Sample average approximation (SAA) is a well-known solution methodology for traditional stochastic programs which are risk neutral in the sense that they consider optimization of expectation functionals. In this thesis we establish sample average approximation methods for two classes of non-traditional stochastic programs. The first class is that of stochastic min-max programs, i.e., min-max problems with expected value objectives, and the second class is that of expected value constrained stochastic programs. We specialize these SAA methods for risk-averse stochastic problems with a bi-criteria objective involving mean and mean absolute deviation, and those with constraints on conditional value-at-risk. For the proposed SAA methods, we prove that the results of the SAA problem converge exponentially fast to their counterparts for the true problem as the sample size increases. We also propose implementation schemes which return not only candidate solutions but also statistical upper and lower bound estimates on the optimal value of the true problem. We apply the proposed methods to solve portfolio selection and supply chain network design problems. Our computational results reflect good performance of the proposed SAA schemes. We also investigate the effect of various types of risk-averse stochastic programming models in controlling risk in these problems.

The combination of two or more portfolio rules is theoretically convex in return-risk space, which provides for a new class of portfolio rules that gives purpose to the Mean-Variance framework out-of-sample. The author investigates the performance loss from estimation risk between the unconstrained Mean-Variance portfolio and the out-of-sample Global Minimum Variance portfolio. A new two-fund rule is developed in a specific class of combined rules, between the equally weighted portfolio and a mean-variance portfolio with the covariance matrix being estimated by linear shrinkage. The study shows that this rule performs well out-of-sample when covariance estimation error and bias are balanced. The rule is performing at least as good as its peer group in this class of combined rules.

This thesis, “Empirical Asset Pricing and Investment Strategies”, examines a number of topics related to portfolio choice, asset pricing, and strategic and tactical asset allocation. The first two papers treat the predictability of asset returns. Since at least the mid-1980s until quite recently, the conventional wisdom has been that it is possible to predict the return on, for example, an index of stocks. However, a series of recent papers have challenged this conventional wisdom. I answer this challenge and show that it is possible to predict returns if structural changes in the underlying economy are taken into account. The third paper examines the comovement between stocks and bonds. I show how it is possible to improve the composition of a portfolio consisting of these two asset classes by taking into account how the comovement changes over time. All three papers are self-contained and can therefore be read in any order. The first paper is entitled “Structural Breaks in Asset Return Predictability: Can They Be Explained?” Here I investigate whether predictability has changed over time and, if so, whether it is possible to tie the change to any underlying economic variables. Dividend yield and the short interest rate are often used jointly as instruments to predict the return on stocks, but several researchers present evidence that the relation has undergone a structural break. I use a model that extends the conventional structural breaks models to allow both for smooth transitions from one state to another (with a break as a special case), and for transitions that depend on a state variable other than time. The latter allows me to directly test whether, for example, the business cycle influences how the instruments predict returns. The results suggest that this is not the case. However, I do find evidence of a structural change primarily in how the instruments predict returns for large firms. The change differs from a break in that it appears to be an extended non-linear transition during the period 1993—1997. After the change, the short rate does not predict returns at all. Dividend yield, on the other hand, is strongly significant, and the return has become more sensitive to it. In the second paper, “Restoring the Predictability of Equity Returns,” I take another perspective on predictability and structural shifts. Several recent papers have questioned the predictability of equity returns, potentially implying serious negative consequences for investment decision-making. With return data including the 1990s, variables that previously predicted returns, such as the dividend yield, are no longer significant and results of out-of-sample tests are often weak. A possible reason is that the underlying structure of the economy has changed. I use an econometric model that allows for regime shifts over time as well as due to changes in a state variable, in this case the price-earnings ratio. This makes it possible to separate influences from these two sources and to determine whether one or both sources have affected return predictability. The results indicate that, first, a structural change occurred during the 1990s, and, second, that the unusually high level of price earnings in the late 1990s and early 2000s temporarily affected predictability at the 12-month horizon. In the third paper, “Coupling and Decoupling: Changing Relations between Stock and Bond Market Returns,” I investigate stock-bond comovement. The correlation between stocks and bonds has changed dramatically over the last ten years, introducing a new type of risk for portfolio managers, namely, correlation risk. I use GARCH estimates of stock volatility, simple regressions, and regime-switching econometric models to assess whether level of volatility, or changes in volatility, can be used to explain some of the changes in comovement in seven different countries. As regards volatility level, strong support is found in almost all countries to suggest that high volatility predicts lower, or negative, comovement. I argue that this can be evidence of a market-timing type of behavior. As for changes in volatility, the results are more mixed. Only for the U.S. market do I find strong support to conclude that large changes tend to coincide with lower, or negative, comovement. This could be evidence of a flight-to-quality (or cross-market hedging) type of behavior. / <p>Diss. Stockholm : Handelshögskolan, 2007</p>

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...

