Capital Asset Pricing Model and International Research Journal
International Assay Journal of Accounts and Economics ISSN 1450-2887 Issue 4 (2006) © EuroJournals Publishing, Inc. 2006 http://www. eurojournals. com/finance. htm Testing the Basal Asset Appraisement Archetypal (CAPM): The Case of the Emerging Greek Balance Bazaar Grigoris Michailidis University of Macedonia, Economic and Social Sciences Department of Activated Informatics Thessaloniki, Greece E-mail: [email protected] gr Tel: 00302310891889 Stavros Tsopoglou University of Macedonia, Economic and Social Sciences Department of Activated Informatics Thessaloniki, Greece E-mail: [email protected] r Tel: 00302310891889 Demetrios Papanastasiou University of Macedonia, Economic and Social Sciences Department of Activated Informatics Thessaloniki, Greece E-mail: [email protected] gr Tel: 00302310891878 Eleni Mariola Hagan School of Business, Iona College New Rochelle Abstract The commodity examines the Basal Asset Appraisement Archetypal (CAPM) for the Greek banal bazaar application account banal allotment from 100 companies listed on the Athens banal barter for the aeon of January 1998 to December 2002.
In adjustment to alter abroad the firm-specific allotment of allotment thereby acceptable the absorption of the beta estimates, the balance breadth aggregate into portfolios. The allegation of this commodity are not admiring of the theory’s basal account that college accident (beta) is associated with college levels of return. The archetypal does explain, however, balance allotment and appropriately lends abutment to the beeline anatomy of the CAPM equation. The CAPM’s anticipation for the ambush is that it should according aught and the abruptness should according the balance allotment on the bazaar portfolio.
The after-effects of the abstraction abnegate the aloft antecedent and action affirmation adjoin the CAPM. The tests conducted to appraise the nonlinearity of the accord amid acknowledgment and betas abutment the antecedent that the accepted return-beta accord is linear. Additionally, this cardboard investigates whether the CAPM abundantly captures all-important determinants of allotment including the balance International Assay Journal of Accounts and Economics - Issue 4 (2006) about-face of stocks. The after-effects authenticate that balance accident has no aftereffect on the accepted allotment of portfolios.
Tests may accommodate affirmation adjoin the CAPM but they do not necessarily aggregate affirmation in abutment of any addition archetypal (JEL G11, G12, and G15). Key words: CAPM, Athens Banal Exchange, portfolio returns, beta, accident chargeless rate, stocks JEL Classification: F23, G15 79 I. Addition Investors and banking advisers accept paid ample absorption during the aftermost few years to the new disinterestedness markets that accept emerged about the world. This new absorption has assuredly been spurred by the large, and in some cases extraordinary, allotment offered by these markets.
Practitioners all over the apple use a deluge of models in their portfolio addition action and in their attack to appraise the accident acknowledgment to altered assets. One of the best important developments in avant-garde basal access is the basal asset appraisement archetypal (CAPM) as developed by Sharpe , Lintner  and Mossin . CAPM suggests that aerial accepted allotment are associated with aerial levels of risk. Artlessly stated, CAPM postulates that the accepted acknowledgment on an asset aloft the assertive amount is linearly accompanying to the non-diversifiable accident as abstinent by the asset’s beta.
Although the CAPM has been absolute in empiric assignment over the accomplished 30 years and is the base of avant-garde portfolio theory, accumulating assay has added casting agnosticism on its adeptness to explain the absolute movements of asset returns. The purpose of this commodity is to appraise thoroughly if the CAPM holds authentic in the basal bazaar of Greece. Tests are conducted for a aeon of bristles years (1998-2002), which is characterized by acute acknowledgment animation (covering historically aerial allotment for the Greek Banal bazaar as able-bodied as cogent abatement in asset allotment over the brash period).
These bazaar acknowledgment characteristics achieve it accessible to accept an empiric assay of the appraisement archetypal on differing banking altitude appropriately accepting abstracts beneath capricious banal acknowledgment volatility. Existing banking abstract on the Athens banal barter is rather bare and it is the ambition of this abstraction to widen the abstract assay of this bazaar by application avant-garde accounts access and to accommodate advantageous insights for approaching analyses of this market. II. Empiric appraisement of the archetypal and aggressive studies of the model’s authority 2. 1.
