Evaluation of Stocks from Zagreb Stock Exchange

Transcription

1 Evaluaton of Stocks from Zagreb Stock Exchange Jasmnka Dobša, Krsto Kero, Danjel Raoševć Faculty of Organzaton an Informatcs Unversty of Zagreb Pavlnska 2, 42 Varažn, Croata {jasmnka.obsa, krsto.kero, Abstract. hs paper eals wth evaluaton of chosen stocks from the Zagreb Stock Exchange base on ata collecte urng the recent pero. wenty stocks have been chosen on the bass of ther solvency an completeness of corresponng ata. Stocks are compare to the offcal nex of the Zagreb Stock Exchange CROBEX an compare mutually. For analyss of tme seres of prces for chosen stocks we use the methos of correlaton, tren, an prncpal components analyss. Means an means of change of stock prces were compare to mean an mean values of CROBEX changes urng the observe pero of tme. Keywors. Zagreb Stock Exchange, techncal analyss, statstcs 1 Introucton he am of ths paper s to fn out how the changes of stock prces follow the changes of the stock market nex CROBEX an to nvestgate epenence between stock prces an the CROBEX nex. Our hypothess s that magntue an recton of the fference between changes of CROBEX an changes of prces for the specfc stock coul be a goo prector of stablty an prectablty of that stock. For experment we have use the tme seres of stock prces n the pero of half a year or 124 workng ays. wenty stocks are chosen on the bass of ther solvency an completeness of corresponng ata. All of these stocks were nclue n the offcal nex of the Zagreb Stock Exchange CROBEX n the begnnng of the observe pero, but some of them were scare untl the en of that pero, because CROBEX was revse n the meantme. Analyss of stocks usng graphs of ther prces s part of so calle techncal analyss. Unlke funamental analyss of stocks whch eals wth busness results of a frm n the past pero of tme, techncal analyss eals only wth prces an volumes of trang for a specfc stock [2]. Here we wll not use stanar methos of techncal analyss use for analyss of the Croatan stock market, but propose the usage of statstcal methos approprate for analyss of chosen stocks. he Croatan stock market s one of the fronter markets that are evelopng n post-communst countres of east an southeast Europe. Characterstcs of these markets are: a small number of stocks on the trae market, lack of transparency an solvency an short hstory of trang. here are no much publcatons ealng wth statstcal analyss of Croatan stock market. Rsk of nsolvency present n portfolo management on the Croatan stock market s nvestgate n [5]. In [1] authors are ealng wth moelng of volatlty of stocks on the Croatan stock market. Volatlty of varable s a measure of ts unprectable change n a certan pero of tme. Research conucte on Croatan stock market reveals that small number of stocks present on Croatan stock market results by unsatsfactory level of portfolo versfcaton. Analyss on evelope stock markets [1] an on Croatan stock market as well [1] shows that there s possbllty of prectng volatlty of fnancal tme seres. In ths paper, tme seres of stock prces are analyze by methos of correlaton, tren an prncpal components analyss. Correlatons between tme seres of prces for stocks are very hgh for all but one of the chosen stocks. Prces for all but one (the same one) stock are hghly correlate wth CROBEX as well. Prncpal component analyss of tme seres of prces reveals that there s only one

2 relevant component whch s hghly correlate wth CROBEX. me seres of prces for each stock was moele by exponental tren. It s shown that all prces of stocks (except one) an CROBEX ha a ecreasng tren n the observe pero of tme. As most of the stocks ecrease n value urng the chosen pero, our ntenson was to nvestgate how changes of stock prces follow the changes of CROBEX. For that reason, means an means of changes of prces are compare to the mean an mean of change of CROBEX usng the pare t-test (parametrc) an the Wlcoxon matche pars test (nonparametrc). We suggest the usage of p-value of mentone tests as a measure of smlarty between CROBEX an tme seres of prces for the specfc stock. he paper s organze as follows: n the secon secton we offer an nse look at methos use for the analyss, n the thr secton we escrbe the ata set, whle n the forth secton we escrbe experments an gve numercal results. he last secton contans conclusons an rectons for further research. 