Abstract
A otimização robusta de carteiras tem recebido grande interesse nos últimos anos devido a possibilidade de considerar o erro de estimação dentro do problema da seleção de carteiras. Uma questão abordada por poucos estudos é se esta nova abordagem é capaz de gerar uma performance fora-da-amostra superior aos métodos tradicionais. Além disso, é importante saber esta abordagem é capaz de gerar carteiras mais estáveis ao longo do tempo, contribuindo assim para reduzir os custos de administração e facilitando a implementação na prática. Este estudo analisa a performance fora-da-amostra e a estabilidade das composições ótimas das carteiras obtidas com otimização robusta e com métodos tradicionais. Os resultados indicam que, para dados simulados, a otimização robusta obtém uma performance superior aos métodos tradicionais tanto em termos de índice de Sharpe como em termos de portfolio turnover. Os resultados para dados reais de indicam que a performance ajustada ao risco foi estatisticamente equivalente, entretanto as composições ótimas foram mais estáveis do que as obtidas através de métodos tradicionais de otimização.
Highlights
The portfolio optimization approach proposed by Markowitz (1952) is undoubtedly one of the most important models in financial portfolio selection
This paper aims at shedding light on the recent debate concerning the importance of the estimation error and weights stability in the portfolio allocation problem, and the potential benefits coming from robust portfolio optimization in comparison to traditional techniques
For the data set FF5, the results shown in Tables 11 and 12 indicate that the two highest Sharpe ratios were obtained by the mean-variance and standard robust optimization approaches (0.281 and 0.258), with no statistical significance for the difference (p-value of 0.6)
Summary
The portfolio optimization approach proposed by Markowitz (1952) is undoubtedly one of the most important models in financial portfolio selection. The idea behind Markowitz’s work (hereafter mean-variance optimization) is that individuals will decide their portfolio allocation based on the fundamental trade-off between expected return and risk Under this framework, individuals will hold portfolios located in the efficient frontier, which defines the set of Pareto-efficient portfolios. Taking into account that stock returns usually violate the normality assumption, we should expect the estimation error to affect the performance of optimization techniques that rely on sample estimates. It is well known in the financial literature that the mean-variance optimization suffers from the problem of estimation error, since it uses estimated means and covariances as inputs. It is well known in the financial literature that the mean-variance optimization suffers from the problem of estimation error, since it uses estimated means and covariances as inputs. Michaud (1989), for instance, refers to the traditional mean-variance approach as an “error-maximization” approach
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