Risk-Adjusted Performance: A two-model Approach Application in Amman Stock Exchange

Transcription

1 Internatonal Journal of Busness and Socal Scence Vol. 3 No. 7; Aprl 01 Rsk-Adjusted Performance: A two-model Approach Applcaton n Amman Stock Exchange Hussan Al Bekhet 1 Al Matar Abstract The purpose of the paper s to nvestgate the rsk-adjusted performance of stock portfolos through the applcaton of the Markowtz and sngle-ndex models. The monthly closng prces of 115 companes lsted n Amman Stock Exchange (ASE) and ASE ndex over the perod ( ) were used. Two elementary developed models wll be appled namely; Markowtz and sngle-ndex. Furthermore, the paper offers better optons for decson makng process n choosng optmal portfolos n ASE. Results show that there s no sgnfcant dfference between the two tested models, and that the numbers of stocks n the portfolos do not affect the result when comparng the two portfolo models. Key Words: Markowtz model; Sngle-Index model (SIM); Amman Stock Exchange (ASE); ASE Portfolos. 1. Introducton Investors n an deal nvestment envronment are normally faced wth a complcated task of selectng good nvestments, thus makng them to consder trade-offs between rsk and return and to combne varous types of nvestments n an optmal portfolo. A ratonal nvestor always seeks to mnmze rsks and maxmze returns on hs nvestment. To reach the optmal portfolos, nvestors ought to maxmze the level of return for a gven level of rsk. Alternatvely they seek to reduce the rsk for a gven level of return. Ths s done through the constructon of a portfolo of assets whch s subject to the nvestor s portfolo. Although the majorty of the studes were carred out n developed countres, only a lmted number of studes were conducted n developng countres. The study seeks to test whether the Markowtz or SIM of a portfolo selecton model provdes better nvestment optons to nvestors n ASE. The study s problem s related to how to begn the portfolo selecton models whch are regarded as vtal for nvestors n order to select ther nvestment. Presently, the Markowtz model s the best normatve model of stock selecton usng a full covarance matrx. It was notced by shape (1963) that consderable savngs could be explaned by a sngle ndex of the market snce prces of all securtes often tend to rse and fall at the same tme. Indeed, most of the covarances between securtes could be explaned by a reference to a sngle market ndex. He estmated best fttng lne for each stock wth the market ndex usng regresson model analyss. So, the man problem of ths study les wth the nvestor s ndecson due to hs/her nablty to decde whch model he/she selects owng to the dffculty of performance n the Markowtz model. The study s sgnfcance arses from the fact that the applcatons of these fundamental models develop an offer to nvestors for makng decson n the choce of optmal portfolos n the ASE. The comparson of these models s very mportant for nvestors to choose the approprate one to construct ther portfolos. It s correctly asserted that the approprate varance for the portfolo selecton model reflects portfolo rsk, that measures the rsks created not only by the nherent fluctuatons of returns, but also by the decson makers who lack the complete nformaton about the parameters of models. It conductng an emprcal analyss that has entered nto actual portfolo selecton decsons s seen as an added value n ths study. 1 Prof.Hussan Al Bekhet, College of Gratuate Studes, Unverst Tenaga Nasonal (UNITEN) Al Matar, PhD Student, Gratuate Busness School, College of Gratuate Stustudes, Unverst Tenaga Nasonal (UNITEN), Lecturer at Jadara Unversty-Jordan 34

2 Centre for Promotng Ideas, USA The study ams to realse the followng objectves: 1. Evaluatng the rsk-adjusted performance of stocks portfolos formed from ASE usng Markowtz and the SIM models.. Comparng a sample wth the results of the full covarance (Markowtz model) and the results of SIM model. 3. Examnng the performance of the Markowtz model n relaton to the SIM model n portfolo selecton process. 