In response to the world-wide market downturn since 2000 and because of some unfavourable

Transcription

1 THE RETURN AND RISK PROFILE OF EQUITIES AND EQUITY PORTFOLIOS AT THE BUDAPEST STOCK EXCHANGE* GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER 3 Ths paper examnes the rsk and return characterstcs of equtes lsted and traded n category A at the Budapest Stock Exchange n the tme perod of The performance of two portfolo strateges s also evaluated. It s shown emprcally that a systematc portfolo allocaton has several advantages to stock pckng. Indeed, the portfolo strateges examned performed well not only on an ex post but also on an ex ante bass. KEYWORDS: Rsk and return of equtes. Equty portfolos. Budapest Stock Exchange. In response to the world-wde market downturn snce 000 and because of some unfavourable governmental steps and taxaton reasons, the turnover and the captalsaton on the equty market of the Budapest Stock Exchange (BSE) has fallen sgnfcantly. Partcularly, n 00 the market turnover fell by 60 percent and the captalsaton of equtes decreased by 6 percent as compared to the end of the year 000 (Statstcal Report [00], p. 6 8). The negatve trends of the earler year seemed to take an upward turn n 00. It s ndcated by the fact that both the turnover and captalsaton of the equty market have ncreased by more than 9 and 3.5 percent, respectvely (Statstcal Report [00], p. 3 4). The am of ths paper s to study the rsk and return characterstcs of equtes lsted n category A of the BSE over the perod The performance of two portfolo strateges s also analysed. We ntend to show that a systematc portfolo allocaton has several advantages over the approach of pckng some ndvdual equtes to nvest n, especally n tmes of undesrable market processes. The structure of the paper s as follows. The next secton provdes a descrpton of the database used n the analyss and the methodology appled. Emprcal results are presented next, followed by some concludng remarks. * The frst author was generously supported n wrtng ths paper by the Hungaran Academy of Scences n the framework of the Bolya Scholarshp. The authors wsh to thank Eszter Kocss (Informaton Centre of the Budapest Stock Exchange) for all her help n data collecton and provdng up-to date nformaton. Assocate Professor, Unversty of Pécs, Faculty of Busness and Economy. Fnalst Student, Unversty of Padua, Faculty of Economcs at the tme of wrtng the paper: ERASMUS Student at the Unversty of Pécs. 3 Supply Chan Leader, Elcoteq Hungary. At the tme of wrtng the paper: Fnalst Student, Unversty of Pécs, Faculty of Busness and Economcs, Busness Degree Programmes n Englsh. Hungaran Statstcal Revew, Specal number

2 BUGÁR BARATTO PREHOFFER: THE RETURN AND RISK PROFILE OF EQUITIES 3 DATA AND METHODOLOGY The database for the analyss conssts of the daly closng prces of the equtes lsted and traded n category A at the Budapest Stock Exchange and those of the BUX ndex wthn the perod of 3 January 00 to 3 December 00. In 00, the category system for equtes at the BSE was revsed and equtes were grouped nto two categores, A and B, usng a modfed set of crtera (Annual Report [00], p..). The captalsaton of the equtes lsted n category A represented more than 90 percent of the total equty captalsaton n both years studed n our current paper (Statstcal Report [00] and [00], p.4.). Frstly, we excluded from our analyss the tme seres that were not complete, snce t s not possble to compare securtes on the base of dfferent (or n any case, excessvely dfferent) tme seres. In partcular, we excluded Graboplast and Csopak. The former was removed from the tradng lst n December 00 and the latter was delsted n January 00. Although, Pck was also removed from the tradng lst on 7 November 00, n that partcular case, we had enough data to perform the analyss. Therefore, there were altogether 4 securtes ncluded n the study: Antenna Hungára, BorsodChem, Danubus, DÉMÁSZ, Egs, Fotex, Globus, Graphsoft, Humet, Inter-Európa Bank, MATÁV, Mezőgép, MOL, NABI, OTP Bank, Pannonplast, Pck, Prímagáz, RÁBA, Rchter Gedeon, Synergon, TVK, Zalakeráma and Zwack Uncum. We also consdered the BUX ndex. Moreover, we had to fnd and adjust the prces resultng from splt and reverse splt 4 : In case of OTP, there was a 0-to- splt n March 00. It means that each shareholder receved 0 new shares wth the face value of /0 th of the orgnal for each old (pre-splt) shares held, and the old shares were wthdrawn. Ths type of transacton has the drect result that the face value of all shares held remans unchanged. In order to handle the above-mentoned splt properly, we multpled all the after-splt values (closng prces) n the tme seres by 0. In case of Humet, a -to-0 reverse splt was made n September 00, n whch the exstng stocks were replaced by new ones, for each 0 old share a new share was gven wth a face value 0 tmes hgher than the orgnal one. Therefore, we dvded the aftersplt prces by 0. 5 We decded to use weekly returns as the bass for the analyss. In our opnon, to a large extent ths tme unt s not nfluenced by the events that have but a lmted and only daly mpact on the tradng of securtes and, at the same tme, t has the rght senstvty to the changes n the trend of the tme seres. For ths reason, we took the closng prces of Wednesdays, as t s a day n the mddle of the week and therefore ther prces do not carry the effect of varables related to the begnnng nor the end of the week. In those few cases, when Wednesdays were not applcable for ordnary busness reasons we took the nearest day at our dsposal. 4 The announcement on splt/reverse splt can always be found among the BSE News (Press Releases/Orders) on the homepage of the BSE: 5 Throughout the analyss we took the vewpont of the nvestor who keeps the securty once acqured durng the whole perod studed,.e. we consdered buy-and-hold decsons. Dong t otherwse, especally n case of splt/reverse splt, one can easly make a mstake when calculatng returns based on unmodfed securty prces.

