MATEMATIČNA OPTIMIZACIJA PORTFELJA S PRISTOPI MEAN-VARIANCE, MEAN-CVAR IN MAX-OMEGA Z OMEJITVIJO NABORA DELNIC

Ortl, Aljoša

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Title:	MATEMATIČNA OPTIMIZACIJA PORTFELJA S PRISTOPI MEAN-VARIANCE, MEAN-CVAR IN MAX-OMEGA Z OMEJITVIJO NABORA DELNIC
Authors:	ID Ortl, Aljoša (Author) ID Jagrič, Timotej (Mentor) More about this mentor...
Files:	MAG_Ortl_Aljosa_2014.pdf (3,00 MB) MD5: 0D9B9ED138F3A369CFC8E0D0B4AB519E
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	EPF - Faculty of Business and Economics
Abstract:	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.
Keywords:	Omega, optimizacija portfelja, genetski algoritem, diferencialna evolucija, CVaR, omejitev izbora največjega števila delnic v portfelj
Place of publishing:	Maribor
Publisher:	[A. Ortl]
Year of publishing:	2014
PID:	20.500.12556/DKUM-45792
UDC:	336.76
COBISS.SI-ID:	11805724
NUK URN:	URN:SI:UM:DK:WKI70GQX
Publication date in DKUM:	13.10.2014
Views:	2733
Downloads:	479
Metadata:
Categories:	EPF
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Secondary language

Language:	English
Title:	MATHEMATICAL PORTFOLIO OPTIMIZATION WITH MEAN-VARIANCE, MEAN-CVAR IN MAX-OMEGA APPROACHES WITH CARDINALITY CONSTRAINT
Abstract:	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.
Keywords:	Omega, portfolio optimization, genetic algorithm, differential evolution, CVaR, cardinality constraint

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