Title: Project portfolio optimization with time and resources Author: Bc. Tomáš Huml Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: Doc. RNDr. Roman Barták, Ph.D Abstract: Traditional project portfolio optimization deals with static projects that are not evolving in time. The focus of this diploma thesis is on projects that are spread in time, typically such projects consists of a sequence (or other partially ordered structure) of actions that require some resources (money, people, etc.) for realization. Then the project portfolio optimization deals with selecting a subset of projects according to given time and space (resource) restrictions and optimizing certain criteria such as overall profit. This problem is very close to oversubscribed scheduling where the most profitable subset of orders is being scheduled. Hence scheduling techniques will be the main inspiration for solving this new type of problems. Lots of modelling algorithms for optimal portfolio selection are proposed in this diploma thesis and several of them are implemented in a program which is part of this thesis as well. Keywords: portfolio optimization, integer linear programming (ILP), workflow optimization, project interdependencies

This thesis performs portfolio optimization using three allocation methods, Certainty Equivalence Tangency (CET), Global Minimum Variance (GMV) and Minimum Conditional Value-at-Risk (MinCVaR). We estimate expected returns and covariance matrices based on 7 stock market indices with a DCC-GARCH model including an ARMA (1.1) process and an external regressor of an implied volatility index (VIX). We then simulate returns using a rolling window of 500 daily observations and construct portfolios based on the allocation methods. The results suggest that the model can sufficiently estimate expected returns and covariance matrices and we can outperform benchmarks in form of equally weighted and historical portfolios in terms of higher returns and lower risk. Over the whole out-of-sample period the CET portfolio yields the highest mean returns and GMV and MinCVaR can significantly lower the variance. The inclusion of VIX has marginal effects on the forecasting accuracy and it seems to impair the estimation of risk.

Com a crescente desregulamentação dos mercados de energia, os diferentes participantes dos mercados se deparam com a necessidade de gerenciar de maneira eficiente seus investimentos em energia elétrica. Nesse cenário, a otimização das Carteiras de Contratos mostra-se uma técnica interessante no planejamento estratégico dos agentes de mercados de energia. Os mercados estão frequentemente expostos a riscos de diversas fontes, assim, a mitigação dos mesmos é fundamental. A Teoria do Portfólio, proposta por Harry Markowitz, tem sido utilizada em análises envolvendo diversos mercados. Este trabalho analisa um problema de Gestão de Carteiras de Contratos de energia elétrica, com Gestão de Risco. A relação contratual entre a ANDE (Administración Nacional de Electricidad Paraguai) e Itaipu Binacional é utilizada como estudo de caso. A metodologia proposta para tratar o problema extende a teoria de Markowitz em um contexto de tomada de decisão multiobjetivo, no qual se busca minimizar os gastos da ANDE em contratação de energia (via programação não-linear) e também o risco do portfólio, avaliado por meio da variância do mesmo. Por meio do modelo proposto é possível obter a decisão contratual ótima de ANDE, que minimiza o custo de seu portfólio para cada nível de risco. Os resultados obtidos indicam que o modelo é eficiente em termos de redução de custos e risco. / Due to the increasing deregulation of electricity markets, different market participants were faced with the necessity to effectively manage their investment in electricity. In this scenario, portfolio optimization is a relevant technique that can be investigated for strategic planning by agents on energy markets. In general, markets are exposed to risks from multiple sources, the mitigation of such risks, thus, is important. The portfolio theory proposed by Harry Markowitz has been used in analyses involving several markets. This work analyzes the problem of electricity Portfolio Management, with Risk Management. The contractual relationship between ANDE and Itaipu Binacional is used as a study case. The methodology proposed for addressing the problem extends Markowitz´s theory (applying non-linear programming) for a context of multi-objective decision making, searching for the minimization of ANDEs power contract costs, as well the portfolio risk, evaluated by its variance. With the proposed model, it is possible to obtain the optimal contract decision, which minimizes the portfolio cost for each risk level. Results indicate that the model proposed is efficient in cost and risk minimization.

