Possibilities of Applying Markowitz Portfolio Theory on the Croatian Capital Market

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POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL MARKET

Dubravka Pekanov Starčević, Ph.D. J. J. Strossmayer University of Osijek, Faculty of Economics in Osijek E-mail: [email protected]

Ana Zrnić, Ph.D. Student, J. J. Strossmayer University of Osijek, Faculty of Economics in Osijek E-mail: [email protected]

Tamara Jakšić, BEcon, student J. J. Strossmayer University of Osijek, Faculty of Economics in Osijek E-mail: [email protected]

Abstract In order to achieve the maximum possible profit by taking the lowest possible risk, investors build a stock portfolio consisting of a specific number of stocks which, according to the principle of diversification, significantly reduce the risk of loss. To build a portfolio, in developed capital markets investors have used the Markowitz portfolio optimization model for many years that enables us to find an optimal risk-return trade-off by selecting certain stock combinations. Despite the development of the Zagreb Stock Exchange, i.e., the central trading venue in the Republic of Croatia, the Croatian capital market is still underdeveloped. It is characterized by numerous shortcomings such as low liquidity, lack of transparency, high stock price volatility and insufficient traffic. Accord- ingly, the aim of this paper is to provide an insight into the functioning of the POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara

520 Croatian capital market and to examine the possibility of building an optimal stock portfolio by using the Markowitz model. The analysis was carried out on a sample of seventeen stocks of companies listed on Zagreb Stock Exchange, which were taken for analysis on the basis of the following criteria: liquidity, affiliation to certain sectors and a positive financial result. The results have shown that underdeveloped capital markets, like the Croatian capital market, have some shortcomings that are, to a greater or lesser extent, problems in the proper application of the Markowitz model. Keywords: stock portfolio, Croatian capital market, Markowitz portfolio optimization model, risk diversification, efficient frontier JEL Classification: G11, O16

1. INTRODUCTION In recent times, entities have started to move away from traditional forms of saving in banks and invest their money in capital market instruments. The capital market is a meeting place for supply and demand of long-term securities - stocks and bonds. Regardless of the type of securities an investor invests in, each investor aims at earning profits in the future. However, they are aware of the fact that such investments carry a certain risk of loss. Given their attitude to risk, investors may be risk-averse, they may be more prone to risk or completely indifferent to risk. Taking a greater risk offers the possibility of achieving higher total returns and vice versa. When investing, investors should take into account the principle of diversification. In other words, they need to invest in a variety of different securities, thus reducing the risk of losing the funds invested. The fundamental question is how to find a combination of securities that will allow a maximum return to being achieved at an acceptable level of risk. In 1952, Harry Max Markowitz developed a model that allows for finding an optimal risk-return trade-off by selecting a particular combination of securities. By applying the model, investors can build an optimal portfolio that will consist of those securities that promise the highest possible return at the level of risk they are willing to accept. The model is based on several basic assumptions, such as returns that are normally distributed, the existence of rational investors and the existence of a liquid and efficient market. Although there has been a lot of criticism of the applicability of the model, it has been applied in more INTERDISCIPLINARY MANAGEMENT RESEARCH XV

521 developed markets for many years and it is used as a basis for developing new, more complex models. Due to numerous recent crises in capital markets, it is very important for investors to make a good investment decision in order to protect themselves from potential investment losses. The application of the Markowitz model for the purpose of finding an optimal portfolio is certainly efficient in more favor- able market conditions, but its applicability is questionable in underdeveloped markets, such as the Croatian market, that do not meet the basic assumptions of the model. This paper analyses the application of the Markowitz model to theC roatian capital market. Despite the development of the Zagreb Stock Exchange as the central trading venue in the Republic of Croatia, the Croatian capital market is still underdeveloped. It is characterized by numerous shortcomings such as low liquidity, lack of transparency, high stock price volatility and insufficient traffic. Accord- ingly, the aim of this paper is to determine whether, despite the aforementioned problems, the model can provide satisfactory results. The aim is also to clarify the theoretical assumptions of the Markowitz model and its applications, provide an insight into the situation on the Croatian capital market and examine the possibility of building an optimal stock portfolio by using the Markowitz model. Four research hypotheses have been set up according to the research subject. The main hypotheses: • The Markowitz model is applicable to the Croatian capital market. • An increased number of stocks in the portfolio reduces the overall risk. Auxiliary hypotheses: • All joint stock companies whose shares are part of the CROBEX index achieved a positive financial result in 2017. • The selected optimal portfolio will be sectorally diversified.

2. LITERATURE REVIEW When building a portfolio, most investors want to take advantage of the ben- efits of diversification in order to achieve the expected return with the least risk possible. The key issue here is how to determine and measure the optimal risk- return trade-off. Fabozzi et al. (2002) state that the trade-off between risk and return is explained by modern portfolio theory (MPT). Harry Max Markowitz POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara

522 is considered the founder of modern portfolio theory. Although the fundamen- tals of the portfolio model were set up in 1952, seven years later, he developed a theory according to which it is possible to achieve the optimal risk-return trade- off by selecting a certain combination of securities. Xia et al. (2000) state that the basis of the Markowitz model is to achieve the expected return of a portfolio as return on investment and variance of the expected return of a portfolio as investment risk. Accordingly, Wang & Zhu (2002) indicate that every investor has the following two goals: to maximize the expected return and to minimize portfolio risks. Therefore, the Markowitz model is a mathematical model that enables us to find such a combination of securities that will enable investors to achieve the highest possible return at the level of risk they are willing to accept. A portfolio consisting of such securities is called an efficient portfolio. An efficient portfolio is a portfolio that, among all combinations of the same level of risk, promises the highest return, i.e., the one which, of all combinations, gives the same return at the lowest risk (Sharpe; 1963, 278; Mao & Särndal; 1966, 324). The Markowitz model (1952) is based on several basic assumptions: returns on stocks are normally distributed, investors want to maximise their economic utility, investors are rational and risk-averse, investors are well informed about all relevant facts necessary to make an investment decision, there are neither transaction nor tax costs and securities are perfectly divisible. One of the assumptions of the model is that investors are risk-averse and that they wish to maximise their profit or wealth. Steinbach (2001) explains that the final issue in the portfolio selection context is related to how investors forecast the future, which is presented by the probability of property restitution. If the investors have to choose between two securities that will enable them to achieve the same return, they will choose the one with a lower risk of loss. The investors will be prepared to assume a higher risk only if it will enable them to achieve a much higher return. Hence, when selecting a portfolio, a rational investor will always invest in the portfolio with the best trade-off between risk and return, i.e., in the one that yields a higher expected return for the same level of risk. Although the Markowitz model is one of the most significant innovations in the area of portfolio construction, his basic assumptions have been criticised. Jerončić & Aljinović (2011) criticise the assumption referring to returns on stocks that are normally distributed since they are the result of prices formed by market forces that are not random but are based on economic rules as well as investor’s forecasts and expectations. This deviation from normal distribution becomes INTERDISCIPLINARY MANAGEMENT RESEARCH XV

