EKONOMETRIA. Zastosowanie matematyki w ekonomii. Redaktor naukowy Janusz Łyko

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1 EKONOMETRIA 26 Zasosowanie maemayki w ekonomii Redakor naukowy Janusz Łyko Wydawnicwo Uniwersyeu Ekonomicznego we Wrocławiu Wrocław 2009

2 Spis reści Wsęp... 7 Beaa Bal-Domańska, Ekonomeryczna analiza sigma i bea konwergencji regionów Unii Europejskiej... 9 Andrzej Bąk, Anea Rybicka, Marcin Pełka, Modele efeków głównych i modele z inerakcjami w conjoin analysis z zasosowaniem programu R. 25 Kaarzyna Budny, Kuroza wekora losowego Wikor Ejsmon, Opymalna liczebność grupy sudenów Kamil Fijorek, Model regresji dla cechy przyjmującej warości z przedziału (0,1) ujęcie bayesowskie Paweł Hanczar, Wyznaczanie zapasu bezpieczeńswa w sieci logisycznej Roman Hupas, Meody szacowania wewnąrzdziennej sezonowości w analizie danych finansowych pochodzących z pojedynczych ransakcji Aleksandra Iwanicka, Wpływ zewnęrznych czynników ryzyka na prawdopodobieńswo ruiny w skończonym horyzoncie czasowym w wieloklasowym modelu ryzyka Agnieszka Lipiea, Sany równowagi na rynkach warunkowych Krysyna Melich-Iwanek, Polski rynek pracy w świele eorii hiserezy Rafał Piszczek, Zasosowanie modelu logi w modelowaniu upadłości Marcin Salamaga, Próba weryfikacji eorii paryeu siły nabywczej na przykładzie kursów wybranych walu Anoni Smoluk, O zasadzie dualności w programowaniu liniowym Małgorzaa Szulc-Janek, Influence of recommendaions announcemens on sock prices of fuel marke Jacek Welc, Regresja liniowa w szacowaniu fundamenalnych współczynników Bea na przykładzie spółek giełdowych z sekorów: budownicwa, informayki oraz spożywczego Andrzej Wilkowski, O współczynniku korelacji Mirosław Wójciak, Klasyfikacja nowych echnologii energeycznych ze względu na deerminany ich rozwoju Andrzej Wójcik, Wykorzysanie modeli wekorowo-auoregresyjnych do modelowania gospodarki Polski Kaarzyna Zeug-Żebro, Rekonsrukcja przesrzeni sanów na podsawie wielowymiarowych szeregów czasowych

3 6 Spis reści Summaries Beaa Bal-Domańska, Economeric analysis of sigma and bea convergence in he European Union regions Andrzej Bąk, Anea Rybicka, Marcin Pełka, Main effecs models and main and ineracions models in conjoin analysis wih applicaion of R sofware Kaarzyna Budny, Kurosis of a random vecor Wikor Ejsmon, Opimal class size of sudens Kamil Fijorek, Regression model for daa resriced o he inerval (0,1) Bayesian approach Paweł Hanczar, Safey sock level calculaion in a supply chain nework Roman Hupas, Esimaion mehods of inraday seasonaliy in ransacion financial daa analysis Aleksandra Iwanicka, An impac of some ouside risk facors on he finie- -ime ruin probabiliy for a muli-classes risk model Agnieszka Lipiea, Saes of coningen marke equilibrium Krysyna Melich-Iwanek, The Polish labour marke in ligh of he hyseresis heory Rafał Piszczek, Logi model applicaions for bankrupcy modelling Marcin Salamaga, Aemp o verify he purchasing power pariy heory in he case of some foreign currencies Anoni Smoluk, On dual principle of linear programming Małgorzaa Szulc-Janek, Analiza wpływu rekomendacji analiyków na ceny akcji branży paliwowej (Analiza wpływu rekomendacji analiyków na ceny akcji branży paliwowej) Jacek Welc, A linear regression in esimaing fundamenal beas in he case of he sock marke companies from consrucion, i and food indusries Andrzej Wilkowski, Abou he coefficien of correlaion Mirosław Wójciak, Classificaion of new energy relaed echnologies based on he deerminans of heir developmen Andrzej Wójcik, Using vecor-auoregressive models o modelling economy of Poland Kaarzyna Zeug-Żebro, Sae space reconsrucion from mulivariae ime series

