Transaction costs and resampling are two important issues that need great attention in every portfolio investment planning. In practice costs are incurred to rebalance a portfolio. Every investor tries to find a way of avoiding high transaction cost as much as possible. In this thesis, we investigated how transaction costs and resampling affect portfolio investment. We modified the basic mean-variance optimization problem to include rebalancing costs we incur on transacting securities in the portfolio. We also reduce trading as much as possible by applying the resampling approach any time we rebalance our portfolio. Transaction costs are assumed to be a percentage of the amount of securities transacted. We applied the resampling approach and tracked the performance of portfolios over time, assuming transaction costs and then no transaction costs are incurred. We compared how the portfolio is affected when we incorporated the two issues outlined above to that of the basic mean-variance optimization.

Um dos problemas fundamentais em finanças é a escolha de ativos para investimento. O primeiro método para solucionar este problema foi desenvolvido por Markowitz em 1952 com a análise de como a variância dos retornos de um ativo impacta no risco do portifólio no qual o mesmo está inserido. Apesar da importância de sua contribuição, o método desenvolvido para a otimização de carteiras não leva em consideração características como a existência de lotes de compra para os ativos e a existência de custos de transação. Este trabalho apresenta uma abordagem alternativa para o problema de otimização de carteiras utilizando algoritmos genéticos. Para tanto são utilizados três algoritmos, o algoritmo genético simples, o algoritmo genético multiobjetivo (Multi Objective Genetic Algorithm - MOGA) e o algoritmo genético de ordenação não dominante (Non Dominated Sorting Genetic Algorithm - NSGA II). O desempenho apresentado pelos algoritmos genéticos neste trabalho mostram a perspectiva para a solução desse problema tão importante e complexo, obtendo-se soluções de alta qualidade e com menor esforço computacional. / One of the basic problems in finance is the choice of assets for investment. The first method to solve this problem was developed by Markowitz in 1952 with the analysis of how the variance of the returns of an asset impacts in the portfolio risk in which the same is inserted. Despite the importance of its contribution, the method developed for the portfolio optimization does not consider characteristics as the existence of round lots and transaction costs. This work presents an alternative approach for the portfolio optimization problem using genetic algorithms. For that three algorithms are used, the simple genetic algorithm, the multi objective genetic algorithm (MOGA) and the non dominated sorting genetic algorithm (NSGA II). The performance presented for the genetic algorithms in this work shows the perspective for the solution of this so important and complex problem, getting solutions of high quality and with lesser computational effort.

Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip stocks and well-established companies have folded and filed for bankruptcy, an event that might have thought to been absurd two years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for investment problems of the 21st century. Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of managing constraints that are coupled to general historic risk and return models. We identify three well-known portfolio problems and add an array of practical managing constraints that form three different types of Mixed-Integer Programs. The product is advanced mathematical models related to risk-return portfolios, index tracking portfolios, and an integrated stock-bond portfolio selection model. The numerous sources of uncertainty are captured in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We minimize trade-offs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market. Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.

Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip stocks and well-established companies have folded and filed for bankruptcy, an event that might have thought to been absurd two years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for investment problems of the 21st century. Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of managing constraints that are coupled to general historic risk and return models. We identify three well-known portfolio problems and add an array of practical managing constraints that form three different types of Mixed-Integer Programs. The product is advanced mathematical models related to risk-return portfolios, index tracking portfolios, and an integrated stock-bond portfolio selection model. The numerous sources of uncertainty are captured in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We minimize trade-offs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market. Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.

