W3LC0Me yA UkHti Wa Akhi

WelCoMe Ya UKHti wa AkHi

Jumat, 28 Januari 2011

jurnal CAPM

International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 4 (2006)
© EuroJournals Publishing, Inc. 2006
http://www.eurojournals.com/finance.htm
Testing the Capital Asset Pricing Model (CAPM): The Case of
the Emerging Greek Securities Market
Grigoris Michailidis
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: mgrigori@uom.gr
Tel: 00302310891889
Stavros Tsopoglou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: tsopstav@uom.gr
Tel: 00302310891889
Demetrios Papanastasiou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: papanast@uom.gr
Tel: 00302310891878
Eleni Mariola
Hagan School of Business, Iona College
New Rochelle
Abstract
The article examines the Capital Asset Pricing Model (CAPM) for the Greek stock
market using weekly stock returns from 100 companies listed on the Athens stock
exchange for the period of January 1998 to December 2002. In order to diversify away the
firm-specific part of returns thereby enhancing the precision of the beta estimates, the
securities where grouped into portfolios. The findings of this article are not supportive of
the theory’s basic statement that higher risk (beta) is associated with higher levels of return.
The model does explain, however, excess returns and thus lends support to the linear
structure of the CAPM equation.
The CAPM’s prediction for the intercept is that it should equal zero and the slope
should equal the excess returns on the market portfolio. The results of the study refute the
above hypothesis and offer evidence against the CAPM. The tests conducted to examine
the nonlinearity of the relationship between return and betas support the hypothesis that the
expected return-beta relationship is linear. Additionally, this paper investigates whether the
CAPM adequately captures all-important determinants of returns including the residual
International Research Journal of Finance and Economics - Issue 4 (2006) 79
variance of stocks. The results demonstrate that residual risk has no effect on the expected
returns of portfolios. Tests may provide evidence against the CAPM but they do not
necessarily constitute evidence in support of any alternative model (JEL G11, G12, and
G15).
Key words: CAPM, Athens Stock Exchange, portfolio returns, beta, risk free rate, stocks
JEL Classification: F23, G15
I. Introduction
Investors and financial researchers have paid considerable attention during the last few years to the
new equity markets that have emerged around the world. This new interest has undoubtedly been
spurred by the large, and in some cases extraordinary, returns offered by these markets. Practitioners
all over the world use a plethora of models in their portfolio selection process and in their attempt to
assess the risk exposure to different assets.
One of the most important developments in modern capital theory is the capital asset pricing model
(CAPM) as developed by Sharpe [1964], Lintner [1965] and Mossin [1966]. CAPM suggests that high
expected returns are associated with high levels of risk. Simply stated, CAPM postulates that the
expected return on an asset above the risk-free rate is linearly related to the non-diversifiable risk as
measured by the asset’s beta. Although the CAPM has been predominant in empirical work over the
past 30 years and is the basis of modern portfolio theory, accumulating research has increasingly cast
doubt on its ability to explain the actual movements of asset returns.
The purpose of this article is to examine thoroughly if the CAPM holds true in the capital market of
Greece. Tests are conducted for a period of five years (1998-2002), which is characterized by intense
return volatility (covering historically high returns for the Greek Stock market as well as significant
decrease in asset returns over the examined period). These market return characteristics make it
possible to have an empirical investigation of the pricing model on differing financial conditions thus
obtaining conclusions under varying stock return volatility.
Existing financial literature on the Athens stock exchange is rather scanty and it is the goal of this
study to widen the theoretical analysis of this market by using modern finance theory and to provide
useful insights for future analyses of this market.
II. Empirical appraisal of the model and competing studies of the model’s validity
2.1. Empirical appraisal of CAPM
Since its introduction in early 1960s, CAPM has been one of the most challenging topics in financial
economics. Almost any manager who wants to undertake a project must justify his decision partly
based on CAPM. The reason is that the model provides the means for a firm to calculate the return that
its investors demand. This model was the first successful attempt to show how to assess the risk of the
cash flows of a potential investment project, to estimate the project’s cost of capital and the expected
rate of return that investors will demand if they are to invest in the project.
The model was developed to explain the differences in the risk premium across assets. According to
the theory these differences are due to differences in the riskiness of the returns on the assets. The
model states that the correct measure of the riskiness of an asset is its beta and that the risk premium
per unit of riskiness is the same across all assets. Given the risk free rate 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 academic debate
about its usefulness and validity. In general, the empirical testing of CAPM has two broad purposes
(Baily et al, [1998]): (i) to test whether or not the theories should be rejected (ii) to provide information
that can aid financial decisions. To accomplish (i) tests are conducted which could potentially at least
reject the model. The model passes the test if it is not possible to reject the hypothesis that it is true.
Methods of statistical analysis need to be applied in order to draw reliable conclusions on whether the
80 International Research Journal of Finance and Economics - Issue 4 (2006)
model is supported by the data. To accomplish (ii) the empirical work uses the theory as a vehicle for
organizing and interpreting the data without seeking ways of rejecting the theory. This kind of
approach is found in the area of portfolio decision-making, in particular with regards to the selection of
assets to the bought or sold. For example, investors are advised to buy or sell assets that according to
CAPM are underpriced or overpriced. In this case empirical analysis is needed to evaluate the assets,
assess their riskiness, analyze them, and place them into their respective categories. A second
illustration of the latter methodology appears in corporate finance where the estimated beta coefficients
are used in assessing the riskiness of different investment projects. It is then possible to calculate
“hurdle 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 1960’s, 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 1960’s by Sharpe [1964], Lintner [1965] and Mossin [1966]. In
its simple form, the CAPM predicts that the expected return on an asset above the risk-free rate is
linearly related to the non-diversifiable risk, which is measured by the asset’s beta.
One of the earliest empirical studies that found supportive evidence for CAPM is that of Black,
Jensen and Scholes [1972]. Using monthly return data and portfolios rather than individual stocks,
Black et al tested whether the cross-section of expected returns is linear in beta. By combining
securities into portfolios one can diversify away most 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 measurement errors in beta
estimates. The authors found that the data are consistent with the predictions of the CAPM i.e. the
relation between the average return and beta is very close to linear and that portfolios with high (low)
betas have high (low) average returns.
Another classic empirical study that supports the theory is that of Fama and McBeth [1973]; they
examined whether there is a positive linear relation between average returns and beta. Moreover, the
authors investigated whether the squared value of beta and the volatility of asset returns can explain the
residual variation in average returns across assets that are not explained by beta alone.
2.3. Challenges to the validity of the theory
In the early 1980s several studies suggested that there were deviations from the linear CAPM riskreturn
trade-off due to other variables that affect this tradeoff. The purpose of the above studies was to
find the components that CAPM was missing in explaining the risk-return trade-off and to identify 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 CAPM’s 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 concluded that the average returns on
stocks of small firms (those with low market values of equity) were higher than the average returns on
stocks of large firms (those with high market values of equity). This finding has become known as the
size effect.
The research has been expanded by examining different sets of variables that might affect the riskreturn
tradeoff. In particular, the earnings yield (Basu [1977]), leverage, and the ratio of a firm’s 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 utilized in testing the validity of CAPM.
International Research Journal of Finance and Economics - Issue 4 (2006) 81
The general reaction to Banz’s [1981] findings, that CAPM may be missing some aspects of reality,
was to support the view that although the data may suggest deviations from CAPM, these deviations
are not so important as to reject the theory.
However, this idea has been challenged by Fama and French [1992]. They showed that Banz’s
findings might be economically so important that it raises serious questions about the validity of the
CAPM. Fama and French [1992] used the same procedure as Fama and McBeth [1973] but arrived at
very different conclusions. Fama and McBeth find a positive relation between return and risk while
Fama and French find no relation at all.
2.4. The academic debate continues
The Fama and French [1992] study has itself been criticized. In general the studies responding to the
Fama and French challenge by and large take a closer look at the data used in the study. Kothari,
Shaken and Sloan [1995] argue that Fama and French’s [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
too noisy to invalidate the CAPM. In fact, they show that when a more efficient statistical method is
used, 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 sample period effect i.e. the size
effect is observed in some periods and not in others.
Despite the above criticisms, 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 basic assumptions made to facilitate the empirical analysis. For example, most
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 constantly changing. When one considers a time-varying return distribution, one must refer
to the conditional mean, variance, and covariance that change depending on currently available
information. In contrast, the usual estimates of return, variance, and average squared deviations over a
sample period, provide an unconditional 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 generalized 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
also been numerous modifications to the models and whether the earliest or the subsequent alternative
models validate or not the CAPM is yet to be determined.
III. Sample selection and Data
3.1. Sample Selection
The study 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 100 stocks that are included in the formation of the FTSE/ASE 20,
FTSE/ASE Mid 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 following 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 Economics - Issue 4 (2006)
(ii) The FTSE/ASE Mid 40 index is the mid cap index and captures the performance 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 included in the indices are traded on the ASE on a continuous basis throughout the
full Athens stock exchange trading day, and are chosen according to prespecified liquidity criteria set
by the ASE Advisory Committee1.
For the purpose of the study, 100 stocks were selected from the pool of securities included 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 irregularly
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 order to obtain better estimates of the value of the beta coefficient, the study utilizes weekly
stock returns. Returns calculated using a longer time period (e.g. monthly) 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 span can result in the use of
very noisy data and thus yield inefficient estimates.
All stock returns used in the study are adjusted for dividends as required by the CAPM.
The ASE Composite 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 highly capitalized shares of the main market, and
reflects general trends of the Greek stock market.
Furthermore, the 3-month Greek Treasury 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 Bank of Greece. The yield
on the 3-month Treasury bill is specifically chosen as the benchmark that better reflects the short-term
changes in the Greek financial markets.
IV. Methodology
The first step 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 stock’s weekly return
against the market index according to the following equation:
ft Rit -R ft = ai +βi ⋅ (Rmt -R ) + eit (1)
where,
it R is the return on stock i (i=1…100),
ft R is the rate of return on a risk-free asset,
mt R is the rate of return on the market index,
i β
is the estimate of beta for the stock i , and
eit is the corresponding random disturbance term in the regression equation.
[Equation 1 could also be expressed using excess return notation, where ( - )= it ft it R R r and
ft mt ( - )=r mt R R ]
In spite of the fact that weekly returns were used to avoid short-term noise effects the estimation
diagnostic tests for equation (1) indicated, in several occasions, departures from the linear assumption.
1 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 excess returns of stocks ( rpt ) ordered according to
their beta coefficient computed by Equation 1. Let,
1 r = =
Σk
it
i
pt
r
k
(2)
where,
k is the number of stocks included in each portfolio (k=1…10),
p is the number of portfolios (p=1…10),
it r is the excess 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 clearly examined. The most obvious way to form portfolios is to rank 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 likely to have a positive measurement error in estimating beta. This would introduce a
positive bias into beta for high-beta portfolios and would introduce a negative bias into an estimate of
the intercept. (Elton and Gruber [1995], p. 333).
Combining securities into portfolios diversifies away most of the firm-specific 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 measurement error in the
beta estimates.
The following equation was used to estimate portfolio betas:
mt = + ⋅ r + e pt p p pt r a β (3)
where,
rpt is the average excess portfolio return,
p β is the calculated portfolio beta.
The study continues by estimating the ex-post Security Market Line (SML) by regressing the
portfolio returns against the portfolio betas obtained by Equation 3. The relation examined is the
following:
0 1 = + +e P P P r γ γ ⋅β (4)
where,
p r 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 β is an estimate of beta of the portfolio p ,
1 γ is the market price of risk, the risk premium for bearing one unit of beta risk,
0 γ is the zero-beta rate, the expected return on an asset which has a beta of zero, and
ep is random disturbance term in the regression equation.
In order to test for nonlinearity between total portfolio returns and betas, a regression was run on
average portfolio returns, calculated portfolio beta, and beta-square from equation 3:
2
0 1 2 = + + +e p p p p r γ γ ⋅β γ ⋅β (5)
Finally in order to examine whether the residual variance of stocks affects portfolio returns, an
additional term was included in equation 5, to test for the explanatory power of nonsystematic risk:
2
0 1 2 3 p = + + + RV+e p p p p r γ γ ⋅β γ ⋅β γ ⋅ (6)
where
84 International Research Journal of Finance and Economics - Issue 4 (2006)
RVp is the residual variance of portfolio returns (Equation 3), = 2 (e ) p pt RV σ .
The estimated parameters allow us to test a series of hypotheses regarding the CAPM. The tests are:
i) 3 γ = 0 or residual risk does not affect return,
ii) 2 γ = 0 or there are no nonlinearities in the security market line,
iii) 1 γ > 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 also conducted for each year separately (1998-2002), by changing
the portfolio compositions according to yearly estimated betas.
V. Empirical results and Interpretation of the findings
The first part of the methodology 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 range of the estimated stock betas is between 0.0984 the minimum and 1.4369 the maximum
with a standard deviation of 0.2240 (Table 1). Most 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 accurate estimation of betas an EGARCH (1,1) model was used wherever it was
necessary, in order to correct for nonlinearities.
