In recent years socially responsible investing has become an increasingly more popular subject with both private and institutional investors. At the same time, a number of scientific papers have been published on socially responsible investments (SRIs), covering a broad range of topics, from what actually defines SRIs to the financial performance of SRI funds in contrast to non-SRI funds. In this paper, we revisit Markowitz' Portfolio Selection Theory and propose a modification allowing to incorporate not only asset-specific return and risk but also a social responsibility measure into the investment decision making process. Together with a risk-free asset, this results in a three-dimensional capital allocation plane that allows investors to custom-tailor their asset allocations and incorporate all personal preferences regarding return, risk and social responsibility. We apply the model to a set of over 6,231 international stocks and find that investors opting to maximize the social impact of their investments do indeed face a statistically significant decrease in expected returns. However, the social responsibility/risk-optimal portfolio yields a statistically significant higher social responsibility rating than the return/risk-optimal portfolio.

A gestão de clientes é um processo que envolve a tomada de decisões estratégicas, que influenciam a composição do portfólio de clientes da companhia, e operacionais, que afetam o relacionamento dos clientes com a empresa no dia a dia. O framework sugerido nesta tese propicia a integração dessas duas perspectivas, permitindo aos gestores alocarem melhor os recursos de marketing, por possibilitarem (a) o incremento da eficiência da carteira de clientes, a partir da sua otimização, e (b) a identificação dos clientes mais propensos a gerarem lucros futuros, com base na modelagem de customer lifetime value (CLV) desenvolvida. A abordagem de otimização do portfólio de clientes foi elaborada para auxiliar os gestores a definirem os segmentos que devem ser alvo dos investimentos de marketing e tem como objetivo indicar a composição da carteira de clientes que proporcionará a rentabilidade, a diversificação do risco e a lucratividade desejadas pelos acionistas. A abordagem sugerida é uma adaptação para o marketing da teoria financeira do portfólio. Foram incluídas restrições específicas para a área de gestão de clientes que asseguram a exequibilidade dos portfólios recomendados, tanto em relação à necessidade de aquisição de clientes ou de redução da participação dos segmentos na carteira, quanto em relação à manutenção da lucratividade da empresa. Ademais, foram incorporadas opções de estimação do retorno, tais como a inclusão da tendência à série com base na modelagem SUR, além de serem avaliadas a utilização de duas proxies para o risco, a variância e o Conditional Value at Risk. De acordo com o framework de gestão de clientes proposto, a implementação das decisões estratégicas é viabilizada a partir da integração da análise dos resultados obtidos pela otimização com a avaliação proporcionada pelo modelo de CLV sugerido. Este, além de englobar a evolução do comportamento do cliente ao longo do relacionamento da empresa, considera o retorno e a matriz de probabilidade de troca de segmento de maneira individualizada. A heterogeneidade da matriz de Markov foi alcançada a partir da combinação convexa da matriz de transição geral com a matriz personalizada de cada cliente, possibilitando, assim, a priorização de clientes pertencentes a um mesmo segmento. O framework sugerido foi aplicado na base de clientes de uma grande empresa que atua nacionalmente na indústria de serviços financeiros. Após a constatação de que os segmentos podem gerar diferentes retornos e representar distintos níveis de risco para a companhia, foi feita a comparação dos resultados dos portfólios recomendados com o realizado. Os portfólios sugeridos desempenharam melhor de maneira consistente em termos de lucratividade e de eficiência, medida a partir do sharpe ratio. Em relação ao modelo de CLV, os resultados foram comparados com os obtidos a partir do modelo de Pfeifer & Carraway (2000), utilizado como ponto de partida para o seu desenvolvimento. As modificações incorporadas, além de possibilitarem a individualização por cliente, aumentaram a precisão da previsão dos valores individuais e a qualidade do ordenamento, mantendo a capacidade de avaliação do valor da base. Para resumir, foi proposto um framework de gestão de clientes que inclui a avaliação do risco, possibilitando aos gestores uma visão holística do negócio e particular de cada cliente. / Customer management is a process that involves strategic decision-making, which influence the composition of the customer portfolio, and operational decision making, which affect the relationship of each customer with the company. The proposed framework provides the integration of the strategic and operational perspectives, empowering managers to better allocate marketing resources as it enables (a) the increase of the efficiency of the customer portfolio, through its optimization, and (b) the identification of the customers that are more likely to bring profit in the future, through the customer lifetime value (CLV) model developed. The customer portfolio optimization method was built to help managers to define the customer segments that should be the target of their marketing investments. Its purpose is to indicate the customer portfolio composition that will provide the return, profitability and risk diversification desired by shareholders. The suggested approach is an adaptation to marketing of financial portfolio theory. In this way, customer management specific constrains were included to ensure the applicability of the recommended portfolios in terms of either the necessity of acquiring new customers or reducing the importance of a given segment in the portfolio as well as in terms of maintaining the company’s profitability. Furthermore, options of estimating return were incorporated such as the inclusion of the trend in the time series based SUR modeling as well as the optimizations were evaluated considering two proxies for risk, variance and Conditional Value at Risk. According to the proposed framework, the implementation of the strategic decisions concerning the changes needed in the customer portfolio become possible through the integration of the results of the optimization with the estimation of the value of each customer provided by the CLV model developed. In this model, besides accounting for the evolution of the customer behavior throughout the duration of his relationship with the company, we also consider, for each customer, his individual return and his individual transition matrix. The heterogeneity of the Markov matrix was reached with a convex combination of the general transition matrix and the personalized matrix of each customer. It, therefore, enables managers to priorize customers of the same segment. The suggested framework was applied to the customer database of a large national company from the financial services industry. Once evidenced that the customer segments can generate different returns and can have different levels of risk for the company, we compared the results of the recommended with the current. The portfolios suggested by the optimization performed consistently better in terms of profitability and efficiency, measured through sharpe ratio. Concerning the CLV model developed, we compared the results with Pfeifer & Carraway (2000) model, which was used as the start point for our model. The improvements implemented not only allowed the estimation of CLV at the individual level, but also increased the precision of the predictions for the customer lifetime values and for the customer ranking, maintaining the quality of the customer equity forecast. To sum up, our proposed framework which includes risk assessment enables marketing managers to have a holistic vision of their customer portfolio and to drilldown into a particular vision of each customer.

