An evolutionary algorithm with a new operator and an adaptive strategy for large-scale portfolio problems

Predicting stock returns is difficult due to numerous dynamic and interrelated factors such as interest rates, exchange rates, economic conditions, corporate policies, investor behavior, and political developments. This study proposes a hybrid trading strategy that integrates the Decision Tree (DT) algorithm with the Markowitz Mean-Variance (MV) portfolio optimization model to improve prediction accuracy and optimize investment returns. Using data from 94 companies continuously listed on the NASDAQ 100 (NDX100) index between 2015 and 2024, the model uses technical analysis indicators as input for the DT to predict short-term stock returns and then applies MV optimization to allocate weights within dynamically generated portfolios. The empirical analysis includes 64 portfolio variations derived from different parameter settings and is evaluated using the Sharpe ratio, Sortino ratio, maximum drawdown, total return, and turnover ratios. The results show that portfolios created with higher trading target ratios and moderate MV optimization significantly outperform the NDX100 index, providing superior risk-adjusted returns and better stability. These findings highlight the effectiveness of combining machine learning-based regressor with classical optimization for dynamic portfolio creation and underscore its practical potential for improving trading decisions in volatile markets.

Multi-criteria algorithms for portfolio optimization under practical constraints

This paper presents a hybrid framework for multi-stock trading that combines the decision-making ability of Deep Q-Networks (DQN) with the allocation precision of portfolio optimization models. Realistic markets are noisy and non-stationary, and complex action spaces can hinder reinforcement learning (RL) performance. The DQN generates buy/sell signals based on market conditions. The framework passes buy-listed assets to an optimizer, which computes portfolio weights. Five allocation strategies are examined: naïve 1/N, Markowitz Mean–Variance, Global Minimum Variance, Risk Parity, and Sharpe Ratio Maximization. Empirical evaluations on emerging-market exchange-traded funds (ETFs), as well as additional tests on U.S. equities, show that even the baseline DQN outperforms traditional technical indicators. Furthermore, integrating any of the optimization approaches with DQN yields measurable improvements in return-risk performance metrics. Among the hybrid frameworks, DQN combined with Sharpe Ratio Maximization delivers the most consistent gains. The findings highlight the value of decomposing stock selection from capital allocation and demonstrate the effectiveness of the proposed DQN-optimization framework on our testbed.

In spite of theoretical benefits, Markowitz mean-variance (MV) optimized portfolios often fail to meet practical investment goals of marketability, usability, and performance, prompting many investors to seek simpler alternatives. Financial experts Richard and Robert Michaud demonstrate that the limitations of MV optimization are not the result of conceptual flaws in Markowitz theory but unrealistic representation of investment information. What is missing is a realistic treatment of estimation error in the optimization and rebalancing process. The text provides a non-technical review of classical Markowitz optimization and traditional objections. The authors demonstrate that in practice the single most important limitation of MV optimization is oversensitivity to estimation error. Portfolio optimization requires a modern statistical perspective. Efficient Asset Management, Second Edition uses Monte Carlo resampling to address information uncertainty and define Resampled Efficiency(TM) (RE) technology. RE optimized portfolios represent a new definition of portfolio optimality that is more investment intuitive, robust, and provably investment effective. RE rebalancing provides the first rigorous portfolio trading, monitoring, and asset importance rules, avoiding widespread ad hoc methods in current practice. The Second Edition resolves several open issues and misunderstandings that have emerged since the original edition. The new edition includes new proofs of effectiveness, substantial revisions of statistical estimation, extensive discussion of long-short optimization, and new tools for dealing with estimation error in applications and enhancing computational efficiency. RE optimization is shown to be a Bayesian-based generalization and enhancement of Markowitz’s solution. RE technology corrects many current practices that may adversely impact the investment value of trillions of dollars under current asset management. RE optimization technology may also be useful in other financial optimizations and more generally in multivariate estimation contexts of information uncertainty with Bayesian linear constraints. Michaud and Michaud’s new book includes numerous additional proposals to enhance investment value including Stein and Bayesian methods for improved input estimation, the use of portfolio priors, and an economic perspective for asset-liability optimization. Applications include investment policy, asset allocation, and equity portfolio optimization. A final chapter includes practical advice for avoiding simple portfolio design errors. A simple global asset allocation problem illustrates portfolio optimization techniques. The presentation is intuitive, rigorous and informed with institutional management experience to appeal to investment management executives, consultants, fund trustees, brokers, academics, and anyone seeking to stay abreast of the future of investment technology. With its important implications for investment practice, Efficient Asset Management’s highly intuitive yet rigorous approach to defining optimal portfolios will appeal to investment management executives, consultants, brokers, and anyone seeking to stay abreast of current investment technology. Through practical examples and illustrations, Michaud and Michaud update the practice of optimization for modern investment management.