3 4 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER Based on the Wednesdays prces, the weekly rates of return were calculated as follows: P, t P, t R, t = // P, t P, t R, t where and are the prce and the rate of return on equty on the week t, respectvely. The weekly return defned above s gven n percentage and can be regarded as a relatve measure of proftablty. After ths step we had altogether 5 data n each tme seres of weekly returns for both years (the only excepton was Pck, for whch 44 return data were avalable n 00). From the tme seres of the weekly returns we calculated 6 the followng values for each equtes: Average (weekly) return: where T s the number of weeks consdered. Standard devaton of return 7 : T R = T R t t=, // σ = T ( R, T t= t R ) /3/ Covarance of return wth that of the BUX: σ, BUX T = T t = ( R R )( R RBUX ), t BUX, t /4/ where R BUX, t s the return on the BUX ndex on the week t and R BUX s the average return on the BUX. Rsk ndex beta wth respect to the BUX: σ β = σ, BUX BUX /5/ where σ BUX denotes the standard devaton of return of the BUX. Correlaton of returns for each pars of equtes: ρ, j = T T ( R, t R)( R j, t t = σ σ j R ) j /6/ 6 Strctly speakng, we estmated the parameters n queston relyng on the sample, namely on the tme seres of weekly returns. 7 To be more exact, nstead of the above formula we used the emprcal unbased estmator for the standard devaton.

4 BUGÁR BARATTO PREHOFFER: THE RETURN AND RISK PROFILE OF EQUITIES 5

5

6 THE RETURN AND RISK PROFILE OF EQUITIES 5 The rsk ndex beta above s regarded as a measure of market related rsk, often referred to as systematc rsk (Levy Sarnat [984], p ). It can be nterpreted and estmated as the slope of the lnear tme-seres regresson of the securty return ( ) on the return of the market portfolo, the BUX ( where e, t R BUX, t ). In our case: R, t α + βrbux, t + e, t R, t = /7/ s the error term (the devaton from the regresson lne) and α s the regresson constant (vertcal ntercept). Assumng that the error term s uncorrelated wth the return on the market portfolo and takng the varance of both sdes of Equaton /7/ we obtan: σ = β σ BUX e + σ /8/ At ths pont we had all the nput data to make a portfolo optmsaton based on Markowtz s [999] theory, the Mean-Varance crteron. A portfolo s a combnaton of the dfferent securtes selected by the nvestor. Techncally, t s a vector of weghts,.e. the percentages of the total captal nvested nto the dfferent securtes. The return on a securty as well as on the portfolo of securtes must be handled as a random varable, because t s unknown at the begnnng of the nvestment perod when the nvestment decson makng takes place. In the Markowtz model the rule upon whch the selecton between dfferent nvestment optons s made s the followng: an opton F s preferred to an opton G f and only f ( R) E ( R) F EF G and σ ( R) σ ( R) /9/ for all values of R (wth strct nequalty for at least one value of R). 8 In /9/ E(R) and σ (R) denote the expected return and varance (the square of the standard devaton) of return, respectvely. The expected return s taken as an ndcator of the nvestment s average proftablty; the varance of return serves as an ndcator of ts rsk. Instead of the varance, the standard devaton of return can also be regarded and nterpreted as a rsk measure. As an estmator of the expected return, the average return (.e. the mean) R can be used. In ths context formula /8/ can be referred to as the decomposton of rsk, where β σ BUX s the systematc rsk component and σ e s the non-systematc rsk component (the former can also be called non-dversfable rsk and the latter s cted as dversfable rsk). The return on a portfolo can be formulated as: G p N R = x R = /0/ 8 Regardng a more detaled dscusson of the above mentoned Mean-Varance Effcency Crteron and ts applcatons see e.g. Markowtz [999], p. 9 0 or Levy Sarnat [984], p