Table 1: Stock beta coefficient estimates (Equation 1)
Stock name beta Stock name beta Stock name beta Stock name beta
OLYMP .0984 THEMEL .8302 PROOD .9594 EMP 1.1201
EYKL .4192 AIOLK .8303 ALEK .9606 NAOYK 1.1216
MPELA .4238 AEGEK .8305 EPATT .9698 ELBE 1.1256
MPTSK .5526 AEEXA .8339 SIDEN .9806 ROKKA 1.1310
FOIN .5643 SPYR .8344 GEK .9845 SELMK 1.1312
GKOYT .5862 SARANT .8400 ELYF .9890 DESIN 1.1318
PAPAK .6318 ELTEX .8422 MOYZK .9895 ELBAL 1.1348
ABK .6323 ELEXA .8427 TITK .9917 ESK 1.1359
MYTIL .6526 MPENK .8610 NIKAS .9920 TERNA 1.1392
FELXO .6578 HRAKL .8668 ETHENEX 1.0059 KERK 1.1396
ABAX .6874 PEIR .8698 IATR 1.0086 POYL 1.1432
TSIP .6950 BIOXK .8747 METK 1.0149 EEGA 1.1628
AAAK .7047 ELMEK .8830 ALPHA 1.0317 KALSK 1.1925
EEEK .7097 LAMPSA .8848 AKTOR 1.0467 GENAK 1.1996
ERMHS .7291 MHXK .8856 INTKA 1.0532 FANKO 1.2322
LAMDA .7297 DK .8904 MAIK 1.0542 PLATH 1.2331
OTE .7309 FOLI .9005 PETZ 1.0593 STRIK 1.2500
MARF .7423 THELET .9088 ETEM 1.0616 EBZ 1.2520
MRFKO .7423 ATT .9278 FINTO 1.0625 ALLK 1.2617
KORA .7520 ARBA .9302 ESXA 1.0654 GEBKA 1.2830
RILK .7682 KATS .9333 BIOSK 1.0690 AXON 1.3030
LYK .7684 ALBIO .9387 XATZK 1.0790 RINTE 1.3036
ELASK .7808 XAKOR .9502 KREKA 1.0911 KLONK 1.3263
NOTOS .8126 SAR .9533 ETE 1.1127 ETMAK 1.3274
KARD .8290 NAYP .9577 SANYO 1.1185 ALTEK 1.4369
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
The 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 higher beta
portfolios are related with higher returns. Portfolio 10 for example, the highest beta portfolio
(β = 1.2024), yields negative portfolio returns. In contrast, portfolio 1, the lowest beta portfolio
(β = 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: Average excess portfolio returns and betas (Equation 3)
Portfolio rp beta (p) Var. Error R2
a10 .0001 .5474 .0012 .4774
b10 .0000 .7509 .0013 .5335
c10 -.0007 .9137 .0014 .5940
d10 -.0004 .9506 .0014 .6054
e10 -.0008 .9300 .0009 .7140
f10 -.0009 .9142 .0010 .6997
g10 -.0006 1.0602 .0012 .6970
h10 -.0013 1.1066 .0019 .6057
i10 -.0004 1.1293 .0020 .6034
j10 -.0004 1.2024 .0026 .5691
Average Rf .0014
Average rm=(Rm-Rf) .0001
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
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 approximation of the risk-free rate. For theRm , the ASE Composite Share index is
taken as the best approximation for the market portfolio.
The basic equation used was 0 1 = + +e P P P r γ γ ⋅β (Equation 4) where 0 γ is the expected excess
return on a zero beta portfolio and 1 γ 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 intercept 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 combined into portfolios. This approach 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 tend to be
larger compared to those on suitably 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 another than the
shares of individual companies.
The high value of the estimated correlation 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 γ0 γ1
Value .0005 -.0011
t-value (.9011) (-1.8375)
p-value .3939 .1034
Residual 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 = γ γ ρ .9818
However, the fact that the intercept has a value around zero weakens the above explanation. The
results of this paper appear to be inconsistent 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 CAPM’s prediction for 0 γ 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
clearly 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 also 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
(0.0014), 1 γ was negative and different from zero while 2 γ , 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 relationship is linear (Table 4).
Table 4: Testing for Non-linearity (Equation 5)
Coefficient γ0 γ1 γ2
Value .0036 -.0084 .0041
t-value (1.7771) (-1.8013) (1.5686)
p-value 0.1188 0.1147 0.1607
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
According 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 task 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 γ 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) 87
Table 5: Testing for Non-Systematic risk (Equation 6)
Coefficient γ0 γ1 γ2 γ3
Value .0017 -.0043 .0015 .3503
t-value (.5360) (-.6182) (.3381) (.8035)
p-value 0.6113 0.5591 0.7468 0.4523
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
Since the analysis on the entire five-year period did not yield strong 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)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0053 (3.7665) .0014 .0050
γ1 .0050 (2.2231) .0022 .0569
1999 γ0 .0115 (2.8145) .0041 .2227
γ1 .0134 (4.0237) .0033 .0038
2000 γ0 -.0035 (-1.9045) .0019 .0933
γ1 -.0149 (-9.4186) .0016 .0000
2001 γ0 .0000 (.0025) .0024 .9981
γ1 -.0057 (-2.4066) .0028 .0427
2002 γ0 -.0017 (-.8452) .0020 .4226
γ1 -.0088 (-5.3642) .0016 .0007
Table 7: Testing for Non-linearity (yearly series, Equation 5)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0035 (1.7052) .0020 .1319
γ1 .0139 (1.7905) .0077 .1165
γ2 -.0078 (-1.1965) .0065 .2705
1999 γ0 .0030 (2.1093) .0142 .0729
γ1 -.0193 (-.7909) .0243 .4549
γ2 .0135 (1.3540) .0026 .0100
2000 γ0 -.0129 (-3.5789) .0036 .0090
γ1 .0036 (.5435) .0067 .6037
γ2 -.0083 (-2.8038) .0030 .0264
2001 γ0 .0092 (1.2724) .0072 .2439
γ1 -.0240 (-1.7688) .0136 .1202
γ2 .0083 (1.3695) .0060 .2132
2002 γ0 -.0077 (-2.9168) .0026 .0224
γ1 .0046 (.9139) .0050 .3911
γ2 -.0059 (-2.7438) .0022 .0288
88 International Research Journal of Finance and Economics - Issue 4 (2006)
Table 8: Testing for Non-Systematic risk (yearly series, Equation 6)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0016 (.7266) .0022 .4948
γ1 .0096 (1.2809) .0075 .2475
γ2 -.0037 (-.5703) .0065 .5892
γ3 3.0751 (.5862) 1.9615 .1680
1999 γ0 .0017 (1.4573) .0125 .1953
γ1 -.0043 (-.0168) .0211 .9846
γ2 .0015 (.0201) .0099 .9846
γ3 .3503 (2.2471) 1.4278 .0657
2000 γ0 -.0203 (-4.6757) .0043 .0034
γ1 .0199 (2.2305) .0089 .0106
γ2 -.0185 (-3.6545) .0051 .0106
γ3 2.2673 (2.2673) .9026 .0639
2001 γ0 .0062 (.6019) .0103 .5693
γ1 -.0193 (-1.0682) .0181 .3265
γ2 .0053 (.5635) .0094 .5935
γ3 1.7024 (.4324) 3.9369 .6805
2002 γ0 -.0049 (-.9507) .0052 .3785
γ1 .0000 (.0054) .0089 .9959
γ2 -.0026 (-.4576) .0058 .6633
γ3 -5.1548 (-.6265) 8.2284 .5541
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
2002.
The findings of the article are not supportive of the theory’s 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 combined 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 CAPM’s 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 the study contradict the above hypothesis
and indicate evidence against the CAPM.
The inclusion 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 strong 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 not 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
portfolio. 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.
The tests may provide evidence against the CAPM but that does not necessarily constitute evidence
in support of any alternative model.
90 International Research Journal of Finance and Economics - Issue 4 (2006)
References
[1] Amihud Yakov, Christensen Bent and Mendelson Haim, 1992. Further evidence on the risk
relationship. Working paper S-93-11. Salomon Brother Center for the Study of the Financial
Institutions, Graduate School of Business Administration, New York University.
[2] Bailey J.W, Alexander J.G, Sharpe W.1998. Investments. 6th edition, London: Prentice-Hall.
[3] Banz, R. 1981. The relationship between returns and market value of common stock. Journal of
Financial Economics 9: 3-18.
[4] Basu Sanjoy. 1977. Investment performance of common stocks in relation to their priceearnings
ratios: A test of the efficient market hypothesis. Journal of Finance 32:663-82.
[5] Bekaert, G., Harvey, C. 1997. Emerging equity market volatility. Journal of Financial
Economics 43: 29-78.
[6] Black, F., Jensen, M. C. and Scholes, M. 1972. The Capital asset pricing model: Some
empirical tests. Studies in the Theory of Capital Markets. pp.79-121. New York: Praeger.
[7] Black, Fischer. 1993. Beta and return. Journal of Portfolio Management 20: 8-18.
[8] Blume, M. 1975. Betas and their regression tendencies. Journal of Finance 30: 785-795.
[9] Bodie, Z., Kane, A. and Marcus, A. J. 1999. Investments. 4th edition, New York New York:
McGraw- Hill.
[10] Brealey, R.A., and S.C. Meyers. 2002. Principles of Corporate Finance. New York: McGraw-
Hill.
[11] Campbell, J. Y., Lo, A. W. and MacKinlay, A. C. 1997. The Econometrics of Financial
Markets. Princeton, N. J.: Princeton University Press.
[12] Chan L., Hamao Y., Lakonishok J. 1991. Fundamentals and stock returns in Japan .Journal of
Finance 46 :1739-64.
[13] Chen, N., R. Roll, and S. A. Ross 1986. Economic forces and the stock market. Journal of
Business 59: 383-403.
[14] Cochrane, J. H. 1991. Volatility tests and efficient markets: A Review Essay. Journal of
Monetary Economics 127: 463-485.
[15] Cochrane, John H. 2001. Asset Pricing. Princeton, N. J.: Princeton University Press.
[16] Elton, E. J. and Gruber, M. J. 1995. Modern Portfolio Theory and Investment Analysis. 5th
edition, New York: John: Wiley & Sons, Inc.
[17] Fama, E. and K. French. 1992. The cross-section of expected stock returns Journal of Finance
47: 427-465.
[18] Fama, E. and K. French. 1993. Common risk factors in the returns on stocks and bonds. Journal
of Financial Economics 33: 3-56
[19] Fama, E. F. 1976. Foundations of Finance. New York: Basic Books.
[21] Fama, E. F. and MacBeth, J. 1973. Risk, return and equilibrium: Empirical tests. Journal of
Political Economy 81: 607-636.
[22] Fama, E. F., 1991. Efficient Capital Markets II. Journal of Finance 46: 1575-1617.
[23] Gibbons, M. R., S. A. Ross, and J. Shanken. 1989. A test of the efficiency of a given portfolio.
Econometrica 57: 1121-1152.
[24] Graham, J. R., Harvey, C. R. 2001. The theory and practice of corporate finance: Evidence
from the field, Journal of Financial Economics 60: 187-243.
[25] Greene, William H. Econometric Analysis. 4th Edition, London: Prentice Hall.
[26] Hamilton, James D. 1994. Time Series Analysis. Princeton University Press, Princeton
[27] Jagannathan, R. and McGratten, E. R. 1995. The CAPM Debate. Quarterly Review of the
Federal Reserve Bank of Minneapolis 19: 2-17.
[28] Jagannathan, R. and Wang, Z. 1996. The conditional CAPM and the cross-section of expected
returns. Journal of Finance 51: 3-53.
International Research Journal of Finance and Economics - Issue 4 (2006) 91
[29] Johnston, J. and DiNardo, J. 1997. Econometric Methods. 4th edition, New York: Mc-Graw-
Hill.
[30] Kothari S.P., Shaken Jay and Sloan Richard G. 1995. Another look at the cross section of
expected stock returns. Journal of Finance 50: 185-224.
[31] Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock
portfolios and capital budgets, Review of Economics and Statistics 47: 13-37.
[32] Miller, M.H., and Scholes , M. 1972. Rates of return in relation to risk: a re-examination of
some recent findings , in Jensen (ed.). Studies in the theory of capital markets. New York:
Praegar.
[33] Mossin, J. 1966. Equilibrium in a capital asset market. Econometrica 34: 768-783.
[34] Rosenberg B., Reid K., Lanstein R. 1985. Persuasive evidence of market inefficiency. Journal
of Portfolio Management 11: 9-17.
[35] Sharpe, W. 1964. Capital asset prices: a theory of market equilibrium under conditions of risk.
Journal of Finance 33:885-901.
[36] Sharpe, William F. Investments. 3rd edition, London: Prentice Hall International editions
[37] Stambaugh, R. F. 1999. Predictive regressions. Journal of Financial Economics 54
[38] Statman Dennis. 1980. Book values and stock returns, Chicago MBA: A Journal of Selected
Papers 4:25-45.
[39] Stein, J. C. 1996. Rational capital budgeting in an irrational world. Journal of Business 69: 429-
55.
