Capital Asset Pricing Model and International Research Journal

International Discovery Journal of Finance and Economics ISSN 1450-2887 Issue 4 (2006) © EuroJournals Publishing, Inc. 2006 http://www. eurojournals. com/finance. htm Testing the Excellent Asset Pricing Copy (CAPM): The Occurrence of the Emerging Greek Securities Traffic Grigoris Michailidis University of Macedonia, Economic and Social Sciences Department of Applied Informatics Thessaloniki, Greece E-mail: [email protected] gr Tel: 00302310891889 Stavros Tsopoglou University of Macedonia, Economic and Social Sciences Department of Applied Informatics Thessaloniki, Greece E-mail: [email protected] r Tel: 00302310891889 Demetrios Papanastasiou University of Macedonia, Economic and Social Sciences Department of Applied Informatics Thessaloniki, Greece E-mail: [email protected] gr Tel: 00302310891878 Eleni Mariola Hagan School of Business, Iona College New Rochelle Abstract The expression trials the Excellent Asset Pricing Copy (CAPM) for the Greek supply traffic using weekly supply receipts from 100 companies listed on the Athens supply vary for the duration of January 1998 to December 2002. In command to alter detached the attached-specific portio of receipts thereby enhancing the accuracy of the beta reveres, the securities where clumped into portfolios. The ascertainings of this expression are not stayive of the supposition’s basic declaration that surpassing facilitate (beta) is associated after a conjuncture surpassing rolls of retaliate. The copy does expound, thus-far, intemperance receipts and thus loans stay to the straight edifice of the CAPM equation. The CAPM’s prognostication for the stop is that it should resembling cipher and the excel should resembling the intemperance receipts on the traffic portfolio. The products of the con-aggravate repel the aggravate supposition and exaid sign counter the CAPM. The trials conducted to trial the nonlinearity of the conformity betwixt retaliate and betas stay the supposition that the expected retaliate-beta conformity is straight. Additionally, this disquisition endueigates whether the CAPM adequately abides all-weighty determinants of receipts including the residual International Discovery Journal of Finance and Economics - Issue 4 (2006) strife of supplys. The products unfold that residual facilitate has no concontinuity on the expected receipts of portfolios. Tests may prepare sign counter the CAPM but they do not necessarily frame sign in stay of any resource copy (JEL G11, G12, and G15). Key words: CAPM, Athens Supply Exchange, portfolio receipts, beta, facilitate uncounted reprimand, supplys JEL Classification: F23, G15 79 I. Importation Investors and financial discoveryers accept paid extensive care during the familiar few years to the new equity traffics that accept emerged encircling the globe. This new curiosity-behalf has undoubtedly been spurred by the extensive, and in some occurrences unusual, receipts extended by these traffics. Practitioners all aggravate the globe use a plethora of copys in their portfolio preference system and in their underneathchoose to assess the facilitate peril to irrelative possessions. One of the most weighty developments in later excellent supposition is the excellent asset pricing copy (CAPM) as familiar by Sharpe [1964], Lintner [1965] and Mossin [1966]. CAPM allude-tos that tall expected receipts are associated after a conjuncture tall rolls of facilitate. Solely stated, CAPM postulates that the expected retaliate on an asset aggravate the facilitate-uncounted reprimand is straightly skinred to the non-diversifiable facilitate as appraised by the asset’s beta. Although the CAPM has been balanceruling in tentative exertion aggravate the gone-by 30 years and is the buildation of later portfolio supposition, accumulating discovery has increasingly character dubitate on its authority to expound the explicit movements of asset receipts. The scope of this expression is to trial utterly if the CAPM abides penny in the excellent traffic of Greece. Tests are conducted for a duration of five years (1998-2002), which is characterized by eager retaliate incongruity (crust historically tall receipts for the Greek Supply traffic as polite as weighty decrow in asset receipts aggravate the triald duration). These traffic retaliate characteristics amiables it feasible to accept an tentative exploration of the pricing copy on differing financial conditions thus gaining conclusions underneathneath varying supply retaliate incongruity. Existing financial con-aggravate on the Athens supply vary is rather parsimonious and it is the sight of this con-aggravate to stretch the presumptive resolution of this traffic by using later finance supposition and to prepare helpful insights for advenient analyses of this traffic. II. Tentative appraisal of the copy and competing studies of the copy’s vigor 2. 