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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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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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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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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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