[40] Stewart, J. and Gill, L. 1998. Econometrics. 2nd edition, London: Prentice-Hall.

jurnal CAPM

International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 4 (2006)
© EuroJournals Publishing, Inc. 2006
http://www.eurojournals.com/finance.htm
Testing the Capital Asset Pricing Model (CAPM): The Case of
the Emerging Greek Securities Market
Grigoris Michailidis
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: mgrigori@uom.gr
Tel: 00302310891889
Stavros Tsopoglou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: tsopstav@uom.gr
Tel: 00302310891889
Demetrios Papanastasiou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: papanast@uom.gr
Tel: 00302310891878
Eleni Mariola
Hagan School of Business, Iona College
New Rochelle
Abstract
The article examines the Capital Asset Pricing Model (CAPM) for the Greek stock
market using weekly stock returns from 100 companies listed on the Athens stock
exchange for the period of January 1998 to December 2002. In order to diversify away the
firm-specific part of returns thereby enhancing the precision of the beta estimates, the
securities where grouped into portfolios. The findings of this article are not supportive of
the theory’s basic statement that higher risk (beta) is associated with higher levels of return.
The model does explain, however, excess returns and thus lends support to the linear
structure of the CAPM equation.
The CAPM’s prediction for the intercept is that it should equal zero and the slope
should equal the excess returns on the market portfolio. The results of the study refute the
above hypothesis and offer evidence against the CAPM. The tests conducted to examine
the nonlinearity of the relationship between return and betas support the hypothesis that the
expected return-beta relationship is linear. Additionally, this paper investigates whether the
CAPM adequately captures all-important determinants of returns including the residual
International Research Journal of Finance and Economics - Issue 4 (2006) 79
variance of stocks. The results demonstrate that residual risk has no effect on the expected
returns of portfolios. Tests may provide evidence against the CAPM but they do not
necessarily constitute evidence in support of any alternative model (JEL G11, G12, and
G15).
Key words: CAPM, Athens Stock Exchange, portfolio returns, beta, risk free rate, stocks
JEL Classification: F23, G15
I. Introduction
Investors and financial researchers have paid considerable attention during the last few years to the
new equity markets that have emerged around the world. This new interest has undoubtedly been
spurred by the large, and in some cases extraordinary, returns offered by these markets. Practitioners
all over the world use a plethora of models in their portfolio selection process and in their attempt to
assess the risk exposure to different assets.
One of the most important developments in modern capital theory is the capital asset pricing model
(CAPM) as developed by Sharpe [1964], Lintner [1965] and Mossin [1966]. CAPM suggests that high
expected returns are associated with high levels of risk. Simply stated, CAPM postulates that the
expected return on an asset above the risk-free rate is linearly related to the non-diversifiable risk as
measured by the asset’s beta. Although the CAPM has been predominant in empirical work over the
past 30 years and is the basis of modern portfolio theory, accumulating research has increasingly cast
doubt on its ability to explain the actual movements of asset returns.
The purpose of this article is to examine thoroughly if the CAPM holds true in the capital market of
Greece. Tests are conducted for a period of five years (1998-2002), which is characterized by intense
return volatility (covering historically high returns for the Greek Stock market as well as significant
decrease in asset returns over the examined period). These market return characteristics make it
possible to have an empirical investigation of the pricing model on differing financial conditions thus
obtaining conclusions under varying stock return volatility.
Existing financial literature on the Athens stock exchange is rather scanty and it is the goal of this
study to widen the theoretical analysis of this market by using modern finance theory and to provide
useful insights for future analyses of this market.
II. Empirical appraisal of the model and competing studies of the model’s validity
2.1. Empirical appraisal of CAPM
Since its introduction in early 1960s, CAPM has been one of the most challenging topics in financial
economics. Almost any manager who wants to undertake a project must justify his decision partly
based on CAPM. The reason is that the model provides the means for a firm to calculate the return that
its investors demand. This model was the first successful attempt to show how to assess the risk of the
cash flows of a potential investment project, to estimate the project’s cost of capital and the expected
rate of return that investors will demand if they are to invest in the project.
The model was developed to explain the differences in the risk premium across assets. According to
the theory these differences are due to differences in the riskiness of the returns on the assets. The
model states that the correct measure of the riskiness of an asset is its beta and that the risk premium
per unit of riskiness is the same across all assets. Given the risk free rate 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 academic debate
about its usefulness and validity. In general, the empirical testing of CAPM has two broad purposes
(Baily et al, [1998]): (i) to test whether or not the theories should be rejected (ii) to provide information
that can aid financial decisions. To accomplish (i) tests are conducted which could potentially at least
reject the model. The model passes the test if it is not possible to reject the hypothesis that it is true.
Methods of statistical analysis need to be applied in order to draw reliable conclusions on whether the
80 International Research Journal of Finance and Economics - Issue 4 (2006)
model is supported by the data. To accomplish (ii) the empirical work uses the theory as a vehicle for
organizing and interpreting the data without seeking ways of rejecting the theory. This kind of
approach is found in the area of portfolio decision-making, in particular with regards to the selection of
assets to the bought or sold. For example, investors are advised to buy or sell assets that according to
CAPM are underpriced or overpriced. In this case empirical analysis is needed to evaluate the assets,
assess their riskiness, analyze them, and place them into their respective categories. A second
illustration of the latter methodology appears in corporate finance where the estimated beta coefficients
are used in assessing the riskiness of different investment projects. It is then possible to calculate
“hurdle 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 1960’s, 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 1960’s by Sharpe [1964], Lintner [1965] and Mossin [1966]. In
its simple form, the CAPM predicts that the expected return on an asset above the risk-free rate is
linearly related to the non-diversifiable risk, which is measured by the asset’s beta.
One of the earliest empirical studies that found supportive evidence for CAPM is that of Black,
Jensen and Scholes [1972]. Using monthly return data and portfolios rather than individual stocks,
Black et al tested whether the cross-section of expected returns is linear in beta. By combining
securities into portfolios one can diversify away most 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 measurement errors in beta
estimates. The authors found that the data are consistent with the predictions of the CAPM i.e. the
relation between the average return and beta is very close to linear and that portfolios with high (low)
betas have high (low) average returns.
Another classic empirical study that supports the theory is that of Fama and McBeth [1973]; they
examined whether there is a positive linear relation between average returns and beta. Moreover, the
authors investigated whether the squared value of beta and the volatility of asset returns can explain the
residual variation in average returns across assets that are not explained by beta alone.
2.3. Challenges to the validity of the theory
In the early 1980s several studies suggested that there were deviations from the linear CAPM riskreturn
trade-off due to other variables that affect this tradeoff. The purpose of the above studies was to
find the components that CAPM was missing in explaining the risk-return trade-off and to identify 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 CAPM’s 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 concluded that the average returns on
stocks of small firms (those with low market values of equity) were higher than the average returns on
stocks of large firms (those with high market values of equity). This finding has become known as the
size effect.
The research has been expanded by examining different sets of variables that might affect the riskreturn
tradeoff. In particular, the earnings yield (Basu [1977]), leverage, and the ratio of a firm’s 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 utilized in testing the validity of CAPM.
International Research Journal of Finance and Economics - Issue 4 (2006) 81
The general reaction to Banz’s [1981] findings, that CAPM may be missing some aspects of reality,
was to support the view that although the data may suggest deviations from CAPM, these deviations
are not so important as to reject the theory.
However, this idea has been challenged by Fama and French [1992]. They showed that Banz’s
findings might be economically so important that it raises serious questions about the validity of the
CAPM. Fama and French [1992] used the same procedure as Fama and McBeth [1973] but arrived at
very different conclusions. Fama and McBeth find a positive relation between return and risk while
Fama and French find no relation at all.
2.4. The academic debate continues
The Fama and French [1992] study has itself been criticized. In general the studies responding to the
Fama and French challenge by and large take a closer look at the data used in the study. Kothari,
Shaken and Sloan [1995] argue that Fama and French’s [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
too noisy to invalidate the CAPM. In fact, they show that when a more efficient statistical method is
used, 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 sample period effect i.e. the size
effect is observed in some periods and not in others.
Despite the above criticisms, 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 basic assumptions made to facilitate the empirical analysis. For example, most
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 constantly changing. When one considers a time-varying return distribution, one must refer
to the conditional mean, variance, and covariance that change depending on currently available
information. In contrast, the usual estimates of return, variance, and average squared deviations over a
sample period, provide an unconditional 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 generalized 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
also been numerous modifications to the models and whether the earliest or the subsequent alternative
models validate or not the CAPM is yet to be determined.
III. Sample selection and Data
3.1. Sample Selection
The study 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 100 stocks that are included in the formation of the FTSE/ASE 20,
FTSE/ASE Mid 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 following 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 Economics - Issue 4 (2006)
(ii) The FTSE/ASE Mid 40 index is the mid cap index and captures the performance 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 included in the indices are traded on the ASE on a continuous basis throughout the
full Athens stock exchange trading day, and are chosen according to prespecified liquidity criteria set
by the ASE Advisory Committee1.
For the purpose of the study, 100 stocks were selected from the pool of securities included 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 irregularly
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 order to obtain better estimates of the value of the beta coefficient, the study utilizes weekly
stock returns. Returns calculated using a longer time period (e.g. monthly) 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 span can result in the use of
very noisy data and thus yield inefficient estimates.
All stock returns used in the study are adjusted for dividends as required by the CAPM.
The ASE Composite 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 highly capitalized shares of the main market, and
reflects general trends of the Greek stock market.
Furthermore, the 3-month Greek Treasury 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 Bank of Greece. The yield
on the 3-month Treasury bill is specifically chosen as the benchmark that better reflects the short-term
changes in the Greek financial markets.
IV. Methodology
The first step 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 stock’s weekly return
against the market index according to the following equation:
ft Rit -R ft = ai +βi ⋅ (Rmt -R ) + eit (1)
where,
it R is the return on stock i (i=1…100),
ft R is the rate of return on a risk-free asset,
mt R is the rate of return on the market index,
i β
is the estimate of beta for the stock i , and
eit is the corresponding random disturbance term in the regression equation.
[Equation 1 could also be expressed using excess return notation, where ( - )= it ft it R R r and
ft mt ( - )=r mt R R ]
In spite of the fact that weekly returns were used to avoid short-term noise effects the estimation
diagnostic tests for equation (1) indicated, in several occasions, departures from the linear assumption.
1 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 excess returns of stocks ( rpt ) ordered according to
their beta coefficient computed by Equation 1. Let,
1 r = =
Σk
it
i
pt
r
k
(2)
where,
k is the number of stocks included in each portfolio (k=1…10),
p is the number of portfolios (p=1…10),
it r is the excess 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 clearly examined. The most obvious way to form portfolios is to rank 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 likely to have a positive measurement error in estimating beta. This would introduce a
positive bias into beta for high-beta portfolios and would introduce a negative bias into an estimate of
the intercept. (Elton and Gruber [1995], p. 333).
Combining securities into portfolios diversifies away most of the firm-specific 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 measurement error in the
beta estimates.
The following equation was used to estimate portfolio betas:
mt = + ⋅ r + e pt p p pt r a β (3)
where,
rpt is the average excess portfolio return,
p β is the calculated portfolio beta.
The study continues by estimating the ex-post Security Market Line (SML) by regressing the
portfolio returns against the portfolio betas obtained by Equation 3. The relation examined is the
following:
0 1 = + +e P P P r γ γ ⋅β (4)
where,
p r 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 β is an estimate of beta of the portfolio p ,
1 γ is the market price of risk, the risk premium for bearing one unit of beta risk,
0 γ is the zero-beta rate, the expected return on an asset which has a beta of zero, and
ep is random disturbance term in the regression equation.
In order to test for nonlinearity between total portfolio returns and betas, a regression was run on
average portfolio returns, calculated portfolio beta, and beta-square from equation 3:
2
0 1 2 = + + +e p p p p r γ γ ⋅β γ ⋅β (5)
Finally in order to examine whether the residual variance of stocks affects portfolio returns, an
additional term was included in equation 5, to test for the explanatory power of nonsystematic risk:
2
0 1 2 3 p = + + + RV+e p p p p r γ γ ⋅β γ ⋅β γ ⋅ (6)
where
84 International Research Journal of Finance and Economics - Issue 4 (2006)
RVp is the residual variance of portfolio returns (Equation 3), = 2 (e ) p pt RV σ .
The estimated parameters allow us to test a series of hypotheses regarding the CAPM. The tests are:
i) 3 γ = 0 or residual risk does not affect return,
ii) 2 γ = 0 or there are no nonlinearities in the security market line,
iii) 1 γ > 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 also conducted for each year separately (1998-2002), by changing
the portfolio compositions according to yearly estimated betas.
V. Empirical results and Interpretation of the findings
The first part of the methodology 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 range of the estimated stock betas is between 0.0984 the minimum and 1.4369 the maximum
with a standard deviation of 0.2240 (Table 1). Most 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 accurate estimation of betas an EGARCH (1,1) model was used wherever it was
necessary, in order to correct for nonlinearities.
