slaba efikasnost trŽiŠta kapitala · slaba efikasnost trŽiŠta kapitala rezime rad ne daje...

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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

Dr Dragan S. JovićCentralna banka Bosne i Hercegovine,

Glavna banka Republike Srpske [email protected]

stručni priloziUDK 338.57:336.763(497.6)

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WEAK-FORM EFFICIENCY

OF THE STOCK MARKET

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.

Key words: weak-form efficiency market hypothesis (weak-form EMH), stock market, Republic of Srpska

Dragan S. Jović PhDCentral bank of Bosnia and Herzegovina, Glavna banka of the Republic of [email protected]

expert contributionsUDC 338.57:336.763(497.6)

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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 indeksa2 na domaćem tržištu akcĳa (Banjalučka berza AD Banjaluka - BLSE) u periodu od početka razvoja tržišta do 30.06.2009. 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 akcĳaa) 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. 1999. Osnovi finansĳskog tržišta, IP Princip, Beograd.2 BIRS-Berzanski indeks Republike Srpske, ERS-Indeks preduzeća Elektroprivrede Republike Srpske, FIRS-Indeks

investicionih fondova Republike Srpske.

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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 weak-form 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 values2 at the domestic stock market (Banjalucka berza a.d. Banjaluka - Banjaluka Stock Exchange/BLSE)

from the beginning of the market development until 30.06.2009.

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 trendsa) 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, Beograd2 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

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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 vremena4

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. 2001. Risk management, McGraw- Hill, New York-Toronto. p. 411.

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%), pt - tekuća cĳena, pt-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. 2000. Portfolio analiza. Čigoja štampa, Beograd. s. 156.

3 h�p://www.riskglossary.com/link/volatility.htm.4 Više o načinu izvođenja formule vidjeti u Crouhy, Michel, Galai, Dan, Mark, Robert. 2001. Risk management, McGraw - Hill,

New York-Toronto. p. 409-411.

Tabela 1. Faktori konverzĳe

BIRS ERS FIRSZa

DEP*Za

KEP** Za DEP Za KEP Za DEP Za KEP

- 58.5 - 60.0 58.912.0 3.0 12.0 3.0 12.0 3.04.0 - 4.0 - 4.0 -

Izvor podataka: www.blberza.com (obradio autor).* DEP - dnevni empirĳski podaci. ** KEP - kvartalni empirĳski podaci.

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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.

Formula 1. Square root of time rule4

with: σT - standard deviation for a long time period, σt - 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,

do not contain 252 days, we shall use different conversion factors in this paper.

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 2. Autocorrelation tests - stock return change

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%), pt - current price, pt-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. 156

3 h�p://www.riskglossary.com/link/volatility.htm4 More on how to use this formula in Crouchy, Michel, Galai, Dan, Mark, Robert (2001), Risk Management, McGraw - Hill,

New York - Toronto, p. 409-411

Table 1. Conversion factors

BIRS ERS FIRSFor

DED*For

QED**For

DEDFor

QEDFor

DEDFor

QED- 58.5 - 60.0 58.9

12.0 3.0 12.0 3.0 12.0 3.04.0 - 4.0 - 4.0 -

Source of data: www.blberza.com (processed by the author)* DED - Daily empirical data** QED - Quarterly empirical data

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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 H0: β=0, a alternativna hipoteza kao H1: 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.

Izvor podataka: Popović, M. Saša. 2000. Portfolio analiza. Čigoja štampa, Beograd. str. 50. gdje su; n2 - ukupan broj negativnih opservacĳa, n1 - ukupan broj pozitivnih opservacĳa. z - vrjednost statistike testa za standardizovan normalan raspored, µ - aritmetička sredina, R- broj tokova, N=n1+n2 - ukupan broj opservacĳa.

Testiranje se sprovodi dvosmĳernim testom. Nulta hipoteza (H0) označava postojanje serĳske korelacĳe, što je ekvivalentno negacĳi HSET. Alternativna hipoteza (H1) 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.

5 Više o prostoj linearnoj regresĳi i korelacĳi vidjeti u Žižić M., Lovrić, M. Pavličić D. 1992. Metodi statističke analize, Ekonomski fakultet, Beograd. 273-315.

6 Ibid. str. 294. 7 Ibid.

Formula 3. Aritmetička sredina

Formula 4. Standardna devĳacĳa

Formula 5. Z statistika

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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 H0 : β = 0, and alternative hypothesis as H1 : 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.

