Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach

Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.

A branch-and-bound algorithm for discrete multi-factor portfolio optimization model

In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.

Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures

In this study,we analyze three portfolio selection strategies for loss-averse investors:semi-variance,conditional value-at-risk,and a combination of both risk measures.Moreover,we propose a novel version of the non-dominated sorting genetic algorithm II and of the strength Pareto evolutionary algorithm 2 to tackle this optimization problem.The effectiveness of these algorithms is compared with two alternatives from the literature from five publicly available datasets.The computational results indicate that the proposed algorithms in this study outperform the others for all the examined performance metrics.Moreover,they are able to approximate the Pareto front even in cases in which all the other approaches fail.

Take Bitcoin into your portfolio:a novel ensemble portfolio optimization framework for broad commodity assets

The emergence and growing popularity of Bitcoins have attracted the attention of the financial world.However,few empirical studies have considered the inclusion of the newly emerged commodity asset in the global commodity market.It is of great importance for investors and policymakers to take advantage of this asset and its potential benefits by incorporating it as a part of the broad commodity trading portfolio.In this study,we propose a novel ensemble portfolio optimization(NEPO)framework utilized for broad commodity assets,which integrates a hybrid variational mode decomposition-bidirectional long short-term memory deep learning model for future returns forecast and a reinforcement learning-based model for optimizing the asset weight allocation.Our empirical results indicate that the NEPO framework could effectively improve the prediction accuracy and trend prediction ability across various commodity assets from different sectors.In addition,it could effectively incorporate Bitcoins into the asset pool and achieve better financial performance compared to traditional asset allocation strategies,commodity funds,and indices.

Portfolio optimization of credit risky bonds: a semi-Markov process approach

This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds.The criteria to optimize the credit portfolio is based on l_(∞)-norm risk measure and the proposed optimization model is formulated as a linear programming problem.The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process.Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models,i.e.,it addresses the ageing effect present in the credit rating dynamics.The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds.The empirical performance of the proposed model is analyzed using the real data.Further,comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models.

An improved portfolio optimization model for oil and gas investment selection

For oil company decision-makers,the principal concern is how to allocate their limited resources into the most valuable opportunities.Recently a new management philosophy,＂Beyond NPV＂,has received more and more international attention.Economists and senior executives are seeking effective alternative analysis approaches for traditional technical and economic evaluation methods.The improved portfolio optimization model presented in this article represents an applicable technique beyond NPV for doing capital budgeting.In this proposed model,not only can oil company executives achieve trade-offs between returns and risks to their risk tolerance,but they can also employ an ＂operational premium＂ to distinguish their ability to improve the performance of the underlying projects.A simulation study based on 19 overseas upstream assets owned by a large oil company in China is conducted to compare optimized utility with non-optimized utility.The simulation results show that the petroleum optimization model including ＂operational premium＂ is more in line with the rational investors＇ demand.

Matrix decomposition and Lagrangian dual method for discrete portfolio optimization under concave transaction costs

In this paper, the discrete mean-variance model is considered for portfolio selection under concave transaction costs. By using the Cholesky decomposition technique, the convariance matrix to obtain a separable mixed integer nonlinear optimization problem is decomposed. A brand-and-bound algorithm based on Lagrangian relaxation is then proposed. Computational results are reported for test problems with the data randomly generated and those from the US stock market.

Stressed portfolio optimization with semiparametric method

Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.

A Decision Support System for Energy Trading and Portfolio Optimization

In the new competitive environment of the electricity market, risk analysis is a powerful tool to guide investors under both contract uncertainties and energy prices of the spot market. Moreover, simulation of spot price scenarios and evaluation of energy contracts performance, are also necessary to the decision maker, and in particular to the trader to foresee opportunities and possible threats in the trading activity. In this context, computational systems that allow what-if analysis, involving simulation of spot price, contract portfolio optimization and risk evaluation are rather important. This paper proposes a decision support system not only for solving the problem of contracts portfolio optimization, by using linear programming, but also to execute risks analysis of the contracts portfolio performance, with VaR and CVaR metrics. Realistic tests have demonstrated the efficiency of this system.

Portfolio optimization based on network centralities:Which centrality is better for asset selection during global crises?