4. Provdng the nvestors n ASE wth complete nformaton n order to assst them n portfolo selecton process. The outlne of ths paper s as follows: The next secton offers a theoretcal background of the Markowtz and SIM models; secton 3 sheds lght on the stock exchange market n Jordan; secton 4 exhbts the lterature revew; secton 5 llustrates methodology, data sources and sample; secton 6 reports the emprcal results. Conclusons, lmtaton and manageral mplcatons are presented n the last secton.. Theoretcal Background Markowtz's (195 and 1959) was the poneer work on portfolo analyss. The major assumpton of the Markowtz s approach to portfolo analyss s that nvestors are bascally rsk-averse. Ths means that nvestors must be gven hgher returns n order to accept hgher rsk. Markowtz then developed a model of portfolo analyss. The three hghlghts of ths model are normally; the two relevant characterstcs of a portfolo are ts expected return and some measure of the dsperson of possble returns around the expected return; ratonal nvestors wll be chosen to hold effcent portfolos, those that maxmze expected returns for a gven level of rsk or, alternatvely, mnmze rsk for a gven level of return.; t s theoretcally possble to dentfy effcent portfolos by analysng of nformaton for each securty on expected return, varance of return, and the nterrelatonshp between the return for each securty and for every other securty as measured by the covarance (James and Farrell, 1997). Sharpe (1963) attempted to smplfy the process of data nput, data tabulaton, and reachng a soluton. He also developed a smplfed varant of the Markowtz model that reduces data and computatonal requrements. Although Markowtz model was theoretcally elegant ts serous lmtaton was the sophstcated and volume of work was well beyond the Markowtz model. Index models can handle large populaton of stocks. They serve as smplfed alternatves to the full-covarance approach to portfolo optmzaton. Although the SIM model offers a smple formula for portfolo rsk, t also makes an assumpton about the process generatng securty returns. The accuracy of the formula of the SIM model for portfolo varance s as good as the accuracy of ts assumpton (Haugen, 1993). Accordng to Terol et al. (006) Markowtz model s a conventonal model proposed to solve the portfolo selecton problems by assumng that the stuaton of stock markets n the future can be characterzed by the past asset data. However, t s dffcult to ensure the accuracy of ths tradtonal assumng because of the large number of extensons to problems of the tradtonal portfolo selecton. As for SIM model, t ncludes fuzzy betas obtaned not only from statstcal data but also from expert knowledge. The generalzaton of the Markowtz mean-varance model whch ncludes cardnalty and boundng constrants ensure the nvestment n a gven number of dfferent assets and lmt the amount of captal to be nvested n each asset (Fernandes & Gomez, 007). Markowtz model contrbutes n geometrc mean optmzaton advocated for long term nvestments. On the other hand, the SIM models are no longer good approxmatons to mult perod (Brec & Kerstens, 009). 3. An Overvew of the Stock Exchange Market n ASE 76 companes traded on ASE untl March 011. The performance of ASE n the years 009 and 010 was exceptonal. The tradng value of ASE that ended the tradng transactons for 010 was JD6.7 bllon compared to JD9.7 bllon for 009. The ASE prce ndex weghted by free float shares closed at 374 ponts n 010 wth a decrease of 6.3% when compared wth the closng of shares that stood at 534 ponts and 758 ponts at the end of 009 and 008 respectvely. However, non-jordanan ownershp as a percentage of market captalzaton of the ASE rose to 49.6% at the end of the 010, compared wth 48.9% at the end of the 009, and 49.% at the end of 008. Although, The net non-jordanan nvestments n the ASE wtnessed sharp declne by JD14.6 mllon for the year 010, compared wth a declne of only JD3.8 mllon for 009. Fve new companes were lsted at the ASE durng 010 rasng the number of lsted companes to 77. In addton, the market captalzaton of lsted shares at the ASE stands at JD1.9 bllon, consttutng 1.7% of the GDP. 35

3 Internatonal Journal of Busness and Socal Scence Vol. 3 No. 7; Aprl 01 The number of traded shares wtnessed an ncrease durng 010 reachng 7 bllon shares, traded through 1.9 mllon transactons, compared wth 6 bllon shares traded durng 009 through 3 mllon transactons. The share turnover rato also ncreased to reach 10.% durng the perod 010, compared wth 91.3% durng the perod 009. Fgure (1) shows the tradng movements of the Amman Fnancal Market snce ts ncepton n 1978 untl 010. The fgure records the value and amount traded n Jordanan Dnars (JD) durng the stated perod. Fgure (1): Value Traded. Fgure (1) of ASE value traded shows dfferences n the pattern of tradng between 1978 and 010. Tradng started at JD5,615,891 n 1978, rsng gradually to reach the frst peak n 005 wth a value of JD16,871,051,948 then dropped dramatcally n 006 and 007 to JD14,09,870,59, JD 1,348,101,910 respectvely and then clmbed back to reach the second peak wth a value of JD 0,318,014,547 n 008, only to drop agan to JD 6,689,987,155 n 010 ( Fgure () shows the ASE General Free Float Prce Index for the perod. 36 Fgure (): Prce ndex.

