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Robustness of the Markowitz portfolios
Petráš, Tomáš ; Dupačová, Jitka (advisor) ; Kopa, Miloš (referee)
This diploma thesis deals with the problem of portfolio optimization in relation to the mean vector and the variance matrix of yields. The emphasis is put on Mar- kowitz model. In the thesis there are explored some possibilities of robustification based on the used parametric set. Beside the classic formulation of the task our focus is also devoted to the cases in which short sales are not allowed. The core of the thesis constitutes of a simulation study that models the impact of errors in the estimation of the input parameters of Markowitz model. It takes into account different types of risk aversions and different approaches to modelling parameter perturbations . Therefore it specifies the hypothesis of the dominating influence of the mean vector estimate which is valid only for a risk lover. 1
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Optimal investment problems solvable using linear programming
Jančařík, Joel ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
Portfolio optimization problem is a classical optimization problem, where the expected return of the portfolio is maximized and the risk is minimized. In this bachelor thesis some LP solvable portfolio optimization models are studied. Application on real life financial data is also included. Model with Conditional Value at Risk, MAD-model and Minimax model are described. In numerical analysis data from Frankfurt Stock Exchange are used and optimization has been made by Wolfram Mathematica 9.0 function LinearProgramming. As a result we got optimal portfolios for eleven different models for each of six minimal expected return constraints. The portfolios have been then evaluated according to the data from next year period. Powered by TCPDF (www.tcpdf.org)
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Stochastic Programming Problems via Economic Problems
Kučera, Tomáš ; Kaňková, Vlasta (advisor) ; Dupačová, Jitka (referee)
This thesis' topic is stochastic programming, in particular with regard to portfolio optimization and heavy tailed data. The first part of the thesis mentions the most common types of problems associated with stochastic programming. The second part focuses on solving the stochastic programming problems via the SAA method, especially on the condition of data with heavy tailed distributions. In the final part, the theory is applied to the portfolio optimization problem and the thesis concludes with a numerical study programmed in R based on data collected from Google Finance.
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Optimization and stress tests
Fašungová, Diana ; Dupačová, Jitka (advisor) ; Kozmík, Václav (referee)
Title: Optimization and stress tests Author: Diana Fašungová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Jitka Dupačová, DrSc., Department of Probability and Mathematical Statistics Abstract: In the thesis we apply contamination technique on a portfolio optimiza- tion problem using minimization of risk measure CVaR. The problem is considered from a risk manager point of view. We stress correlation structure of data and of revenues using appropriately chosen data for this kind of problem and for ge- nerated stress scenarios. From behaviour of CVaR with regard to contamination bounds, we formulate recommendations for the risk manager optimizing his port- folio. The recommendations are interpreted for both types of stress scenarios. In the end, limitations of the model and possible ways of improvement are discussed. Keywords: contamination bounds, stress tests, portfolio optimization, risk mana- gement
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The Investment Models in an Environment of Financial Markets
Krňávek, Jan ; Lukeš, Zdeněk (referee) ; Budík, Jan (advisor)
The thesis deals with the optimization of the selected investment portfolio. Solver suggests automated investment model that will use advanced algorithms based on artificial intelligence and principles of technical analysis. Optimization of parameters and verifying the performance of the investment model is realized on historical market data. The result of this thesis is optimized investment model with an emphasis on maximizing profits and stability. The thesis is realized in an environment Python programming language and freely available analytical libraries.
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Project portfolio optimisation with time and resources
Huml, Tomáš ; Barták, Roman (advisor) ; Vlach, Milan (referee)
Title: Project portfolio optimization with time and resources Author: Bc. Tomáš Huml Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: Doc. RNDr. Roman Barták, Ph.D Abstract: Traditional project portfolio optimization deals with static projects that are not evolving in time. The focus of this diploma thesis is on projects that are spread in time, typically such projects consists of a sequence (or other partially ordered structure) of actions that require some resources (money, people, etc.) for realization. Then the project portfolio optimization deals with selecting a subset of projects according to given time and space (resource) restrictions and optimizing certain criteria such as overall profit. This problem is very close to oversubscribed scheduling where the most profitable subset of orders is being scheduled. Hence scheduling techniques will be the main inspiration for solving this new type of problems. Lots of modelling algorithms for optimal portfolio selection are proposed in this diploma thesis and several of them are implemented in a program which is part of this thesis as well. Keywords: portfolio optimization, integer linear programming (ILP), workflow optimization, project interdependencies
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Stock Portfolio Optimalization on Czech Capital Market
Šebestíková, Sabina ; Štěpánková, Jana (referee) ; Sojka, Zdeněk (advisor)
The master's thesis is focused on Stock portfolio optimalization on Czech capital market. The analysis of each stock, estimation and portfolio optimalization proposal are included. In the practical part the Fundamental analysis is applied. The portfolio optimalization is estemated by portfolio theory which is consist in the relationship between stock price and market trends represents by PX Index and expressing correlation of them by beta coefficient.
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Dynamic Asset Allocation
Kudrna, Aleš ; Málek, Jiří (advisor) ; Fučík, Vojtěch (referee)
Today, there is a large amount of assets which are offered to investors, and if we consider the possibility of relocating the investor's funds, we come to a very complicated problem, which this thesis aims to cover. The main objective is to explore the basics of the portfolio theory and its real usage in practice. Emphasis is put on the periodic re-optimizing of the investor's portfolio and getting the answer to the question of whether such conduct is more successful than the standard and investment in equity indices. The theoretical part summarizes the currently used approaches to optimization which are tested in the practical part on real data and evaluated.
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Stochastic Programming Methods for Investment Decisions
Kubelka, Lukáš ; CFA, Tomáš Menčík, (referee) ; Popela, Pavel (advisor)
This thesis deals with methods of stochastic programming and their application in financial investment. Theoretical part is devoted to basic terms of mathematical optimization, stochastic programming and decision making under uncertainty. Furter, there are introduced basic principles of modern portfolio theory, substantial part is devoted to risk measurement techniques in the context of investment, mostly to the methods Value at Risk and Expected shortfall. Practical part aims to creation of optimization models with an emphasis to minimize investment risk. Created models deal with real data and they are solved in optimization software GAMS.
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Security Portfolio Optimalization
Dopita, Radim ; Heralecký, Tomáš (referee) ; Sojka, Zdeněk (advisor)
This thesis is focused on security portfolio optimalization using the value of stock screener. The theoretical section discusses the basic theory of markets, modern portfolio theory, diversification and the types of risks associated with financial activities, the basic steps to become an investor. The practical part is designed to build optimized stocks portfolio using the value of screening, its feigned purchase on New York Stock Exchange (NYSE), followed by monitoring the evolution rate of the portfolio thus created.
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