Multi-objective Portfolio Optimization Research Articles

Multiobjective Optimization of Stock Portofolio

Diversification is a method used to reduce risks by allocating several financial, industrial, and other instruments. Investors might need to use this method to allocate their companies’ funding as efficient as they should be. Mean variance portfolio is a diversification theory designated for investors who are aware of potential risks. On the other hand, multi-objective portfolio optimization is another theory that suits for investors who are more unaware, or choose to neglect potential business risks. Multi-objective optimization can boost source of income and minimize the risks while utilizing k weighting coefficient as risk aversion index. This research aims to form an optimal portfolio from each perspective of selected investors using multi-objective optimization, as well as to analyze the benefits and risks that the investors will have. Samples used in this research are sharia stocks actively involved in Jakarta Islamic Index (JII) and non-sharia stocks which are actively involved in LQ-45 from January 2013 to January 2018.

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.

An improved learning automata based multi-objective whale optimization approach for multi-objective portfolio optimization in financial markets

An improved learning automata based multi-objective whale optimization approach for multi-objective portfolio optimization in financial markets

Predictive multi-period multi-objective portfolio optimization based on higher order moments: Deep learning approach

We propose a Multi-Period Multi-Objective Portfolio Optimization model (MPMOPO). We used deep-learning approach to predict future behavior of stock returns. We consider four objectives, i.e., wealth, variance, skewness, and kurtosis and several constraints such as cardinality, budget, upper and lower limits of purchase, and diversification to address real-world situations. The investor can rebalance the portfolio through daily trade by buying or selling subject to transaction costs. We applied the proposed method in a daily closing price prediction of six stocks from FTSE 100. Goal programming method was used to solve the models. The results of statistical analysis show the applicability and efficacy of the proposed method in comparison with those methods which used historical data to form the portfolio.

Multiobjective portfolio optimization: Forecasting and evaluation under investment horizon heterogeneity

AbstractThis study designs a methodological framework to forecasting allocation weights and evaluating multiobjective portfolios considering the investment horizon heterogeneity. The investment horizon heterogeneity may induce the terrible data loss problem under traditional asset return definition, while in the real world, there are many portfolio makers whose investment horizons are not consistent. The methodological framework has three parts. First, this paper gives a novel multitimescale analysis (MTA) tool as a computation procedure to decompose the raw return series, and the decomposed subreturn series could represent the information for a portfolio maker with specific investment horizon and has the same data length as the raw return series. Second, proposed methodological framework uses a time‐varying parameter GAS‐D‐Vine‐Copula model to construct the joint distribution of subreturn series of multiassets in a portfolio. Third, due to the stochastic dominance consistency issue, this paper applies three different utility functions as the outputs of a portfolio strategy and two cost functions as the inputs of a portfolio strategy in an efficiency evaluation model. The empirical example of US aviation stock market data from 2013 to 2021 reveals that the Mean‐Skewness‐Volatility‐HMCR‐LPM multiobjective has the greatest numbers of optimal strategy timings for portfolio makers with 2‐, 3–5‐, and 10–50‐day‐length investment horizons. The investment horizon of 1‐day length is the least efficient, and the investment horizon between 10‐ and 50‐day length is the most efficient. The proposed methodology indicates that more multiobjectives in a portfolio strategy are not necessarily better, and there is an optimal range of investment horizons for portfolio makers.

MOPO-LSI: An open-source multi-objective portfolio optimization library for sustainable investments

MOPO-LSI: An open-source multi-objective portfolio optimization library for sustainable investments

Multi-Guide Set-Based Particle Swarm Optimization for Multi-Objective Portfolio Optimization

Portfolio optimization is a multi-objective optimization problem (MOOP) with risk and profit, or some form of the two, as competing objectives. Single-objective portfolio optimization requires a trade-off coefficient to be specified in order to balance the two objectives. Erwin and Engelbrecht proposed a set-based approach to single-objective portfolio optimization, namely, set-based particle swarm optimization (SBPSO). SBPSO selects a sub-set of assets that form a search space for a secondary optimization task to optimize the asset weights. The authors found that SBPSO was able to identify good solutions to portfolio optimization problems and noted the benefits of redefining the portfolio optimization problem as a set-based problem. This paper proposes the first multi-objective optimization (MOO) approach to SBPSO, and its performance is investigated for multi-objective portfolio optimization. Alongside this investigation, the performance of multi-guide particle swarm optimization (MGPSO) for multi-objective portfolio optimization is evaluated and the performance of SBPSO for portfolio optimization is compared against multi-objective algorithms. It is shown that SBPSO is as competitive as multi-objective algorithms, albeit with multiple runs. The proposed multi-objective SBPSO, i.e., multi-guide set-based particle swarm optimization (MGSBPSO), performs similarly to other multi-objective algorithms while obtaining a more diverse set of optimal solutions.