We consider a portfolio selection problem in the presence of transaction costs. Transaction costs on each asset are assumed to be a convex function of the amount sold or bought. This function can be nondifferentiable in a finite number of points. The objective function of this problem is a sum of a convex twice differentiable function and a separable convex nondifferentiable function. We first consider the problem in the presence of linear constraints and later generalize the results to the case when the constraints are given by the convex piece-wise linear functions. <br /><br /> Due to the special structure, this problem can be replaced by an equivalent differentiable problem in a higher dimension. It's main drawback is efficiency since the higher dimensional problem is computationally expensive to solve. <br /><br /> We propose several alternative ways to solve this problem which do not require introducing new variables or constraints. We derive the optimality conditions for this problem using subdifferentials. First, we generalize an active set method to this class of problems. We solve the problem by considering a sequence of equality constrained subproblems, each subproblem having a twice differentiable objective function. Information gathered at each step is used to construct the subproblem for the next step. We also show how the nonsmoothness can be handled efficiently by using spline approximations. The problem is then solved using a primal-dual interior-point method. <br /><br /> If a higher accuracy is needed, we do a crossover to an active set method. Our numerical tests show that we can solve large scale problems efficiently and accurately.

We consider a portfolio selection problem in the presence of transaction costs. Transaction costs on each asset are assumed to be a convex function of the amount sold or bought. This function can be nondifferentiable in a finite number of points. The objective function of this problem is a sum of a convex twice differentiable function and a separable convex nondifferentiable function. We first consider the problem in the presence of linear constraints and later generalize the results to the case when the constraints are given by the convex piece-wise linear functions. <br /><br /> Due to the special structure, this problem can be replaced by an equivalent differentiable problem in a higher dimension. It's main drawback is efficiency since the higher dimensional problem is computationally expensive to solve. <br /><br /> We propose several alternative ways to solve this problem which do not require introducing new variables or constraints. We derive the optimality conditions for this problem using subdifferentials. First, we generalize an active set method to this class of problems. We solve the problem by considering a sequence of equality constrained subproblems, each subproblem having a twice differentiable objective function. Information gathered at each step is used to construct the subproblem for the next step. We also show how the nonsmoothness can be handled efficiently by using spline approximations. The problem is then solved using a primal-dual interior-point method. <br /><br /> If a higher accuracy is needed, we do a crossover to an active set method. Our numerical tests show that we can solve large scale problems efficiently and accurately.

A number of researchers have proposed several Bayesian methods for portfolio selection, which combine statistical information from financial time series with the prior beliefs of the portfolio manager, in an attempt to reduce the impact of estimation errors in distribution parameters on the portfolio selection process and the effect of these errors on the performance of 'optimal' portfolios in out-of-sample-data. This thesis seeks to reverse the direction of this process, inferring portfolio managers’ probabilistic beliefs about future distributions based on the portfolios that they hold. We refer to the process of portfolio selection as the forward problem and the process of retrieving the implied probabilities, given an optimal portfolio, as the inverse problem. We attempt to solve the inverse problem in a general setting by using a finite set of scenarios. Using a discrete time framework, we can retrieve probabilities associated with each of the scenarios, which tells us the views of the portfolio manager implicit in the choice of a portfolio considered optimal. We conduct the implied views analysis for portfolios selected using expected utility maximization, where the investor's utility function is a globally non-optimal concave function, and in the mean-variance setting with the covariance matrix assumed to be given. We then use the models developed for inverse problem on empirical data to retrieve the implied views implicit in a given portfolio, and attempt to determine whether incorporating these views in portfolio selection improves portfolio performance out of sample.

It has been shown in the literature that the oil and gas industry deals with a substantial number of biases that impact project evaluation and portfolio performance. Previous studies concluded that properly estimating uncertainties will significantly impact the success of risk takers and their profits. Although a considerable number of publications investigated the impact of cognitive biases, few of these publications tackled the problem from a quantitative point of view. The objective of this work is to demonstrate the value of quantifying uncertainty and evaluate its impact on the optimization of oil and gas portfolios, taking into consideration the risk of each project. A model has been developed to perform portfolio optimization using Markowitz theory. In this study, portfolio optimization has been performed in the presence of different levels of overconfidence and directional bias to determine the impact of these biases on portfolio performance. The results show that disappointment in performance occurs not only because the realized portfolio net present value (NPV) is lower than estimated, but also because the realized portfolio risk is higher than estimated. This disappointment is due to both incorrect estimation of value and risk (estimation error) and incorrect project selection (decision error). The results of the cases analyzed show that, in a high-risk-tolerance environment, moderate overconfidence and moderate optimism result in an expected decision error of about 19% and an expected disappointment of about 50% of the estimated portfolio. In a low-risk-tolerance environment, the same amounts of moderate overconfidence and optimism result in an expected decision error up to 103% and an expected disappointment up to 78% of the estimated portfolio. Reliably quantifying uncertainty has the value of reducing the expected disappointment and the expected decision error. This can be achieved by eliminating overconfidence in the process of project evaluation and portfolio optimization. Consequently, overall industry performance can be improved because accurate estimates enable identification of superior portfolios, with optimum reward and risk levels, and increase the probability of meeting expectations.