4 Centre for Promotng Ideas, USA The ASE prce ndex weghted by free float show growth rate of 10.4 percent durng the perod, t shows also a decrease from 758 ponts to 534 ponts at the end of 008, wth the number of traded shares ncreasng durng the perod n 009. One of the features of Free Float Index s to gve better reflecton for the changes of stocks prces n the market by not beng based to the companes that have large market captalzaton. Ths provdes dversfcaton n the ndex sample by gvng better chances to small and medum companes to reflect the ndex. 4. Lterature Revew The majorty of prevous studes n ths feld are based on Markowtz s or the SIM Model, as tools to nvestgate ssues n portfolo. These studes are mostly carred out n developed countres. As seen by Frankfurter et al. (1976) the SIM approach s based on Markowtz model. However, ths approach adds the smplfyng assumpton that returns on varous securtes are related only through common relatonshp wth some basc underlyng factors. Accordng to ths study, under condtons of certanty, the Markowtz and SIM approaches wll arrve at the same decson set n the experment. These results demonstrate that under condtons of uncertanty, SIM approach s advantageous over the Markowtz approach. It was found that varaton n performance s explaned n terms of the two essental dfferences n the models. Frst, fewer and dfferent estmators are used n the SIM model to summarze past hstory. Second, the lnear assumpton of the SIM model does not necessarly hold. They fnally found that n experments, the SIM process performs worse than Markowtz process, and gves superor results when only short data hstores are avalable. Yamazak and Konno (1991) show that the mean absolute rsk functon can remove most of the problems and obstacles assocated wth the classcal Markowtz model whle mantanng ts advantages over equlbrum models. The mean absolute devaton rsk model can be used as an alternatve to Markowtz s rsk model as t generates a portfolo resemblng that of the Markowtz model wthn a fracton of tme requred to solve the latter. By applyng portfolo selecton models examnng the relatve performance of varous estmators and the effectveness of short sales Board and Sutclffe (1994) forecasted the means varances and covarances. Results show that the short sales decson was consderably more mportant than the choce of estmaton method n mprovng the performance of actual portfolos The relatvely good performance of the non-markowtz technques and of the smplstc overall mean method s an nterestng fndng as t suggests that sophstcated portfolo selecton technques and forecastng methods may not offer sgnfcant benefts over much more straghtforward methods. A study by Ledot and Wolf (003) revealed that the covarance matrx of stock returns s estmated by an optmally weghted average of two exstng estmators: covarance matrx and sngle-ndex covarance matrx. The authors developed a flexble method for some structures nto a large dmensonal estmaton problem, namely the problem of estmatng the covarance matrx of a large number of stock returns, and the estmated covarance matrx s the nput of the well known portfolo selecton method of Markowtz. It was also found by Edward et al. (005) that the generalzed Markowtz's portfolo selecton theory and generalzed Sharpe's rule mproved decson makng from nvestment addressng a dynamc portfolo nvestment problem and dscussed how we can dynamcally choose canddate assets, achevng the possble maxmum revenue and reducng the rsk to the mnmum. They generalzed Markowtz's portfolo selecton theory and Sharpe's rule for nvestment decson. An analytcal soluton s exhbted to show how an nsttutonal or ndvdual nvestor can combne Markowtz's portfolo selecton theory, generalzed Sharpe's rule and Value-at- Rsk to fnd canddate assets and optmal level of poston szes for nvestment (ds-nvestment). An emprcal comparson among suggested portfolo choce models comparng the fnal wealth, expected total realzed return of the optmal portfolo, and performance ratos for obtaned sequences of excess