4 PRACE NAUKOWE UNIWERSYTETU EKONOMICZNEGO WE WROCŁAWIU nr 76 Ekonomeria Małgorzaa Szulc-Janek Wrocław Universiy of Economics INFLUENCE OF RECOMMENDATIONS ANNOUNCEMENTS ON STOCK PRICES OF FUEL MARKET Summary: In he aricle he auhor answers he quesion wheher in accordance o effeciveness heory of capial marke, recommendaions of analyss have a linear influence on sock prices or maybe he resuls are closer o chaos heory and is combinaion of fracal analysis. Sock prices irrespecive of he capial marke secor are he reflecion of he public informaion available on he marke. Neverheless invesor decisions are commonly driven by individual needs, requiremens and paerns of behaviour, very ofen irraional and no conneced wih public informaion. Chaos heory is offering an alernaive o he classical approach owards he way capial marke is funcioning. From is perspecive capial marke is a nonlinear, dynamic sysem driven by deerminisic chaos. According o E. Peeres here exiss long-erm influence of informaion from he pas and endency so as no o include fundamenal informaion abou he sock prices ino marke valuaion. The ool used in he aricle o measure he impac of marke influx of informaion on he sock prices is even analysis. Key words: even analysis, esimaion window, even window, abnormal rae of reurn, recommendaion, p-value. 1. Inroducion In he aricle he auhor is answering he quesion wheher in accordance wih effeciveness heory of capial marke, recommendaions of analyss have a linear influence on sock prices or maybe he resuls are closer o chaos heory and is combinaion of fracal analysis. Sock prices, irrespecively of he capial marke secor, are he reflecion of he public informaion available on he marke. Neverheless invesors decisions are commonly driven by individual needs, requiremens and paerns of behaviour, very ofen irraional and no being conneced wih public informaion. Chaos heory is offering an alernaive o he classical approach owards he way he capial marke is funcioning. From is perspecive capial marke is a nonlinear, dynamic sysem driven by deerminisic chaos. According o E. Peeres here exiss long-erm influence of informaion from he pas and endency so as no o include fundamenal informaion abou he sock prices ino

5 Influence of recommendaions announcemens on sock prices marke valuaion [Szablewski, Pniewski, Barosiewicz 2008, p. 213]. The ool used in he aricle o measure he impac of marke influx of informaion on he sock prices is he even analysis. 2. The even analysis A company is an insiuion paricipaing in he marke and being managed in order o creae income for is owners. I is no an isolaed uni bu is prone o various ouside and inside facors. Even analysis is an alernaive way of esing he resuls of differen facors on financial markes or resuls of decisions made inside he companies on heir marke value. I analyses closer and disan background of he organizaion. Figure 1 depics main facors which cause sock prices variaions. I is worh menioning ha inside facors such as splis, dividends or income forecass may influence he prices sronger han ouside poliical changes and differen ypes of risk such as for insance ineres rae risk. Inside facors are playing he role of hedge insrumens, seps aken by company so as o hedge from ouside independen facors. This relaion depends on a company profile. Recommendaions Poliical changes Changes in indexes Managemen changes Sock prices Income forecas, new conracs Dividends Splis Ineres rae changes Changes in correlaed marke secors Fig. 1. Inside and ouside facors changing value of sock prices Source: own figure on he basis of [Gurgul 2006].

