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Investment Optimization
Bujnovský, Daniel ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This work is focused on description of two models of mathematical programming - the network model and the Markowitz portfolio model, their connection and application in transportation problems. The goal of the practical section is to approach the description of these problems to the real situations and look for their efficient solutions at the same time. All of that is accompanied by examples on real data from capital market or own model data. The theoretical considerations and thoughts are implemented in programming language Matlab. All results are explained in context to both models. The thesis also includes the introduction to economical and statistical theory which is necessary to understand the problem.
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Use of mathematical methods in creating an investment portfolio
Holub, Miroslav ; Novotná, Veronika (referee) ; Janková, Zuzana (advisor)
The bachelor thesis is focused on the use of mathematical methods in creating an investment portfolio, which is designed for small investor. The theoretical part of the thesis describes the necessary knowledge to understand Markowitz model, selected indicators of financial analysis and the Value at Risk method. The practical part contains a selection of investment instruments traded on the US market according to established criteria, the creation of a real portfolio of these investment instruments and the final evaluation of results.
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Optimization Models of Financial Risk
Danko, Erik ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with optimization models of financial risks. The first part, which is devoted to the theoretical background, introduces the basic concepts of optimization, modern portfolio theory, fundamental and technical analysis and statistical background. The basic principles of operation of modern portfolio theory are presented. The methods for analysis and selection of assets called Growth at A Reasonable Price and portfolio optimization approach according to Harry Markowitz were used with selected methods. The practical part is focused on the data analysis, selection of assets and design of a portfolio optimization model according to selected conditions with an emphasis on minimizing investment risk. The used models examine the selected data and are solved using the MS Excel add-in Solver version.
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Optimization in Financial Applications
Večeřa, Tomáš ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The main purpose of this thesis is to create an efficient stock portfolio, specifically to optimize current distribution of stock index S&P 500. The building process consist of well-established mathematical-economical methods, which are then improved by applying mathematical models from statistics and optimization. Firstly, we define essential terms in order to reach deeper understanding of used methods. Afterwards, process of thorough selection of stocks and sectors comes to place. Data are then processed in program GAMS in three different ways, depending on investors preference. Although this approach was applied to current era, its principles are applicable to any given timeline.
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Optimization in Financial Applications
Večeřa, Tomáš ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The main purpose of this thesis is to create an efficient stock portfolio, specifically to optimize current distribution of stock index S&P 500. The building process consist of well-established mathematical-economical methods, which are then improved by applying mathematical models from statistics and optimization. Firstly, we define essential terms in order to reach deeper understanding of used methods. Afterwards, process of thorough selection of stocks and sectors comes to place. Data are then processed in program GAMS in three different ways, depending on investors preference. Although this approach was applied to current era, its principles are applicable to any given timeline.
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Use of mathematical methods in creating an investment portfolio
Holub, Miroslav ; Novotná, Veronika (referee) ; Janková, Zuzana (advisor)
The bachelor thesis is focused on the use of mathematical methods in creating an investment portfolio, which is designed for small investor. The theoretical part of the thesis describes the necessary knowledge to understand Markowitz model, selected indicators of financial analysis and the Value at Risk method. The practical part contains a selection of investment instruments traded on the US market according to established criteria, the creation of a real portfolio of these investment instruments and the final evaluation of results.
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Optimization Models of Financial Risk
Danko, Erik ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with optimization models of financial risks. The first part, which is devoted to the theoretical background, introduces the basic concepts of optimization, modern portfolio theory, fundamental and technical analysis and statistical background. The basic principles of operation of modern portfolio theory are presented. The methods for analysis and selection of assets called Growth at A Reasonable Price and portfolio optimization approach according to Harry Markowitz were used with selected methods. The practical part is focused on the data analysis, selection of assets and design of a portfolio optimization model according to selected conditions with an emphasis on minimizing investment risk. The used models examine the selected data and are solved using the MS Excel add-in Solver version.
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Investment Optimization
Bujnovský, Daniel ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This work is focused on description of two models of mathematical programming - the network model and the Markowitz portfolio model, their connection and application in transportation problems. The goal of the practical section is to approach the description of these problems to the real situations and look for their efficient solutions at the same time. All of that is accompanied by examples on real data from capital market or own model data. The theoretical considerations and thoughts are implemented in programming language Matlab. All results are explained in context to both models. The thesis also includes the introduction to economical and statistical theory which is necessary to understand the problem.
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Portfolio diversification
ŠÍP, Martin
The goal of this bachelor thesis is to show how the choice of stocks impacts the portfolio diversification in relation to risk and return. The risk was calculated as standard deviation and historical return rate was considered. The theoretical part explains basic terms related with portfolio diversification, Markowitz model, capital stock and most important factors that lead to the optimal portfolio creation such as return, risk and covariance. The practical part explains in detail, how to create an optimal portfolio. Ten companies from different sectors were randomly chosen for this bachelor thesis. These companies' shares are traded on the New York Stock Exchange. The covariance of these shares is lower than one. The next step was to calculate historical return rate and historical risk of portfolios. The highest value of historical return rate was 2.31 % and the lowest value of historical risk achieved 22.77 %. Subsequently, the efficient frontier was determined. The efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. The lowest value of portfolio risk was 2.97 % with a return of 1.38 % and the highest value of portfolio risk was 4.03 % with a return of 2.13 %. The investor chooses the portfolio which maximizes his expected benefit.
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The efficient frontier during the financial crisis.
Kocholová, Soňa ; Pošta, Vít (advisor) ; Makovský, Petr (referee)
Bachelor thesis deals with the basics of portfolio theory and its applications, mathematical and graphical models in the theory of portfolio and, finally, an estimate of the specific efficient frontiers during the financial crisis. The aim of the work is to estimate, graphically illustrate and to compare the efficient frontier for specific states in the course of eight years. These sets of portfolios are composed of two assets and that is one risk and one risk-free asset. A result of this combination is an efficient frontier illustrated in a form of the capital market line and its slope given by so called risk premium. We will focus on the comparison in time for each state individually and at the same time each year separately between the states themselves. Finally, a specific example of portfolios with various share of risk and risk-free assets are compiled lying on the line of an efficient frontier.
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