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Otimização de uma carteira internacional com base na semi-variância
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Dada a incerteza associada à evolução dos preços dos ativos e das respetivas taxas de câmbio num mercado internacional, o investidor de hoje atribui maior relevância à conservação do capital investido do que à obtenção de largos ganhos. Assim, o risco torna-se no foco da análise na construção de uma carteira de investimentos. Como tal, o presente trabalho procura, em particular, analisar o risco de perda numa carteira de investimentos, considerando os ganhos como uma oportunidade para o investidor. Consequentemente, recorre-se à semi-variâcia para efetuar a medição do risco e procura-se comparar o modelo de seleção de carteiras utilizando esta medida de risco como tradicional modelo de Markowitz. O retorno esperado com o investimento é outro fator importante, sendo essencial para a escolha de ativos na integração dessa carteira. É no binómio retorno e risco que se irá basear o modelo em estudo, realçando a importância da interação entre os ativos, representada por uma matriz de semi-covariâncias e que será gerada de forma a ser de natureza simétrica e exógena. Uma estratégia de backtesting encontra-se implementada de forma a observar a evolução do comportamento em ambos os modelos com base nos dados históricos. Para investimentos por vários períodos, tornam-se necessários ajustes na carteira através da compra e venda de ativos. Face a isto, será apresentado um modelo linear recursivo de decisões de investimentos sequenciais para dois períodos. Em ambos os casos, o modelo com base na semi- variância tende a apresentar um melhor desempenho do que o modelo tradicional baseado na variância dos retornos.
Due to the uncertainty associated with the evolution of asset prices and their respective exchange rate in an international market, investors give nowadays more importance to maintaining a certain level of capital than to obtaining large gains. Thus, risk becomes the focus of the analysis on the construction of an investment portfolio. The present work aims, in particular, to analyse the risk of loss in an invest- ment portfolio, while considering the price movements above a pre-defined value as an opportunity to the investor. Consequently, the semivariance is used to measure risk and a comparison is made between the portfolio selection model using this risk measurement and the Markowitz’s traditional model. The minimum required return on the investment is another important factor, essential to the assets’selection to integrate the portfolio. The model in this study will be based on the trade-off between risk and return, highlighting the importance of the interaction between the assets, represented by the semicovariance matrix, which will be generated to be symmetrical and exogenous. A backtesting strategy will be im- plemented in order to observe the portfolio’s behavior in both models based on historical data. For investments over multiple periods, portfolio adjustments are required through the sale and acquisition of the available assets. Having this in consideration, a model based on linear decisions rules for two periods of investment will be developed. In both cases, the model based on the semivariance tends to achieve better results than the traditional model based on returns variance.
Due to the uncertainty associated with the evolution of asset prices and their respective exchange rate in an international market, investors give nowadays more importance to maintaining a certain level of capital than to obtaining large gains. Thus, risk becomes the focus of the analysis on the construction of an investment portfolio. The present work aims, in particular, to analyse the risk of loss in an invest- ment portfolio, while considering the price movements above a pre-defined value as an opportunity to the investor. Consequently, the semivariance is used to measure risk and a comparison is made between the portfolio selection model using this risk measurement and the Markowitz’s traditional model. The minimum required return on the investment is another important factor, essential to the assets’selection to integrate the portfolio. The model in this study will be based on the trade-off between risk and return, highlighting the importance of the interaction between the assets, represented by the semicovariance matrix, which will be generated to be symmetrical and exogenous. A backtesting strategy will be im- plemented in order to observe the portfolio’s behavior in both models based on historical data. For investments over multiple periods, portfolio adjustments are required through the sale and acquisition of the available assets. Having this in consideration, a model based on linear decisions rules for two periods of investment will be developed. In both cases, the model based on the semivariance tends to achieve better results than the traditional model based on returns variance.
Descrição
Trabalho de projecto de mestrado, Matemática Aplicada à Economia e Gestão, Universidade de Lisboa, Faculdade de Ciências, 2019
Palavras-chave
Carteira de Investimentos Internacional Otimização de Carteiras Semi-variância Multiperíodo Regras Lineares de Decisão Trabalhos de projecto de mestrado - 2019