2 Methos 2.1 Exponental tren In orer to measure epenence between prces for chosen stocks, we use methos of correlaton an one-mensonal exponental tren [7]. One-mensonal exponental tren moels tren of varable Y by relaton t Y = AB (1) where = 1,2, K, n are observatons an t s the varable of tme. he parameter B ncates the relatve change n epenent varable Y gven a unt pero of tme. Coeffcent of etermnaton r 2 s efne as rato of varaton of ata explane by the moel an total varaton of ata. he parameter of r 2 an ts root square coeffcent of correlaton r are use as a measure of ft of orgnal ata to the moel. he coeffcent of correlaton r assumes values between -1 an Prncpal components analyss he prncpal components analyss proves nsght nto the most relevant factors aroun whch varables are groupe [8]. It allows expressng large proporton of total varance of ata wth smaller number of varables n rectons of maxmum varaton of ata. he frst prncpal component s the lnear combnaton of orgnal varables wth maxmum varance, the secon prncpal component s the lnear combnaton wth maxmum varance orthogonal to the frst component an so on. 2.3 Methos for comparson of means an means for two epenent samples Dfference of mean values of two epenent samples s teste by the parametrc metho of the t-test for matche pars, whle the fference of means of two epenent samples s teste by the nonparametrc Wlcoxon match pars test [7,11]. Here we wll test f there s a fference between aly change of stock prce for the chosen stock an aly change of the CROBEX nex. Daly change of stock prce (or CROBEX) s calculate by formula p+1 p c = (2) p = 1,2, K, n 1 where n s the total number of ata n the tme seres an p s the prce on the -th ay. Let, = 1,2, K, n be fferences of pars for two samples. he sample mean of pare fferences s gven by =, (3) n whle the estmate stanar error of s gven by S 2 ( ) = 2. (4) n 1 When the populaton of fferences s normally strbute, the statstc gven by t µ S = (5) has a t-strbuton wth (n-1) egrees of freeom. In Eq. 5, µ s the fference of pare populatons assume by hypothess. he Wlcoxon match pars test s the nonparametrc alternatve to the pare t-test. Usually, the Wlcoxon match pars test s less powerful then the t-test when assumptons on normalty of fferences are satsfe. Lke the other nonparametrc tests, ths test substtutes orgnal ata by ts rank an, because of that, t loses part of the nformaton present n t. Absolute values of fferences between the corresponng pars are ranke n ascenng orer. he sgn of the fference s assocate wth each fference. Let + be the sum of the postve fferences, the sgn of the negatve fferences an = {, } mn +. he normal approxmaton proceure (or z-test) s use when n > 15 where n s number of non-zero fferences. he test statstc s ( +.5) µ z = (6) where σ

3 an 3 Data set 1 µ = n ( n + 1) (7) 4 1 σ = n ( n + 1)(2n + 1). (8) 24 he experments are conucte on the ata set of tme seres of prces of twenty chosen stocks from Zagreb Stock Exchange n the pero from 8th November 27 to 9th May 28. Stocks are chosen on the bass of ther solvency an completeness of corresponng ata.. Our research nclue stocks from the foo nustry sector (Franck, Kraš, Poravka), toursm (Arenaturst, Rabac, Istraturst, Sunčan Hvar), electrcal nustry (Dalekovo, Ercsson Nkola esla, Končar, ehnka), shpbulng (Atlanska plovba, ankerska plovba, Uljank plovba), cvl engneerng (Insttut građevnarstva Hrvatske, Vjaukt) an the fnancal sector (Centar banka, Croata osguranje, Hrvatska poštanska banka, Karlovačka banka). At the begnnng of the observe pero all of the chosen stocks were nclue n CROBEX, but by the en of the pero some of them were scare. Revson of CROBEX s regularly carre out twce a year, on the thr Fray n March an September. Bascally, crtera for ncluson of stock to CROBEX are connecte