In this Portfolio Optimization Project, we used Markowitz¡¯s modern portfolio theory for portfolio optimization. We selected fifteen stocks traded on the New York Stock Exchange and gathered these stocks¡¯ historical data from Yahoo Finance [1]. Then we used Markowitz¡¯s theory to analyze this data in order to obtain the optimal weights of our initial portfolio. To maintain our investment in a current tangency portfolio, we recalculated the optimal weights and rebalanced the positions every week. In the CAPM project, we used the security characteristic line to calculate the stocks¡¯ daily returns. We also computed the risk of each asset, portfolio beta, and portfolio epsilons. In the Factor Modeling project, we computed estimates of each asset¡¯s expected returns and return variances of fifteen stocks for each of our factor models. Also we computed estimates of the covariances among our asset returns. In order to find which model performs best, we compared each portfolio¡¯s actual return with its corresponding estimated portfolio return.

In this Portfolio Optimization Project, we used Markowitz¡¯s modern portfolio theory for portfolio optimization. We selected fifteen stocks traded on the New York Stock Exchange and gathered these stocks¡¯ historical data from Yahoo Finance [1]. Then we used Markowitz¡¯s theory to analyze this data in order to obtain the optimal weights of our initial portfolio. To maintain our investment in a current tangency portfolio, we recalculated the optimal weights and rebalanced the positions every week. In the CAPM project, we used the security characteristic line to calculate the stocks¡¯ daily returns. We also computed the risk of each asset, portfolio beta, and portfolio epsilons. In the Factor Modeling project, we computed estimates of each asset¡¯s expected returns and return variances of fifteen stocks for each of our factor models. Also we computed estimates of the covariances among our asset returns. In order to find which model performs best, we compared each portfolio¡¯s actual return with its corresponding estimated portfolio return.

[pt] O estudo das anomalias existentes no mercado de capitais brasileiro vem ganhando força em pesquisas recentes, tanto pela curiosidade de pesquisadores como pela necessidade de pessoas do mercado em entender alguns fenômenos que persistem em ocorrer, mesmo com a disseminação da informação por todo o mercado, contrariando os pressupostos da eficiência de mercado. Dentro deste contexto, esta tese se propôs a estudar alguns deles, e também realizar modificações em modelos já consolidados. Foram feitas aqui três modificações na maneira tradicional de análise de modelos de anomalias, dentro de quatro capítulos distintos, porém inter-relacionados, além da introdução e da conclusão. O primeiro capítulo se propõe a verificar dois pressupostos básicos de modelos estatísticos, que são a normalidade e a estacionariedade da série de retornos de ações no Brasil. O segundo capítulo modifica a metodologia tradicional de formação de carteiras, aplicando uma técnica conhecida como análise de cluster em detrimento das medidas de posição. A terceira parte apresenta uma modificação do modelo de Grinblatt e Moskowitz (2004), analisando os aspectos que seriam importantes para o mercado brasileiro nos retornos futuros das ações. Por fim, é feita uma modificação importante no Modelo de Multifatores de Fama e French (1996), incorporando elementos da variância condicional, através da modelagem ARCH e GARCH na equação do modelo. Concluí-se que o mercado brasileiro apresenta algumas anomalias comuns a outros mercados, e que uma melhoria pode ser realizada nos modelos tradicionais, levando-se em consideração características específicas do caso brasileiro. / [en] The anomalies that exist in the Brazilian Capital Markets have been increasingly discused in recent research, as much for the curiosity of researchers as for the need of the market to understand some phenomena that persist in occurring, opposing the assumptions of market efficiency. In this context, this thesis aimed at studying some of them, and also to carry through some modifications in consolidated models. Three modifications were made in the traditional analysis of anomalies models, resulting in four distinct chapters, but interrelated, and the introduction and conclusion. The first study verified two estimated assumptions of statistical models, that are the normality and the stationarity of returns of the shares in Brazil. The second study modifies the traditional way of portfolio formation, applying the cluster analysis technique instead of by the ranking of position. The third study presents a modification of the Grinblatt and Moskowitz Model (2004), analyzing the aspects that would be important for the Brazilian market in determines the returns of the shares. Finally, in the fourth study, an important modification in the Multifactor Model of Fama and French (1996) is proposed, incorporating elements of the conditional variance, through applying modeling; ARCH and GARCH in the equation of the model. It can be concluded that the Brazilian market presents some common anomalies to other markets, and that an improvement can be implemented in the traditional models.