Izrada optimalnog portfelja uz rizik modeliran VaR-om

master's thesis

• Title (english): Creation of an optimal portfolio with risk modeled by VaR
• Author: Filip Gomerčić
• Mentor: Nikola Sandrić (mentor)
• Committee member: Nikola Sandrić (predsjednik povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog rada bio je predstaviti te pojasniti dvije bitne strane investiranja - najprije odabir portfelja te zatim kontrolu rizika povezanih s investiranjem. U svrhu optimizacije portfelja predstavili smo optimizaciju portfelja kako ju je zamislio Markowitz u svojoj modernoj teoriji portfelja, raspravljali smo o svrsi diverzifikacije te smo uveli pojam efikasne granice te s njom povezanih efikasnih portfelja. Radi jasnijeg razumijevanja mjere rizika, tzv. rizične vrijednosti (eng. Value-at-Risk), pokazali smo nekoliko načina za njen izračun (povijesna metoda, parametarska metoda te metoda Monte Carlo simulacija) te komentirali prednosti i nedostatke svakog načina. Na kraju, kako bi se odmaknuli od teorijskog pogleda, prikazali smo primjerom kako se može izračunati portfelj minimalne varijance te smo na njemu izračunali VaR koristeći povijesnu metodu.

Abstract (english)

The aim of this paper was to present and clarify two important aspects of investing - firstly, the concept of portfolio selection, and then the control of investment-related risks. For the purpose of portfolio optimization, we introduced portfolio optimization as envisioned by Markowitz in his Modern Portfolio Theory, furthermore, we discussed the purpose of diversification and introduced the concept of the efficient frontier and with it related efficient portfolios. In order to better understand the risk measure Value-at-Risk, we presented several methods for its calculation (historical method, parametric method and Monte Carlo simulation method) and commented on the advantages and disadvantages of each method. Finally, to step away from the theoretical view, we constructed an example of the process to calculate the minimum-variance portfolio and calculated the Value-at-Risk metric on it by implementing the historical method.

• Keywords: investiranje; optimizacija portfelja; Markowitz; rizične vrijednosti
• Language: croatian
• URN:NBN: urn:nbn:hr:217:550500
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-13 10:06:20