6 172 Małgorzaa Szulc-Janek An advanage of his mehod is coming from is simpliciy and few requiremens, which makes i adjused o various secors and companies. According o A. McWilliams and D. Siegel even analysis is consising of he following seps [McWilliams, Siegel 1997, pp ]: 1. Definiion of evens providing new informaion for he company. 2. Economic heories research clarifying he influence of he paricular evens on he sock prices. 3. Creaing he group of companies affeced by he evens. 4. Even window seing (required clarificaions for windows longer han wo days). 5. Eliminaion of companies affeced by evens no aken ino analysis. 6. Saisical measuremens of esimaed and abnormal raes of reurn, and heir significance level. 7. Simulaing he resuls of negaive abnormal raes of reurn in he sample and Wilcoxon es resuls. 8. Boosrap analysis for small samples and is impac on he whole resuls. 9. Economic heories and zero hypohesis verificaion. 10. Aaching he lis of companies aken ino consideraion in he analysis wih daes of evens lised. The approach presened above is very ofen discussed as some poins such as for insance very shor even windows (suggesed no longer han wo days) may be no appropriae for all evens. Even is defined as new public informaion available on he marke which may be conneced wih plans or implemened acions wihin he companies affeced [Gurgul 2006, pp ]. The informaion should fulfil he following requiremens [Tabak, Dunbar 1999]: 1) i has o be explici and precise, 2) public appearance on he marke mus be easy o idenify, 3) informaion canno be driven by marke paricipan before is appearance, 4) informaion used in he even analysis is he only one for he ime being available for he secor, company. There are some dispuable poins in he even analysis such as he lengh of even window and window of esimaion. The even window is a period in which he impac of informaion is analyzed. I can have fixed or flexible lengh bu he fixed windows may be used only for appropriaely large samples (due o he fac ha only in considerably numerous samples effecs of under- and overesimaed evens can be balanced). In he experimen fixed windows equal five days (wo days before he even, he day of he even occurrence and wo days afer he even) are applied wha will be furher explained. General rule is ha he even window should be as long as required so as o cover he whole even. I is also imporan o apply appropriae esimaion window. As opposed o he even window, his is he window used for esimaion parameers of he model for calculaions esimaed rae of reurn in even window. I is crucial o choose he esimaion windows wihou

7 Influence of recommendaions announcemens on sock prices disurbing evens. In realiy i is difficul o choose periods for pre-even windows wihou an influence of oher evens and o decrease heir impac bu no omi hem oally in he aricle he arificial variable z i is used for days of esimaion window: z i } z = {0,1, where i 1, he dae of even =. 0, he res of he days In he aricle esimaed and abnormal raes of reurns are used. Imporan sep of he even analysis is conneced wih choosing he righ dependence beween marke insrumen (in he aricle WIG20 index) and he insrumen analyzed (for insance sock prices). The mos common model is marke model [Gurgul 2006, p. 44]: Rˆ = α + β R, i, i i m, where: R ˆi, rae of reurn on sock prices in period, α i free parameer, β i sensiiviy of marke changes, rae of reurn on marke insrumen in period (e.g. index WIG20). R m, Parameers of his model are esimaed using OLS mehod: T 1 = 1 ( R R )( R R ) ˆ β =, i i, i m, m T 1 2 ( R 1 i, Ri) = 1 T 1 T 1 ˆ α ( ˆ i = R 1 i, β R 1, ) =, = m T 1 where: = 1,..., T 1 belongs o he group of indexes of observaions in pre-even window. T is an index of firs observaion in he even window. The model wih arificial variable Z i menioned above is applied in his analysis: Rˆ = α + β R + z. i, i i m, i Using arificial variable for abnormal raes of reurn esimaion in pre-even window, he evens wih he same direcion as he esimaed one (buy, sell or keep he sock) are aken ino analysis bu do no have he considerable impac on he resuls. Marke model was checked by economerical es for auocorrelaion, heeroscedasciy, normaliy of he residuals.

