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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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Parameter choice in portfolio optimization problems based on out-of-sample performance
Vaňková, Kateřina ; Kopa, Miloš (advisor) ; Večeř, Jan (referee)
This thesis investigates three optimization models using the rolling window method. These models are based on maximizing profits and minimizing risk. Two statistics are considered in the models: expected value and a risk measure. Risk measures analyzed in this thesis are: the variance, the Conditional Value-at-Risk at a specified confidence level, and the Mean Absolute Deviation. Models are tested on the real US stock data of ten companies in the time period of twenty years: from January 30th, 1999 to January 30th, 2019. The aim of this thesis is to analyze these models using the rolling window method and to investigate its sensitivity towards changes in the values of several parameters in order to identify the best parameter setting.
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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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Multivariate stochastic dominance and its application in portfolio optimization problems
Petrová, Barbora ; Kopa, Miloš (advisor) ; Ortobelli, Sergio (referee) ; Branda, Martin (referee)
Title: Multivariate stochastic dominance and its application in portfolio optimization Problems Author: Barbora Petrová Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: This thesis discusses the concept of multivariate stochastic dominance, which serves as a tool for ordering random vectors, and its possible usage in dynamic portfolio optimization problems. We strictly focus on different types of the first-order multivariate stochastic dominance for which we describe their generators in the sense of von Neumann-Morgenstern utility functions. The first one, called strong multivariate stochastic dominance, is generated by all nondecreasing multivariate utility functions. The second one, called weak multivariate stochastic dominance, is defined by relation between survival functions, and the last one, called the first-order linear multivariate stochastic dominance, applies the first-order univariate stochastic dominance notion to linear combinations of marginals. We focus on the main characteristics of these types of stochastic dominance, their relationships as well as their relation to the cumulative and marginal distribution functions of considered random vectors. Formulated...
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Portfolio optimization using risk premia
Novotná, Tereza ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
The main topic of this thesis is Portfolio Optimization Using Risk Premia. Basic terms are defined there such as utility function, investor's risk aversion, risk premia, absolute risk aversion measure and portfolio optimization. There are also stated important theorems about risk aversion. For better understanding, there can be found few examples. At the end of this thesis is shown empirical study. It presents how the restriction of risk premia affects optimal investment and other numerical results.
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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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The Creation of Own Portfolio on a Stock Market
OBSTOVÁ, Marie
This bachelor thesis is dedicated to the characterization of selected sectors of the stock market in terms of yield and risk and to the suggestion optimal portfolio based on the detected results. The thesis consists of two main parts, the theoretical and practical ones. The first section is dedicated to characteristic basic concepts and portfolio characteristics. The second part of this thesis deals with selection of 60 shares of the five shares sectors, calculations of the main characteristics and creating the optimal portfolio. The used characteristics for rating of the shares are yield, risk, systematic risk, individual risk, median, coefficient of variation and factor beta. At a portfolio of 15 shares were confirmed the theoretical conclusions about the drop in the overal risk due to individual risk. The values of individual risk fell from 8,35 % to 1,56 %. In practice this is unworkable portfolio. The reason is the high fees and systematic risk, what for they are created three portfolio after 5 shares. These portfolio can be seen as the result of work.
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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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Creation of equity portfolio under unusual market conditions by using the methods of decision making
Čižmař, Adam ; Borovička, Adam (advisor) ; Sokol, Ondřej (referee)
This bachelor thesis deals with problems of investing in stock market. There are plenty of different approaches to investing into stocks, however methods used in this thesis belong among multi-criteria decision making methods. Such an aproach is not commonly used which provides an interesting point of view that differs from widely used methods. This thesis consists of theoretical background to market environment and stocks themselves and also of theoretical description of multi-criteria evaluation and multi-criteria programming. Specifically I use ELECTRE I method as multi-criteria evaluation and aggregation of linear functions as multi-criteria programming method. By using these two methods I create two different portfolios based on two separate strategies. First of them aims to maximize capital gains whereas the second one aims to maximize dividend profits and to minimize risk, as well.
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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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