523 evident during the economic crisis or exceptional economic progress. It is also considered that the assumption about risk-averse investors is not fully accurate, that investors cannot be fully informed and have at their disposal all the facts necessary to make a good investment decision. Omisore et al. (2011) point out that the theory does not take into account the personal, ecological, strategic or social dimensions of investment decisions. An obstacle to the model includes the absence of transaction and tax costs and the assumption that securities can be perfectly divisible. Nevertheless, it is undeniable that Markowitz’s theory has enabled previous analyses to be supplemented by new statistical methods and that it represents a very important portfolio management tool. The contribution of Markowitz’s theory is also reflected in the ability of companies to diversify their risks, i.e., to reduce the risk of an entire portfolio by increasing the number of securities, which is the fundamental principle investors must stand by when building portfolios. However, risk is reduced by intensifying diversification, so it is not desirable to form a portfolio that will consist of a large number of securities. The number of securities that make up a diversified portfolio is the subject of numerous studies (Statman, 1987; Evans & Archer, 1968). The trade-off between risk and return is analyzed based on a probability distribution. The following two basic probability distribution parameters are applied: the expected return and variance, i.e., standard deviation. Each individual The trade-off between risk and return is analyzed based on a probability distribution. The following two basic probabilityportfolio distribution is determined parameters by its are return applied: and therisk expected and a certain return numberand variance, of securities i.e., standard deviation. Each individualcan be portfolio used to isbuild determined a portfolio. by its A return set of and portfolios risk and givena certain in Figurenumber 1 of is securitiesobtained can be used to build a portfolio.by showing A set of all portfolios possible givenportfolios in Figure in the 1 iscoordinate obtained by system. showing all possible portfolios in the coordinate system.

FigureFigure 1. A set 1. of A possible set of portfoliospossible portfolios

Source: Aljinović et al., 2011:135 Source: Aljinović et al., 2011:135

The shaded area shows possible combinations of multiple investments, and it represents the trade-off between POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara risk and returns referring to these investments. Standard deviations and the expected portfolio returns are shown on the horizontal and the vertical axis, respectively. On the left-hand side, a set of possible portfolios is bounded by a 524line called a set of minimum variances.

Figure 2. A set of minimum variances

Source: Authors’ elaboration

Figure 2 shows a set of portfolios that have the minimum standard deviation for a certain level of return. Given that the minimum standard deviation implies the smallest risk possible, the portfolios on the line represent the dominant portfolios that should be observed as the only ones when finding efficient portfolios. However, not all dominant portfolios are efficient portfolios. If we look at Figure 2 again, we can see a portfolio marked with a dot. This portfolio is located closest to the vertical axis and it divides the line into two parts, with efficient portfolios on the upper part of the line and inefficient portfolios on the lower part of the line, since at the same level of risk they yield lower returns. Thus, a set of efficient portfolios is located at the upper left boundary of a set of potential portfolios, and this boundary is called the efficient frontier.

The trade-off between risk and return is analyzed based on a probability distribution. The following two basic probability distribution parameters are applied: the expected return and variance, i.e., standard deviation. Each individual portfolio is determined by its return and risk and a certain number of securities can be used to build a portfolio. A set of portfolios given in Figure 1 is obtained by showing all possible portfolios in the coordinate system.

Figure 1. A set of possible portfolios

The shaded area shows possible combinations of multiple investments, and Source: Aljinovićit representset al., 2011:135 the trade-off between risk and returns referring to these investments. Standard deviations and the expected portfolio returns are shown on The shaded area shows possible combinations of multiple investments, and it represents the trade-off between risk and returnsthe referring horizontal to these and investments.the vertical Standardaxis, respectively. deviations On and the the left-hand expected portfolioside, a set returns of are shown on the horizontalpossible and the portfolios vertical axis,is bounded respectively. by a lineOn thecalled left-hand a set ofside, minimum a set of possible variances. portfolios is bounded by a line called a set of minimum variances.

Figure 2. A setFigure of minimum 2. A variances set of minimum variances

Source: Authors’ elaboration Source: Authors’ elaboration

Figure 2 shows aFigure set of portfolios2 shows athat set have of portfolios the minimum that standa haverd the deviation minimum for astandard certain level devia of- return. Given that the minimum standard deviation implies the smallest risk possible, the portfolios on the line represent the dominant portfoliostion for that a certainshould belevel observed of return. as the G onlyiven ones that wh theen minimum finding efficient standard portf deviationolios. However, not all dominant portfoliosimplies are the efficient smallest portfolios. risk possible, If we thelook portfolios at Figure on2 again, the line we representcan see a theportfolio domi marked- with a dot. This portfolionant portfolios is located that closest should to the be vertical observed axis as and the itonly divides ones the when line finding into two efficient parts, with efficient portfolios on the upper part of the line and inefficient portfolios on the lower part of the line, since at the same level of risk theyportfolios. yield lower However, returns. not Thus, all adominant set of efficien portfoliost portfolios are isefficient located at portfolios.the upper leftIf boundarywe of a set of potentiallook portfolios, at Figure and 2 this again, boundary we can is seecalled a portfolio the efficient marked frontier. with a dot. This portfolio is located closest to the vertical axis and it divides the line into two parts, with efficient portfolios on the upper part of the line and inefficient portfolios on the lower part of the line, since at the same level of risk they yield lower returns. Thus, a set of efficient portfolios is located at the upper left boundary of a set of potential portfolios, and this boundary is called the efficient frontier. INTERDISCIPLINARY MANAGEMENT RESEARCH XV