Diversification of investment is a well-established practice for reducing the total risk of investing. Portfolio optimization is an effective way for investors to disperse investment risk and increase portfolio return. Under the assumption of no short selling, a bi-objective minimizing portfolio optimization model, in which the first objective is a semi-absolute deviation mean function used to measure the portfolio risk, and the second objective is a maximum entropy smooth function used to measure the portfolio return, is given in this paper. Also, a maximum entropy multi-objective evolutionary algorithm is designed to solve the bi-objective portfolio optimization model. In order to obtain a sufficient number of uniformly distributed portfolio Pareto optimal solutions located on the true Pareto frontier and fully exploit the useful asset combination modes which can lead the search process toward the frontier direction quickly in the objective space, a subspace multi-parent uniform crossover operator and a subspace decomposition mutation operator are given. Furthermore, a normalization method to deal with the tight constraint and the convergence analysis of the proposed algorithm are also discussed. Finally, the performance of the proposed algorithm is verified by five benchmark investment optimization problems. The performance evaluations and results analyses illustrate that the proposed algorithm is capable of identifying good Pareto solutions and maintaining adequate diversity of the evolution population. Also, the proposed algorithm can obtain faster and better convergence to the true portfolio Pareto frontier compared with the three state-of-the-art multi-objective evolutionary algorithms. The result can also provide optimal portfolio plan and investment strategy for investors to allocate and manage asset effectively.

This paper presents a detailed analysis of portfolio construction strategies aimed at maximizing risk-adjusted returns for investors, utilizing Python-based methodologies. By leveraging historical data on stock returns and risks, a meticulous selection process identified 5 stocks with superior risk-return profiles, outperforming the dataset's average measures with higher returns and lower risks. The selected stocks from the defense industry formed the foundation of an optimal portfolio designed to minimize sector-specific risks while maximizing growth potential. Through rigorous portfolio optimization techniques, including Markowitz's mean-variance optimization, an optimal portfolio allocation was identified with a return of 62.40% and volatility of 27.74%. Insights from the study provide valuable perspectives for investors seeking realistic and sustainable wealth accumulation strategies. The research also highlights future avenues for exploration, such as integrating alternative asset classes, incorporating behavioral finance insights, and leveraging advancements in risk management technologies. This study contributes to advancing portfolio theory and offers practical guidance for investment decision-making.This study demonstrates the effectiveness of Python in financial analysis and portfolio optimization while furthering the theory of portfolios and providing valuable guidance for making investment decisions. Keywords: Returns, Risk, Volatility, Optimal Portfolio Construction, Defense Sector, Markowitz Portfolio Theory,

Portfolio optimization of electricity markets participation using forecasting error in risk formulation

The allocation of limited capital to a variety of assets available is one of the important problems in financial management. It is actually a constrained multi-objective optimization problem called portfolio selection. Most studies have been made to solve the problem with single-objective optimization techniques by aggregating conflicting and incommensurate objectives into a single one. The solutions obtained may be unsatisfactory because their nondominance is not guaranteed, especially when some practical constraints, such as cardinality constraints, are incorporated into the portfolio optimization models. This paper presents an evolutionary multi-objective optimization technique, which called Knapsack Multi-Objective Particle Swarm Optimization (K-MOPSO) to generate the efficient portfolios in terms of expected return and variance under short sales and/or cardinality constraints. Finally, a Multi-Attribute Decision Making (MADM) method named Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is employed to outrank the efficient portfolio that decision makers satisfy most.

Purpose – The purpose of this paper is to analyse and compare the performances of portfolio optimisation models including Markowitz's mean-variance model (MV model), Konno and Yamazaki's mean-absolute deviation portfolio optimisation model (MAD model), Young's minimax portfolio model and the VaR model. Design/methodology/approach – Historical data on 43 constituent shares listed on the Hong Kong Hang Seng Index (HSI) covering a four-year period are obtained. The paper then tests the performance of each model under different scenarios and against different sets of historical data. Findings – The paper finds that different levels of required annual returns impact on portfolio composition, historical data have a major impact on the determination of portfolio composition and the level of required annual return impacts on how optimisation models perform. Practical implications – The paper posits that with a comprehensive understanding of the performance of each of these performance optimisation models, investors may be able to develop a better understanding of how to adjust investment risk strategies, thus preventing serious losses. Originality/value – There are two major points of value to this paper. In the first place, the paper presents an original review of portfolio optimisation models. Second, using “real” data, the paper utilises five different scenarios to test the performance of each model under different situations.

