proračun beta koeficĳenata za akcĳe koje se kotiraju na sarajevskoj

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PRORAČUN BETA KOEFICĲENATA ZA AKCĲE KOJE SE KOTIRAJU NA SARAJEVSKOJ, BANJALUČKOJ I BEOGRADSKOJ BERZI

Rezime

Beta koeficĳent predstavlja tendencĳu promene vrednosti akcĳe u skladu sa promenema na tržištu. Predstavlja meru sistematskog rizika investicĳe ili pak investicionog portfolĳa i pokazuje osetljivost investicĳe ili portfolĳa na promene tržišta hartĳa od vrednosti. U ovom radu se razmatra problematika investiranja u hartĳe od vrednosti, tačnĳe analiza rizika investiranja u iste, gde se na osnovu statističkih analiza dolazi do proračuna pokazatelja rizika.

Ključne reči: beta koeficĳent, podešeni beta koeficĳent, fundamentalni beta koeficĳent

Mr Almir AlihodžićRadiotelevizĳa Federacĳe BiH

almir.alihodzic@rtv�ih.ba

stručni priloziUDK 657.92:336.761.5 (497.11+497.6)

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CALCULATION OF BETA COEFFICIENTS FOR THE

SHARES QUOTED AT SARAJEVO, BANJALUKA AND BELGRADE STOCK

EXCHANGE

Summary

Beta coefficient indicates the tendency of shares value changes in accordance with the market fluctuations. It is a measure of systemic risk of an investment or of an investment portfolio, indicating the sensitivity of the investment or the portfolio in respect of the securities market fluctuations. This paper examines the issue of investment in securities, more precisely, its risk analysis, which calculates the risk indicators on the basis of statistical methods.

Key Words: beta coefficient, adjusted beta coefficient, fundamental beta coefficient

Almir Alihodžić, MScRadio and Television of Bosnia and Herzegovina almir.alihodzic@rtv�ih.ba

expert contributionsUDC 657.92:336.761.5 (497.11+497.6)

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Uvod

U prvom polugodištu 2009. godine na BiH berzama ostvaren je ukupni promet od KM 144.208.646 odnosno EUR 73.732.709 (na Sarajevskoj berzi vrednosnih papira je ostvaren promet od KM 101.753.620 odnosno EUR 52.025.799 i na Banjalučkoj berzi hartĳa od vrednosti u iznosu od KM 42.455.026 ili EUR 21.706.910), što predstavlja samo 19,17% ostvarenja prošlogodišnjeg prometa. Takođe, za period: 1.1. - 30.6.2009. godine, Beogradska berza je ostvarila promet od 12,5 mlrd dinara (133,5 mil. EUR), što predstavlja samo 17,49% prometa iz 2008. godine.

Navedeni podaci svrstavaju oba tržišta kapitala (tržište kapitala u BiH i tržište kapitala Republike Srbĳe) u red manje razvĳenih tržišta. Primena koncepta beta kao mere rizika na oba tržišta kapitala predstavlja poseban izazov usled nedostajućeg iskustva i ograničenih istorĳskih podataka, kao i usled rizika investiranja.

Beta koeficĳent predstavlja meru sistematskog rizika. Kod agresivnog portfolĳa reaguje intenzivnĳe na promene tržišta β>1, kod defanzivnog portfolĳa reaguje sporĳe na promjene tržišta β<1 i kod prosečnog portfolĳa reaguje proporcionalno promenama tržišta β=1, tačnĳe prosečno rizična akcĳa je ona čĳa se vrednost menja u skladu sa promenama na tržištu mereno tržišnim indeksom. Beta koeficĳent te akcĳe jednak je 1,00, što znači da ako vrednost indeksa poraste za 10% i vrednost te akcĳe porašće za 10%. U suprotnom slučaju pad vrednosti indeksa za 10% pratiće i pad vrednosti te akcĳe za 10%. Portfolio akcĳa β=1 se kreće u skladu sa kretanjem na tržištu i njegova rizičnost je prosečna. Ukoliko je β=0,5 onda su te akcĳe upola rizičnĳe od proseka, ili pak ako je β=2 to znači da je ta akcĳa duplo rizičnĳa od proseka.

Postoje tri načina za izračunavanje beta koeficĳenata i to: a) istorĳski beta koeficĳent; b) podešeni ili prilagođeni beta koeficĳent1 i c) fundamentalni beta koeficĳent.

1. Proračun beta koeficĳenata

Istorĳski beta koeficĳent Beta koeficĳent akcĳe je mera njenog

ponašanja u odnosu na prosek, mereno kretanjem tržišnog indeksa. Proračun se vrši na bazi prošlih (realizovanih) prinosa određene akcĳe i prošlih realizovanih prinosa na tržištu, jednačinom linearne regresĳe.

Na osnovu podataka iz tabele br. 1 o petogodišnjim ostvarenim prinosima konkretne akcĳe „X” i tržišta uspostavlja se veza u jednačini proste linearne regresĳe:

Y = a + bX + e (1.1)

Zavisna varĳabla Y je u ovom slučaju ostvareni prinos akcĳe , nezavisna varĳabla X je ostvareni prinos tržišta - , a e je slučajna greška. Tako prinos akcĳe zavisi od promena na tržištu i efekta slučajnosti koja utiče na tu akcĳu, ali ne i na većinu drugih akcĳa.

(1.2)

ili

(1.3)

1 Pored datih, postoji i BAYES-ovo prilagođavanje koje istorĳski beta koeficĳent koriguje probabilističkom nesigurnošću.

Tabela br. 1: Primer proračuna β koeficĳenta

IZVOR: Brigham, E., & Gapenski, L., & Ehrhardt, M. „Financial Management - Theory and Practice”. New York: Dryden press, 1999., str. 282.

GodinaOstvareni

prinos dionice “x”

Ostvareni prinos tržišta

*

1 0,386 0,238 0,0918682 -0,247 -0,072 0,0177843 0,123 0,066 0,0081184 0,082 0,205 0,016815 0,401 0,306 0,122706S 0,745 0,743 0,257286

Arit. sred. 0,149 0,1486SX2 0,392659 0,201845

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Introduction

In the first half of 2009 the total turnover at the stock exchanges in Bosnia and Herzegovina amounted to KM 144,208,646, i.e. EUR 73,732,709 (Sarajevo Securities Exchange yielded the turnover of KM 101,753,620, i.e. EUR 21,706,910), which is only 19.17% of the last year’s turnover. Also, in the period 1.1- 30.6.2009, Belgrade Stock Exchange recorded the turnover of RSD 12.5 billion (EUR 133.5 million), which is only 17.49% of the 2008 turnover.

The above data rank both capital markets (the capital market of Bosnia and Herzegovina, and the capital market of the Republic of Serbia) among the less developed markets. The implementation of beta concept as a risk measure in these capital markets is quite a challenge due to the lacking experience, and limited historical data, as well as due to the investment risk.

Beta coefficient is a systemic risk measure. In case of an aggressive portfolio it reacts more intensively to market fluctuations β > 1, whereas in case of a defensive portfolio it reacts more slowly to market fluctuations β < 1. In case of an average portfolio, the coefficient reacts proportionately to market fluctuations β = 1, more precisely, a share with average risk is the one whose value changes according to market fluctuations measured by market index. Beta coefficient of this share equals 1.00, meaning that if the index value increases by 10%, the value of the relevant share will increase by 10%, too. Conversely, the drop of the index value by 10% will be followed by the drop in the relevant share’s value by 10%. The trends of the shares portfolio β = 1 follow market fluctuations and the risk it bears is average. If β = 0.5, then those shares bear half-less risk than the average, and if β = 2, it means that the concerned shares bear double risk compared to the average.

There are three ways to calculate beta coefficients: a) historic beta coefficient, b) adjusted beta coefficient1 and c) fundamental beta coefficient.

1. Calculation of Beta Coefficient

Historic Beta CoefficientBeta coefficient of a share is the measure of

its behavior in respect of the market average, measured by the market index trends. The calculation is done on the basis of the past (achieved) returns in the market, using the linear regression equation.

Based on the data from Table 1 regarding the five-year achieved returns of the concrete share ‘x’ and the market, the connection is established in the simple linear regression equation:

Y = a + bX + e (1.1)

The dependant variable Y is, in this case, the achieved return of the share the independent variable X is the achieved return of the market - whereas e stands for accidental error. Hence, the share’s return depends on market fluctuations and coincidence effect affecting this share, but not the majority of other shares.

(1.2)or

(1.3)

1 In addition to these, there is Bayesian adjustment which corrects historic beta coefficient by means of probabilistic uncertainty.

Table 1: Example of Beta Coefficient Calculation

SOURCE: Brigham, E., & Gapenski, L., & Ehrhardt, M. “Financial Management - Theory and Practice”, New York: Dryden Press, 1999, p. 282

Year

Achieved return

of the ‘x’ share

Achieved market return

*

1 0,386 0,238 0,0918682 -0,247 -0,072 0,0177843 0,123 0,066 0,0081184 0,082 0,205 0,016815 0,401 0,306 0,122706S 0,745 0,743 0,257286

Arithmetic mean 0,149 0,1486

SX2 0,392659 0,201845

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Rešavanjem sistema jednačina sa dve nepoznate dobĳa se vrednost β koeficĳenta, β - 1,61.