Table 1: Stock beta coefficient estimates (Equation 1)
Stock name beta Stock name beta Stock name beta Stock name beta
OLYMP .0984 THEMEL .8302 PROOD .9594 EMP 1.1201
EYKL .4192 AIOLK .8303 ALEK .9606 NAOYK 1.1216
MPELA .4238 AEGEK .8305 EPATT .9698 ELBE 1.1256
MPTSK .5526 AEEXA .8339 SIDEN .9806 ROKKA 1.1310
FOIN .5643 SPYR .8344 GEK .9845 SELMK 1.1312
GKOYT .5862 SARANT .8400 ELYF .9890 DESIN 1.1318
PAPAK .6318 ELTEX .8422 MOYZK .9895 ELBAL 1.1348
ABK .6323 ELEXA .8427 TITK .9917 ESK 1.1359
MYTIL .6526 MPENK .8610 NIKAS .9920 TERNA 1.1392
FELXO .6578 HRAKL .8668 ETHENEX 1.0059 KERK 1.1396
ABAX .6874 PEIR .8698 IATR 1.0086 POYL 1.1432
TSIP .6950 BIOXK .8747 METK 1.0149 EEGA 1.1628
AAAK .7047 ELMEK .8830 ALPHA 1.0317 KALSK 1.1925
EEEK .7097 LAMPSA .8848 AKTOR 1.0467 GENAK 1.1996
ERMHS .7291 MHXK .8856 INTKA 1.0532 FANKO 1.2322
LAMDA .7297 DK .8904 MAIK 1.0542 PLATH 1.2331
OTE .7309 FOLI .9005 PETZ 1.0593 STRIK 1.2500
MARF .7423 THELET .9088 ETEM 1.0616 EBZ 1.2520
MRFKO .7423 ATT .9278 FINTO 1.0625 ALLK 1.2617
KORA .7520 ARBA .9302 ESXA 1.0654 GEBKA 1.2830
RILK .7682 KATS .9333 BIOSK 1.0690 AXON 1.3030
LYK .7684 ALBIO .9387 XATZK 1.0790 RINTE 1.3036
ELASK .7808 XAKOR .9502 KREKA 1.0911 KLONK 1.3263
NOTOS .8126 SAR .9533 ETE 1.1127 ETMAK 1.3274
KARD .8290 NAYP .9577 SANYO 1.1185 ALTEK 1.4369
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
The 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 higher beta
portfolios are related with higher returns. Portfolio 10 for example, the highest beta portfolio
(β = 1.2024), yields negative portfolio returns. In contrast, portfolio 1, the lowest beta portfolio
(β = 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: Average excess portfolio returns and betas (Equation 3)
Portfolio rp beta (p) Var. Error R2
a10 .0001 .5474 .0012 .4774
b10 .0000 .7509 .0013 .5335
c10 -.0007 .9137 .0014 .5940
d10 -.0004 .9506 .0014 .6054
e10 -.0008 .9300 .0009 .7140
f10 -.0009 .9142 .0010 .6997
g10 -.0006 1.0602 .0012 .6970
h10 -.0013 1.1066 .0019 .6057
i10 -.0004 1.1293 .0020 .6034
j10 -.0004 1.2024 .0026 .5691
Average Rf .0014
Average rm=(Rm-Rf) .0001
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
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 approximation of the risk-free rate. For theRm , the ASE Composite Share index is
taken as the best approximation for the market portfolio.
The basic equation used was 0 1 = + +e P P P r γ γ ⋅β (Equation 4) where 0 γ is the expected excess
return on a zero beta portfolio and 1 γ 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 intercept 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 combined into portfolios. This approach 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 tend to be
larger compared to those on suitably 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 another than the
shares of individual companies.
The high value of the estimated correlation 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 γ0 γ1
Value .0005 -.0011
t-value (.9011) (-1.8375)
p-value .3939 .1034
Residual 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 = γ γ ρ .9818
However, the fact that the intercept has a value around zero weakens the above explanation. The
results of this paper appear to be inconsistent 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 CAPM’s prediction for 0 γ 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
clearly 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 also 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
(0.0014), 1 γ was negative and different from zero while 2 γ , 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 relationship is linear (Table 4).
Table 4: Testing for Non-linearity (Equation 5)
Coefficient γ0 γ1 γ2
Value .0036 -.0084 .0041
t-value (1.7771) (-1.8013) (1.5686)
p-value 0.1188 0.1147 0.1607
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
According 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 task 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 γ 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) 87
Table 5: Testing for Non-Systematic risk (Equation 6)
Coefficient γ0 γ1 γ2 γ3
Value .0017 -.0043 .0015 .3503
t-value (.5360) (-.6182) (.3381) (.8035)
p-value 0.6113 0.5591 0.7468 0.4523
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
Since the analysis on the entire five-year period did not yield strong 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)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0053 (3.7665) .0014 .0050
γ1 .0050 (2.2231) .0022 .0569
1999 γ0 .0115 (2.8145) .0041 .2227
γ1 .0134 (4.0237) .0033 .0038
2000 γ0 -.0035 (-1.9045) .0019 .0933
γ1 -.0149 (-9.4186) .0016 .0000
2001 γ0 .0000 (.0025) .0024 .9981
γ1 -.0057 (-2.4066) .0028 .0427
2002 γ0 -.0017 (-.8452) .0020 .4226
γ1 -.0088 (-5.3642) .0016 .0007
Table 7: Testing for Non-linearity (yearly series, Equation 5)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0035 (1.7052) .0020 .1319
γ1 .0139 (1.7905) .0077 .1165
γ2 -.0078 (-1.1965) .0065 .2705
1999 γ0 .0030 (2.1093) .0142 .0729
γ1 -.0193 (-.7909) .0243 .4549
γ2 .0135 (1.3540) .0026 .0100
2000 γ0 -.0129 (-3.5789) .0036 .0090
γ1 .0036 (.5435) .0067 .6037
γ2 -.0083 (-2.8038) .0030 .0264
2001 γ0 .0092 (1.2724) .0072 .2439
γ1 -.0240 (-1.7688) .0136 .1202
γ2 .0083 (1.3695) .0060 .2132
2002 γ0 -.0077 (-2.9168) .0026 .0224
γ1 .0046 (.9139) .0050 .3911
γ2 -.0059 (-2.7438) .0022 .0288
88 International Research Journal of Finance and Economics - Issue 4 (2006)
Table 8: Testing for Non-Systematic risk (yearly series, Equation 6)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0016 (.7266) .0022 .4948
γ1 .0096 (1.2809) .0075 .2475
γ2 -.0037 (-.5703) .0065 .5892
γ3 3.0751 (.5862) 1.9615 .1680
1999 γ0 .0017 (1.4573) .0125 .1953
γ1 -.0043 (-.0168) .0211 .9846
γ2 .0015 (.0201) .0099 .9846
γ3 .3503 (2.2471) 1.4278 .0657
2000 γ0 -.0203 (-4.6757) .0043 .0034
γ1 .0199 (2.2305) .0089 .0106
γ2 -.0185 (-3.6545) .0051 .0106
γ3 2.2673 (2.2673) .9026 .0639
2001 γ0 .0062 (.6019) .0103 .5693
γ1 -.0193 (-1.0682) .0181 .3265
γ2 .0053 (.5635) .0094 .5935
γ3 1.7024 (.4324) 3.9369 .6805
2002 γ0 -.0049 (-.9507) .0052 .3785
γ1 .0000 (.0054) .0089 .9959
γ2 -.0026 (-.4576) .0058 .6633
γ3 -5.1548 (-.6265) 8.2284 .5541
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
2002.
The findings of the article are not supportive of the theory’s 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 combined 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 CAPM’s 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 the study contradict the above hypothesis
and indicate evidence against the CAPM.
The inclusion 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 strong 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 not 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
portfolio. 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.
The tests may provide evidence against the CAPM but that does not necessarily constitute evidence
in support of any alternative model.
90 International Research Journal of Finance and Economics - Issue 4 (2006)
References
[1] Amihud Yakov, Christensen Bent and Mendelson Haim, 1992. Further evidence on the risk
relationship. Working paper S-93-11. Salomon Brother Center for the Study of the Financial
Institutions, Graduate School of Business Administration, New York University.
[2] Bailey J.W, Alexander J.G, Sharpe W.1998. Investments. 6th edition, London: Prentice-Hall.
[3] Banz, R. 1981. The relationship between returns and market value of common stock. Journal of
Financial Economics 9: 3-18.
[4] Basu Sanjoy. 1977. Investment performance of common stocks in relation to their priceearnings
ratios: A test of the efficient market hypothesis. Journal of Finance 32:663-82.
[5] Bekaert, G., Harvey, C. 1997. Emerging equity market volatility. Journal of Financial
Economics 43: 29-78.
[6] Black, F., Jensen, M. C. and Scholes, M. 1972. The Capital asset pricing model: Some
empirical tests. Studies in the Theory of Capital Markets. pp.79-121. New York: Praeger.
[7] Black, Fischer. 1993. Beta and return. Journal of Portfolio Management 20: 8-18.
[8] Blume, M. 1975. Betas and their regression tendencies. Journal of Finance 30: 785-795.
[9] Bodie, Z., Kane, A. and Marcus, A. J. 1999. Investments. 4th edition, New York New York:
McGraw- Hill.
[10] Brealey, R.A., and S.C. Meyers. 2002. Principles of Corporate Finance. New York: McGraw-
Hill.
[11] Campbell, J. Y., Lo, A. W. and MacKinlay, A. C. 1997. The Econometrics of Financial
Markets. Princeton, N. J.: Princeton University Press.
[12] Chan L., Hamao Y., Lakonishok J. 1991. Fundamentals and stock returns in Japan .Journal of
Finance 46 :1739-64.
[13] Chen, N., R. Roll, and S. A. Ross 1986. Economic forces and the stock market. Journal of
Business 59: 383-403.
[14] Cochrane, J. H. 1991. Volatility tests and efficient markets: A Review Essay. Journal of
Monetary Economics 127: 463-485.
[15] Cochrane, John H. 2001. Asset Pricing. Princeton, N. J.: Princeton University Press.
[16] Elton, E. J. and Gruber, M. J. 1995. Modern Portfolio Theory and Investment Analysis. 5th
edition, New York: John: Wiley & Sons, Inc.
[17] Fama, E. and K. French. 1992. The cross-section of expected stock returns Journal of Finance
47: 427-465.
[18] Fama, E. and K. French. 1993. Common risk factors in the returns on stocks and bonds. Journal
of Financial Economics 33: 3-56
[19] Fama, E. F. 1976. Foundations of Finance. New York: Basic Books.
[21] Fama, E. F. and MacBeth, J. 1973. Risk, return and equilibrium: Empirical tests. Journal of
Political Economy 81: 607-636.
[22] Fama, E. F., 1991. Efficient Capital Markets II. Journal of Finance 46: 1575-1617.
[23] Gibbons, M. R., S. A. Ross, and J. Shanken. 1989. A test of the efficiency of a given portfolio.
Econometrica 57: 1121-1152.
[24] Graham, J. R., Harvey, C. R. 2001. The theory and practice of corporate finance: Evidence
from the field, Journal of Financial Economics 60: 187-243.
[25] Greene, William H. Econometric Analysis. 4th Edition, London: Prentice Hall.
[26] Hamilton, James D. 1994. Time Series Analysis. Princeton University Press, Princeton
[27] Jagannathan, R. and McGratten, E. R. 1995. The CAPM Debate. Quarterly Review of the
Federal Reserve Bank of Minneapolis 19: 2-17.
[28] Jagannathan, R. and Wang, Z. 1996. The conditional CAPM and the cross-section of expected
returns. Journal of Finance 51: 3-53.
International Research Journal of Finance and Economics - Issue 4 (2006) 91
[29] Johnston, J. and DiNardo, J. 1997. Econometric Methods. 4th edition, New York: Mc-Graw-
Hill.
[30] Kothari S.P., Shaken Jay and Sloan Richard G. 1995. Another look at the cross section of
expected stock returns. Journal of Finance 50: 185-224.
[31] Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock
portfolios and capital budgets, Review of Economics and Statistics 47: 13-37.
[32] Miller, M.H., and Scholes , M. 1972. Rates of return in relation to risk: a re-examination of
some recent findings , in Jensen (ed.). Studies in the theory of capital markets. New York:
Praegar.
[33] Mossin, J. 1966. Equilibrium in a capital asset market. Econometrica 34: 768-783.
[34] Rosenberg B., Reid K., Lanstein R. 1985. Persuasive evidence of market inefficiency. Journal
of Portfolio Management 11: 9-17.
[35] Sharpe, W. 1964. Capital asset prices: a theory of market equilibrium under conditions of risk.
Journal of Finance 33:885-901.
[36] Sharpe, William F. Investments. 3rd edition, London: Prentice Hall International editions
[37] Stambaugh, R. F. 1999. Predictive regressions. Journal of Financial Economics 54
[38] Statman Dennis. 1980. Book values and stock returns, Chicago MBA: A Journal of Selected
Papers 4:25-45.
[39] Stein, J. C. 1996. Rational capital budgeting in an irrational world. Journal of Business 69: 429-
55.