returns was suggested by Bglova and Rachev (007). They also showed the strongly reject sequences of the normalty assumpton n favour of the stable Paretan hypothess. Celk (007) proposed that the market rsk ndcator (Beta) of Turksh banks common stocks s much hgher than those of USA. By analyzed bankng sector n USA and Turkey focusng on 18 bggest banks' common stocks and measured the rsk of common stocks and show ther relatons wth the market portfolo's return based on theoretcal framework of modern portfolo theory and Captal Assets Prcng Model (CAPM). Also the volatlty of Amercan banks common stocks are lower than those of Turksh and the rsk and return relatonshp s not totally supported by Captal Asset Prcng model. 37

5 Internatonal Journal of Busness and Socal Scence Vol. 3 No. 7; Aprl 01 Omet (1995) argued that the two models are smlar. Also, nvestors mght be able to use the more practcal approach n generatng ther effcent fronters. In other words the SIM model can be used, whch s more practcal than the Markowtz model n generatng ASE effcent fronter. Omet s study (1995) was much related to ths research. However, there are some dfferences such as the perod of study, the sample, and the portfolo structure, and concentrated on the effcent fronter. Al-Qudah et al. (004) nvestgated the effects of dversfcaton on the portfolo rskness n ASE, and the methodology based on the Markowtz Model (195). The results proved the exstence of a sgnfcant statstcal relatonshp between portfolo sze and the rsk reducton. Yet, the t-test stated that sgnfcant reducton benefts of dversfcaton were vrtually exhausted when a portfolo contans stocks. Furthermore, nvestors should mplement margnal analyss n order to determne the number of stocks requred n a well-dversfed portfolo. Segot and Lucey (005) examned the captal market ntegraton n the MENA countres and ts mplcatons for an nternatonal portfolo nvestment allocaton. Results showed that Israel and Turkey were the most promsng markets n the regon. They are followed by Jordan, Egypt and Morocco, whle Tunsa and Lebanon lagged behnd. Paudel and Korala (006) tested whether Markowtz and SIM models of portfolo selecton offer better nvestment alternatves to Nepalese nvestors by applyng these models to a sample of 30 stocks traded n Nepalese stock market from Results show that the applcaton of the elementary model developed about a half century ago offered better optons for makng decson n the choce of optmal portfolos n Nepalese stock market. Abdelazm and Wahba (006) argue that even n a bearsh market, the optmally selected portfolo, whch was weekly managed usng Neural Networks, was able to generate postve returns utlzng the Markowtz Effcent Fronter. Ther results also demonstrated the usefulness of applyng the proposed approach represented by Genetc Algorthms and Neural Networks n actve portfolo selecton and management. The US stock market represented by a pool of 40 US companes from , and the Egyptan stock market, represented by a pool of 37 companes from addressed the portfolo selecton and management problem, modern portfolo theory and Markowtz effcent fronter usng Artfcal Intellgence technques and Genetc Algorthms Technques (GAs) to construct an optmal portfolo. GAs s tested on stock markets, the US stock market, and the Egyptan stock market. Bergh & Rensburg (008) drew a comparson between the results of the Markowtz mean varance optmzaton technque wth the hgher moment methodology proposed by Daves et al. (005) usng world hedge fund ndex and asset class data from Result affrm the fndngs of Daves et al. (005) and Feldman et al. (00) suggestng that the applcaton of Markowtz mean varance portfolo selecton to an array of publshed hedge fund ndces produces fund-of-fund portfolos wth hgher ex post returns but naı ve exposure to undesrable hgher moment rsks. Whle the hgher moments of hedge fund ndex return dstrbuton are accounted for n the portfolo optmzaton algorthm, the resultant portfolos have mproved dversfcaton and hgher moment statstcs. An optmal combnaton of