Some insurance firms are faced with the unique challenge of managing risks that are large, infrequent, and potentially highly correlated within geographic regions and/or across product lines. An example of this is crop insurance, which includes weather risk, and leads to a portfolio of risks with high variance. A solution to this problem is undertaken in this study, through using a combination of pooling and private reinsurance in a portfolio approach. This approach takes advantage of offsetting risks across regions, in order to reduce risk in a cost effective manner. An asset liability management (ALM) approach is used to examine the entire crop insurance sector for Canada. This is the first study to focus on pooling for an entire insurance sector in a country, and it uses all major crops from 1978-2009, across 10 regions (provinces). Chapter two develops an innovative insurance portfolio under a full premium pool, combining a self managed insurance pool and private reinsurance using the coefficient of variation (CV) of the loss coverage ratio (LCR), Model 3. Results show that this portfolio approach reduces risk across regions. Chapter three, in contrast to chapter two, uses a reinsurance premium pool, where regions contribute only a portion of their risk to a reinsurance pool. An improved insurance portfolio model is developed in chapter three, using combinatorial optimization with a genetic algorithm to combine a self managed reinsurance pool and private reinsurance, Model C. Results show that this reinsurance portfolio model efficiently reduces risk. Chapter four uses a similar approach to chapter three, except that it allows for dependence (correlation) across regions. Results for this model (Model CC) are consistent with those of chapter three, indicating the effectiveness of the portfolio approach when correlation is present across regions. Overall, the portfolio models developed in each of the three chapters (Model 1, Model C, and Model CC), produce acceptable surplus, survival probability, and deficit at ruin, indicating that the portfolio approach using pooling is efficient for reducing risk. Beyond crop insurance, the portfolio models can be applied to other large natural disaster and weather related insurance, and other portfolio applications.

Some insurance firms are faced with the unique challenge of managing risks that are large, infrequent, and potentially highly correlated within geographic regions and/or across product lines. An example of this is crop insurance, which includes weather risk, and leads to a portfolio of risks with high variance. A solution to this problem is undertaken in this study, through using a combination of pooling and private reinsurance in a portfolio approach. This approach takes advantage of offsetting risks across regions, in order to reduce risk in a cost effective manner. An asset liability management (ALM) approach is used to examine the entire crop insurance sector for Canada. This is the first study to focus on pooling for an entire insurance sector in a country, and it uses all major crops from 1978-2009, across 10 regions (provinces). Chapter two develops an innovative insurance portfolio under a full premium pool, combining a self managed insurance pool and private reinsurance using the coefficient of variation (CV) of the loss coverage ratio (LCR), Model 3. Results show that this portfolio approach reduces risk across regions. Chapter three, in contrast to chapter two, uses a reinsurance premium pool, where regions contribute only a portion of their risk to a reinsurance pool. An improved insurance portfolio model is developed in chapter three, using combinatorial optimization with a genetic algorithm to combine a self managed reinsurance pool and private reinsurance, Model C. Results show that this reinsurance portfolio model efficiently reduces risk. Chapter four uses a similar approach to chapter three, except that it allows for dependence (correlation) across regions. Results for this model (Model CC) are consistent with those of chapter three, indicating the effectiveness of the portfolio approach when correlation is present across regions. Overall, the portfolio models developed in each of the three chapters (Model 1, Model C, and Model CC), produce acceptable surplus, survival probability, and deficit at ruin, indicating that the portfolio approach using pooling is efficient for reducing risk. Beyond crop insurance, the portfolio models can be applied to other large natural disaster and weather related insurance, and other portfolio applications.