Esta tese é dedicada ao estudo de modelos de otimização de carteiras de investimento multi-período. Daremos ênfase a um modelo com restrições intermediárias formulado como um problema de controle ótimo e resolvido utilizando técnicas de programação dinâmica. Serão tratados aspectos teóricos e práticos desta classe de problemas. Primeiramente faremos uma revisão das principais hipóteses dos modelos de otimização de carteiras e o caso uni-período. Analisaremos a seguir as generalizações para o caso multi-período, onde os modelos utilizam apenas restrições para o valor esperado e/ou para a variância da carteira no instante final do período analisado. Apresentaremos então o principal resultado proposto neste trabalho onde consideramos o problema de seleção ótima de ativos multi-período no qual podemos incorporar ao modelo restrições intermediárias para o valor esperado e variância da carteira durante o período de análise. A grande vantagem desta técnica é permitir o controle do valor esperado e/ou da variância da carteira ao longo de todo o horizonte de análise. Faremos uma comparação o entre as formulações apresentadas e realizaremos experimentos numéricos com o modelo proposta nesta tese. Os principais resultados originais desta tese encontram-se no Capítulo 5. No Capítulo 6 apresentamos as simulações numéricas realizadas com o modelo proposto. / The subject of this thesis is the study of multi-period portfolio optimization problems. We focus on a model with intermediate constraints formulated as an optimal control problem and solved by using dynamic programming techniques. Both theoretical and practical issues are addressed. Firstly we will analyze the main hypothesis of portfolio optimization models and the single period case. Then we will present the generalization for the multi-period case, where the models use only constraints for the expected value and variance at the final period. The main result proposed in this work considers the multi-period portfolio selection problem with intermediate constraints on the expected value and variance of the portfolio taken into account in the optimization problem. The main advantage of this technique is that it is possible to control the intermediate expected value or variance of the portfolio during the time horizon considered. Comparison between the presented formulations and numerical experiments of the proposed model will be exposed. The main original results of this thesis can be found in Chapter 5. In Chapter 6 we present numerical simulations with the proposed model.

