Otimização multiobjetivo utilizando algoritmos evolutivos em seleção de carteiras: uma abordagem envolvendo ômega, assimetria e antifragilidade

Abstract

Profitability in investments has always been the desire of any investor, whether an individual or a company. In periods of declining interest rates in world economies, as well as the existence of an unstable performance of stock exchange assets due to recurringfinancial crises, such as the recent one caused by COVID-19, the profitability of Fixed and Variable Income assets is increasingly threatened.This context causes investors to increasingly search for assets that manage toreconcile profitability and a minimum of security in the composition of their portfolios. Itmakes the selection of asset portfolios undoubtedly one of the most challenging topics inthe Finance area.Since Markowitz’s initial contribution, several researchers have sought to studymethods, techniques, and models applicable to the topic. A crucial theoretical landmarkwas the proposal in the 1960s of the CAPM model, which has severe empirical flaws,although robust and consistent. Its empirical limitation is pointed out by the fact that themarket portfolio proxy idealized by the model does not take effect in practice. In additionto this, some premises as normal distribution and the quadratic utility function make theCAPM model less and less likely to succeed when implemented in practice.Therefore, new approaches have been presented, with a recent highlight for theOCAPM model, in which the Omega measure allows us to relax these CAPM premisesand represent the investor’s preference more effectively. Thus, new attributes that notonly mean and variance become relevant in the process of building new approaches to themodel, transforming the problem into a multiobjective approach.As OCAPM does not yet have a full empirical application, this research splits intothree parts: the first works with mono-objective optimization and seeks to empirically knowif the OCAPM model performs better than the CAPM model in the studied markets. Thesecond part works with the optimization of purely convex attributes. It aims to ratify theview that the mean and variance may not be sufficient to represent the entire distributionof return on assets and, therefore, investors’ decisions. The third part, the central part ofthe research, deals with the optimization of multiobjective portfolios involving convex andnon-convex attributes through the use of evolutionary algorithms.In this experiment, there are three multiobjective portfolios: i) Global, involvingthe optimization of the omega, mean, asymmetry, kurtosis, drawdown, and antifragilityattributes; ii) Antifragile, involving drawdown and antifragility and iii) Asymmetric,involving omega, skewness, and kurtosis.The results of the research show that the antifragile portfolio brought higher averagereturns than CAPM and OCAPM models, and the American market showed better riskconditions. Valuing assets that have a low drawdown and have relative resilience in times of turbulence becomes advantageous in investment management. Losing little in crisistimes seems to be more significant than winning in periods of calm and stability. Amongthe evolutionary algorithms used, the highlight is the NSGA3, which presented the bestperformance out of the sample in the optimization of multiobjective portfolios.