SLABA EFIKASNOST TRŽIŠTA KAPITALA

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1 stručni prilozi UDK : (497.6) Dr Dragan S. Jović Centralna banka Bosne i Hercegovine, Glavna banka Republike Srpske djovic@bl.cbbh.ba SLABA EFIKASNOST TRŽIŠTA KAPITALA Rezime Rad ne daje jedinstven odgovor na pitanje da li tržište akcija u Republici Srpskoj funkcioniše na nivou slabe efikasnosti tržišta. Odabrane metode potvrđuju, ali i negiraju hipotezu o slaboj efikasnosti tržišta. Testovi znakova i autokorelacije su u saglasnosti sa slabom efikasnosti tržišta. Za razliku od ovih testova rezultati dobijeni primjenom pravila korijena vremena istupaju kao suprotnost u odnosu na ovu hipotezu. Isto važi, u različitoj mjeri, i za neke od odabranih instrumenata tehničke analize. Sposobnost predviđanja promjene trenda cjene ispoljavaju indeks relativne moći (RSI) i stopa promjene cjene (ROC), a u manjoj mjeri i momentum (MOM). Sposobnost intrumenata tehničke analize da predvide promijenu trenda jednaka je odbacivanju hipoteze o slaboj efikasnosti tržišta. Od odabranih indikatora najslabije prediktivne sposobnosti ispoljava indeks novčanog toka (MFI). Stav pojedinih metoda u odnosu na hipotezu o slaboj efikasnosti tržišta je u potpunoj i očiglednoj suprotnosti. Ključne reči: hipoteza o slaboj efikasnosti tržišta (HSET), tržište akcija, Republika Srpska, volatilnost, autokorelacija, tehnička analiza bankarstvo 5 -

2 UDC : (497.6) expert contributions WEAK-FORM EFFICIENCY OF THE STOCK MARKET Dragan S. Jović PhD Central bank of Bosnia and Herzegovina, Glavna banka of the Republic of Srpska Summary The paper, does not provide a homogeneous answer to the question of whether the stock market in Republic of Srpska operates as a weak-form EMH. The selected methods confirm, but also disprove the weak-form EMH. Sign tests and autocorrelation tests are in accordance with week-form EMH. In contrast to these tests, the results obtained from square root of time rule challenge such hypothesis. The same is true, to a different extent, for some selected instruments of technical analysis. The relative strength index (RSI), the prices rate of change (ROC), and to some extent the momentum (MOM) express the ability to predict the changes in the price trend. The capability of the technical analysis instruments to predict the trend s changes is equal to rejecting the weaк-form EMH. Out of the selected indicators, money flow index (MFI) demonstrates the weakest ability of prediction, that is, the lowest ability to confirm the hypothesis. The position of particular methods, with regard to the weak-form EMH, is in complete and obvious opposition. bankarstvo 5 - Key words: weak-form efficiency market hypothesis (weak-form EMH), stock market, Republic of Srpska

3 Jedan od predmeta istraživanja finansijske ekonomije je stepen informacione efikasnosti finansijskog tržišta. Efikasnost tržišta se utvrđuje u odnosu na jedan od tri skupa informacija: informacije o prošlim cjenama i volumenima, sve javno dostupne informacije, sve privatne i javno dostupne informacije. Informaciona efikasnost tržišta se u svom osnovnom obliku svodi na hipotezu o slaboj efikasnosti tržišta (u daljem tekstu HSET). Tržište funkcioniše na nivou slabe efikasnosti ukoliko se na osnovu informacija o prethodnim cijenama i volumenima aktive ne mogu predvidjeti buduće cjene. HSET je analogna stavu da se pomoću studiranja cijena i volumena, upotrebom instrumentarija tehničke analize, ne mogu na konzistentan i predvidljiv način realizovati nadprosiječni prinosi. Hipoteza negira korisnost alata tehničke analize u predviđanju budućih cijena, a samim tim i indirektno postojanje bilo kakve korelacije, pozitivne ili negativne, između serija cijena finansijske aktive. Rad istražuje odnos tržišta akcija u Republici Srpskoj prema teorijskoj postavci o slaboj efikasnosti tržišta. Cilj rada je odgovor na pitanje da li tržište akcija u Republici Srpskoj funkcioniše na nivou slabe efikasnosti. Rad se zasniva na hipotezi da je domaće tržište akcija efikasno u odnosu na informacije o prošlim cjenama. Hipoteza polazi od empirijskih dokaza da većina tržišta funkcioniše na nivou polujake efikasnosti tržišta. 1 Hipoteza rada afirmiše pretpostavku o slaboj efikasnosti tržišta i odbacuje tehničku analizu kao koristan instrument u donošenju investicionih odluka. Proces dokazivanja hipoteze se odvija na uzorku kretanja cijena akcija i vrjednosti berzanskih indeksa 2 na domaćem tržištu akcija (Banjalučka berza AD Banjaluka - BLSE) u periodu od početka razvoja tržišta do godine. Materijal i metode Za ispitivanje HSET upotrebljeno je nekoliko metoda i testova: komparativna metoda, metoda vremenskog agregiranja - pravilo korjena vremena (square root of time rule), statistička metoda - prosta linearna regresija, test autokorelacije, test znakova i metoda tehničke analize. Način upotrebe komparativne metode i metode vremenskog agregiranja najlakše je objasniti ako se pođe od određenih, karakterističnih vrsta vremenskih serija cjena akcija. Grafikon 1. Osnovni modeli kretanja cjena akcija a) Povrat ka sredini b) Slučajni hod c) Trend Prvi karakterističan oblik kretanja cijena akcija predstavljen je kao povrat ka sredini (mean reversion). Pretpostavka modela je da cijena akcije ukoliko se posmatra u nekom dovoljno dugom vremenskom periodu teži ka srednjoj vrjednosti. Cjena akcije se uvijek vraća ili približava referentnoj vrjednosti. Posljedica opisanog ponašanja cijene je ujednačenost 1 Vasiljević, Branko Osnovi finansijskog tržišta, IP Princip, Beograd. 2 BIRS-Berzanski indeks Republike Srpske, ERS-Indeks preduzeća Elektroprivrede Republike Srpske, FIRS-Indeks investicionih fondova Republike Srpske. bankarstvo 5 -

4 bankarstvo 5 - One of the research subjects of financial economy is the level of financial market information efficiency. Market efficiency is determined in relation to one of the three groups of information: information on past prices and volumes, all publicly available information, and all privately and publicly available information. The information efficiency of the market is, in its basic form, reduced to the weak-form efficiency market hypothesis (herea er to be referred to as weakform EMH). The market functions at the level of weak efficiency if the future prices cannot be predicted on the basis of information on past prices and asset volumes. The weak-form EMH is analogous to the opinion that the above-average returns cannot be realized in a consistent and predictable manner, by means of price and volume examination using the technical analysis instruments. The hypothesis denies the usefulness of technical analysis tools in the prediction of future prices, and, thus, indirectly, the existence of any correlation, either positive or negative, among the series of financial assets prices. The paper examines the relation of the stock market in the Republic of Srpska towards the theoretical weak-form market hypothesis. The objective of the paper is to provide the answer to the question of whether the stock market in the Republic of Srpska functions at the level of weak efficiency. The paper is based on the hypothesis that the domestic stock market is efficient in terms of information on past prices. The hypothesis starts from the empirical evidence that most markets function at the level of semi-strong market efficiency. 1 The hypothesis of the paper promotes the assumption about the weak-form efficiency market and rejects technical analysis as a useful instrument in investment decision-making. The hypothesis validation process is conducted on a sample of stock prices trends and stock exchange indices values 2 at the domestic stock market (Banjalucka berza a.d. Banjaluka - Banjaluka Stock Exchange/BLSE) from the beginning of the market development until Materials and methods Several methods and tests were used for the examination of the weak-form EMH, including the following: comparative method, time aggregation method - square root of time rule, statistical method - simple linear regression, autocorrelation test, sign test and technical analysis method. The easiest way to explain the application of comparative method and time aggregation method is by starting from certain, characteristic types of time series of stock prices. Graph 1. Basic models of stock prices trends a) Mean reversion b) Random walk c) Trend The first characteristic type of stock price movements is represented as mean reversion. The assumption of the model is that, if monitored for a sufficiently long time period, the stock price gravitates toward mean values. The stock price always returns to or leans to the 1 Vasiljevic, Branko (1999), Osnovi finansijskog trzista, IP Princip, Beograd 2 BIRS - Stock Exchange Index of the Republic of Srpska, ERS - Index of the Power Utility of the Republic of Srpska, FIRS - Index of Investment Funds of the Republic of Srpska

