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Otimização de carteiras com o modelo Treynor-Black: Aplicação Empírica e Avaliação de Desempenho no Mercado Português
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Resumo(s)
O presente trabalho investiga a aplicação prática do modelo Treynor-Black à otimização de
carteiras no mercado acionista português, utilizando o PSI-20 e PSI-Geral como índice de
referência. Recorrendo a cotações mensais das empresas admitidas à negociação no mercado
portguês e dos principais índices nacionais entre 2009 e 2024, foram implementadas
simulações trimestrais que testam o desempenho do portfólio otimizado pelo modelo face às
alternativas puramente passivas. Os resultados empíricos demonstram que, embora o modelo
Treynor-Black não permita a obtenção recorrente de ganhos extraordinários nem a superação
consistente dos benchmarks em todos os períodos, consegue entregar um resultado
acumulado ligeiramente superior ao do próprio PSI-Geral, sendo substancialmente mais
eficiente do que a indexação ao PSI-20, que teria implicado perdas relevantes. A principal
mais-valia do modelo reside no controlo rigoroso do risco e na disciplina quantitativa que
impõe, nomeadamente ao evitar grandes perdas em trimestres mais adversos, limitando a
exposição a títulos penalizadores. Os resultados sugerem que a adoção do Treynor-Black pode
ser vantajosa sobretudo para investidores que valorizam estabilidade e controlo do risco,
confirmando que, no contexto português, a gestão quantitativa ativa é, na melhor das
hipóteses, tão eficiente quanto uma abordagem passiva diversificada, mas raramente oferece
vantagens estruturais sustentadas.
This study investigates the practical application of the Treynor-Black model to portfolio optimization in the Portuguese stock market, using the PSI-20 and PSI-Geral as reference indices. Using monthly price data for companies listed on the Portuguese market and for the main national indices between 2009 and 2024, quarterly simulations were implemented to test the performance of the model-optimized portfolio against purely passive alternatives. The empirical results show that, although the Treynor-Black model does not allow for the consistent achievement of extraordinary gains nor the systematic outperformance of benchmarks in all periods, it is able to deliver a slightly higher cumulative return than the PSIGeral itself, and is substantially more efficient than indexation to the PSI-20, which would have implied significant losses. The main advantage of the model lies in its rigorous risk control and the quantitative discipline it imposes, notably by avoiding large losses in more adverse quarters and by limiting exposure to underperforming stocks. The results suggest that adopting the Treynor-Black model may be especially advantageous for investors who value stability and risk control, confirming that, in the Portuguese context, active quantitative management is, at best, as efficient as a diversified passive approach, but rarely offers sustained structural advantages.
This study investigates the practical application of the Treynor-Black model to portfolio optimization in the Portuguese stock market, using the PSI-20 and PSI-Geral as reference indices. Using monthly price data for companies listed on the Portuguese market and for the main national indices between 2009 and 2024, quarterly simulations were implemented to test the performance of the model-optimized portfolio against purely passive alternatives. The empirical results show that, although the Treynor-Black model does not allow for the consistent achievement of extraordinary gains nor the systematic outperformance of benchmarks in all periods, it is able to deliver a slightly higher cumulative return than the PSIGeral itself, and is substantially more efficient than indexation to the PSI-20, which would have implied significant losses. The main advantage of the model lies in its rigorous risk control and the quantitative discipline it imposes, notably by avoiding large losses in more adverse quarters and by limiting exposure to underperforming stocks. The results suggest that adopting the Treynor-Black model may be especially advantageous for investors who value stability and risk control, confirming that, in the Portuguese context, active quantitative management is, at best, as efficient as a diversified passive approach, but rarely offers sustained structural advantages.
Descrição
Dissertation presented as the partial requirement for obtaining a Master's degree in Information Management, specialization in Business Intelligence
Palavras-chave
Otimização de carteiras Modelo Treynor-Black Gestão ativa Gestão quantitativa PSI-Geral Alfa Risco Mercado português Investimento passivo Eficiência de mercado