525 Figure 3. The efficientFigure frontier 3. The efficient frontier

Source: Authors’ elaboration Source: Authors’ elaboration

3. METHODOLOGY 3. METHODOLOGY Data referring to stocks selected for analysis are downloaded from the official Zagreb Stock Exchange (ZSE) website. The choiceData of referring stocks that to will stocks form selected the initial for sample analysis is primarily are downloaded based on the from liquidity the criterion. of- According toficial Jerončić Zagreb & Aljinovi Stockć (2011), Exchange as a r ule,(Z SE)stock website. liquidity shouldThe choiceensure fair of valuationstocks that of the will stock itself, becauseform in theory the initiala large samplenumber ofis primarilytransactions based the co nvergenceon the liquidity of the stock criterion. price to According the equilibrium price of supply and demand, which depend on investor expectations and market conditions. to Jerončić & Aljinović (2011), as a rule, stock liquidity should ensure fair valu- 3.1. Sampleation description of the stock itself, because in theory a large number of transactions the

The initial sampleconvergence consists of of stocks the stockincluded price in CROBEX, to the equilibrium an official index price of of Zagreb supply Stock and Exchange. demand, Table A1 in the annexwhich shows depend a list of on stocks investor that were expectations included in thande CROBEX market indexconditions. on 19 March 2018 on the basis of a regular audit of the Index Committee and that are, as such, included in the initial sample for the formation of an optimal stock portfolio. Apart from creating a portfolio with an optimal trade-off between risk and return, it should also be sectorally diversified. The3.1. companies Sample whose description stocks are included in the initial sample for the formation of an optimal portfolio are grouped into individual sectors depending on their main business activity. For the purpose of classifying companiesThe intoinitial sectors sample based consists on their mainof stocks activity included, the Zagreb in C ROBEX,Stock Exchange an official uses the Nationalindex Classificationof of ZActivitiesagreb Stock 2007 (OG Exchange. 58/07 and Table 72/07). A1 Sectors in the are determinedannex shows based a onlist the of A*38 stocks intermediate- that level aggregation,were whichincluded consists in the of 38CROBEX categories. index Table on A2 19 in theMarch annex 2018 shows on that the the basis selected of a regu stocks- are grouped into twelve different sectors, indicating a high likelihood of forming a sectorally diversified optimal portfolio. lar audit of the Index Committee and that are, as such, included in the initial Financial statementsample analysis for the of formation joint stock companiesof an optimal was carri stocked outportfolio. with the aim of eliminating undesirable stocks, which led to a reduction in the sample to be used for the Markowitz model. In order to identify undesirable stocks,Apart we from calculated creating financial a portfolio indicators with clustere an optimald into the trade-off following between five different risk groups:and profitability indicators, activity indicators, liquidity indicators, debt indicators, and investment indicators. Consolidated return, annual financialit should statements also be for sectorally 2017 of all diversified. joint stock companies The companies from the initial whose sample stocks were analyzed. Theare results included of the analysis in the areinitial shown sample in Table for 1. the formation of an optimal portfolio are

Table 1. Financialgrouped indicators into ofindividual joint stock sectorscompanies depending for 2017 on their main business activity. For STOCK theEPS purpose ROE of classifyingROA Turno companiesTurno into sectorsP/E P/BVbased onBVPS their Curremain activity,Quick Debt the(in Zagreb Stock Exchangever uses thever National ClassificationPS (in of Activitiesnt ratio2007 ratio HRK ratio ratio HRK) ratio (O) G 58/07 and 72/07). SectorsDI areKI determined based on the A*38 interme- ADPL diate-level16.82 9.36% aggregation, 5.85% which 1.19 consists 2.52 of 38 11.77 categories. 1.11 Table 178.54 A2 in 1.10 the annex 0.70 44.51% ADRS2 shows18.12 that 3.63% the selected 2.24% stocks 0.32 are grouped 1.02 into 27.04 twelve 0.78 different 627.13 sectors, 1.16 indicat 1.04- 47.80% ARNT 20.87 5.63% 4.17% 0.39 0.87 20.41 1.40 305.28 4.98 4.95 41.50% ATGR CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara ing82.69 a high 12.28% likelihood 6.96% of forming 1.87 a sectorally 2.41 12.34 diversified 1.51 optimal 674.76 portfolio. 1.47 1.11 56.11% ATPL 58.85 14.42% 5.71% 0.41 5.17 8.12 1.18 404.87 0.24 0.18 59.06% DDJH 526-3.19 -39.54% -5.19% 1.45 2.17 -5.24 1.96 8.51 0.77 0.42 83.84% DLKV 0.50 5,23% 2.13% 2.95 1.81 26.70 1.40 9.56 1.19 1.05 82.06% ERNT 51.13 28.81% 8.90% 6.97 2.41 20.63 5.96 177.12 1.10 1.10 71.34% HT 10.55 6.39% 6.25% 0.76 1.48 14.22 0.98 153.54 2.20 2.15 20.11% IGH - -22.09% -2.61% 0.83 2.12 -7.52 -1.86 -82.11 0.39 0.39 111.82% 20.34 Financial statement analysis of joint stock companies was carried out with the aim of eliminating undesirable stocks, which led to a reduction in the sample to be used for the Markowitz model. In order to identify undesirable stocks, we calculated financial indicators clustered into the following five different groups: profitability indicators, activity indicators, liquidity indicators, debt indicators, and investment indicators. Consolidated annual financial statements for 2017 of all joint stock companies from the initial sample were analyzed. The results of the analysis are shown in Table 1.

