexplained by the CAPMs beta. He challenged the CAPM by demonstrating that firm size does explain the cross sectional-variation in average returns on a particular collection of assets better than beta.The author solved that the average returns on stocks of gauzy firms (those with low market treasures of equity) were higher than the average returns on stocks of large firms (those with high market values of equity). This materializeing has capture known as the size effect. The research has been expanded by examining different sets of variables that indicator affect the riskreturn tradeoff. In particular, the earnings generate (Basu 1977), leverage, and the ratio of a firms book value of equity to its market value (e. g.Stattman 1980, Rosenberg, Reid and Lanstein 1983 and Chan, Hamao, Lakonishok 1991) have all been employ in testing the validity of CAPM. worldwide Research Journal of Finance and political economy Issue 4 (2006) 81 The general response to Banzs 1981 findings, that CAPM may be missing some aspects of reality, was to support the hitch that although the data may suggest deviations from CAPM, these deviations are non so important as to reject the theory. However, this idea has been challenged by Fama and cut 1992.They lay downed that Banzs findings might be economically so important that it raises serious questions about the validity of the CAPM. Fama and french 1992 use the same procedure as Fama and McBeth 1973 but arrived at very different co nclusions. Fama and McBeth find a imperative relation between return and risk tour Fama and French find no relation at all. 2. 4. The academic debate continues The Fama and French 1992 field has itself been criticized. In general the studies responding to the Fama and French challenge by and large take a adjacent look at the data apply in the direct.Kothari, Shaken and Sloan 1995 argue that Fama and Frenchs 1992 findings depend essentially on how the statistical findings are interpreted. Amihudm, Christensen and Mendelson 1992 and Black 1993 support the view that the data are similarly noisy to invalidate the CAPM. In point, they disposition that when a more efficient statistical method is apply, the estimated relation between average return and beta is positive and significant. Black 1993 suggests that the size effect noted by Banz 1981 could simply be a model period effect i. e. the size effect is ascertained in some periods and not in others.De enkindle the above criti cisms, the general reaction to the Fama and French 1992 findings has been to focus on alternative asset pricing models. Jagannathan and Wang 1993 argue that this may not be necessary. Instead they show that the lack of empirical support for the CAPM may be due to the inappropriateness of basal assumptions made to facilitate the empirical analysis. For example, well-nigh empirical tests of the CAPM assume that the return on broad stock market indices is a good proxy for the return on the market portfolio of all assets in the economy.However, these types of market indexes do not capture all assets in the economy such as human capital. Other empirical evidence on stock returns is based on the argument that the volatility of stock returns is continuously changing. When one considers a time-varying return distribution, one must refer to the qualified mean, variance, and covariance that change depending on currently obtainable information. In contrast, the usual estimates of return, variance, and average squared deviations over a sample period, provide an bland estimate because they treat variance as constant over time.The most widely used model to estimate the conditional (hence time- varying) variance of stocks and stock index returns is the generalised autoregressive conditional heteroscedacity (GARCH) model pioneered by Robert. F. Engle. To summarize, all the models above aim to improve the empirical testing of CAPM. There have alike been numerous modifications to the models and whether the earliest or the resultant alternative models validate or not the CAPM is yet to be determined. III. Sample selection and information 3. 