[40] Stewart, J. and Gill, L. 1998. Econometrics. 2nd edition, London: Prentice-Hall.International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 4 (2006)
© EuroJournals Publishing, Inc. 2006
http://www.eurojournals.com/finance.htm
Testing the Capital Asset Pricing Model (CAPM): The Case of
the Emerging Greek Securities Market
Grigoris Michailidis
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: mgrigori@uom.gr
Tel: 00302310891889
Stavros Tsopoglou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: tsopstav@uom.gr
Tel: 00302310891889
Demetrios Papanastasiou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: papanast@uom.gr
Tel: 00302310891878
Eleni Mariola
Hagan School of Business, Iona College
New Rochelle
Abstract
The article examines the Capital Asset Pricing Model (CAPM) for the Greek stock
market using weekly stock returns from 100 companies listed on the Athens stock
exchange for the period of January 1998 to December 2002. In order to diversify away the
firm-specific part of returns thereby enhancing the precision of the beta estimates, the
securities where grouped into portfolios. The findings of this article are not supportive of
the theory’s basic statement that higher risk (beta) is associated with higher levels of return.
The model does explain, however, excess returns and thus lends support to the linear
structure of the CAPM equation.
The CAPM’s prediction for the intercept is that it should equal zero and the slope
should equal the excess returns on the market portfolio. The results of the study refute the
above hypothesis and offer evidence against the CAPM. The tests conducted to examine
the nonlinearity of the relationship between return and betas support the hypothesis that the
expected return-beta relationship is linear. Additionally, this paper investigates whether the
CAPM adequately captures all-important determinants of returns including the residual
International Research Journal of Finance and Economics - Issue 4 (2006) 79
variance of stocks. The results demonstrate that residual risk has no effect on the expected
returns of portfolios. Tests may provide evidence against the CAPM but they do not
necessarily constitute evidence in support of any alternative model (JEL G11, G12, and
G15).
Key words: CAPM, Athens Stock Exchange, portfolio returns, beta, risk free rate, stocks
JEL Classification: F23, G15
I. Introduction
Investors and financial researchers have paid considerable attention during the last few years to the
new equity markets that have emerged around the world. This new interest has undoubtedly been
spurred by the large, and in some cases extraordinary, returns offered by these markets. Practitioners
all over the world use a plethora of models in their portfolio selection process and in their attempt to
assess the risk exposure to different assets.
One of the most important developments in modern capital theory is the capital asset pricing model
(CAPM) as developed by Sharpe [1964], Lintner [1965] and Mossin [1966]. CAPM suggests that high
expected returns are associated with high levels of risk. Simply stated, CAPM postulates that the
expected return on an asset above the risk-free rate is linearly related to the non-diversifiable risk as
measured by the asset’s beta. Although the CAPM has been predominant in empirical work over the
past 30 years and is the basis of modern portfolio theory, accumulating research has increasingly cast
doubt on its ability to explain the actual movements of asset returns.
The purpose of this article is to examine thoroughly if the CAPM holds true in the capital market of
Greece. Tests are conducted for a period of five years (1998-2002), which is characterized by intense
return volatility (covering historically high returns for the Greek Stock market as well as significant
decrease in asset returns over the examined period). These market return characteristics make it
possible to have an empirical investigation of the pricing model on differing financial conditions thus
obtaining conclusions under varying stock return volatility.
Existing financial literature on the Athens stock exchange is rather scanty and it is the goal of this
study to widen the theoretical analysis of this market by using modern finance theory and to provide
useful insights for future analyses of this market.
II. Empirical appraisal of the model and competing studies of the model’s validity
2.1. Empirical appraisal of CAPM
Since its introduction in early 1960s, CAPM has been one of the most challenging topics in financial
economics. Almost any manager who wants to undertake a project must justify his decision partly
based on CAPM. The reason is that the model provides the means for a firm to calculate the return that
its investors demand. This model was the first successful attempt to show how to assess the risk of the
cash flows of a potential investment project, to estimate the project’s cost of capital and the expected
rate of return that investors will demand if they are to invest in the project.
The model was developed to explain the differences in the risk premium across assets. According to
the theory these differences are due to differences in the riskiness of the returns on the assets. The
model states that the correct measure of the riskiness of an asset is its beta and that the risk premium
per unit of riskiness is the same across all assets. Given the risk free rate 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 academic debate
about its usefulness and validity. In general, the empirical testing of CAPM has two broad purposes
(Baily et al, [1998]): (i) to test whether or not the theories should be rejected (ii) to provide information
that can aid financial decisions. To accomplish (i) tests are conducted which could potentially at least
reject the model. The model passes the test if it is not possible to reject the hypothesis that it is true.
Methods of statistical analysis need to be applied in order to draw reliable conclusions on whether the
80 International Research Journal of Finance and Economics - Issue 4 (2006)
model is supported by the data. To accomplish (ii) the empirical work uses the theory as a vehicle for
organizing and interpreting the data without seeking ways of rejecting the theory. This kind of
approach is found in the area of portfolio decision-making, in particular with regards to the selection of
assets to the bought or sold. For example, investors are advised to buy or sell assets that according to
CAPM are underpriced or overpriced. In this case empirical analysis is needed to evaluate the assets,
assess their riskiness, analyze them, and place them into their respective categories. A second
illustration of the latter methodology appears in corporate finance where the estimated beta coefficients
are used in assessing the riskiness of different investment projects. It is then possible to calculate
“hurdle 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 1960’s, 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 1960’s by Sharpe [1964], Lintner [1965] and Mossin [1966]. In
its simple form, the CAPM predicts that the expected return on an asset above the risk-free rate is
linearly related to the non-diversifiable risk, which is measured by the asset’s beta.
One of the earliest empirical studies that found supportive evidence for CAPM is that of Black,
Jensen and Scholes [1972]. Using monthly return data and portfolios rather than individual stocks,
Black et al tested whether the cross-section of expected returns is linear in beta. By combining
securities into portfolios one can diversify away most 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 measurement errors in beta
estimates. The authors found that the data are consistent with the predictions of the CAPM i.e. the
relation between the average return and beta is very close to linear and that portfolios with high (low)
betas have high (low) average returns.
Another classic empirical study that supports the theory is that of Fama and McBeth [1973]; they
examined whether there is a positive linear relation between average returns and beta. Moreover, the
authors investigated whether the squared value of beta and the volatility of asset returns can explain the
residual variation in average returns across assets that are not explained by beta alone.
2.3. Challenges to the validity of the theory
In the early 1980s several studies suggested that there were deviations from the linear CAPM riskreturn
trade-off due to other variables that affect this tradeoff. The purpose of the above studies was to
find the components that CAPM was missing in explaining the risk-return trade-off and to identify 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 CAPM’s 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 concluded that the average returns on
stocks of small firms (those with low market values of equity) were higher than the average returns on
stocks of large firms (those with high market values of equity). This finding has become known as the
size effect.
The research has been expanded by examining different sets of variables that might affect the riskreturn
tradeoff. In particular, the earnings yield (Basu [1977]), leverage, and the ratio of a firm’s 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 utilized in testing the validity of CAPM.
International Research Journal of Finance and Economics - Issue 4 (2006) 81
The general reaction to Banz’s [1981] findings, that CAPM may be missing some aspects of reality,
was to support the view that although the data may suggest deviations from CAPM, these deviations
are not so important as to reject the theory.
However, this idea has been challenged by Fama and French [1992]. They showed that Banz’s
findings might be economically so important that it raises serious questions about the validity of the
CAPM. Fama and French [1992] used the same procedure as Fama and McBeth [1973] but arrived at
very different conclusions. Fama and McBeth find a positive relation between return and risk while
Fama and French find no relation at all.
2.4. The academic debate continues
The Fama and French [1992] study has itself been criticized. In general the studies responding to the
Fama and French challenge by and large take a closer look at the data used in the study. Kothari,
Shaken and Sloan [1995] argue that Fama and French’s [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
too noisy to invalidate the CAPM. In fact, they show that when a more efficient statistical method is
used, 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 sample period effect i.e. the size
effect is observed in some periods and not in others.
Despite the above criticisms, 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 basic assumptions made to facilitate the empirical analysis. For example, most
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 constantly changing. When one considers a time-varying return distribution, one must refer
to the conditional mean, variance, and covariance that change depending on currently available
information. In contrast, the usual estimates of return, variance, and average squared deviations over a
sample period, provide an unconditional 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 generalized 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
also been numerous modifications to the models and whether the earliest or the subsequent alternative
models validate or not the CAPM is yet to be determined.
III. Sample selection and Data
3.1. Sample Selection
The study 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 100 stocks that are included in the formation of the FTSE/ASE 20,
FTSE/ASE Mid 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 following 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 Economics - Issue 4 (2006)
(ii) The FTSE/ASE Mid 40 index is the mid cap index and captures the performance 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 included in the indices are traded on the ASE on a continuous basis throughout the
full Athens stock exchange trading day, and are chosen according to prespecified liquidity criteria set
by the ASE Advisory Committee1.
For the purpose of the study, 100 stocks were selected from the pool of securities included 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 irregularly
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 order to obtain better estimates of the value of the beta coefficient, the study utilizes weekly
stock returns. Returns calculated using a longer time period (e.g. monthly) 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 span can result in the use of
very noisy data and thus yield inefficient estimates.
All stock returns used in the study are adjusted for dividends as required by the CAPM.
The ASE Composite 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 highly capitalized shares of the main market, and
reflects general trends of the Greek stock market.
Furthermore, the 3-month Greek Treasury 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 Bank of Greece. The yield
on the 3-month Treasury bill is specifically chosen as the benchmark that better reflects the short-term
changes in the Greek financial markets.
IV. Methodology
The first step 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 stock’s weekly return
against the market index according to the following equation:
ft Rit -R ft = ai +βi ⋅ (Rmt -R ) + eit (1)
where,
it R is the return on stock i (i=1…100),
ft R is the rate of return on a risk-free asset,
mt R is the rate of return on the market index,
i β
is the estimate of beta for the stock i , and
eit is the corresponding random disturbance term in the regression equation.
[Equation 1 could also be expressed using excess return notation, where ( - )= it ft it R R r and
ft mt ( - )=r mt R R ]
In spite of the fact that weekly returns were used to avoid short-term noise effects the estimation
diagnostic tests for equation (1) indicated, in several occasions, departures from the linear assumption.
1 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 excess returns of stocks ( rpt ) ordered according to
their beta coefficient computed by Equation 1. Let,
1 r = =
Σk
it
i
pt
r
k
(2)
where,
k is the number of stocks included in each portfolio (k=1…10),
p is the number of portfolios (p=1…10),
it r is the excess 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 clearly examined. The most obvious way to form portfolios is to rank 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 likely to have a positive measurement error in estimating beta. This would introduce a
positive bias into beta for high-beta portfolios and would introduce a negative bias into an estimate of
the intercept. (Elton and Gruber [1995], p. 333).
Combining securities into portfolios diversifies away most of the firm-specific 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 measurement error in the
beta estimates.
The following equation was used to estimate portfolio betas:
mt = + ⋅ r + e pt p p pt r a β (3)
where,
rpt is the average excess portfolio return,
p β is the calculated portfolio beta.
The study continues by estimating the ex-post Security Market Line (SML) by regressing the
portfolio returns against the portfolio betas obtained by Equation 3. The relation examined is the
following:
0 1 = + +e P P P r γ γ ⋅β (4)
where,
p r 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 β is an estimate of beta of the portfolio p ,
1 γ is the market price of risk, the risk premium for bearing one unit of beta risk,
0 γ is the zero-beta rate, the expected return on an asset which has a beta of zero, and
ep is random disturbance term in the regression equation.
In order to test for nonlinearity between total portfolio returns and betas, a regression was run on
average portfolio returns, calculated portfolio beta, and beta-square from equation 3:
2
0 1 2 = + + +e p p p p r γ γ ⋅β γ ⋅β (5)
Finally in order to examine whether the residual variance of stocks affects portfolio returns, an
additional term was included in equation 5, to test for the explanatory power of nonsystematic risk:
2
0 1 2 3 p = + + + RV+e p p p p r γ γ ⋅β γ ⋅β γ ⋅ (6)
where
84 International Research Journal of Finance and Economics - Issue 4 (2006)
RVp is the residual variance of portfolio returns (Equation 3), = 2 (e ) p pt RV σ .
The estimated parameters allow us to test a series of hypotheses regarding the CAPM. The tests are:
i) 3 γ = 0 or residual risk does not affect return,
ii) 2 γ = 0 or there are no nonlinearities in the security market line,
iii) 1 γ > 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 also conducted for each year separately (1998-2002), by changing
the portfolio compositions according to yearly estimated betas.
V. Empirical results and Interpretation of the findings
The first part of the methodology 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 range of the estimated stock betas is between 0.0984 the minimum and 1.4369 the maximum
with a standard deviation of 0.2240 (Table 1). Most 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 accurate estimation of betas an EGARCH (1,1) model was used wherever it was
necessary, in order to correct for nonlinearities.