Beta koeficĳent akcĳe određene kompanĳe pokazuje koliko su akcĳe te kompanĳe bile rizične u prethodnom periodu u odnosu na akcĳe drugih kompanĳa koje ulaze u berzanski indeks. Stoga, beta koeficĳent nĳe stabilan tokom vremena, već je podložan promenama. Shodno tome, dešava se situacĳa da kompanĳe čĳe su akcĳe imale visoku vrednost beta koeficĳenata, što odražava visoki rizik ulaganje u te akcĳe, u narednom periodu imaju znatno niže beta koeficĳente, i obrnuto. Na osnovu prethodnog može se konstatovati da je istorĳski beta koeficĳent ograničeno upotrebljiv, budući da su investitori isključivo zainteresovani za budući prinos i buduću rizičnost akcĳe.

Podešeni beta koeficĳentZapaženo je da beta koeficĳenti uglavnom

konvergiraju ka jedinici. Data gravitacĳa oko jedinice, podstakla je na modifikacĳu istorĳskog beta koeficĳenta, uključivanjem i njegove anticipirane promene. Time se dobĳa beta koeficĳent veće upotrebne vrednosti. Tako dobĳeni beta koeficĳent naziva se podešenim, ili pak prilagođenim beta koeficĳentom, a sama metoda izračunavanja naziva se Blume metod.2

β Podešeni = 0,677 β istorijski + 0,343

Primenom formule na podatke iz tabele br. 1 dobĳa se vrednost podešenog β koeficĳenta za akcĳu "X"

β Podešeni = 0,677 (1,61) + 0,343

β Podešeni = 1,43297

Kao što se vidi iz date formule ulaganje u akcĳe dotične kompanĳe je manje rizično primenom β podešenog koeficĳenta, nego što to pokazuju podaci dobĳeni primenom β istorĳskog koeficĳenta i iznosi 1,43, a ne 1,6 u odnosu na prinos tržišta.

Dva su osnovna razloga koja doprinose da beta koeficĳenti uglavnom konvergiraju ka

jedinici, i to:• Prvi je intuitivan: nova privredna društva se

ponašaju nekonvencionalno, imaju drugačĳu tehnologĳu i stilove menadžmenta, te time proizvode manji broj proizvoda. Kako društvo raste, ono ulazi u nove poslove, diversifikuje time proizvodni program, prihvata uobičajenu tehnologĳu, te je samim tim i logično da kretanje cena akcĳa bude više usklađeno sa kretanjem tržišta.

• Drugi razlog je statistički: što se više beta pojedine akcĳe razlikuje od jedinice, to je i veća verovatnoća da će i greška procene biti veća.

Fundamentalni beta koeficĳentZa razliku od istorĳskog i podešenog beta

koeficĳenta, fundamentalni beta koeficĳent odražava promjene operacĳa preduzeća, kao i strukture kapitala, što nĳe bio slučaj sa prethodna dva načina izračunavanja beta koeficĳenata posmatrano u kratkom roku.

2. Način odabira tržišnog indeksa

Tržišni indeksi kao indikatori kretanja cena akcĳa pokazuju koliko se cena akcĳe promenila u odnosu na prethodni period, a ne ukazuju na to koliko će se cene kretati u narednom periodu. Promena cena na tržištu pokazatelj je da li se tržište nalazi u fazi ekspanzĳe ili kontrakcĳe, na osnovu čega se vrše procene budućih kretanja na tržištu.

Izračunavanje indeksa ima smisla samo ukoliko su ti indeksi relevantni. Da bi indeks bio relevantan, pored ostalih karakteristika treba da dobro predstavlja stanje na tržištu (da bude reprezentativan) i da bude sastavljen od likvidnih akcĳa. Prema mišljenju menadžera fondova, najznačajnĳa karakteristika je postojanje likvidnih akcĳa. Pored značaja likvidnosti akcĳa za samo trgovanje, likvidnost akcĳa predstavlja značajan kriterĳum za svrstavanje akcĳa u indeks i za ponderisanje. Indeks je reprezentativan ako uključuje što veći dio tržišne kapitalizacĳe, ima sličnu sektorsku strukturu i ima slične finansĳske pokazatelje kao tržište koje predstavlja (kao tržišna cena

2 Bernstein, R. „Style Investing“, New York: John Wiley&Sons, 1995., str. 114.

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By solving the system of equations in two variables we get the value of β coefficient, β - 1.61.

Beta coefficient of the certain company’s shares indicates the level of risk of those shares in the past, in comparison with the shares of other companies comprised into the stock exchange index. Hence, beta coefficient is not stable in time, but susceptible to changes. Therefore, it happens that the companies whose shares had high beta coefficient value, reflecting the high risk of investing in those shares, in the forthcoming period have significantly lower beta coefficients, and vice versa. Based on the previous information, it may be stated that the historic beta coefficient has a limited scope of use, given that the investors are exclusively interested in future returns and future risk of the relevant share.

Adjusted Beta CoefficientIt has been observed that beta coefficients

mainly converge towards the value of one. The given convergence around the value of one triggered the modification of historic beta coefficient, by including its anticipated changes, too. This creates beta coefficient of a higher utility value. Thus created beta coefficient is called adjusted beta coefficient, and the method for its calculation itself is called Bloom method.2

β Adjusted = 0,677 β historic + 0,343

By applying this formula onto the data from Table 1, we get the value of adjusted β coefficient for the share ‘X’, as follows:

β Adjusted = 0,677 (1,61) + 0,343

β Adjusted = 1,43297

As can be seen from the given formula, the investment in shares of the concerned company is less risky when the adjusted β coefficient is applied, than according to the data received by application of the historic β coefficient, and amounts to 1.43, and not 1.6, in respect of the market return.

There are two main reasons contributing to the fact that beta coefficients mostly converge towards the value of one, as follows:• The first reason is intuitive: new business

companies behave unconventionally, employ different technology and management styles, and hence produce a smaller number of products. As the company grows, it enters new business operations, thus diversifying its products programme, accepting the common technology, which, subsequently, makes it logical for the trends of the shares prices to be more coordinated with the market fluctuations.

• The second reason is statistical: the more beta coefficient of a certain share diverges from the value of one, the higher the probability that the assessment error will be bigger.

Fundamental Beta CoefficientAs opposed to the historic and adjusted beta

coefficient, fundamental beta coefficient reflects the changes in the company’s operations, as well as capital structure, which was not the case with the previous two methods of calculation of beta coefficients observed in a short-term.

2. Market Index Selection Method

Market indices as indicators of the fluctuations in shares prices reflect the level of change of the shares prices in comparison with the previous period, but do not indicate the prices fluctuations in the future period. The price changes in the market indicate whether the market is in the expansion or contraction stage, on the basis of which the future market fluctuations are anticipated.

Calculation of indices is only meaningful if those indices are relevant. In order for an index to be relevant, in addition to other characteristics, it has to be a sound indicator of market situation (to be representative) and composed of liquid shares. According to fund managers, the existence of liquid shares is the most significant characteristic. In addition to the significance of shares’ liquidity for the trade itself, liquidity of shares also is an

2 Bernstein, R., “Style Investing”, New York: John Wiley&Sons, 1995, p.114

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akcĳe/prinos po akcĳi, isplaćena dividenda po akcĳi/prinos po akcĳi). Prilikom razvĳanja novog indeksa, važno je doneti odluke o broju kompanĳa čĳe će akcĳe ulaziti u indeks, ograničenjima u vezi učešća pojedine akcĳe u indeksu, kao i čime ponderisati akcĳe u indeksu (tržišna kapitalizacĳa, free float, neponderisani indeks).

U SAD se najčešće koriste Dow Jones Industrial, Standard & Poor’s 500 i NYSE indeks. Londonska berza ima brojne indekse, među kojima je najrelevantnĳi FTSE100. S obzirom na način izračunavanja, razlikuju se pokazatelji ponderisani cenom i pokazatelji ponderisani tržišnom vrednošću:• cenovno ponderisani pokazatelji

izračunavaju se sabiranjem cena akcĳa odabranih kompanĳa i deljenjem tog zbira brojem akcĳa. Na taj način ponder firme određen je cenom akcĳe. Vrednosti proseka i pondera menjaju se samo u zavisnosti od kretanja cena akcĳa. Najpoznatĳi ovakvi pokazatelji su Dow Jones Averages, Value Line Composite Average, Nikkei Average i dr.

