Abstract
This paper extends the stochastic mean-semivariance model to a fuzzy multiobjective model, where apart from return and risk, also liquidity is considered to measure the performance of a portfolio. Uncertainty of future return and liquidity of each asset are modeled using L-R type fuzzy numbers that belong to the power reference function family. The decision process of this novel approach takes into account not only the multidimensional nature of the portfolio selection problem but also realistic constraints by investors. Particularly, it optimizes the expected return, the semivariance and the expected liquidity of a given portfolio, considering cardinality constraint and upper and lower bound constraints. The constrained portfolio optimization problem resulting is solved using the algorithm NSGA-II. As a novelty, in order to select the optimal portfolio, this study defines the credibilistic Sortino ratio as the ratio between the credibilistic risk premium and the credibilistic semivariance. An empirical study is included to show the effectiveness and efficiency of the model in practical applications using a data set of assets from the Latin American Integrated Market.
Highlights
Multi-criteria decision making includes a group of operational research methods that pursue decision making in the presence of multiple criteria, goals, or objectives
This type of method differs from traditional single-objective operational research methods and is intended to support decision makers in the simultaneous optimization of several objectives that usually conflict with each other (Čižo et al, 2020) and those related to financial investments are not an exception (Aznar & Guijarro, 2016; García et al, 2013, 2018; García, González-Bueno, ENTREPRENEURSHIP AND SUSTAINABILITY ISSUES ISSN 2345-0282 http://jssidoi.org/jesi/ 2020 Volume 8 Number 2 (December) http://doi.org/10.9770/jesi.2020.8.2(62)
Data description The Latin American Integrated Market is an integrated trading venture between the stock markets of Chile, Colombia, Mexico and Peru that began operating in May 30, 2011
Summary
Multi-criteria decision making includes a group of operational research methods that pursue decision making in the presence of multiple criteria, goals, or objectives. When portfolio returns are typically asymmetric, the variance becomes a less appropriate risk measure, because it considers high returns that investors want as undesirable as low returns that investors dislike (Li & Qin, 2014) In other words, both risk measures penalize extreme upside (gains) and downside (losses) deviations from the expected return (Gupta, Mittal, et al, 2013). Its main advantage over variance is that it does not consider values beyond the critical value (i.e. gains) as risk (Gupta, Mittal, et al, 2013) It is a more appropriate risk measure when an investor is concerned about underperformance rather than over performance of the portfolio (Markowitz et al, 1993)
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