1. Empirical appraisal of CAPM Past its importation in existing 1960s, CAPM has been one of the most challenging topics in financial economics. Almost any superintendent who wants to underneathchoose a scheme must excuse his resolution portioly invetescold on CAPM. The prove is that the copy prepares the media for a attached to reckon the retaliate that its endueors claim. This copy was the proudest happy underneathchoose to answerance how to assess the facilitate of the consummate flows of a immanent cannonade scheme, to revere the scheme’s absorb of excellent and the expected reprimand of retaliate that endueors earn claim if they are to endue in the scheme. The copy was familiar to expound the disagreements in the facilitate recompense athwart possessions. According to the supposition these disagreements are due to disagreements in the facilitateiness of the receipts on the possessions. The copy states that the set-right appraise of the facilitateiness of an asset is its beta and that the facilitate recompense per distribute of facilitateiness is the identical athwart all possessions. Given the facilitate uncounted reprimand and the beta of an asset, the CAPM prophesys the expected facilitate recompense for an asset. The supposition itself has been criticized for past than 30 years and has created a authorityful academic dispute environing its helpfulness and vigor. In open, the tentative trialing of CAPM has two indelicate scopes (Baily et al, [1998]): (i) to trial whether or not the theories should be unordinary (ii) to prepare notification that can aid financial resolutions. To end (i) trials are conducted which could immanently at paltryest repel the copy. The copy passes the trial if it is not feasible to repel the supposition that it is penny. Methods of statistical resolution demand to be applied in command to delineate genuine conclusions on whether the 80 International Discovery Journal of Finance and Economics - Issue 4 (2006) copy is stayed by the events. To end (ii) the tentative exertion uses the supposition as a behavior for organizing and interpreting the events after a conjunctureout seeking ways of repeling the supposition. This skin of admission is build in the area of portfolio resolution-making, in portioicular after a conjuncture commendations to the preference of possessions to the bought or sold. For scantling, endueors are advised to buy or vend possessions that according to CAPM are underneathpriced or aggravatepriced. In this occurrence tentative resolution is demanded to evaluate the possessions, assess their facilitateiness, irritate them, and fix them into their relative categories. A succor illustration of the cessation mannerology answers in corporeprimand finance where the revered beta coefficients are used in assessing the facilitateiness of irrelative cannonade schemes. It is then feasible to reckon “hurdle reprimands” that schemes must gratify if they are to be underneathtaken. This portio of the disquisition centrees on trials of the CAPM past its importation in the mid 1960’s, and describes the products of competing studies that underneathchoose to evaluate the helpfulness of the excellent asset pricing copy (Jagannathan and McGrattan [1995]). 2. 2. The fashionable stay of the supposition The copy was familiar in the existing 1960’s by Sharpe [1964], Lintner [1965] and Mossin [1966]. In its sincere frame, the CAPM prophesys that the expected retaliate on an asset aggravate the facilitate-uncounted reprimand is straightly skinred to the non-diversifiable facilitate, which is appraised by the asset’s beta. One of the primitive tentative studies that build stayive sign for CAPM is that of Black, Jensen and Scholes [1972]. Using monthly retaliate events and portfolios rather than single supplys, Bstagnation et al trialed whether the cantankerous-section of expected receipts is straight in beta. By combining securities into portfolios one can alter detached most of the attached-specific element of the receipts, thereby enhancing the accuracy of the beta reveres and the expected reprimand of retaliate of the portfolio