• indeksi ponderisani tržišnom vrednošću dobĳaju se stavljanjem u odnos ukupne sadašnje tržišne vrednosti odabranih kompanĳa i ukupne tržišne vrednosti u prethodnom, odnosno baznom periodu. Vrednost indeksa i pondera menja se u zavisnosti od dva faktora: cene i broja akcĳa. Najpoznatĳi indeksi iz ove grupe su: Standard & Poor’s 500, indeksi koje objavljuje NYSE; American Stock Exchange (AMEX), Market Value Index koji obuhvataju svih 800 akcĳa koje se kotiraju na ovoj berzi, za praćenje cena akcĳa malih preduzeća Rusell 2000 i dr.Kao što se vidi iz prethodnog navedenog,

beta koeficĳent se može izračunati na nekoliko načina, što dovodi i do različitih vrednosti koeficĳenata. U tabeli br. 2 prikazane su ove razlike. Izračunati su beta koeficĳenti za ista preduzeća, ali su agencĳe Merrill Lynch i Value Line primenjivale različite načine izračunavanja.3

Berzanski indeks treba da bude reprezentativan za ocenu privrednih kretanja u zemlji berze. To dalje znači da odabir preduzeća koja ulaze u indeks treba da bude takav da predstavlja čitavu privredu. Jedna od ključnih stvari prilikom izračunavanja β koeficĳenata jeste odabir odgovarajućeg indeksa. Kod tržišta u razvoju teško je imati reprezentativan indeks usled sledećih ograničenja:• mali broj akcĳa predstavlja veliki deo tržišne

kapitalizacĳe;• određene akcĳe imaju vrlo mali procenat

akcĳa u free float-u i• pojedini sektori se sastoje od samo jedne ili

dve akcĳe.Tržišta u razvoju su plitka, a karakteriše ih

mali broj likvidnih akcĳa, dok se sa određenim akcĳama ne trguje i po nekoliko dana. Sve navedeno odnosi se i na Sarajevsku, Banjalučku i Beogradsku berzu. Na kretanja indeksa utiču, pored makroekonomskih pokazatelja, i kretanja cena sirovina (prĳe svega na�e) i pojedine političke izjave vodećih političara. Rast indeksa u BiH i Srbĳi ne odražava dobro kretanje indeksa, te se može zakljičiti da indeksi nisu reprezentativni.

Beta koeficĳent se izračunava na osnovu istorĳskih podataka. Izračunati beta koeficĳenti treba da omoguće donošenje odluka koje će se u budućnosti pokazati ispravnim ili pak neispravnim. Investitori prognoziraju beta koeficĳente regresionom analizom na osnovu

Tabela br. 2: Vrĳednosti β koeficĳenata

IZVOR: Brigham, E., & Gapenski, L., & Ehrhardt, M. „Financial Management - Theory and Practice”. New York: Dryden press, 1999., str. 416.

Merrill LYNCH

VALUE LINE

Chrysler 1,26 1,20Polaroid 0,86 0,90IBM 0,89 0,95Mobil 0,64 0,70

Southwestern Public Service 0,51 0,60

3 Merrill Lynch je koristila tržišni indeks S&P 500, a za metodu izračunavanja istorĳski β koeficĳent sa petogodišnjim mesečnim prinosima 60 - opservacĳa. Za razliku od Merrill Lynch, Value Line je koristila tržišni indeks NYSE Composite Index a za metodu podešeni β koeficĳent sa petogodišnjim nedeljnim prinosima 260 opservacĳa.

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important criterion for classification of shares into indices, and for the weighting process. The index is representative if it includes the largest possible portion of market capitalization, has the similar sector structure and similar financial indicators as the market it represents (as the share’s market price/return per share, dividend paid out per share/return per share). When developing a new index, it is crucial to make a decision on the number of companies whose shares will enter the index, on limitations in respect of the inclusion of a certain share in the index, and on what will be used as a weight for the indexed shares (market capitalization, free float, unweighted index).

In the USA, the most used indices are Dow Jones Industrial, Standard & Poor’s 500 and NYSE. The London Stock Exchange has numerous indices, the most relevant of which is FTSE100. According to the calculation method, the difference is made between the indicators weighted by price and indicators weighted by market value, as follows:• Price-weighted indicators are calculated

by summing the prices of the selected companies’ shares, and dividing the sum with the number of shares. Thus the company’s weight is defined by the share’s price. The values of averages and weights change only depending on the fluctuations in shares prices. The most famous indicators of this sort are Dow Jones Averages, Value Line Composite Average, Nikkei Average, etc.

• Indices weighted by market value are calculated by the ratio between the total net present market value of the selected companies and the total market value in the preceding, i.e. basic period. The value of indices and weights changes depending on two factors: price and number of shares. The most famous indices from this group are the following: Standards & Poor’s 500, indices published by NYSE; American Stock Exchange (AMEX), Market Value Index, which include all 800 shares quoted at this stock exchange, for monitoring the prices of small

companies’ shares - Rusell 2000, etc. As can be seen from the above stated, beta

coefficient can be calculated in several ways, which results in different coefficient values. Table 2 shows these differences. Beta coefficients were calculated for the same companies, but the agencies Merrill Lynch and Value Line applied different calculation methods.3

Stock exchange index should be representative for the assessment of economic trends in the country of the stock exchange. This, in turn, means that the selection of companies to enter the index should be representative of the entire economy. One of the key things when calculating β coefficient is choosing the appropriate index. In the case of emerging markets it is difficult to have a representative index due to the following constraints:• Small number of shares represents the large

portion of market capitalization;• Certain shares have a very small percentage

of shares in free float; and• Certain sectors consist of only one or two

shares.Emerging markets are shallow, and

characterized by a small number of liquid shares, with certain shares not being traded for several days. All the mentioned also refers to Sarajevo, Banjaluka and Belgrade Stock Exchange. In addition to macroeconomic indicators, the fluctuations of indices are influenced by the fluctuations in the prices of raw materials

3 Merrill Lynch used S&P 500 market index and the historic β coefficient with five-year monthly returns in 60 observations as its calculation method. As opposed to Merrill Lynch, Value Line used NYSE Composite Market Index and the adjusted β coefficient with five-year weekly returns in 260 observations.

Table 2: Beta Coefficient Values

SOURCE: Brigham, E., & Gapenski, L., & Ehrhardt, M. “Financial Management - Theory and Practice”, New York: Dryden Press, 1999, p. 416

Merrill LYNCH

VALUE LINE

Chrysler 1,26 1,20Polaroid 0,86 0,90IBM 0,89 0,95Mobil 0,64 0,70

Southwestern Public Service 0,51 0,60

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ekstrapolacĳe. Ekstrapolacĳa ima smisla ukoliko postoji kontinuitet između prošlosti i budućnosti. U skladu s tim, izračunavanje beta koeficĳenata ima smisla samo ukoliko postoji kontinuitet. Posmatrano s druge strane na tržištu kapitala u BiH i Srbĳi postoji popriličan diskontinuitet i izražena promenljivost u privrednim performansama tokom prethodnog perioda.

Promenljivost (volatilnost) je posebno izražena usled okolnosti da je razvoj tržišta akcĳa neposredno vezan za različite modele privatizacĳe koji su primenljivi u zemljama u tranzicĳi, kao što je BiH i Srbĳa. Pored visoke nezaposlenosti, niskog bruto domaćeg proizvoda i niske štednje, koji negativno utiču na razvoj tržišta akcĳa generalno, u BiH i Srbĳi su posebno došle do izražaja velike promene cena pre i nakon preuzimanja preduzeća. Cene akcĳa preuzetih preduzeća padale su u velikom broju slučajeva. Ovo se posebno odnosi na preduzeća preuzeta putem berze. Zabeleženi su slučajevi i prestanka trgovanja i povlačenja kompanĳa sa berze nakon koncentracĳe vlasništva.

3. Proračun beta koeficĳenata u BiH i Republici Srbĳi

Upravljanje i kontrola portfolĳom vrednosnih papira na osnovama moderne portfolio teorĳe je vrlo kompleksan zadatak, koji uključuje sva polja moderne portfolio teorĳe od procene vrednosti akcĳa pojedinih kompanĳa u budućnosti, ekonometrĳskih analiza i predviđanja kretanja prinosa akcĳa, pa sve do metoda koje dovode do kreiranja optimalnog portfolĳa. Upravljanje portfolĳom je funkcĳa mnogih faktora, kao npr. stanje na tržištu kapitala, tj. broj akcĳa u kotacĳi, njihova likvidnost, transparentnost poslovanja, povezanost sa drugim tržištima i slično. Na razvĳenim tržištima kapitala mnogi pobrojani faktori ne predstavljaju poseban problem za upravljanje portfolĳom, jer je na osnovu istih lako doći do praktičnog kreiranja optimalnog portfolĳa od strane investitora. Za tržišta

kapitala u tranzicĳi kakva su tržišta kapitala BiH i Republike Srbĳe, treba obratiti veću pažnju svim navedenim faktorima, kako bi se prevazišao problem uspešnog upravljanja portfolĳom.