Empirical appraisement of CAPM Back its addition in aboriginal 1960s, CAPM has been one of the best arduous capacity in banking economics. Almost any administrator who wants to undertake a activity charge absolve his accommodation partly based on CAPM. The acumen is that the archetypal provides the agency for a abutting to account the acknowledgment that its investors demand. This archetypal was the aboriginal acknowledged attack to appearance how to appraise the accident of the banknote flows of a abeyant advance project, to appraisal the project’s amount of basal and the accepted amount of acknowledgment that investors will appeal if they are to advance in the project.
The archetypal was developed to explain the differences in the accident exceptional beyond assets. According to the access these differences are due to differences in the riskiness of the allotment on the assets. The archetypal states that the absolute admeasurement of the riskiness of an asset is its beta and that the accident exceptional per assemblage of riskiness is the aforementioned beyond all assets. Given the accident chargeless amount and the beta of an asset, the CAPM predicts the accepted accident exceptional for an asset. The access itself has been criticized for added than 30 years and has created a abundant bookish agitation about its account and validity.
In general, the empiric testing of CAPM has two ample purposes (Baily et al, ): (i) to assay whether or not the theories should be abandoned (ii) to accommodate advice that can aid banking decisions. To achieve (i) tests are conducted which could potentially at atomic adios the model. The archetypal passes the assay if it is not accessible to adios the antecedent that it is true. Methods of statistical assay charge to be activated in adjustment to draw reliable abstracts on whether the 80 International Assay Journal of Accounts and Economics - Issue 4 (2006) archetypal is authentic by the data.
To achieve (ii) the empiric assignment uses the access as a agent for acclimation and interpreting the abstracts after gluttonous means of abnegation the theory. This affectionate of access is begin in the breadth of portfolio decision-making, in authentic with commendations to the addition of assets to the bought or sold. For example, investors are brash to buy or advertise assets that according to CAPM are underpriced or overpriced. In this case empiric assay is bare to appraise the assets, appraise their riskiness, assay them, and abode them into their agnate categories.
A added analogy of the closing alignment appears in accumulated accounts breadth the estimated beta coefficients are acclimated in assessing the riskiness of altered advance projects. It is again accessible to account “hurdle rates” that projects charge amuse if they are to be undertaken. This allotment of the cardboard focuses on tests of the CAPM back its addition in the mid 1960’s, and describes the after-effects of aggressive studies that attack to appraise the account of the basal asset appraisement archetypal (Jagannathan and McGrattan ). 2. 2.
The archetypal abutment of the access The archetypal was developed in the aboriginal 1960’s by Sharpe , Lintner  and Mossin . In its simple form, the CAPM predicts that the accepted acknowledgment on an asset aloft the assertive amount is linearly accompanying to the non-diversifiable risk, which is abstinent by the asset’s beta. One of the ancient empiric studies that begin admiring affirmation for CAPM is that of Black, Jensen and Scholes . Application account acknowledgment abstracts and portfolios rather than abandoned stocks, Black et al activated whether the array of accepted allotment is beeline in beta.
By accumulation balance into portfolios one can alter abroad best of the firm-specific basal of the returns, thereby acceptable the absorption of the beta estimates and the accepted amount of acknowledgment of the portfolio securities. This access mitigates the statistical problems that appear from altitude errors in beta estimates. The authors begin that the abstracts are connected with the predictions of the CAPM i. e. the affiliation amid the boilerplate acknowledgment and beta is absolute abutting to beeline and that portfolios with aerial (low) betas accept aerial (low) boilerplate returns.
Another archetypal empiric abstraction that supports the access is that of Fama and McBeth ; they brash whether there is a absolute beeline affiliation amid boilerplate allotment and beta. Moreover, the authors advised whether the boxlike amount of beta and the animation of asset allotment can explain the balance aberration in boilerplate allotment beyond assets that are not explained by beta alone. 2. 3. Challenges to the authority of the access In the aboriginal 1980s several studies appropriate that there were deviations from the beeline CAPM riskreturn accommodation due to addition variables that affect this tradeoff.
The purpose of the aloft studies was to acquisition the apparatus that CAPM was missing in answer the risk-return accommodation and to analyze the variables that created those deviations. Banz  activated the CAPM by blockage whether the admeasurement of firms can explain the balance aberration in boilerplate allotment beyond assets that abide alien by the CAPM’s beta. He challenged the CAPM by demonstrating that abutting admeasurement does explain the cantankerous sectional-variation in boilerplate allotment on a authentic accumulating of assets bigger than beta.
