RISK DIVERSIFICATION BETWEEN STOCK MARKETS IN GERMANY AND BOSNIA AND HERZEGOVINA

Transcription

1 South East Europea Joural of Ecoomics ad Busiess - Special Issue ICES Coferece, Volume 9 (1) 2014, DOI: /jeb RISK DIVERSIFICATION BETWEEN STOCK MARKETS IN GERMANY AND BOSNIA AND HERZEGOVINA Azra Zaimović, Almira Araut Berilo * Abstract The itegratio of global equity markets has bee a well-studied topic i the last few decades, particularly after stock market crashes. Most studies have focused o developed markets such as the US, Wester Europe ad Japa. The fidigs were that the degree of iteratioal co-movemets amog stock prices has substatially icreased i the postcrash regime. I this paper we research the co-movemets of Germa ad Bosia stock markets durig ad after the recet ecoomic ad fiacial crisis. Iteratioal market itegratio meas that assets of equal risk provide the same expected returs across itegrated markets. This meas fewer opportuities for risk diversificatio if the markets are itegrated. It is also believed that stock market idices of itegrated markets move together over the log ru with the possibility of short-ru divergece. There is cosiderable academic research o the beefits of iteratioal diversificatio. Ivestors who buy stocks i domestic as well i foreig markets seek to reduce risk through iteratioal diversificatio. The risk reductio takes place if the various markets are ot perfectly correlated. The icreasig correlatio amog markets durig ad after the crises has restricted the scope for iteratioal diversificatio. Iteratioal stock market likages are the subject of extesive research due to rapid capital flows betwee coutries because of fiacial deregulatio, lower trasactio ad iformatio costs, ad the potetial beefits from iteratioal diversificatio. Most stock markets i the world ted to move together, i the same directio, implyig positive correlatio. I ad after crises they ted to move together eve more strogly. Thus, this paper aims to research if there are ay diversificatio opportuities by spreadig out ivestmets across developed ad uderdeveloped capital markets. This research attempts to examie the scope of iteratioal diversificatio betwee Germa ad Bosia equity markets durig the 6-year period from 2006 to We test the hypothesis of whether there are ay risk diversificatio possibilities by spreadig out the ivestmets betwee Germa ad Bosia equity markets. I order to determie the mea-variace efficiecy of portfolios we use the method of covex (quadratic ad liear) programmig. The hypothesis is tested with the Markowitz portfolio optimizatio method usig our ow software. Azra Zaimović, Ph.D. Assistat Professor of Fiace The results of this research might ehace the efficiecy of portfolio maagemet for both types of capital School of Ecoomics ad Busiess Uiverity of Sarajevo market uder aalysis, ad prove especially useful for istitutioal ivestors such as ivestmet fuds. azra.zaimovic@efsa.usa.ba Almira Araut-Berilo Keywords: Risk Diversificatio, Germa ad Bosia Assistat Professor of Quatitative Ecoomy Uiversity of Sarajevo Capital Markets, Markowitz method School of Ecoomics ad Busiess JEL Classificatio: G11, G32 almira.araut@efsa.usa.ba* Copyright 2014 by the School of Ecoomics ad Busiess Sarajevo Dowload Date 11/7/18 1:03 PM

2 1. INTRODUCTION Ivestors prefer holdig portfolios of securities rather tha a sigle security due to a risk-reductio effect called risk diversificatio. I additio to providig arbitrage opportuities, diversificatio is ofte called the free luch i fiace. Iteratioal stock market likages are the subject of extesive research for the followig reasos: (1) the rapid flow of capital amog coutries due to fiacial deregulatio, 1 (2) iformatio availability, (3) the reductio of trasactio costs, ad (4) the potetial gais from iteratioal diversificatio of ivestmet portfolios (I, Kim ad Yoo, 2002). Most stock markets i the world ted to move together, i the same directio, implyig positive correlatio. However, the icreasig correlatios amog developed ad emergig markets have restricted the scope of iteratioal diversificatio (Srivastava, 2007). Thus, this paper aims to research if there are ay diversificatio opportuities