5 standardnih devijacija (volatilnosti) za različite vremenske periode. Ukoliko se dnevna, mjesečna, kvartalna i godišnja volatilnost prinosa značajno razlikuju serija cjena ne odgovara modelu povrata ka sredini. Kod slučajnog hoda (grafikon 1 pod b) izuzetno visoka i kontinuirana varijacija cijena stvara značajnu razliku između volatilnosti različitih vremenskih perioda. Volatilnosti prinosa na dnevnom, mjesečnom, kvartalnom i godišnjem nivou nisu ni približno jednake. Volatilnost se isto ponaša, pokazuje značajne vremenske varijacije, i kod kretanja cijena u obliku trenda. Trendni model kretanja cijena je negacija slabe efikasnosti tržišta i uslov za efikasnu i produktivnu primjenu tehničke analize u predviđanju kretanja cjena. Osnovna razlika između kretanja cjena po modelu trenda i kretanja cjena po modelu slučajnog hoda je u tome što se u drugom slučaju može uspostaviti direktna algebarska veza između volatilnosti različitih vremenskih perioda. 3 Vremensko agregiranje (time agregation) prinosa i volatilnosti omogućava formulisanje odnosa između standardnih devijacija u obliku pravila korjena vremena. Formula 1. Pravilo korjena vremena 4 gdje su: -standardna devijacija za neki duži vremenski period, - standardna devijacija za neki kraći vremenski period, T - faktor konverzije, odnosno broj perioda tokom vremenskog horizonta u frakcijama godine (za kvartalne podatke 4, za mjesečne 12, za dnevne 252). Izvor podataka: Crouhy, Michel, Galai, Dan, Mark, Robert Risk management, McGraw- Hill, New York-Toronto. p Zbog različite dužine vremenskih serija cijena, koje na godišnjem nivou u prosjeku nemaju 252 dana, u radu koristimo drugačije faktore konverzije. Ako se volatilnosti različitih vremenskih perioda razlikuju, tj. ako nije moguće uspostaviti približnu jednakost stvarnih/ empirijskih i teorijskih, na pravilu korjena vremena zasnovanih volatilnosti, onda se cijene akcija kreću po modelu trenda, što predstavlja indirektan način za odbacivanje HSET. U slučaju da se cjene kreću po modelu trenda odbacujemo hipotezu o informacionoj efikasnosti tržišta u odnosu na set podataka o prošlim prinosima/cjenama. Testovi autokorelacije ispituju jačinu linearne veze između tekuće promijene i prethodnih promijena cijena/prinosa. Prost linearni regresioni model, koji inkorporira dnevni prinos akcije, predstavljen je u obliku donje fomule. Formula 2. Testovi autokorelacije - promijena prinosa akcije gdje su: α - slobodni član regresionog modela, β - nagib funkcije (pokazuje za koliko će se promijeniti tekući prinos akcije ako se predhodni prinos promijeni za 1%), p t - tekuća cijena, p t-1 - predhodna cijena, ε - slučajno odstupanje, T - vremenski interval između sadašnje i predhodne cijene (ako je nula onda se porede dvije sukcesivne cijene). Izvor podataka: Popović, M. Saša Portfolio analiza. Čigoja štampa, Beograd. s h p:// 4 Više o načinu izvođenja formule vidjeti u Crouhy, Michel, Galai, Dan, Mark, Robert Risk management, McGraw - Hill, New York-Toronto. p Tabela 1. Faktori konverzije Za DEP* BIRS ERS FIRS Za KEP** Za DEP Za KEP Za DEP Za KEP Izvor podataka: (obradio autor). * DEP - dnevni empirijski podaci. ** KEP - kvartalni empirijski podaci. bankarstvo 5 -

6 benchmark value. The result of the described price behaviour is the equalization of standard deviations (volatilities) for different time periods. If daily, monthly, quarterly and annual volatilities of return vary significantly, the price series does not respond to the mean reversion model. In the random walk model (graph 1b)), the extremely high and continuous variation of prices creates a significant difference between the volatilities in different time periods. Return volatilities on a daily, monthly, quarterly and annual level differ greatly. Volatility behaves in the same way, showing considerable time variations, when it comes to the price movements forming a trend, too. The trend model of price movements is the negation of the weak-form market efficiency and a precondition for the efficient and productive implementation of technical analysis in price movements prediction. The major difference between the trend model of price movements and random walk price movements is that in the la er case a direct algebraic connection can be established between the volatility of different time periods. 3 Time aggregation of returns and volatilities enables the formulation of relations between standard deviation in the form of the square root of time rule. do not contain 252 days, we shall use different conversion factors in this paper. Table 1. Conversion factors For DED* BIRS ERS FIRS For QED** For DED For QED For DED For QED Source of data: (processed by the author) * DED - Daily empirical data ** QED - Quarterly empirical data If the volatilities in various time periods differ, i.e. if it is impossible to establish an approximate equality of the actual/empirical and theoretical volatilities based on the square root of time rule, then the stock prices follow the trend model, which is an indirect method for rejecting the weak-form EMH. If the prices follow the trend model, we reject the hypothesis about the information efficiency of the market in relation to the data set on past returns/prices. Autocorrelation tests examine the strength of the linear relation between the current change and the past changes in prices/returns. Simple linear regression model, which incorporates the daily stock return, is represented by the formula below. Formula 1. Square root of time rule 4 Formula 2. Autocorrelation tests - stock return change bankarstvo 5 - with: σ T - standard deviation for a long time period, σ t - standard deviation for a short time period, T - conversion factor, i.e. the number of periods during the time horizon in the fractions of a year (for quarterly data 4, for monthly data 12, for daily data 252). Source of data: Crouchy, Michel., Galai, Dan., Mark, Robert (2001), Risk Management, McGraw - Hill, New York - Toronto, p. 411 Due to different lengths of time series of prices, which, at the annual level, on average, with: α - free member of the regression model, β - slope of the function (indicating the amount by which the current stock return will change if the previous return changes by 1%), p t - current price, p t-1 - previous price, ε - random deviation, T - time interval between the current and previous price (if it equals zero, two successive prices are being compared). Source of data: Popovic, M. Sasa (2000), Portfolio analiza, Cigoja stampa, Beograd, p h p:// 4 More on how to use this formula in Crouchy, Michel, Galai, Dan, Mark, Robert (2001), Risk Management, McGraw - Hill, New York - Toronto, p