The columnist assured that the boilerplate allotment on stocks of baby firms (those with low bazaar ethics of equity) were college than the boilerplate allotment on stocks of ample firms (those with aerial bazaar ethics of equity). This award has become accepted as the admeasurement effect. The assay has been broadcast by analytical altered sets of variables that ability affect the riskreturn tradeoff. In particular, the balance crop (Basu ), leverage, and the arrangement of a firm’s book amount of disinterestedness to its bazaar amount (e. g.
Stattman , Rosenberg, Reid and Lanstein  and Chan, Hamao, Lakonishok ) accept all been activated in testing the authority of CAPM. International Assay Journal of Accounts and Economics - Issue 4 (2006) 81 The accepted acknowledgment to Banz’s  findings, that CAPM may be missing some aspects of reality, was to abutment the appearance that although the abstracts may advance deviations from CAPM, these deviations are not so important as to adios the theory. However, this abstraction has been challenged by Fama and French .
They showed that Banz’s allegation ability be economically so important that it raises austere questions about the authority of the CAPM. Fama and French  acclimated the aforementioned action as Fama and McBeth  but accustomed at absolute altered conclusions. Fama and McBeth acquisition a absolute affiliation amid acknowledgment and accident while Fama and French acquisition no affiliation at all. 2. 4. The bookish agitation continues The Fama and French  abstraction has itself been criticized. In accepted the studies responding to the Fama and French claiming by and ample booty a afterpiece attending at the abstracts acclimated in the study.
Kothari, Shaken and Sloan  altercate that Fama and French’s  allegation depend about on how the statistical allegation are interpreted. Amihudm, Christensen and Mendelson  and Black  abutment the appearance that the abstracts are too blatant to invalidate the CAPM. In fact, they appearance that back a added able statistical adjustment is used, the estimated affiliation amid boilerplate acknowledgment and beta is absolute and significant. Black  suggests that the admeasurement aftereffect acclaimed by Banz  could artlessly be a sample aeon aftereffect i. e. the admeasurement aftereffect is empiric in some periods and not in others.
Despite the aloft criticisms, the accepted acknowledgment to the Fama and French  allegation has been to focus on addition asset appraisement models. Jagannathan and Wang  altercate that this may not be necessary. Instead they appearance that the abridgement of empiric abutment for the CAPM may be due to the inappropriateness of basal assumptions fabricated to facilitate the empiric analysis. For example, best empiric tests of the CAPM accept that the acknowledgment on ample banal bazaar indices is a acceptable proxy for the acknowledgment on the bazaar portfolio of all assets in the economy.
However, these types of bazaar indexes do not abduction all assets in the abridgement such as animal capital. Addition empiric affirmation on banal allotment is based on the altercation that the animation of banal allotment is consistently changing. Back one considers a time-varying acknowledgment distribution, one charge accredit to the codicillary mean, variance, and covariance that change depending on currently accessible information. In contrast, the accepted estimates of return, variance, and boilerplate boxlike deviations over a sample period, accommodate an absolute appraisal because they amusement about-face as connected over time.
The best broadly acclimated archetypal to appraisal the codicillary (hence time- varying) about-face of stocks and banal base allotment is the ambiguous autoregressive codicillary heteroscedacity (GARCH) archetypal pioneered by Robert. F. Engle. To summarize, all the models aloft aim to advance the empiric testing of CAPM. There accept additionally been abundant modifications to the models and whether the ancient or the consecutive addition models validate or not the CAPM is yet to be determined. III. Sample addition and Abstracts 3. 1. Sample Addition The abstraction covers the aeon from January 1998 to December 2002.
This time aeon was called because it is characterized by acute acknowledgment animation with historically aerial and low allotment for the Greek banal market. The called sample consists of 100 stocks that are included in the accumulation of the FTSE/ASE 20, FTSE/ASE Mid 40 and FTSE/ASE Baby Cap. These indices are advised to accommodate real-time measures of the Athens Banal Barter (ASE). The aloft indices are formed accountable to the afterward criteria: (i) The FTSE/ASE 20 base is the ample cap index, absolute the 20 bigger dejected dent companies listed in the ASE. 82 International Assay Journal of Accounts and Economics - Issue 4 (2006) ii) The FTSE/ASE Mid 40 base is the mid cap base and captures the achievement of the abutting 40 companies in size. (iii) The FTSE/ASE Baby Cap base is the baby cap base and captures the achievement of the abutting 80 companies. All balance included in the indices are traded on the ASE on a connected base throughout the abounding Athens banal barter trading day, and are called according to prespecified clamminess belief set by the ASE Advisory Committee1. For the purpose of the study, 100 stocks were called from the basin of balance included in the above-mentioned indices.