Source of data: Popovic, M. Sasa (2000), Portfolio analiza, Cigoja stampa, Beograd, p. 50with: n2 - total number of negative observations, n2 - total number of positive observations. z - statistical value of the test for standardized normal distribution, µ - arithmetic mean, R - number of flows, N = n1 + n2 - total number of observations.

The testing is conducted by means of a two-way test. Zero hypothesis (H0) marks the existence of a serial correlation, which is equivalent to the negation of the weak-form EMH. Alternative hypothesis (H1) 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 -1.96 to 1.96.

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.

5 More on simple linear regression and correlation in Zizic M., Lovric M., Pavlicic D. (1992), Metodi statisticke analize, Ekonomski fakultet, Beograd, p. 273-315

6 Ibid., p. 2947 Ibid.

Formula 3. Arithmetic mean

Formula 4. Standard deviation

Formula 5. Z statistics

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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

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 2009. 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

Formula 6. Tipična cjena

gdje su TP, HP, LP, CP - tipična, najviša, najniža i zatvarajuća cjena respektivno

Formula 7. Novčani tok - MF

gdje su MR, PMF i NMF, novčani racio, pozitivni novčani tok i negativni novčani tok respektivno

Formula 8. Novčani racio

gdje su MR, PMF i NMF, novčani racio, pozitivni novčani tok i negativni novčani tok respektivno

Tabela 2. Indeks novčanog toka

Izvor podataka: Steven B. Achelis. 2001. Technical Analysis from A to Z, McGraw-Hill.

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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: 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

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 2009.

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

Formula 6. Typical price

with: TP, HP, LP, CP - standing for typical, highest, lowest and closing price, respectively

Formula 7. Money flow

with: MF and V standing for money flow and volume of turnover, respectively

Formula 8. Money ration

with: MR, PMF and NMF standing for money ratio, positive money flow and negative money flow, respectively

Table 2. Money flow index

Source of data: Steven B. Achelis (2001), Technical Analysis from A to Z, McGraw - Hill

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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.

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

zbog razlike između empirĳskih i teorĳskih volatilnosti (tabela 4 i tabela 5).8

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.

Vremenski period

Empirĳska volatilnost

(u %)

Teorĳska volatilnost (u %)

Na bazi dnevne

volatilnosti

Na bazi kvartalne

volatilnosti Dan 1,33 - 3,1Mjesec 10,41 5,9 13,8Kvartal 23,87 10,2 -

Tabela 3. Empirĳske i teorĳske volatilnosti, BIRS 27.04.2004 - 30.06.2009.*

Izvor podataka: Ibid.* Prosječan godišnji broj dana trgovanja je 234,2.

Vremenski period


(u %)


Na bazi dnevne

volatilnosti

Na bazi kvartalne


Tabela 4. Empirĳske i teorĳske volatilnosti, ERS 01.01.2006 - 30.06.2009. g.*

Izvor podataka: Ibid.* Prosječan godišnji broj dana trgovanja je 240

Vremenski period


(u %)


Na bazi dnevne

volatilnosti

Na bazi kvartalne


Tabela 5. Empirĳske i teorĳske volatilnosti, FIRS 29.07.2006-30.06.2009.*

Izvor podataka: Ibid.* Prosječan godišnji broj dana trgovanja je 235,8.

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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.

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

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

The results of autocorrelation tests are not in line with the previous results. Low value of determination coefficient confirms the weak-form 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.

Time period

Empirical volatility

(in %)

Theoretical volatility (in %)

Based on daily volatility

Based on quarter

volatilityDay 1,33 - 3,1Month 10,41 5,9 13,8Quarter 23,87 10,2 -

Table 3. Empirical and theoretical volatilities, BIRS 27.04.2004 - 30.06.2009*

Source of data: Ibid.* Average number of trading days per year is 234.2.

Time period


(in %)



Based on quarter


Table 4. Empirical and theoretical volatilities, ERS 01.01.2006 - 30.06.2009*

Source of data: Ibid.* Average number of trading days per year is 240.

Time period


(in %)



Based on quarter


Table 5. Empirical and theoretical volatilities, FIRS 29.07.2006 - 30.06.2009*

Source of data: Ibid.* Average number of trading days per year is 235.8.

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Grafikon 2. Dĳagram raspršenosti dnevnih prinosa, BIRS vs. BIRS (-4)*

Izvor podataka: www.blberza.com. (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.