Table 1: Stock beta coefficient estimates (Equation 1)
Stock name beta Stock name beta Stock name beta Stock name beta
OLYMP .0984 THEMEL .8302 PROOD .9594 EMP 1.1201
EYKL .4192 AIOLK .8303 ALEK .9606 NAOYK 1.1216
MPELA .4238 AEGEK .8305 EPATT .9698 ELBE 1.1256
MPTSK .5526 AEEXA .8339 SIDEN .9806 ROKKA 1.1310
FOIN .5643 SPYR .8344 GEK .9845 SELMK 1.1312
GKOYT .5862 SARANT .8400 ELYF .9890 DESIN 1.1318
PAPAK .6318 ELTEX .8422 MOYZK .9895 ELBAL 1.1348
ABK .6323 ELEXA .8427 TITK .9917 ESK 1.1359
MYTIL .6526 MPENK .8610 NIKAS .9920 TERNA 1.1392
FELXO .6578 HRAKL .8668 ETHENEX 1.0059 KERK 1.1396
ABAX .6874 PEIR .8698 IATR 1.0086 POYL 1.1432
TSIP .6950 BIOXK .8747 METK 1.0149 EEGA 1.1628
AAAK .7047 ELMEK .8830 ALPHA 1.0317 KALSK 1.1925
EEEK .7097 LAMPSA .8848 AKTOR 1.0467 GENAK 1.1996
ERMHS .7291 MHXK .8856 INTKA 1.0532 FANKO 1.2322
LAMDA .7297 DK .8904 MAIK 1.0542 PLATH 1.2331
OTE .7309 FOLI .9005 PETZ 1.0593 STRIK 1.2500
MARF .7423 THELET .9088 ETEM 1.0616 EBZ 1.2520
MRFKO .7423 ATT .9278 FINTO 1.0625 ALLK 1.2617
KORA .7520 ARBA .9302 ESXA 1.0654 GEBKA 1.2830
RILK .7682 KATS .9333 BIOSK 1.0690 AXON 1.3030
LYK .7684 ALBIO .9387 XATZK 1.0790 RINTE 1.3036
ELASK .7808 XAKOR .9502 KREKA 1.0911 KLONK 1.3263
NOTOS .8126 SAR .9533 ETE 1.1127 ETMAK 1.3274
KARD .8290 NAYP .9577 SANYO 1.1185 ALTEK 1.4369
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
The 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 higher beta
portfolios are related with higher returns. Portfolio 10 for example, the highest beta portfolio
(β = 1.2024), yields negative portfolio returns. In contrast, portfolio 1, the lowest beta portfolio
(β = 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: Average excess portfolio returns and betas (Equation 3)
Portfolio rp beta (p) Var. Error R2
a10 .0001 .5474 .0012 .4774
b10 .0000 .7509 .0013 .5335
c10 -.0007 .9137 .0014 .5940
d10 -.0004 .9506 .0014 .6054
e10 -.0008 .9300 .0009 .7140
f10 -.0009 .9142 .0010 .6997
g10 -.0006 1.0602 .0012 .6970
h10 -.0013 1.1066 .0019 .6057
i10 -.0004 1.1293 .0020 .6034
j10 -.0004 1.2024 .0026 .5691
Average Rf .0014
Average rm=(Rm-Rf) .0001
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
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 approximation of the risk-free rate. For theRm , the ASE Composite Share index is
taken as the best approximation for the market portfolio.
The basic equation used was 0 1 = + +e P P P r γ γ ⋅β (Equation 4) where 0 γ is the expected excess
return on a zero beta portfolio and 1 γ 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 intercept 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 combined into portfolios. This approach 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 tend to be
larger compared to those on suitably 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 another than the
shares of individual companies.
The high value of the estimated correlation 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 γ0 γ1
Value .0005 -.0011
t-value (.9011) (-1.8375)
p-value .3939 .1034
Residual 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 = γ γ ρ .9818
However, the fact that the intercept has a value around zero weakens the above explanation. The
results of this paper appear to be inconsistent 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 CAPM’s prediction for 0 γ 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
clearly 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 also 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
(0.0014), 1 γ was negative and different from zero while 2 γ , 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 relationship is linear (Table 4).
Table 4: Testing for Non-linearity (Equation 5)
Coefficient γ0 γ1 γ2
Value .0036 -.0084 .0041
t-value (1.7771) (-1.8013) (1.5686)
p-value 0.1188 0.1147 0.1607
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
According 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 task 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 γ 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) 87
Table 5: Testing for Non-Systematic risk (Equation 6)
Coefficient γ0 γ1 γ2 γ3
Value .0017 -.0043 .0015 .3503
t-value (.5360) (-.6182) (.3381) (.8035)
p-value 0.6113 0.5591 0.7468 0.4523
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
Since the analysis on the entire five-year period did not yield strong 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)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0053 (3.7665) .0014 .0050
γ1 .0050 (2.2231) .0022 .0569
1999 γ0 .0115 (2.8145) .0041 .2227
γ1 .0134 (4.0237) .0033 .0038
2000 γ0 -.0035 (-1.9045) .0019 .0933
γ1 -.0149 (-9.4186) .0016 .0000
2001 γ0 .0000 (.0025) .0024 .9981
γ1 -.0057 (-2.4066) .0028 .0427
2002 γ0 -.0017 (-.8452) .0020 .4226
γ1 -.0088 (-5.3642) .0016 .0007
Table 7: Testing for Non-linearity (yearly series, Equation 5)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0035 (1.7052) .0020 .1319
γ1 .0139 (1.7905) .0077 .1165
γ2 -.0078 (-1.1965) .0065 .2705
1999 γ0 .0030 (2.1093) .0142 .0729
γ1 -.0193 (-.7909) .0243 .4549
γ2 .0135 (1.3540) .0026 .0100
2000 γ0 -.0129 (-3.5789) .0036 .0090
γ1 .0036 (.5435) .0067 .6037
γ2 -.0083 (-2.8038) .0030 .0264
2001 γ0 .0092 (1.2724) .0072 .2439
γ1 -.0240 (-1.7688) .0136 .1202
γ2 .0083 (1.3695) .0060 .2132
2002 γ0 -.0077 (-2.9168) .0026 .0224
γ1 .0046 (.9139) .0050 .3911
γ2 -.0059 (-2.7438) .0022 .0288
88 International Research Journal of Finance and Economics - Issue 4 (2006)
Table 8: Testing for Non-Systematic risk (yearly series, Equation 6)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0016 (.7266) .0022 .4948
γ1 .0096 (1.2809) .0075 .2475
γ2 -.0037 (-.5703) .0065 .5892
γ3 3.0751 (.5862) 1.9615 .1680
1999 γ0 .0017 (1.4573) .0125 .1953
γ1 -.0043 (-.0168) .0211 .9846
γ2 .0015 (.0201) .0099 .9846
γ3 .3503 (2.2471) 1.4278 .0657
2000 γ0 -.0203 (-4.6757) .0043 .0034
γ1 .0199 (2.2305) .0089 .0106
γ2 -.0185 (-3.6545) .0051 .0106
γ3 2.2673 (2.2673) .9026 .0639
2001 γ0 .0062 (.6019) .0103 .5693
γ1 -.0193 (-1.0682) .0181 .3265
γ2 .0053 (.5635) .0094 .5935
γ3 1.7024 (.4324) 3.9369 .6805
2002 γ0 -.0049 (-.9507) .0052 .3785
γ1 .0000 (.0054) .0089 .9959
γ2 -.0026 (-.4576) .0058 .6633
γ3 -5.1548 (-.6265) 8.2284 .5541
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
2002.
The findings of the article are not supportive of the theory’s 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 combined 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 CAPM’s 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 the study contradict the above hypothesis
and indicate evidence against the CAPM.
The inclusion 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 strong 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 not 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
portfolio. 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.
The tests may provide evidence against the CAPM but that does not necessarily constitute evidence
in support of any alternative model.
90 International Research Journal of Finance and Economics - Issue 4 (2006)
References
[1] Amihud Yakov, Christensen Bent and Mendelson Haim, 1992. Further evidence on the risk
relationship. Working paper S-93-11. Salomon Brother Center for the Study of the Financial
Institutions, Graduate School of Business Administration, New York University.
[2] Bailey J.W, Alexander J.G, Sharpe W.1998. Investments. 6th edition, London: Prentice-Hall.
[3] Banz, R. 1981. The relationship between returns and market value of common stock. Journal of
Financial Economics 9: 3-18.
[4] Basu Sanjoy. 1977. Investment performance of common stocks in relation to their priceearnings
ratios: A test of the efficient market hypothesis. Journal of Finance 32:663-82.
[5] Bekaert, G., Harvey, C. 1997. Emerging equity market volatility. Journal of Financial
Economics 43: 29-78.
[6] Black, F., Jensen, M. C. and Scholes, M. 1972. The Capital asset pricing model: Some
empirical tests. Studies in the Theory of Capital Markets. pp.79-121. New York: Praeger.
[7] Black, Fischer. 1993. Beta and return. Journal of Portfolio Management 20: 8-18.
[8] Blume, M. 1975. Betas and their regression tendencies. Journal of Finance 30: 785-795.
[9] Bodie, Z., Kane, A. and Marcus, A. J. 1999. Investments. 4th edition, New York New York:
McGraw- Hill.
[10] Brealey, R.A., and S.C. Meyers. 2002. Principles of Corporate Finance. New York: McGraw-
Hill.
[11] Campbell, J. Y., Lo, A. W. and MacKinlay, A. C. 1997. The Econometrics of Financial
Markets. Princeton, N. J.: Princeton University Press.
[12] Chan L., Hamao Y., Lakonishok J. 1991. Fundamentals and stock returns in Japan .Journal of
Finance 46 :1739-64.
[13] Chen, N., R. Roll, and S. A. Ross 1986. Economic forces and the stock market. Journal of
Business 59: 383-403.
[14] Cochrane, J. H. 1991. Volatility tests and efficient markets: A Review Essay. Journal of
Monetary Economics 127: 463-485.
[15] Cochrane, John H. 2001. Asset Pricing. Princeton, N. J.: Princeton University Press.
[16] Elton, E. J. and Gruber, M. J. 1995. Modern Portfolio Theory and Investment Analysis. 5th
edition, New York: John: Wiley & Sons, Inc.
[17] Fama, E. and K. French. 1992. The cross-section of expected stock returns Journal of Finance
47: 427-465.
[18] Fama, E. and K. French. 1993. Common risk factors in the returns on stocks and bonds. Journal
of Financial Economics 33: 3-56
[19] Fama, E. F. 1976. Foundations of Finance. New York: Basic Books.
[21] Fama, E. F. and MacBeth, J. 1973. Risk, return and equilibrium: Empirical tests. Journal of
Political Economy 81: 607-636.
[22] Fama, E. F., 1991. Efficient Capital Markets II. Journal of Finance 46: 1575-1617.
[23] Gibbons, M. R., S. A. Ross, and J. Shanken. 1989. A test of the efficiency of a given portfolio.
Econometrica 57: 1121-1152.
[24] Graham, J. R., Harvey, C. R. 2001. The theory and practice of corporate finance: Evidence
from the field, Journal of Financial Economics 60: 187-243.
[25] Greene, William H. Econometric Analysis. 4th Edition, London: Prentice Hall.
[26] Hamilton, James D. 1994. Time Series Analysis. Princeton University Press, Princeton
[27] Jagannathan, R. and McGratten, E. R. 1995. The CAPM Debate. Quarterly Review of the
Federal Reserve Bank of Minneapolis 19: 2-17.
[28] Jagannathan, R. and Wang, Z. 1996. The conditional CAPM and the cross-section of expected
returns. Journal of Finance 51: 3-53.
International Research Journal of Finance and Economics - Issue 4 (2006) 91
[29] Johnston, J. and DiNardo, J. 1997. Econometric Methods. 4th edition, New York: Mc-Graw-
Hill.
[30] Kothari S.P., Shaken Jay and Sloan Richard G. 1995. Another look at the cross section of
expected stock returns. Journal of Finance 50: 185-224.
[31] Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock
portfolios and capital budgets, Review of Economics and Statistics 47: 13-37.
[32] Miller, M.H., and Scholes , M. 1972. Rates of return in relation to risk: a re-examination of
some recent findings , in Jensen (ed.). Studies in the theory of capital markets. New York:
Praegar.
[33] Mossin, J. 1966. Equilibrium in a capital asset market. Econometrica 34: 768-783.
[34] Rosenberg B., Reid K., Lanstein R. 1985. Persuasive evidence of market inefficiency. Journal
of Portfolio Management 11: 9-17.
[35] Sharpe, W. 1964. Capital asset prices: a theory of market equilibrium under conditions of risk.
Journal of Finance 33:885-901.
[36] Sharpe, William F. Investments. 3rd edition, London: Prentice Hall International editions
[37] Stambaugh, R. F. 1999. Predictive regressions. Journal of Financial Economics 54
[38] Statman Dennis. 1980. Book values and stock returns, Chicago MBA: A Journal of Selected
Papers 4:25-45.
[39] Stein, J. C. 1996. Rational capital budgeting in an irrational world. Journal of Business 69: 429-
55.