Table 1. Financial indicators of joint stock companies for 2017

STOCK EPS (in HRK) ROE ROA Turnover DI ratio Turnover KI ratio P/E P/BVPS BVPS (in HRK) ratio Current ratio Quick Debt ratio ADPL 16.82 9.36% 5.85% 1.19 2.52 11.77 1.11 178.54 1.10 0.70 44.51% ADRS2 18.12 3.63% 2.24% 0.32 1.02 27.04 0.78 627.13 1.16 1.04 47.80% ARNT 20.87 5.63% 4.17% 0.39 0.87 20.41 1.40 305.28 4.98 4.95 41.50% ATGR 82.69 12.28% 6.96% 1.87 2.41 12.34 1.51 674.76 1.47 1.11 56.11% ATPL 58.85 14.42% 5.71% 0.41 5.17 8.12 1.18 404.87 0.24 0.18 59.06% DDJH -3.19 -39.54% -5.19% 1.45 2.17 -5.24 1.96 8.51 0.77 0.42 83.84% DLKV 0.50 5,23% 2.13% 2.95 1.81 26.70 1.40 9.56 1.19 1.05 82.06% ERNT 51.13 28.81% 8.90% 6.97 2.41 20.63 5.96 177.12 1.10 1.10 71.34% HT 10.55 6.39% 6.25% 0.76 1.48 14.22 0.98 153.54 2.20 2.15 20.11% IGH -20.34 -22.09% -2.61% 0.83 2.12 -7.52 -1.86 -82.11 0.39 0.39 111.82% INGR 0.95 12.02% 1.27% 0.09 0.67 4.25 0.51 7.91 0.38 0.30 87.55% JDPL -22.64 -14.37% -5.19% 0.29 5.60 -1.11 0.16 156.65 0.14 0.10 63.85% KOEI 32.59 4.35% 3.36% 2.06 1.30 19.94 0.67 966.09 2.60 2.07 33.00% KRAS 21.87 4.57% 3.23% 1.59 1.85 17.74 0.80 484.71 1.54 1.10 44.30% LKRI -0.10 -0.19% -0.14% 0.24 1.62 -460.00* 0.89 51.58 1.88 1.87 11.83% MAIS 14.82 10.33% 6.30% 0.39 17.25 20.24 2.09 143.40 0.06 0.05 46.79% OPTE -0.89 -303.64%* -10.73% 0.96 3.45 -2.18 6,466.67* 0.00 0.52 0.52 102.53% PODR 2.63 0.82% 1.01% 1.49 1.79 121.67* 0.77 416.66 2.08 1.35 42.77% RIVP 1.96 9.74% 4.78% 0.38 4.89 20.56 2.02 19.97 0.72 0.67 49.64% ULPL 7.72 80.58% 0.03% 0.19 7.52 13.73 11.36 9.33 0.14 0.14 94.15% VLEN 2.30 14.87% 11.20% 1.75 4.68 4.04 0.63 14.70 1.20 0.99 38.90% ZABA 3.25 5.76% 1.01% - ** - ** 18.46 1.06 56.56 - ** - ** 85.72% AVERAGE 13.66 7.27% 2.30% 1.27 3.46 12.21 1.68 217.49 1.23 1.06 59.96% *The value is not taken into account when calculating the average due to a great deviation from other values. **Due to the specific structure of financial statements issued by Zagrebačka banka d.d., it is not possible to calculate activity indicators and liquidity indicators. Source: Authors’ elaboration based on data from Zagreb Stock Exchange d.d. Available online at http://www.zse.hr/default.aspx?id=36774 [Accessed: 27 June 2018] INTERDISCIPLINARY MANAGEMENT RESEARCH XV

527 Based on financial indicators of joint stock companies for 2017 that are listed in Table 1, the following stocks will be removed from the initial sample: • DDJH (Đuro Đaković Grupa d.d.) - due to negative financial results, low liquidity and a high debt ratio, • IGH (Institut IGH d.d.) - due to negative financial results, low liquidity and a very high debt ratio, • JDPL (Jadroplov d.d.) - due to negative financial results, very low liquidity and a high debt ratio, • LKRI (Luka Rijeka d.d.) - due to negative financial results, and • OPTE (Optima Telekom d.d.) - due to negative financial results, an overvalued stock, low liquidity, and a very high debt ratio. Following the analysis of financial statements and the elimination of undesirable stocks, there are 17 stocks remaining in the sample that are involved in the further process of forming an optimal portfolio.

4. RESULTS In order to create an optimal portfolio by using the Markowitz model, the following variables should be calculated: the expected return on the stock E(r), the standard deviation (σ) and the variance-covariance matrix. The expected return on the stock E(r) requires us to calculate historical price change. Stock price changes are calculated on a monthly basis for the period from 1 Janu- ary 2017 to 31 May 2018. As historical data are downloaded from the Zagreb Stock Exchange official website, which supplies data only on a daily basis, the average monthly prices necessary for the calculation of monthly price changes are calculated as the arithmetic means of all daily prices in a given month. The expected monthly returns on the stocks E(r) represent the average of monthly price changes for each stock. POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara

528 Table 2. Expected monthly returns, variances and standard deviations of stocks making up a sample for the formation of an optimal portfolio STOCK EXPECTED RETURN VARIANCE ST. DEV. ADPL 2.25% 0.00145 3.81% ADRS2 -0.17% 0.00074 2.72% ARNT 0.07% 0.00308 5.55% ATGR 0.77% 0.00185 4.30% ATPL 3.43% 0.00962 9.81% DLKV 1.29% 0.01235 11.11% ERNT -0.27% 0.00177 4.21% HT -0.44% 0.00039 1.97% INGR 2.89% 0.01253 11.19% KOEI 0.12% 0.00204 4.52% KRAS -1.28% 0.00162 4.03% MAIS 1.27% 0.00263 5.13% PODR -0.99% 0.00313 5.60% RIVP 1.29% 0.00185 4.30% ULPL -1.58% 0.00695 8.33% VLEN 2.36% 0.01627 12.75% ZABA 0.98% 0.00542 7.36% Source: Excel calculation done by the authors

It can be seen in the table that 6 out of 17 companies have a negative expected return. Particularly interesting is the fact that the companies Uljanik plovidba d.d. and Ericsson Nikola Tesla d.d. with the highest return on equity (80.58% and 28.81%, respectively) have negative expected returns. However, these companies are not as risky as Brodogradilište Viktor Lenac d.d., which has the highest standard deviation of as much as 12.75%, but also the third highest expected return of 2.36%. The least risky business is the Hrvatski Telekom d.d. company with a standard deviation of 1.97%, and a negative expected return. The highest expected return of 3.43% is registered by the Atlantska plovidba d.d. company. According to average standard deviations of companies per sector, the most vulnerable and the least risky sectors are Construction and Telecommunications, respectively. The next step is to create a variance-covariance matrix. INTERDISCIPLINARY MANAGEMENT RESEARCH XV