Broj modela Specifikacĳa modela β t

statistika p R koeficĳent determinacĳe

1. 0,298 10,91 0,0000 0,089

2. 0,0078 2,751 0,006 0,0062

3. 0,395 12,443 0,000 0,1562

4. 0,0519 1,5023 0,133 0,0027

5. 0,489 19,07 0,000 0,239

6. 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.

Tabela 6. Testovi autokorelacĳe a

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- 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: www.blberza.com (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.

Мodel number Model specification β t

statistics p R determination coefficĳent

1. 0,298 10,91 0,0000 0,089

2. 0,0078 2,751 0,006 0,0062

3. 0,395 12,443 0,000 0,1562

4. 0,0519 1,5023 0,133 0,0027

5. 0,489 19,07 0,000 0,239

6. 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.

Table 6. Autocorrelation testsa

10 Almost identical sca�er plot, inconsistent with the strong linear connection, is present in other regression models, too.

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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 31.12.2005. godine, od 01.01.2006. godine do 31.12.2007. godine i od 01.01.2008 do 30.06.2009. 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-A11 tokom 2007. 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 31.12.2005.- 24 22 116 105

+ 31 29 138 132

Ukupno 55 51

01.01.2006 - 31.12.2007.- 45 51 23 116 105

+ 51 47 25 138 132

Ukupno 96 98 48

01.01.2008.-30.06.2009. - 48 46 44 239 221 233

+ 28 16 32 127 104 130

Ukupno 76 62 76

Cjeli period- 117 97 89 562 435 547

+ 110 63 86 531 363 526

Ukupno 227 160 175

Tabela 7. Indeksi BLSE*, raspored tokova i znakova

Izvor podataka: www.blberza.com (obradio autor).

* Banjalučka berza AD Banjaluka.

BIRS ERS FIRS

do 31.12.05.

01.01.06- 31.12.07

01.01.08.-30.06.09.

Cjeli period

do 31.12.05.

01.01.06- 31.12.07

01.01.08.-30.06.09.

Cjeli period

do 31.12.05.

01.01.06- 31.12.07

01.01.08.-30.06.09.

Cjeli period

n1 138 266 127 531 259 104 363 132 264 130 526

n2 116 207 239 562 214 221 435 105 209 233 547

R 55 96 76 227 98 62 160 51 48 76 175

µ 127.0 233.8 166.9 547.1 235.4 142.4 396.8 118.0 234.3 167.9 537.3

δ 7.9 10.7 8.7 16.5 10.8 7.8 14.0 7.6 10.7 8.7 16.4

z -9.1 -12.9 -10.5 -19.4 -12.8 -10.3 -16.9 -8.8 -17.4 -10.5 -22.1

Izvor podataka: Ibid.

Tabela 8. Test znakova - indeksi BLSE

11 Rafinerĳa ulja Modriča AD Modriča

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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 31.12.2005, from 01.01.2006 to 31.12.2007, and from 01.01.2008 to 30.06.2009, 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: -9.1 - 12.9, -10.5 and -19.4; ERS: -12.8, -10.3, -16.9; FIRS: -8.8, -17.4, -10.5, and 22.1. 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 -1.96 and 1.96. 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-A11 stocks price movements throughout 2007. 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, -29.14%, 24.66 and 28.04. 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

11 Oil Refinery Modriča a.d. Modriča

Flows Signs

BIRS ERS FIRS BIRS ERS FIRS

As of 31.12.2005.- 24 22 116 105

+ 31 29 138 132

Total 55 51

01.01.2006 - 31.12.2007.- 45 51 23 116 105

+ 51 47 25 138 132

Total 96 98 48

01.01.2008.-30.06.2009. - 48 46 44 239 221 233

+ 28 16 32 127 104 130

Total 76 62 76

Entire period- 117 97 89 562 435 547

+ 110 63 86 531 363 526

Total 227 160 175

BIRS ERS FIRS

As of 31.12.05.

01.01.06- 31.12.07

01.01.08.-30.06.09.

Entire period

As of 31.12.05.

01.01.06- 31.12.07

01.01.08.-30.06.09.

Entire period

As of 31.12.05.

01.01.06- 31.12.07

01.01.08.-30.06.09.