7 6 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER where R s the return on securty, x s the weght n securty (.e. the proporton of money nvested n t) and N s the number of securtes held n the portfolo. In order to determne the expected return on a portfolo, the weghted average of the expected returns of the securtes t ncludes need to be calculated. Therefore, the portfolo s expected return can be expressed as: E x R = N p = // where R s the average return on securty. The varance of a portfolo s nfluenced both by the varance of the ndvdual securtes wthn and by the correlaton between the varous pars of securtes: N σ = x σ + p = N N xxjσσjρ, j = j= j>. // The portfolos we seek to dentfy are the effcent portfolos. A portfolo s effcent f there s no other portfolo preferred wth respect to the condtons n /9/. It means that an effcent portfolo s the nvestment wth the hghest expected return on a certan level of rsk or t s the one wth the lowest rsk on a certan level of expected return. In order to determne the combnatons of securtes that comprse the effcent portfolos one has to solve the optmsaton problem as follows: subject to N mn σ p N = x σ = E + N N xxjσσjρ, j = j= j> x R = N p = x = 0 x =,,..., N = /3/ The objectve functon expresses the am to dentfy the portfolo weghts ( ) for each feasble expected portfolo return ( ) so that the rsk of the portfolo ( ) s E p mnmsed. The expected return, the standard devaton of return of each securty and the correlaton matrx of returns are used as the nput parameters estmated from the sample. The last constrant n /3/ means that only long postons are allowed,.e. short sales are excluded. It mples that t s not possble to sell securtes the nvestor does not own and use the proceeds to nvest n other securtes. Ths restrcton s n concdence wth the regulaton predomnant at the BSE where short sales are 9 forbdden. x σ p 9 A detaled dscusson of short sales can be found n Sharpe Alexander [990].

8 THE RETURN AND RISK PROFILE OF EQUITIES 7 To make the optmsaton n practce we used the software Invest 0, whch has been developed to accompany Modern Investment Theory by Haugen [997]. EMPIRICAL RESULTS The man fgures on rsk and return characterstcs of the equtes are presented n Table and Table, for the year 00 and 00, respectvely. In addton to the equtes, the BUX ndex s also shown n the tables. The BUX ndex s used as the proxy of the market portfolo, namely the benchmark wth respect to the beta values are estmated. Beyond the average (weekly) return and the standard devaton, we report the performance rato, defned as the average return per unt of standard devaton. Because the standard devaton s consdered as a measure of rsk, the performance rato can be regarded as the rsk-adjusted average return. Furthermore, we lst the beta, the t-statstc (that shows whether beta s sgnfcantly dfferent from 0), the R (that ndcates the explanatory power of the model /7/) and also the term labelled by rsk rato. Accordng to our defnton, the last one s the rato of the non-systematc (or the so-called dversfable) and the total rsk component (see the decomposton of rsk gven by formula /8/). The man rsk and return fgures of category A equtes of the BSE n 00 Table Equty Average return (percent) Standard devaton Performance rato Beta Rsk rato t-value R ANTENNA * 0.8 BCHEM * 0.4 DANUBIUS DÉMÁSZ EGIS * 0.9 FOTEX * 0.8 GLOBUS * 0. GRAPHISOFT * 0. HUMET IEB * 0.3 MATÁV * 0.7 MEZŐGÉP * 0.3 MOL * 0.6 NABI * 0.5 OTP * 0.4 PICK * 0. PPLAST * 0.3 PRÍMAGÁZ * 0.5 RÁBA * 0. RICHTER * 0.8 SYNERGON * 0.5 TVK * 0.34 ZALAKERÁMIA * 0.0 ZWACK ** 0.07 BUX * β s sgnfcantly dfferent from zero at 5 percent level. ** β s sgnfcantly dfferent from zero at 0 percent level. 0 The software was programmed by Davd Y. Tan, Joe Dada III, Km Peters and Crag Lews. However, one should be cautous n usng the performance measure when the average return s negatve because ts value s completely msleadng. If we compare two securtes wth the same negatve return, the negatve performance rato s hgher for the securty whch s less rsky. That s why we smply omtted the values n the case of equtes wth negatve average return.

