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The robustness of portfolio efficient frontiers: a comparative analysis of bi-objective and multi-objective approaches

Pavlou Antonios, Doumpos Michail, Zopounidis Konstantinos

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Purpose: The optimization of investment portfolios is a topic of major importance in financial decision making, with many relevant models available in the relevant literature. The purpose of this paper is to perform a thorough comparative assessment of different bi-objective models as well as multi-objective one, in terms of the performance and robustness of the whole set of Pareto optimal portfolios. Design/methodology/approach: In this study, three bi-objective models are considered (mean-variance (MV), mean absolute deviation, conditional value-at-risk (CVaR)), as well as a multi-objective model. An extensive comparison is performed using data from the Standard and Poor’s 500 index, over the period 2005–2016, through a rolling-window testing scheme. The results are analyzed using novel performance indicators representing the deviations between historical (estimated) efficient frontiers, actual out-of-sample efficient frontiers and realized out-of-sample portfolio results. Findings: The obtained results indicate that the well-known MV model provides quite robust results compared to other bi-objective optimization models. On the other hand, the CVaR model appears to be the least robust model. The multi-objective approach offers results which are well balanced and quite competitive against simpler bi-objective models, in terms of out-of-sample performance. Originality/value: This is the first comparative study of portfolio optimization models that examines the performance of the whole set of efficient portfolios, proposing analytical ways to assess their stability and robustness over time. Moreover, an extensive out-of-sample testing of a multi-objective portfolio optimization model is performed, through a rolling-window scheme, in contrast static results in prior works. The insights derived from the obtained results could be used to design improved and more robust portfolio optimization models, focusing on a multi-objective setting.

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