the nave1/n rule wth one of the four sophstcated strateges namely the Markowtz rule, the MacKnlay and Pa stor (000) rule, the Joron (1986) rule, and the Kan and Zhou (007) rule as a way to mprove performance proposed by Tu & Zhou (011). It was found that the combned rules not only outperform the 1/N rule n most scenaros, but also have a sgnfcant mpact n mprovng the sophstcated strateges. The study s nterpreted as reaffrmng the usefulness of the Markowtz theory n practce. Based on the study s objectves, orentatons and the lterature revew the followng hypotheses can be formulated: H1: There exsts a sgnfcant dfference between portfolo selecton n terms of rsk, based on the Markowtz and SIM model, n ASE. H: There exsts a sgnfcant dfference between Markowtz varance and sngle ndex varance. H3: There exsts a sgnfcant dfference between Markowtz and SIM varance n case of the change n the number of Stocks n ASE constructed portfolos. 5. Methodology and Data 5.1 Data Source and Sample The stock market prce ndex s vewed as the study s populaton. It ncludes stocks of all companes dstrbuted n three sectors (Fnancal, Servces and Industral), lsted n ASE durng the study perod ( ). 38

6 Centre for Promotng Ideas, USA Snce stock prce ndex reflects both the rsks and returns of the commonly traded stocks of ASE, ths ndex s constructed by ncludng prces of all the securtes traded n ASE. The conduct of ths ndex wll be nvestgated by resortng to statstcal testng (SPSS.18 and Mcrosoft excel) to determne the varablty of the stock returns n ASE durng the study perod. The data wll cover the 1/1/000-31/1/006 perod for duraton of the seven years. The perod at the begnnng of the thrd mllennum, a tme perod that preceded the global fnancal crss; pre-007, gves an opportunty for supportve studes to show f there are any dfferences, durng and after the fnancal crss, and to evaluate the relatve effectveness of the Markowtz and SIM models. The selected sample fulfls the followng condtons: 1. Companes lsted on the ASE market durng the perod of ths study.. All companes share the same fscal year, endng on 31 December of each year. 3. Companes havng no change n poston (e.g. mergers, stock splt, and suspenson of trade). Gven these condtons, a sample of 115 companes lsted on the ASE satsfed our requrements. The data were obtaned from the Department of Research and Internatonal Relatonshp of the ASE market. It conssted of daly reports ssued by the ASE market on closng prces, volume of trade, and the number of shares traded. 5. Methodology The research methodology s centred on the applcaton of two models, namely; Markowtz and SIM models. The actual (realzed) return on each stock s calculated as follows (Al-Qudah et al., 004): R R,t1 P,t1 n P P,t R t 1 R n n t1,t,t1 ( R, t1 n 1 R Where R,t 1 s the return on stock n the month t 1;,1 the closng prce of stock n the month t 1; ) (1) () (3) P s the closng prce of stock of the month ; P,t 1 s R s the average rate of return for stock ; n s the number of holdng months of stock ; R s the varance of stock. The expected return on a portfolo E(R p,t 1) s calculated usng equaton (4). The rsk of a portfolo s gven by formula (5), and the expresson covarance ( R,R j) s gven by equaton (6): n E(R ) WE(R ) (4) p,t1 1 p n n n 1 1 j1 j j j ( R, R j),jsd(r )SD(R j Var(R ) W Var(R ) W W Co var ance(r,r ) (5) Covarance ) (6) Where n s the number of securtes n the portfolo; W s the proporton (weght) of nvested funds n securty (=1,...,n); E(R ) s the expected return on securty (=1,...,n); Var (R p ) s the varance of the return n the portfolo; Var (R) s the varance of the return on securty ; W j s the proporton (weght) of nvested funds n each of the securtes n the portfolo; Covarance ( R, R j) s the covarance between the returns of securtes and j;, j s the correlaton coeffcent whch measures the extent to whch the returns on securtes and j are lnearly related; and SD s the standard devaton of securtes and j. If we substtute equaton (6) nto equaton (5) we have Jones, (1991): 39

