Linkages and Performance Comparison among Eastern Europe Stock Markets

Transcription

1 Easern Europe Sock Marke hp://dx.doi.org/ / x_39_4 Linkages and Performance Comparison among Easern Europe Sock Markes Faculdade de Economia da Universidade de Coimbra and GEMF absrac This aricle sudies he linkages among he sock markes of Bulgaria, Czech Republic, Esonia, Hungary, Poland, Romania, Russia, Serbia, Slovenia and Ukraine. The empirical analysis begins wih he esimaion of a regional marke model, whose bea parameers depend on predeermined informaion variables. Those parameers suppor he calculaion of ime-varying Treynor raios used on a comparaive performance analysis. A Vecor Auo Regressive Model (VAR) is used o esimae he performance causaliy wihin his group of markes. The VAR model resuls provide evidence ha here is reciprocal performance across he majoriy of he seleced sock markes. JEL Classificaion: F36, G15

2 Junho '14 / (71/81) Inroducion The empirical analysis of he presen aricle evaluaes he linkages beween he Easern Europe sock markes of Bulgaria, Czech Republic, Esonia, Hungary, Poland, Romania, Russia, Serbia, Slovenia and Ukraine. All he markes belong o former socialis economies, whose sock marke aciviy is relaively recen, and which are classified as emerging markes (Czech Republic, Hungary, Poland, Russia) and fronier markes (Bulgaria, Esonia, Romania, Serbia, Slovenia, and Ukraine), by he Morgan Sanley Capial Inernaional (MSCI) classificaion. The differences beween hose economies during he period under analysis is an addiional challenge o sudy he linkages beween heir sock markes. In fac his group includes Esonia and Slovenia, which are boh members of he European Union and of he Euro area, Bulgaria, Czech Republic, Hungary, Poland and Romania, which are members of he European Union bu no of Euro area, and Russia, Serbia and Ukraine, which are no members of he European Union. The procedure used o evaluae he linkages beween hese markes begins wih he esimaion of regional marke models. The parameers of he regional marke models suppor he calculaion of ime-varying Treynor raios, which are performance measures, and also can provide informaion on he marke prices of risk, if heir values are in close proximiy, according o he argumens presened by Adcock (2007). The marke model approach o financial inegraion analysis is srongly suppored by financial inegraion heory, since he seminal aricle of Solnik (1973) who proposed he firs asse pricing model in a perfecly inegraed financial marke. Furher developmens were made by Harvey (1991), who analysed he dependence of he world price of risk on macroeconomic and financial variables, and by Bekaer and Harvey (1995), who exended Harvey s sudy, o include he possibiliy of regime shifs which cause changes on he models parameers. The marke model esimaions in he presen aricle use a ime-varying beas approach, o ake ino consideraion he possibiliy of regime shifs. The major par of he aricles on he marke model, published during he sixies and he sevenies, were based on consan beas. However, he issue of beas variabiliy is presen in lieraure since he marke-iming procedure proposed by Treynor and Mazuy (1966) o evaluae he beas response o changes in he marke condiions. The limis of he explanaory power of consan beas were subjec o furher analysis by Fama and French (1992), which showed ha hey depend on firms and macroeconomic variables, and laer by Jagannahan and Wang (1996), who showed ha are unable o explain saisfacorily he average reurn across differen asses. Emerging and fronier sock markes are subjec o permanen changes in heir asses liquidiy, and marke capializaion. These changing condiions are naural sources of bea variabiliy, which will be aken ino consideraion in he presen aricle. The ime-varying beas approach used here is based on a recen conribuion o his problem, given by Adcock e al. (2012), who proposed he inclusion of predeermined informaion variables o capure bea variabiliy. This procedure is based on he assumpion ha asses reurns are uncondiionally disribued as an exended quadraic form of he predeermined informaion variables. An addiional advanage of his mehod is ha i can include he mos radiional answer o he bea variabiliy problem, he marke-iming procedure, as one of is paricular cases. The esimaion of he marke model wih ime-varying beas suppors he calculaion of Treynor raios, which are boh performance measures and essenial informaion on he inegraion beween hese markes. The linkages beween he Treynor raios of hese markes are esimaed by a Vecor Auo Regressive Model. This aricle is organized as follows. Secion 2 presens he heoreical background of he regional marke model esimaed, and of he comparaive performance analysis based on Treynor raios. Secion 3 presens he daabase and he resuls of he marke models esimaion. Secion 4 presens he Treynor raios calculaion and he esimaion of he Vecor Auo Regressive Model, ogeher wih Granger and Sims causaliy ess. The conclusion finishes he aricle.