betwee two Europea, ad i may aspects differet equity markets: those of Germay ad Bosia & Herzegovia. This research examies the scope of iteratioal diversificatio over a six-year period before, durig ad after the recet crisis, from 2006 to We test the hypothesis of whether there are ay risk diversificatio possibilities by spreadig out ivestmets betwee Germa ad Bosia equity markets. The hypothesis is tested by statistical methods ad with the Markowitz portfolio optimizatio process (Markowitz, 1952, 1991). The research results might allow more efficiet securities portfolio maagemet o Europea capital markets. This paper is orgaized ito five sectios, icludig a itroductio. Sectio 2 outlies the theoretical backgroud ad methodology, Sectio 3 deals with data, Sectio 4 presets the results, ad i Sectio 5 we coclude the study. 2. THEORETICAL AND METHODOLOGICAL FRAMEWORK The itegratio of global equity markets has bee a well-studied topic i the last two ad a half decades, particularly sice the October 1987 stock market crash. Most studies are coducted for developed markets like the US, Wester Europe ad Japa. The fidigs were that the degree of iteratioal co-movemets amog stock prices has substatially icreased i the post-crash regime (Arshaapalli ad Doukas, 1993). After the Asia crisis, the literature started focusig o 1 The global fiacial ad ecoomic crisis has revealed the eed for ew regulatio of fiacial markets ad baks. emergig Asia markets as well. The recet fiacial ad ecoomic crisis has reewed the topic of capital market co-movemets. Iteratioal market itegratio has several defiitios. Oe states that assets of equal risk provide the same expected returs across itegrated markets. This meas that there are fewer opportuities for risk diversificatio if the markets are itegrated. The secod defiitio states that i itegrated markets atioal stock market idices move together over the log ru with the possibility of short ru divergece. Vizek ad Dadić (2005) researched multilateral itegratio betwee the emergig markets of Cetral ad Easter Europe (CEE) ad the Germa equity market for the period from Jauary 1997 till Jue The authors fid that the equity markets of Croatia ad other CEE emergig equity markets, amely those of Polad, the Czech Republic, Sloveia ad Hugary, are multilaterally itegrated. I additio, their results idicate multilateral itegratio betwee the CEE equity markets ad the Germa equity market. Whe aalyzig Croatia ad Germa equity markets aloe, they fid o evidece of bilateral itegratio. Zaimović ad Delalić (2010) ivestigate the risk diversificatio possibilities of the four West Balka capital markets: the Sarajevo, Baja Luka, Zagreb ad Belgrade Stock Exchages. By aalyzig the six mai stock market idices i a 34-moth period, from 2006 till 2008, they foud a low to medium positive statistically sigificat correlatio betwee idices returs pairs. The equally weighted portfolio of three idex fud stocks would have a very good stadard deviatio mea trade-off, lyig almost o the efficiet frotier. This study ecourages the creatio of idex replicatig fuds i the aalyzed markets. Withi the theoretical cotext of market itegratio, iteratioal stock market likages ad iterdepedece form a corerstoe of moder portfolio theory, especially i relatio to asset diversificatio. This theory suggests that ivestors diversify their assets across atioal borders as log as stock returs i other markets are less tha perfectly correlated with those of the domestic market (Masih ad Masih, 1997). Fiacial itegratio betwee equity markets ca be assessed by a differet methodology. Fratzscher (2001) used ucovered iterest parity, Korajczyk (1995) used multifactor Arbitrage Pricig Theory, Bekaert ad Harvey (1995) ad Dumas ad Solik (1995) used the Capital Asset Pricig Model. Co-itegratio aalysis is used to test the stability of log ru relatioship across fiacial markets (Dickiso, 2000, Vizek ad Tadić, 2005). Risk diversificatio has two basic sources: oe cocept was developed by Markowitz (1952) ad aother South East Europea Joural of Ecoomics ad Busiess - Special Issue ICES Coferece, Volume 9 (1) 2014 Dowload Date 11/7/18 1:03 PM 31

