Otimização de uma carteira de investimentos aplicada ao PSI
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Data
2023
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O presente estudo teve como finalidade proceder a uma análise do mercado de ações português,
mais concretamente ao seu índice PSI, e apresentar algumas carteiras otimizadas constituídas
por ativos que componham o índice à data de realização.
Inicialmente, foi realizada uma revisão literária sobre a Teoria do Portfólio Moderna
e os seus componentes estatísticos, bem como aos Índices de Sharpe e Treynor e ao Alfa de
Jensen, com o intuito de apresentar uma explicação dos componentes analíticos aplicados ao
longo deste estudo. Para terminar esta revisão, são apresentados alguns estudos semelhantes
anteriormente realizados dentro da mesma área.
Como metodologia de estudo, foi aplicada uma análise quantitativa às cotações
históricas de empresas que compunham o PSI, da qual resultou a rendibilidade mensal e desvio
padrão dos ativos, o que permitiu criar uma carteira teórica na qual os ativos tinham igual
ponderação. Com recurso ao Solver e alterando a ponderação das ações mediante certas
restrições impostas ao software, apuraram-se três portfólios de investimento eficientes: o
Portfólio 1, que maximizou a relação risco/rendibilidade; o Portfólio 2, que maximizou a
rendibilidade mantendo o risco da carteira original; o Portfólio 3, que minimizou o risco para a
rendibilidade da carteira original.
Finalizando, na análise de resultados, são discutidas e justificadas as melhorias das
carteiras eficientes em relação à carteira original e ainda são facultadas algumas sugestões para
futuros trabalhos.
The purpose of this study was to analyze the Portuguese stock market, more specifically its PSI index, and to present some optimized portfolios composed of assets that made up the index at the timeframe of the study. Initially, a literature review was conducted on Modern Portfolio Theory and its statistical components, the Sharpe and Treynor indexes and the Jensen Alpha, in order to present an explanation of the analytical components applied throughout this study. To finish this review, some similar studies previously done within the same area are presented. As a study methodology, a quantitative analysis was applied to the historical stock prices of the companies that made up the PSI, from which resulted the monthly return and standard deviation of the assets, which allowed the creation of a theoretical portfolio in which the assets had equal weighting. Using Solver and changing the weighting of the stocks through certain restrictions imposed on the software, three efficient investment portfolios were found: Portfolio 1, which maximized the risk/return ratio; Portfolio 2, which maximized the return while maintaining the risk of the original portfolio; Portfolio 3, which minimized the risk for the return of the original portfolio. Finally, in the results analysis, the improvements of the efficient portfolios relative to the original portfolio are discussed and justified, and some suggestions for future work are provided.
The purpose of this study was to analyze the Portuguese stock market, more specifically its PSI index, and to present some optimized portfolios composed of assets that made up the index at the timeframe of the study. Initially, a literature review was conducted on Modern Portfolio Theory and its statistical components, the Sharpe and Treynor indexes and the Jensen Alpha, in order to present an explanation of the analytical components applied throughout this study. To finish this review, some similar studies previously done within the same area are presented. As a study methodology, a quantitative analysis was applied to the historical stock prices of the companies that made up the PSI, from which resulted the monthly return and standard deviation of the assets, which allowed the creation of a theoretical portfolio in which the assets had equal weighting. Using Solver and changing the weighting of the stocks through certain restrictions imposed on the software, three efficient investment portfolios were found: Portfolio 1, which maximized the risk/return ratio; Portfolio 2, which maximized the return while maintaining the risk of the original portfolio; Portfolio 3, which minimized the risk for the return of the original portfolio. Finally, in the results analysis, the improvements of the efficient portfolios relative to the original portfolio are discussed and justified, and some suggestions for future work are provided.
Descrição
Orientação: Paulo Fernando de Sousa Pereira Alves
Palavras-chave
MESTRADO EM GESTÃO DE EMPRESAS, ECONOMIA, ANÁLISE DE RISCO, RENDIBILIDADE FINANCEIRA, ECONOMY, RISK ANALYSIS, FINANCIAL PROFITABILITY