securities. This admission moderates the statistical problems that start from appraisement hallucinations in beta reveres. The makers build that the events are congruous after a conjuncture the prognostications of the CAPM i. e. the proportion betwixt the balance retaliate and beta is very rest to straight and that portfolios after a conjuncture tall (low) betas accept tall (low) balance receipts. Another fashionable tentative con-aggravate that stays the supposition is that of Fama and McBeth [1973]; they triald whether there is a definitive straight proportion betwixt balance receipts and beta. Moreover, the makers endueigated whether the balanced appraise of beta and the incongruity of asset receipts can expound the residual diversity in balance receipts athwart possessions that are not expounded by beta uneven. 2. 3. Challenges to the vigor of the supposition In the existing 1980s sundry studies allude-toed that there were gaps from the straight CAPM facilitateretaliate trade-off due to other capriciouss that concern this tradeoff. The scope of the aggravate studies was to asregular the elements that CAPM was privation in expounding the facilitate-retaliate trade-off and to substantiate the capriciouss that created those gaps. Banz [1981] trialed the CAPM by checking whether the dimension of attacheds can expound the residual diversity in balance receipts athwart possessions that abide unexplained by the CAPM’s beta. He defyd the CAPM by demonstrating that attached dimension does expound the cantankerous sectional-diversity in balance receipts on a portioicular gathering of possessions rectify than beta. The maker deduced that the balance receipts on supplys of slender attacheds (those after a conjuncture low traffic appraises of equity) were surpassing than the balance receipts on supplys of extensive attacheds (those after a conjuncture tall traffic appraises of equity). This ascertaining has beseem known as the dimension consequence. The discovery has been extensive by examining irrelative sets of capriciouss that susceptibility concern the facilitateretaliate tradeoff. In portioicular, the rights relinquish (Basu [1977]), leverage, and the proportion of a attached’s book appraise of equity to its traffic appraise (e. g. Stattman [1980], Rosenberg, Reid and Lanstein [1983] and Chan, Hamao, Lakonishok [1991]) accept all been utilized in trialing the vigor of CAPM. International Discovery Journal of Finance and Economics - Issue 4 (2006) 81 The open reaction to Banz’s [1981] ascertainings, that CAPM may be privation some aspects of existence, was to stay the conception that although the events may allude-to gaps from CAPM, these gaps are not so weighty as to repel the supposition. However, this intention has been defyd by Fama and French [1992]. They answeranceed that Banz’s ascertainings susceptibility be economically so weighty that it raises grave questions environing the vigor of the CAPM. Fama and French [1992] used the identical proceeding as Fama and McBeth [1973] but arrived at very irrelative conclusions. Fama and McBeth asregular a definitive proportion betwixt retaliate and facilitate conjuncture Fama and French asregular no proportion at all. 2. 4. The academic dispute continues The Fama and French [1992] con-aggravate has itself been criticized. In open the studies responding to the Fama and French defy by and extensive choose a restr answer at the events used in the con-over. Kothari, Shaken and Sloan [1995] prove that Fama and French’s [1992] ascertainings stop essentially on how the statistical ascertainings are interpreted. Amihudm, Christensen and Mendelson [1992] and Bstagnation [1993] stay the conception that the events are too loud to annul the CAPM. In event, they answerance that when a past prolific statistical manner is used, the revered proportion betwixt balance retaliate and beta is definitive and weighty. Bstagnation [1993] allude-tos that the dimension concontinuity illustrious by Banz [1981] could solely be a scantling duration concontinuity i. e. the dimension concontinuity is observed in some durations and not in others. Deill-will the aggravate criticisms, the open reaction to the Fama and French [1992] ascertainings has been to centre on resource asset pricing copys. Jagannathan and Wang [1993] prove that this may not be essential. Instead they answerance that the stagnation of tentative stay for the CAPM may be due to the inappropriateness of basic presumptions made to facilitate the tentative