3 Easern Europe Sock Marke 2. The heoreical background for he use of a marke model o sudy he linkages beween Easern Europe sock markes The sock marke model is a relaion beween he excess expeced reurn of an individual asse or porfolio, and he excess reurn of a marke porfolio. Similarly, an inernaional, or regional, marke model is he relaion beween a domesic marke porfolio and an inernaional (worldwide or regional) porfolio, and akes he following represenaion: ( ) ( ) α β ( ) E R r = + E R r (1) i f, i i, W f, where E (R i ) is he expeced reurn of he domesic porfolio on period, E (R W ) is he expeced reurn of he inernaional porfolio, during he same period, r f, is he inernaional risk free shorerm ineres rae, a i is he auonomous reurn componen of he domesic marke (no dependen on he inernaional facor), and b i, is he sensiiviy of he domesic marke expeced excess reurn of he inernaional sock marke. The esimaion of he inernaional marke model in he presen aricle uses wo predeermined informaion variables o explain he bea coefficiens variabiliy: he inernaional marke curren excess reurn (which is he marke-iming variable), and he lagged excess reurn of he domesic marke. The ime-varying bea parameers are defined as follows, according o his predeermined informaion variable approach: ( R r ) ( R r ) βi, = βi,0 + βi,1 W, f, + βi,2 i, 1 (2) f, 1 where b i,0 is he bea consan erm, b i,1 is he bea erm relaed o marke iming effec, i.e., he bea change caused by he inernaional index excess reurn, and b i,2 is he bea erm relaed o he lagged dependen variable, R i,-1 -r f,. The Treynor raios, proposed by Treynor (1965) o evaluae funds performance, are given by he following relaion beween excess reurn and bea parameers: T i, ( i ) E R r = β, f, i, The original Treynor raios were proposed o be calculaed wih consan beas. In he presen aricle, by he conrary, hey are calculaed using ime-varying beas, dependen on he predeermined informaion variables. The Treynor raios differences beween a group of counries are caused by heir auonomous reurn, represened by he consan a in he marke model. By consequence, if all he counries in he group are perfecly inegraed in he inernaional marke heir auonomous reurn componens are zero, and hus, heir Treynor raios are equal. According o Adcock (2007), he marke price of risk is a performance measure whose value is common o all he asses in a marke. This argumen can be exended o he inernaional level, when performance measures, here represened by he Treynor raios have he same value across differen markes. In ha case, he Treynor raio value is equal o he inernaional marke price of risk, and hose markes are perfecly inegraed. (3) 3. Esimaion of ime-varying bea marke models The empirical research of he presen aricle uses MSCI (Morgan Sanley Capial Inernaional) Indexes of he sock markes under sudy, expressed in Euros. The daabase consiss of daily

