THE APPLICATION OF ALTERNATIVE PORTFOLIO OPTIMIZATION MODELS ON ZAGREB STOCK EXCHANGE

Glavni problem kod ulaganja na tržište kapitala predstavlja izbor dionica, odnosno koliki bi trebao biti udio pojedine dionice u sastavu portfelja. Harry Markowitz je 1959. godine prvi postavio matematički model ovog problema. Narednih godina zbog određenih nedostataka Markowitzevog modela počinju se razvijati i alternativni modeli optimizacije portfelja. S obzirom na određene prednosti alternativnih modela optimizacije portfelja u odnosu na originalni Markowitzev model, veoma je korisno razmotriti mogućnosti njihove primjene na tržištu poput hrvatskoga, što zapravo i predstavlja cilj rada. Odabrani alternativni modeli koji se razmatraju u ovom radu su model optimizacije portfelja s apsolutnom devijacijom, minimax model optimizacije portfelja i model optimizacije portfelja s donjom polu-varijancom. Kao podaci za formiranje efikasnih portfelja modela korišteni su mjesečni prinosi deset dionica koji su kroz cijelo promatrano razdoblje od siječnja 2015. do siječnja 2020. godine neprekidno bile uključene u CROBEX indeks. U radu je prvo primijenjen Markowitzev modela na hrvatsko tržište kapitala. Formirano je petnaest efikasnih portfelja prema Markowitzevom modelu te su rezultati modela grafički prikazani i interpretirani. Nakon Markowitzevog modela, na red su došli alternativni modeli. Potom su na hrvatsko tržište kapitala primijenjeni odabrani alternativni modeli. Za svaki alternativni model formirano je petnaest efikasnih portfelja te su rezultati alternativnih modela grafički prikazani i interpretirani. Napravljena je i usporedba rezultata između odabranih modela. Prvo su komentirane razlike između sastava portfelja odabranih modela. Pokazalo se da najviše razlike u sastavima portfelja ima između minimax modela i Markowitzevog modela, dok su najsličniji portfelji koje generiraju model optimizacija s apsolutnom devijacijom i Markowitzev model. Drugi način usporedbe rezultata optimizacije odabranih modela bio je odabir jedne „zajedničke“ mjere rizika. Kao „zajednička“ mjera rizika odabrana je standardna devijacija koja je mjera rizika u Markowitzevom modelu, te je za sve portfelje alternativnih modela izračunata njihova varijanca. Pokazalo se da je pri nižim razinama prinosa portfelja Markowitzev model bolji od alternativnih modela jer generira manji rizik portfelja u smislu standardne devijacije. No pri višim razinama prinosa portfelja nema velike razlike između Markowitzevog modela i alternativnih modela gledajući kriterij prinosa portfelja i standardne devijacije kao mjere rizika.The main problem with investment in capital market is the choice of stocks, that is which share of individual stock should be part of portfolio composition. In 1959, Harry Markowitz first formulates this problem mathematically. In following years due to certain limitations of the Markowitz's model, alternative models of portfolio optimization started to develop. Considering some advantages of alternative models of portfolio optimization compared to the original Markowitz model, it is very useful to consider possibility of applying alternative models to the Croatian capital market, which is actually the purpose of this thesis. Selected alternative models considered are portfolio optimization model with absolute deviation, minimax portfolio optimization model and portfolio optimization model with lower semi-variance. Monthly yields of ten stocks, which were continuously included in the CROBEX index throughout the observed period from January 2015 to January 2020, were used as data for formation of efficient model portfolios. First, Markowitz's model was applied to the Croatian capital market. Fifteen efficient portfolios were formed according to the Markowitz model, and the results of the model were graphically presented and interpreted. After the Markowitz's model, alternative models were applied. All selected alternative models have been applied to the Croatian capital market. Fifteen efficient portfolios were formed for each alternative model, and results of alternative models were graphically presented and interpreted. A comparison of results between selected models was also made. First, differences among portfolio compositions of selected models were discussed. It turned out that the greatest differences in portfolio composition occur between the minimax model and the Markowitz's model, while portfolios generated by the optimization model with absolute deviation and the Markowitz model are the most similar. Another way to compare the optimization results of the selected models was to select a “common” risk measure. The standard deviation, that is the risk measure in Markowitz's model, was chosen as a "common" risk measure, and standard deviation was calculated for all portfolios of alternative models. It has been shown that at lower levels of portfolio return the Markowitz's model is better than alternative models because it generates less portfolio risk in terms of standard deviation. But at higher levels of portfolio returns there is not much difference between the Markowitz's model and alternative models when compared by using the criterion of portfolio return and standard deviation as a measure of risk