Kako znamo da na tržištu kapitala BiH i Republike Srbĳe ne postoji dovoljan broj finansĳskih instrumenata, i s obzirom na činjenicu da je likvidnost akcĳa na niskom nivou, vrlo je teško postići efikasnu diversifikacĳu rizika portfolĳa. Isto tako, na istim tržištima postoje mnogi tzv. nevidljivi rizici sa kojima se suočavaju investitori i koje je vrlo teško vrednovati i uključiti u optimizacĳu, kao npr. politički rizik, rizik zemlje, ekonomski rizik, rizik malog preduzeća ili pak rizik nelikvidnosti. Rizik nelikvidnosti predstavlja otežavajuću okolnost predviđanja kretanja prinosa na akcĳe.4

Proračun beta koeficĳenata za akcĳe koje se kotiraju na Sarajevskoj, Banjalučkoj i Beogradskoj berzi, isto se bazira na prošlim (realizovanim) prinosima određene akcĳe i prošlim (realizovanim) prinosima na tržištu jednačinom linearne regresĳe. U ovom djelu rada bavićemo se analizom jednog segmenta tržišta kapitala u BiH i Republici Srbĳi (Sarajevska berza vrednosnih papira, Banjalučka berza hartĳa od vrednosti i Beogradska berza hartĳa od vrednosti) tj., slobodnog tržišta, tačnĳe pratićemo kretanje vrednosti berzanskih indeksa SASX-10 i BIRS BELEX 15 i strukturu najlikvidnĳih akcĳa preduzeća koje su sastavni dio istih. Međutim, zbog nedostatka svih istorĳskih podataka, odnosno zbog određenih dana bez trgovanja u toku godine, proračun je napravljen na osnovu mesečnih podataka za period: 01.01.2008. - 30.06.2009. godine. U okviru date analize su izabrane najlikvidnĳe akcĳe, koje čine sastavni dio indeksa SASX - 10, BIRS - a i BELEX 15.

Zvaničan indeks Sarajevske berze je SASX - 10 (engl. Sarajevo Stock Exchange Index - SASX). SASX - 10 je benčmark indeks Sarajevske berze vrĳednosnih papira, koji prati kretanje cena prvih deset kompanĳa na tržištu (izuzimajući investicione fondove), mereno po tržišnoj

4 Alihodžić, mr. Almir. „Upravljanje prinosom i rizikom na tržištu kapitala Federacĳe Bosne i Hercegovine sa osvrtom na tržište kapitala Srbĳe i Hrvatske“ FEB časopis br. 9 (2008.) str. 54 - 55.

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(first and foremost oil), and certain political statements of the leading politicians. The growth of indices in Bosnia and Hercegovina and Serbia does not reflect the fluctuations of indices well, hence it may be concluded that the indices are not representative.

Beta coefficient is calculated based on the historic data. The calculated beta coefficients should enable decision-making which will prove to be correct or incorrect in the future. Investors forecast beta coefficients by regression analysis based on extrapolation. Extrapolation is meaningful if there is continuity between the past and the future. According to this, calculation of beta coefficients is only meaningful if there is continuity. Viewed from another perspective, there is quite a large discontinuity in the capital markets in Bosnia and Herzegovina and Serbia, along with the prominent volatility in economic performance in the past.

Volatility is particularly prominent due to the fact that stock market development is directly related to various privatization models applicable to the countries in transition, such as Bosnia and Herzegovina and Serbia. In addition to high unemployment level, low GDP and low savings rates, which have an adverse effect on the stock market development in general, what was especially manifested in Bosnia and Herzegovina and Serbia were the large fluctuations in prices before and a�er companies’ takeovers. The prices of shares of the taken-over companies were plummeting in a large number of cases. This particularly refers to the companies taken over through stock exchange. There were even cases when the trade was brought to a close, the company withdrawing from the stock exchange a�er the concentration of ownership.

3. Calculation of Beta Coefficient in Bosnia and Herzegovina and the Republic of Serbia

Securities portfolio management and supervision based on the modern portfolio theory is a very complex task, involving all

fields of the modern portfolio theory from the assessment of the future value of certain companies’ shares, econometric analyses and forecasts of shares’ returns fluctuations, to the methods resulting in optimum portfolio creation. Portfolio management depends on many factors, such as, for instance, the situation in the capital market, i.e. number of quoted shares, its liquidity, transparency of operation, interconnectedness with other markets, etc. In the developed capital markets many of the above mentioned factors do not present much of a problem for portfolio management, because, on the basis of them, it is easy to achieve practical creation of the optimum portfolio by the investors. In case of capital markets in transition, such as the capital markets in Bosnia and Herzegovina and Serbia, greater a�ention should be paid to all the above mentioned factors, in order to achieve successful portfolio management.

Since we know that there are not enough financial instruments at the capital markets of Bosnia and Herzegovina and the Republic of Serbia, and given the fact that liquidity of shares is low, it is very difficult to achieve efficient diversification of risk portfolio. Similarly, those same markets entail the so-called invisible risks, which investors have to face, and which are very difficult to evaluate and include into optimization, such as, for instance, political risk, country risk, economic risk, small enterprise risk, or illiquidity risk. Illiquidity risk is one of the factors hindering the forecasting of stock returns fluctuations.4

Calculation of beta coefficients for the shares quoted at Sarajevo, Banjaluka and Belgrade Stock Exchange is also based on the past (achieved) returns of a certain share and the past (achieved) returns in the market, by using the linear regression equation. In this part of the paper we will be dealing with the analysis of one segment of capital market in Bosnia and Herzegovina and the Republic of Serbia (Sarajevo Securities Exchange, Banjaluka Securities Exchange and Belgrade Securities Exchange), i.e. the free market. More precisely,

4 Alihodzic, MSc, Almir, “Managing Return and Risk in the Capital Market of Bosnia and Herzegovina with a Review of Serbian and Croatian Capital Markets”, FEB Magazine, No. 9 (2008), p. 54-55

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kapitalizacĳi i frekvencĳi trgovanja. Ovaj indeks nĳe ograničen samo na jedan tržišni segment, u njegov sastav mogu biti uvršteni kako emitenti sa kotacĳe, tako i sa slobodnog tržišta. Nakon ograničavanja učešća emitenata u sastavu indeksa, vrednost indeksa na dan t se izračunava prema sledećoj formuli:

(3.1)

gdje je:Pi,t - cena akcĳe i na dan t;Pi,o - cena akcĳe i na dan t = 0 (početni bazni datum indeksa); qi,R - broj akcĳa i na dan revizĳe i Ct - korekcioni faktor (Co = 0)

Zaključno sa 30.06. 2009. godine, strukturu indeksa SASX - 10 su činili sledeći emitenti: 1) JP Elektroprivreda BiH doo Sarajevo, 2) BH Telecom dd Sarajevo, 3) Energoinvest dd Sarajevo, 4) Fabrika Duhana Sarajevo dd Sarajevo, 5) Energopetrol dd Sarajevo, 6) Bosnalĳek dd Sarajevo, 7) Šipad komerc dd Sarajevo, 8) Sarajevoosiguranje dd Sarajevo, 9) Hidrogradnja dd Sarajevo i 10) IK Banka dd Zenica. Vrĳednost indeksa SASX - 10 je za period 01.01. - 30.06.2009. godine, pala za 15,66% u odnosu na isti period prethodne godine.

Na osnovu analize jednog dela tržišta kapitala u Federacĳi BiH tačnĳe slobodnog tržišta, tj. praćenja kretanja berzanskog indeksa SASX - 10 i strukture najlikvidnĳih akcĳa za navedeni period došlo se do sledećih rezultata analize.

Tabela br. 3.1 ilustruje kretanje vrednosti indeksa SASX - 10 i akcĳa emitenata u njegovom sastavu. U analizi strukture indeksa SASX - 10 su uključene najlikvidnĳe akcĳe slĳedećih emitenata: 1) BH - Telecom d.d Sarajevo (simbol: BHTSR), 2) JP Elektroprivreda BiH d.d Sarajevo (simbol: JPESR), 3) Bosnalek d.d Sarajevo (simbol: BSNLR), 4) Fabrika duhana, Sarajevo (simbol: FDSSR), 5) IK Banka d.d Zenica (simbol: IKBZRK) i 6) Sarajevo osiguranje d.d Sarajevo (simbol: SOSOR).

Pokazatelj koji je ujedno i predmet analize je beta koeficĳent.5 Pošto je za tržište (dobro diversifikovani portfolio) β = 1, i u ovoj analizi za indeks slobodnog tržišta kapitala FBiH je uzeta vrednost 1. Kako znamo ako je β>1 onda će akcĳa sa datom betom uvećati rizik portfolĳa, i obrnuto ako je β<1 ona će umanjiti rizik portfolĳa. U analizi jednog dela tržišta kapitala u BiH (Federacĳa BiH) vrednost beta i podešenog beta koeficĳenta za sve akcĳe uključene u indeks SASX - 10 za dati period je ispod 1, što je pozitivno sa aspekta rizika ali ne i prinosa, jer svaki manje rizičan vrednosni papir nosi i manju stopu prinosa. Najveća vrednost kako beta koeficĳenta tako i podešenog beta koeficĳenta pripala je akcĳi emitenta Fabrika duhana Sarajevo (beta koeficĳent: 0.69, podešeni beta koeficĳent: 0,810), dok s druge strane najmanju vrednost zauzima emitent IK Banka d.d Zenica (beta koeficĳent: 0.25, podešeni beta koeficĳent: 0.512). Najveći prosečni dnevni promet za period: 1.1.2009. - 30.6.2009. je ostvario emitent IK Banka d.d Zenica od KM 62.694 (EUR 32.054), što predstavlja 30%

5 Beta koeficĳent objašnjava za koliko će se promeniti stopa prinosa posmatrane akcĳe ako se stopa prinosa tržišnog portfolĳa promeni za 1.