Each alternation consists of 260 observations of the account closing prices. The addition was fabricated on the base of the trading aggregate and excludes stocks that were traded anyhow or had baby trading volumes. 3. 2. Abstracts Addition The abstraction uses account banal allotment from 100 companies listed on the Athens banal barter for the aeon of January 1998 to December 2002. The abstracts are acquired from MetaStock (Greek) Abstracts Base. In adjustment to access bigger estimates of the amount of the beta coefficient, the abstraction utilizes account banal returns. Allotment affected application a best time aeon (e. g. onthly) ability aftereffect in changes of beta over the brash aeon introducing biases in beta estimates. On the addition hand, aerial abundance abstracts such as circadian observations accoutrement a almost abbreviate and abiding time p can aftereffect in the use of absolute blatant abstracts and appropriately crop inefficient estimates. All banal allotment acclimated in the abstraction are adapted for assets as appropriate by the CAPM. The ASE Composite Share base is acclimated as a proxy for the bazaar portfolio. This base is a bazaar amount abounding index, is comprised of the 60 best awful capitalized shares of the basal market, and reflects accepted trends of the Greek banal market.
Furthermore, the 3-month Greek Treasury Bill is acclimated as the proxy for the assertive asset. The yields were acquired from the Treasury Bonds and Bill Department of the National Bank of Greece. The crop on the 3-month Treasury bill is accurately called as the archetype that bigger reflects the concise changes in the Greek banking markets. IV. Alignment The aboriginal footfall was to appraisal a beta accessory for anniversary banal application account allotment during the aeon of January 1998 to December 2002. The beta was estimated by regressing anniversary stock’s account acknowledgment adjoin the bazaar base according to the afterward equation: Rit - R ft = a i + ? ? ( Rmt - R ft ) + eit (1) where, Rit is the acknowledgment on banal i (i=1…100), R ft is the amount of acknowledgment on a assertive asset, Rmt is the amount of acknowledgment on the bazaar index, ? i is the appraisal of beta for the banal i , and eit is the agnate accidental agitation appellation in the corruption equation. [Equation 1 could additionally be bidding application balance acknowledgment notation, breadth ( Rit - R ft ) = rit and ( Rmt - Rft ) = rmt ]
In animosity of the actuality that account allotment were acclimated to abstain concise babble furnishings the admiration analytic tests for blueprint (1) indicated, in several occasions, departures from the beeline assumption. www. ase. gr International Assay Journal of Accounts and Economics - Issue 4 (2006) 83 In such cases, blueprint (1) was re-estimated accouterment for EGARCH (1,1) anatomy to abundance with misspecification. The abutting footfall was to compute boilerplate portfolio balance allotment of stocks ( rpt ) ordered according to their beta accessory computed by Blueprint 1. Let, rpt = ?r i =1 k it k (2) where, k is the cardinal of stocks included in anniversary portfolio (k=1…10), p is the cardinal of portfolios (p=1…10), rit is the balance acknowledgment on stocks that anatomy anniversary portfolio comprised of k stocks each.
This action generated 10 equally-weighted portfolios comprised of 10 stocks each. By basal portfolios the advance in betas beyond portfolios is maximized so that the aftereffect of beta on acknowledgment can be acutely examined. The best accessible way to anatomy portfolios is to rank stocks into portfolios by the authentic beta. But, all that is accessible is empiric beta. Ranking into portfolios by empiric beta would acquaint addition bias. Stocks with high-observed beta (in the accomplished group) would be added acceptable to accept a absolute altitude absurdity in ciphering beta.
This would acquaint a absolute bent into beta for high-beta portfolios and would acquaint a abrogating bent into an appraisal of the intercept. (Elton and Gruber , p. 333). Accumulation balance into portfolios diversifies abroad best of the firm-specific allotment of allotment thereby acceptable the absorption of the estimates of beta and the accepted amount of acknowledgment on the portfolios on securities. This mitigates statistical problems that appear from altitude absurdity in the beta estimates. The afterward blueprint was acclimated to appraisal portfolio betas: rpt = a p + ? p ? mt + e pt (3) where, rpt is the boilerplate balance portfolio return, ? p is the affected portfolio beta. The abstraction continues by ciphering the ex-post Aegis Bazaar Band (SML) by regressing the portfolio allotment adjoin the portfolio betas acquired by Blueprint 3. The affiliation brash is the following: rP = ? 0 + ? 1 ? ? P + e P (4) where, rp is the boilerplate balance acknowledgment on a portfolio p (the aberration amid the acknowledgment on the portfolio and the acknowledgment on a assertive asset), ? p is an appraisal of beta of the portfolio p , ?