7 Internatonal Journal of Busness and Socal Scence Vol. 3 No. 7; Aprl 01 n n n Var (R p ) W Var(R ) (W )(W j), jsd(r )SD(R j) (7) 1 1 j1 j From equaton (5) or (6), one realzes that the rsk of a portfolo s a weghted average of the ndvdual securtes n the portfolo plus the covarance between each securty and every other securty n the chosen portfolo. Sharpe (1964) suggested the sngle ndex model to make the calculaton of rsk more practcal. The essence of ths model s that all shares are affected by the movement of the market n general. The SIM can be expressed by: R,t R M,t e,t (8) Where perod t; R, t s the return on securty for the tme perod t; M t s the constant term, error term for perod t. R, s the return on the market ndex for the tme s the senstvty of stock to the return of the market; e, t s the resdual Usng the SIM model, one needs to apply the followng equatons (Haugen, 001): (R) (R ) ( ) (9) m ( ) r (R m,r j) j ) (10) Cov(R (R ) (11) m Where ( R ) s the varance of the return; represents the systematc rsk; ( ) s the resdual varance (unsystematc rsk) and ( R m ) s the varance of market return. The return on each share as well on the market ndex s calculated as follows: R (p p ) / p (1) Where t t t1 t1 Pt s the prce level of a share or ndex for the tme perod t. 6. Results Analyss The examnaton of the relatonshp between the Markowtz and the SIM models requred the selecton of 35 equally weghted portfolos wth two szes of portfolo. The frst sze (10 stock portfolo) generated 1 portfolos based on queung randomze portfolo that were randomly selected to smulate equally weghted portfolos of second szes, 5 stock portfolos (3 portfolos from the second sze were generated based on queung randomze portfolo selecton). As shown n table (1) ten and fve stocks were selected. The next step nvolves computng the varance for each portfolo generated n order to determne the relatonshp between the two selecton models accordng to the output of methodology equatons (1-1) as llustrated n Appendx 1 and. The results obtaned show the portfolo sze splt was used to examne the portfolo sze does affect the relatonshp between the two selecton models. In order to test the hypotheses formulated above, the researchers conducted a prmary analyss, monthly mean rates of return, stock varances, betas, Standard Devaton, Correlatons, and Covarance between stocks and Market (see Equatons as clarfed n secton 6 and the Appendx 1 & ). 40

8 Centre for Promotng Ideas, USA Table1: fve and ten stocks portfolo varance. Number of stocks Markowtz SIM. Number of stocks Markowtz SIM. Varance n portfolo Varance Varance n portfolo Varance Source: Appendces 1 and. Table (1) llustrates the relatonshp between Markowtz and SIM models. Furthermore, the results n Table 1 show that the two selecton models have nearly smlar varance. As shown n the Table (), whle the mean for Markowtz and SIM models n the case of 10 stocks portfolos are and respectvely and the mean for Markowtz and SIM models n the case of 5 stocks portfolos are and respectvely. However, the dfferences between the two means are very small; Table : Descrptve Summary of Table stocks portfolos 5 stocks portfolos Measure Markowtz SIM Markowtz SIM Measure Model Model Model Model Mean Mean Mn Mn Max Max Standard Devaton Standard Devaton Source: Table 1. The ANOVA analyss of 10 stocks portfolos whch are reported n Table (3) ndcate that the effectve score for Markowtz and SIM models are relatvely the same. However, the dfference between the two means and standard devatons are very small; and respectvely. Table 3: ANOVA Table for Markowtz Varance versus SIM Varance I. ANOVA Analyss Sum of Squares df condton Mean Std. Devaton Std. Error Mean F Sg. Between Groups Wthn Groups Total Source: Output of SPSS Package, verson