9 8 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER The frst result we got from our research s that the number of stocks wth postve average return s only 7 n 00 and 3 n 00 out of the total pool of 4 equtes analysed (the rows of the tables belongng to the securtes wth postve returns are hghlghted). Indeed, the market passed through a crss for whch the man causes are wellknown. The negatve trend n securty returns was a global phenomenon and therefore we consder t to be a systematc reacton of the Budapest Stock Exchange to a world-wde recesson. It s confrmed by a workng paper (A csatlakozás előtt álló [003], BSE Publcaton, p. 6) that descrbes the man characterstcs of the stock exchanges of the accesson countres of Central and Eastern Europe n the perod of As an ndcator of the global downturn n Europe, the study refers to a 35 percent change n the value of the FTSE Eurotop 00 ndex (whch conssts of the shares of 00 blue-chp companes n the European Unon) from 00 to 00. In 00 the average weekly return ranged between.3 and 0.7 percent and the standard devaton of returns altered between 3.4 and.96 percent. In 00, the average return was wthn the range of.08 and.47 percent, whle the standard devaton of returns was between.53 and.9 percent. The performance rato seems to be qute low on average: few stocks have a good payout for the rsk mplct n the share. In 00, the hghest performance rato (0.) was regstered for the equty wth the hghest average return (Globus). In 00 IEB has shown the hghest performance (0.) wth a relatvely bg average return (.%) and modest rsk (5.7%). Table Equty The man rsk and return fgures of category A equtes of the BSE n 00 Average return (percent) Standard devaton Performance rato Beta Rsk rato t-value R ANTENNA * 0.8 BCHEM * 0.9 DANUBIUS DÉMÁSZ * 0.09 EGIS * 0.34 FOTEX * 0.33 GLOBUS * 0.09 GRAPHISOFT * 0.4 HUMET IEB * 0.0 MATÁV * 0.67 MEZŐGÉP * 0.4 MOL * 0.58 NABI * 0. OTP * 0.83 PICK PPLAST * 0.4 PRÍMAGÁZ ** 0.07 RÁBA * 0. RICHTER * 0.57 SYNERGON * 0.39 TVK ZALAKERÁMIA * 0.4 ZWACK BUX * β s sgnfcantly dfferent from zero at 5 percent level. ** β s sgnfcantly dfferent from zero at 0 percent level.

10 THE RETURN AND RISK PROFILE OF EQUITIES 9 Based on the fgures reported n Table and Table, we can observe some mprovement throughout the two-year perod. The crss had ts worst effects n 00 and ths lne of reasonng can be supported by several facts: there were only 7 securtes wth postve average returns n 00 aganst 3 n 00. when comparng the values of average return and standard devaton of return (rsk) for the same securty we realse that n 6 cases (out of the 4) the average return was hgher, and n 6 cases the rsk was lower n 00 than n equtes had a preferable rsk and return profle (.e. the hgher return and lower rsk at the same tme) n 00 than n the prevous year. Consequently, n 00 there were only two securtes wth lower average return and hgher rsk as compared to 00. the grand mean of the average returns was hgher n 00 ( 0.07%) than n 00 ( 0.7%) but t was stll negatve, and t was accompaned by a lower mean rsk (standard devaton). For the latter the respectve values were 5.35 percent (n 00) and 6.7 percent (n 00). by lookng at Fgure, where the values of the BUX ndex are dsplayed over the perod studed, t s easy to recognse that the negatve trend of prce movements has changed to a postve one. Ths can be confrmed by calculatng and comparng the annual returns. In fact, the annual return of the BUX ndex was 4.9 percent n 00 and 0.7 percent n 00. Accordng to the Annual Report (BSE [00], p. 4), consderng the return on the BUX n 00, the BSE became the fourth best-performng exchange n the world. Fgure. The values of the BUX ndex from January 00 to December January 00 July 00 December 00 July 00 December 00 It s worth mentonng that the annualsed standard devatons fall nto the range of percent n 00 and percent n 00, respectvely. The annualsed The annualsed standard devaton can be calculated by multplyng the weekly standard devaton by 5.