Tabela br. 3.1: Praćenje vrednosti indeksa SASX - 10 za period: 1.1.2009. - 30.6.2009. i proračun beta koeficĳenta za određene akcĳe

IZVOR: Proračun autora

Simbol SASX - 10 BHTSR JPESR BSNLR FDSSR IKBZRK SOSOR

Beta koeficĳent 1,00 0,60 0,57 0,62 0,69 0,25 0,51

Podešeni beta koeficĳent 1,02 0,749 0,728 0,762 0,810 0,512 0,688

Prosečni dnevni promet u 2008. (u KM)

- 70.450 31.912 73.538 81.972 48.188 33.267

Prosečni dnevni promet za period: 1.1.2009. - 30.6.2009. (u KM)

- 42.846 37.542 31.261 32.033 62.694 6.970

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we will be monitoring the fluctuations of the values of the exchange indices SASX-10 and BIRS BELEX 15, along with the structure of the most liquid shares of the companies which are the integral part of the concerned indices. However, due to the lack of all historical data, i.e. due to the certain days in a year without any trade, the calculation was made on the basis of the monthly data for the period 01.01.2008 - 30.06.2009. Within the given analysis, the most liquid shares were selected, being the integral part of the indices SASX, BIRS and BELEX 15.

The official index of Sarajevo Stock Exchange is SASX-10. SASX-10 is the benchmark index of Sarajevo Securities Exchange, which reflects the fluctuations of the prices of the first ten companies in the market (excluding investment funds), measured in respect of market capitalization and trading frequency. This index is not limited to just one market segment; it can include issuers both from the quotation, and from the free market.

A�er limiting the participation of issuers in the index, the value of index as of that day - t is calculated according to the following formula:

(3.1)

where Pi,t is the price of a share i as of day t; Pi,o is the price of a share i as of day t = 0 (initial basic index date); qi,r - number of shares i as of the revision day, and Ct - correction factor (C0 = 1).

As of 30.06.2009, the structure of SASX index was composed of the following issuers: 1) JP Elektroprivreda BiH doo Sarajevo, 2) BH Telecom dd Sarajevo, 3) Energoinvest dd Sarajevo, 4) Fabrika Duhana Sarajevo dd Sarajevo, 5) Energopetrol dd Sarajevo, 6) Bosnalĳek dd Sarajevo, 7) Šipad komerc dd Sarajevo, 8) Sarajevo osiguranje dd Sarajevo, 9) Hidrogradnja dd Sarajevo and 10) IK Banka dd Zenica. The value of SASX-10 index for the period 01.01-30.06.2009 dropped by 15.66% in comparison with the same period last year.

Based on the analysis of one part of the capital market in Bosnia and Herzegovina, more precisely, the free market, i.e. monitoring the fluctuations of the stock exchange SASX-10 index and the structure of the most liquid shares for the stated period, we have come to the following results of the analysis.

Table 3.1 illustrates the fluctuations of the values of SASX-10 index and the shares of its integral issuers. The analysis of the SASX-10 index structure includes the most liquid shares of the following issuers: 1) BH-Telekom dd Sarajevo (symbol: BHTSR), 2) JP Elektroprivreda BiH doo Sarajevo (symbol: JPESR), 3) Bosnalĳek dd Sarajevo (symbol: BSNLR), 4) Fabrika Duhana Sarajevo dd Sarajevo (symbol: FDSSR), 5) IK Banka dd Zenica (symbol: IKBZRK) and 6) Sarajevo osiguranje dd Sarajevo (symbol: SOSOR).

The indicator which is at the same time the subject of the analysis is beta coefficient.5 Since the market (well diversified portfolio)

5 Beta coefficient indicates the amount of change of the observed share’s return rate if the return rate of the market portfolio changes by 1.

Table 3.1: Monitoring SASX-10 index values for the period: 1.1.2009 - 30.6.2009 and calculation of beta coefficients for certain shares

SOURCE: Author’s calculation

Symbol SASX - 10 BHTSR JPESR BSNLR FDSSR IKBZRK SOSOR

Beta coefficient 1,00 0,60 0,57 0,62 0,69 0,25 0,51

Adjusted beta coefficient 1,02 0,749 0,728 0,762 0,810 0,512 0,688

Average daily turnover in 2008 (in KM)

- 70.450 31.912 73.538 81.972 48.188 33.267

Average daily turnover for the period: 1.1.2009 - 30.6.2009 (in KM)

- 42.846 37.542 31.261 32.033 62.694 6.970

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ostvarenje prošlogodišnjeg prosječnog dnevnog prometa. S druge strane najmanji prosječni dnevni promet za isti period je ostvario emitent Sarajevo osiguranje d.d Srajevo u iznosu od KM 6.970, odnosno EUR 3.563 što predstavlja 21% prošlogodišnjeg ostvarenja.

Zvanični indeks Banjalučke berze je BIRS (Berzanski indeks Republike Srpske - BIRS). BIRS uključuje najkvalitetnĳe akcĳe preduzeća i banaka. Formiran je 1. maja 2004. godine. Broj akcĳa koje ulaze u sastav BIRS - a može varirati od 5 do 15, zavisno o ispunjavanju kriterĳa za ukljuèivanje akcĳa u BIRS indeks. Broj emitenata čĳe akcĳe ulaze u sastav BIRS - a zavisi od broja emitenata na službenom berzanskom tržištu i broja emitenata koji ispunjavaju uslove za sastav BIRS - a. U sastav BIRS - a mogu da ulaze akcĳe emitenata koji ispunjavaju opšte uslove i kriterĳume za uključivanje akcĳa u BIRS, izuzev akcĳa investicionih fondova. Početna vrednost indeksa iznosila je 1.000 poena. Vrednost BIRS-a se izračunava prema sledećoj formuli:

(3.2)

gde je:i = 1, ..., n; n - broj emitenata uvršćenih u BIRS; t - dan trgovanja;R - dan formiranja ili revizĳe BIRS-a;T - trenutak pre početka računanja BIRS-a po novom sastavu;Pi,t - cena akcĳe i na dan t;Pi,o - cena akcĳe i na dan t = 0 (cena na dan formiranja revizĳe BIRS-a);qi,R - prilagođeni broj akcĳa emitenta i; pri

računanju tržišne kapitalizacĳe uzima se prilagođeni broj akcĳa zbog broja akcĳa u vlasništvu javnosti i prilagođavanja učešća akcĳa u sastavu BIRS-a i Ct - korekcioni faktor za osiguranje kontinuiteta BIRS-a.

U periodu 1.1. - 30.6.2009. službeni indeks Banjalučke berze BIRS je zabeležio pad vrednosti od 3,15% u odnosu na isti period prethodne godine. Takođe, pad je zabeležen i kod indeksa preduzeća Elektroprivrede Republike Srpske od 3,89%. Za razliku od službenog indeksa i indeksa preduzeća Elektroprivrede Republike Srpske, indeks investicĳskih fondova Republike Srpske je zabeležio porast vrednosti od 14,63%.

Na osnovu analize jednog dela tržišta kapitala u Republici Srpskoj tačnĳe slobodnog tržišta, tj. praćenja kretanja berzanskog indeksa BIRS -a i strukture najlikvidnĳih akcĳa za period: 1.1. - 30.6.2009. došlo se do sledećih rezultata analize. (tabela br. 3.2)

Tabela br. 3.2 ilustruje kretanje vrednosti indeksa BIRS - a i akcĳa emitenata u njegovom sastavu. U analizi strukture indeksa BIRS-a su uključene najlikvidnĳe akcĳe sledećih emitenata: 1) Telekom Srpske a.d. Banja Luka (simbol: TLKM-R-A), 2) Nova banka a.d. Banja Luka (simbol: NOVB-R-A), 3) Boksit a.d. Milići (simbol: BOKS-R-A), 4) Meridian a.d. Banja Luka (simbol: MRDN-R-A), 5) Banjalučka pivara a.d. Banja Luka (simbol: BLPV-R-A) i 6) Rafinerĳa na�e Bosanski Brod (simbol: RNAF-R-A). Na osnovu analize jednog dela tržišta kapitala u Republici Srpskoj, tačnĳe slobodnog tržišta najveća vrednost β koeficĳenta pripala je akcĳi emitenta Banjalučka pivara a.d. Banja Luka (β = 2,92, podešeni β koeficijent 2,319),

Tabela br. 3.2: Praćenje vrednosti indeksa BIRS-a za period: 1.1.2008. - 30.6.2009. i proračun beta koeficĳenta za određene akcĳe


Simbol BIRS TLKM-R-A NOVB-R-A BOKS-R-A MRDN-R-A BLPV-R-A RNAF-R-A

Beta koeficĳent 1,00 1,04 0,61 0,20 0,43 2,92 -0,15

Podešeni beta koeficĳent 1,02 1,047 0,755 0,478 0,634 2,319 -0,444

Prosečni dnevni promet u 2008. (u KM)

- 59.127 12.155 8.354 1.542 6.473 11.268

Prosečni dnevni promet za period: 1.1.2009. - 30.6.2009. (u KM)

- 52.182 7.940 1.794 847 3.898 1.348

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has β=1, this analysis too takes the value of 1 for the index of the free capital market of Bosnia and Herzegovina. Taking into account that β>1, the share with larger beta value will increase the portfolio risk, and vice-versa if β<1, it will reduce the portfolio risk. In the analysis of one part of the capital market in Bosnia and Herzegovina the value of beta and adjusted beta coefficient for all shares integrated in the SASX-10 index for the given period was below 1, which is positive from the aspect of risk, but not from the aspect of returns, because less risky securities entail smaller return rate. The largest value of both beta coefficient and adjusted beta coefficient was that of the shares of Fabrika duhana Sarajevo as issuer (beta coefficient: 0.69, adjusted beta coefficient 0.810), whereas on the other hand the lowest value was the one of the issuer IK Banka dd Zenica (beta coefficient: 0.25, adjusted beta coefficient 0.512). The largest average daily turnover for the period: 1.1.2009 - 30.6.2009 was achieved by the issuer IK Banka dd Zenica in the amount of KM 62,694 (EUR 32,054), which is 30% of the average daily turnover in the last year. On the other hand, the smallest average daily turnover for the same period was achieved by the issuer Sarajevo osiguranje dd Sarajevo in the amount of KM 6,970, i.e. EUR 3,563, which is 21% of the last year’s result.

