Upravljanje tržišnim rizikom u bankarskom sektoru primjenom moderne teorije portfelja i CAPM modela

master's thesis

• Author: Ana Zaplatić
• Mentor: Ilko Vrankić (mentor)
• Committee member: Ilko Vrankić (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu analizirana je moderna teorija portfelja i model vrednovanja kapitalne imovine i pokazana je njihova primjena u bankarskom sektoru pri upravljanju tržišnim rizikom. Model moderne teorije portfelja počinje s pretpostavkama modela koje je postavio Markowitz 1952. godine. On je sa svojim modelom postavio osnove moderne teorije portfelja. Najbitnije stavke modela su prinos portfelja i rizik. Model je postavljen tako što je očekivani prinos portfelja modeliran statističkim očekivanjem, a rizik standardnom devijacijom prinosa. Nakon što je definiran optimizacijski problem i riješen metodom Lagrangeovim multiplikatorima, proučavane su efikasne granice portfelja i optimalan pravac alokacije kapitala. Sljedeći korak je bio proučavanje modela vrednovanja kapitalne imovine. Definiran je Sharpeov omjer i pravilo poboljšanja portfelja pomoću kojih je uspostavljen model vrednovanja kapiralne imovine. U tom modelu je bitan i beta indeks. Njegov značaj u modelu pokazan je u primjeru. Na kraju poglavlja proučavana je korisnost CAPM modela te je navedeno nekoliko njegovih proširenja. Ta dva modela primjenjeni su na modeliranje aktivnosti banaka prilikom upravljanja tržišnim rizikom. Modeli su formulirani kako bi banku izjednačili s upraviteljem portfelja. Praćeno je ponašanje banaka kod nedostatka regulativne solventnosti i nakon uvođenja regulative solventnosti. Uveden je omjer kapitala koji se pokazao kao dobar pokazatelj rizika neuspjeha banke.

Abstract (english)

In this paper modern portfolio theory and the capital asset pricing model are analyzed. Furthermore, their application in managing market risk in the banking sector is demonstrated. The model of modern portfolio theory starts with theories which Markowitz wrote in 1952. His model laid the foundations of modern portfolio theory. Key components of this model are portfolio return and risk. The model is set so that the expected portfolio return is modeled by statistical expectations and the risk is modeled by the standard deviation of return. After the optimization problem is defined and solved with the method of Lagrange multipliers, the efficient portfolio frontier and the optimum capital allocation line is studied. The next step is to study the capital asset pricing model (CAPM). The Sharpe ratio and the portfolio improvement rule are defined in order to explain their role in the development capital asset pricing model. A beta index has a major role in this model as well, and there is an example which verifies its importance. At the end of the chapter, the benefits of the CAPM are examined and several additions to the model are listed. The two models are used to model activities of banks in managing market risk. The models are created in order to equalize a bank with a portfolio manager. The activity of a bank in the absence of solvency regulations and after the same regulations are introduced is monitored. A capital ratio, which has proved to be a good indicator of the risk of bank failure, is introduced.

• Keywords: moderna teorija portfelja; model vrednovanja kapitalne imovine; optimizacijski problem; Lagrangeovi multiplikatori; Sharpeov omjer; beta indeks; CAPM model; tržišni rizik
• Keywords (english): modern portfolio theory; capital asset pricing model; optimization problem; Lagrange multipliers; Sharpe ratio; beta index; CAPM; market risk
• Language: croatian
• URN:NBN: urn:nbn:hr:217:320403
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2021-07-01
• Created on: 2020-07-01 10:45:50