PurposeThis paper aims to propose an improved version of portfolio optimization model through the prediction of the future behavior of stock returns using a combined wavelet-based long short-term memory (LSTM).Design/methodology/approachFirst, data are gathered and divided into two parts, namely, “past data” and “real data.” In the second stage, the wavelet transform is proposed to decompose the stock closing price time series into a set of coefficients. The derived coefficients are taken as an input to the LSTM model to predict the stock closing price time series and the “future data” is created. In the third stage, the mean-variance portfolio optimization problem (MVPOP) has iteratively been run using the “past,” “future” and “real” data sets. The epsilon-constraint method is adapted to generate the Pareto front for all three runes of MVPOP.FindingsThe real daily stock closing price time series of six stocks from the FTSE 100 between January 1, 2000, and December 30, 2020, is used to check the applicability and efficacy of the proposed approach. The comparisons of “future,” “past” and “real” Pareto fronts showed that the “future” Pareto front is closer to the “real” Pareto front. This demonstrates the efficacy and applicability of proposed approach.Originality/valueMost of the classic Markowitz-based portfolio optimization models used past information to estimate the associated parameters of the stocks. This study revealed that the prediction of the future behavior of stock returns using a combined wavelet-based LSTM improved the performance of the portfolio.

Summary This study demonstrates how portfolio insights can be created by combining well-known optimization methods that are generally used individually—genetic algorithm (GA), linear programming (LP), and portfolio filtering (PF). An integrated optimization approach combines the advantages of individual methods while mitigating their shortcomings. Effective portfolio management requires a comprehensive understanding of the tradeoffs between different portfolio choices. Given a set of constraints, portfolio-optimization techniques based on LP and GAs can be applied to identify an optimal portfolio. However, this optimal portfolio might not be the preferred portfolio. Decision makers have to understand the tradeoffs between generally conflicting objectives and constraints before one portfolio can be identified as the preferred option. Such assessment of the overall search space is not made with LP and GAs when used to identify a single best solution, and many portfolio options will have been eliminated before an understanding of these alternatives has been developed. Markowitz's mean-variance (M-V) approach and the traditional “rank and cut” approach are used typically to establish a relationship between a portfolio's value and its variance or associated development cost. Although these methods enable decision makers to compare and contrast different options, the optimization is limited to the portfolio value measure and a single other metric. This latter limitation is overcome by the more recently developed PF approach. This method is practical and transparent and allows for a quick development of strategic portfolio alternatives while considering a large number of portfolio attributes. Its main drawback is that the analyzed set of portfolios generally represents a subset of the total search space. Thus, as the number of feasible portfolio options increases, so does the chance that the optimal portfolio is not present in the population of sampled portfolios.

Portfolio optimization models are usually based on several distribution characteristics, such as mean, variance or Conditional Value-at-Risk (CVaR). For instance, the mean-variance approach uses mean and covariance matrix of return of instruments of a portfolio. However this conventional approach ignores tails of return distribution, which may be quite important for the portfolio evaluation. This chapter considers the portfolio optimization problems with the Stochastic Dominance constraints. As a distribution-free decision rule, Stochastic Dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. We implemented efficient numerical algorithms for solving the optimization problems with the Second-Order Stochastic Dominance (SSD) constraints and found portfolios of stocks dominating Dow Jones and DAX indices. We also compared portfolio optimization with SSD constraints with the Minimum Variance and Mean-Variance portfolio optimization.

Risk is one of the important parameters in portfolio optimization problem. Since the introduction of the mean-variance model, variance has become the most common risk measure used by practitioners and researchers in portfolio optimization. However, the mean-variance model relies strictly on the assumptions that assets returns are multivariate normally distributed or investors have a quadratic utility function. Many studies have proposed different risk measures to overcome the drawbacks of variance. The purpose of this paper is to discuss and compare the portfolio compositions and performances of four different portfolio optimization models employing different risk measures, specifically the variance, absolute deviation, minimax and semi-variance. Results of this study show that the minimax model outperforms the other models. The minimax model is appropriate for investors who have a strong downside risk aversion.

This thesis consists of three essays in financial economics, more precisely in the field of asset pricing and optimal portfolio choice. The first essay studies the asset pricing implications of heterogeneity in preferences coupled with long run risk in a dynamic general equilibrium pure exchange economy. It is concerned with the understanding of how risk sharing among different types of agents affects the assets returns moments in equilibrium and moreover, how these agents reacts dynamically to the long run risk that they perceive. The second and third essay approach the question of optimal portfolio with stochastic opportunity sets. The second essay proposes an approximation methodology for deriving approximate closed form solutions of dynamic optimal portfolio allocation problems. The third essay examines the optimal consumption, portfolio rule and life insurance purchase problem of a wage earner having uncertain lifetime when the market price of risk follows a mean-reverting stochastic process.

Islamic and conventional portfolios optimization under investor sentiment states: Bayesian vs Markowitz portfolio analysis