3 developed by Sharpe (1964). Markowitz itroduced the otio of a (mea-variace) efficiet portfolio that (1) provides miimum variace for a give expected retur or (2) provides maximum expected retur for a give variace. Diversifyig risk by selectig weakly correlated securities implies that the decisio is made based o iformatio about stadard deviatio ad correlatio betwee securities returs. This diversificatio is called Markowitz or efficiet diversificatio, because Markowitz was the first who developed the procedure for calculatig efficiet portfolios. Sharpe fids that oe ca reduce the risk of a portfolio just by addig radomly selected securities i a portfolio, i such a way that all the securities have the same but small weights. Through this procedure, usystematic risk is diversified, while systematic risk becomes the oly risk to be rewarded o the capital market. This approach does ot explicitly assume that the securities returs are ucorrelated. Sharpe calls this diversificatio radom diversificatio, essetially because a ivestor does ot have to kow iformatio about the stadard deviatio ad correlatio betwee securities returs. I this paper we adopted Markowitz s methodology to demostrate the diversificatio possibilities o the selected capital markets. The efficiet frotier of ay possible portfolio of stocks, regardless of the umber of stocks i the portfolio, lies betwee the portfolio with the miimum stadard deviatio (also miimum variace) ad the portfolio with the maximum rate of retur (mea). The portfolio with the maximum rate of retur is the upper, fial poit o the efficiet frotier. If the short sales are ot allowed, the fial portfolio (up o the right) i the efficiet frotier will always be represeted by oly the stock with the highest retur i the portfolio. The classical Markowitz portfolio model is used to determie the efficiet portfolios returs R p = Ri xi i= 1 ad portfolio variaces 2 σ p = x j xicov( Ri, R j ) (2) j = 1i = 1 if portfolio ivestmets satisfy the costraits xi = 1 i= 1 (3) x 0, i = 1, i (1) There are two types of costraits i this model. The first costrait appears i all models, ad it requires that the sum of all ivestmet weights be 1, with ivestmets x i ( i = 1, ) defied as portios of moey ivested i each idividual security i a portfolio. The other set of costraits requires that the ivestmet be o-egative, which meas that there is o ledig or short-sells. The mea-variace combiatio of securities is efficiet if there are o other portfolios with the same retur ad lower variace, or the same variace ad higher retur. I determiig the efficiet combiatio of a set of securities (or i efficiet portfolio determiatio) several optimizatio problems are detected. First, i this model the set of possible portfolios is limited, where the miimum limit is represeted by the portfolio with the lowest possible variace, ad the maximum limit beig the portfolio with the highest possible retur. I additio, i the very defiitio of the efficiet portfolio we ca see that for every rate of retur the lowest variace portfolio has to be determied, ad for every variace, the highest retur portfolio has to be determied. Let us assume a ivestor cosiders ivestig i a portfolio, with a give value of expected retur o ivestmet E, ad is iterested i the lowest variace with which the retur ca be achieved. The optimizatio model is formed as: miσ x 2 = i= 1 j = 1 xi = 1 i= 1 Ri xi i= 1 x σ x ij 0, i = E x j i = 1, 2 σ mi i where the costat E has to be betwee the efficiet portfolio with the lowest variace, R mi ad the efficiet portfolio with the highest expected retur, Rmax. If the followig is true E > Rmax, model (4) would be usolvable, ad if E < R mi the the solutio to the system (4) would ot be a elemet of the efficiet set. As a result of applyig the complemetary algorithm (used for solvig the quadratic programmig model 4) we will get the ivestmet vectors that provide the absolutely miimum portfolio retur variace with the pre-set retur E. By choosig a radomly expected retur of ivestmet i the rage Rmi E R max we ca determie the efficiet set of observed security. (4) 32 South East Europea Joural of Ecoomics ad Busiess Dowload - Special Issue Date ICES 11/7/18 Coferece, 1:03 Volume PM 9 (1) 2014