4 Junho '14 / (71/81) daa, covering he period beween he 1 s January 2009 and he 31 s December 2012, and comprising 1043 observaions of each naional index. The original series were ransformed ino new series whose values were 100, a 1 s January 2009, for all he indexes. The European Overnigh Ineres Average (EONIA) was used as a proxy of he shor-erm ineres rae. There are wo main reasons o choose his proxy of he risk-free asse. The firs reason is he absence of a money marke common o his group of counries. The second reason is ha EONIA is a variable suiable o represen he shor-erm opporuniy cos of invesing in hese Easern Europe counries, from he poin of view of an inernaional invesor. An equally weighed porfolio, composed by he domesic indexes of he daabase, was creaed o serve as regional index in his empirical analysis. The equally weighed porfolio offers several advanages over oher inernaional indexes, such as he Emerging Markes Index and he Fronier Markes Index, supplied by MSCI. In fac, none of he wo MSCI indexes covers he enire group of sock markes under analysis. Furhermore, he equally weighed index consruced in he presen aricle precludes he esimaion bias caused by differences of marke capializaion. The esable version of he model esimaed in his empirical analysis is he following: ( ) R r = α + β R r + ε (4) i, f, i i, W, f, i, where R i, -r f, is he ex pos excess curren reurn of he counry i sock index, R W, -r f, is he excess reurn of he regional index, and e i, is he error erm. The marke model was esimaed under he assumpion ha he residual series, e i,, follow 2 GARCH(p,q) models, according o which heir condiional volailiy, h, akes he following general represenaion: q p = 0 + i i + jh j i= 1 j= 1 h φ φ ε θ (5) This procedure correcs he auoregressive heeroskedasiciy pu in evidence by preliminary esimaions. Table I, Panel A, presens he resuls of he esimaions of he bea coefficiens of he Euro area marke model and he GARCH processes. The sandardized residuals (i.e. he residuals divided by he squared roo of he condiional variance) were esed for auocorrelaion, by a Ljung-Box es, and for ARCH (Auoregressive Condiional Heeroskedasiciy) by an F es on he coefficiens of he following auo regressive model: l *2 *2 i, = a + bj i, j + i, (6) j= 1 ε ε µ where εi *, = εi, / hi, is he sandardized residual of he esimaion of he marke model. Boh he Ljung-Box es and he ARCH es were carried ou for a maximum of 24 lags, wih a span of 4 lags. The resuls of he ess for residual auocorrelaion, represened in Table I, Panel B, show ha he residuals of he esimaions are no auo correlaed. Table I, Panel C, shows he resuls of he ess of ARCH effecs on he squared sandardized residuals. According o hese resuls, he GARCH models esimaed enirely eliminae he ARCH effecs from he regressions residuals. The esimaions resuls show ha GARCH(1,1) is suiable o explain he residual volailiy in he esimaions of he marke model of almos all hese domesic indexes, he only excepion being Romania, which required a GARCH(2,1).

5 Easern Europe Sock Marke Table I - Marke Model Esimaions

6 Junho '14 / (71/81) Table I - Marke Model Esimaions (con.)

7 Easern Europe Sock Marke Table II shows he saisics of he ime-varying beas, which include he mean, sandarddeviaion, minimum and maximum. The average of he beas mean is The domesic markes whose mean beas are closer o he average are Esonia, Serbia and Poland. The domesic markes wih he mean beas more disan from he average are Hungary and Slovenia, which indicaes a weak linkage beween hese wo markes and he ohers. Addiionally, several cases of negaive beas calculaed for Hungary and Slovenia, preclude he calculaion of Treynor raios for hese wo markes. Thus he sock indexes of Hungary and Slovenia are excluded from he Treynor raios linkage analysis, presened in he following secion. Table II - Basic Saisics on Time-Varying Beas Mean Sd. Error Min Max Bulgaria Czech R Esonia Hungary Poland Romania Russia Serbia Slovenia Ukraine Average A Vecor Auoregressive model on performance ransmission beween he differen domesic indexes Some ex pos excess reurns have negaive values, which produce negaive ex pos Treynor raios. As shown by Fonseca (2013), ex pos excess reurns mus be scaled o be non-negaive, by adding a consan, o all of hem, when Treynor raios are used for he purpose of porfolio consrucion. This procedure was also used in he presen aricle, by adding a consan erm, c, o he ex pos excess reurns, before he calculaion of ex pos Treynor raios. The value given o he consan is c= -min(r i, -r f, ), which, aking ino consideraion ha min(r i, -r f, )<0, ensures ha posiive values are calculaed for he Treynor raios. Thus, he final formula for he modified Treynor raios, whose basic saisics are presened in Table III, becomes: T i, Ri, rf, + c = β i, (7) The basic saisics of he Treynor raios show ha he sock markes whose Treynor raios mean is closer o he sample average are Esonia, Poland and Serbia.