7 HSET prihvatamo ako ne postoji korelacija između sadašnjih i prošlih cijena/prinosa akcije. U tom slučaju koeficjent determinacije je nizak, 5 a regresioni model neupotrebljiv. Između tekućih i predhodnih prinosa ne postoji jaka linearna veza. U prostoj linearnoj regresiji se testira i hipoteza o vrjednosti koeficjenta nagiba. Nulta hipoteza je definisana kao H 0 : β=0, a alternativna hipoteza kao H 1 : β=0. Test je dvosmjeran, oblast odbacivanja nulte hipoteze se nalazi na krajevima rasporeda. Statistika testa ima Studentov raspored sa n-2 stepena slobode. 6 Ako se odbaci nulta hipoteza i prihvati alternativna hipoteza,, onda između varijabli postoji bar slaba linearna veza. 7 Međutim to ne znači automatsko odbacivanje HSET - validnost modela zavisi od vrjednosti koeficjenta determinacije. Test znakova se koristi da bi se izbijegao uticaj ekstremnih vrjednosti promijena cjena/ prinosa na reprezentativnost regresionog modela. U testu znakova intenzitet promijene cijene nije bitan. Dnevni smjer promjene cjene je označen kao rast (+), pad (-) ili stagnacija (0). Tok je ponavljanje iste promijene, znaka, (+ ili -) u dva sukcesivna intervala. Ponavljanje perioda stagnacije cijena ne predstavlja tok. Česte promjene smjera kretanja cjena i veliki broj tokova su indicija slabe efikasnosti tržišta. Metodološka osnova testa znakova predstavljena je kroz formule koje sljede. Formula 3. Aritmetička sredina Formula 4. Standardna devijacija Izvor podataka: Popović, M. Saša Portfolio analiza. Čigoja štampa, Beograd. str. 50. gdje su; n 2 - ukupan broj negativnih opservacija, n 1 - ukupan broj pozitivnih opservacija. z - vrjednost statistike testa za standardizovan normalan raspored, µ - aritmetička sredina, R- broj tokova, N=n 1+ n 2 - ukupan broj opservacija. Testiranje se sprovodi dvosmijernim testom. Nulta hipoteza (H 0 ) označava postojanje serijske korelacije, što je ekvivalentno negaciji HSET. Alternativna hipoteza (H 1 ) je da između promijena cijena ne postoji međuzavisnost. Na nivou povjerenja od 5%, interval prihvatanja nulte hipoteze obuhvata sve vrjednosti z statistike od - 1,96 do 1,96. Poslednja skupina metodologija, upotrebljena u radu, mali isječak iz instrumentarija tehničke analize, predstavljena je u formi tehničkih pokazatelja: a) impulsa/ momentuma (MOM) b) stope promijene (Rate of change - ROC) c) indeksa novčanog toka (money flow index - MFI) d) indeksa relativne moći (relative strength index - RSI). Tehnički pokazatelji prate tržišne trendove i cikluse cjena i volumena. Ukoliko tehnički pokazatelji mogu anticipirati kretanje cjene, to je dokaz prediktivnih svojstava tehničke analize i antiteza slaboj efikasnosti tržišta. Indeks novčanog toka - MFI, mjeri intenzitet novca koji zauzima dugu/kratku poziciju, odnosno koji ulazi ili izlazi iz akcije. Prije izračunavanja MFI određuje se: tipična cjena (typical price), novčani tok (money flow), racio novca (money ratio). Ako je današnja tipična cjena veća od jučerašnje tipične cjene novčani tok je pozitivan. Novčani racio je količnik između sume pozitivnih i negativnih novčanih tokova. Na osnovu njega se određuje indeks novčanog toka. Formula 5. Z statistika 5 Više o prostoj linearnoj regresiji i korelaciji vidjeti u Žižić M., Lovrić, M. Pavličić D Metodi statističke analize, Ekonomski fakultet, Beograd Ibid. str Ibid. bankarstvo 5 -

8 We accept the weak-form EMH if there is no correlation between the present and past stock prices/returns. In that case, the determination coefficient is low, 5 and the regression model unusable. There is no strong linear relation between the current and past returns. In simple linear regression we also test the hypothesis about the slope coefficient value. Zero hypothesis is defined as H 0 : β = 0, and alternative hypothesis as H 1 : β 0. The test is two-way, and the field of zero hypothesis rejection is at the distribution ends. The test s statistics shows Student s distribution with n-2 degree of freedom. 6 If we reject the zero hypothesis and accept the alternative hypothesis, β 0, then there is at least a weak linear relation between the variables. 7 However, this does not imply an automatic rejection of the weak-form EMH - the model s validity depends on the determination coefficient value. The sign test is used in order to avoid the influence of extreme values of price/returns changes on the representative quality of the regression model. The intensity of price changes is irrelevant in sign tests. The daily price change trend is marked as growth (+), decline (-) or stagnation (0). The flow marks the repetition of the same change, sign (+ or -) in two successive intervals. The repetition of the price stagnation periods is not considered to be a flow. Frequent changes in price trends and a large number of flows indicate the weak market efficiency. The methodological basis of the sign test is represented by the following formulas. Formula 3. Arithmetic mean Formula 4. Standard deviation Source of data: Popovic, M. Sasa (2000), Portfolio analiza, Cigoja stampa, Beograd, p. 50 with: n 2 - total number of negative observations, n 2 - total number of positive observations. z - statistical value of the test for standardized normal distribution, µ - arithmetic mean, R - number of flows, N = n 1 + n 2 - total number of observations. The testing is conducted by means of a two-way test. Zero hypothesis (H 0 ) marks the existence of a serial correlation, which is equivalent to the negation of the weak-form EMH. Alternative hypothesis (H 1 ) implies that there is no inter-dependence between the price changes. At the 5% confidence level, the zero hypothesis acceptance interval includes all values of z statistics in the range from to The last group of methodologies used in the paper, a small section of technical analysis instruments, is represented in the form of technical indicators: a) impulse/momentum (MOM), b) rate of change (ROC), c) money flow index (MFI), and d) relative strength index (RSI). These technical indicators monitor market trends as well as price and volume cycles. If technical indicators may anticipate price trends, it is a proof of the predictive power of the technical analysis and an anti-thesis of the weak-form market efficiency. Money flow index - MFI measures the intensity of money on the long/short position, i.e. money entering or exiting the stock. Before calculating MFI we determine the following: typical price, money flow and money ratio. If today s typical price is higher than yesterday s typical price, money flow is positive. Money ratio is a proportion between the sum of positive and negative money flows. Based on this ratio, we determine the money flow index. Formula 5. Z statistics bankarstvo 5-5 More on simple linear regression and correlation in Zizic M., Lovric M., Pavlicic D. (1992), Metodi statisticke analize, Ekonomski fakultet, Beograd, p Ibid., p Ibid.

