Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory

Abstract

The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio’s performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.

Projecting Financial Technical Indicators Into Networks as a Tool to Build a Portfolio

“…Yue et al [5] considered simultaneously semi-variance and semi-absolute deviation as double-risk measures. The second type of study is mainly to add new criteria in the portfolio selection process [6], [7]. Garcia et al [6] considered the non-financial criteria, such as social responsibility performance, in their portfolio selection process.…”

“…Garcia et al [6] considered the non-financial criteria, such as social responsibility performance, in their portfolio selection process. Garcia et al [7] used liquidity to quantify the performance of portfolio in addition to the usual metrics such as return and risk. The third type of study focuses on the new portfolio selection models [8]- [11].…”

Adjustable Security Proportions in the Fuzzy Portfolio Selection under Guaranteed Return Rates

“…García et al [34] proposed a mean-semi-variance multi-objective credibilistic portfolio selection model with a priceto-earnings ratio to measure the portfolio performance. Garcia et al [35] extended the stochastic mean-variance model to a credibilistic multi-objective model in which the semivariance and the CVaR are used to measure portfolio performance and the non-dominated sorting genetic algorithm II is applied to solve efficient portfolios in the fuzzy return-riskliquidity trade-off to create an efficient frontier. Mehlawat et al [36] proposed a multiobjective function with variance and CVaR as risk measures for performance evaluation in the fuzzy portfolio selection models, in which the inherent uncertainty of the investment market is incorporated through trapezoidal fuzzy returns using the credibility theory.…”

Comparison of multicriteria decision-making methods in portfolio formation

“…Since Modern portfolio theory development by H. Markowitz, it has received substantial criticism and many improvement attempts (Rodríguez et al, 2021). Besides return and risk, other parameters are increasingly included in portfolio selection: liquidity (García et al, 2020a), sustainability in the form of environmental, social and governance (ESG) scores (García et al, 2019), skewness (Liechty & Saglam, 2017;Pahade & Jha, 2021), and kurtosis (Naqvi et al, 2017). Sometimes psychological factors impact investor decisionmaking.…”