Orientador: Luziane Ferreira de Mendonça / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-17T11:31:02Z (GMT). No. of bitstreams: 1 Soares_VanessadeCarvalhoAlves_M.pdf: 1540180 bytes, checksum: 198ad552da53ca9cbe2fd6bf7fc77c17 (MD5) Previous issue date: 2011 / Resumo: Neste trabalho, propomos a determinação de uma carteira de investimento ótima via um método sem derivada. Para isso, utilizamos o modelo de média-variância proposto por Harry M. Markowitz. no qual o problema é formulado de modo a se minimizar o risco do portfolio para um dado nível de retorno esperado, ou maximizar o nível de retorno fixado do portfolio associado a um dado nível de risco e determinar todas as carteiras ótimas, no sentido risco e retorno, formando a Fronteira Eficiente. Nosso algoritmo é baseado no Método Nelder-Mead, destinado à resolução de problemas de programação não linear irrestritos. Assim, adequamos a formulação do portfolio, que depende de restrições, para a utilização do mesmo. / Abstract: In this work we perform a portfolio optimization by using a derivative-free method. For this, we use the Mean-Variance Analysis proposed by Harry M. Markowitz, in which the problem is formulated as one of minimizing portfolio risk subject to a targeted expected portfolio return. Or, for a particular level of risk, we can find a combination of assets that is going to give the highest expected return and determine all the optimal portfolios, towards risk and return, forming the Efficient Frontier. Our algorithm is based on Nelder-Mead method, for solving problems of unconstrained nonlinear programming. Therefore, the formulation of the portfolio, subject to constraints, was adapted for its use. / Mestrado / Mestre em Matemática

Orientador: Fernando José Von Zuben / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-26T06:49:07Z (GMT). No. of bitstreams: 1 Azevedo_CarlosRenatoBelo_D.pdf: 3449858 bytes, checksum: 7a1811aa772f1ae996e8851c60627b7c (MD5) Previous issue date: 2012 / Resumo: A presença de incerteza em resultados futuros pode levar a indecisões em processos de escolha, especialmente ao elicitar as importâncias relativas de múltiplos critérios de decisão e de desempenhos de curto vs. longo prazo. Algumas decisões, no entanto, devem ser tomadas sob informação incompleta, o que pode resultar em ações precipitadas com consequências imprevisíveis. Quando uma solução deve ser selecionada sob vários pontos de vista conflitantes para operar em ambientes ruidosos e variantes no tempo, implementar alternativas provisórias flexíveis pode ser fundamental para contornar a falta de informação completa, mantendo opções futuras em aberto. A engenharia antecipatória pode então ser considerada como a estratégia de conceber soluções flexíveis as quais permitem aos tomadores de decisão responder de forma robusta a cenários imprevisíveis. Essa estratégia pode, assim, mitigar os riscos de, sem intenção, se comprometer fortemente a alternativas incertas, ao mesmo tempo em que aumenta a adaptabilidade às mudanças futuras. Nesta tese, os papéis da antecipação e da flexibilidade na automação de processos de tomada de decisão sequencial com múltiplos critérios sob incerteza é investigado. O dilema de atribuir importâncias relativas aos critérios de decisão e a recompensas imediatas sob informação incompleta é então tratado pela antecipação autônoma de decisões flexíveis capazes de preservar ao máximo a diversidade de escolhas futuras. Uma metodologia de aprendizagem antecipatória on-line é então proposta para melhorar a variedade e qualidade dos conjuntos futuros de soluções de trade-off. Esse objetivo é alcançado por meio da previsão de conjuntos de máximo hipervolume esperado, para a qual as capacidades de antecipação de metaheurísticas multi-objetivo são incrementadas com rastreamento bayesiano em ambos os espaços de busca e dos objetivos. A metodologia foi aplicada para a obtenção de decisões de investimento, as quais levaram a melhoras significativas do hipervolume futuro de conjuntos de carteiras financeiras de trade-off avaliadas com dados de ações fora da amostra de treino, quando comparada a uma estratégia míope. Além disso, a tomada de decisões flexíveis para o rebalanceamento de carteiras foi confirmada como uma estratégia significativamente melhor do que a de escolher aleatoriamente uma decisão de investimento a partir da fronteira estocástica eficiente evoluída, em todos os mercados artificiais e reais testados. Finalmente, os resultados sugerem que a antecipação de opções flexíveis levou a composições de carteiras que se mostraram significativamente correlacionadas com as melhorias observadas no hipervolume futuro esperado, avaliado com dados fora das amostras de treino / Abstract: The presence of uncertainty in future outcomes can lead to indecision in choice processes, especially when eliciting the relative importances of multiple decision criteria and of long-term vs. near-term performance. Some decisions, however, must be taken under incomplete information, what may result in precipitated actions with unforeseen consequences. When a solution must be selected under multiple conflicting views for operating in time-varying and noisy environments, implementing flexible provisional alternatives can be critical to circumvent the lack of complete information by keeping future options open. Anticipatory engineering can be then regarded as the strategy of designing flexible solutions that enable decision makers to respond robustly to unpredictable scenarios. This strategy can thus mitigate the risks of strong unintended commitments to uncertain alternatives, while increasing adaptability to future changes. In this thesis, the roles of anticipation and of flexibility on automating sequential multiple criteria decision-making processes under uncertainty are investigated. The dilemma of assigning relative importances to decision criteria and to immediate rewards under incomplete information is then handled by autonomously anticipating flexible decisions predicted to maximally preserve diversity of future choices. An online anticipatory learning methodology is then proposed for improving the range and quality of future trade-off solution sets. This goal is achieved by predicting maximal expected hypervolume sets, for which the anticipation capabilities of multi-objective metaheuristics are augmented with Bayesian tracking in both the objective and search spaces. The methodology has been applied for obtaining investment decisions that are shown to significantly improve the future hypervolume of trade-off financial portfolios for out-of-sample stock data, when compared to a myopic strategy. Moreover, implementing flexible portfolio rebalancing decisions was confirmed as a significantly better strategy than to randomly choosing an investment decision from the evolved stochastic efficient frontier in all tested artificial and real-world markets. Finally, the results suggest that anticipating flexible choices has lead to portfolio compositions that are significantly correlated with the observed improvements in out-of-sample future expected hypervolume / Doutorado / Engenharia de Computação / Doutor em Engenharia Elétrica