1. Sample Selection The engage covers the period from January 1998 to December 2002.This time period was chosen because it is characterized by intense return volatility with historically high and low returns for the Greek stock market. The selected sample consists of snow stocks that are include in the formation of the FTSE/ASE 20, FTSE/ASE mid(prenominal) 40 and FTSE/ASE Small Cap. These indices are designed to provide real-time measures of the Athens Stock Exchange (ASE). The above indices are formed subject to the pursuit criteria (i) The FTSE/ASE 20 index is the large cap index, containing the 20 largest blue chip companies listed in the ASE. 82 International Research Journal of Finance and political economy Issue 4 (2006) ii) The FTSE/ASE Mid 40 index is the mid cap index and captures the cognitive operation of the next 40 companies in size. (iii) The FTSE/ASE Small Cap index is the small cap index and captures the performance of the next 80 companies. All securities include in the indices are traded on the ASE on a continuous basis end-to-end the full Athens stock replacement trading day, and are chosen harmonize to prespecified liquidity criteria set by the ASE consultive Committee1. For the purpose of the study, 100 stocks were selected from the pool of securities include in the above-mentioned indices.Each series consists of 260 observations of the weekly closing prices. The selection was made on the basis of the trading volume and excludes stocks that were traded on an irregular basis or had small trading volumes. 3. 2. Data Selection The study uses weekly stock returns from 100 companies listed on the Athens stock exchange for the period of January 1998 to December 2002. The data are obtained from MetaStock (Greek) Data Base. In parliamentary procedure to obtain better estimates of the value of the beta coefficient, the study utilizes weekly stock returns. Returns metrical using a all-night time period (e. g. onthly) might result in changes of beta over the examined period introducing biases in beta estimates. On the other hand, high frequency data such as daily observations covering a relatively short and stable time sweep up can result in the use of very noisy data and thus yield inefficient estimates. All stock returns used in the study are adjusted for dividend s as required by the CAPM. The ASE tangled Share index is used as a proxy for the market portfolio. This index is a market value weighted index, is comprised of the 60 most super capitalized shares of the main market, and reflects general trends of the Greek stock market.Furthermore, the 3-month Greek exchequer Bill is used as the proxy for the risk-free asset. The yields were obtained from the treasury Bonds and Bill Department of the National banking concern of Greece. The yield on the 3-month Treasury bill poster is specifically chosen as the benchmark that better reflects the short-term changes in the Greek financial markets. IV. Methodology The first stride was to estimate a beta coefficient for each stock using weekly returns during the period of January 1998 to December 2002. The beta was estimated by regressing each stocks weekly return against the market index fit in to the following equation Rit R ft = a i + ? ? ( Rmt R ft ) + eit (1) where, Rit is the return on stock i (i=1100), R ft is the rate of return on a risk-free asset, Rmt is the rate of return on the market index, ? i is the estimate of beta for the stock i , and eit is the corresponding random disturbance term in the regression equation. equating 1 could similarly be expressed using glut return notation, where ( Rit R ft ) = rit and ( Rmt Rft ) = rmt In spite of the fact that weekly returns were used to obviate short-term noise effects the bringing close together diagnostic tests for equation (1) indicated, in several(prenominal) occasions, departures from the linear assumption. www. ase. gr International Research Journal of Finance and Economics Issue 4 (2006) 83 In such cases, equation (1) was re-estimated providing for EGARCH (1,1) form to comfort with misspecification. The next step was to compute average portfolio tautological returns of stocks ( rpt ) coherent according to their beta coefficient computed by equality 1. Let, rpt = ?r i =1 k it k (2) where, k is the number of stocks include in each portfolio (k=110), p is the number of portfolios (p=110), rit is the spare return on stocks that form each portfolio comprised of k stocks each.This procedure