[40] Stewart, J. and Gill, L. 1998. Econometrics. 2nd edition, London: Prentice-Hall.International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 4 (2006)
© EuroJournals Publishing, Inc. 2006
http://www.eurojournals.com/finance.htm
Testing the Capital Asset Pricing Model (CAPM): The Case of
the Emerging Greek Securities Market
Grigoris Michailidis
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: mgrigori@uom.gr
Tel: 00302310891889
Stavros Tsopoglou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: tsopstav@uom.gr
Tel: 00302310891889
Demetrios Papanastasiou
University of Macedonia, Economic and Social Sciences
Department of Applied Informatics
Thessaloniki, Greece
E-mail: papanast@uom.gr
Tel: 00302310891878
Eleni Mariola
Hagan School of Business, Iona College
New Rochelle
Abstract
The article examines the Capital Asset Pricing Model (CAPM) for the Greek stock
market using weekly stock returns from 100 companies listed on the Athens stock
exchange for the period of January 1998 to December 2002. In order to diversify away the
firm-specific part of returns thereby enhancing the precision of the beta estimates, the
securities where grouped into portfolios. The findings of this article are not supportive of
the theory’s basic statement that higher risk (beta) is associated with higher levels of return.
The model does explain, however, excess returns and thus lends support to the linear
structure of the CAPM equation.
The CAPM’s prediction for the intercept is that it should equal zero and the slope
should equal the excess returns on the market portfolio. The results of the study refute the
above hypothesis and offer evidence against the CAPM. The tests conducted to examine
the nonlinearity of the relationship between return and betas support the hypothesis that the
expected return-beta relationship is linear. Additionally, this paper investigates whether the
CAPM adequately captures all-important determinants of returns including the residual
International Research Journal of Finance and Economics - Issue 4 (2006) 79
variance of stocks. The results demonstrate that residual risk has no effect on the expected
returns of portfolios. Tests may provide evidence against the CAPM but they do not
necessarily constitute evidence in support of any alternative model (JEL G11, G12, and
G15).
Key words: CAPM, Athens Stock Exchange, portfolio returns, beta, risk free rate, stocks
JEL Classification: F23, G15
I. Introduction
Investors and financial researchers have paid considerable attention during the last few years to the
new equity markets that have emerged around the world. This new interest has undoubtedly been
spurred by the large, and in some cases extraordinary, returns offered by these markets. Practitioners
all over the world use a plethora of models in their portfolio selection process and in their attempt to
assess the risk exposure to different assets.
One of the most important developments in modern capital theory is the capital asset pricing model
(CAPM) as developed by Sharpe [1964], Lintner [1965] and Mossin [1966]. CAPM suggests that high
expected returns are associated with high levels of risk. Simply stated, CAPM postulates that the
expected return on an asset above the risk-free rate is linearly related to the non-diversifiable risk as
measured by the asset’s beta. Although the CAPM has been predominant in empirical work over the
past 30 years and is the basis of modern portfolio theory, accumulating research has increasingly cast
doubt on its ability to explain the actual movements of asset returns.
The purpose of this article is to examine thoroughly if the CAPM holds true in the capital market of
Greece. Tests are conducted for a period of five years (1998-2002), which is characterized by intense
return volatility (covering historically high returns for the Greek Stock market as well as significant
decrease in asset returns over the examined period). These market return characteristics make it
possible to have an empirical investigation of the pricing model on differing financial conditions thus
obtaining conclusions under varying stock return volatility.
Existing financial literature on the Athens stock exchange is rather scanty and it is the goal of this
study to widen the theoretical analysis of this market by using modern finance theory and to provide
useful insights for future analyses of this market.
II. Empirical appraisal of the model and competing studies of the model’s validity
2.1. Empirical appraisal of CAPM
Since its introduction in early 1960s, CAPM has been one of the most challenging topics in financial
economics. Almost any manager who wants to undertake a project must justify his decision partly
based on CAPM. The reason is that the model provides the means for a firm to calculate the return that
its investors demand. This model was the first successful attempt to show how to assess the risk of the
cash flows of a potential investment project, to estimate the project’s cost of capital and the expected
rate of return that investors will demand if they are to invest in the project.
The model was developed to explain the differences in the risk premium across assets. According to
the theory these differences are due to differences in the riskiness of the returns on the assets. The
model states that the correct measure of the riskiness of an asset is its beta and that the risk premium
per unit of riskiness is the same across all assets. Given the risk free rate 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 academic debate
about its usefulness and validity. In general, the empirical testing of CAPM has two broad purposes
(Baily et al, [1998]): (i) to test whether or not the theories should be rejected (ii) to provide information
that can aid financial decisions. To accomplish (i) tests are conducted which could potentially at least
reject the model. The model passes the test if it is not possible to reject the hypothesis that it is true.
Methods of statistical analysis need to be applied in order to draw reliable conclusions on whether the
80 International Research Journal of Finance and Economics - Issue 4 (2006)
model is supported by the data. To accomplish (ii) the empirical work uses the theory as a vehicle for
organizing and interpreting the data without seeking ways of rejecting the theory. This kind of
approach is found in the area of portfolio decision-making, in particular with regards to the selection of
assets to the bought or sold. For example, investors are advised to buy or sell assets that according to
CAPM are underpriced or overpriced. In this case empirical analysis is needed to evaluate the assets,
assess their riskiness, analyze them, and place them into their respective categories. A second
illustration of the latter methodology appears in corporate finance where the estimated beta coefficients
are used in assessing the riskiness of different investment projects. It is then possible to calculate
“hurdle 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 1960’s, 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 1960’s by Sharpe [1964], Lintner [1965] and Mossin [1966]. In
its simple form, the CAPM predicts that the expected return on an asset above the risk-free rate is
linearly related to the non-diversifiable risk, which is measured by the asset’s beta.
One of the earliest empirical studies that found supportive evidence for CAPM is that of Black,
Jensen and Scholes [1972]. Using monthly return data and portfolios rather than individual stocks,
Black et al tested whether the cross-section of expected returns is linear in beta. By combining
securities into portfolios one can diversify away most 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 measurement errors in beta
estimates. The authors found that the data are consistent with the predictions of the CAPM i.e. the
relation between the average return and beta is very close to linear and that portfolios with high (low)
betas have high (low) average returns.
Another classic empirical study that supports the theory is that of Fama and McBeth [1973]; they
examined whether there is a positive linear relation between average returns and beta. Moreover, the
authors investigated whether the squared value of beta and the volatility of asset returns can explain the
residual variation in average returns across assets that are not explained by beta alone.
2.3. Challenges to the validity of the theory
In the early 1980s several studies suggested that there were deviations from the linear CAPM riskreturn
trade-off due to other variables that affect this tradeoff. The purpose of the above studies was to
find the components that CAPM was missing in explaining the risk-return trade-off and to identify 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 CAPM’s 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 concluded that the average returns on
stocks of small firms (those with low market values of equity) were higher than the average returns on
stocks of large firms (those with high market values of equity). This finding has become known as the
size effect.
The research has been expanded by examining different sets of variables that might affect the riskreturn
tradeoff. In particular, the earnings yield (Basu [1977]), leverage, and the ratio of a firm’s 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 utilized in testing the validity of CAPM.
International Research Journal of Finance and Economics - Issue 4 (2006) 81
The general reaction to Banz’s [1981] findings, that CAPM may be missing some aspects of reality,
was to support the view that although the data may suggest deviations from CAPM, these deviations
are not so important as to reject the theory.
However, this idea has been challenged by Fama and French [1992]. They showed that Banz’s
findings might be economically so important that it raises serious questions about the validity of the
CAPM. Fama and French [1992] used the same procedure as Fama and McBeth [1973] but arrived at
very different conclusions. Fama and McBeth find a positive relation between return and risk while
Fama and French find no relation at all.
2.4. The academic debate continues
The Fama and French [1992] study has itself been criticized. In general the studies responding to the
Fama and French challenge by and large take a closer look at the data used in the study. Kothari,
Shaken and Sloan [1995] argue that Fama and French’s [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
too noisy to invalidate the CAPM. In fact, they show that when a more efficient statistical method is
used, 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 sample period effect i.e. the size
effect is observed in some periods and not in others.
Despite the above criticisms, 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 basic assumptions made to facilitate the empirical analysis. For example, most
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 constantly changing. When one considers a time-varying return distribution, one must refer
to the conditional mean, variance, and covariance that change depending on currently available
information. In contrast, the usual estimates of return, variance, and average squared deviations over a
sample period, provide an unconditional 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 generalized 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
also been numerous modifications to the models and whether the earliest or the subsequent alternative
models validate or not the CAPM is yet to be determined.
III. Sample selection and Data
3.1. Sample Selection
The study 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 100 stocks that are included in the formation of the FTSE/ASE 20,
FTSE/ASE Mid 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 following 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 Economics - Issue 4 (2006)
(ii) The FTSE/ASE Mid 40 index is the mid cap index and captures the performance 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 included in the indices are traded on the ASE on a continuous basis throughout the
full Athens stock exchange trading day, and are chosen according to prespecified liquidity criteria set
by the ASE Advisory Committee1.
For the purpose of the study, 100 stocks were selected from the pool of securities included 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 irregularly
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 order to obtain better estimates of the value of the beta coefficient, the study utilizes weekly
stock returns. Returns calculated using a longer time period (e.g. monthly) 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 span can result in the use of
very noisy data and thus yield inefficient estimates.
All stock returns used in the study are adjusted for dividends as required by the CAPM.
The ASE Composite 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 highly capitalized shares of the main market, and
reflects general trends of the Greek stock market.
Furthermore, the 3-month Greek Treasury 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 Bank of Greece. The yield
on the 3-month Treasury bill is specifically chosen as the benchmark that better reflects the short-term
changes in the Greek financial markets.
IV. Methodology
The first step 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 stock’s weekly return
against the market index according to the following equation:
ft Rit -R ft = ai +βi ⋅ (Rmt -R ) + eit (1)
where,
it R is the return on stock i (i=1…100),
ft R is the rate of return on a risk-free asset,
mt R is the rate of return on the market index,
i β
is the estimate of beta for the stock i , and
eit is the corresponding random disturbance term in the regression equation.
[Equation 1 could also be expressed using excess return notation, where ( - )= it ft it R R r and
ft mt ( - )=r mt R R ]
In spite of the fact that weekly returns were used to avoid short-term noise effects the estimation
diagnostic tests for equation (1) indicated, in several occasions, departures from the linear assumption.
1 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 excess returns of stocks ( rpt ) ordered according to
their beta coefficient computed by Equation 1. Let,
1 r = =
Σk
it
i
pt
r
k
(2)
where,
k is the number of stocks included in each portfolio (k=1…10),
p is the number of portfolios (p=1…10),
it r is the excess 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 clearly examined. The most obvious way to form portfolios is to rank 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 likely to have a positive measurement error in estimating beta. This would introduce a
positive bias into beta for high-beta portfolios and would introduce a negative bias into an estimate of
the intercept. (Elton and Gruber [1995], p. 333).
Combining securities into portfolios diversifies away most of the firm-specific 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 measurement error in the
beta estimates.
The following equation was used to estimate portfolio betas:
mt = + ⋅ r + e pt p p pt r a β (3)
where,
rpt is the average excess portfolio return,
p β is the calculated portfolio beta.
The study continues by estimating the ex-post Security Market Line (SML) by regressing the
portfolio returns against the portfolio betas obtained by Equation 3. The relation examined is the
following:
0 1 = + +e P P P r γ γ ⋅β (4)
where,
p r 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 β is an estimate of beta of the portfolio p ,
1 γ is the market price of risk, the risk premium for bearing one unit of beta risk,
0 γ is the zero-beta rate, the expected return on an asset which has a beta of zero, and
ep is random disturbance term in the regression equation.
In order to test for nonlinearity between total portfolio returns and betas, a regression was run on
average portfolio returns, calculated portfolio beta, and beta-square from equation 3:
2
0 1 2 = + + +e p p p p r γ γ ⋅β γ ⋅β (5)
Finally in order to examine whether the residual variance of stocks affects portfolio returns, an
additional term was included in equation 5, to test for the explanatory power of nonsystematic risk:
2
0 1 2 3 p = + + + RV+e p p p p r γ γ ⋅β γ ⋅β γ ⋅ (6)
where
84 International Research Journal of Finance and Economics - Issue 4 (2006)
RVp is the residual variance of portfolio returns (Equation 3), = 2 (e ) p pt RV σ .
The estimated parameters allow us to test a series of hypotheses regarding the CAPM. The tests are:
i) 3 γ = 0 or residual risk does not affect return,
ii) 2 γ = 0 or there are no nonlinearities in the security market line,
iii) 1 γ > 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 also conducted for each year separately (1998-2002), by changing
the portfolio compositions according to yearly estimated betas.
V. Empirical results and Interpretation of the findings
The first part of the methodology 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 range of the estimated stock betas is between 0.0984 the minimum and 1.4369 the maximum
with a standard deviation of 0.2240 (Table 1). Most 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 accurate estimation of betas an EGARCH (1,1) model was used wherever it was
necessary, in order to correct for nonlinearities.