A geração hidrelétrica é dependente da afluência, no entanto, é possível minimizar a variação da energia natural afluente por meio dos reservatórios. Por sua vez, a geração eólica tem como desvantagem a volatilidade devido a sua dependência em relação ao vento. Nesse sentido, uma carteira otimizada de projetos eólicos possibilita a redução da volatidade da energia gerada pelo conjunto, na medida em que aproveita as complementariedades do vento. No Brasil, os Estados da Bahia, Rio Grande do Norte, Ceará, Rio Grande do Sul e Piauí concentram 90% da capacidade instalada das usinas eólicas em operação, em construção ou contratada, com uma previsão da fonte atingir 11,6% de participação na matriz elétrica. A pesquisa tem como objetivo desenvolver uma metodologia de apoio baseada na teoria de portifólio de Markowitz que poderá ser utilizada pelo órgão de planejamento energético brasileiro para a definição da quantidade de energia a ser contratada por fonte e local, por meio de leilões de energia regionais e por fonte, com o objetivo de se obter uma carteira otimizada de empreendimentos, que reduza a volatilidade. O método também pode servir de apoio ao investidor para se obter um portfólio de usinas que minimize o risco de exposição financeira no mercado de curto prazo. Nenhum estudo aplicando a teoria de portifólio de Markowitz em usinas eólicas do Brasil foi encontrado na literatura. Os resultados obtidos demonstram que a carteira formada pelas usinas eólicas existentes não está na fronteira eficiente e poderia ser otimizada com aumento da expectativa de geração ou redução do risco. No mesmo sentido, a otimização da carteira também reduziu o risco de exposição ao mercado de curto prazo. / Even though the hydroelectric generation is highly dependent on the river flows, it is possible to minimize the volatility of the energy generation in a given period using the storage capacity of the reservoirs. In contrast, to minimize the volatility of the wind generation is burdensome due to its dependency on wind. Accordingly, an optimized portfolio of wind projects all together allows the reduction of the volatility of the energy generation for the complementarity of wind from different locations. In Brazil, the states of Bahia, Rio Grande do Norte, Ceara, Rio Grande do Sul and Piauí concentrate 90% of the installed capacity of wind power plants in operation, under construction or contracted with a font forecast to reach 11.6% share the electric matrix. The Thesis aims to develop a support methodology based in portfolio theory of Markowitz that can be used by the Brazilian-planning agency in future, to define the amount of energy to be contracted by source and location, through regional and source energy auctions, to obtain an optimized portfolio projects, with reduced volatility. The methodology can also serve to support the investor to obtain a portfolio of plants that minimize the risk of financial exposure to short-term market. No study applying Markowitz\'s portfolio theory in wind farms of Brazil was found in the literature. The results show that the portfolio of the existing wind farms is not on the efficient frontier and could be optimized with increased expectation of generating or reducing the risk. Similarly, the optimization of the portfolio also reduced the risk of exposure to short-term market.