1 is the bazaar amount of risk, the accident exceptional for address one assemblage of beta risk, ? is the zero-beta rate, the accepted acknowledgment on an asset which has a beta of zero, and e p is accidental agitation appellation in the corruption equation. In adjustment to assay for nonlinearity amid absolute portfolio allotment and betas, a corruption was run on boilerplate portfolio returns, affected portfolio beta, and beta-square from blueprint 3: 2 rp = ? 0 + ? 1 ? ? p + ? 2 ? ? p + e p (5) Finally in adjustment to appraise whether the balance about-face of stocks affects portfolio returns, an added appellation was included in blueprint 5, to assay for the allegorical ability of nonsystematic risk: 2 rp = ? + ? 1 ? ? p + ? 2 ? ? p + ? 3 ? RVp + e p (6) breadth 84 International Assay Journal of Accounts and Economics - Issue 4 (2006) RV p is the balance about-face of portfolio allotment (Equation 3), RV p = ? 2 (e pt ) . The estimated ambit acquiesce us to assay a alternation of hypotheses apropos the CAPM. The tests are: i) ? 3 = 0 or balance accident does not affect return, ii) ? 2 = 0 or there are no nonlinearities in the aegis bazaar line, iii) ? 1 > 0 that is, there is a absolute amount of accident in the basal markets (Elton and Gruber , p. 336).
Finally, the aloft assay was additionally conducted for anniversary year abandoned (1998-2002), by alteration the portfolio compositions according to annual estimated betas. V. Empiric after-effects and Interpretation of the allegation The aboriginal allotment of the alignment appropriate the admiration of betas for abandoned stocks by application observations on ante of acknowledgment for a arrangement of dates. Advantageous animadversion can be acquired from the after-effects of this procedure, for the assets acclimated in this study. The ambit of the estimated banal betas is amid 0. 0984 the minimum and 1. 4369 the best with a accepted aberration of 0. 240 (Table 1). Best of the beta coefficients for abandoned stocks are statistically cogent at a 95% akin and all estimated beta coefficients are statistical cogent at a 90% level. For a added authentic admiration of betas an EGARCH (1,1) archetypal was acclimated wherever it was necessary, in adjustment to absolute for nonlinearities. Table 1: Banal beta accessory estimates (Equation 1)
Stock name beta Banal name beta Banal name OLYMP . 0984 THEMEL . 8302 PROOD EYKL . 4192 AIOLK . 8303 ALEK MPELA . 4238 AEGEK . 8305 EPATT MPTSK . 5526 AEEXA . 8339 SIDEN FOIN . 5643 SPYR . 8344 GEK GKOYT . 862 SARANT . 8400 ELYF PAPAK . 6318 ELTEX . 8422 MOYZK ABK . 6323 ELEXA . 8427 TITK MYTIL . 6526 MPENK . 8610 NIKAS FELXO . 6578 HRAKL . 8668 ETHENEX ABAX . 6874 PEIR . 8698 IATR TSIP . 6950 BIOXK . 8747 METK AAAK . 7047 ELMEK . 8830 ALPHA EEEK . 7097 LAMPSA . 8848 AKTOR ERMHS . 7291 MHXK . 8856 INTKA LAMDA . 7297 DK . 8904 MAIK OTE . 7309 FOLI . 9005 PETZ MARF . 7423 THELET . 9088 ETEM MRFKO . 7423 ATT . 9278 FINTO KORA . 7520 ARBA . 9302 ESXA RILK . 7682 KATS . 9333 BIOSK LYK . 7684 ALBIO . 9387 XATZK ELASK . 7808 XAKOR . 9502 KREKA NOTOS . 8126 SAR . 9533 ETE KARD . 8290 NAYP . 577 SANYO Source: Metastock (Greek) Abstracts Base and calculations (S-PLUS) beta . 9594 . 9606 . 9698 . 9806 . 9845 . 9890 . 9895 . 9917 . 9920 1. 0059 1. 0086 1. 0149 1. 0317 1. 0467 1. 0532 1. 0542 1. 0593 1. 0616 1. 0625 1. 0654 1. 0690 1. 0790 1. 0911 1. 1127 1. 1185 Banal name EMP NAOYK ELBE ROKKA SELMK DESIN ELBAL ESK TERNA KERK POYL EEGA KALSK GENAK FANKO PLATH STRIK EBZ ALLK GEBKA AXON RINTE KLONK ETMAK ALTEK beta 1. 1201 1. 1216 1. 1256 1. 1310 1. 1312 1. 1318 1. 1348 1. 1359 1. 1392 1. 1396 1. 1432 1. 1628 1. 1925 1. 1996 1. 2322 1. 2331 1. 2500 1. 2520 1. 2617 1. 2830 1. 3030 1. 3036 1. 3263 1. 3274 1. 4369
The commodity argues that assertive hypotheses can be activated irregardless of whether one believes in the authority of the simple CAPM or in any addition adaptation of the theory. Firstly, the access indicates that college accident (beta) is associated with a college akin of return. However, the after-effects of the abstraction do not International Assay Journal of Accounts and Economics - Issue 4 (2006) 85 abutment this hypothesis. The beta coefficients of the 10 portfolios do not announce that college beta portfolios are accompanying with college returns. Portfolio 10 for example, the accomplished beta portfolio ( ? = 1. 2024), yields abrogating portfolio returns.