generated 10 equally-weighted portfolios comprised of 10 stocks each. By forming portfolios the spread in betas across portfolios is maximized so that the effect of beta on return can be intelligibly examined. The most obvious way to form portfolios is to come out stocks into portfolios by the true beta. But, all that is available is observed beta. Ranking into portfolios by observed beta would introduce selection bias. Stocks with high-observed beta (in the highest group) would be more apparent to have a positive beat error in estimating beta.This would introduce a positive bias into beta for high-beta portfolios and would introduce a prohibit bias into an estimate of the interfere. (Elton and Gruber 1995, p. 333). unite securities into portfolios diversifies away most of the firm-spec ific part of returns thereby enhancing the precision of the estimates of beta and the expected rate of return on the portfolios on securities. This mitigates statistical problems that arise from amount error in the beta estimates. The following equation was used to estimate portfolio betas rpt = a p + ? p ? mt + e pt (3) where, rpt is the average excess portfolio return, ? p is the calculated portfolio beta. The study continues by estimating the ex-post Security Market railroad line (SML) by regressing the portfolio returns against the portfolio betas obtained by Equation 3. The relation examined is the following rP = ? 0 + ? 1 ? ? P + e P (4) where, rp is the average excess return on a portfolio p (the difference between the return on the portfolio and the return on a risk-free asset), ? p is an estimate of beta of the portfolio p , ?1 is the market price of risk, the risk premium for bearing one unit of beta risk, ? is the zero-beta rate, the expected return on an asset which ha s a beta of zero, and e p is random disturbance term in the regression equation. In order to test for nonlinearity between ingrained portfolio returns and betas, a regression was run on average portfolio returns, calculated portfolio beta, and beta-square from equation 3 2 rp = ? 0 + ? 1 ? ? p + ? 2 ? ? p + e p (5) in the end in order to examine whether the residual variance of stocks affects portfolio returns, an excess term was included in equation 5, to test for the informative power of nonsystematic risk 2 rp = ? + ? 1 ? ? p + ? 2 ? ? p + ? 3 ? RVp + e p (6) where 84 International Research Journal of Finance and Economics Issue 4 (2006) RV p is the residual variance of portfolio returns (Equation 3), RV p = ? 2 (e pt ) . The estimated parameters allow us to test a series of hypotheses regarding the CAPM. The tests are i) ? 3 = 0 or residual risk does not affect return, ii) ? 2 = 0 or there are no nonlinearities in the security market line, iii) ? 1 > 0 that is, there is a positive price of risk in the capital markets (Elton and Gruber 1995, p. 336).Finally, the above analysis was in like manner conducted for each year separately (1998-2002), by changing the portfolio compositions according to each year estimated betas. V. Empirical results and Interpretation of the findings The first part of the methodological analysis required the estimation of betas for individual stocks by using observations on rates of return for a sequence of dates. Useful remarks can be derived from the results of this procedure, for the assets used in this study. The ply of the estimated stock betas is between 0. 0984 the minimum and 1. 4369 the upper limit with a modular deviation of 0. 240 ( circumvent 1). or so of the beta coefficients for individual stocks are statistically significant at a 95% level and all estimated beta coefficients are statistical significant at a 90% level. For a more intact estimation of betas an EGARCH (1,1) model was used wheresoever it was necessary, in order to correct for nonlinearities. board 1 Stock beta coefficient estimates (Equation 1)Stock name beta Stock name beta Stock name OLYMP . 0984 THEMEL . 8302 PROOD EYKL . 4192 AIOLK . 8303 ALEK MPELA . 4238 AEGEK . 8305 EPATT MPTSK . 5526 AEEXA . 8339 SIDEN FOIN . 5643 SPYR . 8344 GEK GKOYT . 862 SARANT . 8400 ELYF PAPAK . 6318 ELTEX . 8422 MOYZK ABK . 6323 ELEXA . 8427 TITK MYTIL . 6526 MPENK . 8610 NIKAS FELXO . 6578 HRAKL . 8668 ETHENEX ABAX . 6874 PEIR . 8698 IATR TSIP . 6950 BIOXK . 8747 METK AAAK . 