Submitted by Maicon Juliano Schmidt (maicons) on 2015-05-25T14:00:15Z No. of bitstreams: 1 Jorge Augusto Dias Samsonescu.pdf: 443638 bytes, checksum: 0ac887f981377608fa611c1016a91b22 (MD5) / Made available in DSpace on 2015-05-25T14:00:15Z (GMT). No. of bitstreams: 1 Jorge Augusto Dias Samsonescu.pdf: 443638 bytes, checksum: 0ac887f981377608fa611c1016a91b22 (MD5) Previous issue date: 2015-02-20 / Banco do Brasil S.A. / Este trabalho analisa o desempenho fora da amostra de carteiras de mínima variância e baixa volatilidade no mercado de ações brasileiro entre 2003 e 2013, comparativamente ao índice IBOVESPA e a uma carteira igualmente ponderada. As carteiras de mínima variância foram otimizadas com restrição de posições vendidas e limite de peso para os ativos. A matriz de covariância foi estimada pelo método amostral e método shrinkage proposto por Ledoit e Wolf (2003). A carteira de baixa volatilidade foi estruturada de forma similar ao método do índice S&P 500 Low Volatility. O período utilizado para o rebalanceamento das carteiras foi quadrimestral e os ativos elegíveis para as carteiras foram os componentes do IBOVESPA em cada quadrimestre analisado. A comparação das carteiras foi feita através dos indicadores de retorno, desvio padrão e índice de Sharpe anualizados, MVaR e maximum drawdown. Os resultados apontam para a importância na escolha do limite de pesos para os ativos das carteiras de mínima variância. As carteiras de menor risco obtiveram os melhores resultados em todos os indicadores testados. / This study analyzes the out-of-sample performance of minimum-variance and low volatility portfolios in the Brazilian stock market from 2003 to 2013, when compared to IBOVESPA index and an equally weighted portfolio. The minimum variance portfolios have been optimized with short selling restriction and weight limits for the assets. The covariance matrix was estimated by sample method and shrinkage method proposed by Ledoit & Wolf (2003). The low volatility portfolio was structured in a similar way to the S&P 500 Low Volatility index method. The portfolios rebalancing period were quarterly and the eligible assets for the portfolios were IBOVESPA components in each analyzed period. The portfolios performance was evaluated through indicators such return, standard deviation, Sharpe ratio, maximum drawdown and MVAR indicators. The results point to the importance in choosing the weight limits for the assets of minimum-variance portfolios. Lower risk portfolios delivered the best results in all tested indicators.

Com a crescente desregulamentação dos mercados de energia, os diferentes participantes dos mercados se deparam com a necessidade de gerenciar de maneira eficiente seus investimentos em energia elétrica. Nesse cenário, a otimização das Carteiras de Contratos mostra-se uma técnica interessante no planejamento estratégico dos agentes de mercados de energia. Os mercados estão frequentemente expostos a riscos de diversas fontes, assim, a mitigação dos mesmos é fundamental. A Teoria do Portfólio, proposta por Harry Markowitz, tem sido utilizada em análises envolvendo diversos mercados. Este trabalho analisa um problema de Gestão de Carteiras de Contratos de energia elétrica, com Gestão de Risco. A relação contratual entre a ANDE (Administración Nacional de Electricidad Paraguai) e Itaipu Binacional é utilizada como estudo de caso. A metodologia proposta para tratar o problema extende a teoria de Markowitz em um contexto de tomada de decisão multiobjetivo, no qual se busca minimizar os gastos da ANDE em contratação de energia (via programação não-linear) e também o risco do portfólio, avaliado por meio da variância do mesmo. Por meio do modelo proposto é possível obter a decisão contratual ótima de ANDE, que minimiza o custo de seu portfólio para cada nível de risco. Os resultados obtidos indicam que o modelo é eficiente em termos de redução de custos e risco. / Due to the increasing deregulation of electricity markets, different market participants were faced with the necessity to effectively manage their investment in electricity. In this scenario, portfolio optimization is a relevant technique that can be investigated for strategic planning by agents on energy markets. In general, markets are exposed to risks from multiple sources, the mitigation of such risks, thus, is important. The portfolio theory proposed by Harry Markowitz has been used in analyses involving several markets. This work analyzes the problem of electricity Portfolio Management, with Risk Management. The contractual relationship between ANDE and Itaipu Binacional is used as a study case. The methodology proposed for addressing the problem extends Markowitz´s theory (applying non-linear programming) for a context of multi-objective decision making, searching for the minimization of ANDEs power contract costs, as well the portfolio risk, evaluated by its variance. With the proposed model, it is possible to obtain the optimal contract decision, which minimizes the portfolio cost for each risk level. Results indicate that the model proposed is efficient in cost and risk minimization.