The official index of Banjaluka Stock Exchange is BIRS. BIRS includes the highest quality shares of companies and banks. It was established on May 1st 2004. The number of shares entering BIRS ranges from 5 to 15, depending on the fulfillment of criteria for incorporating shares into BIRS index. The number of issuers whose shares are integrated into BIRS depends on the number of issuers at the official stock market and the number of issuers fulfilling the conditions for ge�ing integrated into BIRS. BIRS may incorporate the shares of issuers fulfilling the general conditions and the criteria for incorporating share into BIRS, except from the investment fund shares. The initial index value amounted to 1,000 points. BIRS index value is calculated according to the following formula:

(3.2)

where i = 1,…,n; n is the number of issuers integrated into BIRS; t is the trading day; R is the day of forming or revising BIRS; T - moment before the commencement of BIRS calculation according to the new composition; Pi,t - price of a share of the issuer i as of day t; Pi,o - basic price of a share of the issuer i (the price as of the day of formation/revision of BIRS); qi,r - adjusted number of shares of the issuer i; when calculating market capitalization the adjusted number of shares is taken because of the number of shares in public ownership and the adjustment of participation of shares in BIRS composition; and Ct - correction factor for ensuring BIRS continuity.

In the period 1.1- 30.6.2009 the official index of Banjaluka Stock Exchange - BIRS recorded a drop in value by 3.15% in comparison with the same period last year. Also, the drop of 3.89% was recorded in the index of the company Elektroprivreda Republike Srpske. As opposed to the official index and the index of Elektroprivreda Republike Srpske, the index of investment funds of Republika Srpska increased in value by 14.63%.

Based on the analysis of one part of the capital market in Republika Srpska, more precisely, the free market, i.e. monitoring the fluctuations of BIRS stock exchange index structure and the most liquid shares for the period: 1.1 - 30.6.2009, we have come to the following results of the analysis.

Table 3.2 illustrates the fluctuations of value of the BIRS index and the shares of its integral issuers. The analysis of the BIRS index structure includes the most liquid shares of the following issuers: 1) Telekom Srpske a.d. Banka Luka (symbol: TLKM-R-A), 2) Nova banka a.d. Banja Luka (symbol: NOVB-R-A), 3) Boksit a.d. Milići (symbol: BOKS-R-A), 4) Meridian a.d. Banja Luka (symbol: MRDN-R-A), 5) Banjalučka pivara a.d. Banja Luka (symbol: BLPV-R-A), and 6) Oil Refinery Bosanski Brod (symbol: RNAF-R-A). Based on the analysis of one part of the capital market in Republika Srpska, more precisely, the free market, the largest value of β coefficient is that of a share issued by Banjalučka pivara a.d. Banja Luka

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što je znatno uvećala vrednost indeksa BIRS-a, drugo mesto pripalo je akcĳi emitenta Telekom Srpske a.d Banja Luka (β = 1,04, podešeni β koeficijent 1,047). Bete ostalih emitenata u sastavu indeksa BIRS-a su ispod jedinice, što je pozitivno sa aspekta rizika. Kada je reč o prosečnom dnevnom prometu za period: 1.1.2009. - 30.6.2009. najveću vrednost je ostvario emitent Telekom Srpske a.d. Banja Luka KM 52.182 odnosno EUR. 26.680, što predstavlja 88% ostvarenja u odnosu na 2008. godinu. Najniži prosečni dnevni promet za posmatrani period pripada emitentu Meridian a.d. Banja Luka, i iznosi KM 847 ili EUR. 433.

Zvanični indeks Beogradske berze je: Indeks najlikvidnĳih akcĳa slobodnog berzanskog tržišta Beogradske berze (skraćeni naziv: BELEX15). Indeks je ponderisan tržišnom kapitalizacĳom, i ne prilagođava se za isplaćene dividende i nĳe zaštićen od dilutacionog efekta koji se javlja usled isplate dividendi. BELEX15 je ponderisan isključivo tržišnom kapitalizacĳom koja se nalazi u slobodnom prometu (free float). BELEX15 se sastoji od akcĳa kojima se trguje metodom kontinuiranog trgovanja i koje su ispunile kriterĳume za ulazak u indeksnu korpu. Težina komponenti u indeksu je ograničena na maksimalnih 20% u odnosu na ukupnu tržišnu kapitalizacĳu indeksa na datum revizĳe. Indeks je namenjen da meri promene cena (price index) akcĳa kojima se trguje metodom kontinuiranog trgovanja, a koje su prethodno zadovoljile kriterĳum za uključivanje u indeksnu korpu. Indeks BELEX15 je prevashodno namenjen unapređenju investicionog procesa, kroz merenje performansi najlikvidnĳeg segmenta srpskog tržišta kapitala, kao i kroz mogućnost unapređenja potencĳalnih investicionih strategĳa prema indeksu. S druge strane, BELEX15 je dizajniran na način na koji najbolje opisuje tržišna kretanja najlikvidnĳih akcĳa i može služiti kao podloga (underlying) za kreiranje struktuiranih proizvoda i derivata na domaćem i inostranom tržištu. Isto tako, namenjen je da bude analitičko sredstvo kako za portfolio menadžere, profesionalne analitičare, stručnu javnost, investitore, tako i za sve druge koji proučavaju dinamiku kretanja cena na srpskom tržištu kapitala.

Prilikom izračunavanja vrednosti indeksa u bilo kojem trenutku relevantna količina akcĳa

određenog izdavaoca koja se koristi prilikom računanja, obuhva ukupan broj običnih akcĳa pomnožen free float faktorom (FFc) na dan poslednje revizĳe indeksne korpe.

Free float faktor (FFc) je procenat akcĳa koje se nalaze u slobodnom prometu i koji je javno dostupan potencĳalnim investitorima. FFc se dobĳa kada se od ukupnog broja akcĳa oduzmu akcĳe koje se ne nalaze u slobodnom prometu (non free float). Pod pojmom akcĳa koje nisu u slobodnom prometu smatraju se akcĳe koje su u vlasništvu:• lica koja pojedinačno posjeduju više od 5%

akcĳa od ukupno izdatih akcĳa izdavaoca, izuzimajući akcĳe koje se nalaze u vlasništvu investicionih i penzionih fondova, kao i druge akcĳe na kastodi računima, društva za upravljanje fondovima, osiguravajućih društava, brokersko - dilerskih društava, i drugih investicionih kompanĳa sa kratkoročnim investicionim strategĳama;

• sopstvene akcĳe izdavaoca;• akcĳe koje poseduju međunarodne

organizacĳe i institucĳe za razvoj;• akcĳe koje poseduje Republika Srbĳa,

izuzimajući akcĳe u vlasništvu Akcĳskog fonda, Fonda za penzĳsko i invalidsko osiguranje.Indeks BELEX15 se izračunava upotrebom

Lasprejerove formule:

(3.3)gde jeBELEX15(t) - vrĳednost indeksa selektovanih hartĳa kojima se trguje metodom kontinuiranog trgovanja u vremenu t, zaokružena na dvĳe decimale; n - broj izdavalaca čĳe akcĳe se nalaze u indeksnoj korpi - selektovane hartĳe su nepromjenljive do momenta revizĳe; i - brojač koji uzima vrĳednost od 1 do 15 i predstavlja određenog izdavaoca čĳe su akcĳe u indeksnoj korpi; C(i,t) - cĳena akcĳe izdavaoca i u trenutku t, koja se uzima u realnom vremenu iz sistema za trgovanje; K(i,t) - količina akcĳa izdavaoca i u trenutku t; d(t) - vrednost delioca u trenutku t; FFc(i,t) - free float faktor izdavaoca i u trenutku t; A(i) - prilagođavajući faktor izdavaoca i.

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(β - 2.92, adjusted β coefficient - 2.319), which considerably increased BIRS index value, the second largest share being the one issued by Telekom Srpske a.d. Banka Luka (β - 1.04, adjusted β coefficient - 1.047).

Betas of other issuers integrated into BIRS index are below one, which is positive from the aspect of risk. When it comes to the average daily turnover for the period: 1.1.2009 - 30.6.2009, the largest value was achieved by the issuer Telekom Srpske a.d. Banka Luka - KM 52,182, i.e. EUR 26,680, which is 88% of the result in 2008. The lowest average daily turnover in the observed period is that of the issuer Meridian a.d. Banja Luka, in the amount of KM 847 or EUR 433.