resolution. For scantling, most tentative trials of the CAPM presume that the retaliate on indelicate supply traffic indices is a amiable delegate for the retaliate on the traffic portfolio of all possessions in the rule. However, these types of traffic condemnationes do not abide all possessions in the rule such as ethnical excellent. Other tentative sign on supply receipts is invetescold on the manifestation that the incongruity of supply receipts is faithfully changing. When one considers a date-varying retaliate division, one must allude to the occupied balance, strife, and absorbrife that qualify stoping on currently profitable notification. In opposition, the ordinary reveres of retaliate, strife, and balance balanced gaps aggravate a scantling duration, prepare an unoccupied revere owing they discuss strife as faithful aggravate date. The most widely used copy to revere the occupied (hence date- varying) strife of supplys and supply condemnation receipts is the openized autoregressive occupied heteroscedacity (GARCH) copy pioneered by Robert. F. Engle. To summarize, all the copys aggravate aim to redevise the tentative trialing of CAPM. There accept too been deep modifications to the copys and whether the primitive or the posterior resource copys validate or not the CAPM is yet to be rooted. III. Scantling preference and Facts 3. 1. Scantling Preference The con-aggravate covers the duration from January 1998 to December 2002. This date duration was separated owing it is characterized by eager retaliate incongruity after a conjuncture historically tall and low receipts for the Greek supply traffic. The separated scantling consists of 100 supplys that are intervening in the frameation of the FTSE/ASE 20, FTSE/ASE Mid 40 and FTSE/ASE Slender Cap. These indices are planned to prepare real-date appraises of the Athens Supply Vary (ASE). The aggravate indices are frameed matter to the subjoined criteria: (i) The FTSE/ASE 20 condemnation is the extensive cap condemnation, containing the 20 extensivest cerulean driblet companies listed in the ASE. 82 International Discovery Journal of Finance and Economics - Issue 4 (2006) ii) The FTSE/ASE Mid 40 condemnation is the mid cap condemnation and abides the achievement of the instant 40 companies in dimension. (iii) The FTSE/ASE Slender Cap condemnation is the slender cap condemnation and abides the achievement of the instant 80 companies. All securities intervening in the indices are traded on the ASE on a unidevise buildation throughout the ample Athens supply vary trading day, and are separated according to prespecified liquidity criteria set by the ASE Advisory Committee1. For the scope of the con-over, 100 supplys were separated from the pool of securities intervening in the aggravate-mentioned indices. Each course consists of 260 observations of the weekly closing figures. The preference was made on the buildation of the trading quantity and excludes supplys that were traded irregularly or had slender trading quantitys. 3. 2. Facts Preference The con-aggravate uses weekly supply receipts from 100 companies listed on the Athens supply vary for the duration of January 1998 to December 2002. The events are gained from MetaStock (Greek) Facts Base. In command to gain rectify reveres of the appraise of the beta coefficient, the con-aggravate utilizes weekly supply receipts. Receipts reckond using a longer date duration (e. g. onthly) susceptibility product in qualifys of beta aggravate the triald duration introducing disadvantagees in beta reveres. On the other apostacy, tall quantity events such as daily observations crust a proportionately defective and perpetual date p can product in the use of very loud events and thus relinquish inprolific reveres. All supply receipts used in the con-aggravate are adjusted for dividends as required by the CAPM. The ASE Composite Share condemnation is used as a delegate for the traffic portfolio. This condemnation is a traffic appraise weighted condemnation, is intervening of the 60 most tallly excellentized shares of the ocean traffic, and reflects open trends of the Greek supply traffic. Furthermore, the 3-month Greek Treasury Charges is used as the delegate for the facilitate-uncounted asset. The relinquishs were gained from the Treasury Bonds and Charges Department of the National Bank of Greece. The relinquish on the 3-month Treasury charges is specifically separated as the benchmark that rectify reflects the defective-expression qualifys in the Greek financial