8 Junho '14 / (71/81) 78 Table III - Basic Saisics on he Modified Treynor Raios 79 Mean Sd. Error Min Max Bulgaria Czech R Esonia Poland Romania Russia Serbia Ukraine Average The performance ransmission beween hese eigh markes was esimaed by a VAR model, modified o include leads. The lags influence on he variables curren values, designaed in lieraure by Granger causaliy, depends on observed pas daa. By he conrary, he leads influence on he variables curren values, designaed in lieraure by Sims causaliy, depends on he forecas capabiliy of he markes paricipans, which is more limied han heir abiliy o follow pas informaion. Thus, he esimaed VAR has he following general represenaion: I [ TR ] = A0 + Ai [ TR + i ] + Aj TR j + [ ε ] (8) i= 1 j= 1 J where [TR ] is a vecor of curren values of he Treynor raios (each value refers o one domesic sock marke), A 0 is he consan erms vecor, A i and A j are parameers marices, [TR +j ] is a vecor of lead values of he Treynor raios, I is he VAR lead-lengh, [TR -i ] is a vecor of lag values of he Treynor raios, J is he VAR lag-lengh model, and [e ] is he vecor of error erms. The deerminaion of he VAR lag-lengh, and he VAR lead-lengh was based on he calculaion of he Akaike Informaion Crieria (AIC) and he Schwarz Bayesian Crieria (SBC), which are defined, respecively, as follows: AIC = T log Σ + 2N ( ) SBC = T log Σ + N log T (9) where T is he number of usable observaions, S is he deerminan of he variance/ covariance marix of he residuals, and N is he oal number of parameers esimaed in all equaions. The deerminaion of he VAR lead and lags lenghs was done in wo separae seps. In he firs sep, he number of leads was fixed o be equal o one, and he AIC and SBC saisics were calculaed for five differen lags, i=1,...,5. The lag-lengh was chosen according o saisics resuls in he firs sep, and i was used as a fixed value in he second sep, in which he AIC and SBC saisics were calculaed for five differen leads, j=1,...,5. The resuls of he calculaion of he AIC and SBC saisics are shown in he Table IV.

9 Easern Europe Sock Marke Table IV - AIC and SBC Saisics on he Treynor Raios VAR Model Panel A) Lag-lengh deerminaion (lag-lengh =1) Lag AIC SBC Panel B) Lead-lengh deerminaion (lead-lengh =3) Lead AIC SBC According o he resuls shown in Table IV- Panel A) he AIC saisic indicaes ha he VAR laglengh is of 3 lags, while he SBC saisic indicaes a VAR lag-lengh of 1 lag. The 3 lag-lengh was chosen o be included in he lead-lengh calculaions. The resuls of hese calculaions, repored in Panel B, show ha AIC and SBC saisics converge o a 1 lead-lengh. Taking ino consideraion he AIC and SBC resuls, he Treynor raios VAR model used in he causaliy ess includes 3 lags and 1 lead. The resuls of causaliy ess, given by he F saisics of he VAR model esimaions, are shown in Table V Panel A) for Granger causaliy and in Table V Panel B) for Sims causaliy. According o he saisics significan a he 1%, 5% and 10% levels, he dominan marke, in Granger causaliy, is he Polish sock marke, whose lagged Treynor raios influence he performance of five oher markes. This sock marke is followed by he Czech, Romanian and Serbian sock markes which have Granger causaliy on hree oher sock markes. No significan Granger causaliy is pu in evidence from he sock markes of Bulgaria, Esonia, Russia and Ukraine. The resuls on Sims causaliy, presened in Panel B, which are significan a he 1%, 5% and 10% levels, provide evidence ha he influence of he forward performance of each marke on he oher is of five cases, from Czech Republic and Ukraine, four cases from Serbia, hree cases from Bulgaria and Esonia, wo cases from Romania and one case from Poland and Russia.