The official Belgrade Stock Exchange index is the Index of the most liquid shares in the free stock exchange market of the Belgrade Stock Exchange (abbreviation: BELEX15). The index is weighted by market capitalization; it is not adjusted for dividends paid out, and is not protected from the dilution effect occurring due to payment of dividends. BELEX15 is weighted exclusively by market capitalization in free float. BELEX15 consists of shares traded in the manner of continuous trading, which have fulfilled the criteria for being incorporated into the index basket. The weight of the components in the index is limited to maximum 20% of the total market capitalization of index as of the day of revision. The index is intended for measuring fluctuations of prices of shares traded in the manner of continuous trading, which have previously met the criterion for being incorporated into the index basket. BELEX15 index is primarily intended for enhancing the

investment process, by means of measuring performances of the most liquid segment of the Serbian capital market, as well as through the possibility of enhancing the potential investment strategies towards the index. On the

other hand, BELEX15 is designed in the manner which best describes market fluctuations of the most liquid shares and may serve as an underlying basis for the creation of structured products and derivatives in the domestic and foreign markets. Similarly, it is intended to be an analytical instrument for portfolio managers, professional analysts, expert public, investors, and all others studying the dynamics of price fluctuations in the Serbian capital market.

When calculating the index values in any time, the relevant amount of shares of a certain issuer used in the calculation includes the total number of common shares multiplied by free float factor (FFc) as of the day of the last index basket revision.

Free float factor (FFc) is the percentage of shares in free float which is publicly available to the potential investors. FFc is calculated by subtracting the non-free float shares from the total number of shares. Non-free float shares are the shares owned by the following: • Persons who individually own more than 5%

of shares out of the total number of shares issued by a certain issuer, excluding the shares owned by investment and pension funds, as well as other shares at custody accounts, fund management agencies, insurance companies, broker-dealer agencies, and other investment companies with short-term investment strategies;

• Issuer’s own shares;

Table 3.2: Monitoring BIRS index values for the period: 1.1.2009 - 30.6.2009, and calculation of beta coefficients for certain shares


Symbol BIRS TLKM-R-A NOVB-R-A BOKS-R-A MRDN-R-A BLPV-R-A RNAF-R-A

Beta coefficient 1,00 1,04 0,61 0,20 0,43 2,92 -0,15

Adjusted beta coefficient 1,02 1,047 0,755 0,478 0,634 2,319 -0,444

Average daily turnover in 2008 (in KM)

- 59.127 12.155 8.354 1.542 6.473 11.268

Average daily turnover for the period: 1.1.2009 - 30.6.2009 (in KM)

- 52.182 7.940 1.794 847 3.898 1.348

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Na osnovu analize jednog dela tržišta kapitala u Republici Srbĳi tačnĳe slobodnog tržišta, tj. praćenja kretanja berzanskog indeksa BELEX15 i strukture najlikvidnĳih akcĳa za period: 1.1. - 30.6.2009. došlo se do sledećih rezultata analize.

Tabela br. 3.3 prikazuje kretanje vrednosti indeksa BELEX15 i akcĳa emitenata u njegovom sastavu. U analizi strukture indeksa BELEX15 su uključene najlikvidnĳe akcĳe slĳedećih emitenata: 1) AIK banka a.d. Niš (Simbol: AIKB), 2) Komercĳalna banka a.d. Beograd (Simbol: KMBN), 3) Energoprojekt holding a.d. Beograd, (Simbol: ENHL),4) Univerzal banka a.d. Beograd (Simbol: UNBN), 5) Metalac a.d. Gornji Milanovac (Simbol: MTLC) i 6) Metals banka a.d. Novi Sad (Simbol: MTBN). Na osnovu analize slobodnog tržišta kapitala u Republici Srbĳi došlo se do rezultata da je najveću vrednost beta koeficĳenta ostvarila akcĳa emitenta Metals banka a.d. Novi Sad (β = 1,71, podešeni β koeficijent 1,50) što je znatno uvećala vrednost indeksa BELEX15. Drugo mesto po vrednosti beta koeficĳenta je pripalo akcĳi emitenta Komercĳalna banka a.d. Beograd (β = 1,20, podešeni β koeficijent 1,155). S druge strane najmanju vrednost beta koeficĳenta je ostvarila akcĳa emitenta Univerzal banka a.d Beograd (β = 0,54, podešeni β koeficijent 0,708) što je takođe uticalo na smanjenje vrednosti indeksa. Kada je u pitanju prosečni dnevni promet, najveću vrednost prosečnog dnevnog prometa za period: 1.1. - 30.6.2009. godine je ostvario emitent AIK banka a.d. Niš od 5,2 mil. dinara (55.701 EURA), što predstavlja 15,24% ostvarenja iz 2008. godine. Najmanju vrednost

prosečnog dnevnog prometa je ostvario emitent Metalac a.d. Gornji Milanovac, RSD 456.511 odnosno EUR. 4.870, što predstavlja 32,34% ostvarenja iz 2008. godine.

Problem koji se javlja na rastućim tržištima je izbor samog indeksa, jer veoma često njegovo

kretanje odražava kretanje cene dominantne akcĳe koja se uključuje u obračun indeksa, a ne kretanje tržišta. To je problem gotovo svih rastućih tržišta, mala su i relativno nelikvidna, uz izraženu potencĳalnu nestabilnost kojoj mogu doprineti strani investitori (rizik likvidnosti).

U svakom slučaju izračunavanje beta koeficĳenata nĳe imalo za cilj promovisanje investicionih alternativa, već promovisanje beta koncepta, koji može biti interesantan sastavni deo investicionog odlučivanja, kada se za to steknu potrebni uslovi, odnosno kada budu dostupne serĳe potrebnih podataka. I tada on neće biti presudni faktor donošenja odluka već samo deo procesa investiranja.

Zaključak

Prilikom analize vrednosti akcĳa navedenih emitenata, da se primetiti da postoji vremenski raskorak koji se ogleda u nelikvidnosti jednog ili pak više dana bez trgovanja, a što bi predstavljalo poteškoće u određivanju kratkoročnih i dugoročnih prinosa za akcĳe sa malom likvidnošću, broj ekstremnih događaja koji ne predstavljaju realni odnos ponude i potražnje akcĳa kao osnovnog postulata stvaranja cena, može biti prevelik te se vrlo teško mogu dati pouzdane ocene o kretanju prinosa.

Tabela br. 3.3: Praćenje vrednosti indeksa BELEX15 za period: 1.1.2009. - 30.6.2009. i proračun beta koeficĳenta za određene akcĳe


Simbol BELEX15 AIKB KMBN ENHL UNBN MTLC MTBN

Beta koeficĳent 1,00 1,03 1,20 0,96 0,54 0,78 1,71Podešeni beta koeficĳent 1,02 1,04 1,155 0,99 0,708 0,871 1,50

Prosečni dnevni promet u 2008. (mil RSD)

- 34.244.335 2.843.122 5.154.857 12.220.244 1.411.369 4.608.228

Prosečni dnevni promet za period: 1.1.2009. - 30.6.2009. (mil RSD)

- 5.220.481 2.177.808 2.189.752 1.496.157 456.511 520.424

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• Shares owned by international organizations and development institutions;

• Shares owned by the Republic of Serbia, excluding shares owned by the Shares Fund, and Pension and Invalid Insurance Fund.BELEX15 index is calculated according to

the Laspeyres’ formula:

(3.3)

where BELEX15(t) is the value of index of selected shares traded in the manner of continuous trading within time t, rounded to two decimal places; n - number of issuers whose shares are in the index basket - selected shares are unchangeable until the moment of revision; i -index taking the values ranging from 1 to 15, representing a certain issuer whose shares are in the index basket; C(i,t) - price of a share of the issuer i at time t, taken in real time from the trading system; K(i,t) - amount of shares of the issuer i at time t; d(t) - value of denominator at time t; FFc(i,t) - free float factor of the issuer i in time t; A(i) - adjusting factor of the issuer i.

Based on the analysis of one part of the capital market in the Republic of Serbia, more precisely, the free market, i.e. monitoring the fluctuations of BELEX15 stock exchange index structure and the most liquid shares for the period: 1.1 - 30.6.2009, we have come to the following results of the analysis.

Table 3.3 illustrates the fluctuations of value of the BELEX15 index and the shares of

its integral issuers. The analysis of the BELEX15 index structure includes the most liquid shares of the following issuers: 1) AIK Banka a.d. Niš (symbol: AIKB), 2) Komercĳalna banka a.d. Beograd (symbol: KMBN), 3) Energoprojekt holding a.d. Beograd (symbol: ENHL), 4) Univerzal banka a.d. Beograd (symbol: UNBN), 5) Metalac a.d. Gornji Milanovac (symbol: MTLC), and 6) Metals banka a.d. Novi Sad (symbol: MTBN). Based on the analysis of the free capital market in the Republic of Serbia we have come to the result that the largest value of beta coefficient was achieved by a share of the issuer Metals banks a.d. Novi Sad (β - 1.71, adjusted β coefficient - 1.50), which considerably increased the value of BELEX15 index. The second largest beta coefficient was that of a share issued by Komercĳalna banka a.d. Beograd (β - 1.20, adjusted β coefficient - 1.155). On the other hand, the lowest value of beta coefficient was achieved by a share issued by Univerzal banka a.d. Beograd (β - 0.54, adjusted β coefficient - 0.708), which also influenced the reduction in index value. When it comes to average daily turnover, the largest value of the average daily turnover for the period: 1.1 - 30.6.2009 was achieved by the issuer AIK banka a.d. Niš, in the amount of 5.2 million dinars (EUR 55,701), which equals 15.24% of the result in 2008. The lowest value of average daily turnover was achieved by the issuer Metalac a.d. Gornji Milanovac, amounting to RSD 456,511, i.e. EUR4,870, which equals 32.34% of the result in 2008.

