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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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Selected financial optimization models
Bujnovský, Daniel ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This work is focused on models of optimal asset and liability management. The practical section illustrates various ways of modelling strategies depending on the problem formulation, chosen set of assets and the type of the used optimization technique. The main examples are portfolio immunization and the Yasuda-Kasai model together with the extended version of Markowitz model. The author provides across the work an overview of different financial risks and various tools for their measurement together with possible formulations of expected returns relevant to the studied models. The individual models are compared and often extended by other constraints in order to improve their practical applicability. From the point of view of the mathematical optimization several ways of input data generation are described for example by using the extended Brownian motion. All practical parts go hand in hand with illustrative pictures and codes. The necessary financial and mathematical theory is included as well.
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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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Application of Machine Learning in Portfolio Construction
Karlíček, Ondřej ; Šíla, Jan (advisor) ; Baruník, Jozef (referee)
The thesis investigates the application of machine learning in portfolio con- struction. The analysis was conducted on a dataset consisting of 442 Amer- ican stocks. Initially, we cluster stocks using Principal Component Analysis and K-means algorithms. Then we select stock from each cluster based on return/risk metrics. Where risk was estimated by Value at Risk, and return was predicted using Random Forest and GARCH models. This leaves us with 11 stocks for every monthly period during 2020. The results indicate that the portfolios constructed from the selected stocks were able to outperform the market benchmark. However, the return predictions were not accurate enough. Thus, the portfolio from selected stock using the 1/N approach achieved better results than the portfolio optimized by the Mean-Variance model. 1
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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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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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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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Markowitzův model optimalizace portfolia
POSTLOVÁ, Šárka
The thesis deals with modern portfolio theory. The theoretical part of the thesis describes the historical development of portfolio optimization and presents the basic theoretical background of the Markowitz model, the Tobin model and the Capital asset pricing model. In the practical part of the thesis, the models are applied to real data from two Czech securities markets, PSE and RM-S. An optimal portfolios composition is proposed by the three models mentioned above and then the outputs of the models are compared to the real datas from the next period. Finally, the benefits and drawbacks of the used models are evaluated.
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Sensitivity analysis for the Markowitz model of portfolio
Sommer, Tadeáš ; Borovička, Adam (advisor) ; Pieter, Michal (referee)
The thesis mainly deals with sensitivity analysis of risk and return of portfolio in dependence on outer parameters during generating a stock portfolio. The theoretical section consist of description of risk in context of shares, the definition of characteristics of shares and portfolio, and the assumptions for modern theory of portfolio. Also the specifications of mathematical model, the model of quadratic programming and modified model are parts of this section. The modified model adds condition for maximal weight of shares. The practical section begins with statistical description of data, while the data consist of shares which are included in FTSEurofirst 100 index. Sensitivity analysis is made for two approches where we allow or disallow the short-selling. Consecutive part propose final portfolios for three types of investors.
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