Multi-objective Portfolio Optimization Research Articles

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.

Gated Neural Network-Based Mean–EVaR–Skewness Portfolio Optimization under Uncertain Environment

Numerous empirical studies show that portfolio returns are generally asymmetric, and investor would prefer a portfolio return with larger degree of asymmetry along with risk and return. In this paper, a concept of skewness is defined as the third central moment and studied its mathematical properties. To predict the stock prices, a novel recurrent neural network with gated recurrent unit (GRU) cell is preferred. Based on these predictions, stock returns, entropic value at risks and skewness are calculated. A mean–EVaR–skewness multi-objective portfolio optimization model is devised to account for market uncertainty. Cardinality, bounding restrictions, and liquidity are considered in addition to risk and return to make the model more effective. Uncertain goal programming is used to solve the proposed model. Finally, an example portfolio is presented to display the efficacy and the feasibility of the model suggested in this paper.

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.

Multi-objective portfolio optimization under tempered stable Lévy distribution with Copula dependence

Taking into account the leptokurtosis nature of financial returns distribution and the non-linear dependence structure of the underlying assets variables in portfolio, the tempered stable Lévy distribution and the Copula function (TS Copula) are employed to describe the multi-objective portfolio optimization problem. In order to investigate the modeling ability of TS distribution coupling with different Copula functions, the model is designed to maximize the benefits while minimizing the risk in finding a set of non-dominant Pareto solutions. The problem of constrained TS Copula multi-objective investment optimization is solved by using three intelligent algorithms, namely the NSGA-II, SPEA-II and MOPSO. Then the empirical studies in Chinese stock markets illustrate that the returns distribution is leptokurtic and heavy tailed. Furthermore, the Skewed-t Copula function coupling with tempered stable marginal distribution can effectively capture the thick tail distribution of portfolio returns and the non-linear asymmetric dependence structure among assets. It is the Skewed-t Copula coupling with tempered stable Lévy distribution that gets the best fitting performance. In addition, the MOPSO and NSGA-II intelligent algorithms are effective in solving TS Copula based multi-objective portfolio optimization.

A multi-objective instance-based decision support system for investment recommendation in peer-to-peer lending

Peer-to-peer (P2P) lending has attracted many investors and borrowers since 2005. This financial market helps investors and borrowers to invest in or get loans without a traditional financial intermediary. Investors in the P2P lending market are allowed to invest in multiple loans instead of financing one loan entirely, so investment decision-making in P2P lending can be challenging for lenders because they are not usually expert in loan investing. The goal of this paper is to propose a data-driven investment decision-making framework for this competitive market. We use the artificial neural network and logistic regression to estimate the return and the probability of default (PD) of each individual loan. The return variable is the internal rate of return (IRR). Moreover, we formulate the investment decision-making in P2P lending as a multi-objective portfolio optimization problem based on the mean-variance theory by the use of the non-dominated sorting genetic algorithm (NSGA2). To validate the proposed model, we use a real-world dataset from one of the most popular P2P lending marketplaces. In addition, our model is compared with a single-objective model and a profit-based approach. Throughout the experiment, the empirical results reveal that our multi-objective model in comparison with the single-objective model can improve a lender's investment decision based on both objectives of investments. It means that while the return increases, the risk decreases, simultaneously. On the other hand, it is concluded that the profit scoring model leads to a more profitable investment but with a high level of risk. Finally, a sensitivity analysis is done to check the sensitivity of our model to the total investment amount.

On convex multiobjective programs with application to portfolio optimization

AbstractFocusing on (strictly) convex multiobjective programs (MOPs), we review some well‐established scalarizations in multiobjective programming from the perspective of parametric optimization and propose a modified hybrid scalarization suitable for a class of specially structured convex MOPs. Because multiobjective quadratic programs are a prominent class of convex MOPs due to their broad applicability, we review the state‐of‐the‐art algorithms for computing their efficient solutions. These two lines of investigation are merged to solve multiobjective portfolio optimization problems with three or more quadratic objective functions, a class of problems that has not been solved before. Computational examples are provided.