A geração hidrelétrica é dependente da afluência, no entanto, é possível minimizar a variação da energia natural afluente por meio dos reservatórios. Por sua vez, a geração eólica tem como desvantagem a volatilidade devido a sua dependência em relação ao vento. Nesse sentido, uma carteira otimizada de projetos eólicos possibilita a redução da volatidade da energia gerada pelo conjunto, na medida em que aproveita as complementariedades do vento. No Brasil, os Estados da Bahia, Rio Grande do Norte, Ceará, Rio Grande do Sul e Piauí concentram 90% da capacidade instalada das usinas eólicas em operação, em construção ou contratada, com uma previsão da fonte atingir 11,6% de participação na matriz elétrica. A pesquisa tem como objetivo desenvolver uma metodologia de apoio baseada na teoria de portifólio de Markowitz que poderá ser utilizada pelo órgão de planejamento energético brasileiro para a definição da quantidade de energia a ser contratada por fonte e local, por meio de leilões de energia regionais e por fonte, com o objetivo de se obter uma carteira otimizada de empreendimentos, que reduza a volatilidade. O método também pode servir de apoio ao investidor para se obter um portfólio de usinas que minimize o risco de exposição financeira no mercado de curto prazo. Nenhum estudo aplicando a teoria de portifólio de Markowitz em usinas eólicas do Brasil foi encontrado na literatura. Os resultados obtidos demonstram que a carteira formada pelas usinas eólicas existentes não está na fronteira eficiente e poderia ser otimizada com aumento da expectativa de geração ou redução do risco. No mesmo sentido, a otimização da carteira também reduziu o risco de exposição ao mercado de curto prazo. / Even though the hydroelectric generation is highly dependent on the river flows, it is possible to minimize the volatility of the energy generation in a given period using the storage capacity of the reservoirs. In contrast, to minimize the volatility of the wind generation is burdensome due to its dependency on wind. Accordingly, an optimized portfolio of wind projects all together allows the reduction of the volatility of the energy generation for the complementarity of wind from different locations. In Brazil, the states of Bahia, Rio Grande do Norte, Ceara, Rio Grande do Sul and Piauí concentrate 90% of the installed capacity of wind power plants in operation, under construction or contracted with a font forecast to reach 11.6% share the electric matrix. The Thesis aims to develop a support methodology based in portfolio theory of Markowitz that can be used by the Brazilian-planning agency in future, to define the amount of energy to be contracted by source and location, through regional and source energy auctions, to obtain an optimized portfolio projects, with reduced volatility. The methodology can also serve to support the investor to obtain a portfolio of plants that minimize the risk of financial exposure to short-term market. No study applying Markowitz\'s portfolio theory in wind farms of Brazil was found in the literature. The results show that the portfolio of the existing wind farms is not on the efficient frontier and could be optimized with increased expectation of generating or reducing the risk. Similarly, the optimization of the portfolio also reduced the risk of exposure to short-term market.

<p>Hedge funds are a debated subject in today’s financial industry. During 2008, despite hedge funds absolute return target, the global hedge fund industry showed a negative performance whilst the Swedish hedge fund market performed relatively well in comparison. Many studies have been made investigating the effect on incorporating hedge funds in a traditional portfolio though none focused separately on the Swedish market. In a global perspective it is quite easy to invest in hedge fund portfolios due to the existence of investable indices. To invest on the Swedish market is a more complex matter. SIX Harcourt HFXS Index is a Swedish hedge fund index representing the Swedish hedge fund market though it is not investable. Hence it would be interesting to see if it is possible to create an investable version of SIX Harcourt HFXS. When creating an investable index, several administrative costs will arise and in order to cover these costs it would be interesting to see whether or not it possible to optimize SIX Harcourt HFXS Index in purpose of achieving a outperformance which could cover any administrative costs for setting up the investable version. Also, since the optimized version must replicate the standard SIX Harcourt HFXS Index it must maintain a certain level of correlation.</p><p>This thesis, which is based on a positivistic epistemology, is built upon a quantitative case study where SIX Harcourt HFXS Index is optimized in purpose of achieving an outperformance in terms of the risk-adjusted return. The optimization uses an adjusted mean-variance methodology and is limited to a maintained correlation above 0,9 towards the standard SIX Harcourt HFXS Index. The optimization is created through the use of an Excel application created by Harcourt Investment Consulting.</p><p>Also, based on the outperformance by Swedish hedge funds compared to global hedge funds, this study aims to show the effect of incorporating Swedish hedge funds in a traditional portfolio consisting of equities and bonds. This effect is analyzed by the use of several performance-and risk measures.</p><p>The study shows that it is possible to optimize SIX Harcourt HFXS Index and produce an outperformance of approximately 1,5% per annum with a maintained correlation above 0,9. It also shows that the effect of incorporating Swedish hedge funds to a traditional portfolio is positive in regards to both risk and return.</p>