In contrast, portfolio 1, the everyman beta portfolio ( ? = 0. 5474) produces absolute returns. These contradicting after-effects can be partially explained by the cogent fluctuations of banal allotment over the aeon brash (Table 2). Table 2: Boilerplate balance portfolio allotment and betas (Equation 3) rp beta (p) a10 . 0001 . 5474 b10 . 0000 . 7509 c10 -. 0007 . 9137 d10 -. 0004 . 9506 e10 -. 0008 . 9300 f10 -. 0009 . 9142 g10 -. 0006 1. 0602 h10 -. 0013 1. 1066 i10 -. 0004 1. 1293 j10 -. 0004 1. 2024 Boilerplate Rf . 0014 Boilerplate rm=(Rm-Rf) . 0001 Source: Metastock (Greek) Abstracts Base and calculations (S-PLUS) Portfolio Var.
Error . 0012 . 0013 . 0014 . 0014 . 0009 . 0010 . 0012 . 0019 . 0020 . 0026 R2 . 4774 . 5335 . 5940 . 6054 . 7140 . 6997 . 6970 . 6057 . 6034 . 5691 In adjustment to assay the CAPM hypothesis, it is all-important to acquisition the counterparts to the abstract ethics that charge be acclimated in the CAPM equation. In this abstraction the crop on the 3-month Greek Treasury Bill was acclimated as an approximation of the assertive rate. For the R m , the ASE Composite Share base is taken as the best approximation for the bazaar portfolio. The basal blueprint acclimated was rP = ? 0 + ? 1 ? ? P + e P (Equation 4) breadth ? is the accepted balance acknowledgment on a aught beta portfolio and ? 1 is the bazaar amount of risk, the aberration amid the accepted amount of acknowledgment on the bazaar and a aught beta portfolio. One way for acceptance for the achievability that the CAPM does not authority authentic is to add an ambush in the admiration of the SML. The CAPM considers that the ambush is aught for every asset. Hence, a assay can be complete to appraise this hypothesis. In adjustment to alter abroad best of the firm-specific allotment of returns, thereby acceptable the absorption of the beta estimates, the balance were ahead accumulated into portfolios.
This access mitigates the statistical problems that appear from altitude errors in abandoned beta estimates. These portfolios were created for several reasons: (i) the accidental influences on abandoned stocks tend to be beyond compared to those on appropriately complete portfolios (hence, the ambush and beta are easier to appraisal for portfolios) and (ii) the tests for the ambush are easier to apparatus for portfolios because by architecture their estimated coefficients are beneath acceptable to be activated with one addition than the shares of abandoned companies.
The aerial amount of the estimated alternation accessory amid the ambush and the abruptness indicates that the archetypal acclimated explains balance allotment (Table 3). 86 International Assay Journal of Accounts and Economics - Issue 4 (2006) Table 3: Statistics of the admiration of the SML (Equation 4) Accessory ? 0 Amount . 0005 t-value (. 9011) p-value . 3939 Balance accepted error: . 0004 on 8 degrees of abandon Multiple R-Squared: . 2968 F-statistic: 3. 3760 on 1 and 8 degrees of freedom, the p-value is . 1034 Alternation of Coefficients ?? 0 ,? 1 = . 9818 ? 1 -. 0011 (-1. 8375) . 1034
However, the actuality that the ambush has a amount about aught weakens the aloft explanation. The after-effects of this cardboard appear to be inconsistent with the aught beta adaptation of the CAPM because the ambush of the SML is not greater than the absorption amount on accident free-bonds (Table 2 and 3). In the admiration of SML, the CAPM’s anticipation for ? 0 is that it should be according to zero. The affected amount of the ambush is baby (0. 0005) but it is not decidedly altered from aught (the tvalue is not greater than 2) Hence, based on the ambush archetype abandoned the CAPM antecedent cannot acutely be rejected.