We construct correlation-based networks linking 86 assets(stock indices,bond indices,foreign exchange rates,commodity futures,and cryptocurrencies)and analyze the impact of asset selection on portfolio optimization using different centrality measures(including degree,eigenvector,eccentricity,betweenness,PageRank,and hybrid centralities).In times of a global crisis,peripheral assets located in cross-market networks are more suitable for investment.By comparing portfolio performance based on different centrality measures,we find that(i)hybrid,eigenvector,and PageRank centralities can best improve portfolio performance;(ii)degree centrality is suitable for larger portfolios;and(iii)eccentricity and betweenness centralities are unsuitable for network optimization portfolios.In response,we explain them based on the construction principle of centrality measures.Additionally,our optimal portfolios suggest that investors pay more attention to the role of emerging countries,which are less exposed to external shocks and whose financial markets are more likely to remain stable.

I_(ϵ+)LGEA:A Learning-Guided Evolutionary Algorithm Based on I_(ϵ+) Indicator for Portfolio Optimization

Portfolio optimization is a classical and important problem in the field of asset management,which aims to achieve a trade-off between profit and risk.Previous portfolio optimization models use traditional risk measurements such as variance,which symmetrically delineate both positive and negative sides and are not practical and stable.In this paper,a new model with cardinality constraints is first proposed,in which the idiosyncratic volatility factor is used to replace traditional risk measurements and can capture the risks of the portfolio in a more accurate way.The new model has practical constraints which involve the sparsity and irregularity of variables and make it challenging to be solved by traditional Multi-Objective Evolutionary Algorithms(MOEAs).To solve the model,a Learning-Guided Evolutionary Algorithm based on I_(ϵ+)indicator(I_(ϵ+)LGEA)is developed.In I_(ϵ+)LGEA,the I_(ϵ+)indicator is incorporated into the initialization and genetic operators to guarantee the sparsity of solutions and can help improve the convergence of the algorithm.And a new constraint-handling method based on I_(ϵ+)indicator is also adopted to ensure the feasibility of solutions.The experimental results on five portfolio trading datasets including up to 1226 assets show that I_(ϵ+)LGEA outperforms some state-of-the-art MOEAs in most cases.

A Multi-Period Constrained Multi-Objective Evolutionary Algorithm with Orthogonal Learning for Solving the Complex Carbon Neutral Stock Portfolio Optimization Model

Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization(PO).At present,due to the influence of modeling and algorithm solving,the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multiobjective models.PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios.It is more difficult than the previous single-stage PO model for meeting the realistic requirements.In this paper,the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate(M-ISTARR-MD)PO model which effectively characterizes the real investment scenario.In order to solve the multi-stage multi-objective PO model with complex multi-constraints,the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning(MSCMOEA-OL).Comparing with four well-known intelligence algorithms,the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset.This paper provides a new way to construct and solve the complex PO model.

Solving constrained portfolio optimization model using stochastic fractal search approach

Purpose-Optimum utilization of investments has always been considered one of the most crucial aspects of capital markets.Investment into various securities is the subject of portfolio optimization intent to maximize return at minimum risk.In this series,a population-based evolutionary approach,stochastic fractal search(SFS),is derived from the natural growth phenomenon.This study aims to develop portfolio selection model using SFS approach to construct an efficient portfolio by optimizing the Sharpe ratio with risk budgeting constraints.Design/methodology/approach-This paper proposes a constrained portfolio optimization model using the SFS approach with risk-budgeting constraints.SFS is an evolutionary method inspired by the natural growth process which has been modeled using the fractal theory.Experimental analysis has been conducted to determine the effectiveness of the proposed model by making comparisons with state-of-the-art from domain such as genetic algorithm,particle swarm optimization,simulated annealing and differential evolution.The real datasets of the Indian stock exchanges and datasets of global stock exchanges such as Nikkei 225,DAX 100,FTSE 100,Hang Seng31 and S&P 100 have been taken in the study.Findings-The study confirms the better performance of the SFS model among its peers.Also,statistical analysis has been done using SPSS 20 to confirm the hypothesis developed in the experimental analysis.Originality/value-In the recent past,researchers have already proposed a significant number of models to solve portfolio selection problems using the meta-heuristic approach.However,this is the first attempt to apply the SFS optimization approach to the problem.