A Firefly Algorithm for Portfolio Optimization

Portfolio optimization is the process of allocating capital among a universe of assets to achieve better risk – return trade-off. Portfolio optimization is a solution for investors to get the return as large as possible and make the risk as small as possible. Due to the dynamic nature of financial markets, the portfolio needs to be rebalanced to retain the desired risk-return characteristics. This study proposed multi objective portfolio optimization model with risk, return as the objective function. For multi objective portfolio optimization problems will be used mean-variance model as risk measures. All these portfolio optimization problems will be solved by Firefly Algorithm (FA).

A multi-objective robust possibilistic model for technology portfolio optimization considering social impact and different types of financing

With respect to limited financial resources, prioritization of technology fields in order to be supported financially is a matter of paramount significance that governmental organizations, such as “Technology Development Funds (TDFs)”, face with. Innovation and technology development, as the cornerstone of the economic development of countries, requires making decisions in terms of assigning the best-suited form of financial resources mainly by governments. Accordingly, this study addresses a multi-objective portfolio optimization problem in a multi-period setting with the aim of maximizing the created jobs – as a key factor in social welfare – as well as intended profit while minimizing the risk of inappropriate portfolio selection. To formulate the proposed mathematical model, different financing methods, technology readiness levels (TRL), and return on investment (ROI) associated with each technological project are taken into account. Afterward, to deal with the uncertainty arisen from fuzzy parameters, the Multi-Objective Robust Possibilistic Programming approach (MORPP) is applied, the performance of which is examined under several computational tests. Finally, to illustrate the performance of the proposed model and its applicability in practice, the computational results are shown through a real case study in Iran Innovation & Prosperity Fund (IIPF). The results show that selecting small and medium-sized enterprises (SMEs) for being financed, is the best option when increasing job creation is considered in portfolio optimization. Furthermore, the comparison of the MORPP model results with the deterministic model shows that the solutions obtained from the robust possibilistic approach outweighed the deterministic model.

P-Optimality-Based Multiobjective Root System Growth Algorithms for Multiobjective Applications

In this paper, a multiobjective root system growth algorithm-based p-optimality (p-MORSGA) is proposed. The proposed p-MORSGA extended original root system growth algorithm with multiobjective nondomination strategy. To enhance its effect of convergence of solution groups, the p-optimality criterion is employed to determine the solutions of last nondominated front into the next generation group. In the evolution process, global general (GG), concerning the margin information and population density, is selected as the suitable optimality criterion of evaluating the performance of solutions. Application of the new p-MORSGA on several multiobjective benchmark functions shows a marked improvement in performance over the modified classical MOEAs with such criterion. Finally, the proposed p-MORSGA is applied to solve two real-world problems, multiobjective portfolio optimization problems (MOPOPs) and multiobjective optimal power flow (OPF) problems. The experimental results demonstrate that p-MORSGA is extremely effective for real-world application problems.

Multi-period and Multi-objective Stock Selection Optimization Model Based on Fuzzy Interval Approach

The optimization of investment portfolios is the most important topic in financial decision making, and many relevant models can be found in the literature. According to importance of portfolio optimization in this paper, deals with novel solution approaches to solve new developed portfolio optimization model. Contrary to previous work, the uncertainty of future returns of a given portfolio is modeled using LR-FUZZY numbers while the function of its return are evaluated using possibility theory. We used a novel Lp-metric method to solve the model. The efficacy of the proposed model is tested on criterion problems of portfolio optimization on LINGO provides a framework to optimize objectives when creating the loan portfoliso, in a search for a dynamic markets decision. In addition to, the performance of the proposed efficiently encoded multi-objective portfolio optimization solver is assessed in comparison with two well-known MOEAs, namely NSGAII and ICA. To the best of our knowledge, there is no research that considered NSGAΠ, ICA fuzzy simultaneously. Due to improve the performance of algorithm, the performance of this approach more study is probed by using a dataset of assets from the Iran’s stock market for three years historical data and PRE method. The results are analyzed through novel performance parameters RPD method. Thus, the potential of our comparison led to improve different portfolios in different generations.

