20.500.12556/DKUM-45792 MATEMATIČNA OPTIMIZACIJA PORTFELJA S PRISTOPI MEAN-VARIANCE, MEAN-CVAR IN MAX-OMEGA Z OMEJITVIJO NABORA DELNIC MATHEMATICAL PORTFOLIO OPTIMIZATION WITH MEAN-VARIANCE, MEAN-CVAR IN MAX-OMEGA APPROACHES WITH CARDINALITY CONSTRAINT Vprašanje, kam vložiti finančna sredstva, je zelo zahtevno. Pri tem nam lahko pomaga matematična optimizacija portfelja. Tradicionalni pristopi kot, je Markowitzevega Mean-Variance optimizacija s kvadratičnim programiranjem, imajo svoje slabosti, npr. predpostavko normalne porazdelitve donosov. Namesto variance kot simetrične mere tveganja lahko uporabimo alternativno mero tveganja, t. j. CVaR, ki se je v zadnjih letih zelo uveljavila tudi zaradi enostavnosti implementacije in hitrosti delovanja algoritma linearnega programiranja. Zelo zanimiva mera, ki ne zahteva nobenih predpostavk glede porazdelitve donosov, je tudi razmerje Omega, ki predstavlja razmerje med arbitrarno določenimi dobički in izgubami. Maksimizacija razmerja Omega nam lahko ponudi boljše rezultate od prej omenjenih mer, kar smo potrdili tudi s testiranjem za nazaj izven vzorca. Optimizacija razmerja zahteva uporabo hevrističnega algoritma. Uporabili smo algoritem diferencialne evolucije. Zaradi praktične uporabnosti smo dodali tudi omejitev izbora največjega števila delnic v portfelj. Pri implementaciji smo se oprli na celoštevilski genetski algoritem. It is very hard to answer the question: where to invest the money. One way to answer this question is to use mathematical portfolio optimization techniques. Traditional approach of portfolio optimization is Markowitz's Mean-Variance optimization. It has its own pitfalls, for instance the assumption of normally distributed returns. Instead of using variance, which is a symmetric risk measure, we can use alternative risk measure such as CVaR. The practical importance of this measure has grown in the last years. This is because of its simplicity in implementation and fast execution of linear programming algorithm which is used for its optimization. Very interesting measure that requires no distributional assumptions is Omega ratio. It represents the ratio between profits and gains, where the threshold is arbitrarily chosen. Maximization of Omega ratio can lead to better results and we show this with our out-of-sample backtesting. However, the optimization of this ratio requires the use of heuristic optimization algorithms. In this paper we use differential evolution algorithm. In addition we also implement the cardinality constraint. Omega optimizacija portfelja genetski algoritem diferencialna evolucija CVaR omejitev izbora največjega števila delnic v portfelj Omega portfolio optimization genetic algorithm differential evolution CVaR cardinality constraint true true false [A. Ortl] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2014-09-03 20:29:44 2014-10-13 11:41:44 2022-05-16 03:06:34 2021-05-03 03:36:18 2014 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 336.76 11805724 URN:SI:UM:DK:WKI70GQX MAG_Ortl_Aljosa_2014.pdf MAG_Ortl_Aljosa_2014.pdf 1 0D9B9ED138F3A369CFC8E0D0B4AB519E 54d7d18ae7944b5a7437ba7926477f5c11a5a1eacfc8462f6326499681f74fa4 29404598-7c0b-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=66542 Ekonomsko-poslovna fakulteta 0 0 0