A comparative study of heuristic methods for cardinality constrained portfolio optimization

The cardinality constrained mean–variance(CCMV)portfolio selection model aims to identify a subset of the candidate assets such that the constructed portfolio has a guaranteed expected return and minimum variance.By formulating this model as the mixed-integer quadratic program(MIQP),the exact solution can be solved by a branch-and-bound algorithm.However,computational efficiency is the central issue in the time-sensitive portfolio investment due to its NP-hardness properties.To accelerate the solution speeds to CCMV portfolio optimization problems,we develop various heuristic methods based on techniques such as continuous relaxation,l1-norm approximation,integer optimization,and relaxation of semi-definite programming(SDP).We evaluate our heuristic methods by applying them to the US equity market dataset.The experimental results show that our SDP-based method is effective in terms of the computation time and the approximation ratio.Our SDP-based method performs even better than a commercial MIQP solver when the computational time is limited.In addition,several investment companies in China have adopted our methods,gaining good returns.This paper sheds light on the computation optimization for financial investments.

Social responsibility portfolio optimization incorporating ESG criteria

Social responsibility investment(SRI)has attracted worldwide attention for its potential in promoting investment sustainability and stability.We developed a three-step framework by incorporating environmental,social,and governance(ESG)performance into portfolio optimization.In comparison to studies using weighted ESG rating scores,we constructed a data envelopment analysis(DEA)model with quadratic and cubic terms to enhance the evidence of two or more aspects,as well as the interaction between the environmental,social,and governance attributes.We then combined the ESG scores with financial indicators to select assets based on a cross-efficiency analysis.The portfolio optimization model incorporating ESG scores with selected assets was constructed to obtain a social responsibility investment strategy.To illustrate the effectiveness of the proposed approach,we applied it in the United States industrial stock market from 2005 to 2017.The empirical results show that the obtained SRI portfolio may be superior to traditional investment strategies in many aspects and may simultaneously achieve the consistency of investment and social values.

Portfolio Optimization under Entropic Risk Management

framework in the risk uniqueness In this paper, properties of the entropic risk measure are examined rigorously in a general This risk measure is then applied in a dynamic portfolio optimization problem, appearing management constraint. By considering the dual problem, we prove the existence and of the solution and obtain an analytic expression for the solution.

A multicountry comparison of cryptocurrency vs gold: Portfolio optimization through generalized simulated annealing

The last few years have seen a paradigm shift in the financial sector with the development of cryptocurrencies as an alternative mode of payment as well as an investment scheme.The aim of this study is two-fold.The first is to quantify the volatility of cryptocurrencies in terms of the dynamics of tail-end behavior using different approaches and choose the one with the lowest value-at-risk.The second is to investigate the effect of its inclusion in a portfolio with and without gold,to see if Bitcoin is indeed the“digital gold”.This paper uses the generalized simulated annealing optimization technique to compare portfolios for ten countries across the world.The data provide convincing evidence in favor of the inclusion of Bitcoin in the optimized portfolios.Rolling-window analyses(three-year and five-year)confirm the same.However,for some countries,the empirical pattern suggests that instead of replacing gold from the portfolio,both should be comprised.Our results are robust in terms of the inclusion of non-linear constraints.

A Novel Smart Beta Optimization Based on Probabilistic Forecast

Rule-based portfolio construction strategies are rising as investmentdemand grows, and smart beta strategies are becoming a trend amonginstitutional investors. Smart beta strategies have high transparency, lowmanagement costs, and better long-term performance, but are at the risk ofsevere short-term declines due to a lack of Risk Control tools. Although thereare some methods to use historical volatility for Risk Control, it is still difficultto adapt to the rapid switch of market styles. How to strengthen the RiskControl management of the portfolio while maintaining the original advantagesof smart beta has become a new issue of concern in the industry. Thispaper demonstrates the scientific validity of using a probability prediction forposition optimization through an optimization theory and proposes a novelnatural gradient boosting (NGBoost)-based portfolio optimization method,which predicts stock prices and their probability distributions based on non-Bayesian methods and maximizes the Sharpe ratio expectation of positionoptimization. This paper validates the effectiveness and practicality of themodel by using the Chinese stock market, and the experimental results showthat the proposed method in this paper can reduce the volatility by 0.08 andincrease the expected portfolio cumulative return (reaching a maximum of67.1%) compared with the mainstream methods in the industry.

Portfolio Optimization Model with Transaction Costs

The purpose of the article is to formulate, under the ∞ risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.