7047 ELMEK . 8830 ALPHA EEEK . 7097 LAMPSA . 8848 AKTOR ERMHS . 7291 MHXK . 8856 INTKA LAMDA . 7297 DK . 8904 MAIK OTE . 7309 FOLI . 9005 PETZ MARF . 7423 THELET . 9088 ETEM MRFKO . 7423 ATT . 9278 FINTO KORA . 7520 ARBA . 9302 ESXA RILK . 7682 KATS . 9333 BIOSK LYK . 7684 ALBIO . 9387 XATZK ELASK . 7808 XAKOR . 9502 KREKA NOTOS . 8126 SAR . 9533 ETE KARD . 8290 NAYP . 577 SANYO blood Metastock (Greek) Data Base and calculations (S-PLUS) beta . 9594 . 9606 . 9698 . 9806 . 9845 . 9890 . 9895 . 9917 . 9920 1. 0059 1. 0086 1. 0149 1. 0317 1. 0467 1. 0532 1. 0542 1. 0593 1. 0616 1. 0625 1. 0654 1. 0690 1. 0790 1. 0911 1. 1127 1. 1185 Stock name EMP NAOYK ELBE ROKKA SELMK DESIN ELBAL ESK TERNA KERK POYL EEGA KALSK GENAK FANKO PLATH STRIK EBZ ALLK GEBKA AXON RINTE KLONK ETMAK ALTEK beta 1. 1201 1. 1216 1. 1256 1. 1310 1. 1312 1. 1318 1. 1348 1. 1359 1. 1392 1. 1396 1. 1432 1. 1628 1. 1925 1. 1996 1. 2322 1. 2331 1. 2500 1. 2520 1. 2617 1. 2830 1. 3030 1. 3036 1. 3263 1. 3274 1. 4369The article argues that certain hypotheses can be tested irregardless of whether one believes in the validity of the simple CAPM or in any other version of the theory. Firstly, the theory indicates that higher risk (beta) is associated with a higher level of return. However, the results of the study do not International Research Journal of Finance and Economics Issue 4 (2006) 85 support this hypothesis. The beta coefficients of the 10 portfolios do not indicate that hig her beta portfolios are related with higher returns. Portfolio 10 for example, the highest beta portfolio ( ? = 1. 2024), yields negative portfolio returns.In contrast, portfolio 1, the lowest beta portfolio ( ? = 0. 5474) produces positive returns. These contradicting results can be partially explained by the significant fluctuations of stock returns over the period examined (Table 2). Table 2 second-rate excess portfolio returns and betas (Equation 3) rp beta (p) a10 . 0001 . 5474 b10 . 0000 . 7509 c10 -. 0007 . 9137 d10 -. 0004 . 9506 e10 -. 0008 . 9300 f10 -. 0009 . 9142 g10 -. 0006 1. 0602 h10 -. 0013 1. 1066 i10 -. 0004 1. 1293 j10 -. 0004 1. 2024 Average Rf . 0014 Average rm=(Rm-Rf) . 0001 Source Metastock (Greek) Data Base and calculations (S-PLUS) Portfolio Var.Error . 0012 . 0013 . 0014 . 0014 . 0009 . 0010 . 0012 . 0019 . 0020 . 0026 R2 . 4774 . 5335 . 5940 . 6054 . 7140 . 6997 . 6970 . 6057 . 6034 . 5691 In order to test the CAPM hypothesis, it is necessary to find the counterparts to the theoretical values that must be used in the CAPM equation. In this study the yield on the 3-month Greek Treasury Bill was used as an similarity of the risk-free rate. For the R m , the ASE Composite Share index is taken as the best approximation for the market portfolio. The elemental equation used was rP = ? 0 + ? 1 ? ? P + e P (Equation 4) where ? is the expected excess return on a zero beta portfolio and ? 1 is the market price of risk, the difference between the expected rate of return on the market and a zero beta portfolio. One way for allowing for the possibility that the CAPM does not hold true is to add an hold on in the estimation of the SML. The CAPM considers that the intercept is zero for every asset. Hence, a test can be constructed to examine this hypothesis. In order to diversify away most of the firm-specific part of returns, thereby enhancing the precision of the beta estimates, the securities were previously combine into portfolios.This app roach mitigates the statistical problems that arise from measurement errors in individual beta estimates. These portfolios were created for several reasons (i) the random influences on individual stocks run away to be larger compared to those on fitly constructed portfolios (hence, the intercept and beta are easier to estimate for portfolios) and (ii) the tests for the intercept are easier to implement for portfolios because by construction their estimated coefficients are less likely to be correlated with one some other than the shares of individual companies.The high value of the estimated correlational statistics coefficient between the intercept and the slope indicates that the model used explains excess returns (Table 3). 86 International Research Journal of Finance and Economics Issue 4 (2006) Table 3 Statistics of the estimation of the SML (Equation 4) Coefficient ? 