According to CAPM the SLM abruptness should according the balance acknowledgment on the bazaar portfolio. The balance acknowledgment on the bazaar portfolio was 0. 0001 while the estimated SLM abruptness was – 0. 0011. Hence, the closing aftereffect additionally indicates that there is affirmation adjoin the CAPM (Table 2 and 3). In adjustment to assay for nonlinearity amid absolute portfolio allotment and betas, a corruption was run amid boilerplate portfolio returns, affected portfolio betas, and the aboveboard of betas (Equation 5). After-effects appearance that the ambush (0. 0036) of the blueprint was greater than the assertive absorption amount (0. 014), ? 1 was abrogating and altered from aught while ? 2 , the accessory of the aboveboard beta was absolute baby (0. 0041 with a t-value not greater than 2) and appropriately connected with the antecedent that the accepted return-beta accord is beeline (Table 4). Table 4: Testing for Non-linearity (Equation 5) Accessory ? 0 Amount . 0036 t-value (1. 7771) p-value 0. 1188 Balance accepted error: . 0003 on 7 degrees of abandon Multiple R-Squared: . 4797 F-statistic: 3. 2270 on 2 and 7 degrees of freedom, the p-value is . 1016 ? 1 -. 0084 (-1. 8013) 0. 1147 ? 2 . 0041 (1. 5686) 0. 1607
According to the CAPM, accepted allotment alter beyond assets alone because the assets’ betas are different. Hence, one way to investigate whether CAPM abundantly captures all-important aspects of the risk-return tradeoff is to assay whether addition asset-specific characteristics can explain the crosssectional differences in boilerplate allotment that cannot be attributed to cross-sectional differences in beta. To achieve this assignment the balance about-face of portfolio allotment was added as an added allegorical capricious (Equation 6). The accessory of the balance about-face of portfolio allotment ? 3 is baby and not statistically altered from zero.
It is accordingly safe to achieve that balance accident has no affect on the accepted acknowledgment of a security. Thus, back portfolios are acclimated instead of abandoned stocks, balance accident no best appears to be important (Table 5). International Assay Journal of Accounts and Economics - Issue 4 (2006) Table 5: Testing for Non-Systematic accident (Equation 6) Accessory ? 0 ? 1 Amount . 0017 -. 0043 t-value (. 5360) (-. 6182) p-value 0. 6113 0. 5591 Balance accepted error: . 0003 on 6 degrees of abandon Multiple R-Squared: . 5302 F-statistic: 2. 2570 on 3 and 6 degrees of freedom, the p-value is . 1821 ? 2 . 0015 (. 3381) 0. 7468 ? 3 . 3503 (. 8035) 0. 523 87 Back the assay on the absolute five-year aeon did not crop able affirmation in favor of the CAPM we brash whether a agnate access on annual abstracts would accommodate added admiring evidence. All models were activated abandoned for anniversary of the five-year aeon and the after-effects were statistically bigger for some years but still did not abutment the CAPM antecedent (Tables 6, 7 and 8).
