Research Article

A multiobjective portfolio optimization for energy assets using D-Optimal design and mixture design of experiments

Gustavo dos Santos Leal; Estevão Luiz Romão; Daniel Leal de Paula Esteves dos Reis; Pedro Paulo Balestrassi; Anderson Paulo de Paiva

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Paper aims: Frequently, researchers try to find a better way to allocate assets in order to have maximum return and low variability in a portfolio as diverse as possible. This paper aims to apply D-Optimal Design in the context of Mixture Design and portfolio optimization to efficiently select the runs of the proposed experimental design.

Originality: A new approach to find the optimal weights that maximize the returns and minimize the risk using D-Optimal Design was used. A multi-response optimization problem considering returns, variability and entropy as functions of the weights was proposed. However, as there is a significant correlation between the objective functions, a Factor Analysis combined with FMSE to dimensionality reduction was used.

Research method: All the steps for both stages of the methodology applied in this paper are presented below: select real time series; predict one step ahead; generate a D-Optimal mixture design; apply weights and generate mathematical models; solve the optimization problem.

Main findings: Using the desirability method, the optimal values were determined, obtaining approximately 79% for the compound desirability function. The proposed method presented a 16.80% higher return with a 4.98% higher risk exposure if compared against Naïve method.

Implications for theory and practice: The proposed methodology can be applied to any portfolio optimization study. Mixture Design studies have already been proposed for modeling portfolio optimization problems. However, the D-Optimal Design proved to be adequate, which represents less computational effort.


Portfolio optimization, D-Optimal design, Mixture design, Multivariate analysis


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