Robust multiobjective portfolio optimization: a set order relations approach

We consider Markowitz’s portfolio optimization problem that heavily suffers from uncertainties of input parameters. And based on set order relations, uncertain portfolio optimization problem at various extreme cases is modelled as robust multiobjective formulations. At first, borrowing set order relations, three concepts of set less ordered efficiency are defined for multiobjective portfolio optimization problems with uncertainties. Subsequently, following from Ben-Tal and Nemirovski (Math Oper Res 23(4):769–805, 1998; Oper Res Lett 25:1–13, 1999), several multiobjective robust counterparts are introduced, and tackled by multiobjective particle swarm optimization approach. As such, the properties of the obtained (robust) efficient solutions are further characterized. Finally, the empirical researches from the real stock market show that (robust) efficient solutions based on set order relations are highly advisable for the investors.

A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model

In this paper, we discuss the fuzzy portfolio selection problems in multi-objective frameworks. A comprehensive model for multi-objective portfolio selection in fuzzy environment is proposed by incorporating mean-semivariance model and data envelopment analysis cross-efficiency model. In the proposed model, the cross-efficiency model is formulated within the framework of Sharpe ratio; bounds on holdings, and cardinality constraints are also considered. The nonlinear constrained multi-objective portfolio optimization problem cannot be efficiently solved by using traditional approaches. Thus, a multi-objective firefly algorithm is developed to solve the relevant model. Finally, an example verifies the validity of the proposed approaches.

The robustness of portfolio efficient frontiers

PurposeThe optimization of investment portfolios is a topic of major importance in financial decision making, with many relevant models available in the relevant literature. The purpose of this paper is to perform a thorough comparative assessment of different bi-objective models as well as multi-objective one, in terms of the performance and robustness of the whole set of Pareto optimal portfolios.Design/methodology/approachIn this study, three bi-objective models are considered (mean-variance (MV), mean absolute deviation, conditional value-at-risk (CVaR)), as well as a multi-objective model. An extensive comparison is performed using data from the Standard and Poor’s 500 index, over the period 2005–2016, through a rolling-window testing scheme. The results are analyzed using novel performance indicators representing the deviations between historical (estimated) efficient frontiers, actual out-of-sample efficient frontiers and realized out-of-sample portfolio results.FindingsThe obtained results indicate that the well-known MV model provides quite robust results compared to other bi-objective optimization models. On the other hand, the CVaR model appears to be the least robust model. The multi-objective approach offers results which are well balanced and quite competitive against simpler bi-objective models, in terms of out-of-sample performance.Originality/valueThis is the first comparative study of portfolio optimization models that examines the performance of the whole set of efficient portfolios, proposing analytical ways to assess their stability and robustness over time. Moreover, an extensive out-of-sample testing of a multi-objective portfolio optimization model is performed, through a rolling-window scheme, in contrast static results in prior works. The insights derived from the obtained results could be used to design improved and more robust portfolio optimization models, focusing on a multi-objective setting.

Algorithm research based on multi period fuzzy portfolio optimization model

Because the investment market in real life is complex and mobile, there are many other factors to consider when meeting the risk and income equilibrium, such as transaction cost, diversification degree and so on. To simulate the real transactions in financial market, multiple decision criteria in portfolio selection should be considered to provide investors with additional choices. This paper discusses a multi-objective portfolio optimization problem for practical portfolio selection in fuzzy environment, in which the return rates and the turnover rates are characterized by fuzzy variables. Under the premise of meeting the two wishes level of investors’ maximum and minimum risk, we assume that the rate of return is a fuzzy variable, and get the corresponding fuzzy portfolio optimization model. What’s more, we apply a particle swarm optimization algorithm to solve the proposed multi-period fuzzy portfolio selection models. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Finally, a numerical example is given to illustrate the application of our models. Comparative results show that the designed algorithm is effective for solving the proposed models.

2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization

Portfolio optimization is a serious challenge for financial engineering and has pulled down special attention among investors. It has two objectives: to maximize the reward that is calculated by expected return and to minimize the risk. Variance has been considered as a risk measure. There are many constraints in the world that ultimately lead to a non–convex search space such as cardinality constraint. In conclusion, parametric quadratic programming could not be applied and it seems essential to apply multi-objective evolutionary algorithm (MOEA). In this paper, a new efficient multi-objective portfolio optimization algorithm called 2-phase NSGA II algorithm is developed and the results of this algorithm are compared with the NSGA II algorithm. It was found that 2-phase NSGA II significantly outperformed NSGA II algorithm.