to ther solvency. he frst column of able 1 contans the label of the stock 1 ; n the secon s the stock ssuer; an the thr contans nformaton whether the stock was nclue n CROBEX at the en of the observe tme pero. 4 Experment an results me seres of stock prces for most of the chosen stocks are mutually hghly postvely correlate. he excepton s the stock IS, whch has low negatve correlatons wth almost all other stocks. Also, correlatons between CROBEX an chosen stocks are generally hgher then.5, but many of them are even hgher then.9 (p<.5). For the stock ULPL, correlatons between other stocks an CROBEX are somewhat lower then for other stocks. Results of experments usng metho of prncpal components analyss are n lne wth hgh correlatons between tme seres of prces. able 2 shows loans of varables (tme seres of chosen stock prces) n the frst two prncpal components, whch account for 88.9% of ata varaton. he frst prncpal component alone accounts for 82.2% of ata varaton. 1 Proper labels of chosen stocks from Zagreb Stock Exchange shoul be NAME-R-A. Here we use shorter labels n the sake of smplcty of notaton. able 1. Lst of stocks chosen for experment. he frst column marks the stock labels, the secon lsts stock ssuers an the thr contans the nformaton whether the stock was nclue n CROBEX at the en of the observe tme pero (all the stocks were nclue n the begnnng). Label Issuer In CROBEX ARN Arenaturst.. No APL Atlanska plovba.. Yes CEBA Centar banka.. No CROS Croata osguranje.. Yes DLKV Dalekovo.. Yes ERN Ercsson Nkola esla Yes.. FRNK Franck prehrambena No nustrja.. HPB Hrvatska poštanska No banka.. HRBC Rabac, ugostteljstvo turzam. Yes IGH Insttut građevnarstva Yes Hrvatske. IS Istraturst Umag, No hoteljerstvo turzam. KABA Karlovačka banka.. No KOEI Končar Yes elektronustrja.. KRAS Kraš prehrambena No nustrja.. PODR Poravka prehrambena Yes nustrja.. SUNH Sunčan Hvar.. No HNK ehnka.. Yes NPL ankerska plovba.. Yes ULPL Uljank plovba.. Yes VDK Vjaukt.. Yes here s only two egenvalues greater then 1; the frst one has the value of an secon Loans of all varables except varable of IS stock are large n the frst component. We can say that all stocks except the stock of IS belong to the frst component. he last row of the table shows the correlaton of components to CROBEX. he frst component s hghly correlate wth CROBEX, whle the secon component s not correlate to CROBEX at all. In the secon component, only the stocks of IS an ULPL have greater loans, but the stock of ULPL have great loan n the frst component as well. Generally, we can conclue that n the frst component are stocks whch follow the CROBEX nex well, whle n the secon component are stocks whose correlatons wth CROBEX are lower. he stock of ULPL s lmt case belongng to both components.

4 able 2. Loans of varables (tme seres of prces of chosen stocks) n the frst two prncpal components. he last row shows the correlaton of the components to CROBEX. Stock 1 st component 2 n component ARN APL CEBA CROS DLKV ERN FRNK HPB HRBC IGH IS KABA KOEI KRAS PODR SUNH HNK NPL ULPL VDK CROBEX We have moele the tren of tme seres of prces for every stock by means of exponental tren n orer to obtan the average value of the relatve change n prces. he value of the tren of average change rate s compute as s B = 1 B 1 (9) where B s the parameter n exponental tren (Eg. 1). he values of s B for chosen stocks are gven n the secon column of able 3, where one can see that all stocks an CROBEX except the stock of IS have a ecreasng tren. In the brackets are values of r 2 whch gve nformaton about tren fttng. r 2 values are greater then.5 n absolute value for tren moels of all stocks except for stocks of ERN, IGH, IS an ULPL. wo out of four stocks wth lower r 2 value belong to the secon prncpal component whose correlaton wth CROBEX s low. he rest of our research was focuse on the nvestgaton of how changes of stock prces follow the changes of CROBEX. Mean values of changes of stock prces are shown n the thr column of able 3, whle the means are shown n the ffth column of the table. All mean values are negatve except for IS an all mean values are not postve. It s nterestng to note that 1 mean values are zero (to four ecmal places) an another two are less than.1 n absolute value. CROBEX R 2 =,7737 Fgure 1 a. CROBEX an approxmaton by exponental tren. IS Prce Fgure 1 b. Prces of IS stock an approxmaton by exponental tren. FRNK Prce R 2 =, Fgure 1 c. Prces of FRANK stock an approxmaton by exponental tren. APL Prce R 2 =, Fgure 1. Prces of APL stock an approxmaton by exponental tren. R 2 =,5966