9 Internatonal Journal of Busness and Socal Scence Vol. 3 No. 7; Aprl 01 Furthermore, the result (Table 3) reveals that the F-test s (Sg. = > 0.05) meanng that s statstcally nsgnfcant; therefore, H1 and H are rejected. Table (4) shows ANOVA analyss of 5 stocks portfolos. These results ndcate that the F-test value s (Sg. = > 0.05) whch means that s statstcally nsgnfcant; therefore, H1 and H are also rejected. Table 4: ANOVA Table for Markowtz Varance versus SIM Varance II. ANOVA Analyss Sum of Squares df condton Mean Between Groups Wthn Groups Total Std. Devaton Std. Error Mean F Sg Source: Output of SPSS Package, verson 18. It can be seen from Table (4) that the effectve score for Markowtz and SIM models are almost the same. Furthermore, the dfference between the two means and standard devatons are very small and respectvely. Based on the ANOVA analyses for 5 and 10 stocks portfolos as shown n the Tables (3 and 4), also H3 s rejected. Ths s because there s no sgnfcant dfference between Markowtz and SIM varance, regardless of the stock number n ASE constructed portfolos. 7. Concluson, Lmtaton and Manageral Implcatons The Markowtz and SIM models n ASE were appled by usng the monthly closng prces of 115 companes lsted n ASE and ASE ndex for the perod. From the analyss, the followng mportant results can be presented. Frst, the results show how the SIM model s smlar to Markowtz model for portfolos formed. Second, the number of stocks n the portfolos constructed does not seem to affect the result of comparng the two portfolo selecton models. Thrd, t s whether nvestors use Markowtz or SIM model on ther portfolo selecton decsons. Therefore, these results were used to reject the hypotheses of the study, H1, H, and H3. Fourth, the F- test ndcates that there s an nsgnfcant dfference between the Markowtz and SIM models. As the portfolo selecton models are very mportant for rsk test, nvestors should take specal care when selectng ther portfolos. These results are useful to ndvdual and nsttutonal nvestors, managers, and polcy makers n makng decson and adoptng new nvestment polces. Future research of ASE n Jordanan unverstes and research centres should concentrate on portfolo selecton models. It s necessary to buld a network of research and tranng nsttutons to provde a sutable polcy for the development of new portfolo selecton models and polces. The study has a number of lmtatons, namely: Lack of prevous studes nvestgatng smlar purposes, as ths study, refer to that most of the studes were carred out n developed countres, only lmted numbers of studes have been conducted. The excluson of companes that are not lsted on the ASE; companes that are lsted and traded but stopped operatons. Ths study used monthly data rather than daly data. The current paper s mportant for all stakeholders. It s vral for polcy makers, all knds of nvestors, corporatons and other fnancal market partcpants. The study shows that the two models are smlar. There seems to be no sgnfcant dfference between the two models, whereby, the results are almost smlar to the earler results (e.g. Omet, 1994; Paudel and Korala, 006; and Edward et al., 005). On the other hand, Frankfurter et al. (1976) revealed that under condtons of uncertanty, SIM approach had potental advantages over the Markowtz approach. They found that varaton n performance was explaned n terms of the two essental dfferences n the models; namely: 1. Fewer, and dfferent, estmators are used n the SIM model to summarze past hstory.. The lnear assumpton of the SIM model does not necessarly hold. In ths study, we add to the canon of knowledge related to the Markowtz and SIM models. By examnng the H3 hypothess, t was found that changng the number of stocks dd not affect the results whch are used to reject the H3 hypothess.

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11 Internatonal Journal of Busness and Socal Scence Vol. 3 No. 7; Aprl Appendx 1: The Standard Devaton, Correlatons, and Covarance between stocks and Market. Code Standard Correlaton Covarance Standard Correlaton Covarance Code devaton coeffcent ( R,R m) devaton coeffcent R,R ( m )

12 Centre for Promotng Ideas, USA Appendx : Return, varance, and Beta of the Stocks of the [1/1/000-31/1/006] Perod. Stock Code Mean Return Varance Beta Stock Code Mean Return Varance Beta