9 Tabela 2. Indeks novčanog toka Formula 6. Tipična cjena Formula 7. Novčani tok - MF Formula 8. Novčani racio Indeks novčanog toka se interpretira na dva načina; preko divergencije trenda indeksa i trenda cjene i kroz vrjednost samog indeksa. Različito kretanje trenda indeksa i trenda cjene je nagovještaj preokreta u trendu cjene. MFI iznad 80 signalizira vrhunac tržišta i početak silaznog trenda. Tržište dostiže dno za vrjednost MFI od oko 20. Vrjednost indeksa relativne moći (RSI) kao i vrjednost MFI se kreće u intervalu od 0 do 100, s tom razlikom da RSI prati kretanje cjena, a ne volumena. Kritične vrjednosti indeksa su 70 i 30. One označavaju najvišu i najnižu tačku tržišta. RSI dostiže kritične vrjednosti prije preokreta cjene akcije. Po ovoj osobini RSI se svrstava u grupu vodećih indikatora. Formula 9. Indeks relativne snage gdje je: U - prosjek cjena koje su bile veće od prethodne cjene, a D - prosjek cjena koje su bile niže od predhodne cjene. Koncept impulsa ili momentuma (MOM) je preuzet iz prirodnih nauka - fizike i uvršten u alate tehničke analize. MOM mjeri da li se kretanje cjena akcija ubrzava ili usporava. Impuls je vodeći indikator - daje signal za kupovinu/prodaju prije nego što dođe do promjene trenda. Impuls je u analizi trenda cjena akcije predstavljen kao razlika između prve i zadnje cjene u određenom vremenskom gdje su TP, HP, LP, CP - tipična, najviša, najniža i zatvarajuća cjena respektivno gdje su MR, PMF i NMF, novčani racio, pozitivni novčani tok i negativni novčani tok respektivno gdje su MR, PMF i NMF, novčani racio, pozitivni novčani tok i negativni novčani tok respektivno Izvor podataka: Steven B. Achelis Technical Analysis from A to Z, McGraw-Hill. horizontu; petodnevni momentum - razlika između šeste i prve cjene, jedanaestodnevni momentum - razlika između dvanaeste i prve cjene itd. Stopa promjene cjene (Rate of change- ROC) mjeri intenzitet promjene cjene tokom vremena. Indikator stopa promjene cjene je nastao na konceptu impulsa, s tom razlikom da ne mjeri apsolutnu, već relativnu/procentualnu promjenu cjene. ROC raste kada cjena akcije raste, a opada kada cjena akcije pada. Što je ROC veći i njegov rast duži, veća je i vjerovatnoća pada cjene. Visok ROC je indicija da je akcija previše kupljena (overbought), dok nizak ROC upućuje na previše prodatu (oversold) akciju. Prognoza kretanja cjene se zasniva na analizi prethodnih vrjednosti ROC i na njihovoj komparaciji sa aktuelnim vrjednostima ROC. Informacioni osnov analize su kretanja cijena akcija i indeksa na Banjalučkoj berzi AD Banjaluka (BLSE). Vremenski horizont analize se završava sa polovinom godine. Rezultati i diskusija Pretpostavka o slaboj efikasnosti tržišta testirana je komparativnom metodom i pravilom korjena vremena (tabela 3). Empirijske volatilnosti prinosa, dnevna, mjesečna i kvartalna 1,33%, 10,41% i 23,87% respektivno nisu ni približno jednake. Serija prinosa na domaćem tržištu interpretirana kroz kretanje vodećeg berzanskog indeksa, BIRS-a, ne ispoljava karakteristike kretanja ka sredini (mean reversion). Teorijske i empirijske volatilnosti za iste periode vremena nisu ni približno jednake. Mjesečne teorijske volatilnosti su i a empirijska 10,41%. Isti odnos se formira i između dnevne empirijske i teorijske volatilosti bankarstvo 5 -

10 bankarstvo 5 - Table 2. Money flow index Formula 6. Typical price Formula 7. Money flow Formula 8. Money ration Money flow index is interpreted in two ways: by means of divergence between index trend and price trend, and on the basis of the index value itself. Different movements of the index trend and price trend indicate a break in price trends. MFI above 80 signalizes the market peak and the commencement of the downward trend. The market reaches the bo om for MFI values of around 20. Relative strength index - RSI value, just like MFI value, ranges between 0 and 100, the only difference being that RSI follows the price movements, instead of volume movements. Critical index values are 70 and 30. They mark the highest and the lowest market point. RSI reaches the critical values prior to the break in stock prices. Due to this feature, RSI is categorized as one of the leading indicators. Formula 9. Relative strength index with: TP, HP, LP, CP - standing for typical, highest, lowest and closing price, respectively with: U - average of the prices higher than the previous price, and D - average of the prices lower than the previous price. The concept of impulse or momentum (MOM) was taken from natural sciences - physics and included in the technical analysis tools. MOM measures whether the stock price movements are accelerating or slowing down. The impulse is the leading indicator - it gives with: MF and V standing for money flow and volume of turnover, respectively with: MR, PMF and NMF standing for money ratio, positive money flow and negative money flow, respectively Source of data: Steven B. Achelis (2001), Technical Analysis from A to Z, McGraw - Hill the signal for purchase/sale before the break in trend occurs. In the stock price trends analysis, the impulse is represented as a difference between the first and last price in a certain time horizon; five-day momentum - the difference between the sixth and the first price, eleven-day momentum - the difference between the eleventh and the first price, etc. Rate of change - ROC measures the intensity of price changes over time. Rate of change indicator was created on the basis of impulse concept, the only difference being that it does not measure the absolute, but relative/percentage price change. ROC increases as the stock price increases, and decreases as the stock price decreases. The higher ROC and the longer its increase, the higher the probability of stock price decrease. High ROC indicates that the stock is overbought, whereas low ROC indicates that the stock is oversold. The forecast of stock prices is based on the analysis of the previous ROC values and their comparison with the current ROC values. Information basis of the analysis are the movements of stock prices and indices at the Banjalucka berza a.d. Banjaluka (Banjaluka Stock Exchange - BLSE). Time horizon of the analysis ends with the first half of Results and discussion The assumption about the weak-form market efficiency was tested by means of comparative method and square root of time rule (Table 3). Empirical volatilities of returns - daily, monthly and quarterly in the amounts of 1.33%, 10.41% and 23.87% respectively - differ greatly. The series of returns in the domestic market, interpreted through the trends of the leading stock exchange index - BIRS, does not express the characteristics of mean reversion. Theoretical and empirical volatilities for the same time periods also differ greatly. Monthly theoretical volatilities amount to: and