Entire period

n1 138 266 127 531 259 104 363 132 264 130 526

n2 116 207 239 562 214 221 435 105 209 233 547

R 55 96 76 227 98 62 160 51 48 76 175

µ 127.0 233.8 166.9 547.1 235.4 142.4 396.8 118.0 234.3 167.9 537.3

δ 7.9 10.7 8.7 16.5 10.8 7.8 14.0 7.6 10.7 8.7 16.4

z -9.1 -12.9 -10.5 -19.4 -12.8 -10.3 -16.9 -8.8 -17.4 -10.5 -22.1

Source of data: Ibid.

Table 8. Sign test - BLSE indices

Table 7. BLSE* indices, scheme of flows and signs

Source of data: www.blberza.com

(processed by the author)

* Banjalucka berza a.d. Banjaluka (Banjaluka

Stock Exchange)

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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, 2007. godine

Izvor podataka: www.blberza.com (obradio

autor).Učestalost formiranja jednoobraznog

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-A12 (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 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.

22.06.2007. 31.7.2007. 9.10.2007. 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 -35,41 -29.14 7.07 -

24.26

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

Tabela 9. Tehnički indikatori - RFUM-R-A

Izvor podataka: Ibid. a Aritmetička sredina.b Standardna devĳacĳa.c Koeficjent varĳacĳe.

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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: www.blberza.com (processed by the author).

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 movements12 (Graph 4). The average values of MOM, ROC, RSI and MFI are as follows: -0.37, -24.63%, 28.97 and 36.34 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 - 0.31 and 0.29 respectively. The highest level of compliance with the weak-form 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, 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.

12 Oil Refinery Brod a.d. Brod

22.06.2007. 31.7.2007. 9.10.2007. 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 -35,41 -29.14 7.07 -

24.26

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

Table 9. Technical indicators - RFUM-R-A

Source of data: Ibid.a Arithmetic meanb Standard deviationc Variation coefficient

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Grafikon 4. Tehnički indikatori - RNAF-R-A, 2007. godine


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 13.04.2009 g. - mogla se predvidjeti na osnovu prosĳečne vrjednosti ROC i relativno niske disperzĳe.

ROC od 22,15 % (na dan pucanja špekulativnog 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.

23.5.07. 22.6.07. 31.7.07 20.8.07 19.9.07. 9.10.07. 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

Tabela 10. Tehnički indikatori - RNAF-R-A


20.9.04. 2.2.05. 29.8.06. 17.10.06. 28.2.07. 13.4.07. A.D. a S.D. b K.V.c

ROC15 (u%) 23.18 20.49 27.30 30.83 23.69 22.15 25.10 4.02 0.16

Tabela 11. Stopa promjene BIRS-a za ekstremne vrjednosti

Izvor podataka: Ibid.a Prosjek ne uključuje vrjednost ROC za 13.04.2007. g. b Standardna devĳacĳa.c Koeficĳent varĳacĳe.

Grafikon 5. Stopa promjene BIRS-a


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Graph 4. Technical indicators - RNAF-R-A, 2007


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 - 0.16. The change in the primary trend, as of 13.04.2009, 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) c o n v e r g e s towards the average value of the highest ROCs from the previous period.

23.5.07. 22.6.07. 31.7.07 20.8.07 19.9.07. 9.10.07. 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

Table 10. Technical indicators - RNAF-R-A


Graph 5. BIRS volatility rate


20.9.04. 2.2.05. 29.8.06. 17.10.06. 28.2.07. 13.4.07. A.D.a S.D.b K.V.c

ROC15 (u%) 23.18 20.49 27.30 30.83 23.69 22.15 25.10 4.02 0.16

Table 11. BIRS volatility rate for extreme values

Source of data: Ibid.a The average does not include the ROC value as of 13.04.2007b Standard deviationc Variation coefficient

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ZaključakUpotrebljene 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 novih-jačih 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.

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ConclusionThe 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 0.0027 to 0.23. 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 - 0.08 (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 - 0.75.

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 0.16. 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 anti-thesis 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.

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Banja Luka

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Literatura / References

1. Credit Suisse. 1999. Technical analysis explained.

2. Crouhy, Michel, Galai, Dan, Mark, Robert. 2001. Risk management, McGraw- Hill, New York-Toronto.

3. Vasiljević, Branko. 1999. Osnovi finansĳskog tržišta, IP Princip, Beograd.

4. Popović, M. Saša. 2000. Portfolio analiza, Čigoja štampa, Beograd.

5. Žižić M., Lovrić, M. Pavličić D. 1992. Metodi statističke analize, Ekonomski fakultet, Beograd.

6. EViews 3.1. Help System.

7. www.blberza.com8. www.riskglossary.com

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