5 able 3. Characterstcs of chosen stocks. he secon column shows the rate of average change of tren value of prces (n the brackets are r 2 values); the thr an ffth columns show measures of central tenency (mean an mean) for prce changes of chosen stocks an change of CROBEX; the forth column contans stanar evatons of changes; the sxth an seventh columns show p-values of the t-test an the Wlcoxon match pars test. s B (%) t-test Wlcoxon Stock ( R 2 ) X σ Me p-value p-value ARN -,4 (,7616) -,131 5,6656,,8481,957 APL -,32 (,5966) -,884 3,384 -,3,5745,9543 CEBA -,6 (,9328) -,4531 2,7447,,3512,6481 CROS -,34 (,8419) -,2886 3,37,,7361,4278 DLKV -,55 (,882) -,2561 3,383 -,3495,7424,5151 ERN -,16 (,4343) -,793 2,163 -,2,434,5663 FRNK -,29 (,8442) -,2 2,7847,,9874,9668 HPB -,22 (,785) -,2621 3,4766,,8426,8811 HRBC -,35 (,799) -,2669 3,1297,,8154,8234 IGH -,26 (,441) -,711 3,6894 -,17,5681,712 IS,4 (,1462),87 2,8678,,3112,262 KABA -,45 (,8737) -,2793 3,832,,8257,8536 KOEI -,48 (,7586) -,35 2,9441 -,4422,5217,321 KRAS -,44 (,8532) -,393 3,281 -,2369,6349,4163 PODR -,26 (,7916) -,1576 2,85,,8384,7326 SUNH -,34 (,8413) -,1532 3,8171,,8982,9682 HNK -,7 (,8556) -,3483 3,9278 -,321,625,27 NPL -,5 (,8556) -,3593 3,4295 -,186,4797,3446 ULPL -,33 (,3618) -,2426 4,4429 -,411,8943,9722 VDK -,6 (,7441) -,2578 4,396 -,762,8465,3472 CROBEX -,3 (,7737) -,1961 1,7534 -,2 Base on the change mean value, t s possble to gve some estmaton of the stanar measure of techncal analyss calle the relatve strength nex (RSI), whch epens on the rato of stock prce ncrease/ecrease ays. Namely, the mean of zero tells us that the number of ays when the stock rose s exactly the same to the number of ays when the stock fell. Negatve value of the mean s an ncaton of more ays when the stock fell an ts postve value s ncaton of greater number of ays when the stock rose. In our case, half of the chosen stocks ha the same number of ays of stock value ncrease an stock value ecrease. For the rest of the chosen stocks, prces urng the observe pero more often ecrease. Atonally, the zero value of the mean an negatve mean value of stock prce changes ncates that rops were larger than ncreases n absolute value for such a stock. he sxth column of able 3 shows p-values of the t-test, where fferences between mean values of stock prces changes an mean values of CROBEX are teste. It shows that there s no sgnfcant fference between mean values of changes an changes of CROBEX for any of the chosen stocks at the.5 level of sgnfcance. he reason for that are hgh values of stanar evatons (relatve to mean values) shown n the forth column of able 3. Accorng to χ 2 test, sample fferences between changes of stock prces an changes of CROBEX are not normally strbute for any of the chosen stocks. hs s ncaton that the t-test for pare samples shoul not be apple. Nevertheless, n case of large samples ( n 3), as was use n our experment, t- test s goo approxmaton of z-test for whch the normalty of strbuton s not necessary conton [9]. In orer to obtan more relable results we have also apple the nonparametrc test of Wcoxon mach pars. he seventh column of able 3 shows p-values of the Wcoxon mach pars test, testng the fferences between prce change means for stocks an changes of CROBEX. Accorng to p-values, there s no sgnfcant fference between prce change means for chosen stocks an mean of changes of CROBEX. he correlaton coeffcent between p- values for the t-test an p-values for the Wlcoxon mach pars test has the satsfactory value of.588 (p<.5). Although there s no sgnfcant fference between means an means, p-values of respectve