10 Junho '14 / (71/81) Table V - VAR Model Causaliy Tess Panel A - F Saisics on Granger causaliy Dependen variables Bulgaria Czech R. Esonia Poland Romania Russia Serbia Ukraine Bulgaria Czech R *** *** *** Esonia Poland ** *** *** *** *** ** Romania ** *** Russia * ** Serbia ** * * Ukraine Panel B - F Saisics on Sims causaliy Dependen variables Bulgaria Czech R. Esonia Poland Romania Russia Serbia Ukraine Bulgaria * *** * Czech R *** *** *** *** *** Esonia *** *** *** Poland ** Romania ** ** Russia *** Serbia ** *** ** *** Ukraine *** *** *** *** *** Noe: ***, **, and * denoe saisical significance a he 0.01, 0.05, and 0.1 levels.

11 Easern Europe Sock Marke 5. Conclusion The presen aricle sudies he linkages beween he Easern Europe sock markes of Bulgaria, Czech Republic, Esonia, Hungary, Poland, Romania, Russia, Serbia, Slovenia and Ukraine. A regional index was consruced o esimae marke models, using an approach wih bea parameers depending on predeermined informaion variables. The markes whose bea values are closer o he whole sample average are Serbia, Esonia and Poland. On he opposie siuaion are Hungary and Slovenia, wih bea values disan from he whole sample average, which indicaes a weak linkage beween hese wo markes and he ohers. Addiionally, he marke model esimaion for Hungary and Slovenia produced several cases of negaive beas which preclude heir inclusion in he comparaive performance analysis. The esimaion of he marke models was followed by he analysis of he performance causaliy beween hese sock markes, hrough he esimaion of a VAR model on heir Treynor raios. The causaliy ess, suppored by he VAR esimaion, provided a clear evidence of he reciprocal performance influence across he majoriy of hese markes, boh in erms of Granger causaliy and Sims causaliy. References Adcock, C. (2007) Measuring porfolio performance using a modified measure of risk, Journal of Asse Managemen, 7, Adcock, C.; Corez, M.C.; Armada, M.R.; Silva, F. (2012) Time varying beas and he uncondiional disribuion of asse reurns, Quaniaive Finance, 12(6), Bekaer, G.; Harvey, C. (1995) Time-Varying World Inegraion, Journal of Finance, 50(2), Fama, E.; French, K. (1992) The Cross-secion of expeced reurns, Journal of Finance, 47(2), Fonseca, J.S. (2013) Innovaions in reurn ransmission and performance comparison beween he five bigges Euro area sock markes, Inernaional Economics and Economic Policy, 10(3), Harvey, C. (1991) The World Price of Covariance Risk, Journal of Finance, 46(1), Huang, W. (2011) Financial inegraion and he price of world covariance risk: Large-vs. Small cap socks, Journal of Inernaional Money and Finance, 26(8), Jagannahan, R.; Wang, Z. (1996) The condiional CAPM and he cross-secion of expeced reurns, Journal of Finance, 51(1), Solnik, B. (1974) An Equilibrium Model of Inernaional Capial Marke, Journal of Economic Theory, 8, Treynor, J. (1965) How o rae managemen invesmen funds, Harvard Business Review, 43(1), Treynor, J.; Mazuy, M. (1966) Can Muual Funds Ouguess he Marke?, Harvard Business Review, 44(4),