traffics. IV. Methodology The proudest tread was to revere a beta coprolific for each supply using weekly receipts during the duration of January 1998 to December 2002. The beta was revered by regressing each supply’s weekly retaliate counter the traffic condemnation according to the subjoined equation: Rit - R ft = a i + ? ? ( Rmt - R ft ) + eit (1) where, Rit is the retaliate on supply i (i=1…100), R ft is the reprimand of retaliate on a facilitate-uncounted asset, Rmt is the reprimand of retaliate on the traffic condemnation, ? i is the revere of beta for the supply i , and eit is the identical purposeshort mobility expression in the retrogression equation. [Equation 1 could too be explicit using intemperance retaliate notation, where ( Rit - R ft ) = rit and ( Rmt - Rft ) = rmt ] In ill-will of the event that weekly receipts were used to relinquish defective-expression tumult consequences the repute feature trials for equation (1) involved, in sundry occasions, departures from the straight presumption. www. ase. gr International Discovery Journal of Finance and Economics - Issue 4 (2006) 83 In such occurrences, equation (1) was re-estimated providing for EGARCH (1,1) frame to self-approval after a conjuncture misspecification. The instant tread was to appraise balance portfolio intemperance receipts of supplys ( rpt ) commanded according to their beta coprolific appraised by Equation 1. Let, rpt = ?r i =1 k it k (2) where, k is the number of supplys intervening in each portfolio (k=1…10), p is the number of portfolios (p=1…10), rit is the intemperance retaliate on supplys that frame each portfolio intervening of k supplys each. This proceeding generated 10 resemblingly-weighted portfolios intervening of 10 supplys each. By frameing portfolios the expand in betas athwart portfolios is maximized so that the concontinuity of beta on retaliate can be clexisting triald. The most explicit way to frame portfolios is to systematize supplys into portfolios by the penny beta. But, all that is profitable is observed beta. Ranking into portfolios by observed beta would present preference disadvantage. Stocks after a conjuncture tall-observed beta (in the tallest clump) would be past moderated to accept a definitive appraisement hallucination in estimating beta. This would present a definitive disadvantage into beta for tall-beta portfolios and would present a privative disadvantage into an revere of the stop. (Elton and Gruber [1995], p. 333). Combining securities into portfolios diversifies detached most of the attached-specific portio of receipts thereby enhancing the accuracy of the reveres of beta and the expected reprimand of retaliate on the portfolios on securities. This moderates statistical problems that start from appraisement hallucination in the beta reveres. The subjoined equation was used to revere portfolio betas: rpt = a p + ? p ? mt + e pt (3) where, rpt is the balance intemperance portfolio retaliate, ? p is the reckond portfolio beta. The con-aggravate continues by estimating the ex-post Carelessness Traffic Row (SML) by regressing the portfolio receipts counter the portfolio betas gained by Equation 3. The proportion triald is the subjoined: rP = ? 0 + ? 1 ? ? P + e P (4) where, rp is the balance intemperance retaliate on a portfolio p (the disagreement betwixt the retaliate on the portfolio and the retaliate on a facilitate-uncounted asset), ? p is an revere of beta of the portfolio p , ? 1 is the traffic figure of facilitate, the facilitate recompense for aspect one distribute of beta facilitate, ? is the cipher-beta reprimand, the expected retaliate on an asset which has a beta of cipher, and e p is purposeshort mobility expression in the retrogression equation. In command to trial for nonlinearity betwixt completion portfolio receipts and betas, a retrogression was run on balance portfolio receipts, reckond portfolio beta, and beta-balance from equation 3: 2 rp = ? 0 + ? 1 ? ? p + ? 2 ? ? p + e p (5) Finally in command to trial whether the residual strife of supplys concerns portfolio receipts, an joined expression was intervening in equation 5, to trial for the explanatory authority of nonsystematic facilitate: 2 rp = ? + ? 1 ? ? p + ? 2 ? ? p + ? 3 ? RVp + e p (6) where 84 International Discovery Journal of Finance and Economics - Issue 4 (2006) RV p is the residual strife of portfolio receipts (Equation 3), RV p = ? 2 (e pt ) . The revered parameters avow us to trial a course of hypotheses touching the CAPM. The trials are: i) ? 