529 0.0054 0.0056 0.0038 0.0017 0.0014 0.0017 0.0006 0.0013 0.0019 0.0007 0.0018 0.0033 0.0014 0.0023 0.0019 0.0009 0.0005 ZABA 0.0056 0.0163 0.0070 0.0028 0.0021 0.0034 0.0011 0.0021 0.0025 0.0010 0.0018 0.0040 0.0034 0.0023 0.0025 0.0010 0.0004 VLEN 0.0038 0.0070 0.0069 0.0013 0.0000 0.0015 -0.0011 0.0009 -0.0014 0.0003 0.0014 0.0030 0.0043 0.0006 0.0011 -0.0003 -0.0002 ULPL 0.0017 0.0028 0.0013 0.0019 0.0011 0.0012 0.0003 0.0012 0.0024 0.0005 0.0009 0.0027 0.0003 0.0005 0.0018 0.0007 0.0003 RIVP 0.0014 0.0021 0.0000 0.0011 0.0031 0.0009 0.0007 0.0014 0.0029 0.0002 0.0001 0.0003 -0.0021 0.0011 0.0015 0.0010 0.0007 PODR 0.0017 0.0034 0.0015 0.0012 0.0009 0.0026 0.0006 0.0012 0.0034 0.0006 0.0010 0.0037 -0.0008 0.0005 0.0009 0.0007 0.0006 MAIS 0.0006 0.0011 -0.0011 0.0003 0.0007 0.0006 0.0016 0.0008 0.0028 0.0001 0.0005 0.0002 -0.0010 0.0010 0.0005 0.0007 0.0006 KRAS 0.0013 0.0021 0.0009 0.0012 0.0014 0.0012 0.0008 0.0020 0.0040 0.0003 0.0013 0.0022 0.0000 0.0008 0.0018 0.0008 0.0010 KOEI 0.0019 0.0025 -0.0014 0.0024 0.0029 0.0034 0.0028 0.0040 0.0125 0.0011 0.0027 0.0058 -0.0034 0.0019 0.0031 0.0025 0.0028 INGR 0.0007 0.0010 0.0003 0.0005 0.0002 0.0006 0.0001 0.0003 0.0011 0.0004 0.0003 0.0013 0.0000 0.0003 0.0004 0.0003 0.0002 HT 0.0018 0.0018 0.0014 0.0009 0.0001 0.0010 0.0005 0.0013 0.0027 0.0003 0.0018 0.0030 0.0015 0.0005 0.0013 0.0005 0.0007 ERNT 0.0033 0.0040 0.0030 0.0027 0.0003 0.0037 0.0002 0.0022 0.0058 0.0013 0.0030 0.0124 0.0039 -0.0003 0.0011 0.0012 0.0018 DLKV 0.0014 0.0034 0.0043 0.0003 -0.0021 -0.0008 -0.0010 0.0000 -0.0034 0.0000 0.0015 0.0039 0.0096 -0.0007 -0.0006 -0.0008 -0.0001 ATPL 0.0023 0.0023 0.0006 0.0005 0.0011 0.0005 0.0010 0.0008 0.0019 0.0003 0.0005 -0.0003 -0.0007 0.0018 0.0011 0.0007 0.0005 ATGR 0.0019 0.0025 0.0011 0.0018 0.0015 0.0009 0.0005 0.0018 0.0031 0.0004 0.0013 0.0011 -0.0006 0.0011 0.0031 0.0007 0.0002 ARNT 0.0009 0.0010 -0.0003 0.0007 0.0010 0.0007 0.0007 0.0008 0.0025 0.0003 0.0005 0.0012 -0.0008 0.0007 0.0007 0.0007 0.0007 ADRS2 . The variance-covariance. matrix 0.0005 0.0004 -0.0002 0.0003 0.0007 0.0006 0.0006 0.0010 0.0028 0.0002 0.0007 0.0018 -0.0001 0.0005 0.0002 0.0007 0.0014 ADPL ZABA VLEN ULPL RIVP PODR MAIS KRAS KOEI INGR HT ERNT DLKV ATPL ATGR ARNT ADRS2 ADPL POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara 3 Table Source: calculation Excel done by authors the

530 Table 3 shows the variance-covariance matrix of stocks included in the sample to form an optimal portfolio. The shaded cells indicate return variances 0.0054 0.0056 0.0038 0.0017 0.0014 0.0017 0.0006 0.0013 0.0019 0.0007 0.0018 0.0033 0.0014 0.0023 0.0019 0.0009 0.0005 ZABA of individual stocks shown in Table 2 above. After all necessary variables have been calculated, it is possible to create an efficient frontier and select an optimal 0.0056 0.0163 0.0070 0.0028 0.0021 0.0034 0.0011 0.0021 0.0025 0.0010 0.0018 0.0040 0.0034 0.0023 0.0025 0.0010 0.0004 VLEN portfolio. Table 3 shows the variance-covariance matrix of stocks included in the sample to 0.0038 0.0070 0.0069 0.0013 0.0000 0.0015 -0.0011 0.0009 -0.0014 0.0003 0.0014 0.0030 0.0043 0.0006 0.0011 -0.0003 -0.0002 ULPL form an optimal portfolio. The shaded cells indicate return variances of individual stocks4.1. Creating shown in Table an 2efficient above. After frontier all necessary and variables selecting have been an calculated, optimal it 0.0017 0.0028 0.0013 0.0019 0.0011 0.0012 0.0003 0.0012 0.0024 0.0005 0.0009 0.0027 0.0003 0.0005 0.0018 0.0007 0.0003 RIVP is possibleportfolio to create an efficient frontier and select an optimal portfolio.

4.1.The Creating first step an efficientin creating frontier an efficient and selecting frontier an isoptimal to form portfo a setlio of minimum 0.0014 0.0021 0.0000 0.0011 0.0031 0.0009 0.0007 0.0014 0.0029 0.0002 0.0001 0.0003 -0.0021 0.0011 0.0015 0.0010 0.0007 PODR variances. The set of minimum variances is created on the basis of a series of The first step in creating an efficient frontier is to form a set of minimum variances. Thedominant set of minimumportfolios variancesthat are isobtained created by on using the basis the ofExcel a serie Solvers of tool, dominant where 0.0017 0.0034 0.0015 0.0012 0.0009 0.0026 0.0006 0.0012 0.0034 0.0006 0.0010 0.0037 -0.0008 0.0005 0.0009 0.0007 0.0006 MAIS portfoliosthe expected that monthly are obtained returns by using of individual the Excel stocks Solver and tool, the wh variance-covarianceere the expected monthlymatrix shouldreturns beof individualreduced to stocks annual and values. the variance-covariance matrix should be 0.0006 0.0011 -0.0011 0.0003 0.0007 0.0006 0.0016 0.0008 0.0028 0.0001 0.0005 0.0002 -0.0010 0.0010 0.0005 0.0007 0.0006 KRAS reduced to annual values.

