Portfolio selection under uncertainty: a new methodology for computing relative‐robust solutions

Abstract

In this paper, a new methodology for computing relative-robust portfolios based on minimax regret is proposed. Regret is defined as the utility loss for the investor resulting from choosing a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute-robust strategy was also considered and, in this case, the minimum investor's expected utility in the worst-case scenario is maximized. Several subsamples are gathered from the in-sample data and for each subsample a minimax regret and a maximin solution are computed, to avoid the risk of overfitting. Robust portfolios are computed using a genetic algorithm, allowing the transformation of a three-level optimization problem in a two-level problem. Results show that the proposed relative-robust portfolio generally outperforms (other) relative-robust and non-robust portfolios, except for the global minimum variance portfolio. Furthermore, the relative-robust portfolio generally outperforms the absolute-robust portfolio, even considering higher risk aversion levels.

Geometric compromise programming: application in portfolio selection

“…Caçador et al. (2021) proposed a new methodology for computing relative‐robust portfolios based on the minimax regret, which is equivalent to setting $$p=\infty$$ in Equation (5). From the review of the previous works, we argue that further insight can be obtained from the analysis of an alternative set of solutions by setting $$p=0$$ as proposed by GCP.…”

“…Salas-Molina et al (2019) proposed different practical tools to deal with discrete efficient frontiers and uncertain risk preferences for cases p = 1 and p = 2. Caçador et al (2021) proposed a new methodology for computing relative-robust portfolios based on the minimax regret, which is equivalent to setting p = ∞ in Equation (5). From the review of the previous works, we argue that further insight can be obtained from the analysis of an alternative set of solutions by setting p = 0 as proposed by GCP.…”

The Robust Emergency Medical Facilities Location-Allocation Models under Uncertain Environment: A Hybrid Approach

“…However, it assumes that the uncertain parameters fluctuate in an interval [26][27][28][29][30]. Since its emergence, robust optimization theories have been applied to many fields, such as group decision-making [31][32][33][34][35][36], portfolios [37][38][39][40][41], efficiency evaluation [42,43], supply chain management [44][45][46][47][48][49], etc. In emergency medical location decisions, some scholars have adopted the stochastic programming method for modeling [50][51][52][53][54].…”

An omega portfolio model with dynamic return thresholds

“…(2018) show that the Omega ratio is far more severe than just inconsistent with the second‐order stochastic dominance criterion. The second approach involves considering the Omega ratio as an objective function for portfolio optimization in order to introduce DSR into the estimation of optimal portfolio weights (Kapsos et al., 2014a, 2014b; Sharma et al., 2017; Caçador et al., 2021; Sehgal and Mehra, 2021). However, one should be cautious in applying the Omega model, as it can generate misleading asset allocation suggestions.…”