11 30 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER mean values of the standard devaton are 44.5 percent (00) and 38.6 percent (00). These values are hgh even n the context of emergng markets (for comparson see Bernsten [000], p. 6 and 9-8). When lookng at the evoluton of betas t can be observed that n 8 cases out of 4 the beta of the same equty has decreased over the perod studed. The average value of beta was 0.9 n 00 and 0.6 n 00. In 00 altogether 9 equtes fell nto the aggressve category, wth a beta hgher than. In 00 there were only 4 aggressve equtes. All n all, the equtes seemed to become more defensve n 00 than they were n 00. Wth only a few exceptons, the t-statstcs support the noton that beta s sgnfcantly dfferent from zero. However, the explanatory power of model /8/ whch explans the changes n equty prces through that of the market (represented by the BUX) s very low n general. The equty wth the hghest R value s MATÁV n 00 and OTP n 00. Ths can be explaned by the fact that these are the equtes wth the hghest captalsaton, and also wth the hghest weght n the BUX basket (Statstcal Report [00], p. 0, 8 and also Statstcal Report [00], p. 5, 4). Consequently, the overall performance of the market s hghly nfluenced by prce fluctuatons of these securtes (maybe rather than the other way around). So far we have not dscussed the rsk rato, namely the rato of the non-systematc and the total rsk. As shown n Table and Table, the rsk rato s very hgh n general. On average, t s almost the same n the two years studed (0.77 n 00 and 0.76 n 00). It s remarkable that the rsk rato and the value of R sum up to. It s smply a techncal result, mpled by the defnton of beta and the dervaton of formula /8/ for decomposton of rsk. 3 The results ganed from our study on ndvdual securtes confrm that the BUX has qute a low nfluence on the equty prces. It follows that the resultng beta values need to be nterpreted and used wth cauton. Therefore, we do not suggest to apply beta as a rsk measure nstead of the standard devaton of returns (or equvalently the varance), snce a far amount of volatlty n securty returns s not accounted for 4. In the constructon of portfolos for each year we decded to nvolve securtes wth postve return only. Ths way, the number of equtes nvolved n the portfolo optmsaton was 7 n 00 and 3 n 00. As mentoned before, the nput parameters for portfolo optmsaton are the average returns, the standard devatons of returns (see hghlghted values n Table and ) and the correlatons between the dfferent pars of securty returns. It s clear (see formula //) that the lower the correlaton terms of the dfferent pars of securty returns are, the hgher the rsk reducton beneft of a portfolo can be. The correlaton terms for the equtes wth postve average return are reported n Table 3 and Table 4. In 00, all the correlaton coeffcents were postve, wth values below 0.5. The hghest term was experenced between the returns of MOL and Inter-Európa-Bank (0.47). The average of the correlaton terms s 0.3 (by excludng the ones located n the dagonal). 3 A proof of ths statement can be found n Levy Sarnat [984], p An overvew of the problems related to beta as a rsk measure s gven n Bugár [998a].

12 THE RETURN AND RISK PROFILE OF EQUITIES 3 Correlaton matrx of equty returns n 00 Table 3 Equty EGIS GLOBUS IEB MOL OTP PRÍMAGÁZ SYNERGON EGIS GLOBUS IEB MOL OTP PRÍMAGÁZ SYNERGON.00 Correlaton matrx of equty returns n 00 Table 4 Equty BCHEM DANUBIUS DÉMÁSZ EGIS GLOBUS IEB MOL OTP PICK PRÍMAGÁZ RICHTER TVK ZWACK BCHEM DANUBIUS DÉMÁSZ EGIS GLOBUS IEB MOL OTP PICK PRÍMAGÁZ RICHTER TVK ZWACK.00 In 00, the average s sgnfcantly lower, wth the value of 0.5. We can also observe the presence of 7 negatve coeffcents (out of 78), whch amount to about oneffth of the terms. The hghest correlaton regstered s 0.65 (for the par of OTP and Rchter) and the lowest one s 0.5 (n case of Danubus and Globus). Wth a vew to the portfolo optmsaton, we made the calculatons for each year wth the help of the software Invest, excludng short sales as they are not appled n practce (otherwse, t would be a mere theoretcal exercse). The results n terms of effcent fronters are shown n Fgure and 3. The contnuous curve n each fgure represents the effcent fronter. The rsk and return combnaton of the ndvdual equtes nvolved n portfolo optmsaton s gven by the dscrete ponts (each pont s labelled by the name of the equty). In addton, the rsk and return combnaton for the so-called Naïve Portfolo and that of the BUX s also plotted n the fgures. The Naïve Portfolo s the equally weghted portfolo, whch contans all the securtes ncluded n the portfolo selecton process wth equal proporton for each. Clearly, there

