Mean-semiabsolute Deviation Research Articles

Credibilistic portfolio optimization with higher-order moments using coherent triangular fuzzy numbers

Financial portfolio formation is usually a multi-objective decision-making problem concerning return and risk on the investment. In this study, we make use of an extension of regular triangular fuzzy numbers, known as coherent triangular fuzzy numbers, to describe portfolio returns in a credibility-based framework. The paper’s novelty lies in proposing and deriving a crisp equivalent for computing the coherent triangular fuzzy number-based credibilistic semivariance, credibilistic skewness, and credibilistic semikurtosis. Utilizing these analytical expressions, along with additional formulations found in existing literature, we present three multi-objective portfolio optimization models involving the practical constraints related to investment decisions. All the proposed analytical expressions, when used with the returns of the portfolio as a whole, help to overcome the computationally expensive process of simulating results using the returns of individual assets. The proposed models differ with respect to different risk measures, viz. semivariance, Mean-Absolute-Semi-Deviation (MASD), and Conditional Value-at-Risk (CVaR). These models are solved using an adaptation of an efficient Multi-Objective Genetic Algorithm (MOGA) specifically designed to solve portfolio optimization problems with practical constraints. Data from the National Stock Exchange (NSE) in Mumbai, India and the New York Stock Exchange (NYSE) in New York, USA, are used to demonstrate the effectiveness of the proposed portfolio optimization models and solution methodology. All the proposed models are compared with respect to each other and the benchmarks considered in this study to bring out the performance stability.

A Hybrid Fuzzy-SCOOT Algorithm to Optimize Possibilistic Mean Semi-absolute Deviation Model for Optimal Portfolio Selection

A Hybrid Fuzzy-SCOOT Algorithm to Optimize Possibilistic Mean Semi-absolute Deviation Model for Optimal Portfolio Selection

A Nash bargaining solution for a multi period competitive portfolio optimization problem: Co-evolutionary approach

This study focuses on proposing a Nash bargaining model to solve a novel multi-period competitive portfolio optimization problem for large investors in the stock market who want to maximize their terminal wealth while taking into account competitors' profits. In this study, a Competitive Portfolio Model (CPM) is developed in accordance with the Cournot competition principle for a static, non-cooperative, and non-zero-sum game with complete information. Transaction costs, risk-free assets and cash are also included to match real-world conditions. Also, three criteria including the average value at risk, the mean absolute semi-deviation, and entropy are considered to control the investment risk in the model. Moreover, due to common constraints between players (free floating shares of risky assets) in stock markets, this study falls into the category of Generalized Nash Equilibrium Problems (GNEP). Therefore, to overcome the problem, a Cooperative Co-evolutionary Algorithm (CCA) based on Particle Swarm Optimization (PSO) is customized and used. A few experimental tests and a numerical example with descriptive analytics (using real data from two large mutual funds who invest in the Iranian Stock Exchange market) are used to evaluate the feasibility of the proposed model and the efficiency of the design algorithm. After solving the model, for each time period, investors' trading strategies (trading signals and stock volume in their portfolio) are determined. The results show that the volume of transactions due to the market power of an investor has a significant effect on the terminal wealth of competitors. Also, the results of sensitivity analysis show that profit-making is inversely related to the degree of risk aversion of investors.

Portfolio optimization using higher moments in an uncertain random environment

In this paper, a multi-objective portfolio optimization problem is studied in an uncertain random environment using higher moments. We consider a scenario involving an asset universe wherein some assets have sufficient historical return data for modelling as random variables, and others, listed relatively recently, lack historical data. The asset returns of such assets are modelled as uncertain variables. Thus, a hybrid environment involving both uncertain and random variables is considered. We use mean absolute semi-deviation as a risk measure and employ skewness (i.e., third moment) in the portfolio optimization model. The expressions for the mean absolute semi-deviation and skewness of an uncertain random variable have been derived. We show that the derivation of mean absolute semi-deviation is not based on any stipulation and thus is an accurate measure of risk (unlike the variance of an uncertain random variable, which uses stipulation). We propose a hybrid genetic algorithm as a solution methodology and provide empirical proofs to illustrate its advantages. The proposed methodology has been applied to a case study involving 100 assets listed in the NASDAQ-100 index of the U.S. stock market. We do an ex-post analysis to track the performance of our model out-of-sample and illustrate its advantages.

Multiobjective portfolio optimization using coherent fuzzy numbers in a credibilistic environment

In this paper, we propose a new credibility function for a fuzzy variable that can accommodate the attitude of the investor (pessimistic, optimistic, or neutral) along with capturing the return expectations. We use an adaptive index, which the investors can use to specify their general perception of the financial market. We extend the classic mean-variance model so that it provides greater flexibility to the investors in specifying their requirements viz., level of diversification, minimum and maximum level of investment in a particular asset, and the skewness requirement. We also replace variance with mean-absolute semideviation as a measure of quantifying risk, which is more realistic, and solve the resultant multiobjective credibility model with a real-coded genetic algorithm. Numerical examples have been provided at the end to illustrate the methodology and advantages of the model.

