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This thesis focuses on estimating parameters of appropriate model for daily returns using the Markov Chain Monte Carlo method (MCMC) and Bayesian statistics. We describe MCMC methods, such as Gibbs sampling and Metropolis- Hastings algorithm and their basic properties. After that, we introduce different financial models. Particularly we focus on the lognormal autoregressive model. Later we theoretically apply Gibbs sampling to lognormal autoregressive model using principles of Bayesian statistics. Afterwards, we analyze procedu- res, that we used in simulations of posterior distribution using Gibbs sampling. Finally, we present processed output of both simulated and real data analysis.

This thesis analyzes the mean variance optimization problem with respect to cardinalityconstraints. The aim of this thesis is to figure out how much of an impact transactionchanges has on the profit and risk of a portfolio. We solve the problem by implementingmixed integer programming (MIP) and solving the problem by using the Gurobi solver.In doing this, we create a mathematical model that enforces the amount of transactionchanges from the initial portfolio. Our results is later showed in an Efficient Frontier,to see how the profit and risk are changing depending on the transaction changes.Overall, this thesis demonstrates that the application of MIP is an effective approachto solve the mean variance optimization problem and can lead to improved investmentoutcomes.

nÃo hà / This article aims to measure and analyze potential impacts from the financial crisis of 2007 in the sector of transport and vehicles and in Brazil, whose growth in recent years surpassed many other sectors of the economy and the Brazilian Gross Domestic Product. To this end, it was made use of descriptive statistics associated with various forms of risk, and performance of the distributions of nominal daily return of companies that make up this sector, every six months, from 2005 to 2010 was used as benchmark some market and industry indexes. Due to some factors, among them, heavy subjection on credit for the sale of new vehicles and export profile associated with the most important companies in this sector, it was observed that the daily returns of the shares of individual companies, as well as the return of representative aggregated index of this sector, reacted to the crisis with accumulated expressive losses. Some shares have accumulated losses of more than 80% in value, as occurred with TPIS3, and fairly high standard deviation up to 12.66% for WISA4. Both the direction of change as the value of the shares were provided by outline micro founded given by the Capital Asset Pricing Model (CAPM). In the postcrisis period, the industry reacted to a greater extent more than it was expected by fundamentals and the returns of firms and the aggregate index of the sector exceeded all other indexes analyzed in this study. At the same time that the results exceeded the returns of other indices, statistical analyzes were favorable to the sector of transport vehicles and having smaller standard deviation and better indications of Sharpes, Sortino, Treynor and Calmar. / Este artigo visa mensurar e analisar os possÃveis impactos oriundos da crise financeira de 2007 no setor de veÃculos e transportes no Brasil, cujo crescimento nos Ãltimos anos superou o de vÃrios outros setores da economia e do prÃprio Produto Interno Bruto brasileiro. Com este intuito, fez-se uso de estatÃsticas descritivas associadas Ãs diversas formas de risco e de performance das distribuiÃÃes de retorno lÃquido nominal diÃrio das empresas que compÃem este setor, com periodicidade semestral, de 2005 a 2010 e utilizou-se como benchmark alguns Ãndices de mercado e setoriais. Em razÃo de alguns fatores, possivelmente entre eles, forte dependÃncia de crÃdito para a venda de veÃculos novos e do perfil exportador associado Ãs principais empresas deste setor, observou-se que os retornos diÃrios das aÃÃes das empresas individuais, assim como o retorno de um Ãndice agregado representativo desse setor, reagiram à crise com perdas acumuladas expressivas.Algumas aÃÃes sofreram perdas acumuladas de mais de 80% em seu valor, como ocorreu com TPIS3, e desvio padrÃo bastante elevado de atà 12,66% no caso da WISA4. Tanto a direÃÃo da variaÃÃo como o valor das aÃÃes foram previstos pelo arcabouÃo microfundamentado dado pelo Capital Asset Pricing Model (CAPM). No perÃodo pÃs-crise, o setor reagiu em maior intensidade que a prevista pelos fundamentos e os retornos das empresas e do Ãndice agregado do setor superaram o de todos os outros Ãndices analisados neste estudo. Ao mesmo tempo em que os retornos superaram os resultados dos outros Ãndices, as anÃlises estatÃsticas foram favorÃveis ao setor de veÃculos e transportes apresentando menor desvio padrÃo e melhores Ãndices de Sharpe, Sortino, Treynor e Calmar.