A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution

Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails

Mean-Variance-Skewness Portfolio Selection Model Based on RBF-GA

The classical Markowitz’s mean-variance model in modern investment science uses variance as risk measure while it ignores the asymmetry of the return distribution. This article introduces skewness, V-type transaction costs, cardinality constraint and initial investment proportion, and builds a new class of nonlinear multi-objective portfolio model (mean-variance-skewness portfolio selection model). To solve the model, we develop a genetic algorithm(GA) which contains radial basis function(RBF) neural network, called RBF-GA. The experimental results show that the proposed model is more effective and more realistic than others

Optimization of a dynamic supply portfolio considering risks and discount’s constraints

Purpose: Nowadays finding reliable suppliers in the global supply chains has become so important for success, because reliable suppliers would lead to a reliable supply and besides that orders of customer are met effectively . Yet, there is little empirical evidence to support this view, hence the purpose of this paper is to fill this need by considering risk in order to find the optimum supply portfolio. Design/methodology/approach: This paper proposes a multi objective model for the supplier selection portfolio problem that uses conditional value at risk (CVaR) criteria to control the risks of delayed, disrupted and defected supplies via scenario analysis. Also we consider discount’s constraints which are common assumptions in supplier selection problems. The proposed approach is capable of determining the optimal supply portfolio by calculating value-at-risk and minimizing conditional value-at-risk. In this study the Reservation Level driven Tchebycheff Procedure (RLTP) which is one of the reference point methods, is used to solve small size of our model through coding in GAMS. As our model is NP-hard; a meta-heuristic approach, Non-dominated Sorting Genetic Algorithm (NSGA) which is one of the most efficient methods for optimizing multi objective models, is applied to solve large scales of our model. Findings and Originality/value: In order to find a dynamic supply portfolio, we developed a Mixed Integer Linear Programming (MILP) model which contains two objectives. One objective minimizes the cost and the other minimizes the risks of delayed, disrupted and defected supplies. CVaR is used as the risk controlling method which emphases on low-probability, high-consequence events. Discount option as a common offer from suppliers is also implanted in the proposed model. Our findings show that the proposed model can help in optimization of a dynamic supplier selection portfolio with controlling the corresponding risks for large scales of real word problems. Practical implications: To approve the capability of our model various numerical examples are made and non-dominated solutions are generated. Sensitive analysis is made for determination of the most important factors. The results shows that how a dynamic supply portfolio would disperse the allocation of orders among the suppliers combined with the allocation of orders among the planning periods, in order to hedge against the risks of delayed, disrupted and defected supplies. Originality/value: This paper provides a novel multi objective model for supplier selection portfolio problem that is capable of controlling delayed, disrupted and defected supplies via scenario analysis. Also discounts, as an option offered from suppliers, are embedded in the model. Due to the large size of the real problems in the field of supplier selection portfolio a meta-heuristic method, NSGA II, is presented for solving the multi objective model. The chromosome represented for the proposed solving methodology is unique and is another contribution of this paper which showed to be adaptive with the essence of supplier selection portfolio problemPeer Reviewe

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

[EN] 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.García García, F.; González-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2020). Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory. Technological and Economic Development of Economy (Online). 26(6):1165-1186. https://doi.org/10.3846/tede.2020.13189S11651186266Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/s0378-4266(02)00283-2Ahmed, A., Ali, R., Ejaz, A., & Ahmad, I. (2018). 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A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

Multi-objective possibilistic model for portfolio selection with transaction cost

AbstractIn this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples

A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American Integrated Market

[EN] 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.García García, F.; Gonzalez-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J. (2020). A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American Integrated Market. Enterpreneurship and Sustainability Issues. 8(2):1027-1046. https://doi.org/10.9770/jesi.2020.8.2(62)S102710468