3 = 0 or residual facilitate does not concern retaliate, ii) ? 2 = 0 or there are no nonlinearities in the carelessness traffic row, iii) ? 1 > 0 that is, there is a definitive figure of facilitate in the excellent traffics (Elton and Gruber [1995], p. 336). Finally, the aggravate resolution was too conducted for each year peculiarly (1998-2002), by changing the portfolio compositions according to yexisting revered betas. V. Tentative products and Interpretation of the ascertainings The proudest portio of the mannerology required the repute of betas for single supplys by using observations on reprimands of retaliate for a continuity of dates. Helpful remarks can be superficial from the products of this proceeding, for the possessions used in this con-over. The rove of the revered supply betas is betwixt 0. 0984 the poverty and 1. 4369 the ultimatum after a conjuncture a plummet gap of 0. 240 (Table 1). Most of the beta coefficients for single supplys are statistically weighty at a 95% roll and all revered beta coefficients are statistical weighty at a 90% roll. For a past accureprimand repute of betas an EGARCH (1,1) copy was used wherever it was essential, in command to set-right for nonlinearities. Table 1: Supply beta coprolific reveres (Equation 1) Stock manifestation beta Supply manifestation beta Supply manifestation 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: Metasupply (Greek) Facts 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 Supply manifestation 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 expression proves that regular hypotheses can be trialed irregardshort of whether one believes in the vigor of the sincere CAPM or in any other statement of the supposition. Firstly, the supposition manifestations that surpassing facilitate (beta) is associated after a conjuncture a surpassing roll of retaliate. However, the products of the con-aggravate do not International Discovery Journal of Finance and Economics - Issue 4 (2006) 85 stay this supposition. The beta coefficients of the 10 portfolios do not manifestation that surpassing beta portfolios are skinred after a conjuncture surpassing receipts. Portfolio 10 for scantling, the tallest beta portfolio ( ? = 1. 2024), relinquishs privative portfolio receipts. In opposition, portfolio 1, the paltryest beta portfolio ( ? = 0. 5474) produces definitive receipts. These negativeing products can be portioially expounded by the weighty fluctuations of supply receipts aggravate the duration triald (Table 2). Table 2: Balance intemperance portfolio receipts 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 Balance Rf . 0014 Balance rm=(Rm-Rf) . 0001 Source: Metasupply (Greek) Facts 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 command to trial the CAPM supposition, it is essential to asregular the counterparts to the presumptive appraises that must be used in the CAPM equation. In this con-aggravate the relinquish on the 3-month Greek Treasury Charges was used as an access of the facilitate-uncounted reprimand. For the R m , the ASE Composite Share condemnation is choosen as the best access for the traffic portfolio. The basic equation used was rP = ? 0 + ? 1 ? ? P + e P (Equation 4) where ? is the expected intemperance retaliate on a cipher beta portfolio and ? 1 is the traffic figure of facilitate, the disagreement betwixt the expected reprimand of retaliate on the traffic and a cipher beta portfolio. One way for avowing for the possibility that the CAPM does not abide penny is to add an stop in the repute of the SML. The CAPM considers that the stop is cipher for whole asset. Hence, a trial can be false to trial this supposition. In command to alter detached most of the attached-specific portio of receipts, thereby enhancing the accuracy of the beta reveres, the securities were previously fully into portfolios. This admission moderates the statistical problems that start from appraisement hallucinations in single beta reveres. These portfolios were created for sundry proves: (i) the purposeshort influences on single supplys aid to be extensiver compared to those on pleasantly false portfolios (hence, the stop and beta are easier to revere for portfolios) and (ii) the trials for the stop are easier to utensil for portfolios owing by erection their revered coefficients are short moderated to be corkindred after a conjuncture one another than the shares of single companies. The tall appraise of the revered corproportion coprolific betwixt the stop and the excel manifestations that the copy used expounds intemperance receipts (Table 3). 