0 take account . 0005 t-value (. 9011) p-value . 3939 counterpoise standard error . 0004 on 8 degrees of freedom Multiple R-Squared . 2968 F-statistic 3. 3760 on 1 and 8 degrees of freedom, the p-value is . 1034 Correlation of Coefficients 0 ,? 1 = . 9818 ? 1 -. 0011 (-1. 8375) . 1034However, the fact that the intercept has a value some zero weakens the above explanation. The results of this paper appear to be contradictory with the zero beta version of the CAPM because the intercept of the SML is not greater than the interest rate on risk free-bonds (Table 2 and 3). In the estimation of SML, the CAPMs prediction for ? 0 is that it should be equal to zero. The calculated value of the intercept is small (0. 0005) but it is not significantly different from zero (the tvalue is not greater than 2) Hence, based on the intercept criterion alone the CAPM hypothesis cannot distinctly be rejected.According to CAPM the SLM slope should equal the excess return on the market portfolio. The excess return on the market portfolio was 0. 0001 while the estimated SLM slope was 0. 0011. Hence, the latter result withal indicates that there is evidence against the CAPM (Table 2 and 3). In order to test for nonlinearity between total portfolio returns and betas, a regression was run between average portfolio returns, calculated portfolio betas, and the square of betas (Equation 5). Results show that the intercept (0. 0036) of the equation was greater than the risk-free interest rate (0. 014), ? 1 was negative and different from zero while ? 2 , the coefficient of the square beta was very small (0. 0041 with a t-value not greater than 2) and thus consistent with the hypothesis that the expected return-beta consanguinity is linear (Table 4). Table 4 interrogation for Non-linearity (Equation 5) Coefficient ? 0 Value . 0036 t-value (1. 7771) p-value 0. 1188 Residual standard error . 0003 on 7 degrees of freedom Multiple R-Squared . 4797 F-statistic 3. 2270 on 2 and 7 degrees of freedom, the p-value is . 1016 ? 1 -. 0084 (-1. 8013) 0. 1147 ? 2 . 0041 (1. 5686) 0. 1607According to the CAPM, expected returns vary across assets only because the assets betas are different. Hence, one way to investigate whether CAPM adequately captures all-important aspects of the risk-return tradeoff is to test whether other asset-specific characteristics can explain the crosssectional differences in average returns that cannot be attributed to cross-sectional differences in beta. To accomplish this projection the residual variance of portfolio returns was added as an additional explanatory variable (Equation 6). The coefficient of the residual variance of portfolio returns ? 3 is small and not statistically different from zero.It is therefore safe to conclude that residual risk has no affect on the expected return of a security. Thus, when portfolios are used instead of individual stocks, residual risk no longer appears to be important (Table 5). International Research Journal of Finance and Economics Issue 4 (2006) Table 5 Testing for Non-Systematic risk (Equation 6) Coeffi cient ? 0 ? 1 Value . 0017 -. 0043 t-value (. 5360) (-. 6182) p-value 0. 6113 0. 5591 Residual standard error . 0003 on 6 degrees of freedom Multiple R-Squared . 5302 F-statistic 2. 2570 on 3 and 6 degrees of freedom, the p-value is . 1821 ? 2 . 0015 (. 3381) 0. 7468 ? 3 . 3503 (. 8035) 0. 523 87 Since the analysis on the entire five-year period did not yield pie-eyed evidence in favor of the CAPM we examined whether a similar approach on yearly data would provide more supportive evidence. All models were tested separately for each of the five-year period and the results were statistically better for some years but still did not support the CAPM hypothesis (Tables 6, 7 and 8).Table 6 Statistics of the estimation SML (yearly series, Equation 4) 1998 1999 2000 2001 2002 Coefficient ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 Value . 0053 . 0050 . 0115 . 0134 -. 0035 -. 0149 . 0000 -. 0057 -. 0017 -. 0088 t-value (3. 7665) (2. 231) (2. 8145) (4. 0237) (-1. 9045) (-9. 4186) (. 0025) (-2. 4 066) (-. 8452) (-5. 3642) Std. Error . 0014 . 0022 . 0041 . 0033 . 0019 . 0016 . 0024 . 0028 . 0020 . 0016 p-value . 0050 . 0569 . 2227 . 0038 . 0933 . 0000 . 