13 3 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER s a specal portfolo denoted by MVP (Mnmum-Varance-Portfolo), the effcent portfolo wth the lowest possble rsk (varance of return). Pror to performng the analyss of the effcent portfolos there s an mportant ssue that needs clarfcaton. Techncally, we have an nfnte number of effcent portfolos represented by the dfferent rsk-expected return combnatons to choose from. As t can be seen n Fgures and, the average return s a strctly (monoton) ncreasng functon of the rsk (measured by the standard devaton). It means that undertakng a hgher rsk s compensated by a hgher level of expected return. The software we appled to conduct the research gves an opportunty to choose any portfolo on the effcent fronter by typng n the requred return on the portfolo. However, n realty the nvestor has to select a partcular portfolo among the effcent ones,.e. to follow a specfc nvestment strategy. We regard t as a systematc portfolo allocaton. In ths paper we evaluate the performance of two portfolos, namely we smulate two nvestment strateges. The frst one creates the Naïve Portfolo (NP) the second one consttutes the Mnmum-Varance-Portfolo (MVP). Constructng the NP s probably the smplest way to beneft from dversfcaton wthout requrng any sophstcated method for portfolo optmsaton. The advantage of the MVP, especally n a rsky perod wth hghly volatle equty returns, s that t has the hghest potental for reducng the rsk. In bref, these were the reasons for choosng the above mentoned two portfolo allocaton strateges. Lookng at and comparng Fgure and 3 t can be realsed that the equty wth the hghest average return, as the extreme rght pont of the curve, s contaned n the effcent fronter (n 00 the equty wth the hghest return was Globus and Prímagáz n 00). It s always the case when short sales are excluded. In general, the portfolo s becomng more dversfed,.e. contans more securtes as we are gong down on the effcent fronter towards the MVP Fgure. Rsk and Return of Equtes and Effcent Portfolos n 00 (percent) 0.70 Globus Prmagáz Average Return Nave Portfolo IEB Synergon MVP OTP MOL Egs BUX Standard Devaton 5 Here we wll not report the composton of the effcent portfolos other than the MVP. For readers nterested, the results are avalable from the authors upon request.

14 THE RETURN AND RISK PROFILE OF EQUITIES 33 In 00, the average return and the rsk of the effcent portfolos was n the range of percent and percent, respectvely. Lookng at Fgure t can be observed that all ndvdual equtes (except Globus) and the BUX are far from beng effcent. In choosng any of them, there s always an effcent portfolo wth domnant rskreturn characterstcs, namely one wth a hgher average return for the same level of rsk or wth a lower rsk for the same level of expected return. The above statement s more or less true for 00 as well, wth the excepton of Prímagáz (whch s effcent). But n that year there s one more excepton: Inter-Európa-Bank, whch s nearly effcent. Needless to say, t was the equty wth the hghest performance. In both years the performance of the NP seems to be qute good (below ths ssue s analysed more n detal). In 00 the ranges, n whch the average return and the rsk of the effcent portfolos fell, were wder than those of 00. The range of the average return was percent and the rsk fell nto the nterval of.66.4 percent. It s remarkable that the poston of those equtes nvolved n the 00 and 00 portfolo as well has changed greatly on the rsk-return map, referrng to a change both n ther rsk-return profle and n ther performance from 00 to 00. The only excepton s MOL wth a relatvely stable rsk and average return. However, n fve cases out of the total sx, we can report an mprovement n performance..60 Fgure 3. Rsk and Return of Equtes and Effcent portfolos n 00 (percent).40 Prmagáz.0 IEB.00 Average Return 0.80 OTP 0.60 Nave Portfolo TVK Egs MVP Zwack DÉMÁSZ BUX BCHEM Danubus Pck MOL Globus Rchter Standard Devaton In Table 5 the composton of the MVP s presented for both years. In 00, the MVP has contaned only 3 equtes out of the 7 ncluded n the portfolo optmsaton. In 00, t was more balanced n ths sense, excludng only 4 out of the total pool of 3 securtes consdered. Obvously, each year, the equty wth the lowest rsk (standard devaton of return) had the hghest weght n the MVP (see Tables and for comparson). In 00 OTP and n 00 Zwack had the hghest proporton, 50. percent and 40.4 percent, respectvely. It mght seem surprsng that MOL had no part n the portfolos of the years studed, despte the fact that t had lower rsk than some of the equtes that are ncluded.