The presented diploma thesis deals with the issue of multi-criteria decision making in practice. The main aim is to demonstrate the possibilities of involvement the parametric programming in multi-criteria linear programming (MCLP). The first, theoretically oriented chapter, describes the necessary theoretical knowledge. In this chapter is presented the role of financial planning together with essential relationships, by which is determined the rest of the work. This chapter also discusses the issue of multi-criteria linear programming including a description of selected a priori methods. The selected a priori methods are lexicographic method, utility function method, minimization of the distance from the ideal solution and minimal component method. The second chapter is devoted to the practical application of multi-criteria optimization portfolio with a parametric budget. For all the analyzed methods are firstly discussed models without integer conditions, and consequently their modification with these conditions. For the purpose of this work was used solver in MS Excel spreadsheet along with the created macro.

The competitive electricity market faces low margins while the energy transition entails volatile electricity prices and major risks in the market. Along with these problems, there are challenges in optimizing energy portfolios, as they are based on maximized return and minimized risks. Portfolio managers handle electricity contracts for customers with the aim of offering competitive electricity contracts and at the same time achieving profit. This study therefore aims to investigate how electricity trading companies can optimize the energy portfolio for corporate customers in the Swedish electricity market. In addition, it is analyzed how these companies can adapt portfolio optimization to the challenges of the electricity market and what kind of digital systems are needed to support portfolio optimization. Previous studies in the subject have mainly focused on a quantitative approach. In this study on the other hand, a qualitative method is used. This in order to use interviews, models and theories to investigate how electricity trading companies can optimize the portfolio for their corporate customers. The study is divided into an empirical part that includes interviews with 12 electricity trading companies, as well as a theoretical part. The theoretical part deals with theories for risk management, including portfolio optimization, price hedging with electricity derivatives and the Risk Management Payoff model. In addition, the Customer Relationship Management (CRM) model is included, with the aim of strengthening relationships. The theoretical framework has been used to analyze the empirical data of the study and has resulted in conclusions that answer the research questions. The results show that in order to achieve energy portfolio optimization, futures contract is the derivative that provides the lowest risk and can be used as the optimal hedging tool. For larger corporate customers, however, forward contract is a more suitable hedging tool. This is because larger customers prefer to secure monthly contracts, rather than daily settled contracts with futures. To support portfolio management with electricity contracts, there is a need for support systems. Electricity trading companies are in need of a common system for both financial and physical trading to enable easier management. In addition, security functions in systems as well as more informative and customer-friendly systems are of interest. Portfolio optimization is customer centric, thus a strong relationship between portfolio manager and customer, with good trust and reputation, is important. Finally, adaptation in portfolio management with diversification and automation with AI, can be a way to achieve competitiveness in the electricity market also in the future.

The thesis deals with the optimization of the selected investment portfolio. Solver suggests automated investment model that will use advanced algorithms based on artificial intelligence and principles of technical analysis. Optimization of parameters and verifying the performance of the investment model is realized on historical market data. The result of this thesis is optimized investment model with an emphasis on maximizing profits and stability. The thesis is realized in an environment Python programming language and freely available analytical libraries.

Diploma thesis focuses on the issue of an appropriate selection of securities and the subsequent establishment of a portfolio of these securities. Follow detailed discussion about analysis of portfolio and investor’s preferences. Below is a description of the CAPM model, its assumptions and usage of this model to build a portfolio. Then there is the actual calculation of characteristics of securities traded on the Prague Stock Exchange and on the basis of these calculations is made the proposal of several portfolios and their evaluation.