11 1,33 % i 3,1% ( 23,87/(232/4)) respektivno, kao i između kvartalne empirijske i teorijske volatilnosti 23,87% i 10,2%(1,33/(232/4)) respektivno. Na osnovu razlike između stvarne i volatilnosti dobijene pravilom korjena vremena zaključujemo da kretanje vrjednosti BIRS-a odstupa od kretanja po modelu slučajnog hoda. Hipoteza o kretanju BIRS-a po modelu trenda dokazana je dokazivanjem antiteze; da se vrjednosti BIRS-a ne kreću ni po modelu kretanja ka sredini niti po modelu slučajnog hoda. Ako se BIRS kreće po modelu trenda onda alati tehničke analize omogućavaju direktnu identifikaciju faze u kojoj se trend nalazi, a indirektno i prognozu kretanja vrjednosti indeksa/cijene akcije. Opisani proces je kompatibilan sa negacijom HSET. Tabela 3. Empirijske i teorijske volatilnosti, BIRS * Vremenski period Empirijska volatilnost (u %) Teorijska volatilnost (u %) Na bazi dnevne volatilnosti Na bazi kvartalne volatilnosti Dan 1,33-3,1 Mjesec 10,41 5,9 13,8 Kvartal 23,87 10,2 - Izvor podataka: Ibid. * Prosječan godišnji broj dana trgovanja je 234,2. zbog razlike između empirijskih i teorijskih volatilnosti (tabela 4 i tabela 5). 8 Tabela 4. Empirijske i teorijske volatilnosti, ERS g.* Vremenski period Empirijska volatilnost (u %) Teorijska volatilnost (u %) Na bazi dnevne volatilnosti Na bazi kvartalne volatilnosti Dan 1,93-4,4 Mjesec 15,42 8,7 19,7 Kvartal 34,09 15,0 - Izvor podataka: Ibid. * Prosječan godišnji broj dana trgovanja je 240 Tabela 5. Empirijske i teorijske volatilnosti, FIRS * Vremenski period Empirijska volatilnost (u %) Teorijska volatilnost (u %) Na bazi dnevne volatilnosti Na bazi kvartalne volatilnosti Dan 1,890-4,9 Mjesec 17,44 8,4 21,6 Kvartal 37,34 14,5 - Izvor podataka: Ibid. * Prosječan godišnji broj dana trgovanja je 235,8. Istovjetan zaključak, odbacivanje HSET daje i analiza kretanja vrjednosti ostala dva berzanska indeksa, ERS-a i FIRS-a. Empirijske volatilnosti u različitim vremenskim periodima se značajno razlikuju. Dnevna, mjesečna i kvartalna volatilnost ERS-a su 1,93%, 15,42% i 34,1% respektivno. I stvarne volatilnosti indeksa fondova se razlikuju. Za FIRS dnevna, mjesečna i kvartalna volatilnost su 1,89%, 17,44% i 37,34% respektivno. Kod oba indeksa razlika u odnosu na model kretanja prema sredini, mjereno diskrepancom između volatilnosti različitih vremenskih perioda, je nedvosmislena. Kretanje cjena po modelu slučajnog hoda odbacujemo Rezultati testova autokorelacije nisu u saglasnosti sa prethodnim rezultatima. Niska vrjednost koeficjenata determinacije potvrđuje HSET. Mada vrjednost t statistike koeficjenata nagiba pokazuje da postoji linearna veza, 9 ona je vrlo slaba (dijagram raspršenosti - grafikon 2). 10 Visoka p vrjednost ocjene slobodnog člana (od 0,98 do 0,45) konzistentna je sa ovim zaključkom. 8 Teorijske volatilnosti ERS-a i FIRS-a su izračunate na isti način kao i za BIRS. Razlika je samo u prosiječnom godišnjem broju dana trgovanja u analiziranom periodu. 9 P vrjednosti ocjene koeficjenta nagiba, u svim regresionim modelima, osim u jednom (tabela 6, model br. 4) je izuzetno niska. 10 Gotovo identičan dijagram raspršenosti, nekonzistentan sa jakom linearnom vezom, imaju i ostali regresioni modeli. bankarstvo 5 -

12 whereas the empirical volatility amounts to 10.41%. The same relation is formed between daily empirical and theoretical volatilities of 1.33% and 3.1% (23.87/(232/4)) respectively, just like between quarterly empirical and theoretical volatilities of 23.87% and 10.2% (1.33/(232/4)) respectively. Based on the difference between the real volatility and the volatility calculated by means of the square root of time rule, we may conclude that the movements of BIRS values deviate from the movements according to the random walk model. The hypothesis about BIRS movements according to the trend model is proven by means of proving the anti-thesis - BIRS values follow neither mean reversion model nor random walk model. If BIRS follows the trend model, technical analysis tools enable direct identification of the stage in which the trend is at the moment, and indirectly, the forecast of the movements of stock index/price values. The described process is compatible with the negation of the weak-form EMH. quarterly volatilities of ERS are as follows: 1.93%, 15.42% and 34.1% respectively. Real volatilities of the funds indices differ, too. For FIRS, daily, monthly and quarterly volatilities amount to 1.89%, 17.44% and 37.34% respectively. In case of both indices, the difference according to the mean reversion model, measured on the basis of the discrepancy between the volatility in different time periods, is unambiguous. Price movements according to the random walk model are rejected due to the difference between the empirical and theoretical volatilities (Table 4 and Table 5). 8 Table 4. Empirical and theoretical volatilities, ERS * Time period Empirical volatility (in %) Theoretical volatility (in %) Based on daily volatility Based on quarter volatility Day 1,93-4,4 Month 15,42 8,7 19,7 Quarter 34,09 15,0 - Source of data: Ibid. * Average number of trading days per year is 240. Table 3. Empirical and theoretical volatilities, BIRS * Time period Empirical volatility (in %) Theoretical volatility (in %) Based on daily volatility Based on quarter volatility Day 1,33-3,1 Month 10,41 5,9 13,8 Quarter 23,87 10,2 - Source of data: Ibid. * Average number of trading days per year is Table 5. Empirical and theoretical volatilities, FIRS * Time period Empirical volatility (in %) Theoretical volatility (in %) Based on daily volatility Based on quarter volatility Day 1,890-4,9 Month 17,44 8,4 21,6 Quarter 37,34 14,5 - Source of data: Ibid. * Average number of trading days per year is bankarstvo 5 - The same conclusion - rejection of the weak-form EMH, is also reached by means of the analysis of value movements of the other two stock exchange indices, ERS and FIRS. Empirical volatilities in different time periods are significantly different. Daily, monthly and The results of autocorrelation tests are not in line with the previous results. Low value of determination coefficient confirms the weakform EMH. Although the value of t statistics of the slope coefficient indicates that there is a linear connection, 9 it is rather weak (sca er plot 8 Theoretical volatilities of ERS and FIRS are calculated in the same way as BIRS. The only difference is in the average annual number of trading days in the analyzed period. 9 P values of the slope coefficient estimate, in all regression models, except in one (Table 6, Model No.4) is extremely low.

13 Grafikon 2. Dijagram raspršenosti dnevnih prinosa, BIRS vs. BIRS (-4)* Izvor podataka: (obradio autor). * BIRS - tekući dnevni prinos, BIRS (-4) - prinos sa vremenskim pomakom od četiri dana. Kod BIRS-a svega 8,9%, odnosno 0,6% varijabiliteta zavisne promijenljive (tekućeg dnevnog prinosa) objašnjeno je sa varijacijama nezavisne promijenljive (prinosi iz prethodnog perioda). Regresioni model ne pokazuje da postoji statistički signifikantna linearna veza između tekućeg i prethodnog prinosa. Podaci o prethodnim cijenama i prinosima nemaju nikakvu upotrebnu vrjednost u određivanju budućih cijena i prinosa. Odsustvo autokorelacije se poistovjećuje sa prihvatanjem HSET. Neadekvatnost konstruisanih linearnih regresionih modela potvrđuje hipotezu. Ocijena o odsustvu autokorelacije važi i za prinose na berzanske indekse ERS i FIRS. Autokorelacija je najjača između tekućeg dnevnog prinosa na FIRS i njegove prethodne vrjednosti. Međutim, iako je ova veza mnogo jača nego kod prethodnih modela, koeficijent determinacije 24%, ni ovaj regresioni model ne ispoljava visoku autokorelaciju. I u regresionim modelima sa drugačijim vremenskim pomakom nezavisno promijenljive varijable uočavamo nizak koeficjent determinacije. Autokorelacioni regresioni modeli nisu potpuni, ne sadrže varijable koje dodatno objašnjavaju varijabilitet prinosa. Kao takvi oni su neupotrebljivi za predviđanje buduće vrjednosti prinosa. Tabela 6. Testovi autokorelacije a Broj modela Specifikacija modela β t statistika p R koeficijent determinacije 1. 0,298 10,91 0,0000 0, ,0078 2,751 0,006 0, ,395 12,443 0,000 0, ,0519 1,5023 0,133 0, ,489 19,07 0,000 0, ,1347 4,62 0,000 0,0182 Izvor podataka: Ibid. a (-1) u regresionom modelu označava prethodni prinos, a (-4) prinos četiri dana prije tekućeg prinosa. bankarstvo 5 -