Nesta dissertação, discute-se o problema de otimização de carteiras de investimento para estratégia passiva de Index Tracking. Os objetivos principais são (i) apresentar um modelo de otimização de Index Tracking e (ii) a solucionar esse modelo com uso do método heurístico de Algoritmos Genéticos (AG) para formação de carteiras com número reduzido de ativos. O índice de referência utilizado é o Ibovespa, para o período de Janeiro/2009 a Julho/2012, com um total de 890 observações diárias de preços. A partir de uma amostra de 67 ativos, são formadas carteiras sem limite de ativos e limitadas a 40, 30, 20, 10 e 05 ativos; os intervalos de rebalanceamento das carteiras são 20, 40 e 60 períodos (dias úteis), ou seja, rebalanceamento mensal, bimestral e trimestral. É verificado que, para essa amostra, não é possível formar carteiras de 20 ou menos ativos via otimização direta com o solver Cplex com menos de 1 hora de processamento e gap abaixo de 5%. Com uso da heurística de Algoritmos Genéticos, são formadas carteiras de 10 e 05 ativos com tempo de processamento em torno de 5 minutos; nesse caso, o gap médio fica abaixo de 10% para ambos os tipos de carteira. E, com tempo de processamento do AG um pouco maior, em torno de 8 minutos, o algoritmo fornece soluções para carteiras de 10 e 05 ativos com gap médio abaixo de 5%. / In this master’s thesis it is discussed the portfolio optimization problem using the passive investment strategy of Index Tracking. The main goals are (i) to present an optimization model for the Index Tracking problem and (ii) to solve this model using the heuristic approach of Genetic Algorithms (GA) to create portfolios with reduced amount of stocks. The benchmark used is the Ibovespa Index (main reference for the Brazilian Stock Market), during the period from January/2009 to July/2012 (using a total of 890 daily stock prices). The sample contains 67 assets, and the model is used to build portfolios without limit in the amount of assets and portfolios limited to 40, 30, 20, 10 and 05 assets; the ranges of time to rebalance the portfolios are 20, 40, and 60 trading days, which means to rebalance monthly, bimonthly and quarterly. The results show that, considering this sample, it is not possible to build portfolios with 20 stocks (or less than 20) through direct optimization using the solver Cplex with computational processing time less than 1 hour and results with gap below 5%. On the other hand, using the Genetic Algorithms heuristic approach, portfolios limited to 10 and 05 stocks are built with computational time close to 5 minutes; for both types of portfolio, the solutions provided by the GA have average gap below 10%. Also, with a computational time slightly bigger, close to 8 minutes, the algorithm provides solutions with average gap below 5% for portfolios limited to 10 and 05 stocks.

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...

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios.

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios.

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

Hidden Markov models have become a popular tool for modeling long-term investment guarantees. Many different variations of hidden Markov models have been proposed over the past decades for modeling indexes such as the S&P 500, and they capture the tail risk inherent in the market to varying degrees. However, goodness-of-fit testing, such as residual-based testing, for hidden Markov models is a relatively undeveloped area of research. This work focuses on hidden Markov model assessment, and develops a stochastic approach to deriving a residual set that is ideal for standard residual tests. This result allows hidden-state models to be tested for goodness-of-fit with the well developed testing strategies for single-state models. This work also focuses on parameter uncertainty for the popular long-term equity hidden Markov models. There is a special focus on underlying states that represent lower returns and higher volatility in the market, as these states can have the largest impact on investment guarantee valuation. A Bayesian approach for the hidden Markov models is applied to address the issue of parameter uncertainty and the impact it can have on investment guarantee models. Also in this thesis, the areas of portfolio optimization and portfolio replication under a hidden Markov model setting are further developed. Different strategies for optimization and portfolio hedging under hidden Markov models are presented and compared using real world data. The impact of parameter uncertainty, particularly with model parameters that are connected with higher market volatility, is once again a focus, and the effects of not taking parameter uncertainty into account when optimizing or hedging in a hidden Markov are demonstrated.