4 Figure 1: Set of possible portfolios ad Capital Market Lie R max E R mi r 0 M σ mi A σ max We have selected two characteristic portfolios, the miimum variace portfolio ad the portfolio with the best risk-retur trade-off (maximum Sharpe ratio). I Figure 1, these two portfolios are marked as M ad A, respectively. 3. DATA I order to measure diversificatio possibilities ad asset behavior i the Germa ad Bosia equity markets, we have determied ad aalyzed the efficiet portfolios formed from selected stocks from the Frakfurt Stock Exchage () ad the Sarajevo Stock Exchage (SASE), both apart ad together. Iput data for mea-variace (MV) aalysis are the last stock weekly prices sourced from the official webpage of the SASE 2 for the Bosia market ad from the Yahoo Fiace webpage 3 for stocks from the Germa market. The time iterval for diversificatio tests was determied by the global ecoomic crisis ad its effects o diversificatio possibilities o these two markets. The additioal criterio was the liquidity of stocks o the SASE. I 2006 the SASE itroduced the Multi Fixig Tradig Schedule (MFTS) for the most liquid stocks. I the same year turover o SASE was larger tha EUR 332 millio (BAM 650 millio), which is why we have chose the 2006 year for the begiig of our aalysis. Earlier periods o the SASE were characterized by low liquidity, irregular tradig activity ad a small umber of traded stocks. Thus, we have observed 2 Sarajevo Stock Exchage: (accessed i October 2011) 3 Yahoo Fiace: (accessed i October 2011) stocks i the period from the 3 rd of Jauary 2006 till the 1 st of Ju Stock returs were calculated o a weekly basis, based o capital gai/loss, ot icludig divided yield. Accordig to the research goals we have selected stocks from both equity markets that represet overall market movemets. Forty-three stocks have bee selected from the SASE. 4 These stocks have bee traded by the MFTS algorithm i the official market ad i the SASE primary free market. The overall proportio of these 43 stocks i all market turovers i the last three years (2009, 2010 ad 2011) is 51.8%. Moreover, the proportio of the umber of trasactios is eve higher, 77.85%. By aalyzig the collected data we realized that some stocks had less tha 20 weekly tradig data i the observed period. These stocks have bee removed from the sample. I the ed 22 stocks from the SASE represeted the Bosia equity market. 5 Sice the Germa equity market is large, we have selected 50 stocks from 9 differet idustries, which adequately represet the Germa market. There is much evidece that the risk of a portfolio of 40 eve radomly selected stocks cosists oly of market (diversifiable) risk, (Sharpe, 1964). Accordig to the aim of this research, we have divided the observed period ito three time samples: Jauary 2006 Jauary 2008, the period before the crisis, Jauary 2008 Jauary 2010, the period durig the crisis, Jue 2009 Jue 2011, the period after the crisis. There is a 6 moth overlappig period i 2009, due to the fact that the Germa ecoomy started recoverig i I additio, i this way we maaged to divide the 5.5 year-log period ito three equally log sub-periods; each sample cosists of 104 data. 4. RESULTS I order to test the diversificatio possibilities betwee the Germa ad Bosia equity markets i the observed sub-periods, we form MV efficiet portfolios of sample stocks from the ad test the effects of 4 We foud it iappropriate to use oly stocks icluded i idices from the SASE i our aalysis because of the meavariace iefficiecy of idices foud i previous studies (Araut-Berilo, Zaimović, 2012). 5 The missig data were supplemeted by the last occurrig price. The stocks with sufficiet liquidity had ormally distributed returs, at the same time. South East Europea Joural of Ecoomics ad Busiess - Special Issue ICES Coferece, Volume 9 (1) 2014 Dowload Date 11/7/18 1:03 PM 33