8 174 Małgorzaa Szulc-Janek 3. Daa The se of evens for he analysis was prepared on he basis of announcemens on he pages of sock marke newspaper Parkie. The assumpion was made ha recommendaions which appear here are firs recommendaions, his meaning ha hey have no been available for marke paricipans before. Only recommendaions from he bigges rade houses such as DM BZ WBK, DM BH, DB Securiies, ING Securiies, Millennium DM, DI BRE BANK were analyzed. The secor which is analyzed in he aricle is fuel secor due o las ime violaions, considerable number of evens and a share of he bigges fuel companies in marke index WIG20 (for companies creaing he index here is low probabiliy ha prices are he resuls of inside under he couner acions because hese companies are inensively examined by invesors, heir fundamenal informaion is analyzed horoughly). Moreover, he correlaion beween he liquidiy of he companies from his secor and possibiliy o manipulae wih oo opimisic or pessimisic recommendaions is no high. The ime horizon for analyzed socks is from June 2006 ill January Recommendaions o buy, sell or keep were analyzed separaely. The day of even was he day when he recommendaions appeared for he firs ime. If here were oher onedirecion recommendaions in he even window, hey were ignored. In he preeven window arificial variable for oher one-direcion recommendaions was applied. Wha was analyzed in he marke model applied were daily raes of reurn (logarihmic) calculaed according o he equaion: R = ln( P ) ln( P), where: P sock price in period. + 1 Addiionally in he analysis he following hypoheses were esed [Gurgul 2006, p. 77]: recommendaion BUY is a posiive signal from he marke and i generaes increases of he sock prices; recommendaion KEEP does no have any influence on he sock prices; recommendaion SELL is a negaive signal from he marke and i generaes decreases of he sock prices. The fixed even window is applied wih he lengh of five days (wo days before he even, he day of he even, wo days afer he even). This lengh is suggesed in lieraure of his subjec as wihin five days he even has go considerable impac on he prices. In mos cases wo days before is he period when price changes are conneced wih inside rading, influx of informaion coming from inside of he company. Day of he even is he day when marke verifies he price on he basis of informaion announced and wo days afer is he ime when he impac of he even is decreasing. According o he definiion of he even analysis only he days wih visible even impac can be couned for analysis and ha is why he win-

9 Influence of recommendaions announcemens on sock prices dow has go such lengh. I is checked if in he even window he abnormal raes of reurn are significan. Abnormal raes of reurn are calculaed according o he equaion [Gurgul 2006, p. 77]: AR = R E( R Ω ), i, i, i, EW where: Ω EW se of informaion in even window. Significance of esimaed raes of reurn is checked on he basis of saisical Suden es wih (N k 1) degrees of freedom: sa ˆ σ Nk = T 1 2 ˆ AR = ( AR ) AR = 0 Nk T 1 σ 1 Nk = 1 AR = T AR AR 0 + T 1 = 0 i,, AR, where: N k number of even in k group (for k = 1: buy, for k = 2: sell, for k = 3: keep), T' he lengh of esimaion window. The lengh of esimaion window (pre-even) is equal o 20, 25 and 30 days analysis is conduced for differen lenghs. 4. Empirical resuls Firsly, he possibiliy o apply linear marke model for he analysis was checked. The following ess were used: Durbin Wason auocorrelaion es, Goldfeld Quand heeroscedasciy es, Doornik Hansen normaliy of residuals es. The analysis was prepared wih he usage of GRETL. Resuls are shown in Table 1. Irrespecive of he pre-even window (20, 25 or 30 days of esimaion) he linear model can be used. The grea majoriy of each simulaion in every class in each esimaion window is showing he lack of auocorrelaion, homoscedasciy and normaliy of residuals. In he ables 2, 3 and 4 below resuls of Suden es obained for every day in he even window are shown. Presened AR is he average abnormal rae of reurn used for he whole sample of evens (N k is he number of recommendaions analyzed in each group in differen esimaion windows).,

10 176 Małgorzaa Szulc-Janek Table 1. Linear marke model verificaion Esimaion window Linear model esing resuls Tes % of success in simulaion BUY KEEP SELL GQ DW DH GQ DW DH GQ DW DH Source: own calculaions. I is noiceable ha in he firs group BUY here is no significan influence of recommendaions on he sock prices. Abnormal raes of reurn are insignifican. Very low effeciveness of recommendaion can be conneced wih difficulies wih inerpreaion, low level of confidence in analyss, risk aversion of he invesors on fuel marke. The bigges influence of he recommendaion is visible wo days before he even (day 2 ) or, depending on he lenghs of esimaion window a he day of he even (day 0 ). Consrucing models wih he usage of shorer esimaion windows is increasing he significance level of abnormal reurn in he day 0. Table 2. Resuls in he group BUY T' N k T e AR p-value T e AR p-value T e AR p-value Source: own calculaions.