Multi-period portfolio optimization using coherent fuzzy numbers in a credibilistic environment

In this paper, we use an extension of fuzzy numbers, called coherent fuzzy numbers, to model asset returns and an investor’s perception of the stock market (pessimistic, optimistic, or neutral) simultaneously. Two multi-period multi-objective portfolio optimization models are formulated using mean absolute semi-deviation and Conditional Value-at-Risk (CVaR) as risk measures, respectively. We aim to provide more flexibility to the investor in specifying the risk tolerance and devise optimum investment plans for different investment horizons. The proposed models also incorporate bound, cardinality, and skewness constraints for each investment period to capture various stock market scenarios. A real-coded genetic algorithm is employed to solve the resultant models. Two real-life case studies involving 20 assets of the National Stock Exchange (NSE), India, and another involving 50 assets listed in the S&P 500 and NASDAQ-100 indexes have been provided to illustrate the efficacy and advantages of the models. An in-sample and out-of-sample analysis have been done for both the models to analyze the performance in the real-world scenario. The conclusion drawn from the analysis strongly emphasizes on accurately assessing the current stock market prospects, i.e., adopting the right attitude (pessimistic, optimistic, or neutral), is of paramount importance and must be included in the portfolio optimization problem.

A distributionally robust optimization model for designing humanitarian relief network with resource reallocation

Since natural disasters often cause the loss of lives and property, it is necessary to design a reasonable relief network to distribute relief supplies after a disaster. The shortage of relief supplies and timely transportation are the main difficulties in the whole relief network. To overcome these difficulties, we introduce a three-level humanitarian relief network design problem with resource reallocation of relief supplies. Based on the existing relief network system before a disaster, this problem determines the positions of candidate local distribution centers and points of distribution, while considering the relief distribution in the network under an uncertain post-disaster environment. For the uncertain variables, we consider a distributionally robust model with mean absolute semi-deviation (MASD) as a risk measure taken into the transportation time function. Under the partial probability distribution information of the uncertainties, we deduce a tractable framework of the distributionally robust model. Specifically, we derive the worse case form of the MASD objective under an ambiguity set and the safe approximations of the chance constraints under a box + ellipsoid + generalized budget perturbation set. Finally, we demonstrate the efficacy of the model by a real case in Anambra flood.

Two-stage absolute semi-deviation mean-risk stochastic programming: An application to the supply chain replenishment problem

Conventionally, two-stage stochastic programs have been devised to minimize the expectation of recourse actions. However, in the presence of high data variability, the solutions from expected value models may not be robust, and hence weighted risk measures are introduced in the objective function. In this study, we consider a two-stage stochastic program with mean absolute semi-deviation (MASD) as a risk measure for an application in supply chain planning. Models with MASD lack block-angular structures; thus, they are not suitable for traditional decomposition algorithms and pose computational challenges. We therefore propose a heuristic procedure based on the expected excess risk measure for solving the model. Specifically, we propose a heuristic for a generic replenishment problem in supply chains with MASD risk measures. We evaluate the robustness of the MASD model solutions by comparing the fill rate for replenishment plans with the optimal solutions from deterministic and expected value models, and we demonstrate the efficacy of the heuristic based on extensive computational experiments.

Portfolio optimization of the construction sector companies in Malaysia with mean-semi absolute deviation model

Portfolio optimization is an important investment strategy to find the trade-off between the risk and return. In mean-semi absolute deviation model,semi absolute deviation is employed as risk measure while the expected return of the investors is represented by the mean return. The objective of this paper is to construct the optimal portfolio that will minimize the portfolio risk and can achieve the investors target rate of return by using the mean-semi absolute deviation model. The data of this study comprises 20 construction sector companies that listed in Malaysia stock market from July 2011 until June 2016. The results of this paper show that the constructed optimal portfolio can minimize the portfolio risk at the expected rate of return. In addition, the composition of the companies invested in the optimal portfolio is different. Keywords: portfolio risk; return; investment; investors

Multiperiod mean semi-absolute deviation interval portfolio selection with entropy constraints

In this paper, we discuss the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval values, the gain of returns is interval value as well. A new multiperiod mean semi-absolute deviation interval portfolio selection model with the transaction costs, borrowing constraints, threshold constraints and diversification degree of portfolio has been proposed, where the return and risk are characterized by the interval mean and interval semi-absolute deviation of return, respectively. The diversification degree of portfolio is measured by the presented possibilistic entropy. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on interval theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. The discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of differently desired number of assets and different preference coefficients are provided by numerical examples to illustrate the efficiency of the proposed approach and the designed algorithm.

Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

Uncertain portfolio adjusting model using semiabsolute deviation

Since the financial markets are complex, sometimes the future security returns are represented mainly based on experts' judgments. This paper discusses a portfolio adjusting problem with risky assets in which security returns are given subject to experts' estimations. Here, we propose uncertain mean-semiabsolute deviation adjusting models for portfolio optimization problem in the trade-off between risk and return on investment. Various uncertainty distributions of the security returns based on experts' evaluations are used to convert the proposed models into equivalent deterministic forms. Finally, numerical examples with synthetic uncertain returns are illustrated to demonstrate the effectiveness of the proposed models and the influence of transaction cost in portfolio selection.

Interval portfolio selection models within the framework of uncertainty theory

The expected returns for securities are traditionally estimated as crisp values. Since the improper values may bring on an unsuccessful investment decision, portfolio experts generally prefer offering interval estimations for expected returns rather than crisp ones. The portfolio selection problem with interval expected returns is widely studied recently. In this paper, by considering the security returns with interval expected returns as uncertain variables, a mean-semiabsolute deviation model is proposed within the framework of uncertainty theory, which is a crisp nonlinear programming model and can be well solved by the classical optimization algorithms. In order to illustrate the method, some numerical experiments are given and solved.

Linear vs. Quadratic Portfolio Selection Models in Practice

Several risk-return portfolio models take into account practical limitations on the number of assets to include in the portfolio and on their weights. We present here a comparative study, both from the efficiency and from the performance viewpoint, of the Limited Asset Markowitz (LAM), the Limited Asset Mean Semi-Absolute Deviation (LAMSAD) and the Limited Asset Conditional Value at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints.The mixed integer linear LAMSAD and LACVaR models are solved with a state of the art commercial code, while the mixed integer quadratic LAM model is solved both with a commercial code and with a more efficient new method, recently proposed by the authors. Rather unexpectedly, for medium to large sizes it is easier to solve the quadratic LAM model with the new method, than to solve the linear LACVaR and LAMSAD models with the commercial solver. Furthermore, the new method has the advantage of finding all the extreme points of a more general tri-objective problem at no additional computational cost.We compare the out-of-sample performances of the three models and of the equally weighted portfolio. We show that there is no apparent dominance relation among the different approaches and, in contrast with previous studies, we find that the equally weighted portfolio does not seem to have any advantage over the three proposed models. Our empirical results are based on some new and old publicly available data sets often used in the literature.

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.

Empirical Research of Portfolio Selection under M-SAD Model

The mean semi-absolute deviation is the extension and development from the mean-variance theory which proposed by Markowitz. This paper studied the Mean-SAD (semi-variance deviation) model without the short selling and used the Chinese securities markets 20 stocks to test the efficient of the model. We got the conclusion that M-SAD model can effectively direct the decision in portfolio selection. Based on the result of the empirical research, the paper prospects the application of M-SAD model in our country.

Management Insights

Management Insights

Quantitative reliability evaluation of repairable phased-mission systems using Markov approach : Mansoor Alam and Ubaid M. Al-Saggaf. IEEE Trans. Reliab.R-35 (5), 498 (1986)

This study focuses on proposing a Nash bargaining model to solve a novel multi-period competitive portfolio optimization problem for large investors in the stock market who want to maximize their terminal wealth while taking into account competitors' profits. In this study, a Competitive Portfolio Model (CPM) is developed in accordance with the Cournot competition principle for a static, non-cooperative, and non-zero-sum game with complete information. Transaction costs, risk-free assets and cash are also included to match real-world conditions. Also, three criteria including the average value at risk, the mean absolute semi-deviation, and entropy are considered to control the investment risk in the model. Moreover, due to common constraints between players (free floating shares of risky assets) in stock markets, this study falls into the category of Generalized Nash Equilibrium Problems (GNEP). Therefore, to overcome the problem, a Cooperative Co-evolutionary Algorithm (CCA) based on Particle Swarm Optimization (PSO) is customized and used. A few experimental tests and a numerical example with descriptive analytics (using real data from two large mutual funds who invest in the Iranian Stock Exchange market) are used to evaluate the feasibility of the proposed model and the efficiency of the design algorithm. After solving the model, for each time period, investors' trading strategies (trading signals and stock volume in their portfolio) are determined. The results show that the volume of transactions due to the market power of an investor has a significant effect on the terminal wealth of competitors. Also, the results of sensitivity analysis show that profit-making is inversely related to the degree of risk aversion of investors.