5 spreadig out the ivestmets to the sample stocks from the SASE i Figures 2, 3 ad 4. Figure 2: Efficiet portfolios i pre-crisis period 0,04 0,035 0,03 0,025 0,02 0,015 0,01 0, ,05 0,1 SASE +SASE Source: Authors from the official stock exchages databases, usig ow portfolio optimizatio software We use Sharpe ratio (SR) i measurig efficiet portfolio performaces, assumig that the risk free rate is zero 6, i.e. the capital market lie draw from the coordiate origi, (0.0). I additio to the graphical iterpretatio, where we see the efficiet lies shift, we have determied the structure of miimum variace portfolios ad the structure of portfolios with a miimum value of coefficiet of variatio 7 (CV). The last portfolios are highlighted as the portfolios with the smallest dispersio from the expected value. I additio, these portfolios show the chage of the efficiet frotier curvature. Figure 3: Efficiet portfolios i crisis period 0,02 0,015 0,01 0, ,005-0,01 0 0,02 0,04 0,06 0,08 0,1 fse fse + sase SASE Source: Authors from the official stock exchages databases, usig ow portfolio optimizatio software 6. Weekly risk-free rates i observed periods are very low, especially i ad after the crisis. 7 Portfolio with miimum value of CV has the steepest SR, if the capital market lie is draw from the coordiate origi. Our results show that the miimum variace of created portfolios is reduced i the case of combiig the Germa with the Bosia sample stocks i all three sub-periods. I additio, we get more domiat efficiet frotiers i the pre-crisis ad after-crisis periods. Figure 4: Efficiet portfolios i the post-crisis period 0,018 0,016 0,014 0,012 0,01 0,008 0,006 0,004 0, ,02 0,04 0,06 0,08 0,1 0,12 SASE + SASE Source: Authors from the official stock exchages databases, usig ow portfolio optimizatio software I Table 1 we preset the miimum variace portfolio characteristic values i all three sub-periods. I additio, we preset characteristic values of portfolios with the best risk-retur trade-off i Table 2. 8 We ote that i the pre-crisis period there is a beefit i expadig ivestmets from the Germa capital market to the Bosia. The miimum portfolio risk decreases from 1.36% to 1.08% if we spread out the ivestmets to 78% () versus 22% (SASE). The Sharpe ratio of best performig portfolio icreases from 0.50 to We foud o evidece of diversificatio possibilities i the crisis period. I this sub-period Bosia stocks are ot icluded i the optimal portfolio (the portfolio with the steepest Sharpe ratio). Based o this, as well as based o the aalysis of Figure 3, we ca coclude that the Bosia market was more affected by the global crisis tha the Germa. As we ca see from the Figure 4 ad from Tables 1 ad 2, i the post-crisis period the miimum portfolio risk o decreases from 1.43% to 0.8% if we spread out our ivestmet betwee the Germa (34%) ad Bosia markets (66%), but portfolio performace is lower. If we spread out our ivestmet betwee the Germa (70.63%) ad Bosia markets (29.37%) the best performig portfolio has the Sharpe ratio of 0.66 ad we are able to reduce the risk of our ivestmets. By comparig the results of the pre- ad post-crisis 8 The portfolio compositios of miimum variace portfolios i all sub-periods are available from the authors. 34 South East Europea Joural of Ecoomics ad Busiess Dowload - Special Issue Date ICES 11/7/18 Coferece, 1:03 Volume PM 9 (1) 2014

6 Table 1. Mi variace portfolio i observed periods Miimum Variace Portfolio i pre crisis period ad SASE Retur portio 77.90% Risk SASE portio 22.10% Sharpe Ratio Miimum Variace Portfolio i crisis period ad SASE Retur portio 34.70% Risk SASE portio 65.30% Sharpe Ratio N/A N/A Miimum Variace Portfolio i post-crisis period ad SASE Retur portio 34.10% Risk SASE portio 65.90% Sharpe Ratio Source: Authors Table 2. Characteristic values of portfolios with the highest Sharpe ratio i the observed periods Max Sharpe ratio ad SASE Retur portio 63.56% Risk SASE portio 36.44% Sharpe Ratio Max Sharpe ratio ad SASE Retur portio 100% Risk SASE portio 0% Sharpe Ratio Max Sharpe ratio ad SASE Retur portio 70.63% Risk SASE portio 29.37% Sharpe Ratio Source: Authors periods we fid differet diversificatio effects. The largest efficiet frotier shift is observed i the precrisis period, whe both markets obtaied similar MV efficiecy. I the pre-crisis period the miimum variace portfolio also provided a better Sharpe ratio tha the miimum variace portfolio of stocks, i cotrast to the post-crisis period whe the miimum variace portfolio (cosistig majorly of SASE stocks) has a lower Sharpe ratio tha the miimum variace portfolio of stocks. Moreover, SASE stocks participate with 29.37% i the portfolio with the steepest Sharpe ratio, created of stocks from both markets as show i Table 2. Sharpe ratio is the steepest i the post-crisis period compared to the pre-crisis ad crisis periods; durig the recovery most stocks ted to perform better. South East Europea Joural of Ecoomics ad Busiess - Special Issue ICES Coferece, Volume 9 (1) 2014 Dowload Date 11/7/18 1:03 PM 35

