New approximate stochastic dominance approaches for Enhanced Indexation models

In this paper, we first address the multi-objective representation of the Enhanced Indexation (EI) problem proposed by [Roman et al.2013] by an alternative approach based on the Ordered Weighted Average (OWA) operator [Yager1988]. Its advantage is that it allows us to consider a set of the worst realized objectives in the problem, whereas the Minimax operator, used in [Roman et al.2013], pays attention only to the maximum of them. The convenience of this type of scalarizations is that it allows highlighting a broader family of Pareto- optimal portfolios, improving the properties of the Minimax ones (see, e.g., [Nickel and Puerto2006]). Second, we propose a new methodology to select a portfolio that dominates a given benchmark index in terms of Stochastic Dominance (SD). This methodology uses the OWA representation developed in [Marín et al.2020] and leads to solving linear programming problems. Furthermore, it contains as special cases some known SD- based approaches to asset allocation (see [Lizyayev and Ruszczyński2012, Roman et al.2013]). Thus, we develop an innovative optimization model for selecting an investment portfolio that should generate excess return w.r.t. a benchmark index. Third, we introduce a new type of approximate stochastic dominance rule that we call Cumulative Second-order E-Stochastic Dominance (CSESD), and we show that it implies the ε-ASSD rules proposed by [Lizyayev and Ruszczyński2012]. Exploiting some results in multi-criteria optimization, we prove that the optimal solution of our EI model based on OWA selects portfolios that dominate the benchmark index in terms of CSESD. Fourth, to test and validate the performance of the portfolios obtained by our proposed strategies, we provide extensive empirical analysis based on the FTSE100, NASDAQ100, and SP500 datasets, comparing their out-of-sample behavior with that of the portfolios constructed by several SD-based approaches proposed in the literature and with that of the global minimum variance portfolios.