15 34 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER Table 5 Composton of the Mnmum Varance Portfolo (MVP) (percent) Equty BCHEM 6.7 DANUBIUS.4 DÉMÁSZ.6 EGIS GLOBUS IEB.4. MOL OTP PICK.7 PRÍMAGÁZ RICHTER 7.0 SYNERGON 0.0 TVK 3.4 ZWACK 40.4 A lkely explanaton s that MOL s return on average has a hgher correlaton wth the other securty returns nvolved n portfolo optmsaton than the other equtes. Accordng to formula //, when the rsk of the portfolo s beng mnmsed, t s not only the rsk of the ndvdual equtes taken nto account but the correlaton between the returns as well. Next, we examne the performance of the MVP and that of the NP. The BUX ndex s used as a benchmark for evaluaton. The results are summarsed n Tables 6 and 7. The man characterstcs of two portfolo strateges and the BUX ndex n 00 Table 6 Denomnaton Average Return percent Standard Devaton Performance Rato Beta Rsk Rato MVP Naïve Portfolo BUX In drawng a comparson of the rsk of the MVP n Table 6 to the rsk of the ndvdual equtes nvolved n the portfolo optmsaton (see hghlghted rows n Table ), t can be calculated that the standard devaton of the MVP s about 4 percent and 8 percent lower than that of the ndvdual equty wth the lowest and the hghest standard devaton, respectvely. Therefore, n 00 the rsk reducton beneft from creatng the MVP can be regarded as qute good. Further, the rsk and return parameters of the MVP as compared to those of the NP are qute dstnct. The return on the MVP s lower and t s a less rsky portfolo. In tself, the MVP s desgned to reduce the rsk, hence ts lower ex-

16 THE RETURN AND RISK PROFILE OF EQUITIES 35 posure to rsk through nvestment does not come as a surprse. Stll, t s remarkable that the performance of the NP s superor to that of the MVP. Both portfolo allocaton strateges show a low performance but stll a better one than the ndvdual equtes (except Globus 6 ). It s also worth mentonng that the NP has a hgher beta 7 and the hgher rsk rato as well. Usng the BUX ndex as a benchmark to evaluate the performance of the two portfolos, all n all, we can conclude that ther performance s not bad compared to the general state of the stock market n 00. In 00, both the performance of the BUX and the two portfolo allocaton strateges have mproved greatly as compared to 00. It s due to the hgher average returns and, n case of the two portfolo allocaton strateges, to a lower level of rsk as well. The performance rato of the MVP s more than one and a half tmes hgher than t was n 00. The man characterstcs of two portfolo strateges and the BUX ndex n 00 Table 7 Denomnaton Average Return percent Standard Devaton Performance Rato Beta Rsk Rato MVP Naïve Portfolo BUX The NP has produced an even greater mpovement n terms of performance: ts performance rato s more than two tmes hgher n 00 than t was n 00. The betas of both portfolos are lower than they were n 00. The rsk rato of the MVP s hgh, whch s due to ts low beta, namely ts low senstvty to the market volatlty. Comparng the results shown n Table 7 to those presented n Table we can conclude that both portfolos outperform almost all ndvdual equtes. Indeed, for the NP we got a hgher performance rato than for any of the equtes. The NVP was outperformed by IEB and OTP only. It s notable that the NP repeatedly had a better performance than the MVP n 00. In a smlar research made on blue-chps traded at BSE, Bugár [998b] has also reported on the very good performance of the NP. As shown n Fgure 3, the NP s located rather close to the effcent fronter. Decdedly, the effcent portfolo wth the same average return (0.5%) as the NP has a standard devaton of.93 percent. So, t has a performance rato of 0.59, whch s 3 percent hgher than that of the NP. The creaton of an effcent portfolo s a rather sophstcated process, requrng tme and effort to estmate the parameters and to mplement the portfolo optmsaton. Takng ths fact nto account, we can safely say, t s not necessarly worth to carry out the process. One can argue that our analyss was performed on an ex post bass. In fact, the problem of ths approach s that t only reveals past the event what should have been done ear- 6 An nvestment nto Globus s much more rsky than the above-mentoned portfolo selecton strateges. Here t should be emphassed that portfolo allocaton pays n terms of stablsng the return,.e. reducng the rsk but not necessarly n terms of ncreasng the performance. 7 The beta of a portfolo s a weghted average of the securtes betas ncluded n t.