86 International Discovery Journal of Finance and Economics - Issue 4 (2006) Table 3: Statistics of the repute of the SML (Equation 4) Coprolific ? 0 Appraise . 0005 t-appraise (. 9011) p-appraise . 3939 Residual plummet hallucination: . 0004 on 8 degrees of uncounteddom Multiple R-Squared: . 2968 F-statistic: 3. 3760 on 1 and 8 degrees of uncounteddom, the p-appraise is . 1034 Corproportion of Coefficients ?? 0 ,? 1 = . 9818 ? 1 -. 0011 (-1. 8375) . 1034 However, the event that the stop has a appraise encircling cipher weakens the aggravate interpretation. The products of this disquisition answer to be incongruous after a conjuncture the cipher beta statement of the CAPM owing the stop of the SML is not authorityfuler than the curiosity-behalf reprimand on facilitate uncounted-bonds (Table 2 and 3). In the repute of SML, the CAPM’s prognostication for ? 0 is that it should be resembling to cipher. The reckond appraise of the stop is slender (0. 0005) but it is not weightyly irrelative from cipher (the tappraise is not authorityfuler than 2) Hence, invetescold on the stop touchstone uneven the CAPM supposition cannot clexisting be unusual. According to CAPM the SLM excel should resembling the intemperance retaliate on the traffic portfolio. The intemperance retaliate on the traffic portfolio was 0. 0001 conjuncture the revered SLM excel was – 0. 0011. Hence, the cessation product too manifestations that there is sign counter the CAPM (Table 2 and 3). In command to trial for nonlinearity betwixt completion portfolio receipts and betas, a retrogression was run betwixt balance portfolio receipts, reckond portfolio betas, and the balance of betas (Equation 5). Results answerance that the stop (0. 0036) of the equation was authorityfuler than the facilitate-uncounted curiosity-behalf reprimand (0. 014), ? 1 was privative and irrelative from cipher conjuncture ? 2 , the coprolific of the balance beta was very slender (0. 0041 after a conjuncture a t-appraise not authorityfuler than 2) and thus congruous after a conjuncture the supposition that the expected retaliate-beta conformity is straight (Table 4). Table 4: Testing for Non-linearity (Equation 5) Coprolific ? 0 Appraise . 0036 t-appraise (1. 7771) p-appraise 0. 1188 Residual plummet hallucination: . 0003 on 7 degrees of uncounteddom Multiple R-Squared: . 4797 F-statistic: 3. 2270 on 2 and 7 degrees of uncounteddom, the p-appraise is . 1016 ? 1 -. 0084 (-1. 8013) 0. 1147 ? 2 . 0041 (1. 5686) 0. 1607 According to the CAPM, expected receipts vary athwart possessions merely owing the possessions’ betas are irrelative. Hence, one way to endueigate whether CAPM adequately abides all-weighty aspects of the facilitate-retaliate tradeoff is to trial whether other asset-specific characteristics can expound the cantankeroussectional disagreements in balance receipts that cannot be attributed to cantankerous-sectional disagreements in beta. To end this function the residual strife of portfolio receipts was ascititious as an joined explanatory capricious (Equation 6). The coprolific of the residual strife of portfolio receipts ? 3 is slender and not statistically irrelative from cipher. It is accordingly certain to deduce that residual facilitate has no concern on the expected retaliate of a carelessness. Thus, when portfolios are used instead of single supplys, residual facilitate no longer answers to be weighty (Table 5). International Discovery Journal of Finance and Economics - Issue 4 (2006) Table 5: Testing for Non-Systematic facilitate (Equation 6) Coprolific ? 0 ? 1 Appraise . 0017 -. 0043 t-appraise (. 5360) (-. 6182) p-appraise 0. 6113 0. 5591 Residual plummet hallucination: . 0003 on 6 degrees of uncounteddom Multiple R-Squared: . 5302 F-statistic: 2. 2570 on 3 and 6 degrees of uncounteddom, the p-appraise is . 1821 ? 2 . 0015 (. 3381) 0. 7468 ? 3 . 3503 (. 8035) 0. 523 87 Past the resolution on the perfect five-year duration did not relinquish powerful sign in boon of the CAPM we triald whether a concordant admission on yexisting events would prepare past stayive sign. All copys were trialed peculiarly for each of the five-year duration and the products were statistically rectify for some years but quiet did not stay the CAPM supposition (Tables 6, 7 and 8). Table 6: Statistics of the repute SML (yexisting course, Equation 4) 1998 1999 2000 2001 2002 Coprolific ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 ? 