Figure .4. A A set set of ofminimum minimum variances variances 0.0013 0.0021

0.0009 Figure 4 0.0012 0.0014 0.0012 0.0008 0.0020 0.0040 0.0003 0.0013 0.0022 0.0000 0.0008 0.0018 0.0008 0.0010 KOEI 0.0019 0.0025 -0.0014 0.0024 0.0029 0.0034 0.0028 0.0040 0.0125 0.0011 0.0027 0.0058 -0.0034 0.0019 0.0031 0.0025 0.0028 INGR 0.0007 0.0010 0.0003 0.0005 0.0002 0.0006 0.0001 0.0003 0.0011 0.0004 0.0003 0.0013 0.0000 0.0003 0.0004 0.0003 0.0002 HT 0.0018 0.0018 0.0014 0.0009 0.0001 0.0010 0.0005 0.0013 0.0027 0.0003 0.0018 0.0030 0.0015 0.0005 0.0013 0.0005 0.0007 ERNT 0.0033 0.0040 0.0030 0.0027 0.0003 0.0037 0.0002 0.0022 0.0058 0.0013 0.0030 0.0124 0.0039 -0.0003 0.0011 0.0012 0.0018 DLKV 0.0014 0.0034 0.0043 0.0003 -0.0021 -0.0008 -0.0010 0.0000 -0.0034 0.0000 0.0015 0.0039 0.0096 -0.0007 -0.0006 -0.0008 -0.0001 ATPL 0.0023 0.0023 0.0006 0.0005 0.0011 0.0005 0.0010 0.0008 0.0019 0.0003 0.0005 -0.0003 -0.0007 0.0018 0.0011 0.0007 0.0005 ATGR 0.0019 0.0025 0.0011 0.0018 0.0015 0.0009 0.0005 0.0018 0.0031 0.0004 0.0013 0.0011 -0.0006 0.0011 0.0031 0.0007 0.0002 ARNT Source: Excel calculation done by the authors Source: Excel calculation done by the authors 0.0009 0.0010 -0.0003 0.0007 0.0010 0.0007 0.0007 0.0008 0.0025 0.0003 0.0005 0.0012 -0.0008 0.0007 0.0007 0.0007 0.0007 ADRS2 The line shown in the figure represents a set of portfolios that have a minimum variance or standard deviation for a certain rate of return. Therefore, it is the

. The variance-covariance. matrix dominant portfolio with the lowest possible risk. However, not all of the dominant 0.0005 0.0004 -0.0002 0.0003 0.0007 0.0006 0.0006 0.0010 0.0028 0.0002 0.0007 0.0018 -0.0001 0.0005 0.0002 0.0007 0.0014 ADPL The line shown in the figure represents a set of portfolios that have a mini- portfolios are efficient portfolios. If we look again at Figure 4, we can notice a portfoliomum variance marked or in standardred. This deviationportfolio is for located a certain closest rate to of t hereturn. vertical Therefore, axis and itit is ZABA VLEN ULPL RIVP PODR MAIS KRAS KOEI INGR HT ERNT DLKV ATPL ATGR ARNT ADRS2 ADPL Table 3 Table Source: calculation Excel done by authors the dividesthe dominant the line intoportfolio two parts. with The the upper lowest part possible of the linerisk. is However, known as notthe efficientall of the INTERDISCIPLINARY MANAGEMENT RESEARCH XV frontier and it is a set of efficient portfolios that, with the same level of risk, promise higher returns than the portfolios located on the lower part of the line. 531 dominant portfolios are efficient portfolios. If we look again at Figure 4, we can notice a portfolio marked in red. This portfolio is located closest to the vertical axis and it divides the line into two parts. The upper part of the line is known as the efficient frontier and it is a set of efficient portfolios that, with the same level of risk, promise higher returns than the portfolios located on the lower part of the line.

FigureFigure 5 5.. The The efficient efficient frontier frontier

Source:Source: Excel Excel calculation calculation done done by by the the authors authors

Although the efficient frontier represents infinitely many combinations of standard deviationAlthough and expectedthe efficient return frontier points, the represents efficient frontierinfinitely shown many in thecombinations figure is of createdstandard based deviation on eleven and efficient expected portfolios, return i.e., points, eleven the comb efficientinations frontierof the standard shown in deviation and the expected returns shown in Table 4. the figure is created based on eleven efficient portfolios, i.e., eleven combina-

Tabletions 4.of Portfolios the standard that makedeviation the efficient and the frontier expected returns shown in Table 4. PORTF 1 2 3 4 5 6 7 8 9 10 11 OLIO ST. 16.96 33.97 6.00% 6.01% 6.10% 6.23% 7.04% 7.92% 8.96% 10.15% 12.42% DEV. % % E(r) - - 15.00 20.00 35.00 41.16 1.00% 3.00% 10.00% 25.00% 30.00% 3.00% 1.00% % % % % ADPL 13.47 17.45 38.25 44.81 32.91 3.98% 8.73% 30.85% 54.97% 74.89% 0.00% % % % % % ADRS2 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

ARNT 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

ATGR CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara 11.10 12.99 0.00% 0.00% 0.00% 1.65% 9.34% 10.07% 0.00% 0.00% 0.00% % % ATPL 10.31 12.27 44.05 100.0 5.94%532 6.36% 6.79% 7.11% 8.51% 14.94% 22.14% % % % 0% DLKV 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

ERNT 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Table 4. Portfolios that make the efficient frontier