An Agent-Based Co-Evolutionary Multi-Objective Algorithm for Portfolio Optimization

Algorithms based on the process of natural evolution are widely used to solve multi-objective optimization problems. In this paper we propose the agent-based co-evolutionary algorithm for multi-objective portfolio optimization. The proposed technique is compared experimentally to the genetic algorithm, co-evolutionary algorithm and a more classical approach—the trend-following algorithm. During the experiments historical data from the Warsaw Stock Exchange is used in order to assess the performance of the compared algorithms. Finally, we draw some conclusions from these experiments, showing the strong and weak points of all the techniques.

Providing an Evolutionary Approach for Multi-objective Portfolio Optimization Problem by Using Evolutionary Algorithm Multi-objective NSGAⅡ

Providing an Evolutionary Approach for Multi-objective Portfolio Optimization Problem by Using Evolutionary Algorithm Multi-objective NSGAⅡ

A Fuzzy Goal Programming Model for Efficient Portfolio Selection.

This paper considers a multi-objective portfolio selection problem imposed by gaining of portfolio, divided yield and risk control in an ambiguous investment environment, in which the return and risk are characterized by probabilistic numbers. Based on the theory of possibility, a new multi-objective portfolio optimization model with gaining of portfolio, divided yield and risk control is proposed and then the proposed model is solved as a fuzzy goal programming model to fulfill aspiration level of each objective. Furthermore, numerical example of efficient portfolio selection is provided to illustrate that proposed model is versatile enough to be applicable to various unexpected conditions. This paper considers a multi-objective portfolio selection problem imposed by gaining of portfolio, divided yield and risk control in an ambiguous investment environment, in which the return and risk are characterized by probabilistic numbers. Based on the theory of possibility, a new multi-objective portfolio optimization model with gaining of portfolio, divided yield and risk control is proposed and then the proposed model is solved as a fuzzy goal programming model to fulfill aspiration level of each objective. Furthermore, numerical example of efficient portfolio selection is provided to illustrate that proposed model is versatile enough to be applicable to various unexpected conditions.

A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem

This paper proposes a novel multiobjective evolutionary Algorithm (MOEA) for the solution of the cardinality constrained portfolio optimization problem (CCPOP). The proposed algorithm introduces an efficient encoding scheme specially designed for dealing with the difficulties of the CCPOP. Also, the proposed algorithm incorporates a new mutation and recombination operator tailor-made to work well with the new encoding scheme. Datasets from seven different stock markets are utilized for testing the efficiency of the proposed approach. In particular, the performance of the proposed efficiently encoded multiobjective portfolio optimization solver (EEMPOS) is assessed in comparison with two well-known MOEAs, namely NSGAII and MOEA/D. The experimental results indicate that the proposed EEMPOS outperforms the two other MOEAs for all examined performance metrics when is applied to the solution of the CCPOP for a fraction of time required by the other techniques.

Multiobjective portfolio optimization: bridging mathematical theory with asset management practice

We attempt to establish an integrated portfolio optimization business framework, in order to bridge the underlying gap between the complex mathematical theory of multiobjective mathematical programming and asset management practice. Our aim is to assist practitioners and portfolio managers in formulating successful investment strategies, by providing them with an effective decision support tool. In particular, we propose a multiobjective portfolio model, able to support the simultaneous optimization of multiple investment objectives. We also manage to integrate a set of sophisticated real-world non-convex investment policy limitations, such as the cardinality constraints, the buy-in thresholds, the transaction costs, along with particular normative rules. The underlying investment management rationale of the proposed managerial protocol is displayed through an illustrative business flowchart, while we also provide an analytical step-by-step portfolio management business routine. The validity of the model is verified through an extended empirical testing application on the Eurostoxx 50. According to the results, a sufficient number of efficient or Pareto optimal portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.