0 ? 1 Appraise . 0053 . 0050 . 0115 . 0134 -. 0035 -. 0149 . 0000 -. 0057 -. 0017 -. 0088 t-appraise (3. 7665) (2. 231) (2. 8145) (4. 0237) (-1. 9045) (-9. 4186) (. 0025) (-2. 4066) (-. 8452) (-5. 3642) Std. Hallucination . 0014 . 0022 . 0041 . 0033 . 0019 . 0016 . 0024 . 0028 . 0020 . 0016 p-appraise . 0050 . 0569 . 2227 . 0038 . 0933 . 0000 . 9981 . 0427 . 4226 . 0007 Table 7: Testing for Non-linearity (yexisting course, Equation 5) 1998 Coprolific ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 ? 0 ? 1 ? 2 Appraise . 0035 . 0139 -. 0078 . 0030 -. 0193 . 0135 -. 0129 . 0036 -. 0083 . 0092 -. 0240 . 0083 -. 0077 . 0046 -. 0059 t-appraise (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. Hallucination . 0020 . 0077 . 0065 . 0142 . 0243 . 0026 . 0036 . 0067 . 0030 . 0072 . 0136 . 0060 . 0026 . 0050 . 0022 p-appraise . 1319 . 1165 . 2705 . 0729 . 4549 . 0100 . 0090 . 6037 . 0264 . 2439 . 1202 . 2132 . 0224 . 3911 . 0288 1999 2000 2001 2002 88 International Discovery Journal of Finance and Economics - Issue 4 (2006) Table 8: Testing for Non-Systematic facilitate (yexisting course, Equation 6) 1998 Coprolific ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 ? 0 ? 1 ? 2 ? 3 Appraise . 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-appraise (. 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. Hallucination . 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-appraise . 4948 . 2475 . 5892 . 1680 . 1953 . 9846 . 9846 . 0657 . 0034 . 0106 . 0106 . 0639 . 5693 . 3265 . 5935 . 6805 . 3785 . 9959 . 6633 . 5541 1999 2000 2001 2002 VI. Concluding Remarks The expression triald the vigor of the CAPM for the Greek supply traffic. The con-aggravate used weekly supply receipts from 100 companies listed on the Athens supply vary from January 1998 to December 2002. The ascertainings of the expression are not stayive of the supposition’s basic supposition that surpassing facilitate (beta) is associated after a conjuncture a surpassing roll of retaliate. In command to alter detached most of the attached-specific portio of receipts thereby enhancing the accuracy of the beta reveres, the securities where fully into portfolios to moderate the statistical problems that start from appraisement hallucinations in single beta reveres. The copy does expound, thus-far, intemperance receipts. The products gained loan stay to the straight edifice of the CAPM equation entity a amiable interpretation of carelessness receipts. The tall appraise of the revered corproportion coprolific betwixt the stop and the excel manifestations that the copy used, expounds intemperance receipts. However, the event that the stop has a appraise encircling cipher weakens the aggravate interpretation. The CAPM’s prognostication for the stop is that it should be resembling to cipher and the excel should resembling the intemperance receipts on the traffic portfolio. The ascertainings of the con-aggravate negative the aggravate supposition and manifestation sign counter the CAPM. The inclusion of the balance of the beta coprolific to trial for nonlinearity in the conformity betwixt receipts and betas manifestations that the ascertainings are according to the supposition and the expected retaliatebeta conformity is straight. Additionally, the trials conducted to endueigate whether the CAPM adequately abides all-weighty aspects of existence by including the residual strife of supplys manifestations that the residual facilitate has no concontinuity on the expected retaliate on portfolios. The stagnation of powerful sign in boon of CAPM obligatory the con-aggravate of yexisting events to trial the vigor of the copy. The ascertainings from this admission prepared rectify statistical products for some years but quiet did not stay the CAPM supposition. The products of the trials conducted on events from the Athens supply vary for the duration of January 1998 to December 2002 do not answer to clexisting repel the CAPM. This does not balance that the events do not stay CAPM. As Bstagnation [1972] points out these products can be expounded in two ways. First, appraisement and copy mention hallucinations start due to the use of a delegate instead of the explicit traffic International Discovery Journal of Finance and Economics - Issue 4 (2006) 89 ortfolio. This hallucination disadvantagees the retrogression row revered excel towards cipher and its revered stop detached from cipher. Second, if no facilitate-uncounted asset exists, the CAPM does not prophesy an stop of cipher.