PORTFOLIO 1 2 3 4 5 6 7 8 9 10 11 ST. DEV. 6.00% 6.01% 6.10% 6.23% 7.04% 7.92% 8.96% 10.15% 12.42% 16.96% 33.97% E(r) -3.00% -1.00% 1.00% 3.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 41.16% ADPL 3.98% 8.73% 13.47% 17.45% 30.85% 38.25% 44.81% 54.97% 74.89% 32.91% 0.00% ADRS2 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% ARNT 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% ATGR 0.00% 0.00% 0.00% 1.65% 9.34% 11.10% 12.99% 10.07% 0.00% 0.00% 0.00% ATPL 5.94% 6.36% 6.79% 7.11% 8.51% 10.31% 12.27% 14.94% 22.14% 44.05% 100.00% DLKV 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% ERNT 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% HT 70.35% 68.08% 65.80% 63.33% 51.18% 32.96% 14.30% 0.00% 0.00% 0.00% 0.00% INGR 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 1.04% 23.04% 0.00% KOEI 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% KRAS 13.76% 11.39% 9.03% 6.33% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% MAIS 0.00% 0.00% 0.00% 0.00% 0.00% 1.38% 4.97% 7.00% 1.70% 0.00% 0.00% PODR 5.97% 5.44% 4.92% 4.12% 0.07% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% RIVP 0.00% 0.00% 0.00% 0.00% 0.06% 6.01% 10.65% 13.02% 0.09% 0.00% 0.00% ULPL 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% VLEN 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.14% 0.00% 0.00% ZABA 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Source: Excel calculation done by the authors

Table 4 shows a share of individual stocks in the portfolios by different combinations of returns and risks. Expected returns and standard deviations move in the same direction, hence portfolios with lower expected returns have less risk, and vice versa – higher expected returns come with more risk. According to the principle of diversification, less risky portfolios consist of a larger number of stocks, and more risky portfolios consist of a smaller number of stocks. For example, the first portfolio with the smallest standard deviation of 6% consists of stocks of five companies (AD Plastik d.d., Atlantska plovidba d.d., Hrvatski Telekom d.d., Kraš d.d. and Podravka d.d.), while the last portfolio with the highest standard deviation of 33.97% consists of stocks of only one company (Atlantska plovidba d.d.). All portfolios found at an efficient frontier can be called optimal portfolios. Individual investors will select a stock portfolio in accordance with their own views on the risk-return trade-off. Risk-averse investors will choose less risky portfolios from the left-hand segment of the efficient frontier and be ready to INTERDISCIPLINARY MANAGEMENT RESEARCH XV

533 achieve smaller returns. On the other hand, investors prone to risk will invest in a portfolio from the right-hand segment of the efficient frontier, which is characterised by a high level of risk and a higher return. For the purposes of this paper, it is assumed that we deal with a more conservative investor who wants to invest in a moderately risky portfolio with a satisfactory return. Such investors would like to invest their funds in e.g. the portfolio under number 9. The standard deviation of the portfolio is 12.42% and the expected return is 30%. Com- pared to the maximum standard deviation that can be achieved by combining the observed stocks, the standard deviation of this portfolio is as low as 63.44%, and as such, it is ideal for such type of investor who is not a high-risk taker. On the other hand, the expected return is lower by only 27.11% of the maximum expected return achievable, which makes it more than satisfactory. The stock and sector structure of the investor’s optimal portfolio is presented in Table 5.

Table 5. The stock and sector structure of an optimal portfolio STOCK SHARE E(r) ST. DEV. SECTOR ADPL 74.89% 26.99% 45.69% Manufacture of transport equipment ATPL 22.14% 41.16% 117.69% Transportation and storage Legal, accounting, management, architecture, engineering, technical INGR 1.04% 34.66% 134.32% testing and analysis activities MAIS 1.70% 15.29% 61.51% Accommodation and food service activities VLEN 0.14% 28.32% 153.95% Manufacture of transport equipment Source: Authors’ elaboration

The optimal portfolio includes stocks of the following five companies: Ad Plastik d.d., Atlantska plovidba d.d., Ingra d.d., Maistra d.d. and Brodogradilište Viktor Lenac d.d. The largest stock in the portfolio consists of DA Plastik d.d. and Atlantska plovidba d.d. stocks, which is expected since these are stocks with the fourth and the highest annual expected return compared to other seventeen stocks observed. Although individual shares of stocks of other companies are almost insignificantly small, these stocks are among the top seven in terms of the expected annual returns. All observed stocks are among the ten best ones in terms of the return on equity (ROE). When it comes to the portfolio sector structure, it can be noticed that only two stocks belong to the same sector. Given the presence of four different sectors, it can be concluded that the portfolio is sectorally diversified. POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara

534 5. CONCLUSION When investing in stocks, each investor is interested in achieving the maximum profit with the minimum risk possible. In order to achieve this, investors should form a stock portfolio that will consist of a larger number of stocks, which will, according to the principle of diversification, significantly reduce the risk of loss. To form a portfolio, investors in developed capital markets have been using the Markowitz portfolio optimisation model for many years to find an optimal risk-return trade-off by selecting certain stock combinations. The aim of this paper was to investigate whether the Markowitz model can also be applied to the Croatian capital market, despite the fact that this market is young and underdeveloped. For the analysis of the application of the Markow- itz model, a sample of seventeen stocks was used that had to meet several criteria, i.e., liquidity, which is why only the CROBEX index stocks were taken into consideration, affiliation to different sectors and positive financial results of companies. After calculating all variables needed for model application, an efficient frontier was created successfully, i.e., the curve on which there lie the portfolios with a minimum level of risk for a given level of return. Assuming a conservative investor, an optimal portfolio was selected, which contains five different stocks and which, with an acceptable level of risk, promises a satisfactory return. Nevertheless, underdeveloped capital markets such as the Croatian market have some shortcomings which, to a greater or lesser extent, pose problems for its proper application. Due to a limited number of stocks traded on the market, lack of liquidity and transparency and missing trade history data, it is not possible to accurately calculate the average expected returns. Although because of these reasons the use of the Markowitz model is far more efficient in more developed markets, the use of the expected return as an input parameter is no longer recommended. Today, instead of the original model, much more complex models are used that provide more accurate prediction of return, but this model is still used as a basic model. Despite the aforementioned shortcomings, the first main hypothesis according to which the Markowitz model is applicable to the Croatian capital market is not rejected. The second main hypothesis stat- ing that an increased number of stocks in the portfolio reduces the overall risk is not rejected either. Our research has shown that some joint stock companies, whose stocks are part of the CROBEX index and accordingly make the most liquid stocks listed on Zagreb Stock Exchange, have not achieved positive financial results in 2017; hence the first auxiliary hypothesis is rejected. The optimal INTERDISCIPLINARY MANAGEMENT RESEARCH XV

535 portfolio selected by assuming a conservative investor is sectorally diversified so that the second auxiliary hypothesis is not rejected.