7 5. CONCLUSIONS We have aalyzed Germa ad Bosia equity markets diversificatio opportuities before, durig ad after the global fiacial ad ecoomic crisis. I geeral, the Germa equity market is more meavariace efficiet tha the Bosia. The Germa market, as a mature market, has lower market risk i all of the observed sub-periods, i.e. efficiet frotiers are situated more orth-west, especially i the post-crisis period. We used Sharpe ratio as a measure of portfolio performace. Based o this measure we fid that market risk i the Germa market rages from 3.49% i the pre-crisis period, 5.55% i the crisis-period to 1.59% i the post-crisis period, o a weekly basis. Iteratioal diversificatio amog aalyzed markets brigs additioal risk reductio. By spreadig out ivestmets betwee the Germa ad Bosia markets, portfolio risk decreases i the pre-crisis ad postcrisis periods. The best risk-retur trade-off ca be foud i the post-crisis period; the miimum variace portfolio s Sharpe ratio is 0.63, while the best performig portfolio has a Sharpe ratio of As expected, i the recovery period the expected returs icrease. We fid that the recet crisis has affected the Bosia market much more strogly tha the Germa market. I the crisis, the diversificatio effects amog aalyzed markets are egligible, i.e. the Germa market performed much better. The lack of diversificatio durig the crisis is i our opiio less due to the high itegratio betwee aalyzed markets tha the uderperformace of the Bosia equity market. Frotier equity markets should be see as a attractive supplemet to ivestmets i mature ad developed markets. We foud evidece of beefits from iteratioal diversificatio amog the Germa ad Bosia equity markets i the pre- ad post-crisis periods. REFERENCES Araut-Berilo, A., Zaimović, A How efficiet are Bosia stock market idices? Easter Europea Ecoomics Joural, M. E. Sharpe, 50 (1): Arshaapalli, B., Doukas, J Iteratioal Stock Market Likages: Evidece of Pre- ad Post-October 1987 Period Joural of Bakig & Fiace, 17 (1): Bekaert, G., Harver, C. R Time-varyig world market itegratio The Joural of Fiace, 50 (2): Dickiso, D. G Stock Market Itegratio ad Macroecoomic Fudametals: A Empirical Aalysis, Applied Fiacial Ecoomics, 10 (3): Dumas, B., Solik, B The World Price of Foreig Exchage Risk, Joural of Fiace, 50 (2): Fratzscher, M Fiacial Market Itegratio i Europe: o the Effects of EMU o Stock Markets, Workig Paper 48, Europea Cetral Bak I, F., Kim, S., Yoo, J. H Iteratioal Stock Market Likages: Evidece from the Asia Fiacial Crisis, Joural of Emergig Market Fiace, 1: Korajezyk, R A Measure of Stock Market Itegratio for Developed ad Emergig Markets, Policy Research Workig Paper 1482, World Bak Markowitz, H Portfolio Selectio, Joural of Fiace 7 (1): Markowitz, H. M Portfolio Selectio, Blackwell Publishig Masih, A. M. M., Masih, R A Comparative Aalysis of the Propagatio of Stock Market Fluctuatios i Alterative Models of Dyamic Causal Likages, Applied Fiacial Ecoomics, 7 (1): Sharpe, W. F Capital Asset Prices: A Theory of Market Equilibrium uder Coditios of Risk, The Joural of Fiace, 19 (3): Srivastava, A Coitegratio of Asia Markets with US Markets: Iteratioal Diversificatio Perspectives, Global Busiess Review, 8: Vizek, M., Dadić, T Itegratio of Croatia, CEE ad EU Equity Markets: Coitegratio Approach, Ekoomski pregled, 57 (9-10): Zaimović, A., Delalić, A Possibilities of Risk Diversificatio i Regioal Stock Exchages, Ekoomska istraživaja 23 (1): Iteret pages: (Sarajevo Stock Exchage, October 2011) (Frakfurt Stock Exchage, October 2011) (Yahoo Fiace, October 2011) 36 South East Europea Joural of Ecoomics ad Busiess Dowload - Special Issue Date ICES 11/7/18 Coferece, 1:03 Volume PM 9 (1) 2014