GRASP/[formula omitted]: An efficient algorithm for the multi-objective portfolio optimization problem

The multi-objective portfolio optimization problem with fuzzy trapezoidal parameters involves a search for a subset of projects that, within the given available resources, maximizes the benefits while reducing the uncertainty. Traditionally, evolutionary algorithms are used to solve this problem; however, they do not exploit the locality structure of a solution or compute the values of its objective functions using the full set of n decision variables. As a result, the number of evaluations that can be computed within a fixed amount of time decreases as the size of the instances increases, yielding poor performance. This work proposes a new non-evolutionary GRASP/Δ algorithm that includes a novel local search with an efficient local computation strategy. The use of local computation reduces the number of operations required to compute the values of the objective functions from O(n) to O(1). Consequently, the increment in evaluations performed in the proposed approach increases the quality of the obtained solutions, particularly as the search space grows. An experiment conducted with instances of different sizes demonstrates the overall competitiveness of GRASP/Δ compared to other state-of-the-art algorithms. Our results show, as expected, that the differences in performance become statistically more significant when dealing with instances defined by large search spaces. These results were validated using non-parametric statistical tests.

Design of Optimum Portfolio Scheme Based on Improved NSGA-II Algorithm.

In the financial industry, it is of great significance to study the multiobjective portfolio optimization for obtaining a reasonable investment strategy. This paper designs the financial portfolio scheme based on the multiobjective optimization algorithm that is based on the framework of the NSGA-II algorithm. In order to introduce convergence information, aiming at the actual problem of the portfolio, the mixed individual coding mechanism with asset information expands the application of the multiobjective evolutionary algorithm in portfolio optimization. The portfolio scheme obtained is effective, which is helpful to improve the decision-making efficiency of financial investors and enriches the application of modern financial theory.

A multiobjective portfolio optimization for energy assets using D-Optimal design and mixture design of experiments

Paper aims Frequently, researchers try to find a better way to allocate assets in order to have maximum return and low variability in a portfolio as diverse as possible. This paper aims to apply D-Optimal Design in the context of Mixture Design and portfolio optimization to efficiently select the runs of the proposed experimental design. Originality A new approach to find the optimal weights that maximize the returns and minimize the risk using D-Optimal Design was used. A multi-response optimization problem considering returns, variability and entropy as functions of the weights was proposed. However, as there is a significant correlation between the objective functions, a Factor Analysis combined with FMSE to dimensionality reduction was used. Research method All the steps for both stages of the methodology applied in this paper are presented below: select real time series; predict one step ahead; generate a D-Optimal mixture design; apply weights and generate mathematical models; solve the optimization problem. Main findings Using the desirability method, the optimal values were determined, obtaining approximately 79% for the compound desirability function. The proposed method presented a 16.80% higher return with a 4.98% higher risk exposure if compared against Naïve method. Implications for theory and practice The proposed methodology can be applied to any portfolio optimization study. Mixture Design studies have already been proposed for modeling portfolio optimization problems. However, the D-Optimal Design proved to be adequate, which represents less computational effort.

Fuzzy Multi-Objective Portfolio Optimization Considering Investment Return and Investment Risk

Portfolio selection and optimization deal with the selection of the most suitable projects in a portfolio. The expected goals can be achieved while considering the balance among selected projects, to ensure that all selected projects consume resources effectively. This study proposes and compares multi-objective portfolio investment optimization algorithms under uncertain conditions. The investment return (in terms of the fuzzy net present value of the portfolio) and investment risk (in terms of the credibilistic risk index) have simultaneously been considered. In addition, fuzzy chance-constrained programming is introduced as an optimization constraint to handle such uncertainty by specifying a desired confidence level of the decision makers. The outcome of this study can then help decision makers to decide what projects and when to invest. Decision makers can deal with a limited budget with logical relationships, and within their desired financial and risk requirements.