14 - Graph 2). 10 High p value of the free member estimate (from 0.98 to 0.45) is consistent with this conclusion. Graph 2. Sca er plot of daily returns, BIRS vs. BIRS (-4)* Source of data: (processed by the author). * BIRS - current daily return, BIRS (-4) - return with a four-day time distance. When it comes to BIRS, only 8.9%, i.e. 0.6% of variability of the dependent variable (current daily return) is explained by means of the independent variable variations (returns from the previous period). Regression model does not show that there is a statistically significant linear relation between the current and previous returns. The data on past prices and returns do not have any utility value in determining the future prices and returns. The absence of autocorrelation is identified with the acceptance of the weak-form EMH. Inadequacy of the constructed linear regression models confirms the hypothesis. The appraisal on the absence of autocorrelation also refers to the returns on stock exchange indices ERS and FIRS. Autocorrelation is the strongest between the current daily return on FIRS and its previous values. However, although this relation is much stronger than in the previous models, the determination coefficient being 24%, this regression model does not express high correlation either. In regression models with different time horizons, too, regardless of the independent variable, we observe a low determination coefficient. Autocorrelation regression models are not comprehensive; they do not contain variables that additionally explain the return variability. As such, they are useless in terms of prediction of future returns values. Table 6. Autocorrelation tests a Мodel number Model specification β t statistics p R determination coefficijent 1. 0,298 10,91 0,0000 0, ,0078 2,751 0,006 0, ,395 12,443 0,000 0, ,0519 1,5023 0,133 0, ,489 19,07 0,000 0, ,1347 4,62 0,000 0,0182 Source of data: Ibid. a (-1) in regression model marks the previous return, and (-4) the return as of four days before the current return. bankarstvo 5-10 Almost identical sca er plot, inconsistent with the strong linear connection, is present in other regression models, too.

15 Kao i nalazi testova autokorelacije i rezultati testa znakova su argument za prihvatanje HSET. Tabela 7 daje podatke o broju znakova i tokova za četiri perioda, pojedinačno po indeksima. Podatke smo koristili za određivanje vrjednosti z statistike (tabela 8). Vrjednost z statistike testa znakova za berzanske indekse BIRS, ERS, FIRS, u tri perioda, do godine, od godine do godine i od do godine, dokazuju slabu efikasnost tržišta. Sve z statistike se nalaze izvan intervala prihvatanja hipoteze o odsustvu slabe efikasnosti tržišta, BIRS; -9,1, -12,9, -10,5 i -19,4, ERS; -12,8, -10,3, -16,9, FIRS; -8,8, -17,4, -10,5, -22,1. Oblast prihvatanja hipoteze o postojanju serijske korelacije, odnosno o odbacivanju HSET obuhvata z vrjednosti u intervalu od -1,96 do 1,96. Između uzastopnih promijena cijene ne postoji korelacija. Prema rezultatima testa znakova informacije o prošlim cijenama se ne mogu koristiti za predviđanje budućih cijena. Domaće tržište akcija funkcioniše na nivou slabe efikasnosti. HSET testiramo i indirektno, kroz određivanje upotrebne vrjednosti alata tehničke analize u predviđanju smjera kretanja cjena akcija /vrjednosti indeksa na domaćem tržištu akcija. Grafikon 3 ilustruje kretanje cijene akcija RFUM-R-A 11 tokom godine. Tabela 9 sadrži vrjednosti tehničkih pokazatelja u najnižim tačkama tri signifikantna i grafički približno ujednačena preokreta (preokreti su označeni krugovima). U prosjeku preokret se dešava kad su MOM, ROC, RSI i MFI -0,43, -29,14%, 24,66 i 28,04 respektivno. Varijabilitet vrjednosti tehničkih indikatora, mjeren koeficjentom varijacije, je vrlo nizak za RSI (0,08) nizak za MOM i ROC (0,24 i 0,31 respektivno), a vrlo visok za MFI (0,7). Izuzetno nizak varijabilitet RSI u dolji sekundarnog trenda pokazuje da se pomoću ovog tehničkog indikatora može predvidjeti preokret cjene prema gore. Nalaz je u suprotnosti sa negiranjem korisnosti tehničke analize u predviđanju cijena akcija. Niska disperzija vremenske serije RSI kao i malen varijabilitet MOM, ROC u momentima Tokovi Znakovi BIRS ERS FIRS BIRS ERS FIRS do Ukupno Ukupno Ukupno Cjeli period Ukupno Tabela 7. Indeksi BLSE*, raspored tokova i znakova Izvor podataka: (obradio autor). * Banjalučka berza AD Banjaluka. Tabela 8. Test znakova - indeksi BLSE BIRS ERS FIRS do Cjeli period do Cjeli period do n n R µ δ z Izvor podataka: Ibid. 11 Rafinerija ulja Modriča AD Modriča Cjeli period bankarstvo 5 -

16 Just like autocorrelation tests, the sign test results are also the argument for accepting the weak-form EMH. Table 7 shows the data about the number of signs and flows for four periods, per each index individually. We used the data to determine the value of z statistics (Table 8). The values of z statistics for the sign test in respect of the stock exchange indices BIRS, ERS and FIRS, in three observed periods, until , from to , and from to , confirm the weak market efficiency. All z statistics are located beyond the interval for accepting the hypothesis on the absence of the weak-form market efficiency, as follows: BIRS: , and -19.4; ERS: -12.8, , -16.9; FIRS: -8.8, -17.4, -10.5, and The area for acceptance of the hypothesis about the existence of a serial correlation, i.e. about the rejection of the weak-form EMH, includes the z values in the interval between and There is no correlation between the successive price changes. According to the sign test results, the information about the past prices cannot be used for predicting the future prices. The domestic stock market functions at the level of weak efficiency. The weak-form EMH is also tested indirectly, by means of determining the utility value of technical analysis tools in predicting the trend of stock price/index value movements in the domestic stock market. Graph 3 illustrates the RFUM-R-A 11 stocks price movements throughout Table 9 contains the values of technical indicators in the lowest points of the three significant and graphically approximated breaks (the breaks are marked by circles). On average, a break occurs when MOM, ROC, RSI and MFI take the following values, respectively: -0.43, %, and The variability of technical indicators values, measured by variation coefficient, is very low for RSI (0.08), low for MOM and ROC (0.24 and 0.31 respectively), and very high for MFI (0.7). The extremely low variability of RSI in the extreme minimum area of the secondary trend indicates that this technical indicator may be used Table 7. BLSE* indices, scheme of flows and signs Source of data: (processed by the author) * Banjalucka berza a.d. Banjaluka (Banjaluka Stock Exchange) Flows Signs BIRS ERS FIRS BIRS ERS FIRS As of Total Total Total Entire period Total Table 8. Sign test - BLSE indices BIRS ERS FIRS bankarstvo 5 - As of Oil Refinery Modriča a.d. Modriča Entire period As of Entire period As of n n R µ δ z Source of data: Ibid. Entire period

