In this study, the geometric Additive market models are considered. In general, these market models are incomplete, that means: the perfect replication of derivatives, in the usual sense, is not possible. In this study, it is shown that the market can be completed by new artificial assets which are called &ldquo / power-jump assets&rdquo / based on the power-jump processes of the underlying Additive process. Then, the hedging portfolio for claims whose payoff function depends on the prices of the stock and the power-jump assets at maturity is derived. In addition to the previous completion strategy, it is also shown that, using a static hedging formula, the market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity. What is more, the portfolio optimization problem is considered in the enlarged market. The optimization problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. For particular choices of the equivalent martingale measure, it is shown that the optimal portfolio consists only of bonds and stocks.

ABSTRACT PORTFOLIO SELECTION AND RETURN PERFORMANCE: An Application of the Black-Litterman Method in the Istanbul Stock Exchange Bozdemir, Mehmet Burak M.Sc, Department of Financial Mathematics Supervisor : Assist. Prof. Dr. Seza Dani

Most studies view transaction costs and constraints separate in the mean-variance framework. As such, I evaluate the benefits of holding and turnover constraints in the presence of transaction costs on Swedish Asset Returns. In theory, the benefits should be limited when transaction costs are included in the portfolio rebalancing problem. By using the model developed by Mitchell and Braun (2003), my results indicate that there are benefits of holding constraints in the mean-variance optimization. The main issue with the long-only portfolio is its lack of diversification. The strategy allocates the majority of the investment in 15 out of 100 assets. By imposing holding constraints, the portfolio becomes more diversified while reducing turnover volume and increasing Sharpe ratio. I find that the homogenous 1/N holding constraint increases monthly Sharpe ratio performance by 50 percent over the entire sample. However, the results are not consistent over all samples and not statistically significant. Further, turnover constraints only marginally increase performance, which more likely originates from the increase in diversification.

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.

abstract: The ever-changing economic landscape has forced many companies to re-examine their supply chains. Global resourcing and outsourcing of processes has been a strategy many organizations have adopted to reduce cost and to increase their global footprint. This has, however, resulted in increased process complexity and reduced customer satisfaction. In order to meet and exceed customer expectations, many companies are forced to improve quality and on-time delivery, and have looked towards Lean Six Sigma as an approach to enable process improvement. The Lean Six Sigma literature is rich in deployment strategies; however, there is a general lack of a mathematical approach to deploy Lean Six Sigma in a global enterprise. This includes both project identification and prioritization. The research presented here is two-fold. Firstly, a process characterization framework is presented to evaluate processes based on eight characteristics. An unsupervised learning technique, using clustering algorithms, is then utilized to group processes that are Lean Six Sigma conducive. The approach helps Lean Six Sigma deployment champions to identify key areas within the business to focus a Lean Six Sigma deployment. A case study is presented and 33% of the processes were found to be Lean Six Sigma conducive. Secondly, having identified parts of the business that are lean Six Sigma conducive, the next steps are to formulate and prioritize a portfolio of projects. Very often the deployment champion is faced with the decision of selecting a portfolio of Lean Six Sigma projects that meet multiple objectives which could include: maximizing productivity, customer satisfaction or return on investment, while meeting certain budgetary constraints. A multi-period 0-1 knapsack problem is presented that maximizes the expected net savings of the Lean Six Sigma portfolio over the life cycle of the deployment. Finally, a case study is presented that demonstrates the application of the model in a large multinational company. Traditionally, Lean Six Sigma found its roots in manufacturing. The research presented in this dissertation also emphasizes the applicability of the methodology to the non-manufacturing space. Additionally, a comparison is conducted between manufacturing and non-manufacturing processes to highlight the challenges in deploying the methodology in both spaces. / Dissertation/Thesis / Ph.D. Industrial Engineering 2011

Este trabalho estuda o problema de seleção de carteiras de variância mínima com base em uma recente metodologia para otimização de carteiras com restrições nas normas das exposições brutas proposta por Fan, Zhang e Yu (2012). Para esse propósito, consideram-se diferentes estimadores da matriz de covariâncias condicional e incondicional. A grande contribuição deste artigo é de natureza empírica para o mercado de ações brasileiro. Avaliam-se índices de desempenho fora da amostra das carteiras construídas para um conjunto de 61 ações negociadas na Bolsa de Valores de São Paulo (BM&FBovespa). Os resultados mostraram que as restrições nas normas dos vetores de alocação (restrição de exposição bruta) geram ganhos substanciais em relação às carteiras restringidas para venda a descoberto, aumentando o retorno médio ajustado pelo risco e diminuindo o turnover dos portfólios. / This paper studies the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan, Zhang e Yu (2012). To achieve this, different conditional and inconditional covariance matrix estimators are considered. The great contribuition of this paper is one of empirical nature for the brazilian stock market. We evaluate out-of-sample performance indexes for the portfolios constructed for a set with 61 different sotcks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains compared to the no short-sale portfolio, raising the average return adjusted by the risk and lowering the portfolio turnover.

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.

A liquidez é um fator importante no âmbito da gestão de carteiras. Em 2012, no Brasil, a CVM começou a exigir que todos bancos e corretoras mantenham um controle da liquidez de seus ativos/carteiras. Esse trabalho define uma medida e uma restrição de liquidez adequada ao mercado brasileiro, possível de ser incorporada em modelos de otimização de carteiras. As simulações realizadas com o modelo proposto demonstraram um alto nível de liquidação das carteiras formadas, próximo a 85%. / Liquidity is an important element in portfolio management. In 2012, in Brazil, CVM started to require all banks and brokerages to maintain control of the liquidity of its assets/portfolios. This work defines a liquidity measure and liquidity constraints proper to Brazilian market that can be attached to portfolio optimization models. The simulations with the proposed model evidence a high level of portfolio liquidation, close to 85%.

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.

A liquidez é um fator importante no âmbito da gestão de carteiras. Em 2012, no Brasil, a CVM começou a exigir que todos bancos e corretoras mantenham um controle da liquidez de seus ativos/carteiras. Esse trabalho define uma medida e uma restrição de liquidez adequada ao mercado brasileiro, possível de ser incorporada em modelos de otimização de carteiras. As simulações realizadas com o modelo proposto demonstraram um alto nível de liquidação das carteiras formadas, próximo a 85%. / Liquidity is an important element in portfolio management. In 2012, in Brazil, CVM started to require all banks and brokerages to maintain control of the liquidity of its assets/portfolios. This work defines a liquidity measure and liquidity constraints proper to Brazilian market that can be attached to portfolio optimization models. The simulations with the proposed model evidence a high level of portfolio liquidation, close to 85%.