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In this paper we implemented a Bayesian robust optimization model to select an optimal investment portfolio. To do that, we extended the model developed by Meucci, which consists of incorporating the Bayesian approach into the robust portfolio model in order to define an ellipsoidal-type uncertainty set under an Inverse Wishart Distribution. Thus, the uncertainty of the estimated parameters for create the robust counterpart in the portfolio model. The proposed model uses a Gamma distribution function, as a generalization of the Wishart function. Results confirm Meucci's conclusions and, it corroborates the properties attributed to those portfolios. [ABSTRACT FROM AUTHOR]

This paper presents the Hierarchical Risk Parity (hrp) approach proposed by López de Prado (2016, 2018, 2020) for the construction of optimal investment portfolios using unsupervised learning, hierarchical clustering, which allow overcome some limitations of the Mean-Variance (MV) model, in particular those related to the need to invert the covariance matrix when implementing the cla algorithm. A sample of 7 assets from the American market is taken, with which an application of the hrp algorithm proposed by López de Prado is carried out, finding that under this model the distribution of assets in different clusters generates improvements in terms of the expected return, as well as of the Sharpe coefficient compared to the results of the Mean-Variance portfolio. [ABSTRACT FROM AUTHOR]

This paper presents an approach for socially responsible investment portfolio selection through the incorporation of esg criteria: environment (A), social (S) and of good governance (G); to the Markowitz's mean-variance (MV) model. For that, different formulations of the MV optimization problem are revised, as well as its adjustment to incorporate these indicators in the construction and optimization of the portfolio. This new approach, known as the MV-esg model, allows the construction of a complete set of feasible optimal portfolios based on the three relationships: return, risk and the esg score; resulting in an efficient surface (ES) on a three-dimensional space. Results show that the achievement of an increasingly higher esg indicator not only reduces the performance of the portfolio with respect to the MV portfolio, but also reduces its risk diversification capacity. However, the fact that the incorporation of esg criteria allows investors to incorporate their preferences to minimize the social and environmental impact of their investments is highlighted, since the optimal esg portfolio generates better indicators than any portfolio that pursue only the optimal risk-return ratio, in addition to outperforming the benchmark. [ABSTRACT FROM AUTHOR]

Robust optimization (OR) models have made it possible to overcome the limitations of the mean-variance (MV) model, which involves the traditional approach for the optimal portfolio selection, by incorporating the uncertainty of the model parameters (expected returns and covariances). In this paper, the or advances in portfolio theory are presented using the worst-case approach, from which the robust formulations for the mv model are incorporated, considering the Markowitz and Sharpe works. From these formulations, a straightforward application is implemented where the advantages and benefits of the robust counterparts are highlighted compared to the original MV model. At the end, a brief discussion of additional formulations regarding uncertainty sets and other performance measures is presented. [ABSTRACT FROM AUTHOR]