17 preokreta cjene prema gore opovrgavaju HSET. Zaključak ne važi, zbog visokog varijabiliteta, za posljednji izabrani tehnički indikator MFI. Grafikon 3. Kretanje cijena RFUM-R-A, godine Izvor podataka: (obradio autor). Učestalost formiranja jednoobraznog Tabela 9. Tehnički indikatori - RFUM-R-A A.S. a S.D. b K.V. c MOM 10-0,58-0,32-0,39-0,43 0,13-0,31 ROC 10 (u %) -30,53-21,48-35, sekundarnog trenda u uslovima opadajućeg primarnog trenda i tendencija ka ujednačavanju vrjednosti tehničkih indikatora u momentima preokreta sekundarnog trenda uočena je i kod kretanja cijene akcije RNAF-R-A 12 (grafikon 4). Srednje vrjednosti MOM, ROC, RSI i MFI su - 0,37, -24,63%, 28,97 i 36,34 respektivno (tabela 10). Najniži varijabilitet i najveću moć predviđanja preokreta opet ima RSI. Koeficijent varijacije ROC je 0,19, a disperzija MOM i ROC identičan je vrjednostima iz prethodnog primjera 0,31 i 0,29 respektivno. Najveći stepen saglasnosti sa principom slabe efikasnosti tržišta ispoljava MFI. Njegova srednja vrjednost, 36,34, je zbog velike disperzije podataka, neupotrebljiva za predviđanje preokreta (koeficjent varijacije 0,75). U oba primjera analize upotrebne vrjednosti instrumenata tehničke analize uočavamo različit stepen sposobnosti pojedinih tehničkih indikatora u predviđanju kretanja cjena. Odnos izabranih tehničkih indikatora prema teoriji o slaboj efikasnosti tržišta nije identičan, pa je zato nemoguće izvući RSI 15 22,83 26,53 24,62 24,66 1,85 0,08 MFI 14 21,55 12,62 49,94 28,04 19,49 0,70 Izvor podataka: Ibid. a Aritmetička sredina. b Standardna devijacija. c Koeficjent varijacije. jedinstven zaključak o potvrdi ili negaciji slabe efikasnosti tržišta sa aspekta tehničke analize. Najveću sposobnost predviđanja budućeg kretanja cjene pokazuje RSI, nešto manju ROC i MOM, a najmanju MFI. 12 Rafinerija na e Brod AD Brod. bankarstvo 5 -

18 for predicting the upward price trend. This finding is in opposition with the negation of the technical analysis usefulness in predicting the stock prices movements. The low dispersion of the RSI time series, just like the slight variability of MOM and ROC in the upward turns, deny the weak-form EMH. The conclusion is not valid, due to the high variability, for the last chosen technical indicator MFI. Graph 3. RFUM-R-A price movements, 2007 Source of data: (processed by the author). Table 9. Technical indicators - RFUM-R-A A.M. a S.D. b V.C. c MOM 10-0,58-0,32-0,39-0,43 0,13-0,31 ROC 10 (u %) -30,53-21,48-35, The frequency of formation of a uniform secondary trend in the circumstances of a downward primary trend, along with the tendency towards the unification of technical indicators values in the secondary trend breaks, were also observed in respect of the RNAF-R-A stocks price movements 12 (Graph 4). The average values of MOM, ROC, RSI and MFI are as follows: -0.37, %, and respectively (Table 10). The lowest variability and the highest rate of breaks prediction is, again, expressed by RSI. The ROC variation coefficient is 0.19, with the MOM and ROC dispersion being identical to the values from the previous example and 0.29 respectively. The highest level of compliance with the weakform market efficiency principle is expressed by MFI. Its mean value, 36.34, is, due to the high data dispersion, useless in terms of break prediction (variation coefficient 0.75). In both examples examining the utility value of technical analysis instruments, we observe the different level of capability of certain technical indicators to predict price movements. According to the weak-form EMH, the relation between the chosen technical indicators is not identical, hence it is impossible to reach a uniform conclusion about the confirmation or negation of the weak-form EMH, RSI 15 22,83 26,53 24,62 24,66 1,85 0,08 MFI 14 21,55 12,62 49,94 28,04 19,49 0,70 Source of data: Ibid. a Arithmetic mean b Standard deviation c Variation coefficient from the technical analysis aspect. The highest capability of prediction of the future price movements is expressed by RSI, somewhat lower by ROC and MOM, and the lowest by MFI. bankarstvo 5-12 Oil Refinery Brod a.d. Brod

19 Grafikon 4. Tehnički indikatori - RNAF-R-A, godine Izvor podataka: Ibid. Tabela 10. Tehnički indikatori - RNAF-R-A U sljedećem primjeru izolovan je jedan tehnički indikator, stopa promjene cjene - ROC. Pratimo njegovo kretanje za ekstremno visoke vrjednosti u momentima preokreta sekundarnog trenda prema dole (grafikon 5 i tabela 11). Analizirali smo mogućnost korištenja prosječne vrjednosti ROC u predviđanju promjene primarnog trenda. Prosiječna vrjednost najviših ROC i njihova standardna devijacija su 25,10 % i 4,02 % respektivno. Koeficjent varijacije je umjereno nizak, 0,16. Promjena primarnog trenda na dan g. - mogla se predvidjeti na osnovu prosiječne vrjednosti ROC i relativno niske disperzije. ROC od 22,15 % (na dan pucanja špekulativnog A.S. S.D. K.V. MOM 10-0,37-0,58-0,32-0,25-0,33-0,35-0,37 0,11-0,31 ROC 10 (u %) -17,29-30,53-21,48-18,25-24,81-35,41-24,63 7,15-0,29 RSI 15 37,71 22,83 26,53 30,14 31,97 24,62 28,97 5,47 0,19 MFI 14 50,69 21,55 12,62 77,17 6,08 49,94 36,34 27,40 0,75 Izvor podataka: Ibid. m j e h u r a ) k o n v e r g i r a p r o s j e č n o j v r j e d n o s t i najviših ROC iz predhodnog perioda. Grafikon 5. Stopa promjene BIRS-a Izvor podataka: Ibid. Tabela 11. Stopa promjene BIRS-a za ekstremne vrjednosti A.D. a S.D. b K.V. c ROC15 (u%) Izvor podataka: Ibid. a Prosjek ne uključuje vrjednost ROC za g. b Standardna devijacija. c Koeficijent varijacije. bankarstvo 5 -

20 Graph 4. Technical indicators - RNAF-R-A, 2007 Source of data: Ibid. Table 10. Technical indicators - RNAF-R-A In the following example, we have isolated a technical indicator - rate of change (ROC). We follow its movements for extremely high values in the downward breaks of the secondary trend (Graph 5 and Table 11). We analyzed the possibility of using average ROC values in predicting the primary trend changes. The average value of the highest ROCs and their standard deviations are 25.10% and 4.02% respectively. Variation coefficient is moderately low The change in the primary trend, as of , could have been predicted based on the average value of ROC and the relatively low dispersion. ROC in the amount of 22.15% (on the day the speculative bubble burst) A.S. S.D. K.V. MOM 10-0,37-0,58-0,32-0,25-0,33-0,35-0,37 0,11-0,31 ROC 10 (u %) -17,29-30,53-21,48-18,25-24,81-35,41-24,63 7,15-0,29 RSI 15 37,71 22,83 26,53 30,14 31,97 24,62 28,97 5,47 0,19 MFI 14 50,69 21,55 12,62 77,17 6,08 49,94 36,34 27,40 0,75 Source of data: Ibid. c o n v e r g e s towards the average value of the highest ROCs from the previous period. Graph 5. BIRS volatility rate Source of data: Ibid. Table 11. BIRS volatility rate for extreme values bankarstvo A.D. a S.D. b K.V. c ROC15 (u%) Source of data: Ibid. a The average does not include the ROC value as of b c Standard deviation Variation coefficient

