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Stochastic dominance in portfolio optimization
Paulik, Marek ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
The main topic of this thesis is the application of stochastic dominance constrains to portfolio optimization problems. First, we recall Markowitz model. Then we present portfolio selection problems with stochastic dominance constraints. Finally, we compare performance of these two approaches in an empirical study presented in the last chapter.
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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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Optimization problems with chance constraints
Drobný, Miloslav ; Adam, Lukáš (advisor) ; Lachout, Petr (referee)
Autor se v diplomové práci zabývá optimalizačními úlohami s pravděpodob- nostními omezeními. Konkrétně pak situacemi, kdy není známo pravděpo- dobnostní rozdělení přítomného náhodného efektu. K řešení těchto problém· lze přistoupit metodami optimistických a pesimistických scénář·, kdy z dané rodiny možných pravděpodobnostních rozdělení vybíráme bu¤ nejpříznivější možnou variantu, nebo naopak tu nejméně výhodnou. Optimalizační úlohy s pravděpodobnostními omezeními formulovanými pomocí výše zmíněných přístup· byly za učinění jistých předpoklad· transformovány do jednoduš- ších a řešitelných optimalizačních úloh. Dosažené výsledky byly aplikovány na reálná data z oblastí optimalizace portfolia a zpracování obrazu. 1
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Spectral risk measures in portfolio selection problems
Štefánik, Martin ; Kopa, Miloš (advisor) ; Zahradník, Petr (referee)
This thesis examines spectral risk measures. Spectral risk measures, as a subset of coherent risk measures, satisfy all the crucial and reasonable properties that a risk measure should have. A specific characteristic of a spectral risk measure is that it makes it possible for an investor to quantify the risk that arises due to holding a selected group of assets based on his or her personal attitude towards risk. The aim of this bachelor thesis is to discuss the properties of spectral measures of risk and their relations to commonly known measures of risk, but primarily to scrutinize its utilization in the portfolio selection problem. Based on monthly returns of stocks from chosen American stock exchanges we compute the optimal portfolios of stock indices for different risk aversion functions, and consequently we make an analysis of the results. Powered by TCPDF (www.tcpdf.org)
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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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Robust approaches in portfolio optimization with stochastic dominance
Kozmík, Karel ; Kopa, Miloš (advisor)
We use modern approach of stochastic dominance in portfolio optimization, where we want the portfolio to dominate a benchmark. Since the distribution of returns is often just estimated from data, we look for the worst distribution that differs from empirical distribution at maximum by a predefined value. First, we define in what sense the distribution is the worst for the first and second order stochastic dominance. For the second order stochastic dominance, we use two different formulations for the worst case. We derive the robust stochastic dominance test for all the mentioned approaches and find the worst case distribution as the optimal solution of a non-linear maximization problem. Then we derive programs to maximize an objective function over the weights of the portfolio with robust stochastic dominance in constraints. We consider robustness either in returns or in probabilities for both the first and the second order stochastic dominance. To the best of our knowledge nobody was able to derive such program before. We apply all the derived optimization programs to real life data, specifically to returns of assets captured by Dow Jones Industrial Average, and we analyze the problems in detail using optimal solutions of the optimization programs with multiple setups. The portfolios calculated using...
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Multivariate financial time series models in portfolio optimization
Bureček, Tomáš ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
This master thesis deals with the modeling of multivariate volatility in finan- cial time series. The aim of this work is to describe in detail selected approaches to modeling multivariate financial volatility, including verification of models, and then apply them in an empirical study of asset portfolio optimization. The results are compared with the classical approach of portfolio optimization theory based on unconditional moment estimates. The evaluation was based on four known op- timization problems, namely minimization of variance, Markowitz's model, ma- ximization of the Sharpe ratio and minimization of CVaR. The output portfolios were compared by using four metrics that reflect the returns and risks of the port- folios. The results demonstrated that employing the multivariate volatility models one obtains higher expected returns with less expected risk when comparing with the classical approach. 1
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Portfolio Optimization Using Genetic Algorithm
Kuruc, Igor ; Hanušová, Helena (referee) ; Chvátalová, Zuzana (advisor)
This bachelor's thesis focuses on using knowledge of portfolio theory and methods of soft computing. Theoretical backgroung is provided by postmodern portfolio theory and genetic algorithms. The purpose of aplicational section is maximizing risk-return measure. The result is optimized portfolio based on required properties. All calculation are made in Matlab software
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Robust approaches in portfolio optimization with stochastic dominance
Kozmík, Karel ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
We use modern approach of stochastic dominance in portfolio optimization, where we want the portfolio to dominate a benchmark. Since the distribution of returns is often just estimated from data, we look for the worst distribution that differs from empirical distribution at maximum by a predefined value. First, we define in what sense the distribution is the worst for the first and second order stochastic dominance. For the second order stochastic dominance, we use two different formulations for the worst case. We derive the robust stochastic dominance test for all the mentioned approaches and find the worst case distribution as the optimal solution of a non-linear maximization problem. Then we derive programs to maximize an objective function over the weights of the portfolio with robust stochastic dominance in constraints. We consider robustness either in returns or in probabilities for both the first and the second order stochastic dominance. To the best of our knowledge nobody was able to derive such program before. We apply all the derived optimization programs to real life data, specifically to returns of assets captured by Dow Jones Industrial Average, and we analyze the problems in detail using optimal solutions of the optimization programs with multiple setups. The portfolios calculated using...
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