Multiobjective portfolio optimization of ARMA–GARCH time series based on experimental designs

• ARMA–GARCH models mean and variance of heteroskedastic time series.
• MDE defines asset proportions for portfolio optimization.
• Entropy function improves portfolio diversity.
• RSM sets the best weight and importance for desirability routine.
• Optimal portfolio is selected after computer-aided desirability tuning method.

The modern portfolio theory has been trying to determine how an investor might allocate assets among the possible investments options. Since the seminal contribution provided by Harry Markowitz’s theory of portfolio selection, several other tools and procedures have been proposed to deal with return-risk trade-off. Furthermore, diversification across sources of returns and risks based on entropy indexes is another pivotal aspect in portfolio management. An efficient approach to model these portfolio properties with the proportion of each asset can be obtained according to mixture design of experiments. Desirability method can be applied to optimize this nonlinear multiobjective problem. Nevertheless, a tuning procedure is required, since preference articulation parameters in desirability algorithm are unknown a priori. As a result, a computer-aided desirability tuning method is proposed to find an optimal portfolio with time series of returns and risks modeled by ARMA–GARCH models. To assess the proposal feasibility, the method is tested with a heteroskedastic dataset formed by weekly world crude oil spot prices and returns. Computer-aided desirability tuning was able to enhance the global desirability by 79% in relation to the result with no tuning procedure.

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