The problem arising in the emerging markets is the selection of the index itself,

Table 3.3: Monitoring BELEX15 index values for the period: 1.1.2009 - 30.6.2009, and calculation of beta coefficients for certain shares


Symbol BELEX15 AIKB KMBN ENHL UNBN MTLC MTBN

Beta coefficient 1,00 1,03 1,20 0,96 0,54 0,78 1,71Adjusted beta coefficient 1,02 1,04 1,155 0,99 0,708 0,871 1,50

Average daily turnover in 2008 (mil. RSD)

- 34.244.335 2.843.122 5.154.857 12.220.244 1.411.369 4.608.228

Average daily turnover for the period: 1.1.2009 - 30.6.2009(mil RSD)

- 5.220.481 2.177.808 2.189.752 1.496.157 456.511 520.424

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Za određivanje očekivanih prinosa, poseban bi problem bio na tržištu kapitala BiH i Republike Srbĳe upotreba prosečne vrednosti istorĳskih prinosa, kao mere za očekivane prinose. Prinosi akcĳa kroz kraća vremenska razdoblja ne slede normalnu raspodelu, već raspodela prinosa ima zadebljane krajeve (engl. fat - tails), a što dalje znači da je povećana verovatnoća ekstremnih prinosa, negativnih ili pozitivnih.

Posmatrajući izračunate rezultate, i to pre svega beta koeficĳent i podešeni beta koeficĳent koji su objašnjeni kretanjima nezavisne varĳable (prinosom tržišta), vidljivo je da su na pojednim tržištima njihove vrednosti veoma niske, dok su na drugim iznad vrednosti 1, što navodi na pitanje svrsishodnosti samog izračunavanja i primenljivosti ovog koncepta. Međutim, upravo je uočavanje svih tih nelogičnosti ono što izračunavanje čini zanimljivim i daje doprinos finansĳskoj teorĳi i praksi na tržištima kapitala BiH i Republike Srbĳe. Ne može se očekivati promptna primena modela, koji je razvĳen na paradigmi američkog - razvĳenog tržišta kapitala, na tržištima kapitala u BiH i Republici Srbĳi koje još uvek obeležava nedovoljna razvĳenost, mala likvidnost i sve druge „dečĳe bolesti“ tranzicĳskih rastućih tržišta kapitala.

Stvaranje jedne regionalne berze (spajanje

Sarajevske, Banjalučke i Beogradske berze) dovelo bi do objedinjavanja berzi koje su na približno istom nivou razvoja. Osim toga regionalno približavanje je poželjno i zbog bliskosti mentaliteta i finansĳske kulture. Takvo ukrupnjavanje bi umanjilo problem lokalne nelikvidnosti tržišta i stvorilo jaču polaznu pozicĳu za pregovore oko ravnopravnĳe saradnje sa nekim većim berzama. Rešavanje i pitanja likvidnosti je izuzetno važno, jer je poznato da sva manja tržišta, i rastuća tržišta pate od nedovoljne likvidnosti. Prosto utapanje u veliku berzu dovelo bi jednostavno do gutanja male berze i marginalizacĳe tog tržišta. Ujedno dato spajanje bi pomoglo kreiranju jednog regionalnog indeksa koji bi pratio kretanje cĳena najlikvidnĳih akcĳa.

Mora se prihvatiti činjenica da je modeliranje ekonomske stvarnosti vrlo teško jer ekonomsku stvarnost čine ponavljanja koja nisu potrebno manifestaciono jednaka, koja sadrže element stohastičnosti , kao i da se stalno javljaju nove pojave i nova saznanja. U skladu sa datim, modeliranje vodi kontraverzama i stalnom preispitivanju koncepta. Beta koncept koji opstaje toliko dugo na teorĳskom - praktičnom planu i koji svaki put opravda poverenje zaslužuje potrebnu pažnju i u budućnosti, ali uz naglašeno uvažavanje njegovih ograničenja.

Literatura / References

1. Bernstein, R. (1995). „Style Investing“. New York: John Wiley&Sons, Inc Bernstein.

2. Bodie, Z. & Kane, A. & Marcus, A.J. (1996). „Investments“. Boston: Irwin.

3. Brigham, E. & Gapenski, L. & Ehrhardt, M. (1999). „Financial Management - Theory and Practice“. Fort Worth: Dryden press.

4. Erić, D. (2003). „Finansĳska tržišta i instrumenti“, Čigoja štampa, Beograd.

5. Foley, B. J. (1991). „Tržište kapitala“, Zagreb, Mate d.o.o.

6. Mastnak, S. (2004). „Izazovi izračunavanja indeksa na tržištima kapitala u razvoju“, Beograd, Međunarodna konferencĳa Beogradske berze, novembar, 2004.

7. Muminović, S. (2001). „Kontraverze CAPM - a i koncepta beta“. Beograd: Jugoslovensko bankarstvo 5 - 6.

8. Alihodžić, A. (2008). „Upravljanje prinosom i rizikom na tržištu kapitala Federacĳe Bosne i Hercegovine sa asvrtom na tržište kapitala Srbĳe i Hrvatske.“ Sarajevo: FEB časopis, br. 9.

9. Web stranica berze u Beogradu: www.belex.rs

10. Web stranica berze u Sarajevu: www.sase.ba

11. Web stranica berze u Banja Luci: www.blberza.com

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since very o�en its fluctuations reflect the trends of the price of the dominant share incorporated into the index calculation, and not the market trends. This is the problem in all emerging markets; they are small and relative illiquid, with a prominent potential instability which may be increased by foreign investors (illiquidity risk).

In any case, calculation of beta coefficient was not aimed at promoting investment alternatives, but promoting of beta concept, which may be interested integral part of investment-related decision-making, when the necessary preconditions are met, i.e. when the required datasets are available. However, even then, it will not be a decisive factor in decision-making, but only a part of the investment process.

Conclusion

Concerning the analysis of the mentioned issuers’ shares values, it may be observed that there is time discrepancy, reflected in the illiquidity of one or more days without trading, which would cause difficulties in determining short-term and long-term returns for low-liquidity shares - the number of extreme events which do not represent the real relation of supply and demand of shares as the basic pricing postulate may be too large, hence it may be very difficult to provide reliable assessments of returns trends. In respect of determining expected returns, what might be a problem in the capital market of Bosnia and Herzegovina and the Republic of Serbia is the use of average value of historic returns, as a measure of expected returns. Shares’ returns in short time spans are not normally distributed - distribution of returns has fat tails, meaning that the probability of extreme returns, both negative and positive is increased.

Examining the calculated results, first and foremost beta coefficient and adjusted beta coefficient, explained on the fluctuations of an independent variable (market return), one may notice that their values are very low in certain markets, whereas in the other markets their values are above 1, which raises the issue of purposefulness of the calculation and applicability of this concept in the first place.

However, it is this noticing of all illogicalities that makes the calculation interesting and contributes to the financial theory and practice in the capital markets in Bosnia and Herzegovina and the Republic of Serbia. It cannot be expected that a model developed on the paradigm of the American, i.e. developed capital market, should be promptly implemented in the capital markets in Bosnia and Herzegovina and the Republic of Serbia, still characterized by insufficient development, low liquidity, and all other “teething problems” of the transitional, emerging capital markets.

Creation of a single regional stock exchange (by merging Sarajevo, Banjaluka and Belgrade Stock Exchanges) would result in merging stock exchanges which are at the approximately same development level. Furthermore, regional integration is also desirable due to the similar mentality and financial culture. Such a consolidation would reduce the problem of local market illiquidity and create a stronger starting position for negotiations regarding the more equal cooperation with some larger stock exchanges. It is extremely important to solve the liquidity issue, too, since it is well known that all smaller markets, and emerging markets, suffer from insufficient liquidity. Mere merging into a huge stock exchange would simply result in the small stock exchange being swallowed, in turn causing marginalization of the concerned market. At the same time, the given merger would help create a single regional index which would monitor the fluctuations of prices of the most liquid shares.

One must accept the fact that the modeling of economic reality is extremely difficult, because economic reality consists of repetitions whose manifestations are not as equal as necessary, containing a stochastic element, and because new phenomena and new findings keep occurring. Consequently, modeling leads towards controversies and constant re-examining of the concept. Beta concept, which has persisted for so long both in the theoretical and practical fields, and which has proved worthy of confidence each time, deserves special a�ention in the future, yet with a strong emphasis on the acknowledgement of its limitations.

proračun beta koeficĳenata za akcĳe koje se kotiraju na sarajevskoj

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