The selection of investment strategies and managing investment funds via employing portfolio insurance methods play an important role in asset liability management. Insurance strategies are designed to limit downside risk of portfolio while allowing some participation in potential gain of upside markets. In this thesis, we provide an extensive overview and investigation, particularly on the two most prominent portfolio insurance strategies: the Constant Proportion Portfolio Insurance (CPPI) and the Option-Based Portfolio Insurance (OBPI). The aim of the thesis is to examine, analyze and compare the portfolio insurance strategies in terms of their performances at maturity, via some of their statistical and dynamical properties, and of their optimality over the maximization of expected utility criterion. This thesis presents the financial market model in continuous-time containing no arbitrage opportunies, the CPPI and OBPI strategies with definitions and properties, and the analysis of these strategies in terms of comparing their performances at maturity, of their statistical properties and of their dynamical behaviour and sensitivities to the key parameters during the investment period as well as at the terminal date, with both formulations and simulations. Therefore, we investigate and compare optimal portfolio strategies which maximize the expected utility criterion. As a contribution on the optimality results existing in the literature, an extended study is provided by proving the existence and uniqueness of the appropriate number of shares invested in the unconstrained allocation in a wider interval.

Hedge funds are a debated subject in today’s financial industry. During 2008, despite hedge funds absolute return target, the global hedge fund industry showed a negative performance whilst the Swedish hedge fund market performed relatively well in comparison. Many studies have been made investigating the effect on incorporating hedge funds in a traditional portfolio though none focused separately on the Swedish market. In a global perspective it is quite easy to invest in hedge fund portfolios due to the existence of investable indices. To invest on the Swedish market is a more complex matter. SIX Harcourt HFXS Index is a Swedish hedge fund index representing the Swedish hedge fund market though it is not investable. Hence it would be interesting to see if it is possible to create an investable version of SIX Harcourt HFXS. When creating an investable index, several administrative costs will arise and in order to cover these costs it would be interesting to see whether or not it possible to optimize SIX Harcourt HFXS Index in purpose of achieving a outperformance which could cover any administrative costs for setting up the investable version. Also, since the optimized version must replicate the standard SIX Harcourt HFXS Index it must maintain a certain level of correlation. This thesis, which is based on a positivistic epistemology, is built upon a quantitative case study where SIX Harcourt HFXS Index is optimized in purpose of achieving an outperformance in terms of the risk-adjusted return. The optimization uses an adjusted mean-variance methodology and is limited to a maintained correlation above 0,9 towards the standard SIX Harcourt HFXS Index. The optimization is created through the use of an Excel application created by Harcourt Investment Consulting. Also, based on the outperformance by Swedish hedge funds compared to global hedge funds, this study aims to show the effect of incorporating Swedish hedge funds in a traditional portfolio consisting of equities and bonds. This effect is analyzed by the use of several performance-and risk measures. The study shows that it is possible to optimize SIX Harcourt HFXS Index and produce an outperformance of approximately 1,5% per annum with a maintained correlation above 0,9. It also shows that the effect of incorporating Swedish hedge funds to a traditional portfolio is positive in regards to both risk and return.