6. REFERENCES Aljinović Z., Marasović B. & Šego B. (2011). Financijsko modeliranje. Ekonomski fakultet u Splitu, ISBN 978-953-281-031-8, Split. Evans, J. L., & Archer, S. H. (1968). Diversification and the reduction of dispersion: an em- pirical analysis. The Journal of Finance, 23(5), pp. 761-767. Fabozzi, F. J., Gupta, F., & Markowitz, H. M. (2002). The legacy of modern portfolio theory. Journal of Investing, 11(3), pp. 7-22. Jerončić, M., & Aljinović, Z. (2011). Formiranje optimalnog portfelja pomoću Markowit- zevog modela uz sektorsku podjelu kompanija. Ekonomski pregled, 62 (9-10). Mao, J. C., & Särndal, C. E. (1966). A decision theory approach to portfolio selection. Man- agement Science, 12(8), pp. 323-333. Marasović, B. & Šego, B. (2006). Markowitzev model optimizacije portfelja. Računovodstvo i financije, 6, pp. 57-61. Markowitz, H. (1952), Portfolio Selection. Journal of Finance, 7 (1), pp. 77-91. Omisore, I., Yusuf, M., & Christopher, N. (2011). The modern portfolio theory as an investment decision tool. Journal of Accounting and Taxation, 4(2), pp. 19-28. Penavin, S. (2003). Primjena analitičkih metoda u postupku upravljanja portfeljom. Eko- nomski vjesnik: časopis Ekonomskog fakulteta u Osijeku, pp. 89-97. Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management Science, 9(2), pp. 277-293. Statman, M. (1987). How many stocks make a diversified portfolio? Journal of Financial and Quantitative Analysis, 22(3), pp. 353-363. Steinbach, M. C. (2001). Markowitz revisited: Mean-variance models in financial portfolio analysis. SIAM Review, 43(1), pp. 31-85. Wang, S., & Zhu, S. (2002). On fuzzy portfolio selection problems. Fuzzy Optimization and Decision Making, 1(4), pp. 361-377. Xia, Y., Liu, B., Wang, S., & Lai, K. K. (2000). A model for portfolio selection with the order of expected returns. Computers & Operations Research, 27(5), pp. 409-422. Zagreb Stock Exchange: http://zse.hr/ (Accessed: 20 June 2018) POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara

536 Table A1. S tocks included in the initial sample for the formation of an optimal stock portfolio

No SYMBOL ISSUER

1 ADPL AD Plastik d.d. 2 ADRS2 Adris grupa d.d. 3 ARNT Arena Hospitality Group d.d. 4 ATGR Atlantic Grupa d.d. 5 ATPL Atlantska plovidba d.d. 6 DDJH ĐURO ĐAKOVIĆ GRUPA d.d. 7 DLKV Dalekovod d.d. 8 ERNT ERICSSON NIKOLA TESLA d.d. 9 HT HT d.d. 10 IGH Institut IGH d.d. 11 INGR Ingra d.d. 12 JDPL Jadroplov d.d. 13 KOEI Končar - Elektroindustrija d.d. 14 KRAS Kraš d.d. 15 LKRI LUKA RIJEKA d.d. 16 MAIS Maistra d.d. 17 OPTE OT-OPTIMA TELEKOM d.d. 18 PODR Podravka d.d. 19 RIVP VALAMAR RIVIERA d.d. 20 ULPL Uljanik Plovidba d.d. 21 VLEN Brodogradilište Viktor Lenac d.d. 22 ZABA Zagrebačka banka d.d. Source: Zagreb Stock Exchange d.d. Available online at http://www.zse.hr/default.aspx?id=82041 [Accessed: 25 June 2018] INTERDISCIPLINARY MANAGEMENT RESEARCH XV

537 Table A2. Sector affiliation of companies whose stocks are included in the initial sample

SECTOR SYMBOL ISSUER

Accommodation and food service activities ARNT Arena Hospitality Group d.d. Accommodation and food service activities MAIS Maistra d.d. Accommodation and food service activities RIVP VALAMAR RIVIERA d.d. Financial and insurance activities ZABA Zagrebačka banka d.d. Construction DLKV Dalekovod d.d. Legal, accounting, management, architecture, ADRS2 Adris grupa d.d. engineering, technical testing and analysis activities Legal, accounting, management, architecture, DDJH ĐURO ĐAKOVIĆ GRUPA d.d. engineering, technical testing and analysis activities Legal, accounting, management, architecture, INGR Ingra d.d. engineering, technical testing and analysis activities Transportation and storage ATPL Atlantska plovidba d.d. Transportation and storage JDPL Jadroplov d.d. Transportation and storage LKRI LUKA RIJEKA d.d. Transportation and storage ULPL Uljanik Plovidba d.d. Manufacture of electrical equipment KOEI Končar - Elektroindustrija d.d. Manufacture of food products, beverages and tobacco KRAS Kraš d.d. products Manufacture of food products, beverages, and PODR Podravka d.d. tobacco products Manufacture of food products, beverages, and ERNT ERICSSON NIKOLA TESLA d.d. tobacco products Manufacture of transport equipment ADPL AD Plastik d.d. Manufacture of transport equipment VLEN Brodogradilište Viktor Lenac d.d. Telecommunications HT HT d.d. Telecommunications OPTE OT-OPTIMA TELEKOM d.d. Wholesale and retail trade ATGR Atlantic Grupa d.d. Scientific research and development IGH Institut IGH d.d. Source: Authors’ elaboration based on data from Zagreb Stock Exchange d.d. Available online at http://www.zse.hr/default.aspx?id=34348 [Accessed: 25 June 2018] POSSIBILITIES OF APPLYING MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN CAPITAL... MARKOWITZ PORTFOLIO THEORY ON THE CROATIAN Jakšić: POSSIBILITIES OF APPLYING Dubravka Pekanov Starčević • Ana Zrnić Tamara

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