17 36 GYÖNGYI BUGÁR GIANNI BARATTO ISTVÁN PREHOFFER ler on. Consequently, the benefts detected are potental only so they cannot be realsed. In order to overcome ths dffculty we also examned the performance of the MVP and the NP on an ex ante bass,.e. we determned the returns whch would have been realsed on average n 00 on the portfolos set up n 00 and kept unaltered. Based on the nformaton n Table and Table 5, the average (weekly) return n 00 on the MVP(00) s: R ( ) = (%). MVP 00 Smlarly, the average return can be realsed n 00 on the NP(00): R NP ( 00) = ( ) (%). 7 As t can be seen the MVP outperformed the NP on an ex ante bass. Comparng these results to the average return on ndvdual equtes presented n Table, t s clear that n 00 there are only two equtes whch performed better than the MVP(00) and fve equtes whch outperformed the NP(00). In addton, based on the pror nformaton on the average returns as well as the optmal portfolo weghts n 00, the average return was even hgher on the portfolos set up at the end of 00 than t was n case of the portfolos produced wth the help of the data from 00 and ncludng the equtes wth postve return nto the portfolo (see Table 7). It served as a lesson to prove that a systematc portfolo allocaton by usng a buy and hold strategy can be more successful than contnuously changng the equtes selected and ncluded n the portfolo. To conclude, n the long run t mght be more proftable to apply the same portfolo strategy on the stable set of securtes. * In ths paper we studed the rsk and return characterstcs of equtes lsted and traded n category A at the Budapest Stock Exchange over the tme perod We also made a portfolo optmsaton based on Markowtz s [999] theory, the Mean-Varance crteron. The expected return was taken as an ndcator of the nvestment s average proftablty, and the standard devaton of return served as an ndcator of ts rsk. Furthermore, we estmated the beta values, and tested the explanatory power of the lnear regresson model of securty return on the return of the BUX ndex. The performance of two portfolo strateges was also evaluated. The major fndngs of the analyss can be summarsed as follows. Both the analyss of ndvdual equtes and the effcent portfolos supported that the stock exchange passed through a crss whch had ts worst effects n 00. Indeed, we experenced an ncrease of the average return and the performance and a decrease of the rsk from 00 to 00. It was found that the nfluence of the BUX on equty prces s qute low. As a consequence, the beta values we got should only be nterpreted and used wth care. On the bass of our emprcal fndngs t cannot be recommended to apply beta as a rsk measure

18 THE RETURN AND RISK PROFILE OF EQUITIES 37 nstead of the standard devaton of returns, because n ths case a large part of volatlty n securty returns would not be explaned. On an ex post bass the Naïve Portfolo had a better performance than the Mnmum- Varance-Portfolo n both years. Consderng that to create an effcent portfolo s a sophstcated process requrng tme and effort to estmate the parameters and to mplement the portfolo optmsaton, t seems that we can be satsfed wth the benefts promsed by the naïve way of dversfcaton. On an ex ante bass the Mnmum-Varance-Portfolo has shown a better performance than the Naïve Portfolo. However, both of them resulted n an even hgher average return than ther ex post counterparts. The ex post portfolos have been set up under the condton of usng the data from 00 and nvolvng the equtes wth postve return nto the portfolo, whle ther ex ante counterparts have been constructed on the bass of utlsng pror nformaton on the average returns as well as the optmal portfolo weghts at the end of 00. Therefore, t has been confrmed that a systematc portfolo allocaton by usng a buy and hold strategy can be more successful than contnuously changng the equtes selected and ncluded n the portfolo. REFERENCES Annual Report [00]: Budapest Stock Exchange, p. 48. Annual Report [00]: Budapest Stock Exchange, p. 36. BERNSTEIN, W. J. [000]: The ntellgent asset allocator: How to buld a portfolo to maxmze returns and mnmze rsk. McGraw-Hll. New York. BUGÁR GY. [998a]: Az értékpapírok pac kockázatának méréséhez. Bankszemle. Vol. 4. No.. p BUGÁR GY. [998b]: Hatékony részvénykombnácók és kockázatcsökkentés stratégák a BÉT-en. Bankszemle. Vol. 4. No. 8. p A csatlakozás előtt álló kelet-európa országok részvénypaca [003]. Budapest Stock Exchange Publcaton. p. 7. (also publshed n the onlne busness daly paper, Portfolo.hu: (8.5 a.m )) HAUGEN, R. A. [997]: Modern nvestment theory. Prentce-Hall. Englewood Clffs. New Jersey. LEVY, H. SARNAT, M. [984]: Portfolo and nvestment selecton Theory and practce. Prentce Hall. New Yersey. MARKOWITZ, H. M. [999]: Portfolo selecton: effcent dversfcaton of nvestments. Basl Blackwell. Oxford. SHARPE, W. F. ALEXANDER, G. J. [990]: Investments. Prentce-Hall. Englewood Clffs. New Jersey. Statstcal Report [00]. Budapest Stock Exchange, p. 8. Statstcal Report [00]. Budapest Stock Exchange, p. 3.