21 Zaključak Upotrebljene metodologije ne daju jedinstven odgovor na pitanje da li tržište akcija u Republici Srpskoj funkcioniše na nivou slabe efikasnosti tržišta. One potvrđuju, ali i negiraju HSET. Rezultati dobijeni primjenom pravila korijena vremena, su u suprotnosti sa HSET. Između tri karakteristična oblika kretanja cijena akcija, povrata ka sredini, trenda i slučajnog hoda pravilo korjena vremena je kao referentni oblik kretanja odabralo model trenda. HSET je odbačena dokazivanjem antiteze - da se cjene akcija ne kreću po modelu povrata ka sredini i slučajnog hoda. Indirektno kroz odbacivanje HSET potvrđena je korisnost tehničke analize u predviđanju kretanja cjena akcija. Testovi znakova i testovi autokorelacije negiraju postojanje autokorelacije. U testovima znakova, za BIRS, FIRS i ERS, u svim analiziranim vremenskim periodima, vrjednost z statistike ne pripada intervalu prihvatanja nulte hipoteze. Nulta hipoteza je izjednačena sa postojanjem serijske korelacije između promjena cjena akcija. S obzirom da je nulta hipoteza odbačena prihvatili smo alternativnu hipotezu o nepostojanju serijske korelacije između prinosa akcija. Izostanak serijske korelacije znači da se cijene akcija kreću po modelu slučajnog hoda, što je ekvivalentno prihvatanju HSET. Do istog zaključka smo došli i primjenom testova autokorelacije. Konstruisani regresioni modeli imaju vrlo niske koeficjente determinacije - kreću su u rasponu od 0,0027 do 0,23. U regresionim modelima su ispuštene varijable koje objašnjavaju znatan dio varijabiliteta prinosa. Izuzetno nizak koeficjent determinacije potvrđuje hipotezu da je domaće tržište akcija efikasno u odnosu na set informacija o prethodnim cijenama i prinosima. Zadnji način testiranja HSET, preko odabranih alata tehničke analize, ne vodi do nedvosmislenih zaključaka na način na koji to čine prethodne metodologije. U analizi kretanja cjena akcija RNAF-R-A i RFUM-R-A najveću snagu u predviđanju preokreta cijene ispoljio je indeks relativne moći - RSI, znatno manju momentum/impuls (MOM) i stopa promjene cjene (ROC), a najmanju indeks novčanog toka (MFI). Vrjednost RSI u momentima preokreta ima najmanji koeficjent varijacije 0.08 (RFUM) i 0,19 (RNAF). Disperzija podataka MOM i ROC, mjerena koeficjentom varijacije, je 0,31 i 0,29 respektivno, a najveća ja za MFI 0,75. Ako se posmatraju ekstremne vrjednosti ROC za vremensku seriju cjena BIRS-a u cjelom periodu koji prethodi primarnom trendu, ovaj tehnički indikator ispoljava izuzetnu prediktivnu moć. Njegova srednja vrjednost je 25,12%, a koeficjent varijacije 0,16. Srednja vrjednost ROC je vrlo korisna za predviđanje promjene primarnog trenda. Vrjednost ROC u momentu promjene primarnog trenda od 22,5 %, je vrlo bliska srednjoj vrjednosti ekstremnih vrjednosti ROC iz prethodnog perioda. Odabrani tehnički indikatori se nalaze u različitom odnosu prema slaboj efikasnosti tržišta. Uočene karakteristike RSI i djelimično ROC, sposobnost predviđanja promjene sekundarnog (a u slučaju ROC i primarnog trenda) su antiteza HSET. Ovo važi u manjoj mjere i za MOM. Velika disperzija vrjednosti MFI u trenucima promjene sekundarnog trenda, tj. njegova nesposobnost da predvidi promjenu trenda, stavlja ovaj indikator tehničke analize u ravan sa hipotezom o slaboj efikasnosti tržišta. S obzirom da jedan dio metoda potvrđuje HSET, dok rezultati drugih metoda predstavljaju njenu antitezu, nismo u stanju da u potpunosti, niti prihvatimo niti odbacimo HSET. Dalja istraživanja bi trebala ići u pravcu testiranja hipoteze o polujakoj efikasnosti tržišta i na taj način indirektne valorizacije HSET. Alternativni put u daljim istraživanjima je i primjena novihjačih testova za dokazivanje slabe efikasnosti tržišta. Istraživanje se može nastaviti i konstrukcijom regresionih modela koji se sastoje od šireg kruga nezavisno promjenljivih - prinosa i volumena. Pored višestruke linearne regresione i korelacione analize ne treba odbaciti ni upotrebu nelinearnog regresionog modela. bankarstvo 5 -

22 bankarstvo 5 - Conclusion The applied methodologies do not provide a uniform answer to the question of whether the stock market in the Republic of Srpska functions at the level of weak-form market efficiency. They confirm, but also deny the weak-form EMH. The results obtained by means of applying the square root of time rule are in opposition with the weak-form EMH. Out of the three characteristic types of stock price movements - mean reversion, trend and random walk, the square root of time rule singled out the trend model as a benchmark type of movement. The weak-form EMH was rejected by proving its antithesis - that stock prices do not follow mean reversion or random walk models. Indirectly, by rejecting the weak-form EMH, the usefulness of technical analysis in terms of predicting stock prices movements was confirmed. Sign tests and autocorrelation tests deny the existence of autocorrelation. In sign tests, for BIRS, FIRS and ERS, for all analyzed time periods, the value of z statistics does not fall into the interval for accepting the zero hypothesis. Zero hypothesis was taken to imply the existence of a serial correlation between the stock price changes. Given that the zero hypothesis had been rejected, we accepted the alternative hypothesis about the non-existence of a serial correlation between the stock returns. The absence of serial correlation implies that the stock prices are following the random walk model, which is, in turn, equivalent to accepting the weak-form EMH. We reached the same conclusion by applying autocorrelation tests. The constructed regression models have very low determination coefficients - ranging from to These regression models do not contain certain variables that explain a significant part of the returns variability. Extremely low determination coefficient confirms the hypothesis that the domestic stock market is efficient in comparison with the set of information about the previous prices and returns. The last way to test the weak-form EMH, by means of selected technical analysis tools, does not lead to unambiguous conclusions in the manner the previous methodologies do. In the analysis of RNAF-R-A and RFUM-R-A stocks price movements, the highest strength in predicting the price breaks was expressed by the relative strength index - RSI, considerably lower by the momentum/impulse (MOM) an rate of change (ROC), whereas the lowest strength was expressed by the money flow index (MFI). The RSI value in the points of break has the lowest variation coefficient (RFUM) and 0.19 (RNAF). Dispersion of MOM and ROC data, measured by variation coefficient, amounts to 0.31 and 0.29 respectively, and it takes the highest value for MFI If we observe the extreme ROC values for the time series of BIRS prices in the entire period prior to the primary trend, this technical indicator shows extraordinary predictive power. Its mean value is 25.12%, with the variation coefficient being ROC mean value is very useful in predicting the primary trend changes. ROC value in the primary trend break, amounting to 22.5%, is very close to the mean value of the extreme ROC values from the previous period. The selected technical indicators are in different relations with the weak-form EMH. The observed characteristics of RSI and partly ROC, in terms of their capability to predict the changes of the secondary trend (and in case of ROC the primary trend, too) stand as an antithesis to the weak-form EMH. To a lesser extent, this also holds for MOM. The high dispersion of MFI values in the points of secondary trend breaks, i.e. its inability to predict the trend changes, place this technical analysis indicator in line with the weak-form EMH. Given that some methods confirm the weak-form EMH, whereas the results of other methods pose its anti-thesis, we are not in the position to either fully accept or reject the weak-form EMH. Further research should be directed at testing the semi-strong EMH, which would function as an indirect valorization of the weak-form EMH. The alternative direction in further research could be the application of the new, stronger tests for proving the weak-form EMH. Research could also be continued by constructing the regression models consisting of a wider range of independently volatile returns and volumes. In addition to the multiple linear regression and correlation analysis, one should also take into consideration the application of the non-linear regression model.

23 Banja Luka bankarstvo 5 -