6 tests can be nterprete as measures of smlarty between changes of stock prces an changes of CROBEX. In Fgure 1 a the graph shows the value of CROBEX an ts approxmaton by exponental tren. Fgures 1 b- show prce graphs of some of the chosen stocks an ther approxmaton by exponental tren (b-is, c-frnk, -APL). Accorng to p- values of the t-test an the Wlcoxon match pars test, the IS stock s one of the stocks that most ffers from CROBEX base on ther relatve changes, whle FRNK s one of the stocks most smlar to CROBEX. he APL stock s very smlar accorng to the Wlcoxon match pars test, but not so smlar accorng to the t-test. Nevertheless, the prce change graph looks very smlar to the CROBEX graph. he reason for that probably les n the fact that the t-test operates wth numercal values, whle the Wlcoxon match pars test operates wth ranks. 5 Conclusons an scusson Most stocks observe n the allotte tme pero share a smlar ynamc wth that of CROBEX, whch seems to be goo ncator of the state of matters on the Zagreb Stock Exchange. me seres of stock prces for most of the chosen stocks are mutually hghly postvely correlate an they are hghly correlate to CROBEX as well. hs resulte by only one relevant prncpal component whch represents tme seres of prces for all but one chosen stock an whch accounts for 82.2% of ata varaton. Our hypothess s that such a state s the results of the followng fronter market characterstcs: a relatvely small number of stocks on market an the lack of solvency. hese contons cause bg nvestors (penson founs) to concentrate on a small number of solvent stocks because they can not affor the rsk of greater versfcaton of ther portfolo. Prces of the most solvent stocks then epen strongly on current (fnancal) stuaton of bg nvestors. Accorng to some acaemc papers [3,6] nternatonal versfcaton of portfolo coul have postve effects. he tren of tme seres of prces for every stock was moele by means of exponental tren. Average value of the relatve change n prces for almost all stocks showe that prces were ecreasng n observe pero of tme. he major research focuse on nvestgaton of how changes of stock prces follow the changes of CROBEX. It was shown that there s no sgnfcant fference between means an means of changes of stock prces an changes of CROBEX for all chosen stocks. Her we suggest that p-values of respectve tests can be nterprete as measures of smlarty between changes of stock prces an changes of CROBEX. In further work, we plan to expan our research by methos of clusterng an classfcaton, an perform more etale research by comparng stocks from the same sector. In aton to prces of stocks, ata concernng volumes of trang an parameters of funamental analyss coul be nclue n the research. Further, smlar research coul be conucte on other stock markets n orer to compare results wth the results of ths research. References [1]. Bollerslev, R.Y.Chou, K.F. Kroner: ARCH moelng n fnance: A selectve revew of the theory an emprcal evence, Journal of Econometrcs, 52, 1992, pp [2] Dončk portal, Accesse: May 28. [3] E.J. Elton, M.J. Gruber: Moern Portfolo heory an Investment Analyss, ffth eton, John Wley &Sons, New York, [4] Fma vrjenosnce, avalable at Accese: Aprl 28 [5] M. Latkovć, D. Boršć: Rzk nelkvnost aktvno pasvno upravljanh ončkh portfelja, Računovostvo fnancje, Zagreb, June 2. [6] M. Latkovć: Internaconalna verzfkacja portfelja za hrvatsko tržšte kaptala, Hrvatska gospoarska revja, March, Zagreb, 2. [7] P. Newbol, W. L. Carlson, B. horne: Statstcs for Busness an Economcs, ffth eton, Pearson Eucaton, Inc. Upper Sale Rver, New Jersey, 23. [8] A.C. Rencher: Methos of Multvarate Analyss, secon eton, Wley-Interscence, 22. [9] M.R. Spegel, J. Schller, R.A. Srvansan: Probablty an Statstcs, secon eton, Schaum s Outlne Seres, McGraw-Hll, 2. [1] D. Šestovć, M. Latkovć: Moelranje volatlnost vrjenosnca na Zagrebačkoj burz, Ekonomsk pregle, 49(4-5), 1998, pp [11] L. Wasserman: All of Nonparametrc Statstcs, Sprnger Scence &Busness Mea, Inc., 26. [12] Zagrebačka burza, he Zagreb Stock Exchange, avalable at Accesse : March 28.