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Securities portfolio optimization
Pinkava, Ondřej ; Bartošek, Vladimír (referee) ; Sojka, Zdeněk (advisor)
This dissertation deals with the securities portfolio optimization. After introducing the definitions, I try to explain the particular investment instruments with regard to returns and risks. The following part provides a theory which tells more about different market risks and returns on the final securities portfolio. Concerning these models the effective portfolio has been set up.
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Portfolio selection based on hierarchical structure of its components
Ševinský, Robert ; Krištoufek, Ladislav (advisor) ; Rusnák, Marek (referee)
This thesis investigate empirical performance of three portfolio selection and covariance matrix models. The goal is to find a strategy that outperform equally weighted portfolio in the long run and survives even in times of finan- cial distress. Two models based on Markowitz approach absolutely failed in this context, however the last approach based on network analysis indeed out- perform the market even after risk adjustment of returns. Moreover this model have sparse transaction matrix throughout time, therefore exhibit excellent properties even in the presence of transaction costs. Results for network based portfolio were obtained from running a back test on 160 member companies of S&P 500 index for 6'000 trading days. JEL Classification G11, G32, C10 Keywords Portfolio selection, Minimum spanning tree, Transaction costs, Covariance matrix Author's e-mail r.sevinsky@gmail.com Supervisor's e-mail kristoufek@ies-prague.org
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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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Robust methods in portfolio theory
Petrušová, Lucia ; Branda, Martin (advisor) ; Večeř, Jan (referee)
01 Abstract: This thesis is concerned with the robust methods in portfolio theory. Different risk measures used in portfolio management are introduced and the corresponding robust portfolio optimization problems are formulated. The analytical solutions of the robust portfolio optimization problem with the lower partial moments (LPM), value-at-risk (VaR) or conditional value-at-risk (CVaR), as a risk measure, are presented. The application of the worst-case conditional value-at-risk (WCVaR) to robust portfolio management is proposed. This thesis considers WCVaR in the situation where only partial information on the underlying probability distribution is available. The minimization of WCVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. Several numerical examples based on real market data are presented to illustrate the proposed approaches and advantage of the robust formulation over the corresponding nominal approach.
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Scenario reduction in Monte Carlo methods in optimization
Trégner, Tomáš ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
Tato práce se zabývá redukcí scénáøù pøi pou¾ití Monte Carlo metod. Hlavním cílem je posoudit, jaké výhody, èi zlep¹ení nám mù¾e redukce scénáøù poskytnout a zda nám mù¾e být v praxi u¾iteèná. V práci budeme prezentovat výsledky zís- kané pomocí vlastní implementace redukèního algoritmu v jazyku Python. Pro úèely posouzení efektivity redukce scénáøù byly vybrány dva konkrétní problémy. Prvním z nich je odhad konstanty π, který je pro tento úèel vhodný zejména proto, ¾e je znám pøesný výsledek. Druhým problém, na který se soustøedíme, je pak výbìr optimálního portfolia z daných akcií, který jsme vybrali proto, ¾e se jedná o pomìrnì nároèný a zajímavý problém umo¾òující posoudit èasovou efek- tivitu metody redukce scénáøù. Na základì na¹ich výpoètù docházíme k závìru, ¾e redukce scénáøù mù¾e být u¾iteèným nástrojem pro slo¾ité úlohy, je v¹ak tøeba si dávat pozor na vhodnou volbu pou¾ité metriky. 1
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Robust methods in portfolio theory
Petrušová, Lucia ; Branda, Martin (advisor) ; Večeř, Jan (referee)
01 Abstract: This thesis is concerned with the robust methods in portfolio theory. Different risk measures used in portfolio management are introduced and the corresponding robust portfolio optimization problems are formulated. The analytical solutions of the robust portfolio optimization problem with the lower partial moments (LPM), value-at-risk (VaR) or conditional value-at-risk (CVaR), as a risk measure, are presented. The application of the worst-case conditional value-at-risk (WCVaR) to robust portfolio management is proposed. This thesis considers WCVaR in the situation where only partial information on the underlying probability distribution is available. The minimization of WCVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. Several numerical examples based on real market data are presented to illustrate the proposed approaches and advantage of the robust formulation over the corresponding nominal approach.
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Practical usage of optimal portfolio diversification using maximum entropy principle
Chopyk, Ostap ; Krištoufek, Ladislav (advisor) ; Kraicová, Lucie (referee)
"Practical usage of optimal portfolio diversification using maximum entropy principle" by Ostap Chopyk Abstract This thesis enhances the investigation of the principle of maximum entropy, implied in the portfolio diversification problem, when portfolio consists of stocks. Entropy, as a measure of diversity, is used as the objective function in the optimization problem with given side constraints. The principle of maximum entropy, by the nature itself, suggests the solution for two problems; it reduces the estimation error of inputs, as it has a shrinkage interpretation and it leads to more diversified portfolio. Furthermore, improvement to the portfolio optimization is made by using design-free estimation of variance-covariance matrices of stock returns. Design-free estimation is proven to provide superior estimate of large variance-covariance matrices and for data with heavy-tailed densities. To asses and compare the performance of the portfolios, their out-of-sample Sharpe ratios are used. In nominal terms, the out-of- sample Sharpe ratios are almost always lower for the portfolios, created using maximum entropy principle, than for 'classical' Markowitz's efficient portfolio. However, this out-of-sample Sharpe ratios are not statistically different, as it was tested by constructing studentized time-series...
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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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Robust portfolio selection
Horváthová, Inés ; Červinka, Michal (advisor) ; Kraicová, Lucie (referee)
In this thesis, we take the mean-risk approach to portfolio optimi- zation. We will first define risk measures in general and then intro- duce three commonly used ones: variance, Value-at-risk (V aR) and Conditional-value-at-risk (CV aR). For each of these risk measures we formulate the corresponding mean-risk models. We then present their robust counterparts. We focus mainly on the robust mean-variance models, which we also apply to historical data using free statistical software R. Finally, we compare the results with the classical non- robust mean-variance model.
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