11 Influence of recommendaions announcemens on sock prices Table 3. Resuls in he group SELL T' N k T e AR p-value T e AR p-value T e AR p-value Source: own calculaions. In he second group he resuls are also insignifican as above, however, considerably higher influence on sock prices is visible in his group. The significance is he highes on he day afer he recommendaion (p-value = 0.137). Opimal is he window for he pre-even period of 25 days. Table 4. Resuls in he group KEEP T' N k T e AR p-value T e AR p-value T e AR p-value Source: own calculaions. There is also, like in previous groups, insignifican impac of public announcemens on sock prices. Resuls from his class are worse han in BUY and SELL ones. The significance is higher for shorer pre-even windows. Invesors do no pay a lo of aenion o his recommendaion.

12 178 Małgorzaa Szulc-Janek 5. Conclusions To sum up here is no ground on he basis of saisical es used for saing ha recommendaions of analyss have go a significan impac on changes refleced in sock prices (significance level for his es was 5%). The highes influence was visible in he group SELL. Resuls in his group showed ha impac is visible afer he even, however, i is no considerable impac. There is no influence of insider dealers. Announcemens o BUY socks is no being refleced in he prices. I can be, as saed before, he resul of risk aversion and low confidence o financial insiuions or can indicae ha he marke is so effecive ha every informaion available on he marke has been already discouned and is embedded in he prices. Moreover, shorer esimaion windows resul in beer reacion of recommendaions on he sock prices. The mos difficul analysis was choosing he significan evens. This also can be applied so as o improve he resuls and furher assess he significance of he process more accuraely by applying discree wavele ransform which, on he basis of variaion analysis, is reflecing changes in sock prices. Moreover, no every ime series fixed even windows are correc. When sample is oo small such misakes like over- or underesimaions canno be eliminaed. Also dynamic prices wihin he whole day, no only closing prices may be a good maerial for even analysis. This may also resul in increasing significance of he announcemens. Lieraure Gurgul H., Analiza zdarzeń na rynkach akcji, Oficyna Ekonomiczna, Kraków McWilliams A., Siegel D., Even sudies in managemen research: Theoreical and empirical issues, Academy of Managemen Journal 1997, Vol. 40. Szablewski A., Pniewski K., Barosiewicz B., Value Based Managemen, Deloie, Polex, Warszawa Tabak D., Dunbar F., Maerialiy and Magniude: Even Sudies in he Courroom, NERA Working Paper, ANALIZA WPŁYWU REKOMENDACJI ANALITYKÓW NA CENY AKCJI BRANŻY PALIWOWEJ Sreszczenie: Zbadano, czy zgodnie z eorią efekywności rekomendacje analiyków w branży paliwowej przedsawione w rzech grupach: kupuj, rzymaj, sprzedaj, wpływają na kursy akcji. Ceny i sopy zwrou wypadkowe informacji rynkowych i syuacji makroekonomicznej obarczone są mankamenami psychologicznymi. Inwesorzy, podejmując decyzje, opierają się nie ylko na informacjach fundamenalnych spółek, ale akże na subiekywnych

13 Influence of recommendaions announcemens on sock prices przesłankach. Teoria rynku frakalnego zakłada chaoyczność w mechanizmach rynkowych i brak wpływu rekomendacji analiyków na graczy giełdowych. Do analizy wpływu rekomendacji na ceny użyo zwyżkowej sopy zwrou obliczonej za pomocą modelu rynkowego Sharpa oraz esu isoności Sudena. Wyniki świadczą o małym wpływie rekomendacji analiyków na ceny akcji, co jes zgodne z badaniami przedsawionymi w lieraurze przedmiou.