9981 . 0427 . 4226 . 0007 Table 7 Testing for Non-linearity (yearly series, Equation 5) 1998 Coefficient ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 Value . 0035 . 0139 -. 0078 . 0030 -. 0193 . 0135 -. 0129 . 0036 -. 0083 . 0092 -. 0240 . 0083 -. 0077 . 0046 -. 0059 t-value (1. 7052) (1. 7905) (-1. 1965) (2. 1093) (-. 7909) (1. 3540) (-3. 5789) (. 5435) (-2. 8038) (1. 2724) (-1. 7688) (1. 3695) (-2. 9168) (. 139) (-2. 7438) Std. Error . 0020 . 0077 . 0065 . 0142 . 0243 . 0026 . 0036 . 0067 . 0030 . 0072 . 0136 . 0060 . 0026 . 0050 . 0022 p-value . 1319 . 1165 . 2705 . 0729 . 4549 . 0100 . 0090 . 6037 . 0264 . 2439 . 1202 . 2132 . 0224 . 3911 . 0288 1999 2000 2001 2002 88 International Research Journal of Finance and Economics Issue 4 (2006) Table 8 Testing for Non-Systematic risk (yearly series, Equation 6) 19 98 Coefficient ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 Value . 0016 . 0096 -. 0037 3. 0751 . 0017 -. 0043 . 0015 . 3503 -. 0203 . 0199 -. 0185 2. 2673 . 0062 -. 0193 . 0053 1. 7024 -. 0049 . 000 -. 0026 -5. 1548 t-value (. 7266) (1. 2809) (-. 5703) (. 5862) (1. 4573) (-. 0168) (. 0201) (2. 2471) (-4. 6757) (2. 2305) (-3. 6545) (2. 2673) (. 6019) (-1. 0682) (. 5635) (. 4324) (-. 9507) (. 0054) (-. 4576) (-. 6265) Std. Error . 0022 . 0075 . 0065 1. 9615 . 0125 . 0211 . 0099 1. 4278 . 0043 . 0089 . 0051 . 9026 . 0103 . 0181 . 0094 3. 9369 . 0052 . 0089 . 0058 8. 2284 p-value . 4948 . 2475 . 5892 . 1680 . 1953 . 9846 . 9846 . 0657 . 0034 . 0106 . 0106 . 0639 . 5693 . 3265 . 5935 . 6805 . 3785 . 9959 . 6633 . 5541 1999 2000 2001 2002 VI. Concluding Remarks The article examined the validity of the CAPM for the Greek stock market.The study used weekly stock returns from 100 companies listed on the Athens stock exchange from January 1998 to December 2 002. The findings of the article are not supportive of the theorys basic hypothesis that higher risk (beta) is associated with a higher level of return. In order to diversify away most of the firm-specific part of returns thereby enhancing the precision of the beta estimates, the securities where unite into portfolios to mitigate the statistical problems that arise from measurement errors in individual beta estimates. The model does explain, however, excess returns.The results obtained lend support to the linear structure of the CAPM equation being a good explanation of security returns. The high value of the estimated correlation coefficient between the intercept and the slope indicates that the model used, explains excess returns. However, the fact that the intercept has a value around zero weakens the above explanation. The CAPMs prediction for the intercept is that it should be equal to zero and the slope should equal the excess returns on the market portfolio. The findings of t he study contradict the above hypothesis and indicate evidence against the CAPM.The comprehension of the square of the beta coefficient to test for nonlinearity in the relationship between returns and betas indicates that the findings are according to the hypothesis and the expected returnbeta relationship is linear. Additionally, the tests conducted to investigate whether the CAPM adequately captures all-important aspects of reality by including the residual variance of stocks indicates that the residual risk has no effect on the expected return on portfolios. The lack of inviolable evidence in favor of CAPM necessitated the study of yearly data to test the validity of the model.The findings from this approach provided better statistical results for some years but still did not support the CAPM hypothesis. The results of the tests conducted on data from the Athens stock exchange for the period of January 1998 to December 2002 do not appear to clearly reject the CAPM. This does no t mean that the data do not support CAPM. As Black 1972 points out these results can be explained in two ways. First, measurement and model specification errors arise due to the use of a proxy instead of the actual market International Research Journal of Finance and Economics Issue 4 (2006) 89 ortfolio. This error biases the regression line estimated slope towards zero and its estimated intercept away from zero. Second, if no risk-free asset exists, the CAPM does not predict an intercept of zero.