The Multi-Objective Portfolio Optimization Tool Helping the pharmaceutical industry manage its portfolio

The Multi-Objective Portfolio Optimization Tool Helping the pharmaceutical industry manage its portfolio

Analyzing the Performance of a Two-Tail-Measures-Utility Multi-objective Portfolio Optimization Model

Analyzing the Performance of a Two-Tail-Measures-Utility Multi-objective Portfolio Optimization Model

Multi-Objective Pharmaceutical Portfolio Optimization under Uncertainty of Cost and Return

This paper presents the study of multi-objective optimization of a pharmaceutical portfolio when both cost and return values are uncertain. Decision makers in the pharmaceutical industry encounter several challenges in deciding the optimal selection of drug projects for their portfolio since they have to consider several key aspects such as a long product-development process split into multiple phases, high cost and low probability of success. Additionally, the optimization often involves more than a single objective (goal) with a non-deterministic nature. The aim of the study is to develop a stochastic multi-objective approach in the frame of chance-constrained goal programming. The application of the results of this study allows pharmaceutical decision makers to handle two goals simultaneously, where one objective is to achieve a target return and another is to keep the cost within a finite annual budget. Finally, the numerical results for portfolio optimization are presented and discussed.

A novel mathematical approach for fuzzy multi-period multi-objective portfolio optimization problem under uncertain environment and practical constraints

Investment portfolio optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. Accordingly, the main goal of this paper is to propose a novel fuzzy multi-period multi-objective portfolio optimization (FMPMOPO) model that is capable to be used under data ambiguity and practical constraints including budget constraint, cardinality constraint, and bound constraint. It should be noted that three objectives including terminal wealth, risk, and liquidity as well as practical constraints are considered in proposed FMPMOPO model. Also, the alpha-cut method is employed to deal with fuzzy data. Finally, the proposed fuzzy multi-period wealth-risk-liquidity (FMPWRL) model is implemented in real-world case study from Tehran stock exchange (TSE). The experimental results show the applicability and efficacy of the proposed FMPWRL model for fuzzy multi-period multi-objective investment portfolio optimization problem under fuzzy environment.

Performance analysis of the integration between Portfolio Optimization and Technical Analysis strategies in the Brazilian stock market

This article proposes a fusion between Technical Analysis indicators and Multiobjective Portfolio Optimization. It considers four indicators and the optimization performed over two risk measures and the expected return, subject to cardinality constraint, self-financing, and investment limits. The fusion occurs using two scenarios. The first one generates an optimal investment portfolio at the beginning of each month and uses Technical Analysis indicators to carry out the transactions. The second one performs the optimization monthly, considering just the assets filtered by the indicators. Numerical simulations consider an insightful comparison concerning the performance of proposed approaches with indicators and optimization in isolation and with standard benchmarks, covering six years of data from the Brazilian Stock Exchange, as a robust analysis. The portfolios are evaluated under metrics return, maximum drawdown and drawup, Return Over Maximum Drawdown index, and the Draw Ratio index. The results show that these fusions can improve the portfolio performance, providing optimal strategies to the investor giving a higher return for a certain level of risk, even considering realistic constraints.

An improved visual analytics framework for high-dimensional pareto-optimal front: a case for multi-objective portfolio optimization

An improved visual analytics framework for high-dimensional pareto-optimal front: a case for multi-objective portfolio optimization

Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.

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.

Behavioral Portfolio Management with Layered ESG Goals and Ai Estimation of Asset Returns

Portfolio managers and individual investors alike are in quest of efficient asset allocation models that simultaneously express environmental, social, and governance (ESG) considerations along with investor behavioral biases. The current study presents a novel approach to optimize the behavioral portfolio management model in the presence of investor biases for ESG sustainability, loss aversion, and cognitive dissonance. We extend the factor pricing literature by implementing a factor extraction protocol to identify three unique and pervasive ESG factors. Upon examining the interconnectedness of the factors, machine learning methods are applied to a production-theoretic six-factor Fama and French model to predict individual asset returns. Enumeration of efficient asset allocations is obtained by solving a hierarchical multiobjective portfolio optimization model. simulation results from solving alternate specifications of the layered goal ESG-driven model corroborate and extend emergent research on portfolio sustainability, network theory, and the interconnectedness of financial returns. Additionally, we provide results to amplify the existence of a hump-shaped ESG efficiency frontier. The results provide new information about the trade-offs available for resolving cognitive dissonance when investors are conflicted between holding ‘green’ versus ‘brown’ asset diversification plans.