Table 1: Stock beta coefficient estimates (Equation 1)
Stock name beta Stock name beta Stock name beta Stock name beta
OLYMP .0984 THEMEL .8302 PROOD .9594 EMP 1.1201
EYKL .4192 AIOLK .8303 ALEK .9606 NAOYK 1.1216
MPELA .4238 AEGEK .8305 EPATT .9698 ELBE 1.1256
MPTSK .5526 AEEXA .8339 SIDEN .9806 ROKKA 1.1310
FOIN .5643 SPYR .8344 GEK .9845 SELMK 1.1312
GKOYT .5862 SARANT .8400 ELYF .9890 DESIN 1.1318
PAPAK .6318 ELTEX .8422 MOYZK .9895 ELBAL 1.1348
ABK .6323 ELEXA .8427 TITK .9917 ESK 1.1359
MYTIL .6526 MPENK .8610 NIKAS .9920 TERNA 1.1392
FELXO .6578 HRAKL .8668 ETHENEX 1.0059 KERK 1.1396
ABAX .6874 PEIR .8698 IATR 1.0086 POYL 1.1432
TSIP .6950 BIOXK .8747 METK 1.0149 EEGA 1.1628
AAAK .7047 ELMEK .8830 ALPHA 1.0317 KALSK 1.1925
EEEK .7097 LAMPSA .8848 AKTOR 1.0467 GENAK 1.1996
ERMHS .7291 MHXK .8856 INTKA 1.0532 FANKO 1.2322
LAMDA .7297 DK .8904 MAIK 1.0542 PLATH 1.2331
OTE .7309 FOLI .9005 PETZ 1.0593 STRIK 1.2500
MARF .7423 THELET .9088 ETEM 1.0616 EBZ 1.2520
MRFKO .7423 ATT .9278 FINTO 1.0625 ALLK 1.2617
KORA .7520 ARBA .9302 ESXA 1.0654 GEBKA 1.2830
RILK .7682 KATS .9333 BIOSK 1.0690 AXON 1.3030
LYK .7684 ALBIO .9387 XATZK 1.0790 RINTE 1.3036
ELASK .7808 XAKOR .9502 KREKA 1.0911 KLONK 1.3263
NOTOS .8126 SAR .9533 ETE 1.1127 ETMAK 1.3274
KARD .8290 NAYP .9577 SANYO 1.1185 ALTEK 1.4369
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
The 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 higher beta
portfolios are related with higher returns. Portfolio 10 for example, the highest beta portfolio
(β = 1.2024), yields negative portfolio returns. In contrast, portfolio 1, the lowest beta portfolio
(β = 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: Average excess portfolio returns and betas (Equation 3)
Portfolio rp beta (p) Var. Error R2
a10 .0001 .5474 .0012 .4774
b10 .0000 .7509 .0013 .5335
c10 -.0007 .9137 .0014 .5940
d10 -.0004 .9506 .0014 .6054
e10 -.0008 .9300 .0009 .7140
f10 -.0009 .9142 .0010 .6997
g10 -.0006 1.0602 .0012 .6970
h10 -.0013 1.1066 .0019 .6057
i10 -.0004 1.1293 .0020 .6034
j10 -.0004 1.2024 .0026 .5691
Average Rf .0014
Average rm=(Rm-Rf) .0001
Source: Metastock (Greek) Data Base and calculations (S-PLUS)
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 approximation of the risk-free rate. For theRm , the ASE Composite Share index is
taken as the best approximation for the market portfolio.
The basic equation used was 0 1 = + +e P P P r γ γ ⋅β (Equation 4) where 0 γ is the expected excess
return on a zero beta portfolio and 1 γ 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 intercept 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 combined into portfolios. This approach 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 tend to be
larger compared to those on suitably 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 another than the
shares of individual companies.
The high value of the estimated correlation 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 γ0 γ1
Value .0005 -.0011
t-value (.9011) (-1.8375)
p-value .3939 .1034
Residual 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 = γ γ ρ .9818
However, the fact that the intercept has a value around zero weakens the above explanation. The
results of this paper appear to be inconsistent 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 CAPM’s prediction for 0 γ 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
clearly 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 also 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
(0.0014), 1 γ was negative and different from zero while 2 γ , 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 relationship is linear (Table 4).
Table 4: Testing for Non-linearity (Equation 5)
Coefficient γ0 γ1 γ2
Value .0036 -.0084 .0041
t-value (1.7771) (-1.8013) (1.5686)
p-value 0.1188 0.1147 0.1607
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
According 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 task 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 γ 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) 87
Table 5: Testing for Non-Systematic risk (Equation 6)
Coefficient γ0 γ1 γ2 γ3
Value .0017 -.0043 .0015 .3503
t-value (.5360) (-.6182) (.3381) (.8035)
p-value 0.6113 0.5591 0.7468 0.4523
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
Since the analysis on the entire five-year period did not yield strong 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)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0053 (3.7665) .0014 .0050
γ1 .0050 (2.2231) .0022 .0569
1999 γ0 .0115 (2.8145) .0041 .2227
γ1 .0134 (4.0237) .0033 .0038
2000 γ0 -.0035 (-1.9045) .0019 .0933
γ1 -.0149 (-9.4186) .0016 .0000
2001 γ0 .0000 (.0025) .0024 .9981
γ1 -.0057 (-2.4066) .0028 .0427
2002 γ0 -.0017 (-.8452) .0020 .4226
γ1 -.0088 (-5.3642) .0016 .0007
Table 7: Testing for Non-linearity (yearly series, Equation 5)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0035 (1.7052) .0020 .1319
γ1 .0139 (1.7905) .0077 .1165
γ2 -.0078 (-1.1965) .0065 .2705
1999 γ0 .0030 (2.1093) .0142 .0729
γ1 -.0193 (-.7909) .0243 .4549
γ2 .0135 (1.3540) .0026 .0100
2000 γ0 -.0129 (-3.5789) .0036 .0090
γ1 .0036 (.5435) .0067 .6037
γ2 -.0083 (-2.8038) .0030 .0264
2001 γ0 .0092 (1.2724) .0072 .2439
γ1 -.0240 (-1.7688) .0136 .1202
γ2 .0083 (1.3695) .0060 .2132
2002 γ0 -.0077 (-2.9168) .0026 .0224
γ1 .0046 (.9139) .0050 .3911
γ2 -.0059 (-2.7438) .0022 .0288
88 International Research Journal of Finance and Economics - Issue 4 (2006)
Table 8: Testing for Non-Systematic risk (yearly series, Equation 6)
Coefficient Value t-value Std. Error p-value
1998 γ0 .0016 (.7266) .0022 .4948
γ1 .0096 (1.2809) .0075 .2475
γ2 -.0037 (-.5703) .0065 .5892
γ3 3.0751 (.5862) 1.9615 .1680
1999 γ0 .0017 (1.4573) .0125 .1953
γ1 -.0043 (-.0168) .0211 .9846
γ2 .0015 (.0201) .0099 .9846
γ3 .3503 (2.2471) 1.4278 .0657
2000 γ0 -.0203 (-4.6757) .0043 .0034
γ1 .0199 (2.2305) .0089 .0106
γ2 -.0185 (-3.6545) .0051 .0106
γ3 2.2673 (2.2673) .9026 .0639
2001 γ0 .0062 (.6019) .0103 .5693
γ1 -.0193 (-1.0682) .0181 .3265
γ2 .0053 (.5635) .0094 .5935
γ3 1.7024 (.4324) 3.9369 .6805
2002 γ0 -.0049 (-.9507) .0052 .3785
γ1 .0000 (.0054) .0089 .9959
γ2 -.0026 (-.4576) .0058 .6633
γ3 -5.1548 (-.6265) 8.2284 .5541
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
2002.
The findings of the article are not supportive of the theory’s 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 combined 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 CAPM’s 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 the study contradict the above hypothesis
and indicate evidence against the CAPM.
The inclusion 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 strong 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 not 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
portfolio. 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.
The tests may provide evidence against the CAPM but that does not necessarily constitute evidence
in support of any alternative model.
90 International Research Journal of Finance and Economics - Issue 4 (2006)
References
[1] Amihud Yakov, Christensen Bent and Mendelson Haim, 1992. Further evidence on the risk
relationship. Working paper S-93-11. Salomon Brother Center for the Study of the Financial
Institutions, Graduate School of Business Administration, New York University.
[2] Bailey J.W, Alexander J.G, Sharpe W.1998. Investments. 6th edition, London: Prentice-Hall.
[3] Banz, R. 1981. The relationship between returns and market value of common stock. Journal of
Financial Economics 9: 3-18.
[4] Basu Sanjoy. 1977. Investment performance of common stocks in relation to their priceearnings
ratios: A test of the efficient market hypothesis. Journal of Finance 32:663-82.
[5] Bekaert, G., Harvey, C. 1997. Emerging equity market volatility. Journal of Financial
Economics 43: 29-78.
[6] Black, F., Jensen, M. C. and Scholes, M. 1972. The Capital asset pricing model: Some
empirical tests. Studies in the Theory of Capital Markets. pp.79-121. New York: Praeger.
[7] Black, Fischer. 1993. Beta and return. Journal of Portfolio Management 20: 8-18.
[8] Blume, M. 1975. Betas and their regression tendencies. Journal of Finance 30: 785-795.
[9] Bodie, Z., Kane, A. and Marcus, A. J. 1999. Investments. 4th edition, New York New York:
McGraw- Hill.
[10] Brealey, R.A., and S.C. Meyers. 2002. Principles of Corporate Finance. New York: McGraw-
Hill.
[11] Campbell, J. Y., Lo, A. W. and MacKinlay, A. C. 1997. The Econometrics of Financial
Markets. Princeton, N. J.: Princeton University Press.
[12] Chan L., Hamao Y., Lakonishok J. 1991. Fundamentals and stock returns in Japan .Journal of
Finance 46 :1739-64.
[13] Chen, N., R. Roll, and S. A. Ross 1986. Economic forces and the stock market. Journal of
Business 59: 383-403.
[14] Cochrane, J. H. 1991. Volatility tests and efficient markets: A Review Essay. Journal of
Monetary Economics 127: 463-485.
[15] Cochrane, John H. 2001. Asset Pricing. Princeton, N. J.: Princeton University Press.
[16] Elton, E. J. and Gruber, M. J. 1995. Modern Portfolio Theory and Investment Analysis. 5th
edition, New York: John: Wiley & Sons, Inc.
[17] Fama, E. and K. French. 1992. The cross-section of expected stock returns Journal of Finance
47: 427-465.
[18] Fama, E. and K. French. 1993. Common risk factors in the returns on stocks and bonds. Journal
of Financial Economics 33: 3-56
[19] Fama, E. F. 1976. Foundations of Finance. New York: Basic Books.
[21] Fama, E. F. and MacBeth, J. 1973. Risk, return and equilibrium: Empirical tests. Journal of
Political Economy 81: 607-636.
[22] Fama, E. F., 1991. Efficient Capital Markets II. Journal of Finance 46: 1575-1617.
[23] Gibbons, M. R., S. A. Ross, and J. Shanken. 1989. A test of the efficiency of a given portfolio.
Econometrica 57: 1121-1152.
[24] Graham, J. R., Harvey, C. R. 2001. The theory and practice of corporate finance: Evidence
from the field, Journal of Financial Economics 60: 187-243.
[25] Greene, William H. Econometric Analysis. 4th Edition, London: Prentice Hall.
[26] Hamilton, James D. 1994. Time Series Analysis. Princeton University Press, Princeton
[27] Jagannathan, R. and McGratten, E. R. 1995. The CAPM Debate. Quarterly Review of the
Federal Reserve Bank of Minneapolis 19: 2-17.
[28] Jagannathan, R. and Wang, Z. 1996. The conditional CAPM and the cross-section of expected
returns. Journal of Finance 51: 3-53.
International Research Journal of Finance and Economics - Issue 4 (2006) 91
[29] Johnston, J. and DiNardo, J. 1997. Econometric Methods. 4th edition, New York: Mc-Graw-
Hill.
[30] Kothari S.P., Shaken Jay and Sloan Richard G. 1995. Another look at the cross section of
expected stock returns. Journal of Finance 50: 185-224.
[31] Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock
portfolios and capital budgets, Review of Economics and Statistics 47: 13-37.
[32] Miller, M.H., and Scholes , M. 1972. Rates of return in relation to risk: a re-examination of
some recent findings , in Jensen (ed.). Studies in the theory of capital markets. New York:
Praegar.
[33] Mossin, J. 1966. Equilibrium in a capital asset market. Econometrica 34: 768-783.
[34] Rosenberg B., Reid K., Lanstein R. 1985. Persuasive evidence of market inefficiency. Journal
of Portfolio Management 11: 9-17.
[35] Sharpe, W. 1964. Capital asset prices: a theory of market equilibrium under conditions of risk.
Journal of Finance 33:885-901.
[36] Sharpe, William F. Investments. 3rd edition, London: Prentice Hall International editions
[37] Stambaugh, R. F. 1999. Predictive regressions. Journal of Financial Economics 54
[38] Statman Dennis. 1980. Book values and stock returns, Chicago MBA: A Journal of Selected
Papers 4:25-45.
[39] Stein, J. C. 1996. Rational capital budgeting in an irrational world. Journal of Business 69: 429-
55.
[40] Stewart, J. and Gill, L. 1998. Econometrics. 2nd edition, London: Prentice-Hall.