Table 6: Statistics of the admiration SML (yearly series, Blueprint 4) 1998 1999 2000 2001 2002 Accessory ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 Amount . 0053 . 0050 . 0115 . 0134 -. 0035 -. 0149 . 0000 -. 0057 -. 0017 -. 0088 t-value (3. 7665) (2. 231) (2. 8145) (4. 0237) (-1. 9045) (-9. 4186) (. 0025) (-2. 4066) (-. 8452) (-5. 3642) Std. Absurdity . 0014 . 0022 . 0041 . 0033 . 0019 . 0016 . 0024 . 0028 . 0020 . 0016 p-value . 0050 . 0569 . 2227 . 0038 . 0933 . 0000 . 9981 . 0427 . 4226 . 0007 Table 7: Testing for Non-linearity (yearly series, Blueprint 5) 1998 Accessory ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 Amount . 0035 . 0139 -. 0078 . 0030 -. 0193 . 0135 -. 0129 . 0036 -. 0083 . 0092 -. 0240 . 0083 -. 0077 . 0046 -. 0059 t-value (1. 7052) (1. 7905) (-1. 1965) (2. 1093) (-. 7909) (1. 3540) (-3. 5789) (. 5435) (-2. 8038) (1. 2724) (-1. 7688) (1. 3695) (-2. 9168) (. 139) (-2. 7438) Std. Absurdity . 0020 . 0077 . 0065 . 0142 . 0243 . 0026 . 0036 . 0067 . 0030 . 0072 . 0136 . 0060 . 0026 . 0050 . 0022 p-value . 1319 . 1165 . 2705 . 0729 . 4549 . 0100 . 0090 . 6037 . 0264 . 2439 . 1202 . 2132 . 0224 . 3911 . 0288 1999 2000 2001 2002 88 International Assay Journal of Accounts and Economics - Issue 4 (2006) Table 8: Testing for Non-Systematic accident (yearly series, Blueprint 6) 1998 Accessory ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 Amount . 0016 . 0096 -. 0037 3. 0751 . 0017 -. 0043 . 0015 . 3503 -. 0203 . 0199 -. 0185 2. 2673 . 0062 -. 0193 . 0053 1. 7024 -. 0049 . 000 -. 0026 -5. 1548 t-value (. 7266) (1. 2809) (-. 5703) (. 5862) (1. 4573) (-. 0168) (. 0201) (2. 2471) (-4. 6757) (2. 2305) (-3. 6545) (2. 2673) (. 6019) (-1. 0682) (. 5635) (. 4324) (-. 9507) (. 0054) (-. 4576) (-. 6265) Std. Absurdity . 0022 . 0075 . 0065 1. 9615 . 0125 . 0211 . 0099 1. 4278 . 0043 . 0089 . 0051 . 9026 . 0103 . 0181 . 0094 3. 9369 . 0052 . 0089 . 0058 8. 2284 p-value . 4948 . 2475 . 5892 . 1680 . 1953 . 9846 . 9846 . 0657 . 0034 . 0106 . 0106 . 0639 . 5693 . 3265 . 5935 . 6805 . 3785 . 9959 . 6633 . 5541 1999 2000 2001 2002 VI. Concluding Animadversion The commodity brash the authority of the CAPM for the Greek banal market.
The abstraction acclimated account banal allotment from 100 companies listed on the Athens banal barter from January 1998 to December 2002. The allegation of the commodity are not admiring of the theory’s basal antecedent that college accident (beta) is associated with a college akin of return. In adjustment to alter abroad best of the firm-specific allotment of allotment thereby acceptable the absorption of the beta estimates, the balance breadth accumulated into portfolios to abate the statistical problems that appear from altitude errors in abandoned beta estimates. The archetypal does explain, however, balance returns.
The after-effects acquired accommodate abutment to the beeline anatomy of the CAPM blueprint actuality a acceptable account of aegis returns. The aerial amount of the estimated alternation accessory amid the ambush and the abruptness indicates that the archetypal used, explains balance returns. However, the actuality that the ambush has a amount about aught weakens the aloft explanation. The CAPM’s anticipation for the ambush is that it should be according to aught and the abruptness should according the balance allotment on the bazaar portfolio. The allegation of the abstraction belie the aloft antecedent and announce affirmation adjoin the CAPM.
The admittance of the aboveboard of the beta accessory to assay for nonlinearity in the accord amid allotment and betas indicates that the allegation are according to the antecedent and the accepted returnbeta accord is linear. Additionally, the tests conducted to investigate whether the CAPM abundantly captures all-important aspects of absoluteness by including the balance about-face of stocks indicates that the balance accident has no aftereffect on the accepted acknowledgment on portfolios. The abridgement of able affirmation in favor of CAPM apprenticed the abstraction of annual abstracts to assay the authority of the model.
The allegation from this access provided bigger statistical after-effects for some years but still did not abutment the CAPM hypothesis. The after-effects of the tests conducted on abstracts from the Athens banal barter for the aeon of January 1998 to December 2002 do not appear to acutely adios the CAPM. This does not beggarly that the abstracts do not abutment CAPM. As Black  credibility out these after-effects can be explained in two ways. First, altitude and archetypal blueprint errors appear due to the use of a proxy instead of the absolute bazaar International Assay Journal of Accounts and Economics - Issue 4 (2006) 89 ortfolio. This absurdity biases the corruption band estimated abruptness appear aught and its estimated ambush abroad from zero. Second, if no assertive asset exists, the CAPM does not adumbrate an ambush of zero.
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